Process Control, A Perspective - Engineering School · PDF fileProcess Control, A Perspective...

© 2003 by Robert L. Heider

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Process Control,

A Perspective

By: Robert L. Heider, PE

Preface:

The world is not linear or single variant.

Throughout my work experience, I have been asked questions about process control problems

and after explaining my experiences or proposed methods of dealing with the problem; people

have asked me to capture these ideas. That is what this text attempts to accomplish. This is a

perspective, based on experience. It is not a detailed analysis, but rather a practical one. Every

effort has been made to acknowledge those in who I have referenced.

Many process control problems occur because of the process nonlinearity or multi variability was

not considered in the design of the controls. Examples of this are:

• A process runs well during the summer months, but poorly during the winter months.

• A process runs well during grade A, but poorly with grade B.

These types of problems occur because the controls are nonlinear. The controls are tuned for

some optimum point during one condition, but when conditions change, the newer tuning

parameters are quite different.

Multivariable control problems are those where the performance of one loop interacts with

another. Almost all control loops in a plant are multi variant and some form of feedfoward, or

decoupling, can improve the performance.

The objective of this text is to outline some techniques that can be used to solve these problems.

Problem identification will also be emphasized. Some simple simulations and mathematical

treatments will also be presented.

To begin, I would like to define some basic concepts that control engineers use or keep in the

back of our minds when we begin to analyze a problem. I will describe these concepts by

comparisons. The concept of macro will be compared to micro and deterministic will be compared

to heuristic.


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Macro vs. Micro:

Macro is defined as "intended for use with large quantities or on a large scale" while micro is

defined as "involving minute quantities". Control engineers are macro thinkers; all we need is the

total picture. For examples, we are interested in knowing the degree of agitation for a pH control

loop. We may perform some simple calculations to see if the tank is properly agitated. But we

don’t study agitation from a micro viewpoint that is designing the type of impeller, or the details of

each particle in the tank etc. We are interested in the fact that the catalyst degrades in some

manor. We can devise a control system to take this fact into account but the exact way it is

destroyed is of little interest. We are accused of labeling problems as black boxes, a technique

electrical engineers use. We are not trying to distance ourselves from the problem; rather just put

the problem in a frame of reference we can deal with. We are more concerned with interactions of

all process variables rather than exact solution of the details of one variable. Basic unit operations

understand of the plant is usually sufficient. For control engineers the required process reading is

your sophomore physics and chemistry. Most upper level courses just provide a lot of

embellishments on those basic courses. This sounds like the book written several years ago; “All

You Need To Know In Life You Learned In Kindergarten”.

Deterministic vs. Heuristic:

When describing behavior, control engineers like first principal controls or models to control first

principals. This is called the deterministic method. One can calculate the behavior by known

relationships or equations. However, many effects cannot be shown in first principals or the

equations just don’t show the real world or there are too many unknown factors in the whole

system. This is when heuristic systems can be used. These include process model based control,

smart sensors, neural networks etc. Control engineers are interested in these systems for running

operations where operational data can be gathered and correlated. Heuristic controls or

optimization techniques (design of experiments or DOE) determine where the plant can best

operate without regard to why. DOE is a statistical technique where by the process variables

(pressure, temperature, flow, agitator speed etc.) are adjusted over a range in a pre-determined

order, the value of the controlled variable (rate, yield, quality etc.) is noted at each of these points.

Using this array of data, a statistical model is derived which shows the critical variables (i.e.

sometimes a controlled variable has no effect on the operation) and the best operational point

determined, by using a minimum or maximum search algorithm. By using DOE, a production

facility can hone in on its best operational point. Research frequently has voiced concerns about

using this method because is doesn't explain why the optimum operational point it may find works

and because they are not the prime mover in the process, they feel loss of control. I argue who

cares? Let’s get to the best point with whatever tools are at our disposal, start running there and

find out why later. A good control engineer will position him or her self in such a way as to

capitalize on this fact making the project a win win proposition.


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Chemical Processes

Frequently engineers fail to realize the power and energy associated with chemical reactions.

They tend to think of simple flow, level and pressure effects when dealing with chemical (and for

that matter, biological) processes. Chemical processes generate or consume energy and there

are forces involved that we sometimes loose sight of. For example, consider the scrubbing of

SO3 in H2SO4 solution. One would think the SO3 line’s backpressure would be the head of liquid

plus the headspace pressure. But the pressure calculation is more complicated than that because

there is a solubility of the SO3 in the acid solution. These are powerful forces. Control engineers

should pay attention when chemists describe the chemistry they need to control.

I have some chapters devoted to the anatomy of a particular design or control problem. There are

discussions about a real problem and how it was solved. In all these applications I have removed

any process details to prevent disclosure of intellectual property.

I have included a chapter on human factors in engineering. This was done because we all could

sharpen our people skills. This chapter is based on actual experience and just as the title states a

perspective.

I would like to thank those who have encouraged me to write these thoughts.

15 May 2003

St. Louis, MO


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Chapter 1

Basic Controller Tuning Comments

The universe of single input single output control loops can be separated into two classifications;

self-regulating and non self-regulating.

Self regulating - These loops are such that if the controller is placed in manual, the process

variable will go to some stable state, assuming the interacting variables are held constant.

Examples of these are flow, heat exchanger temperature control, and even pH. This is how a self

regulating process behaves. If while the controller is in manual and the process is stable, if the

output is change, the process variable or signal will also change, but it will come to a stable point.

If the output is moved again, the process variable will come to a different point. The system is

stable at an infinite number of points.

Non Self regulating - These loops behave such that if the controller is placed in manual, the

process variable will go to some saturated state. Examples of these are gas pressure and tank

level with a constant input or output.

Imagine a gas volume with a fixed orifice in the outlet, to a "constant" backpressure. Assume that

a control valve drops a gas pressure to this tank from a much higher pressure. If the loop is

placed in manual and the valve moved to some point, the pressure, in time, will either build to a

point almost equal to the supply pressure or drop to a point almost equal to the back pressure.

The system is stable at only one point. Non self-regulating loops have "built in" reset action and

therefore can be tuned without reset. Sometimes, depending on the controller's method of gain,

you may experience some offset, but offsetting the set point or adding bias can compensate for

this.

One can see the differences in these loops by experiments done at home. Try the level

experiment on your bathroom sink drain; higher level will occur for higher water flow rates. This is

an example of a self regulating process. Try not to fall in the trap of assuming every control

system for a particular type of physical or chemical process is one or the other. As you see with

the sink level, an integrating process, it becomes self regulating because as the head increases,

the flow increases.

Deadtime - Now add dead time to the loop. Dead time can be compensated for in self-regulating

loops much easier than non-self regulating loops. In general, reset will make tuning more difficult

in non-self regulating loops, because you have placed two integrators in the closed loop. That

double integrator with dead time is the most difficult loop to tune. Control behavior in process with


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dead time is not considered in most classical control texts. Classical control texts frequently

convert the control dynamics into Laplase transformed control function blocks, and then perform

various algebraic manipulations on these transforms. Classical control theory is frequently taught

in the electrical engineering departments, where things run quire fast and propagating delays are

very short.

In the process industries, such as chemical, food processing and the like, chemical unit

operations are used. These vessels are frequently large and designed such that there is installed

dead time involved in the unit operation itself. In addition, the configuration of these vessels and

their interconnecting piping and ducts also contribute to the overall process dead time.

Digital Filter - Digital filters should only be used to dampen hydraulic noise. The lowest frequency

of this noise is around 1/3 of a hertz. To attenuate this type of noise, never use a digital filter

greater than 0.026 minutes. Large filter values will dampen the signal response and result in

controlling the filter, but not the process.

Controller tuning settings: (My experience)

Process Controlled Gain Reset Rate repeats/min min/repeat Flow 0.3 35 to 50 NEVER Temperature 5.0 0.2 0.5 Pressure 20 none to 0.5 Level 4 to 10 none none

Tuning Methods

The Zeigler Nichols method is based on tuning non-self regulating processes. For loops where all

logic doesn't work, remember that if you cannot establish a stable setting in manual, you probably

will never be able to tune it in auto. On difficult loops, start with gain only. If you want to add reset,

then begin to add reset, but drop the gain value to ½ of what you had in proportional only. Begin

to add in reset, start at 0.1 repeats per minute. Add reset until you get the ¼ decay. Next add

rate, but remember this is a derivative function, so go easy here. If you see the process change

direction before you get to setpoint, decrease it. The only place I want high rate values is in pH;

there I want to see a hot controller.

You will have to drop the reset and gain values when you add rate.

Controller tuning methods assume a linear process. Classical control theory seldom mentions

non linear behavior or the effects of process dead time.

Feedfoward

When you have a signal that you know effects another loop significantly, feedfoward this signal to

the other controller. Remember the objective here is to allow the signal to move the valve before

the controller does. Go easy on the signal feedfoward gain. It doesn't take a lot of this action to

see marked improvement, say 10%.


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Non linearity

Once I tried to tune a loop by the ultimate period method. It worked, but two days later, it went

unstable. By the way, we increased capacity at that time. Why didn't it work?

Probably because that process, as are most processes, non-linear. The output to input

relationship is not the simple y = m*x + b. Even simple processes, like level control of an

atmospheric tank discharging through an open pipe at the bottom, are nonlinear. In that case, the

flow out of the tank is proportional to the square root of the head. In the case of a heat exchanger,

the heat transfer coefficient varies to the 0.8 power of the turbulent flow rate. Linear behavior

means that the controlled or process variable has a constant slope over the whole range of output

changes. As an example, an x% change in the output would cause a y% change in input or

process variable no matter where the output is set initially. This is also called process gain, the

change in controller input divided by the change in output. This non-linearity causes the overall

process gain to be variable. If the tuning constants are fixed over the entire span of control, the

controller behavior will be different at different disturbances and set points. This requires the

controller settings to be set for sluggish or sub optimum behavior because the controller needs to

be tuned for the worst case or the highest process gain.

The situation would seam hopeless explained that way. What can be done?

This non-linear behavior is why equal percentage valve characteristics are used so often; they

compensate for this non-linear behavior. The ultimate objective is to have a linear control system,

but because the real world doesn't behave like that, the control engineer lets the control valve

correct for this non-linearity. The equal percentage characteristic compensates many control

loop's non-linear behavior by causing the installed or the total control loop to be linear. This non-

linear behavior is why some controllers work well at one set point or rate but not at other

conditions. This problem was recognized many years ago with differential pressure flow

transmitters used to measure flow rate. The instrument measured pressure drop in a linear range

however the flow is proportional to the square root of the pressure drop. As a result of this

problem, square root extractors were used to provide a linear range for the flow signal.

Why does this non-linearity cause problems with control? The system closed loop gain changes

as the load changes. The system gain is the closed loop gain, which should be less than one for

a stable system. The process gain is the change in output signal with respect to change in input

signal. When the process is non-linear, the small signal gain is a function of the load. So in the

case of a heat exchanger, there is not much change in output temperature for change in inlet flow

near the maximum flow rate as there is when the flow rate is lower. The control engineer is

always faced with this problem. An easy way to avoid the problem is to reduce the controller gain

to a very low value such that the loop gain will never exceed one. This is why most loops are over

damped.


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A very simple way to linearize a process such as those described is to apply a simple function to

the output signal. For most industrial control systems, the derivative of this small signal gain has

one direction. This means that a rather simple relationship can correct the problem. The load line

shown in Figure 1 is the normalized installed characteristics of a shell and tube heat exchanger.

Figure 1

This non-linearity is the result of the control valve flow coefficient, Cv, equal percentage

characteristic, the pipe head loss and the non-linearity of the heat exchanger. Without the

compensation, if the controller output were set at 50 percent, the process would be at 75 percent

capacity. Shinskey has shown that a large number of non-linear processes can be linearized by

the following equation:

)*)1(/( xLLxy −+=

Where x is the input and y is the output normalized from 0 to 1.0. L is a constant, set such that

the overall system behavior is linear. In the above example L = 2.1828. For the example, a 40

percent output from the controller results in a 22 percent output from the compensation equation.

This 22 percent output results in a 40 percent load. This equation can linearize most industrial

processes. It also simulates the normal behavior of control valves; zero output with zero input, the

way fail closed control valves behave when shut.

0 10 20 30 40 50 60 70 80 90 1000

10

20

30

40

50

60

70

80

90

100

Controller Output in pcnt

Com

pens

atio

n an

d Lo

ad O

utpu

ts

Nonlinear Compensation Network

y=x/(L+(1-L)*x) L=2.18

Load> <Compensation Equation


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For electrical power used in some heating applications the solution is a bit different. Frequently

electrical power is controlled by a time proportional output through a triac power controller. The

triac acts as an electrical switch. The electronic circuits that control the triac switching implement

a zero voltage turn on circuit. This is done to prevent electro magnetic interference that would be

caused by rapid changes in voltage if the AC voltage is switched when the cycle is not at a zero

crossing point. The disadvantage of this method is that the voltage is switched in half cycle

increments. If the time proportioning period is too short, the resolution of the power to the heater

is reduced. If the heater controller proportioning time is increased, the resolution improves but if it

becomes too long it introduces dead time in the heating loop. As an example, if the time

proportioning cycle is set for 2 seconds, the power resolution would be one part in 240. If the

heater is 1200 watt, then the power would cycle plus or minus 5 watts because this is the best

resolution the controller can resolve, or approximately 7 degrees C for a 10 pound mass.

Improved electrical output power resolution can be obtained by using a Silicone Controlled

Rectifier, SCR. This device can switch ac power over fractions of a half cycle. The power

delivered to the load using this method has very non-linear characteristics. This non-linearity

would cause less than optimum control if it were not linearized. The following MATLAB plot shows

the nonlinear characteristics on a phased fired full wave rectified power controller that can be

compensated with a third order polynomial.

The equation is:

output = 1 - 2.219*i + 3.692*i^2 - 2.4685*i^3

Where i is the normalized controller output. This polynomial can be programmed in most newer

configurable controllers. This linearization will allow the use of responsive control settings.

The SCR does generate transients during switching and can be falsely switched due to transients

in the line power. By installing a varistor across the SCR terminals, the transient can be

suppressed through the device. These devices are available from the SCR suppliers.


9

It has been my experience that the closed loop performance can be improved in many loops by

linearizing either the transmitter or the final element.

Back Mixing

One concept that dictates control behavior is the amount of back mixing the unit operation has.

Many unit operations have some type of back mixing or recycle. As an example, a rotary dryer

has internal flights that will flow a portion of the solid back toward the inlet. Some dryer designs

even recycle a portion of the dry solid and mix it with the inlet slurry to improve the handling

characteristics.

An agitated vessel has a portion of the liquid at the surface drawn down to the reactor bottom.

All these effects result in adding a large time constant to the control dynamics. This time constant

can be assumed as the process contents volume divided by the recycle flow rate, or V/F.

In the case of a pipeline, this principal is complicated by the transportation delay. In this case, V/F

term is the delay time. A pipeline does not provide any back mixing, however if the flow is

turbulent, there will be mixing of the contents. If a step change in inlet temperature occurs in a

flowing line, there will be a delay before the outlet temperature senses the change because of the

transportation delay. A step change in temperature will not occur in the outlet either because the

flow pattern is irregular in the piping system. Around bends or fittings and valves in the piping

system the flow pattern will change, some of the fluid will travel faster through the fitting than the


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other portion which will not cause a sharp temperature to change. Rather it will be approximate

an exponential curve. Anyone who has ever drawn water for a bath or shower in a hotel will see

the effect. When the water is first turned on, there will be a time when the temperature will not

change. This is the dead time, when the temperature begins to increase, it takes time for it to get

hot enough to use, that time is considered the time constant.

When considering the dynamic behavior of a process control loop, on should consider the

process in those terms, delay and time constants.

References:

"Is fuzzy logic appropriate for Process Control Applications?" F. Greg Shinskey, Chemical

Processing, December 1996.

General Electric SCR Manual; Third edition, Rectifier Components Dept. West Genesee St.

Auburn, New York, 1964.

Zero-Crossing Triac Drivers Simplify Circuit Design, Control Engineering, March 1982.

Carlo Gavazzi Solid State Switching Controls Catalog, Buffalo Grove, IL.

Schultz, M. A., Control of Nuclear Reactors and Power Plants, McGraw-Hill Book Company, New

York, New York, 1961


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Chapter 2

Feedback Control Systems The ISA defines Control Systems as a system in which deliberate guidance or manipulation is

used to achieve a prescribed value of a variable. This paper will define the process and control

systems in mathematical terms that can be analyzed. The process system should be physically

realizable and dynamic. In many cases it can be described in the form of differential equations.

Differential equations can be defined to have order or the maximum number of derivatives in the

equation. In control theory, a system or function is shown in a block form, with an input and

output.

An example of this would be an RC electrical circuit. A first order differential equation has just a

single derivative term.

The equation for this circuit is:

∫+= IdtC

RIei1

(1)

∫= IdtC

eo1

(2)

Taking the derivative of the equation above yields:

ioo ee

dtdeRC =+ (3)

This can be transformed to Laplase notation as:

11+

=s

ee io τ (4)

SystemInput Output

Iei eo

R

C


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Where tau is RC. Tau is defined as the single time constant that is in seconds for this example

and the 1/(τs+1) term is in the transfer function block. S is equal to j2πf where f is the frequency

of the input voltage. These are complex variable equations; therefore the output relationship

varies as a function of both the magnitude and a phase shift of the input at each frequency. This

particular circuit is called a low pass filter because low frequency signals are passed through

while high frequencies are shunted or shorted by the capacitor.

Another examples of a first order equation is the temperature change of a liquid volume with a

constant inlet and outlet flow rate:

ioo T

VFT

VF

dtdT

=+ (5)

Where To = Outlet temperature Ti = Inlet temperature F= Rate of flow V = Volume Time constant = V/F For second order systems the equation can be shown in the following form:

)(2 22

2

tfdtdy

dtyd

nn =++ ωζω (6)

Where ζ = damping factor ωn = Undamped natural angular frequency = 2πfn fn is the natural frequency.

Examples of second order systems are show above. The transient response to these second

order systems is described as either under damped where zeta is less than 1.0, critically damped

where zeta = 1.0 or over damped where zeta is greater than 1.0. Under damped responses are

not accepted by chemical plant operators because they view the behavior as cyclic and frequently

they do not want the process variable to exceed the set point.

R

C

L

V i

Vdt

idLCi

dtdiR =++ 2

2

LCn1=ω L

CR2

=ζ

Electrical R L C Network, A Second Order SystemMass Spring and Dashpot

Mass

M

BK

FKxdxdtB

dtxdM =++2

2

MK

n =ωMKB

2=ζ


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The second order behavior occurs because energy is transferred from one storage device to

another and dissipated by a third. In the example of the R L C circuit, electrical energy is

alternatively transferred between potential energy stored in the electrical field of the capacitor to

potential energy in the form of a stored magnetic field in the inductor. The resistor dissipates the

electrical energy to thermal energy.

Under Damped ζ < 1.0, Over Damped ζ > 1.0, Critical Damped ζ = 1.0 Frequency Response In the field of servomechanisms studying the sinusoidal frequency response can be used to

define the systems’ behavior. Each of the differential equations can be written in the block

diagram form. This is called a transfer function. All the equations describing the process or

system can be grouped as a transfer function. Each element of the system has its own unique

equation. The output of the previous block is connected to the input of the next. The Laplase

transform of each is multiplied together to form the total function. In the servo field, this function is

written in a fractional form of Laplase transforms. For process transfer functions involving signal

transmitters and valves, the overall process transfer function becomes:


14

The whole process can be written as a steady state non-frequency dependent term K and a time

variant term G(s).

⋅⋅⋅++⋅⋅⋅++=

)1)(1()1)(1()(

21

21

sssssKsKG

ppn

zz

ττττ

(7)

The s terms in the numerator are considered zeros while those in the denominator are called

poles, the value of the fraction at various frequencies. This term is used in a system analysis

technique called Root Locus. For most processes in the chemical process industry, the plant

transfer function seldom has any zero terms.

The magnitude of this transfer function is usually expressed in decibels and is defined as:

inputoutputdb 10log20= (8)

Taking the log operator of each term in the transfer function yields:

))1log()1log()log(

)1log()1log((log*20)(log20

21

21

⋅⋅⋅−+−+−−

⋅⋅⋅+++++=

sssssKsKG

ppn

zz

ττττ

(9)

The phase angle is:

⋅⋅⋅−−−−⋅⋅⋅++= −−−−2

11

12

11

1 tantan)90(tantan)]([ ppzz nsKGangle ωτωτωτωτ ! (10)

Transfer functions with delay require a Laplase operator in the neumerator that is:

se τ−(11)

Where tau is the dead time. The magnitude of pure dead time is 1.0 or 0.0 db. However the

output is phase shifted relative to the input in degrees by:

ωτ3.57−=Φ (12)

ControlValveInput OutputProcess Transmitter


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With the process described in a block diagram form, it is now possible to control the behavior by

adjusting the input signal to force the output to a desired state. A feedback controller does this.

The controller adds its own compensator transfer function block and summer junction where the

desired output value or set point, is compared to actual value. The controller is added to the

system and is shown in dotted lines as:

A single input single output (SISO) feedback control system.

This is the closed loop block diagram. The feedback signal is the line from the output to the

summing junction. In control system terminology, this is H(s). Most process controllers in the

chemical process industries, H(s) does not have any dynamic elements; it is just 1.0, or unity feed

back. The controller, valve process and transmitter function blocks are multiplied together in the

total fraction that is KG(s). This KG(s) and H(s) together are called the open loop transfer

function. When the loop is closed as shown in the figure, the loop behavior is calculated by:

)()(1)(

PointSet Output

sHsKGsKG

+= (13)

If a sinusoidal input is placed at the set point input, there will be a return signal at the summing

point because of the amplification of the forward and feedback loops KG(s) and H(s). The return

signal is compared with the set point input. If the signal has arrived at this summing point, has a

phase shift of 180 degrees and of sufficient magnitude, the input signal will be reinforced which

will provide a greater output and still greater signal. This process continues and the amplitude of

oscillation becomes constant. If the set point reference input is removed the system will continue

to oscillate. It is not even necessary to impress a sinusoid upon an unstable system to cause it to

break into oscillation. Any small amplitude disturbance may bring about an oscillation. Refer to the closed loop transform equation. The condition of instability is for the Output/Set Point

to become infinite. This can occur if either KG(s) becomes infinite or I + KG(s)H(s) to be equal to

zero. The first possibility is a trivial case because it means that the open loop process itself is

infinite. The second condition is that the denominator equals zero or KG(s)H(s) should be equal

ControlValve OutputProcess TransmitterCompensatorΣ

+SetPoint

Controller

-


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to - 1. When this condition occurs, the gain will be infinite and the output will be theoretically

capable of sustained oscillations without any input.

The purpose or function of the “controller” is to adjust the process to a desired set point by modifying the total KG(s) term to insure that the closed loop system will be stable. The stability of the closed loop system can be studied and compensated for with the knowledge

of the open loop transfer function. This is fortunate because it is not necessary to solve the entire

closed loop equation to determine stability. One method is the use of a semi log plot of the

system gain and phase called a Bode plot. These are usually shown as a pair of plots; gain and

phase angle potted on the y-axis and a log plot of the frequency or angular frequency, omega,

2πf, on the x-axis.

The Bode plots below are for a first order lag with dead time transfer function.

151.0)(

34..

+=

−

sesKG

s

(14)

The gain plot begins at 0 db, and decreases because of the lag in the denominator. The phase

plot shows the increasing phase lag as the frequency increases. When the phase angle is at –

180 degrees, the gain is at –10.0 db. If 10 db were multiplied to the K term, the system would be

unstable because the feedback signal would be equal to or greater than the input.

Bode Plot; Gain

-16.00-14.00-12.00-10.00

-8.00-6.00-4.00-2.000.00

1 10 100

omega x10

db gain


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Bode Plot; Phase

-300

-250

-200

-150

-100

-50

0

1 10 100

omega x10

degr

ees

phase

If this transfer function were subjected to a unit step input, the output would be delayed followed

by a lag as the output rose to unity.


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First Order with Dead Time Step Response

PID Controllers

The terms used in the past paragraphs, the terms output and input are generally used by

servomechanism studies. In process control, the input is usually called the set point or SP. The

output of the transmitter block is called the PV. The difference between the SP and the PV is the

signal error or E. The signal between the controller and the process is called the output or

manipulated variable, MV.

The controller function block responds to the error signal. This response is called the control

mode. With microprocessor circuits the digital implementation of this mode or law is called a

control algorithm.

The controller had modes of operation. These are used to define operational states the controller

can have. The Auto mode means that the controller’s algorithm is functioning on the error

between the local set point, SP and the PV. In the manual mode, the user can directly set the

controller’s output independent of the algorithm’s calculation. Other modes such as RSP, Remote

Set Point will allow the output of one controller to set the set point of another. This is called

cascade control. Supervisory and DDC, Direct Digital Control, are terms used where the control


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logic from a supervisory computer either sets the set point of the controller or directly operates

the output.

Another term in the controller lexicon is “action”, either direct or reverse. Direct action means that

the output increases with increasing error. Reverse means the opposite. The action of a controller

is selected based on the failure state of the final element, usually a control valve. This is done to

insure safe operation. This implies a sign term, + or -, to the overall controller algorithm.

The term, PID, stands for proportional, integral and derivative. These refer to the three

fundamental control elements or algorithms of the controller. The following discussion describes

the classical tuning method, Zeigler Nichols.

Proportional only control is the simplest of these. In this mode, proportional refers to a single

static, non-dynamic gain that is inserted after the summer. The previous section discussed the

ultimate gain or that gain where the closed loop control would cycle, continuously with the same

amplitude, indefinitely. With a proportional only controller, there is an offset between the PV and

the SP. Many controllers have a manual bias to this offset such that the PV can be set to the set

point. Operators do not like to see a controller with this offset; they believe the process is out of

control because the PV is not at the SP. This is a frequent criticism of proportional only control.

The higher the gain, the smaller the off set is between the PV and SP. This is because the closed

loop transfer function is Kc*K*G/(1+Kc*KcG*H) with Kc being the controller gain.

Proportional plus Integral controller inserts an integral term to the controller algorithm. The

integral term is traditionally called reset, implying that the controller output is “reset” so that there

is no offset between the SP and the PV. Integral only is a controller type frequently used for

constraint control and other advanced control algorithms. The units of reset are either in “repeats

per minute” or “minutes” where per repeat is generally understood but frequently not written. The

repeats term means that the error amount is “repeated” T times per minute. The user should read

carefully the controller’s instruction manual. Frequently the time units can be in seconds or hours

rather than minutes. Note that it is not possible to set the reset term to zero. The user should be

conscious of this because on some controllers, the user can enter a zero in the reset term, yet the

internal algorithm will truncate the zero to the smallest number to prevent an internal underflow

exception in the controller’s microprocessor. Yet there is a small reset term available, which is not

the same as disabling the function. This small value will cause the loop to develop a long, slow

cycle.

The D term or derivative is called rate, because its contribution to the equation is that of inserting

the derivative of the change. There are two accepted ways to take the derivative, one is with the

error and the other is to take the derivative of the PV. Taking the derivative of the error will cause

the rate term to change due to a set point change, which can cause a large change in the output

just due to set point change. The units of this rate are usually minutes or seconds.


20

There are two different ways to write the control algorithm for a PID controller, the ideal and non-

ideal transfer function. The ideal is also called the non-interactive controller because there is no

interaction between the terms. The ideal controller algorithm is where E is the error term:

++= sT

sTK

EOutput

DI

11 (15)

The real controller takes on the following form:

)1()1)(1(

21

211

+++=

sTsTsTsTK

EOutput

γ (16)

Notice that the static gain is inversely related to the reset time, T1. The rate time, T2, is shown in

the numerator and the denominator where it is reduced by the value of γ that is a value less than

1.0, usually 0.1. The derivative function is reduced with this added pole term in order to prevent

the rate term from causing too high a contribution. The T1 term in the numerator can be

considered as a term to cancel out the dominant process lag, which would be a pole of the same

time constant.

The relationship between the real and ideal controller’s settings is:

1

211 T

TTKK += 21 TTTI +=

ID T

TTT 21= (17)

Define the ultimate gain as Ku and the period as Pu in minutes.

The Ziegler Nichols controller tuning settings can be calculated as follows for non-interactive

controllers:

1) For a proportional only controller:

Gain = 0.5* Ku

2) For a proportional plus reset controller:

Gain = 0.45*Ku Reset = 1.2/Pu

3) For a proportional plus reset plus rate controller:

Gain = 0.6*Ku Reset = 2/Pu Rate = Pu/8

Reset units are repeats per minutes. Rate units are in minutes.

For the first order with dead time process transfer function shown as:


21

151.0)(

34.

+=

−

sesKG

s

(18)

The Bode plot shows the –180 degree gain to be –10 db. The gain required for sustaining the

oscillation, Ku is 3.16. The period, Pu, of the oscillation is 1.1 minutes.

From the above calculation, the PI settings would be:

Gain = 0.45*3.16 = 1.42 Reset = 1/1.2/1.1 = 0.917

A composite Bode plot of the open loop transfer function of the controller, process combined

yields:

(19)

Ss

sesKG

S

917.0)1917.0(*

)151.0(42.1)(

34.0 ++

=−

Open Loop Bode Plot; Gain

-15.00-10.00

-5.000.005.00

10.0015.0020.0025.0030.00

1 10 100

omega x10

db gain


22

The closed loop response for this system is:

The degree of stability of the open loop compensated network can be defined by two terms,

phase margin and gain margin. The concept is to define the amount of additional gain or phase

that if added to the network would cause instability. This defines of the “margin” of stability. The

Open Loop Bode Plot; Phase

-300

-250

-200

-150

-100

-50

0

1 10 100

omega x10

degr

ees

phase


23

gain margin is that amount of gain required to product an unstable network when the phase is at

–180 degrees. For the PI controller in the above example, the gain at –180 degrees is –5.5 db at

an angular frequency of 5.5 radians. Therefore the gain margin is 5.5 db. The phase margin is

defined as 180 degrees minus the phase lag at unity gain or 0 db. For this case, the phase

margin is 180 – 124 or 56 degrees.

For the PID controller, the tuning settings are:

Gain or Kc = 1.89

Reset = 0.55 minutes

Rate = 0.1375 minutes

The Bode plot for this PID controller shows what is an electronic engineering term for a V notch

filter. This filter has a low point at the ultimate period of 1.1 minutes and exhibits higher gain at

frequencies above and below that point. This is the correct behavior. One would expect the gain

to be the lowest at the ultimate period and higher at other frequencies to compensate for the

disturbance. Note the leading or positive phase angle at the ultimate period. This leading phase

compensates for the dead time or rather large negative phase angle contributed by the dead

time.

The real PID controller transfer function is:

)1()1)(1()(

+++=

sTsTsTsTKsKG

DI

DIc

γ


24

The closed loop response of the PID controller becomes:

For this combined process and controller, the gain margin is 2.5 db and the phase margin is 32

degrees. A convent relationship that is valid up to 40 degrees to determine the damping factor is

margin) phase(360πζ = (20)

For the example of 32 degrees, damping factor is 0.279. Note the higher closed loop frequency

with the PID controller than just the PI controller.

(21)

The Bode plots for the combined open loop PID controller and process are:

)11375.0*1.0(55.0)11375.0)(155.0(

)151.0(89.1)(

34.0

+++

+=

−

SSSS

SesKG

S


25

Using the Bode plot to determine the stability of a control system does have limitations. If the

phase shift is –180 degrees or the gain is 1 or greater at more than one frequency, the analysis

by Bode will not give a unique solution and should be avoided. This situation would imply that the

process transfer function contains zero terms that are not frequently observed in the chemical

and allied industries.

Open Loop PID Bode Plot; Gain

-10.00-5.000.005.00

10.0015.0020.0025.0030.0035.00

1 10 100

omega x10

db gain

Open Loop PID Bode Plot; Phase

-250

-200

-150

-100

-50

0

1 10 100

omega x10

degr

ees

phase


26

Note that for the PID controller, the reset time constant is approximately equal to the process lag.

It is frequently said that the reset time should compensate for the dominant lag in the process and

the rate term should be used to compensate for the process dead time.

Time Domain

There are two domains that can be used to describe these differential equations or their

transforms, either in the time domain or the frequency domain. Those in the chemical or allied

industries most frequently analyze systems’ transient behavior therefore study the process in the

time domain. Those who apply servomechanisms usually study these systems in the frequency

domain.

A critical distinction should be made relative to the two domains and the two groups of those

interested in control system dynamics. Both control systems are subjected to two types of inputs.

One type is considered a set point which is a signal representing the instruction to the system,

where the variable should be. The other type is an unintentional, disturbance signal that interferes

with and tends to prevent the system from carrying out the instruction contained in the set point.

This input is an additional input injected in the process transfer function block.

Control systems are often classified as being either regulators or servos, depending on their

primary function. While both classifications are normally subjected to both set point and

disturbance inputs, it is most common for one input or the other to be given primary

consideration. Although it is essential for regulators to follow command inputs, these commands

are usually left at a constant set point for long periods of time. When a set point change is made,

the transient response is often of minor importance. An exception to this statement is taken for

batch processes. In that application, the start up response is important and frequently the major

factor in defining the control behavior. The primary function of a regulatory system is to maintain a

constant value of the controlled variable or system output even in the event of severe load inputs.

A servo-system is normally subjected to a continuously varying command signal or set point and

it has, as its primary function, the job of causing the output to follow the command signal. An

example of this would be an airplane attitude control or the steering controls of an automobile.

The servo output should be made as independent of the load as possible, but, while this may not

be a minor function, it is still secondary to the set point control problem. Many of the control

components such as valve positioners or transmitters, are servo-systems. The term

servomechanism is usually applied to the special case of a servo-system whose output is a

mechanical position or any of its derivatives.

In the case of chemical and allied processing industries, these control applications frequently

have large dead time or transportation delayed responses. Such is not the case in servo or

guidance control systems, where the dead time is most often ignored or just a small fraction of

one of the smaller time constants.


27

Another distinguishing difference between the processing industries and other studies of

automatic control is that in processing industries most processes can be considered self

regulating and have many first order time constants in series as well as a significant dead time

between the time the manipulated variable is changed and any change is detected in the process

variable.

Consider, for example, the temperature control of a shell and tube heat exchanger. A step

change in the utility flow signal will not result in an immediate change in utility flow, the control

valve will have some lag or first order behavior. The change in utility flow will mix with the utility

volume in the exchanger, which is another lag. The heat fill flow across the tubes will behave as a

first order lag also. There is a lag with the change in heat duty of the process fluid in the

exchanger that will result in a new stable temperature. Finally the thermal well and temperature

element have a first order lag due to the new process temperature. There are also dead times

due to utility and process transportation times. The overall step response of all these behaviors

can be simulated as a first order with dead time or a second order with dead time.

Dynamic properties of chemical and allied processes are usually defined in the time domain. The

use of the ultimate period method or testing the process through a frequency response is not the

usually accepted practice. This is because ultimate period analysis requires more time than a

step or impulse methods and cycling a chemical process is generally to be avoided. Operational

personal believe this is harmful to the process. Therefore a step test is generally the preferred

method to determine controller dynamic behavior.

Other Basic Control Methods

There are several other basic control methods or algorithms. One of which is on off or “bang-

bang” control. In this type of control, the PV is compared to the set point as before. The error

signal is compared to some pre set value. If it exceeds the error value the output changes state. If

it drops below some point, it changes to the opposite state. This type of control is like the furnace

in a home. This type of control is highly non-linear. I have found it best to simulate this type of

control action when possible. The problem with using this type of control is that the system will

never operate at any stable state. The output is either on of off and if the output action is not

taken, the process will be driven to an extreme state.

Another control method is called Time Proportioning Control. This control proportions the amount

of ON time and OFF time of a discrete output over a defined cycle time. This type of output

switching can be the output of a PID controller.

Both the on off and time proportioning control methods are frequently used in HVAC applications

and make use of an electrical integrated circuit called a triac.

A triac circuit switches the ac voltage at the zero-cross over point on the sin wave. The triac

circuit is optically isolated between low current dc control circuits and the ac power loads (120,


28

240 or 380 volt, single or 3–phase). The triac device is an inexpensive electrical interface

between solid-state logic circuits, microprocessors and ac power loads.

The electronic circuits that control the triac switching implement the zero voltage turn on circuit.

This is done to prevent electro magnetic interference that would be caused by rapid changes in

voltage if the AC voltage were switched when the cycle is not at a zero crossing point. The

disadvantage of this method is that the voltage is switched in half cycle increments. If the time

proportioning period is too short, the resolution of the power to the load is reduced. If the

controller proportioning time is increased, the resolution improves but if it becomes too long it

introduces dead time in the control loop. As an example, if the time proportioning defined cycle is

set for 2 seconds, the power resolution would be one part in 240, and if the heater is 1200 watt,

then the power would cycle plus or minus 5 watts because this is the best resolution the controller

can resolve, or approximately 7 deg C for a 10 pound mass. The end result of this type of design

is that the output precision approaches that of on off control.

References

Bibbero, Robert J., Microprocessors in Instruments and Control, New York: John Wiley & Sons,

1977.

Liptak, Bela G., Instrument Engineers Handbook, Philadelphia, PA: Chilton Book Company, 1970.

Lloyd, S. G., Anderson, G. D. Industrial Process Control 1st edition, Fisher Controls Company,

Marshalltown, IA, pp. 118-119, 1971.

Schultz, M. A., Control of Nuclear Reactors and Power Plants, New York: McGraw-Hill Book

Company, 1961.

Ziegler, J. G., Nichols, N. B., “Optimum Settings for Automatic Controllers”, Transaction, ASME,

December 1942.


29

Chapter 3

Controller Tuning

What is the best way to tune a controller? How do you do it?

Manual controller-tuning methods require the user to make some test of the process in order to

determine the process dynamics. There are two ways to do this: ultimate period method and

reaction curve method. Both these methods require you to test the process. Sometimes this is not

possible. If this is the case, start with default settings based in the controlled variable. Assuming

you are able to do the test, here are a few pointers. I will describe the Zeigler Nichols (Z-N)

method or ¼ decay method for tuning non-self regulating processes. This method only applies to

a non-self regulating process, a fact that is mentioned in their original paper but seldom quoted.

With both these methods remove all the digital filters from the system before you get started.

All controller tuning methods start with the principal that the process is linear, it has the same

open loop small signal gains over the whole range of operation. As I have previously described,

most processes do not behave this way, which makes these methods valid over a limited range.

However, the have been used in industry for many years and some assumptions have to be met

to simplify the task.

Ultimate Period Method

In this method, the controller is placed in auto in a proportional only mode. Note that with some

controllers, it may be necessary to reconfigure the controller because the reset term may not be

able to be set to zero. Even with a zero setting, there may be a very small reset value in the

controller. Consult the controller's operations manual.

The ultimate period method requires the process to cycle, something that bothers the operators.

Operators like to see smooth process operations and many get very upset with cycling the

process. If the cycles build up, they might even stop your test. So be sure to communicate what

you are trying to do.

The objective of this test, from a control theory viewpoint, is to find the controller's gain setting

where the closed loop process gain is exactly 1.00. At this point, the process will cycle with a sin

wave that neither increases nor decays. Don't spend all day trying to get this perfectly, in most

cases the operators or production won't let you run the test long enough to get the data, besides

you have better things to do with your time.

Once you have a proportional only controller, begin the test by making small, say 5 percent,

changes in the set point and watch the cycles. If the process won't cycle, increase the gain. I

generally do this in increments of two or reductions of one half. Once you get the process to

cycle, note the gain and the cycle periods. Define the ultimate gain as Ku and the period as Pu in

minutes.

The controller tuning settings can be calculated as follows for non-interactive controllers:


30


% PB = 2* Ku


% PB = 2.2*Ku Reset = 1.2/Pu


% PB = 1.6*Ku Reset = 2/Pu Rate = Pu/8

Rate units are repeats per minutes. Reset units are in minutes.

Proportional Band is a term used many years ago when industrial controllers were first

developed. Most controllers use gain instead. Proportional Band can be converted to gain simple

by:

Gain = 100 / % PB

So a high proportional band is equivalent to a low gain.

Also be conscious of the reset setting units. Some controller brands use repeats per minute,

others use minutes per repeat. The concept of repeat is the that the controller will “repeat” the

controller error so many times per time unit, usually minute. This repeat is in the form of a ramp,

that is an integral of the controller error. In addition, be aware of the time unit described. Some

brands will use seconds instead of minutes. Controllers marketed to the machine tool industry

frequently use seconds because their processes are much faster then the process industry

applications.

Reaction Curve Method

This is the method used most often, because it is less upsetting to the operators. If the loop is

always in manual, there is no problem, you just have to get their permission to move the output a

few percent and see what happens. A common problem with this method is the hysteresis of the

control valve or other final element may be so large that the output will not move at all. So get

permission, and cause a step change in the output of X percent, say 5 to 10 %. The process

variable, PV, will, after a time, begin to change and if it is a typical loop, you haven't blown up the

reactor, flooded the column or some other catastrophic event, the process variable will approach

some new value. The curve traced by the change is called the reaction curve. The reaction curve

has in its information all the lumped dynamics of the loop, the valve, process sensor, transmitter

and control system input dynamics. Draw a line tangent to the curve. The time between the point

where this line intersects with the original process variable and the point where the test began is

called the lag time, L. The slope of this tangent curve, dPV/dT, is called the reaction rate or R.

The output step change is DP and is expressed in percent units.


31

Figure 1 First Order with Dead Time Temperature Process

In the above curve, assume the normalized 0 PV is 130 degF and the 1.0 PV is 140 degF for an

input range of 0 to 200 degF and the response was created by a step change of 20 percent or DP

= 20%. The time is in seconds. R is the slope, calculated in minutes, and is:

R = %PV Change / Time = (100*(140 – 130)/200)/((150-70)/60) = 3.75

Lag time is the time expressed in minutes as L = 70/60 = 1.166

With this information, the controller settings can be calculated as follows:


% PB = 100*R*L/DP = 100*3.75*1.166/20 = 21.86

Gain is defined as 100 / % PB = 4.57


% PB = 110*R*L/DP = 110*3.75*1.166/20 = 24 Gain = 4.17

Reset = 0.3/L = 0.3/1.166 = 0.26 repeats/minute


% PB = 83*R*L/DP = 83*3.75*1.166/20 = 18.15 Gain = 5.5

Reset = 0.5/L = 0.5/1.166 = 0.43 repeats/minute

Rate = 0.5*L = 0.5*1.166 = 0.58 minutes

0 50 100 150 2000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1First order plus deadtime response

Nor

mal

ized

PV

Time


32

General Comments on Controller Tuning by Z-N

Z-N tuning method should only be used for linear non-self regulating processes.

The PV response is different for set point changes than for disturbances. For set point changes

the PV will respond with a damped oscillation around the set point; for disturbances the PV will

respond with a damped oscillation either above or below the set point, but should not oscillate

around it. This fact is important, I have observed many co workers trying to get this elusive ¼

decay response and not understanding that set point changes are different than disturbances.

The decayed oscillatory response is not the same waveform as sin wave decayed under an

exponential curve. See the plot below.

The ultimate period method yields better results because the latter requires finding slopes and is

subject to graphical error.

For three mode controller tuning settings, the controller responses' damped period is very close

to the ultimate period.

For three mode tuning settings the damping factor, ζζζζ, is 0.22 and the first peak occurs at 77.6

degrees not at 90. This because the decayed oscillatory response is not the same waveform as

sin wave decayed under an exponential curve.

The so-called ¼ decay possible with a proportional only controller is more often 1/3 for PI and

PID controllers.

Figure 2 Response Curve for Test Controller

0 2 0 4 0 6 0 8 0 1 0 04 0

6 0

8 0

1 0 0

1 2 0

1 4 0

1 6 0


33

The above-simulated temperature controlled process shows the different responses. Between

time zero and 50 minutes, the time the set point changed, the PV was responding to an initial

condition state change, a disturbance. The PV oscillated about above the set point, 120. Note

that the PV oscillated around the set point when it was changed to 150. Also refer to the section

on simulations for another example of single input single output controller behavior.

In the ultimate period method, the oscillation's period is equal to four times the system dead time

plus the overall system's time constant.

Modified Lambda Tuning Method

A very simple way to tune a controller is to use the modified lambda tuning setting. This method is

made easier because it only uses two of the modes, gain and reset, and the reset setting only

requires the user to measure the total time the process variable was in transition. The method

calls this T98 or the time for the change in process variable to reach 98% of its total change. This

happens to be 4 time constants since 1-exp(-4) = 0.9817. For all practical purposes, this can be

assumed to be 100%. It is far easier to note the time when the PV is finished with the disturbance

than it is to calculate slopes. This method works well for many loops and can give you a quick

answer to the settings required.

The controller gain is calculated by:

∆∆=

λ1*

%in PV %in Output

cK

Where lambda is the term used to increase or decrease the speed of response. Decrease to

speed up and increase to slow down the control response.

The reset setting, Ti in minutes per repeat, is calculated by:

CD

i TTTT +==44

98

TD is the process dead time and TC is the time constant.

In the above temperature control example, the D PV is (10 DegF /200 DegF)*100% or 5%.

The change in output is 20% Therefore the Gain should be (20/5)*(1/4) or 1.0.

The reset time is 180/4 or 45 minutes pre repeat.

This controller setting is tuned not have any overshoot. This is generally accepted as by plant

operators. They frequently think overshoot is the sign of a plant out of control.

The following simulation shows the difference between ZN tuning and a “hot” lambda setting.

The principal behind this method is to set the reset value equal to ¼ the total time the controller

was in transition. It assumes the combination of deadtime and the time constants are just one

large first order time constant and sets the reset value to compensate for that assumed lag. This

is the basic concept used for dryer control systems where the rate of moisture removal is

controlled.


34

Figure 3 Simulated First Order with Dead Time Lambda Tuning


35

Figure 4 Simulated First Order with Dead Time ZN Tuning

References

McMillan, G. K., Process/Industrial Instruments and Controls Handbook, New York, McGraw-Hill,

1999, Section 10-186.

Ziegler, J. G., Nichols, N. B., “Optimum Settings for Automatic Controllers”, Transaction, ASME,

December 1942.


36

Chapter 4

Feed Forward Impulse Feed Forward

Feed forward is a control technique that improves the control response by changing the

controller’s output in anticipation of the load change. Most control engineers apply a simple feed

forward algorithm, one without a lead lag element, when they see the need for it. In this case, a

scaled percentage of the signal is added or subtracted directly on the controller output. The

problem with this is that the reset term is still integrating the error and the system will be offset by

some fraction of the feed forward signal. Shinskey suggests a better approach that implements

the feed forward signal through function blocks that create an impulse function. The technique is

called impulse feed forward. Shinskey shows the feed forward signal operating directly on the

controller output. The problem with this is that if the controller is placed in manual, the feed

forward signal will still be active. This gives the operator loss of control of the output. Some

controllers bypass the reset function and implement the feed forward signal directly on the

output. This limits the reset action and forces the output to some elevated level, which the reset

action will have to overcome.

An alternate way is to modify the set point. This technique is similar to the one used to

implement a Smith Predictor. Figure 1 shows how to configure the feed forward controller.


37

Figure 1 Impulse Feed Forward Function Block Diagram

The feed forward signal is sent to a lag control block. The output of this block is then subtracted

from the feed forward signal itself. This resulting signal’s step response will be an impulse. This

impulse will have a steep change almost equal to the feed forward signal. Then it will drop to

zero, the time constant will be that set with the lag block. This resulting impulse is scaled, then

either added to or subtracted from the remote set point signal depending on the desired control

action. This modified set point is then connected to the controller’s remote set point. The

resulting action is to perform the feed forward action by changing the controller’s set point. At a

steady state feed forward signal, the set point biased term, will be zero and the controller’s set

point will be that set through the register value.

The following simulation shows the response with a simulated heat exchanger heater. The

process flow is used as the feed forward signal. The following ACSL plots show the behavior

with and without the feed forward. Note that with both methods set point change has the same

response. However the feed forward control has a reduced overshoot.

In this simulation, the controller gain, reset, rate, feed forward gain and lag values by using a

minimization algorithm on the integral error squared value. The feed forward lag value should be

greater than the reset time, about 50% longer. This gives the controller time to respond to the

upset. The feed forward gain should be set based on the feed forward contribution to load


38

changes, if the entire load change in measured, then the gain setting an be high. There is also a

scaled value based on the change in load compared to the change in value position.

One objection often voiced about these techniques it the number of settings that have to be

adjusted to obtain good control. I recommend that the controller be tuned for good response to

set point changes, then adjust the feed forward settings for load changes.


39

Figure 2 Impulse Feed Forward Simulated Response


40

Figure 3 Impulse Feed Forward Simulated Response


41

Figure 4 Simulated Response without Feed Foward


42

Figure 5 Simulated Response without Feed Foward

References:

Shinskey , F.G., Process Control Systems fourth edition McGraw-Hill, 1996


43

Chapter 5

Flow Control Flow is one of the easiest variables to control. This is a general rule and based on the premise

that there is little to no dead time between the valve movement and the transmitter senses the

change. Flow can be either a volume measurement such as gallons per minute of SCFH or it

can be mass flow as in the case of mass meters.

General Comments on Flow Meters

Today, many of flow meters in use are magnetic or vortex shedding. Despite that, approximately

40% of the flow meters in the industrial marketplace are “ head” (orifice et al) meters. From a

control standpoint, the user should be concerned about the linearity of the transmitted signal. In

the case of magnetic and vortex shedding, the output is linear. In the case of an orifice plate, the

flow signal is proportional to the square root of the pressure drop. A good rule of thumb is to

select the flow meter normal reading to be about 70% of the maximum reading. A change in flow

rate a the lower end of the span will result in a small change in the differential output compared

to the same change at the upper end of the range. This is because the orifice plate flow is

proportional to the square root of the differential.

Example: Assume an orifice plate differential flow meter is used to measure a 25 GPM water

flow in a 1 inch line. With a beta of 0.7, a 10% flow change from 10 to 12.5 GPM results in a

8.9% output change while the same percentage change between 20 to 22.5 GPM creates a 17%

output change. Most differential pressure instruments have a square root extraction option that

will linearize this signal.

Vortex meters generate a linear signal proportional to flow rate, so they do not have to be

linearized. The turn down or the ability to measure low flow signals should be given careful

consideration when applying these meters. The flow signal will not be responsive if control is

below the minimum flow reading. Pay particular considerations to piping geometry and allow

sufficient straight runs both upstream and down.

Magnetic flow meters now are the logical choice for electrically conductive fluids. What the

manufacture now considers conductive has become a great deal lower than they were 30 years

ago. Most of the problems with the installation are due to inadequate grounding. I have observed

that when the meter is used on non-conductive fluids, the meter may not be responsive when a

conductive fluid begins to flow. This is probably due to saturation of the input amplifier because

there is no path for the static electricity that forms on the electrodes in the non-conductive fluid.

Control Valves

In order to obtain linear installed characteristics from the control valve, that is the same

percentage change in valve travel at a lower opening valve results in the same percentage

change in flow as it does at the higher flow rates, equal percentage control valve trim should be

used. The equal percentage trim compensates for the non-linearity of the change in pressure


44

drop through a restriction, which is the same square root factor as it is for an orifice plate.

Centrifugal pump’s performance curve shows a drop from a maximum head at zero flow or “dead

head”. This drop can be simulated as a function of the square root of the flow. The equation is

HHKQ −= max* (1)

A simple test of a typical liquid flow application shows the linear installed characteristics with

equal percent trim. The pump in this example is a 1 X 1.5 inch centrifugal with an 8 3/16”

impeller turning at 1750 RPM. See typical centrifugal pump curve.

Typical Centrifugal Pump Curve

The pipe is 600 equivalent feet of 2 inch pipe and the control valve has a maximum Cv of 59.7.

The maximum flow is 70 GPM. The percentage travel was calculated at the required pressure

drop for the given flow.


45

Flow vs. Stem Travel with Equal Percent Valve Trim

0.0

20.0

40.0

60.0

80.0

100.0

120.0

0.0 20.0 40.0 60.0 80.0 100.0

Valve Travel in %

% F

low

% Flow

Figure 1 Installed Flow Characteristics

General Questions, Comments

I once tried to measure the flow rate across a particular piece of equipment by measuring the

pressure drop. The manufacture told us the pressure drops at different flow rates. I could never

get it to agree with the flow meter. Why?

Process equipment such as a heat exchanger has a pressure drop which increases as the flow

rate increases. If someone wants to measure this drop in order to calculate the flow rate, this can

become a difficult task. If two pressure gauges are used, they will probably not agree. Therefore

the same gauge should be used for both inlet and outlet pressure readings. Also give

consideration to any elevation change between the two points.

Can valve position be used to calculate flow, providing the pressure drop is known? Does this

result in an accurate signal?

By applying the universal valve sizing equations, a known valve position as well as fluid states

can be used to calculate flow. This is not a very accurate way, but can give relative good

comparisons between low and high ranges. These applications are usually done where the

installation of a flow meter is too expensive on not practical, such as a large vent line on an

existing process.

Why should flow loops have low gains?

Almost all flow loops have low gain settings, between 0.1 and 0.3. This is because flow

transmitters sense hydraulic noise. If a high gain is used, the noise is amplified which results in

more noise on the output. This is also the reason rate is not used in flow loops. Reset is usually


46

set to give reasonable response and have little to no overshoot. This is generally 10 to 50

repeats per minute.

Hydraulic noise is common in all flow systems. In order to protect the valve from small signal

jitter as well as dampen the flow signal, a digital filter should be employed. Care should be taken

in setting this filter time. My experience is that most hydraulic noise can be attenuated with a

filter of about 1.5 seconds.

How did you arrive at this number?

This number is based on a representative process, a cage mounted level displacer transmitter.

While this is a level instrument, I believe that hydraulic noise is present in all flowing systems this

is an example that can be calculated easily and, based on my experience is representative.

The level cage displacement ratio is calculated in Laplase transforms as:

1**21

2

2

++=

ωζ

ωss

L (2)

For a caged level transmitter 14 inches long and 3 inches in diameter inside a 4 inch diameter

cage, the frequency is 0.37 Hz. The referenced text shows a dampening factor z as 0.3. At this

frequency and dampening factor, the dampening ratio is 4.4 db. A general value for a first order

filter is to attenuate the signal 6 db. The filter should attenuate the signal by 6 plus 4.4 or 10.4

db.

This is calculated by:

+=−

F

Njωω

1

1log204.10 (3)

Where ωN is the noise frequency and ωF is the filter frequency. Solving this for the filter frequency

results in a frequency of 0.11 Hz or 1.35 seconds. As a rule, Never allow the digital filter to

exceed 5 seconds in a flow loop. If the filter becomes too large, the controller will only be

responsive to the filter and not the process itself.

When should I use a positioner on a control valve?

The question should be when not to use one. Even with flow loops. The positioner can be

considered the outer loop of a cascade loop and must be the fastest. The major concern about

positioners is that on very fast loops, the dynamics of the positioner can be slower than the loop

itself. Another concern is that they are yet another device in the field that can and will fail,


47

requiring maintenance. Newer “smart” positioners have electronics that allow the user to develop

signatures of the valve performance. This is helpful for maintenance.

Installation Details

Why should the transmitter be installed before the control valve? I don’t see the difference from a

control standpoint.

The location of the control valve does not matter from a control viewpoint, but in general it is

better to install the transmitter in the high-pressure side of the piping system. Also because of

the downstream turbulence, the meter would have to be located further down stream than it

would if it is mounted upstream. This way entrained gasses are at a higher pressure and lower

noise results. Most flow transmitter problems are as a result of improper installation. I have found

that if the manufacture’s instructions are followed, problems are minimized. If the distance

between the transmitter and the valve becomes too large, dead time becomes a dominant factor

in the tuning settings.

Split Flow Applications

One common flow control application is splitting a flow stream to two different downstream

processes. In the case described here, a variable flow and pressure inlet stream is split; one flow

is fixed while the other flow takes the difference. See figure 2. Three way valves are not used

that often in plant designs because of the availability, particularly in alloy metals. Two valves are

generally used in the piping configuration as shown. For the arrangement on the left, one valve

is used to control the flow rate to the bottom stream and the second is set manually, with the HC,

to keep the enough backpressure to force the flow to the bottom stream. When the wild inlet flow

rate or pressure varies greatly, HC will have to be adjusted to compensate.

Frequently an additional pressure control loop is used to keep the pressure at the tee constant.

This adds an additional transmitter and controller that result is increased cost.

Another way to avoid the problem is to configure the flow control system as shown on the right.

Use the same flow control signal to actuate both valves at the same time. As the bottom valve is

opened, the top valve closes. The controller’s reset action will locate the correct setting to keep

the bottom flow rate fixed. If it is desired to allow both valves to have the same fail direction, a

signal reversal function block can be used to reverse one signal to achieve the desired control

behavior. This two-valve arrangement can be used in many different equipment designs such as

bypassing heat exchangers for temperature control, etc


48

Figure 2 Split Flow Control

Rate Setting on Loss in Weight Feeders

A common rule of thumb in flow application is to avoid using the D in a PID controller, or rate

unless you absolutely have to. A loss in weight feeder is an exception. If rate setting is set to

zero on a loss in weight feeder, sluggish behavior will result. The feeder control loop sets mass

flow, pounds/hour. Conventional wisdom would have you set rate setting to zero for flow control.

After all, pounds per hour is generally considered flow signal. However a non-zero rate setting is

necessary for this loop. This is because the signal is not flow rather “loss in weight”. Loss in

weight implies that there is a delay in the control loop. The control variable is weight change and

in order for the signal to know loss in weight, it has to subtract the current weight form the

previous weight. This sample interval results in sample dead time. Control loops that have dead

time require some rate setting to compensate for the dead time. Once the rate was set properly,

the feeder will run smoothly and be responsive to disturbances as well as set point changes.

This experience shows that the control engineer needs to understand the fundamental first

principals of the equipment controlled.

References



FC

HC

Fixed Flow Rate

Variable FlowRate and Pressure

FC

Fixed Flow Rate

Variable FlowRate and Pressure


49

Chapter 6 Level Control

Self-Regulating or Non Self-Regulating

In the informal control community, the level property is frequently considered the hardest to

measure but the easiest to control. There are some conditions that must be satisfied to make

level control easy. These are that there is very little or no dead time in the level control loop and

that the level process is free from interacting effects. The level control classification can be either

self or non self- regulating depend in how the inlet and outlet flow are controlled. See figure 1. A

good understanding of the type of level loop will dictate which controller type and settings to use.

Non Self-Regulating - If there is a constant flow either in or out of the vessel, then the level

control loop is non self-regulating. There is one unique solution to the other flow rate to hold the

level constant, which is the same value as the other flow. If this fact were not true, then the tank

would either overflow or run dry. In this case the vessel volume integrates the change in level. In

classical control theory, this level can be considered as an integrating process. In this case,

proportional only control will allow the controller to reach its set point with some offset. This is

because the forward controller and process transfer function is:

sKK pc (1)

Where Kc is the controller gain and Kp is the process gain and s is the Laplase operator. When

this controller and process transfer function is forward transfer function in a feedback control loop,

the classical control response becomes:

1*1

+stau (2)

Where tau is 1/(Kc*Kp). This is a first order response. The time constant is inversely proportional

to the controller gain. If the level is relatively free from noise, very high gains are possible. I have

been told of a reflux accumulator level control loop configured as proportional only with a gain of

128. Adding reset or large filters to this type of controller will only cause the control loop to cycle.

The reset action will effectively act an additional integrator element to the closed loop response

and result in the complex loop cycling. Another interesting observation is that it is theoretically

impossible for a true integrating process to become unstable. This assumes that there is no dead

time in the process. Practical considerations, such as hydraulic noise, dictate that the controller

should have a moderate gain setting, perhaps no more that 10. I recommend starting at 4.


50

Self-Regulating - If one of the flows is load dependant, that is, as an example, a gravity draining

tank, then the outlet flow rate will be proportional to the tank level. In this case the flow rate will be

proportional to the square root of the liquid height. This effect can be observed in a sink, when the

tap flow increases, the level increases to a point where the output flow rate is equal to the inlet

flow rate. In this type of level process, a moderate amount of reset can be used.

Figure 1 Non Self-Regulating and Self-Regulating Level Controllers

Proportional Only

There are two excellent references that discourage the use of reset in level control loops. In both

these articles, the user should consider the reason for the vessel. In many cases, the vessel is

used for surge and an exact level setting is not required. Rather the tank is used to absorb

disturbances or accumulate inventory, or act as a liquid reservoir for pump suction. In these

cases, rapid response is required, but the level setting can be allowed to vary some from the set

point. Reset causes a lag in the control response, which can be a detriment to many level control

loops. For many controllers, selecting a proportional only or proportional plus derivative controller

requires a different configuration or set up selection than a proportional plus integral plus

derivative (rate) or PID controller. Most PID controllers will not permit the user to set the reset

term to zero. Therefore when configuring a level control loop, a conscious effort should be made

to evaluate the level dynamics. Adding a filter to a level signal is frequently done to reduce the

measurement hydraulic noise. This filter should not be confused with the reset term provided by a

controller, even though the initial step response to both functions is the same, which is a

tendency to lag the output response. Further on in time after the set point change or disturbance,

the integral will continue to ramp the error while the filter will just lag the response and not

continue to ramp the output in either direction. A proportional only controller has a manual bias

Constant flow out

LCNon Self-regulatingLevel Control Loop

Flow = K*sqrt(h)

LC

Self-regulating LevelControl Loop

h


51

setting. The bias setting is used for the operator to introduce a term to offset the controller’s

output so that the level is equal to the set point. If the level control is non self-regulating, this

should not be necessary because the integral action of the tank level itself will act as the reset

term. In a perfect non self-regulating system, there will be a small steady state off set, which is an

inverse function of the process gain and the controller gain. With high process gains, it may not

be noticeable.

Recycle Flows

In many processes, a series of tanks are piped together and a portion of the outlet flow is

recycled to one of the tanks upstream. If reset is used on all the level controllers, the total system

will be conditionally stable. Any upset in one of the wild flows will cause all the levels to oscillate

with a very long period. If a series of tanks are piped together with a recycle flow, one of the tanks

must have a level controller with no reset. This is necessary to break this multiple integral cycling.

For many tanks, there are multiple inlet and outlet flows, complicating the self-regulating, non

self-regulating distinction. As a rule, the user should use a proportional only unless dictated by

other process considerations.

Anatomy of a Level Control System

What is the most difficult process you have ever tried to control?

Despite the fact that level is generally considered an easy process to control, the most

challenging process I ever had to control was a Graver water treatment system. A quick check in

the Internet shows the name Graver is used by several companies. The vessel has several

chambers and is quoted by one of the companies from their Internet sight as:

Hot Process Softener

An integrated system combining a number of water treatment processes into a single unit.

An integrated system consisting of water treatment processes such as chemical treatment at elevated temperatures, clarification of chemically treated water, and deaeration and storage of makeup and condensate. The Hot Process Softener, designed specifically for boiler feedwater purification, reduces hardness, alkalinity, silica, oxygen and suspended impurities to prescribed values, regardless of variations in flow or chemical composition of the incoming feedwater.

http://www.graver.com I attempted to control a Graver over thirty years ago. I can only estimate some of the vessel’s

size, and construction. The vessel consisted of a large, perhaps 100 feet high by 50 feet in

diameter conical shaped structure, see figure. The top portion consisted of an internal coned

section and a standpipe that extended almost to the bottom. The water flowed down the

standpipe and filled the inside portion, then overflowing across a rectangular weir. The overflow

was collected in a second chamber, which was vented to the atmosphere. The outlet of this

chamber was the boiler feed water line. The control system consisted of a level controller


52

controlling the level in the overflow chamber. The output of this controller became the set point of

the standpipe level controller. This level controlled the water height in the weir and therefore the

flow to the second chamber. The power plant’s turbine exhaust steam was piped to a 36-inch

manifold header that acted as a steam pad on the top of the vessel’s interior chamber. The cold-

water inlet was heated by condensing this steam. In order to prevent loosing the water level in the

standpipe, the steam was pressure controlled. However this control valve was located several

hundred feet from the vessel. The hydraulic head difference between the water levels in the two

compartments, h2 minus h1, was equal to the static pressure in the top of the vessel.

Control was not a problem at lower water flow rates. However when the rates became high, the

large flow of cold water in caused the steam pressure to collapse that caused the water to rapidly

flow up the standpipe. The pressure control valve closed attempting to increase the pad pressure.

The graver volume then lowered the level across the weir that caused the chamber level

controller output to increase the set point to the outer level controller. This caused increased

demand for cold water, which added more water than required. When the steam pressure

increased enough to push the water down the standpipe, there was too much water in the vessel.

This increased the weir level, increased the chamber level and caused the chamber level

controller to reduce the vessel level. This lowered the cold water inlet flow. The amount of water

was not enough to condense the right amount of steam in the pad. That caused the pressure to

rise and begin the cycle over again. Many control experts tried in vain to fix the problem. I

simulated the problem in MATLAB to try to investigate what types of controls could help control

the levels.

A simulation of this process showed some interesting behaviors. One interesting observation is

that the flow rate across a rectangular weir is reasonably linear. See figure two. The equation for

flow across a rectangular weir is non linear.

5.1*)*2.0(*33.3 HHWF −= (3)

Where F is the flow rate in cubic feet per second, W is the weir width in feet and H is the weir

height in feet.

The simulation showed that if both level controllers were proportional only, the offset in the

chamber level was too great. A PI controller was used for the chamber level and a proportional

only was used for the vessel level. This would be a good choice since the offset in the vessel

would not present a problem for the operators. They were most concerned with the chamber level

because this held the reserve boiler feed water. Any dramatic reduction in that level would require

the plant to use untreated water or cut back steam to the users. The process was simulated by

assuming that the level increase in the vessel was necessary to flow water from the vessel into

the chamber.


53

Figure 2 Rectangular Weir Flow vs. Height The other problem was that the chamber volume is much smaller than the vessel volume. In a

normal cascade loop, the outer loop should be much faster than the inner loop. That is not the

case here. If a proportional only controller is used for the outer loop, the vessel level control, this

was not a problem. There was no dead time between the change in water flow and change in

vessel volume.

The pressure control loop behavior was the major disturbance. The problem was the long pipeline

between the pressure controller and the vessel. This length of line created a pressure wave that

caused most of the problem. As I recall, once the flow increased beyond a certain point, the

pressure dropped very rapidly and the system became upset instantly. The loops would have to

be placed in manual to dampen the oscillation. One suggestion was to relocate the pressure

controller and vent valve to the top of the vessel. This was rejected because of the high cost.

Another idea was to relocate the pressure transmitter to the to of the vessel. This was rejected

because the owner was interested in maintaining the proper turbine backpressure for steady

turbine operation.


54

Figure 3 Graver Water Treatment Vessel

This control system was installed over 30 years ago. Controllers on the market today have many

other functions than they did at that time. If I were solving the problem today, I would consider

using feed forward control to the pressure loop. The feed forward signal would be the vessel level

controller’s output signal, which is the inlet water valve. As this valve is opened, the vent valve

should be closed. This will force more steam to the vessel pad to compensate for the increased

cold-water demand. A velocity limit control block between the controller output and the valve

would also be helpful. A velocity limit function block limits the rate at which an analog input value

36" diameter

Graver Water Treatment Vessel

several hundredfeet

Low PressureSteam

from Turbines

Vent

PCLC5 psig set point

Flow Out

Rectangular Weir

Flow In

LC

RSP

Spray Nozzle(typical of several)

h1

h2

Chamber

Standpipe

velositylimiter

feed foward signal


55

can change. This function has a different response than a first order filter. A first order filter may

exhibit too steep a change to a step input, because the derivative of a first order response is the

inverse of the filter time constant. This may be too fast for some processes. The rate of change

limits can be configured for increasing and decreasing outputs. This would prevent rapid changes

in water flow and allow time for the steam flow to increase.

The simulation showed the effect of increasing the boiler feed water flow rate. At time equal to

150, the feed rate was increased that caused a drop in the pad pressure as shown in figure 4.

Note the increased weir height after the increased boiler feed water demand.

Figure 4 Graver Levels and Pad Pressure

Internal levels are shown in figure 5. Note how the standpipe level increased as the pressure

decreased.


56

Figure 5 Graver Internal Levels

When simulating a liquid level control problem, it is necessary to calculate the change in flow in

and out of the vessel. This change is then integrated to calculate the vessel volume. In this

simulation, the water flows are simply the flow in minus the flow out. The volume in the vessel has

to increase because the weir level is increased to allow more capacity.


57

Figure 6 Graver Flows and Volume


58

Figure 7 Graver Standpipe Level and Set Point

Figure 7 shows the offset between the standpipe level and the set point. In this application, this

off set is not critical. The use of reset in this level loop adds extra complication to an already

difficult control application. Proportional only controllers can help smooth out plant disturbances.

Adding reset to a level control loop should only be done after some thought is given to the overall

performance under both normal and abnormal conditions.

References

Lloyd, S. G., Anderson, G. D., Industrial Process Control 1st edition, Fisher Controls Company, Marshalltown, IA, 1971.

Smith, Cecil L., “Is Reset Action Always Necessary?”, Instruments and Control Systems, p 42, Feb. 1970.

Shinskey, F. Greg, “Averaging Level Control”, Chemical Processing, p 58, September 1997.

Considine, Donald M., Process Instruments and Controls Handbook, p 4-85, McGraw-Hill Book Company,

New York, New York, 1957.


59

Chapter 7 Pressure Control

Introduction

Pressure control can be either a self-regulating or non self-regulating process. Pressure can be

exerted by either liquid or gas forces. The medium phase does not dictate the control behavior

rather the forces pressurizing it and how the media is manipulated dictate the behavior. The

process dynamics are determined by the methods used to control the inlet or outlet flows.

Pressure Regulator

The most simple pressure controller is a pressure regulator. A pressure regulator, either self-

contained or pilot operated, is a proportional only controller built into its internal design. Refer to

the cross section schematic shown in figure 1. In this example, the regulator is built to control the

downstream pressure. At rest or on the shelf, the regulator is fully open. When piped to its service

and operating, the downstream pressure P acts on the diaphragm area A to create a force F. This

force will compress the regulator spring proportionally to the spring constant. The distance

traveled will be x.

xKF *= (1)

The top set screw that presets the spring is used set the regulator downstream pressure.

Figure 1 Pressure Reducing Regulator

As the downstream pressure increases, the resulting force acting on the diaphragm compresses

the spring and closes the internal valve. As the downstream flow demand increases, the valve

has to open more to allow the backpressure to balance the spring force. This will require less

pressure at higher flows. In regulator terminology this is called droop. Droop is the loss in

��

Q P

A

Ks

x

set screw


60

downstream pressure as the flow increases. The table below is from a Cashco Company Model

1000HP instruction manual shows the proportional action.

Figure 2 Regulator Table

This is a classical proportional action because the amount of off set, droop in this case, is

proportional to the demand or load.

Liquid Pressure Control

If a centrifugal pump is used to pressurize a pipeline or a particular piece of equipment, the

dynamics will behave similar to a flow loop, that is a low gain setting and a moderate reset value.

The centrifugal pump curve has a flow curve that reduces the head as the flow increases. The

increased flow will cause the inlet pressure to decrease, which acts to reduce the flow. This loop

is considered to be self-regulating. One common application for pressure controls on centrifugal

pump discharges is to use the control loop to prevent dead head condition. Deadheading a pump

is not a very good idea; it can cause premature seal failures as well as may create critical process

problems with certain fluids. Usually the pressure control valve is used to flow a portion of the

pump discharge back to the supply vessel. When using a pressure control loop in this manor, it

may be necessary to use an override control to drive the valve closed for high demand services.

Gas Pressure Control

Gas Pressure control is quite similar to level control in that the control behavior, either self-

regulation or non self-regulating, depends on the control in or out of the vessel. If a flow controller

controls either the inlet or the outlet flow rate, the process is non self-regulating. This is because

the other flow has one unique flow to balance the pressure. If on the other hand, either the inlet or

outlet flows set through a restriction, such as an orifice, the process is self-regulating. As an

example consider a vessel that is pressurized by an inert gas such as nitrogen. The tank supply

pressure is reduced by a pressure reducing regulator followed by an orifice. The tank is pressure

controlled by venting the off gas to atmosphere. This is frequently done with flammable liquids to

lower the flash point of the vapor space above the liquid surface, Figure 3.


61

Figure 3 Self Regulating Pressure Control

In this case as the pressure increases closer to the downstream regulator set pressure, the flow

through the regulator will decrease. That decreasing behavior will help contribute to reducing the

rate of pressure increase. The pressure in the tank can be simulated easily by integrating the

number of moles in the tank by the following: ' calculate the initial mass in tank p=nRT/V P_tank = (xnew(1) / MW) * R_gas * t / vol ' calculate the change in pressure ' first we need the outlet flow dP = P_tank - p_atm If (dP > P1_orifice - p_atm) Then dP = P1_orifice - p_atm End If If (dP < 0#) Then dP = 0# End If Qout = Cg_valve(Index) * P_tank * _ ((520 / (spgr * t)) ^ 0.5) * _ Sin((59.64 / C1_valve) * (((P_tank - p_atm) / P_tank) ^ 0.5)) Q_valve = Qout Qout = Qout / minperhr n_out = Qout * spgr / 13.1 ' the flow across the orifice plate dP = P1_orifice - P_tank If (dP > P1_orifice - p_atm) Then dP = P1_orifice - p_atm End If If (dP < 0#) Then dP = 0# End If Qin = Cg_orifice * P1_orifice * _ ((520 / (spgr * t)) ^ 0.5) * _ Sin((59.64 / C1_orifice) * ((dP / P1_orifice) ^ 0.5)) Qin = Qin / minperhr n_in = Qin * spgr / 13.1 x_dot(1) = n_in - n_out

PC

PressureReducingRegulator

Orifice

Vent


62

Figure 4 Gas Flows and Pressure for a Self Regulated Pressure Control

SP & PV for Press Controller

30

35

40

45

50

55

0 10 20 30 40 50 60

Time, min

PSI

G

PspP1

Gas Flows

0

2

4

6

8

10

12

0 10 20 30 40 50 60

Time, min

SC

FM

QinQout


63

As the pressure is increased, the flow in and out of the tank decreases. This assumes that the

tank pressure is somewhat close to the regulator set pressure.

If, on the other hand, The inlet gas is flow controlled for a much higher pressure source and the

gas is either used to pad the tank or react with one of its contents yielding an off gas flow rate that

is directly proportional to the inlet gas flow, then the gas pressure could be assumed to be non-

self regulating.

Figure 5 Non-Self Regulating Pressure Control

In this case, as the pressure in the tank increases, the action of the flow controller, assuming it is

tuned to operate much faster than the pressure control loop, will be to maintain the same flow. In

this case there is only one unique stable valve position. This dictates an integrating behavior

therefore non-self regulating control.

As the plots show, the inlet flow was constant. After the pressure set point change, the outlet flow

is equal to the inlet flow, but the tank is at a higher pressure.

The gain for the self regulating pressure control was 7.5 while the reset was at 2.5 repeats per

minute. For the non self regulating pressure control the gain was 20 while the reset was at 10.0

repeats per minute. As a rule, non self regulating control loops require a higher gain setting.

PC

Gas Flow Controller

Orifice Vent

FC


64

Figure 6 Gas Flows and Pressure for a Non Self Regulated Pressure Control

SP & PV for Press Controller

30

35

40

45

50

55

60

0 10 20 30 40 50 60

Time, min

PSI

G

PspP1

Gas Flows

0

5

10

15

20

25

30

35

40

0 10 20 30 40 50 60

Time, min

SC

FM

QinQout


65

Even though the non self regulating behavior is seen as inlet flow limiting, for small pressure

changes, both loops can exhibit integrating behavior. This is because the rate of change for an

increasing exponential is greatest at the start or beginning of the change. For a short interval,

both self and no self regulating loops can show similar behavior. For this case, assuming

integrating behavior can lead to a higher gain setting. It should be emphasized that in this case,

loop instability can occur because the resulting gain may be unstable for extreme disturbances.


66

Chapter 8 Temperature Control

The following discussion describes the behavior of various temperature control loops. In general,

a basic understanding of the physical system, in terms of size, material physical and chemical

properties, is usually sufficient to make a good selection of sensor location, algorithm and final

element selection, placement and size.

Temperature control of non-reactive materials is generally considered to be self-regulated. A fixed

valve position will result in a constant temperature for a constant load.

For large insulated un-agitated tanks, the temperature sensor and the heat source should be

located at the bottom of the tank. The sensor should be located below or on the same vertical

plane as the heat source. The sensor should also be placed close to the heat source. The

concept is to control the heat to the tank contents from the source to the probe. This hot material

will rise to the surface of the tank and cold liquid will displace it. This creates a thermo-siphon. If

the sensor is located too far from the source, the bulk temperature will overheat. If the tank probe

is located above the heat source and the probe is in a vapor space above the liquid surface while

the heat source is in contact with the liquid, the contents will overheat because little heat can be

transferred to the probe. In some cases it is possible to boil or vaporize the remaining contents.

Shell and tube heat exchangers very frequently used to heat or cool liquids. If the thermo-well is

placed close to the exchanger outlet, the transient response approximates second order with

dead time. The thermal lag through the exchanger is usually short compared to the thermo-well.

As an example, consider a 157 square foot 4 pass 104 tube, 1 ¾” # 16 BWG, exchanger

transferring one million BTU per hour heat. The tube side has 100 GPM water flowing through it

while the shell side has 150 GPM water. The shell has an internal tube volume of 33 gallons. The

jacket thermal lag can be approximated as V/F (volume / flow rate) or 0.33 minutes. The

exchanger is 3 feet long and 12 ¾” diameter shell. For a shell and tube heat exchanger, the

thermal lag through the tubes can be ignored because they are usually very thin. In most cases,

the shell flow rate is higher than the process flow rate. The void volume in the shell is a fraction of

the tube volume. Therefore the shell thermal time constant is smaller than the tube volume time

constant. There are time constants associated with the thermal mass of the shell and heads,

however these are usually small because the specific heats are low.

The dead time can be calculated by noting the velocity through the tubes that is shown on the

exchanger design sheet that is 0.65 ft per second. The tube length times the number of passes is

3 X 4 or 12 feet. The transportation or dead time would be 12 feet divided by 0.6 feet/second or

20 seconds. The thermo well time constant cannot be ignored in this case. It is usually the largest


67

lag in the entire control loop. A 316 stainless steel thermo-well in the pipeline exiting the

exchanger would experience a lag time of about 1 minute.

Figure 1 Normal PID response to Set Point Change

This curve shows the normal response to a PID controller set point change. In this case, the dead

time was set at one minute while the thermo well time constant is also one minute. The other time

constants contributed to the total overall lag of about1.5 minutes. The temperature oscillates at a

period equal to 4 times the dead time plus the time constant or 5.5 minutes.

If a thermo well is mounted in a pipeline, it is best to provide a pipe section of slightly larger

diameter around the well. In addition, it is best to have the flow enter at 90 degrees rather than a

large radius elbow. This method keeps the well in contact with the flowing process fluid.

PID Temperature Control Response

100

110

120

130

140

150

160

35 40 45 50

Time, minutes

Deg

F TwF Tsp


68

Figure 2 Thermowell pipe mounting

The thermowell time constant can be calculated by the following formula:

d

P

UfGC1560

=τ (1)

Where

τ is the time constant in minutes

G is the specific gravity of the thermowell

Cp is the specific heat of the thermowell material BTU/lb-degF

U is the heat transfer coefficient in BUT/hr-ft^2-degF

fd is a dimension factor

)(3 22 dDDfd −

= (2)

D is the outside diameter in inches

D is the inside diameter in inches

Thermowell Mounting Detail

ConcentricReducers

Thermowell


69

Set Point Profiles

What can be done to prevent overshoots during startup? I have a process that interlocks out on

high temperature every time we start up.

PID controllers have an effect called reset windup. During the startup, the process variable is well

below the set point for so long that the reset value saturates. This causes overshoot when the

process variable finally reaches the set point, it way too late to begin lowering the output signal

through the reset value. Many controller companies market fuzzy logic or neural network

controllers that can solve the problem. Many of these problems can be corrected with

conventional controllers together with linearization and set point profiles.

A way to avoid this problem is to lower the set point for the first part of the startup. This allows the

controller to begin lowering the reset value at a point below the set point. Once the process

variable reaches its peak and begins to drop, the set point can be increased. The objective is to

program the control system to act the way an intelligent operator would. The following plot shows

a reactor simulated temperature set point profile and the resulting temperature. In many cases, a

ramp is not required just change the set point to the final value some point in time after the start

of the process.

Figure 3 Set point profile minimizes temperature overshoot

Temperatures

160

170

180

190

200

210

220

0 10 20 30 40 50 60Time, min

Deg

F Set PointTemp


70

Heat Transfer Coefficient

The plot below shows that the heat transfer coefficient for in industrial heat transfer fluid is

proportional the flow rate to the 0.8 power. In order to achieve rapid response with heat

exchangers, it is highly desirable to keep the flow rate as high as possible through the exchanger.

One way to obtain this is to use a tempered heat exchange loop. For a tempered loop, a pump

circulates the utility fluid through the exchanger at a high rate. Adding a quantity of the utility fluid

to the loop changes the temperature across the exchanger. This produces a flywheel effect and

the result is very responsive control. In addition, this design will also permit good control at a

reduced load. One disadvantage with this is that fouling can occur on the heat transfer surfaces.

Figure 4 Heat transfer coefficient as a function of flow rate

Heat Transfer Coeff.

0100200300400500600700800900

0 5 10 15 20 25

Velosity ft/sec

HTC HT Coeff. Btu/hr-ft 2̂-degF

HT flow 0̂.8


71

Figure 5 Tempered Loop

Chemical Reactor Temperature Control

All the processes discussed above could be considered as mechanical systems. Any heat

generation due to a chemical reaction was not considered. For chemical reactors, the amount

and direction of heat transferred by the reaction is very important in the design of the cooling

system, the reactor itself as well as the control system. The following discussion is taken from

Shinskey’s text. Anyone involved in the design of reactors is strongly encouraged to review the

reference.

Chemical reactions are either endothermic or exothermic. Endothermic reactions require heat

input to the reactor mass to initiate and sustain the reaction. Exothermic reactions generate heat

during the reaction. The method of this heat removal and reactor design is very important for

these reactions.

Chemical reaction rates are calculated by a reaction rate coefficient, k. For a continuous

backmixed reactor, k is equal to:

RTE

ak−

= ε (3)

Where a, E are the reaction constants, R is the gas constant and T is the absolute temperature.

This equations shows that the reaction rate increases with increasing temperature. As a general

rule, the reaction rate doubles for every 10 Deg C increase in temperature.

TC

Utility Supply

Utility Return


72

For a backmixed reactor the conversion, y is calculated by the residence time and the reaction

rate constant:

FVk

y+

−=1

11 (4)

Where V is the reactor volume and F is the volume flow rate.

For each reactor controlled, the slope of the reaction conversion vs. temperature should be

calculated. This calculation is made considering the reactor type whether plug flow or back mixed.

A continuous plug flow reactor will yield higher conversions than a comparable back mixed

reactor with the same volume and flow rate. The maximum slope for both will occur when kV/F =

1, where V is the reactor volume and F is the feed rate. For a backmixed reactor, the slope is:

yRT

ETy

2=δδ

(5)

For exothermic reactors, the heat transfer coefficient and surface area, UA, and the coolant

temperature can calculate the amount of heat removed:

)( cT TTUAQ −= (6)

The heat evolved due to the reaction is:

yFxHQ rr 0= (7)

Where Hr is the heat of reaction, x0 is the inlet concentration.

These relationships, as well as the sensible heat gained or lost, can be used to calculate the rate

of temperature change:

dtdTCVTTCFTTUAyFxH fcr ρρ =−−−− )()(0 (8)

Where ρ is the density. From these equations, the thermal steady state gain can be calculated as:

)(0 TyFxHCFUA

UAdTdTK

rc

T

δδρ −+

== (9)

And the thermal time constant is:

UACVKt T ρ

= (10)

Note that it is physically possible of this term to be negative. If the steady state gain is negative,

the reaction is steady state unstable. This should be avoided. One way to do this is to limit the

reactor feed rate, F, by using an override control. This implied valve position control reduces the

reactor feed if the cooling demand becomes too great.

For a batch reactor it is best to control the reaction by controlling one of the reactants. This is

called “semi-batch”. Varying the amount of coolant can control the rector temperature. A flow


73

controller can be used to control the flow of one of the reactants. An implied valve position

controller, IVP, would override or lower the reactant flow if the cooling demand became too great.

Another term for this type of control is called constraint control.

Solid Thermal Time Constant

Solids have a thermal time constant. When a solid object or group of solid objects are heated with

hot gasses at a constant flow rate and temperature, the outlet temperature will rise to a steady

state value. This time constant, τ, can be calculated by:

tkAk

CM p

*

*=τ (11)

Where M is the mass, Cp is the solid specific heat, k is the thermal conductivity, A is the exposed

surface area, tk is the thickness. This time constant is dominant if there is sufficient gas flow with

respect to void volume. That is V/F is much less than τ. This equation will calculate the same

result if a single particle is considered or if the entire mass and area is used. This is because the

mass divided by the area will have the same relationship independent of the number or particles

being heated. An analogy of this is to consider the thermal time constant across an insulated

pipe. Neglecting the end effects, a given insulation type, thickness and diameter will have the

same time constant for a foot as it will for a mile. The shape of each particle defines this equation.

For very small objects, such as a powder, the time constant is quite low. This equation is valid for

any heated object be it a catalyst sphere or an agricultural product.

The Anatomy of a Temperature Control Project

The following project will illustrate some simple concepts that can be implemented for good

temperature control.

This project involved the temperature control of a small vessel to study fundamental reaction

chemistry. It is important to provide good, reliable and accurate temperature control to develop an

understanding of the reaction kinetics involved. These reactors are agitated with 1/8" tubing

cooling coil, wound in a hairpin loops. Heat is introduced by an electrical heating element on the

outside of the reactor.

The reactor had temperature control problems. The problems are as a result of the control

scheme used. This scheme control uses a split ranged output signal where ½ of the output span

is to provide electrical power to the external heater and the other ½ of the output span is signaled

to control cooling water flow through an internal cooling coil by a control valve, mounted in the

supply tubing to the cooling coil. This design results in cycling between heating and cooling


74

phases. The reason for the cycling is because the dynamic response due to the heating cycle is

much slower than the cooling response. This is counterintuitive; one would think that electrical

power would respond faster. In actuality, because the heater is mounted on the outside of the

autoclave, the thermal time constant is larger than the thermal time constant of the cooling coil.

This cycling behaves in the following manor. Assume the temperature is below the set point and

the electrical power is on, while the cooling water is off. Heat is slowly transferring across the

reactor jacket. Meanwhile because the control valve is piped to the water supply to the cooling

coil the water in the coil is at atmospheric pressure. This water begins to degas and even boil if

the reactor temperature is high enough. These gasses and vapors displace the water in the coil

that reduces the heat transfer inside the coil. Because of the large thermal lag across the reactor,

by the time the temperature is above the set point, the power shuts off and water begins to flow

through the coil. Good heat transfer across the coil does not occur until the gasses and water

vapors are swept out of the coil and a sufficient velocity of water is established. By then, the

temperature undershoots causing the output signal to shut off the water flow and switch on the

power, repeating the cycle.

Improved temperature control of a small vessel can be accomplished by implementing an

implied valve position control. This method requires the use of two PID controllers, one for the

vessel temperature and one for the temperature controller's cooling water outlet. The reason this

method performs better is that the temperature control response is faster with changes in the

water flow rate than through changes in the power to the electrical heater. The power to the

heater is controlled to provide sufficient cooling water flow through the coil to improve response.

Balancing the heat and cooling loads do not cause excessive utility uses because of the size of

the reactor.

Other changes made were:

Installed a valve positioner in the cooling water valve. This makes the valve more responsive to

signal changes.

The control valve was sized to keep about 7 feet per second flow in the cooler. This would be for

normal flow or about 70% open. Use equal percent trim. As previously explained, the heat

transfer improves with increased flow to the 0.8 power of flow rate so it would be best to keep

cooling water flowing through the coil at all times.

The control valve should be piped to the outlet of the reactor coil rather than the inlet. This is to

keep the water in the coil at a higher pressure, which will minimize the water degassing.

Degassing the water results in increased volume and poor heat transfer inside the coil.

An RTD was used rather than a thermocouple for the primary controlled measurement. Many

temperature element suppliers have documented references that show the RTD to be superior

accuracy when compared to thermocouples. Accurate repeatable temperature measurement


75

and control is essential to calculate reaction kinetics. Typically, reaction rates double every 10

degrees C. Therefore accurate measurement is essential.

A proportional plus reset controller was used to control the heater by the position of the cooling

water valve. The set point is set for about 70 to 85% open. The output of the position controller

adjusts the power to the heater. The reset value of this controller is set to compensate for the

thermal mass of the heater or 1.5 repeats per minute. The time constant was calculated before

start up as shown below:

For the 316 stainless steel reactor wall, the constants in English units are: G=8.02 specific gravity Cp = 0.12 specific heat k=13 thermo conductivity Reactor dimensions, in feet D1=0.1508 inside diameter D2= 0.2133 outside diameter L=0.5833 Vol = pi*L*(D2^2)/4 - pi*L*(D1^2)/4 + pi*(D2^2)*(2.25/12)/4 Vol = 0.0171 cubic feet M = G*62.4*Vol M = 8.5725 pounds A= pi*D1*L A = 0.2764 ft^2 hw=2*k/(D2*log(D2/D1)) hw = 351.5486 tau_wall = 60*M*Cp/(hw*A) tau_wall = 0.6352 minutes The integral time constant of the power controller is set to compensate for the thermal time

constant. In this case 1/0.6352 = 1.574 repeats per minute. In actuality 1.5 repeats per minute

were used.

In addition to this calculation, a calculation was made to predict the cooling rate from the coil.


76

Figure 6 Reactor Temperature Control

In many applications, electrical power is controlled by a time proportional output through a triac

power controller. The triac acts as an electrical switch. The electronic circuits that control the triac

switching implement a zero voltage turn on circuit. This is done to prevent electro magnetic

interference that would be caused by rapid changes in voltage if the AC voltage were switched

when the cycle is not at a zero crossing point. The disadvantage of this method is that the voltage

is switched in half cycle increments. If the time proportioning period is too short, the resolution of

the power to the heater is reduced. If the heater controller proportioning time is increased, the

resolution improves but if it becomes too long it introduces dead time in the heating loop. If the

time proportioning cycle is set for 2 seconds, the power resolution would be one part in 240, if the

heater is 1200 watt, then the power would cycle plus or minus 5 watts because this is the best

resolution the controller can resolve, or approximately 7 deg C for a 10 pound mass. The end

result of this type of design is that the output precision approaches that of on off control.


77

Improved electrical output power resolution can be obtained by using a Silicone Controlled

Rectifier, SCR. This device can switch ac power over fractions of a half cycle. The SCR does

generate transients during switching and can be falsely switched due to transients in the line

power. By installing a varistor across the SCR terminals, the transient can be suppressed through

the device. These devices are available from the SCR suppliers.

The power delivered to the load using this method has very non-linear characteristics. This non-

linearity would cause less than optimum control if it were not linearized. Linearization was

previously discussed in this book.

A simulation mass and energy balance was written in the controller itself. This was done to allow

the operators to experience the different control behavior.

The temperature control system started up quite well and good agreement between the heating

and cooling loads was obtained. One interesting observation was that as the inlet water

temperature was reduced, less electrical power was required. This is surmised to be due to the

reduced heat transfer across the cooling coil due to the increased water viscosity.

References

Hendershot, D. C., “A Checklist for Inherently Safer Chemical Reaction Process Design and

Operation”,. Center for Chemical Process Safety, Jacksonville, FL, October 8-11, 2002.

Richmond, D. W. "Selecting Thermowells for Accuracy and Endurance." InTech,

February 1980

Shinskey , F.G., Process Control Systems fourth edition McGraw-Hill, 1996.


78

Chapter 9 Control of Steam as a Heating Media

Introduction

Frequently the control or instrument engineer is asked to design or solve problems with steam

control systems and, after checking the usual sort of items such as the regulator and control valve

sizing, span and range of the transmitter, they are at a loss as to the solution of the problem. This

article addresses the whole system, some of the frequently overlooked problems, and solutions.

Steam, as a heating media is ubiquitous in the process industries. There are very few process

plants that do not rely on steam for some sort of heating application. The applications are infinite

but can be placed in a few general categories.

Steam Flow Control

Here steam is actually controlled by flow rate to a heat sink. Examples of these are column

reboilers and strippers. Steam can be used to control a variety of process variables such as level,

pressure etc. In most of these applications what is really required is the control of heat input in the

process. This is indirectly steam flow control. The flow rate in many of these applications actually

sets the capacity of the unit. In this type of system, the primary process variable controller's

output sets the set point of the steam flow controller. Tuning of this type of control system is best

done if the steam flow controller is tuned in "local" before the primary process variable controller

is tuned.

Either a vortex-shedding meter or an orifice plate with a differential pressure, d/p, and transmitter

usually measures steam flow.

For some process applications, heat flow is a better measurement than steam flow itself. This is

true in the case of column re-boilers. For orifice plates, the flow signal can be modified to correct

for the enthalpy based on the supply pressure. In the case of saturated steam, the correction can

be calculated by:

)*(** bpahkQ += (1)

Where h is the meter differential, p is the absolute pressure. Constants are k, a, and b. To

calculate the constants for a given orifice plate size, calculate the steam flow rate over a range of

pressures at the same meter differential. Multiply the steam flow rate by the enthalpy change to

calculate the heat flow. Next use the EXCEL solver to calculate the constants.

The following graph shows the actual heat flow compared to the calculated heat flow based on

the above equation. Q is the actual heat flow, Q^ is the calculated heat flow. A similar method

should be used if a vortex meter is installed and the user wants to meter heat flow.


79

If a vortex meter is used, make sure that condensate doesn't hit the shedding element. Watch the

temperature limits on the meter and electronics. Many manufactures have separate electronics

located remotely form the meter.

A major problem with orifice plates is preventing the condensate from freezing in the sensing

lines. Traced sensing lines and commercially available insulation instrument bundles keep the d/p

cell from freezing. The orifice pipe taps should be placed on the top or side to prevent plugage.

Depending on the impurities in the steam and if the d/p elements require large volume

displacements, condensate reservoirs should be piped directly off the pipe taps for accurate d/p

measurements. Because steam is a vapor, pressure variations may cause errors in the

measurement. It may be necessary to use a reducing regulator upstream of the orifice plate.

Temperature Control

Steam is often throttled to a heat sink to keep the process at a controlled temperature. A major

problem is overshoot of the temperature due to the dead time in the heating process because of

changes in load. Proper placement and selection of the temperature thermowell can reduce this.

It is important to place the thermowell in an active portion of the process. Frequently the

thermowell is placed in a non-flowing or cross-ambient location in the process; this insulates the

thermowell from the bulk temperature. The thermowell should be immersed in the process

between 5 to 12 diameters of the thermowell. It should be in a flowing stream and as close to the

heat source as possible. For fluids in a pipe, it is important to measure the temperature in the

Energy Flow Calculation

0

500,000

1,000,000

1,500,000

2,000,000

2,500,000

3,000,000

3,500,000

4,000,000

4,500,000

0 20 40 60 80 100 120 140 160 180Pressure

BTU

/hr

QQ'


80

center of that pipe. Except for large diameter pipes, this is achieved by the installation of the

thermowell in a pipe elbow. The immersion length of the well piped in the side of a pipe elbow can

result in a cross-ambient condition if the elbow's radius is not taken in consideration. Flared or

low schedule pipe can be bent at a long radius. In one application it was necessary to purchase a

12-inch thermowell to measure the temperature in the center of a 2-inch pipe. If the well is located

too far from the heat source, (i.e. heat exchanger or coil) or in a stagnant portion, by the time the

thermowell temperature reaches the set point temperature, the bulk temperature is considerably

higher due to the temperature gradient between the source and the thermowell. One exchanger

company even mounts a thermowell parallel but not touching the exchanger tubes. See Figure 1.

Figure 1 Thermowell inserted in heat exchanger

For tanks, the thermowell should be located in the same horizontal plane or lower than the heat

source. This is very important in tanks of varying inventory. If the thermowell is located above the

heat source and the level drops below the thermowell, the thermowell is then sensing the vapor

temperature and over heating may result. This overheating may result in wasted steam, and

possibly product degradation.

Low mass and sheathed elements as well as high thermal conductivity fills and metals can be

used to improve response time and thereby improve control. In most shell and tube exchanger

temperature control systems, the dominant lag in the system is due to the thermowell. Care

should be taken in the selection of the element, RTD or thermocouple etc. As a general rule, an


81

RTD is a sheath sensitive element while a thermocouple is tip sensitive. Frequently overlooked is

the possible contamination or destruction of the product due to corrosion of the well in any filled

system, both vapor and liquid types. The response time can be improved by placing the element

directly in the process. Periodic inspections of the well or element should be taken.

Commercially produced thermowells should be considered before fabricating one. These wells

are available in a wide variety of materials and connections both screwed and flanged. Lagging

extensions should be used when pipe insulation is required. This prevents insulation removal

when the well is removed. There must be an annular gap between the ID of the well and the

element that is large enough to allow for thermal expansion yet small enough for rapid

temperature response. The ID of commercial wells is machined to fit most types of elements to

assure proper the fit. A fabricated well's temperature response can be improved by filling that

space with a liquid fill. Care should be taken in the selection of this liquid fill. The liquid will

frequently boil away or decompose in the well. Process compatibility with this liquid should be

considered.

Frequently several uncontrolled heat sources are all piped to a vessel in addition to the controlled

source of heat. This can result in complete loss of control. An example of this is a fully insulated

30,000 gallon storage tank with an internal coil which is the controlled source; 2 semi circular

plate coils 1/3 the way up the tank which are trap limited and not controlled. The tank had a

circulation flow of 100 GPM that went through about 50 feet of 2 inch of steam traced and

insulated pipe. On startup, with the tank about 1/4 full, the temperature continued to rise above

the set temperature. A manual valve was closed upstream of the steam control valve and the

temperature kept rising. The plate coils were shut off and the temperature still kept rising. The

product in the tank was ruined due to the high temperature. The tracing from the 50 feet of 2-inch

pipe was the remaining uncontrolled source of heat. An orifice was placed in the pump discharge

of the 50-foot line that corrected the problem.

Regulators and Relief Valves

Regulators are used to reduce the steam pressure for a variety of reasons. Reduction of pressure

may be necessary to protect the steam or plate coil, which may be rated at a lower pressure than

the supply. It is frequently required to reduce the skin temperature of the coil thereby preventing

product decontamination. The reduction in pressure through a regulator is an adiabatic expansion

and superheat will result. Reduction of this superheat should be considered if skin temperatures

are important. This may be accomplished by placing a small thermostatic steam trap together

with a length of uninsulated pipe on the discharge side of the regulator. If the steam supply is in

the quality region, containing some condensate, a steam trap on the supply side of the regulator

will be necessary. Passage of condensate through the regulator will result in reduced capacity.

This trap is a must if the regulator is located lower than the main supply header. A strainer should

be placed upstream of the regulator to filter pipe scale.


82

If a regulator is required, a relief valve on the discharge side of the regulator should be

considered and should be placed upstream of the control valve, see Figure 2. If the control valve

were piped upstream of the regulator, turning on the steam would result in "machine gunning" the

relief valve since the regulator would be fully open. A small steam trap should be placed on the

discharge side of the regulator. The trap will remove the condensate and prevent pressure

buildup since some steam regulators do not shut off tightly, because they use metal to metal

seating surfaces.

Whenever possible, avoid the use of pilot operated regulators. The maintenance of the pilot

piping is a problem with both plugage and freezing. Self-contained pressure reducing regulators

are preferred; however, they usually have a lower capacity rating than a pilot operated device of

the same line size.

Another use for a pressure regulator is to provide a constant upstream pressure supply to the

control or modulating valve. If no regulator is present and the control system is at steady state,

supply pressure fluctuations will result in steam flow upsets and therefore a process upset. A

regulator will quickly correct this problem, preventing the process upset.

The pressure regulator is not a precise pressure control device. It has droop; the outlet pressure

will decrease slightly as the flow rate increases. In many applications requiring wide flow range or

the need for precise control, a pressure controller is necessary.

The uses of a steam supply pressure controller as a secondary (slave) loop for a temperature

control loop offers a performance advantage. For changes in heat load, the pressure loop will

automatically correct for the change in condensing rate before it affects the temperature loop.

Shell and Tube Heat Exchanger

VacuumBreakCheckValve

T

Control Valve

STEAM MAIN

Take off on top of header

T

ColdStream

HotStream

TT

T

Steam Supply Piping for Shelland Tube Heat Exchanger

Figure 2

DirtTrap

Trap BelowExchanger

Condensate Return

Test Valve

Strainer Regulator


83

Control Valves

Control valves underwent considerable change in the 1970s. This is when the cage trim design

was introduced. The main advantage of the cage trim is the balanced actuator forces required

and therefore a lower sized actuator can be used. The cage valve performs well in steam service.

Valve manufactures offer low noise design for large pressure drop applications. On low-pressure

applications, cast iron body with stainless steel trim is suitable. On higher-pressure applications,

piping codes dictate certain type of bodies and may require extended bonnets. A rule of thumb is

to size the valve pressure drop for 20% of the supply pressure at a maximum heat load. With

steam service, use equal percentage trim characteristics for heat exchanger temperature control.

This is because the change in the outlet temperature is inversely proportional to the change in

process flow rate. However, the change in outlet temperature is directly proportional to the

change in process inlet temperature and to a set point change for a properly sized exchanger. For

flow control applications, use equal percentage trim. In all cases, the objective of trim

characteristic selection is to match the process behavior, equipment-piping etc., to obtain linearly

installed flow characteristics. If a larger turn down is required for proper control over the whole

application, rangeability becomes a problem. In this case consider two valves with split range or

implied valve position control (see Reference 2). For higher temperature service, an extended

bonnet is required together with high temperature gaskets.

Steam Traps

The largest amount of heat transferred in steam heating is due to condensing the steam to

condensate. This is also done with the highest heat transfer coefficient, or heat transferred per

unit area. As a result, most heating systems are sized based on the transfer area acting as the

condensing surface. Should any condensate be trapped in the equipment, less heat will be

transferred. The device, which acts as the “condensate passer”, is called the steam trap, trapping

the steam in the steam chest of the equipment while allowing the condensate to pass. Steam

supplies contain entrained air and carbon dioxide, formed during the corrosion of steel that needs

to be vented from the trap, a secondary objective of the steam trap. Proper steam trap design and

installation is just as important in steam heating systems as other items addressed in this article.

Some examples of the consequences of incorrect steam trap design and installation are:

i) A batch reactor start up cycle time was increased by several percent.

ii) A dryer preheater was operating with higher priced electrical power because the preferred

steam source had a trap blowing steam through.

iii) A gas superheater temperature control system was operating with large swings.

There are three groups of steam traps: thermostatic, thermodynamic and mechanical. Some trap

manufactures have literature that covers their operation in detail. The discussion here will be

directed toward applications where throttling the steam supply is required for good control.


84

Thermostatic type traps use a temperature sensitive bellows with a plug and seating orifice,

Figure 3. The principle is for hot steam to expand the bellows and close off the orifice “trapping”

the steam upstream for condensing. The bellows is allowed to cool opening the plug, allowing the

condensate to pass. The trap is good for freeze protection because it fails open during cold

temperatures.

Figure 3 Thermostatic Steam Trap

The problem with using this trap for control service is the time required for the bellows to cool

enough to open and allow the condensate to pass. This time results in increased process

deadtime. It also makes control less responsive to increases in load because the time spent in

opening the valve is used to push the condensate out the trap. Increased heat transfer is not

available until this condensate is removed from the steam chest. While the controller's reset

action continues to drive the valve further open, increased steam flow (and heat flow) is not fully

realized until the added condensate is passed through the trap. Then the full area is available for

��

Condensate flows throughthe trap when bellows

contracts

Steam is "traped" in thebody when bellows

expands


85

condensing. However, by this time the valve has opened too far and the heat delivered is too

much, resulting in steam blowing through the trap. The bellows heats then closes and the cycle

repeats. One manufacture cautions using this type of trap where waterlogging the steam space

cannot be tolerated.

Thermodynamic traps consist of a housing with an inlet and outlet port connected through a small

chamber with a disk blocking the flow. When condensate enters the inlet, the disk is pushed up

and the condensate is allowed to flow out. When steam begins to enter the trap, some of the

condensate flashes to steam in the chamber increasing the pressure above the disk and closing it

against the inlet flow. The condensate cools and the pressure is reduced above the disk and flow

continues.

The problem with this design is somewhat the same as the thermostatic trap. Time is required to

cool the steam in the chamber. This trap requires a minimum inlet pressure and doesn't work well

if the backpressure is too great. Backpressure of the condensate is another design concern for

trap selection since most industrial plants using steam recover their condensate.

The mechanical group consists of three types: floats, float and lever, and the inverted bucket,

Figure 4. The float type contains a float and some way of linking it to a lever arm and a seating

orifice. When condensate enters the chamber, the float rises opening the orifice and allowing

more condensate to pass. In the inverted bucket design, the inverted bucket is connected to a

lever arm, which is connected to a plug and a seating orifice. The orifice is located in the outlet of

the chamber. As steam enters the chamber, the bucket becomes buoyant and closes the orifice.

The advantage of this type of design is the trap's proportional action and rapid response to

changes in demand on the system that is steam flow. NL designation in the figure is the neutral

line, or the level line where the trap begins to open.


86

Figure 4 Inverted Bucket Trap

Another advantage of the mechanical trap is its ability to correct for backpressure variations in the

condensate return. A good analogy of a mechanical trap can be a self contained proportional only

condensate level control system, such as a float valve or displacer. These devices operate very

rapidly, much faster than the dynamics of the heating process. Assume the system is operating at

a steady state condition, and then the condensate backpressure increases. Immediately the

condensate level in the mechanical trap increases, which causes the trap to open further, keeping

the same level in the trap. With a thermostatic trap, time is required for the bellows to cool and

open more. This time can cause a decrease flow of steam, decreasing the process temperature.

One disadvantage of the inverted bucket trap is that the condensate doesn't fully drain and may

freeze. A small thermostatic trap placed in a low spot in the trap inlet piping can prevent this. The

float design can trap air and carbon dioxide, however gasses can be vented with the inverted

bucket design.

Frequently overlooked is the need for vacuum breaking in the steam chest. Steam condensing in

the chest will cause a vacuum to form if the supply is closed. This vacuum could pull condensate

from the trap into the cavity. A vacuum breaker piped in the condensate line before the trap will

allow air to enter the steam chest, thereby allowing the cavity to drain.

When sizing the trap, consider that most of the system pressure drop occurs across the trap

orifice. Make allowances for the condensate backpressure and the gasses in the steam. Vent

them should the trap not have that capability. Use vacuum breakers to prevent condensate

Condensate flows throughthe body, the bucket islow, permitting it to flow

through the orifice.

When steam enters thebody, the bucket is

buoyant, closing the orificethereby trapping the

steam.


87

buildup. Pipe the trap below the condensing cavity. It is recommended that the trap and the

condensate piping one-foot up and down stream of the trap not be insulated. (It may be

necessary to install a guard around the installation for personal protection.) An insulated trap can

cause sluggish operation and make maintenance difficult. Most trap manufactures have design

guides on trap installation, which should be helpful.

Proper installation and maintenance of the steam trap is just as critical to the loop operation as is

the control valve. Providing valves around the trap can inspect trap performance. These valves

should be piped to allow visual inspection of the trap discharge. Condensate and "flash steam"

would be present with a normal trap. Alternately, one could measure of the temperature of the

piping one-foot upstream and downstream of the trap. High differential temperatures across the

trap assure normal operation. In critical applications, using two pipe clamp adapters each with a

spring loaded bayonet style temperature element can make a permanent installation.

Direct Steam Injection

In some applications steam is directly injected in the process, where it is necessary to add water

and heat the process, thereby combining two processing steps. This is done through a sparger

ring in the vessel.

A problem with this design is how to prevent the process from backing into the steam supply

should the steam supply be closed or shut off. As the steam cools in the piping upstream, it

condenses and will draw a vacuum, which can result in filling a large part of the steam supply

piping with the process material. Vacuum breakers as well as automatically actuated valves

interlocked to steam supply pressure and check valves should be considered as prevented

measures.

Steam De-super Heater Control

When high-pressure steam is reduced to a lower pressure, the reduction is adiabatic and higher

temperature steam results. It is known that high temperature superheated steam is ideal for work

but not for heating. It is best to use saturated steam for heat transfer because all the exposed

heat transfer area is used for condensation and not to decrease the temperature to the saturation

temperature. The heat transfer coefficient is a great deal higher for condensation than for de

superheating.

One way to reduce the superheat is to use a shell and tube heat exchanger. For small loads, this

is a practical method. A very expensive exchanger is required if the load is large and the pressure

high. To reduce the superheat from 650 degrees F to 500 degrees F of 100,000 pounds per hour

of 600-psig steam supply would require an exchanger of approximately 2500 square feet.

Adding boiler feed water, BFW, directly to the superheated steam, will reduce the steam

temperature. The high temperature steam delivers heat to the water to vaporize it. The resulting


88

vapor mixture is mixed in the line to obtain a steam with lower superheat. The BFW is injected in

the steam line through a nozzle. See figure below.

Figure 5 Steam De-super heater

One disadvantage with this simple system is that, despite the best efforts to remove solids from

the BFW, solids and scale is deposited in the pipe due to completely flashing the BFW. This scale

will cause line to plug and restrict the flow.

Generally a PID controller is used to control the superheat temperature by modulating the BFW

flow. The problem with temperature control is that it does not compensate for pressure variations.

As the load increases, the pressure will usually decrease. If the same temperature set point is

maintained on the de-super heater temperature controller, the steam will have a higher heat

content.

Another method for controlling superheat is to control the superheat vapor pressure. Shinskey

proposed using a vapor pressure transmitter, actually a d/p cell with one side connected to a

capillary system. The sensing bulb is filled with water, so the d/p cell measures the pressure

difference between the steam pressure and the “saturated pressure at the superheat

temperature”. A vapor pressure transmitter has not been available for over 30 years. Another way

to accomplish this is to calculate the equivalent saturated pressure of the superheat temperature

by a simple regression of the steam tables. The pressure can be calculated by a least error-

squared fit of the following equation:

+

=)(

exp*cT

baP (2)

Where P is the pressure in psig, T is the temperature in degrees F, and a, b and c are constants.

The steam line pressure is subtracted form this calculated pressure. This resulting differential

pressure is the controlled variable to a PID controller. The following diagram shows the control

strategy.

SteamFlow

BFW Flow


89

Figure 6 De-super Heater Control Diagram

The temperature sensor is usually a thermocouple or an RTD. The element should have a rapid

thermal response. If the element is installed without a thermo well, make sure that the sheath is

capable of withstanding the forces of the high velocity steam and occasional condensate. The

element should be mounted per the de-super heater manufacture’s instructions, usually 30 feet

downstream of the injection point for a 12 inch pipe. The control system has very fast dynamics

and should be tuned similar to a flow controller with low gain and moderate reset term. This

method produces better control than temperature alone because the change in pressure actually

acts as a feed forward compensator. The control is now measured by differential pressure rather

than temperature alone.

References: Lloyd, Sheldon G., Anderson, Gerald D., Industrial Process Control, Marshalltown, Iowa: Fisher

Controls Company, 1971

McMillan, Gregory K., Tuning and Control Loop Performance, Research Triangle Park, NC:

Instrument Society of America, 1994

Richmond, D. W. "Selecting Thermowells for Accuracy and Endurance", InTech, February, 1980

Chemical Engineering Deskbook Issue, October 15, 1979

Mackay, B. "Avoid Stream Trap Problems", Chemical Engineering Progress, January, 1992

Shinskey, Francis G., Energy Conservation Through Control, New York: Academic Press, 1978.

TEPT

f(T)∆ +

-

DPC

BFW

Super heated Steam


90

Chapter 10

pH Measurement and Control

The most authoritative source on this subject is Greg K. McMillan. His work is an excellent guide

for this subject. The following perspectives are based on this author's experience.

pH electrodes - Most of their problems can be solved by following the instructions published by

the manufactures. Operating the electrodes outside the velocity and temperature limits usually

result in reduced life. Consider using one of the many inexpensive electrodes, usually a NPT

screwed process plastic connection before relying on some other design. pH measurements in

low salt concentrations are not a serious problem with coating or drift. If the solution has a high

concentration of dissolved salts, it is important to condition the electrode prior to use. This

conditioning involves placing the electrode in a standard sample of the solution at the operating

temperature for several days. pH electrode glass is permeable and it takes time for the ions in the

solution to permeate the glass.

For high reliability concerns, consider using three electrodes and transmitters with a mid select

algorithm. The user should provide the proper valves and drains to facilitate electrode removal

while the process is running.

Agitators

The following equations estimate process deadtime and time constant for agitated vertical

vessels. Correct agitation is very important for good pH control.

Calculate Volume of Vessel, neglect bottom dish

Di Tank diameter in feet

h Tank height in feet

V_ft3 Tank volume in cubic feet

V Tank volume in gallons

Agitator

Da Agitator diameter in feet

N Agitator speed in RPM

Calculate the pumping rate in gpm

Fa = 7.48*(0.4*N*(Da^3))/((Da/Di)^0.55) = 125.26

Inlet Flow; Fi inlet flow in gpm

Calculate the dead time in minutes

td = V/(2*(Fa + Fi))

Calculate the time constant in minutes

tc = (V/Fi) - td

The dead time divided by the time constant should be less than 0.05 for good control.


91

Tank Baffles

Most literature states that the vessel for pH control should be baffled. I would like to take

exception to this comment in particular for slurry applications. An agitator that is off set from the

center of the tank without baffles can provide good agitation. Three impellers are frequently used

instead of the usual two. Because the impellers are offset, the impeller diameter is shorter than if

the agitator is installed in the center of the tank. This is the reason why more impellers are

needed to obtain the same degree of agitation. The agitation profile circulates the slurry the same

way the baffled tank does, except the center of the vortex is not at the center of the tank. This

design is quite common in the pharmaceutical industry. The reason for not using baffles is to

avoid using crevices that cannot be cleaned properly and there are no surfaces for the slurry to

dam up the solids. Agitator manufactures have pilot facilities as well a CFD, computational fluid

dynamic, design capabilities and should provide the proper design for the application. What is

critical in agitator design is to provide the correct level of agitation and establish a profile that

allows for back mixing. Make sure the manufacture is fully knowledgeable about the pH control

service.

pH Control Valves

Control valves should have linear trim. It is very important with small sized reagent control valves

to mount them as close to the process as possible. A large volume between the control valve and

the process act as a tank and lag the reagent delivery. With very small flows, even a close-

coupled pipe nipple can contribute to this problem. Think of the internal volume in the tank

compared to the reagent flow. This volume to flow ratio is the time constant of the reagent

delivery system. Control valve sizing is not very accurate at very low flows therefore viscosity

errors can become significant. Consider purchasing extra trim sets that can be changed out

during startup. Control valve positioners are an absolute must for pH control.

pH Control Basics - Rule one; know your process. This is very important in pH because of the

possible non-linearity of the process. There are several companies that market special fuzzy logic

and other types of controllers for these applications. Not all pH applications require this type of

control. If the application requires operation on a flat portion of the titration curve, conventional

PID controller should work. This is because the closed loop small signal gain is linear in that

region. The controller's reset action will place the output at the correct position. Another way to

improve control is to use multiple stages. Neutralization waste treatment plant frequently uses this

technique. Each stage can then use a narrow span pH control. With some applications the pH

measurement is simply a ratio of two reagents. Control with this system is not very complicated.

pH control is considered a self-regulating process, that is if the controller were placed in manual,

the pH would come to a steady value. However, if the span of the controller is small, the small

signal gain will give the appearance of a non-self regulating controller. This can allow for high


92

gains and low reset controller settings to be used for pH. With a sufficiently large residence time,

no controller rate is necessary.

What should I consider if I want to use an inline pH control system?

pH control is an electrolytic process, so the process kinetics are very fast, not even measurable.

Because of this, an inline system becomes an attractive alternate because of reduced project and

maintenance costs. If both streams have all the ions dissolved, the risk is minimal. If one of the

streams contains a solid, such as lime, there is a risk that not all the solids will be reacted quickly.

In that case, a tank should be used. McMillan and Shinskey both have recommendations about

tank design and agitation, which should be followed. If solids are involved, a minimum of 10

minutes residence time should be used. Lab tests should be conducted to insure that all the

solids are dissolved. The dynamics of an in line system are very fast, similar to a flow loop and

should be tuned accordingly.

There are several other concerns that should be considered when designing an in line pH control

system. One is the design of the mixer itself. There are several companies that make inline

mixers at a very reasonable cost. They can be consulted and can prove to be a valuable source

of information for the design. Another concern is the heat removal. Acid base reactions are

exothermic and heat removal may be a concern. Make sure that the resulting process

temperature is not high enough to cause flashing at the system pressure. From a safety

standpoint, designs need to prevent back flow of the reacted product into any of the reagent

supplies. This is a major concern of inline systems. Many plants refuse to consider this type of

design for that concern. There is a distinct advantage of an agitated tank because if the reagent is

allowed to free fall into the tank, back flow is harder since a siphon break is inherent in the

design.

If the pH control system involves a solid, such as lime, it is very important to consider the degree

of agitation over and above the concerns of the above equation. The type of agitation becomes

critical to insure that the solid is back mixed into the liquid. If the solid tends to float at the surface

of the liquid, the baffles need to be lowered to obtain a vortex action at the top of the vessel

thereby pulling the solids down in the vessel. If the agitation is thought to be a concern, consider

discussing the problem with an agitator manufacture or supplier. If the agitation only involves

liquids and no gasses are released, computational fluid dynamic study of the vessel agitation

should not be necessary.

The Anatomy of a pH control Project; Example 1

The following project can show some of the potential problems encountered in pH control.

Problems can occur in if the feed flow is erratic and no feed forward signal is used. This project

did its homework; developed titration curves for the reagents and sized the control valves


93

properly. An in line mixer was used which performed well. Disposable pH electrodes were used

with success.

What was not evident was the pulsating nature of the flow, which was a centrate flow from a

batch centrifuge. The client failed to tell the designers that production liked to run with the

centrate feed tank almost empty. There was no way for the inline system to respond fast enough.

McMillan's pH book shows a way to recycle the treated stream back to a storage tank. The feed

stream and reagents are introduced to the pump suction and the control is after an inline mixer.

The tank acts as a damper to the disturbances. The modified design and the tank became a large

section of 316ss pipe, which was just a wide space in the line. McMillan shows a tank with a level

control however in our case the pipe was hydrostated and operated at the system pressure.

Agitation is not necessary because the in line mixer provides agitation of the feed stream and

reagent. It is necessary to periodically drain out solids that form as well as purge the trapped

gasses.

This design is quite simple and could be used in place of some of these more complex control

algorithms on the market today. A piece of pipe is easy to maintain.

On this project, the team attempted to calculate the pH for the treated stream. When McMillan’s

pH charge balance equation could reproduce the general shape of the pH curve, but was not able

to calculate the absolute reagent required. The plant reported a different amount and the lab

study showed the plant was correct. The stream contained enough organic species to render

most conventional pH charge balance calculations inaccurate because the water pK is shifted.

Calculation of pH in organic solutions is complex and beyond the scope of this book.


94

Figure 1 PFD of pH control with a tank used to smooth process disturbances

The Anatomy of a pH Control Project; Example 2

The following project involved adding two different basic reagents. The stated objective was to

have the pH controlled by adding one reagent and an analyzer would measure the concentration

of the second reagent. The process consisted of an un-agitated tank, a circulation pump a cooler

to cool the treated stream and the down stream circulated process. The design called for the

reagents to enter at the bottom of the tank through two dip pipes. The pH and second reagent

would be measured downstream of a pump. The treated stream would then be circulated through

another process where acid stream came in contact with the two bases and the equivalent molar

amount of salts are formed.

Waste In

��

InlineMixer

Reagent

pHTransmitter,Controller

TreatedWaste

Out


95

NeutralizationTank

Exchanger

Base 2

Base 1

pH

%Base 2

CoolingTower Water

Level Control Purge

Base 2

pH

Downstream RecycledProcess

Firstreagentlocation

ProposedLocation

Figure 2 Two Reagent pH Control System

In order to properly size reagent control valves, an approximate material balance should be

calculated. In this example, the design team made use of a chemical engineering simulator.

However, this simulation did not calculate pH. The pH of the circulation loop and neutralization

tank was calculated by using a FORTRAN subroutine developed by Greg K. McMillan, phion3.

This routine calculates the pH of any number of acids and bases with up to three dissociation

constants per acid or base. A pH set point of 10 is required in the stream supplying the

downstream equipment. Once the material balance was developed, the phion3 subroutine was

used to calculate the amount of basic reagents required. From this calculation it was learned that

the required base flows were much less than originally calculated. The titration curve also shows

that there should the linearity in the range of interest does not require implementing any non-

linear compensating elements in the control algorithm.


96

Figure 3 Base 1 to Acid Titration Curve

Armed with this new information, there are several considerations that need to be addressed with

this system. First is the entry point of the two reagents. By entering an un-agitated tank, the

change in pH and base 2 concentrations would result in poor control. The tank had no agitation

and the dip pipes would provide large volumes which would result in long dead times. Since the

objective is to control the pH of the liquid entering the down stream equipment, a delivery system

was proposed to add the flows in the pump suction. This results in mixing the reagents with the

liquid as well as improving the system response. Another problem is the concerns that by adding

two basic streams to the same stream and control the pH by manipulating one base flow the

second base flow change would act as a disturbance to the pH signal. The degree of interaction

was calculated by use of the Bristol relative gain array. This calculation showed that the degree of

interaction was not significant.

Using the steady state material balance generated by the simulator, a PID control simulation was

written in MATLAB and later converted to EXCEL using macro code for more wide spread use. It

uses the same reaction chemistry as described in simulator material balance.

Proportional plus reset controllers were employed to control the pH and the second basic

concentration. The controllers should be tuned with low gains and high reset values, similar to

flow loops. This is because the controls are inline applications. The following control simulation

shows the pH behavior as well as the pH in the tank.


97

Figure 4 pH Control Response, Set Point at 10.0

The following sketch shows the piping necessary to deliver small flows of reagent to the system.

If large volumes of reagents are in supply piping between the control valve and the process, the

resulting installed dead times result in unstable control. This is because of the liquid mixing in the

reagent supply piping between the valve and the process line. There can be mixing problems by

introducing a small flow in the pump suction however these were not experienced on this

installation. Because of the small volume lines between the control valve and the process line,

tubing was used. A Plexiglas cover should be placed over the tubing portion for personal

protection. Any check valves should be installed between base and the control valve.


98

Figure 5 Reagent Piping

References: McMillan, Gregory K., pH Measurement and Control, Second Edition, Research Triangle Park, NC, ISA, 1994.


99

Chapter 11 Dryer Control

Summary:

Drying of bulk solids has been a difficult problem in the process industry. Attempts to measure

solid moisture directly have had mixed success and are usually expensive. As a result, material is

over dried at an extra cost for energy. In addition, over dried material is sold at a lower moisture

than specified resulting in a loss of revenue. A need exists for a reliable inexpensive method of

moisture measurement and control. Over dried product sometimes places as extra load on the

dust collection system, resulting in higher maintenance costs and production down time. The dryers proposed in this study are forced air continuous adiabatic type dryers, the type used

frequently by the chemical process industries. Adiabatic dryers are the type where the solids are

dried by direct contact with gases, usually forced air. With these dryers, moisture is on the

surface of the solid. This drying process in this study is not the process used in molecular sieve

gas drying. Frequently adiabatic dryers supply air is heated by natural gas combustion.

This study is for the, simulation and piloting of a proposed method of moisture control. The

approach is to cross link two techniques, inferential moisture measurement and dynamic matrix

control. Both these techniques are based on published material.

Inferential Moisture Measurement

The adiabatic drying process has two zones to describe the rate of water removal, falling rate and

a constant rate. When the product becomes sufficiently dry that there are dry areas on the

product surface. Further drying results in a falling rate of moisture removal. This is the zone

where most industrial dryers discharge product operate.

Inferential measurement of product moisture is accomplished by the measurement of

temperatures of the gas entering and exiting the dryer and performing a calculation using these

temperatures. This technique uses mass and energy balances of the dryer to calculate the

product moisture and is valid during the falling rate zone only.

The relationship between outlet moisture and the temperatures is:

Xp = k*ln( (Ti - Tw) / (To - Tw) )

where

Xp = Outlet Moisture

Ti = Inlet Dry Bulb Temperature

Tw = Wet Bulb Temperature

To = Outlet Dry Bulb Temperature

k = Dryer Constant.


100

For water and air systems, the wet bulb temperature is the same at the inlet as it is in the outlet.

An interesting relationship exists for natural gas combustion; the wet bulb temperature is related

by an empirical relationship that is:

Tw = 164.0 - (16900.0/Ti)

Where the temperature is in degrees Fahrenheit. A simulation of the combustion of methane in a

chemical process simulator over a wide range of inlet air ambient conditions shows this equation

accurate. The validity of both equations was checked by completing a mass energy balance of

both air and product as well as a regression of the wet bulb temperature against the dew point

temperature of the combustion air. In other words, if the above equation showing the relationship

between wet bulb and inlet temperatures is correct then there should be a strong correlation

between the wet bulb temperature and dew point at a given inlet temperature.

With natural gas combustion, only two measured temperatures, the inlet and the outlet, are

required to implement inferential moisture control. If an indirect heat source such as electrical

heater or steam coil is used then a measurement of the inlet wet bulb temperature is required.

The usual method of outlet moisture control is to control the outlet temperature by adjusting the

combustion gas flow valve. If a moisture analyzer is used, a moisture controller is used and the

output of that controller sets an inlet temperature controller set point. Attempts by control

engineers to use conventional PID (proportional integral and derivative) controls with the

inferential method have resulted in poor or quasi stable control, because the technique exhibits

non linear disturbances.

The problem in controlling this relationship is that the dynamics of the equation result in reverse

action, i.e. if the moisture set point is lowered, the instantaneous action would be to increase the

inlet temperature, which causes the calculated moisture to increase before the outlet temperature

is increased to such an extent as to lower the moisture to its new stable set point. This is because

of the dead time and time constant between the inlet and outlet temperatures. Using conventional

PID control on this relationship results in unstable control.

Dynamic Matrix Control

Dynamic matrix control (DMC) is a technique used to calculate the least squared error of a

process variable disturbance where the disturbance is described an array of numerical

coefficients. This is accomplished by matrix manipulation. This technique is excellent for non

linear disturbances and a logical choice for inferential moisture control. DMC first appeared in the

control literature in the early 1980's and has found some support in the process industries. An

example shown in one of the DMC papers is of furnace temperature response due to soot

blowing. This shows a reverse acting response similar to the inferential moisture calculation.

To implement this control, data is taken on the response values due to a step input disturbance.

This data is normalized and described in sample intervals over the entire response to a steady

state point, usually 30 to 36 samples for the total response. This array of future values is used to


101

define a matrix of future values and used to develop a least squared error of the response, a

control matrix. This matrix is used to calculate a control response required for a change in input

error or the process variable minus the set point. Since an array of step responses is known, an

array of future responses is also known. Because the matrix contains the known response

pattern, the control system can correct for the reverse control response inherent with inferential

moisture measurement.

Once the response matrix is found, the actual control equation is rather simple since it only uses

the first row of the matrix, an array. The calculation of the matrix can be done off-line, even in an

Excel spread sheet.

One important technique in implementing DMC is to update all future values of the projection of

future values based on the error from the previous iteration. This has the effect of error correction.

To simulate feed forward compensation, changes in dryer wet feed rate and air flow will change

the outlet moisture. If these variables can be measured, it is possible to adjust the inlet

temperature to compensate for the changes. This technique is called "feed forward". In either

case of the air or the feed can be changed and the change in outlet temperature can be noted

during the change. This array is then used to determine future changes in the outlet moisture and

calculate the changes in inlet temperature to compensate for the disturbances.

The following summarizes how the DMC is calculated. Shown here is as a listing of the data from

a test used to calculate the DMC program. In the step test, the temperature was lowered. The

response is the moisture decrease followed by an increase to the final value. The delta column is

the normalized step response of the outlet moisture. This is also the array of forward model

coefficients used to predict the future values of product moisture based on changes in inlet

temperature. This array of normalized values is placed in the first of a 10 column matrix. Other

columns are shifted as shown; this matrix is called Abar.


102

Abar = 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

-0.569 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

-0.706 -0.569 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

-0.743 -0.706 -0.569 0.000 0.000 0.000 0.000 0.000 0.000 0.000

-0.748 -0.743 -0.706 -0.569 0.000 0.000 0.000 0.000 0.000 0.000

-0.752 -0.748 -0.743 -0.706 -0.569 0.000 0.000 0.000 0.000 0.000

-0.697 -0.752 -0.748 -0.743 -0.706 -0.569 0.000 0.000 0.000 0.000

-0.450 -0.697 -0.752 -0.748 -0.743 -0.706 -0.569 0.000 0.000 0.000

-0.239 -0.450 -0.697 -0.752 -0.748 -0.743 -0.706 -0.569 0.000 0.000

-0.055 -0.239 -0.450 -0.697 -0.752 -0.748 -0.743 -0.706 -0.569 0.000

0.101 -0.055 -0.239 -0.450 -0.697 -0.752 -0.748 -0.743 -0.706 -0.569

0.229 0.101 -0.055 -0.239 -0.450 -0.697 -0.752 -0.748 -0.743 -0.706

0.349 0.229 0.101 -0.055 -0.239 -0.450 -0.697 -0.752 -0.748 -0.743

0.450 0.349 0.229 0.101 -0.055 -0.239 -0.450 -0.697 -0.752 -0.748

0.532 0.450 0.349 0.229 0.101 -0.055 -0.239 -0.450 -0.697 -0.752

0.606 0.532 0.450 0.349 0.229 0.101 -0.055 -0.239 -0.450 -0.697

0.661 0.606 0.532 0.450 0.349 0.229 0.101 -0.055 -0.239 -0.450

0.716 0.661 0.606 0.532 0.450 0.349 0.229 0.101 -0.055 -0.239

0.761 0.716 0.661 0.606 0.532 0.450 0.349 0.229 0.101 -0.055

0.798 0.761 0.716 0.661 0.606 0.532 0.450 0.349 0.229 0.101

0.826 0.798 0.761 0.716 0.661 0.606 0.532 0.450 0.349 0.229

0.853 0.826 0.798 0.761 0.716 0.661 0.606 0.532 0.450 0.349

0.881 0.853 0.826 0.798 0.761 0.716 0.661 0.606 0.532 0.450

0.899 0.881 0.853 0.826 0.798 0.761 0.716 0.661 0.606 0.532

0.917 0.899 0.881 0.853 0.826 0.798 0.761 0.716 0.661 0.606 0.927 0.917 0.899 0.881 0.853 0.826 0.798 0.761 0.716 0.661

0.945 0.927 0.917 0.899 0.881 0.853 0.826 0.798 0.761 0.716

0.954 0.945 0.927 0.917 0.899 0.881 0.853 0.826 0.798 0.761

0.963 0.954 0.945 0.927 0.917 0.899 0.881 0.853 0.826 0.798

0.963 0.963 0.954 0.945 0.927 0.917 0.899 0.881 0.853 0.826

0.972 0.963 0.963 0.954 0.945 0.927 0.917 0.899 0.881 0.853

0.982 0.972 0.963 0.963 0.954 0.945 0.927 0.917 0.899 0.881

0.982 0.982 0.972 0.963 0.963 0.954 0.945 0.927 0.917 0.899

0.991 0.982 0.982 0.972 0.963 0.963 0.954 0.945 0.927 0.917

0.991 0.991 0.982 0.982 0.972 0.963 0.963 0.954 0.945 0.927

0.991 0.991 0.991 0.982 0.982 0.972 0.963 0.963 0.954 0.945

Note the inverse response.

The control matrix, Cbar is calculated as:

Cbar = (( Abar' * Abar ) + const * I )^-1 ) * Abar' where

I = 10 by 10 identity matrix

Abar' = Abar transposed

The change in the output is reduced by constant is used for tuning called move suppression. This

constant has the effect of limiting the output otherwise the program will attempt to make the


103

required change in one sample iteration, resulting in wild control. Cutler gives no mathematical

derivation for this; perhaps it is to increase the eigenvalues of the inter matrix to increase stability.

This is due to the non linearity of the inferential moisture calculation. Only the first row of this

matrix is used as the control matrix. The control program is summarized as follows:

Initialize steps

Measure the process variable, PV.

Set the future values of Ybar equal to PV.

Repeating Code

Measure the process variable, PV.

Correct the previous values for modeling error by adding PV – Ybar(1) to all elements in

the Ybar array.

Shift all projections Ybar(1) = Ybar(2), Ybar(2) = Ybar(3) … Ybar(36) = 2*Ybar(35) –

Ybar(28).

Calculate the output change Delu.

Delu = Σ Cbar(I) * (Ybar(I) - SP) for I = 1 to 36.

Reduce the output move by the gain term Delu = Delu * gain.

Calculate the future values of Ybar.

Ybar(I) = Ybar(I) * Delu for I = 1 to 36.

A good way to obtain operator acceptance of the system is to display the future values of the outlet moisture. This plot is an example of 36 time periods in the future of the estimated outlet moisture.

X axis, Future Time; Yaxis, Predicted Moisture

Dryer Control Algorithm Improvements

Dynamic Matrix Control (DMC), falls into a general classification of control called model based

control. A lot of current attention has been given to these control algorithms. A joint alliance


104

dedicated to this study has been formed by Universities of Texas and Wisconsin. One paper from

a recent conference given by this alliance addressed work done by Richalet where control of

nonlinear systems was implemented by adjusting the sample time to linearize the response.

Using that thought, one way to remove the inverse response of the inferential moisture response

calculation would be to delay the inlet temperature before the calculation is made. If a moisture

analyzer was installed on the outlet of a dryer operating at steady state and a step change was

made to the inlet temperature, the moisture signal would remain constant for a time, ( the system

dead time due to transportation delays ), followed by a lag, eventually approaching a new steady

state value. If the inlet temperature signal was transformed through a dead time and time

constant control function blocks in the control algorithm, then applied to the inferential calculation,

the resultant response would be closer to the actual moisture. This is because the present time

observation of outlet temperature is the result of a past inlet temperature. This approach for the

control similar to that proposed by Shinskey except he did not use a deadtime operation on the

inlet temperature.

A corollary to this approach is to lengthen the sample time sufficiently long enough to ignore the

inverse response. This results in a long sample deadtime. However, control is possible in this

manor using a PID controller. This was simulated and the results proved erratic.

Signal Characterization:

After some experimentation, the best transient response occurs if the deadtime applied to the

inlet temperature is slightly longer than the system delay and if the lag time is shorter than the

outlet temperature lag. The intent is to allow the initial movement of inferential calculation not to

exhibit the inverse response. Since the calculation is related to the inverse outlet temperature, an

increase in outlet temperature infers a decrease in moisture and visa versa. Since it is desirable

to replicate this behavior in the modified calculation, the first observed temperature change

should be the outlet. In like manor, to avoid undershoots or overshoots, the last observed

temperature change should also be the outlet. It is reasonable to expect the inlet temperature to

have a faster response than the outlet. The thermal element is in direct contact with the inlet air,

after the heat source, with a high velocity. A ceramic filled 304 stainless steel tubing

thermocouple element should only have a few seconds time constant. An ISA article by

Richmond estimates the lag time of a thermowell. The outlet temperature would show a longer

time constant due to the back mixing occurring in the dryer. By adjusting the dead time and time

constant of the inlet temperature term in the control algorithm coupled with an outlet temperature

response of a deadtime, and second order under damped response results in the calculated

inferential moisture. There are a number of control algorithms that can be used to control this

response.

Gallier Otto Model Predictive Control Algorithm


105

Second order systems with deadtime can be controller by an algorithm which was originally

proposed for direct digital control (DDC), a control technique used extensively before distributed

control came into use. This model predictive control algorithm was published by Gallier - Otto in

1967. The algorithm calculates the output based on past values of error and output values.

Specifically:

Mi = b0 (ei + b1 ei-1 + b2 ei-2 + a1 mi-1 + a2 mi-2)

Where M is the output at time i

e is the error at time i

ei-1 is the error at time i-1

ei-2 is the error at time i-2

mi-1 is the output at time i-1

mi-2 is the output at time i-2

b0 , b1 , b2 , a1 , a2 are constants

Gallier - Otto's algorithm is derived from state space variables. They assume, through the use of

eigenvalues that the response to a step input to be second order plus deadtime and calculated

the time constants on that basis. There are several errors in the original published article. Bibbero

later corrected these errors, however it is necessary to study both articles because Bibbero

omitted the b0 term in his discussion. Bibbero shows that the constants are calculated from the

two time constants τ1 and τ2 and the control sample time T for each iteration. From Bibbero the constants are calculated as follows:

First find α and β as intermediate terms α = e - T/ τ1 and β = e - T/τ2

Assume the steady state gain of the system is K, then:

a1= K(1 + (α τ1 - β τ2)/( τ2 - τ1 ))

a2 = K(αβ + (β τ1 - α τ2)/( τ2 - τ1 ))

b1 = - ( α + β )

b2 = αβ

b0 = 1/( a1 + a2)

Note: this term is not in shown in the Bibbero text but is shown in the Gallier - Otto paper.

In the field of industrial process control, the process response is not referred as a first order time

constant, but rather to a reaction rate found from the unit step response curve. Most literature on

controller tuning refers to developing step response time, tangent to the response curve, not

locating two time constants. In order to find these times, Gallier - Otto refer to a paper on least

square optimization to obtain the two time constants.

Gallier - Otto reported that with a true second order process with deadtime, the error would be

zero at the end of two sample periods plus the deadtime. This results in violent behavior of the


106

controller output, not very practical for plant use. A filter should be used in the output to avoid

cycling. One of the important benefits of this control is its insensitivity to process deadtime. Note

that the control equation does not use process deadtime in the equation; but sample time is used

by the algorithm. This has obvious benefits and improves the robustness of the controller.

Practical Considerations

Representative temperature measurements can be a problem with dryers. The inlet temperature

should only measure the air temperature and not receive any radiated heat from a flame. The

thermowells should be placed in the dryer at positions that will not build up with either wet or dry

product. Frequently it is necessary to locate these wells away from the solids. The additional

installed deadtime should not be a problem because of the high air velocities usually present in

adiabatic dryers.

References

Bibbero, Robert J., Microprocessors in Instruments and Control, New York: John Wiley & Sons,

1977.

Cook, DuMont, Process Drying Practice, New-York: McGraw-Hill, 1991.

Cutler, C. R., Ramaker, B. L. "Dynamic Matrix Control - A Computer Algorithm", AICh_E 86th

National Meeting, April, 1979.

________, "Dynamic Matrix Control - A Computer Algorithm", JACC Proceedings, Paper WP5-B

San Francisco, CA, 1980.

Cutler, C. R., "Dynamic Matrix Control for Unbalanced Systems", ISA National Meeting, 1980.

Gallier, P.W. and Otto, R. E., " A Self -Tuning Method for Direct Digital Control." 22ed Annual ISA

Conference and Exhibit, September 11-14, 1967, Chicago, Il, Preprint Number 10-4-ACOS-67.

Liptak, Bela G., Instrument Engineers Handbook, Philadelphia, PA: Chilton Book Company, 1970.

McCabe, Warren L., Unit Operations of Chemical Engineering, New York: McGraw-Hill, 1985.

Qin, S. Joe and Badgwell, Thomas A., "An Overview of Industrial Model Predictive Control

Technology." Chemical Process Control V, Tahoe City, CA, January 7 - 12, 1996 ( also Texas-

Wisconsin Modeling and Control Consortium, February 22 -23, 1996 )

Richalet, J. et al, "Model Predictive Heuristic Control: Applications to Industrial Processes."

Automatica, Vol 14, pp. 411 to 428.

Richmond, D. W. "Selceting Thermowells for Accuracy and Endurance." InTech,

February, 1980

Shinskey, Francis G., Energy Conservation Through Control, New York: Academic Press, 1978.

Williams-Gardner, A., Industrial Drying: Cleveland, Ohio: Chemical Rubber Co.


107

Chapter 12 Non-Adiabatic Dryer Control

When a dryer does not use heated air or other gasses to provide the energy required the drying

process is considered a non-adiabatic. The objective of this control scheme is to control the

product moisture exiting the dryer. In this scheme, steam is condensed in a shell portion of

vessel. An application for this type of dryer is drying paper passed over a jacketed mandrel. The

steam condenses in the vessel that allows the product to give up moisture linearly through the

length of the steam-jacketed section. Frequently moisture analyzers are difficult to install on these

applications. As with other dryers found in the process industries there is a need for some

improved product control.

An inferential calculation of the exit product moisture can be made based on the dryer’s steam

and temperature measurements. This calculation is explained as follows. A fundamental basis for

this calculation is that the heat transfer coefficient, U, is a function of the average moisture of the

product in contact with the surface. Assume the product’s solid specific heat value is constant

while that for water is 1.0. This resulting mixture heat transfer should be proportional to the weight

percentages of each in the product.

2/)( *wwKUA ff += (1)

Where U is the heat transfer coefficient, A is the jacket area, wf is the inlet feed moisture and w*

is the moisture percentages exiting the dryer and Kf is a constant. This equation is rearranged to

solve for feed moisture.

*2 wKUAw

ff −= (2)

Neglecting sensible heat and the dryer mechanical heat added, the heat balance equations for

the condensing steam and evaporated water are written as:

)()( *ossfv HHFwwFHQ −=−= (3)

Where Q is the heat flow, F is the dryer mass flow, Hv is the enthalpy of the water evaporated, Fs

is the steam flow rate, Hs and Ho are the enthalpy of the steam and condensate.


108

The amount of steam superheat is assumed to be low and ignored in these calculations. The heat

transferred through the jacket is also a function of the heat transfer coefficient and the area

written as:

)()( ossps HHFTTUAQ −=−= (4)

Where Ts is the steam condensing temperature and Tp is the product temperature. The product is

assumed to be drying in the constant rate zone so the product temperature should be the same

across the dryer through this heated section and equal to the wet bulb temperature.

If a d/p cell measures the steam flow rate, the steam flow the equation for steam flow becomes:

hKF ss = (5)

Where Ks is the orifice meter factor and h the differential pressure.

Arranging equation 4 as a function of UA and substitute Fs term with equation 5 results in:

)/()( psoss TTHHhKUA −−= (6)

Arranging equation 3 as a function of the moisture differences becomes:

)/())((*Vossf FHHHFww −=− (7)

Substitute wf in equation 7 for the right side of equation 2 and UA for the right hand side of

equation 6 then arrange to solve for w*, the exit moisture:

−

−−=

vpsfoss FHTTK

HHhKw2

1)(

1)(* (8)

The combined terms )( oss HHhK − is the steam heat entering the jacket, which can be

calculated by the orifice plate differential, combined with the steam supply pressure, P, in the

form:

)( baPhKQ s += (9)


109

Where a and b are constants.

For the non-adiabatic control system, refer to the figure below. A PID controller cascading to the

dryer jacket pressure controller controls the calculated moisture. This pressure controller may

have to be a self-contained regulator with a pneumatic set point, as a Cashco Model 1000HP

differential pressure-reducing regulator because the small jacket volume may make control by a

normal PID controller sluggish. The value for Ts can be regressed through the jacket pressure

signal. Product temperature should be constant through the length of the jacketed section.

The dryer inlet mass flow, F, can be reasonably measured and controlled by using a loss in

weight feeder. The evaporated water enthalpy, Hv, is calculated based on the product

temperature. The steam flow signal must be lagged before the calculation can be made to insure

the control system stability. The lag time should be slightly longer the thermal lag time across the

jacket. The steam trap size and placement is very critical in this design. A bucket trap and

vacuum break should be used for this application. The condensate should not be permitted to

back up and flood the steam jacket cavity.

The advantage of this control strategy is that no moisture analyzer is required. One possible

disadvantage is that the assumed heat transfer relationship may not be valid because the dryer’s

wall heat transfer does not behave as proposed. The referenced examples for this control

technique are a fibrous material and soaps.


110

Figure1 Non-Adiabatic Dryer Inferential Moisture Control

References:

Shinskey, Francis G., Energy Conservation Through Control, New York, New York: Academic Press, 1978.

Loss in Weight Feeder

Jacket

Motor

Non-Adiabatic Dryer

BucketSteamTrap

Steam Supply

FT

PV

WC

w*ctrl

PT

RSP

Vacuum Break

T

to moisture calculation

Wet Product Feed

fInferentialMositure

Calculation

f(x)

Lag

PCPT Dry Product

Out

WaterVaporOut


111

Chapter 13 Multivariable Control

A control problem arises when manipulating one output causes changes in two or more process

variables. This is called a multivariable control problem. There are several references in the

control literature that describes the problem and how to correct it. Lloyd and Shinskey are

excellent sources. I will not detail these sources here, but will summarize them.

Identification

Recognizing a multivariable control problem is the first step. Multivariable loops are not intuitively

obvious. A classical method of identification is the Bristol relative gain array. This shows the

degree of interaction and input output paring. The objective is to pair the variables such that the

resulting matrix will not create a negative array and result in the best controller to valve operation.

Both previously mentioned references detail this identification method.

Classical Decoupling

Both these references describe a decoupling network as transfer function blocks connected in a

forward and cross coupling manor, see Figure 2. An interesting observation by Lloyd is that static

transfer function blocks are usually sufficient. Should one implement this method, one is

confronted with a problem. How can one properly put such a system in manual and assure

bumpless auto to manual transfers?

Inverted Decoupling

A technique described by Wade shows an improved method by using the feed forward portion of

a conventional PID controller to act as the summation element. The output of the each controller

is connected directly to a final element. The advantage of this technique is that it allows manual

operation of either controller and is better understood by the operators.

Example

The dilution of 20% NaOH and water to 15% NaOH is a multivariable control problem, see Figure

1. The total flow controller's output is connected to the 20% NaOH control valve while the

composition controller's output is connected to the water valve. As the flow of water is increased,

the composition of the diluted caustic is decreased and as the flow of the 20% NaOH is increased

so is the diluted caustic concentration. This calculation demonstrates how to decouple this

interaction. The concentration is calculated as:

X1 = mass flow rate of water to reactor

X2 = mass flow rate of concentrated (20%) NaOH to reactor

h = normalized concentration of "20%" NaOH in Molar fraction ( 0.2 for 20% )


112

The composition controller's process variable, A, is the NaOH concentration in percent of the

mixed flow.

NaOH Concentration of Aqueous Mix :

A = [ ( h * X2 )/( X1 + X2 ) ] * 100%

The total flow is the sum of the 20% NaOH and the water mass flows, shown as Q or

Q = X1 + X2.

The system block diagram of figure 1 is shown in figure 2 illustrates the signal flow through a two

input two output multivariable process. Controller inputs or process variables as shown as A and

Q. Terms X1 and X2 are the controller outputs. Blocks G1 through G4 represent first order

principal process transfer function blocks, while the decoupling network are the D1 through D4

transfer blocks. Blocks G3 and G4 represent the interactions between the two control loops.

FT AT

FC1

AC1

Water

20% NaOH

Mixed Stream

Figure 1

X1

X2

AQ

Multivariable Control ProblemTwo Component Mixer

Flow and Composition Control

Mixer


113

Multivariable Decoupled Process

Figure 2

Decoupling can be accomplished by neglecting any dynamic terms and assuming only steady

state interaction. In this case the process transfer blocks G1 through G4 can be assumed as

steady state gains K1 through K4. Calculation of these can be made assuming a coupled process

(ignore the decoupling for this part of the analysis).

Stream Meter Calibration Setting

X1 (Water) 0 to 500 lbs./hr 250 lbs./hr

X2 (20% NaOH) 0 to 1200 lbs./hr 750 lbs./hr

This mixed stream results in a total flow of 1000 lbs./hr flow and a composition of 15% NaOH.

Notice that the decoupling network is implemented on the controller outputs. Assume that a 1%

change in controller output represents an output change of:

deltaflowX1 = 5 deltaflowX2 = 12

The percentage change and steady state process values for this analysis are:

deltapcnt = -1 X1ss = 250 X2ss = 750

Full scale readings of the controllers are:

Qmax = 2000 Amax = 20

Relative Gain Matrix

The Bristol relative gain array is calculated to show the degree of interaction. A property of this

array is that the sum of each row and column equals 1.0. An interesting property of this matrix is


114

that it is not necessary to scale the values, just as long as the inout and output units remain the

same for all element calculations.

Determine the change in composition while changing just the X1 value:

K1 = (pcnt scale change in composition)/( change in X1 valve)

A1 = (0.2 * X2ss/(X1ss + X2ss))*100

X1 = X1ss - deltaflowX1

X2 = X2ss

A2 = (X2 * 0.2/(X1 + X2))*100

dA = ((A2 - A1)/Amax)*100

K1 = dA/(deltapcnt) K1 = -0.3769

Next determine the change in composition with change in X2 value:

K4 = (pcnt change in composition)/( change in X2 valve)

X1 = X1ss


A2 = (X2 * 0.2/(X1 + X2))*100

dA = ((A2 - A1)/Amax)*100

K4 = dA/(deltapcnt) K4 = 0.3036

Determine the change in composition while changing X1 value while keeping the total flow

constant:

k1 = (pcnt scale change in composition)/( change in X1 valve) with the total Q constant

A1 = ( 0.2 * X2ss/(X1ss + X2ss))*100


X2 = X2ss + deltaflowX1

A2 = (X2 * 0.2/(X1 + X2))*100

dA = ((A2 - A1)/Amax)*100

k1 = dA/(deltapcnt)

Calculate the relative gain interaction:

I11 = K1/k1 l11 = 0.7538

l12 = 1 - l11 l12 = 0.2462

Calculating the other row:


115

k4 = (pcnt scale change in composition)/( change in X2 valve) with the total Q constant.

A1 = (0.2 * X2ss/(X1ss + X2ss))*100

X1 = X1ss + deltaflowX2


A2 = (X2 * 0.2/(X1 + X2))*100

dA = ((A2 - A1)/Amax)*100

k4 = dA/(deltapcnt) k4 = 1.2000

l21 = K4/k4

l22 = 1 - l21

The total relative gain matrix:

l = l11 l12

l21 l22

l = 0.7538 0.2462

0.2530 0.7470

The lack of symmetry in the matrix is due to the non-linearity of the equation.

Pairing of manipulated variables shows the use of X1 for the water flow valve and X2 for the 20%

NaOH flow valve give the best pairing.

Relative gains are within the range to consider decoupling: no term 0.8 < l < 1.2

While some of the terms are close to 0.8 in this example, lowering the composition controller's set

point will result in decreased stability without the decoupling

Classical Decoupling

Other steady state gains are calculated as:

K2 = (pcnt change in flow )/(change in X2 valve)

K2 = (( - deltaflowX2)*100.0/Qmax)/(deltapcnt) K2 = 0.6000

K3 = (pcnt change in flow )/(change in X1 valve)

K3 = (( - deltaflowX1)*100.0/Qmax)/(deltapcnt) K3 = 0.2500

Calculate the decoupling network that allows a change in composition controller output to only

effect the composition (not the flow ) and a change in flow controller output to only effect the flow

(not the composition ) .

Using matrix notation; let the steady state gain matrix be K:

K = K1 K4


116

K3 K2

K = -0.3769 0.3036

0.2500 0.6000

Calculate the decoupling matrix by inverting the steady state gain matrix:

D = inv(K)

D = -1.9865 1.0053

0.8277 1.2478

Decoupling results when there is no interaction between the interactive variables.

interact = D * K

interact = 1.0 0.0

0.0 1.0

This is the identity matrix. The zero terms imply no interaction.

Inverted Decoupling

The improved method proposed by Wade uses the feed forward portion of a conventional PID

controller to act as the summation element. The outputs of the each controller are connected

directly to the respective final element. The advantage of this method is that the operators more

easily understand it. In manual each controller operates only one valve. With any multivariable

control system, care should be taken when placing one of the controllers in manual. The other

control loops may experience erratic operation.

Following this method, first assign the transfer function blocks D1 and D2 to 1.0 and then

calculating new off diagonal elements, which will be the controller's feed forward gains. Designate

the new decoupling network as H;

H1 = 1.0

H2 = 1.0

H4 = K4/K1 H4 = -0.8057

H3 = K3/K2 H3 = 0.4167

Note that the sign of the new terms in the network should be the same as the original network to

obtain the same action, therefore the sign of H4 should be reversed in our case as well as H1.


117

H1 = - H1

H4 = - H4

The new network in matrix designation is:

H = H1 H4 H3 H2

H = -1.0000 0.8057

0.4167 1.0000

In this case the order of the matrix multiplication becomes reversed. Test the decoupling of this

network by:

interact = K*H

interact = 0.5034 0.0000

0.0000 0.8014

Note the decoupling because of the off diagonal zero terms, but the loss of the identify matrix.

This decoupling method may permit the use of controller gains greater than 1.0. This fact was

proven by simulation.

Non Matrix Method

Matrices are hard to work with. Are there any other techniques to decouple interactive loops?

Dumbie presented a method, which does not use matrices. This technique uses a feed forward

block in the output signal to the final controller's setpoint. The example shown in Figure 3, is a

temperature controller of a tempered water system with a cold and hot streams mixed. Total flow

and temperature of the combined streams are the interactive controls. Two equations and two

unknowns are written as:

F F Fw c h= + mass balance and

F T F T F Tc c h h w w* * *+ = energy balance

These two equations are combined and solved for the hot flow:

F F T TT Th w

w c

h c= −

−* The combined temperature in this equation is the output of the

temperature controller Tw'. This system is similar to Wade’s method because feedfoward control

is implemented in both. This system is actually half coupling because the other flow is not

compensated. The technique which implements a controller with a process model is called Model

Predictive Control.


118

Multivariable Control ProblemHot Water Mixer

Flow and Temperature Control

Fwctrl

Twctrl

Hot Water; Th degR

Cold Water; Tc degR Mixed Stream; Fw

Fh

Fc

Fh

FW

Fhctrl

Fw( Tw' - Tc)------------------------------

(Th - Tc)

Tw'

SetPoint

Figure 3

Care should be taken in implementing this system. One should make sure that the engineering

units are correctly scaled when implementing the controls. Division by zero can also be of a

concern if the system is run from a cold start, with both temperatures at the same temperature.

The following plots from an ACSL simulation show that the concept does provide decoupling. The

analysis and implementation is a great deal easier, but does not provide full decoupling. This

design is better than that proposed by Lloyd because manual control is possible and bumpless

transfer can be achieved by output tracking techniques. Care should be taken with output pairing

so that the controller is controlling the output with the maximum sensitivity.


119

Mixer Temp Control

0

20

40

60

80

100

120

140

0 1 2 3 4 5 6 7 8

Time, min

Deg

F, lb

./min

FWTW_F

Steam Water Mixer Flows

0

20

40

60

80

100

120

140

0 1 2 3 4 5 6 7 8

Time, min

lbs.

/min FC

FH*10FW


120

Decoupling by Tuning

Can tuning be used to decouple interactive loops?

Just tuning the PID control constants can, in some circumstances, decouple interactive control

loops. Consider a very simple process, two spray towers, Figure 4, supplied by a common sump

and sump pump. For specifics, each tower requires 100 GPM of water supply. The pump is a

3X1-½ 3500 rpm centrifugal with a 5 5/8 inch impeller. The head follows the normal square root

characteristics falling from 135 feet at dead head to 105 feet at 200 GPM. The towers are

elevated 40 feet from the pump suction. For piping and flow meter pressure drop, assume 2”

schedule 40 carbon steel pipe, 100 equivalent feet are required. The 2” control valve has a

maximum flow coefficient, Cv, of 56. The spray nozzle has a 10-psid drop at 100 GPM. From the

Crane manual, assuming turbulent flow, the K factor for the nozzle is 31.6 and the pipe is 36.3.

When this type of process was started with both controllers tuned to normal flow controller

settings, low gain and high reset, the system cycled indefinitely. As the flow to one tower

reduced, that controller would open its valve further, increasing its flow. The pump would develop

less head which lowers the second flow also, causing its controller to open its valve further and

the cycle would continue. An easy way to stop the cycling is to tune one of the controllers more

sensitive than the other. This way the faster controller can keep up with the changes introduced

by the slower controller. This simple process has been simulated and the results shown are

shown. Symmetrical processes can be usually being decoupled this way.


121

Figure 4

TOWER B TOWER A

SUMP

FCA

FCB

Multivariable Control Twin Towers, Decoupling by Tuning

Spray Nozzle Spray Nozzle


122

Results of Tuning to Reduce Interaction

0 20 40 60 80 100 12050

60

70

80

90

100

110

120Tower Flows, GPM

Unstable flow control; same settings for each controller.

0 20 40 60 80 100 12020

40

60

80

100

120Tower Flows, GPM

Stable flow control; one loop tuned less sensitive than the other.


123

Multiple Controllers

Can more than one controller be used to control the same variable?

Under certain conditions, more than one controller can be used to control the same variable. An

example of this is a large utility of chilled water serving several floors of a sight. It is desired to

maintain the same differential pressure across each user. This is accomplished by controlling a

bypass valve and controller for each floor circuit. It is important for only one controller to have

reset enabled. This is the controller that will control the pressure drop to the set point for the

entire system. The other controllers will serve to maintain their separate pressure differences

through proportional only action.

Bibbero shows an example where four controllers are used to decouple the temperature and

relative humidity interaction. Two controllers are used for temperature and two for humidity. The

outputs of the controllers are cross-multiplied. This actually is another way of implementing the

decoupling techniques described by Lloyd in that the extra controller for each loop is actually

acting as a transfer function block. Once again there should be only one reset for each controller.

Neural Networks

There is a lot of talk about these networks. Are the good for process control?

One thing is certain these days; there will be some article in the trade journals about neural

networks. It is unfortunate that early in their development, many inappropriate problems were

tried and failed, which gave them a bad name. A neural network is nothing more than a non-linear

regression. The regression is usually based on some hyperbolic function of the sums of the input

weights. The network is just a diagram of these equations. The inputs and outputs need to be

scaled so that the hyperbolic function does not saturate.

Network Development – First investigate a polynomial regression. Frequently this is all that is

required. If that doesn’t work, then try a neural network. In order for regressions to be useful, it is

important that the data used to calculate the network follow the same rules that designs of

experiments require, mainly that the design be balanced and orthogonal. The objective is to

prevent "over training" which means the network very accurately measures the process at one

point. Commercial neural network programs can work with very large data sets and what you pay

for is the ability of this system to work with the large data set, i.e. filter and throw out various data

points. It is better to use fewer points in a balanced design than it is to use a lot of data around

one operational point. Once you know this technique, you can use any number of free or

shareware neural network programs available off the Internet.

Neural networks have been shown to work as smart sensors, that is find some relationship with

other variables in the process that results in a relationship to some analytical value. Another use

is to use a neural network as a process model for control. Ramchandran and Rhinehart show an

example of this in an article in InTech, ISA's technical periodical. In this paper, a HYSYS model of

a distillation column was regressed into a neural network, which was used as a model predictive


124

controller. PI controllers were configured such that their outputs are inputs to the network, similar

to the method proposed by Dumdie as described in this article. That technique uses first principal

methods, which would be complicated in a real time simulation. Neural networks can be placed

as compensators with process controllers.

Yes, but that is only an approximation. Why would it work with process control?

Because the model is only used to provide feed forward information to a process controller. The

model only has to show overall magnitude and direction. The reset value in the PI controller will

place the outputs at the required point. This is why model based control doesn't require an exact

model. The neural network can be described as a "shorthand notation" simulation of the process.

Remember, as long as the loop gain is less than one, the loop will be stable. So if the feed

forward signals are not precise, the controller will find the right point and maintain stability. An 85

percent accurate models are all that is required for process control.

References:

Lloyd, S. G., "Basic Concepts of Multivariable Control" Instrumentation Technology Vol. 20 No 12

p 31 (1973) Shinskey , F.G., Process Control Systems fourth edition McGraw-Hill, 1996

Wade, Harold L,. Ph.D., "Inverted Decoupling: A neglected Technique", paper ISA/96 Chicago,

IL, October 1996. Also reprinted in the ISA Automatic Control Systems Division Newsletter; winter

1997.

Dumdie, D. P., “Nonlinear multivariable control made easy” InTech May, 1998, p 48

Bibbero, R. , Microprocessors in Instruments and Control, John Wiley & Sons, New York, 1977,

pp. 160 to 162.

Ramchandran, S; Rhinehart, R. R., "Do neural networks offer something for you?" InTech

November 1995, p 59.


125

Chapter 14 Multivariable Batch Control

Multivariable control does have application in batch processing. Multi component solutions and

blended products frequently exhibit interactive behavior. Small changes in one component can

change the analysis of all components. If the interactions of each component on all analysis were

known, the correct formulation can be made.

Older processes may not have accurate instruments and may have to weigh small trim charges to

correctly formulate a batch. Each of these charges can affect the analysis of the batch. A program

is required to insure the correct analysis is made.

The following example shows how this can be accomplished. This example solution has four

components, two organic liquids, comp1 and comp2, water and salt. In this example, the liquid’s

solubility can be ignored. The solution is sold within a volume specification, 9.81 lb. per gallon,

38.3 percent water, with 1.5 lb. of comp1, 2.5 lb. comp2. The density of pure comp1 liquid is 9.5-

lb. per gallon. Short charging all components, mixing this solution and analyzing it makes the

batch. Based on the analysis, small amounts of comp1, water and salt are added to the batch to

trim the analysis. Water is added to the batch to change the analysis of comp2 in the solution.

The total batch volume is 9400 gallons.

An interaction matrix is defined which show the effect of known small changes of each

component on the resulting analysis. The relationship between the change in densities and

change in mass charged is:

den_matrix .M mass_matrix Where den_matrix is a 3x1 matrix, M is a 3x3 matrix and mass_matrix is a 1x3 matrix. For the

first row, determine the change in comp1 concentrations for each constituent. The change in

density of comp1 due to adding 100-lb. of comp1 to the batch is defined as:

den1.1.5 vol 100

vol100.0

9.5

a11 den1 1.50 =a11 8.948546 10 3

Change in comp1 made by water addition, adding 100-lb. water

den2.1.5 vol

vol100.08.33

a12 den2 1.5 =a12 1.913216 10 3

Adding 100 lb. of salt produces no change in comp1 concentration because the salt is only

soluble in the water.


126

a13 0.0

For the second row, determine the change in comp2 concentrations for each constituent.

By adding 100-lb. of comp1 to the solution:

den4.2.5 vol

vol1009.5

=den4 2.497204 a21 den4 2.5 =a21 2.796421 10 3

Change in comp2 made by water dilution, adding 100-lb. water to the solution:

den5.2.5 vol

vol1008.33

=den5 2.496811 a22 den5 2.5 =a22 3.188694 10 3

Adding salt does not change comp2 concentration.

a23 0.0

For the third row, determine the change in aqueous density for change in each component.

Adding 100-lb. of comp1 produces no aqueous density change.

a31 0.0 Add 100-lb. of water to change comp2 concentration

tot_wt .vol product_density =tot_wt 9.2214 104 water_wt .tot_wt%water100.0

=water_wt 3.531796 104

vol_waterwater_wt

8.33 =vol_water 4.239851 103

mass_disolved_solids .( ).8.33 1.179 8.33 vol_water =mass_disolved_solids 6.321915 10 3

den6

.vol_water100.08.33

8.33 mass_disolved_solid

vol_water100.08.33

=den6 9.81686 spgr1den68.33


127

a32 spgr1 1.179 =a32 5.053933 10 4

Add 100-lb. of salt to batch. An experiment shows that by adding 0.33 lb. of the salt to 1 lb. of

water changes the density from 1.000 to 1.179.

delta_den

.100.0water_wt

0.179

0.33 =delta_den 1.535831 10 3 a33 delta_den

Set up the interaction matrix M and invert:

M

a11

a21

a31

a12

a22

a32

a13

a23

a33

=M 19.410526 101

8.252842 101

2.715748 101

5.646316 101

2.640909 102

8.690395 101

0

0

6.511133 102

For the example batch, a set of lab results is shown. Determine the amount of each component

required making the target batch specifications.

target_den_comp1 1.5 target_den_comp2 2.5 target_den_water 1.179

lab_den_comp1 1.501 lab_den_comp2 2.505 lab_den_water 1.179

delta_comp1 target_den_comp1 lab_den_comp1 =delta_comp1 1 10 3

delta_comp2 target_den_comp2 lab_den_comp2 =delta_comp2 5 10 3

delta_den target_den_water lab_den_water =delta_den 0

Calculate the amount of each component based on the specification’s errors.


128

=.M 1delta_comp1

delta_comp2

delta_den

1.882105 10 1

1.402983

4.616772 10 1

mass_matrix .M 1delta_comp1

delta_comp2

delta_den

=mass_matrix

1.882105 10 1

1.402983

4.616772 10 1

mass_comp1

mass_comp2

mass_salt

mass_matrix

mass_comp1 .mass_comp1 100.0 mass_comp2 .mass_comp2 100

mass_salt .mass_salt100.0

3.0 Trim amounts are:

=mass_comp1 1.882105 101 =mass_comp2 1.402983 102 =mass_salt 1.538924 10 1

In actual practice, each batch is not exactly 9400 gallons. There in variability in the equipment,

sampling and analytical errors. So if the theoretical change were made in each batch, the

analysis would continue to vary. Use an exponential weighted moving average or EWMA of the

changed amount. EWMA is calculated as:

oldmassdeltamassdeltamassdelta __*)1(_*_ λλ −+=

This will allow the process to approach the target set points without overshoot. Upper and lower

statistical limits can be calculated for each variable. As long as the variables are operating within

these limits, it is not necessary to change the trim settings.


129

Chapter 15 Model Based PID Control

Why use a process model in the control loop?

Conventional PID controllers have a closed loop period equal to 4 times the process dead time

plus the time constant for self regulating, non integrating processes. For processes with a large

time dead time, this means the loop takes a long time to stabilize after a set point or disturbance

change. There is also a tendency for loops with dead time to overshoot the set point because the

reset term will cause the output to ramp to a value too far from the required output because there

is no reduction in error until the process variable begins to change. The change in error can occur

only after the dead time has passed.

Summary of Dead Time Compensation Algorithms

There are several control algorithms in the published literatures that can correct for process dead

time. These techniques can be classified as internal model control, model free adaptive control

and model based PID control.

Internal model control is a technique that implements an algorithm that is based on a process

model. Parts of the algorithm may include parts of a PID control algorithm, but the whole control

algorithm is based on an understanding of the process. There are specialized algorithms and not

well understood by most process technicians or engineers. An example of this is the dynamic

matrix control or DMC, where a forward projection of a process change is placed in an array and

output changes are based on a least error squared value of the projected process variable.

Another model-based control is the minimal prototype controller, where the controller output

change is based on a projected change in process variable. This algorithm does not even use

any elements from a conventional PID algorithm.

Model free adaptive control is a relative new technique that uses neural networks to control the

process. The output will move the process variable to the set point based on an internal

mathematic network, which is not determined by the user. It needs some basic understanding of

the process dynamics to begin. These assumptions do not need to be exact, but should be

reasonable. The process dynamics can change and the algorithm will learn the new conditions

without being told to retrain itself. As an example, assume the controlled variable is at the exit of a

plugged flow reactor. The control valve is at the inlet of the reactor and only adds a small fraction

of the total flow through the reactor. The dead time experienced due to a change in valve position

is a function of the rate through the reactor. The model free adaptive controller will learn the

change without intervention. These algorithms are proprietary, somewhat expensive, most often

run in a PC platform. Therefore they require some network interface to a distributed control

system, DCS or programmable logic controller, PLC. Interfacing to legacy control systems

frequently is a major part of the installed cost. On the plus side, many of these companies are

starting and are willing to partner with the user to gain acceptance.


130

Model based PID controllers have been in the industry for several years. These algorithms are

called Smith Predictor or Dahlin algorithms. Frequently these algorithms are described in Laplase

or Z transforms and they are difficult to implement by casual users. The technique is to provide a

representation of the process model in a feedback path between the controller output and the

error term. The signal from the model can be used to modify the error to cancel out the feedback

measurement. Other techniques manipulate internal signals within the PID algorithm such as

integral tracking. Many commercially available PID controllers do not have these features, which

is a disadvantage.

Practical Form of the Smith Predictor

Most technical papers written on the Smith Predictor describe how a “model” of the process is

placed in the feed back path. The user believes that an exact calculation and representation is

required to implement the technique. This is not practical in an industrial plant. A better concept is

to view the elements in the feedback path as compensation elements. However, the

compensation elements are calculated based on the process model, so the user will need to

obtain a model, but it need not be exact.

The process model is divided into two sections, one that models the process first order time

constants and a second that models the process dead time. The process model dead time and

time constants can be obtained by applying an open loop step test, that is the changing the

manipulated variable, the valve, by a known amount and noting the change in process variable.

Processes with dead time and multiple time constants can be simulated as a dead time with two

time constants, frequently called second order. The resulting trace can be fit by placing the data

in Excel and using the solver to calculate the two time constants. The dead time can be estimated

by inspection. Once the terms are calculated, the modified values can be calculated and placed in

the controller’s feedback path as shown below in figure 1. The value of these terms should not be

set exactly equal to the process model. The controller’s compensated dead time should be

smaller that the process dead time and the time constants should be slightly longer than the

largest time constant. A good estimate would be about 25 percent; the compensated dead time

should be 25 percent shorter than the process dead time and the compensated lags 25 percent

longer than the process time constants. Because the compensated values are not exactly the

same values as the process, it is not necessary for these compensating constants to be precisely

defined. The estimated values are usually sufficient. It is not necessary to know the exact process

gain, that is the percentage change process variable per change in output. It is also not

necessary to have linear behavior either because the algorithm is configured to compensate for

the model error.


131

A conventional “standard” PID algorithm with a remote set point can be used if the model

compensating terms can be implemented in a separating computing function block external to the

controller.

The output from the time constants function is the X term and the output from the dead time

function block is the W term. The actual set point for the control loop is a separate register value,

the SP term. In order for the proposed system to function without an offset between set point and

the algorithm output, and to correct for modeling error, a model correction term, MC is the ratio of

the actual process variable to the output of the total process model, W. With this correction

implemented, at steady state the output of W will be equal to X and the controller’s remote set

point will become the external set point. The compensative action is done in the form of modifying

the remote set point to the controller, while the user need only input the desired set point in the

dedicated register.

As a note of caution, it is important to scale the PV, process variable, within a range that does not

contain zero. This is to avoid dividing by zero by the model correction term. Many newer

configurable control systems do not employ a dead time programming function. If this is the case,

the user can program sever small first order filters to simulate the dead time.

Simulation Test

A simulated control using this technique was modeled in a Honeywell UMC800 analog

programmable controller. The following traces show the performance during start up, set point

change and adding a disturbance. The process function included a non-linear steady state gain

and the compensating term was set to be 80% of the highest process gain.

StandardPID Controller

with Remote Set Point

Process

( Dead Time and TimeConstants )

Set Point, SP

RSP Input Controller Output

Compensated Process( Time Constants )

Compensated Process( Dead Time )

Process Variable, PV

XW

WPV

Model Correction,MC

f(x)

)(* XWMCSPRSP −+=

Smith Predictor with Compensation using Standard PID Controller

Figure 1

Smith Predictor Startup

0

10

20

30

40

50

60

70

80

12:43 12:57 13:12 13:26 13:40 13:55 14:09

Time

Perc

ent

CTRLOUTPV R-SP SETPT W X

Smith Predictor Setpoint Change

0

10

20

30

40

50

60

70

80

15:50 16:04 16:19 16:33 16:48 17:02 17:16

Time

Perc

ent



132

Note that the R-SP or remote set point value changes in a direction that lowers the controller

error term. This reduction in error allows the controller to moderate the output to avoid excessive

overshoot. With this technique, controller settings can become optimal. In the above simulation,

the gain term was equal to 0.15, the reset was equal to 2 minutes and the rate was equal to 0.2

minutes.

The disturbance test was done without implementing any feed forward. I recommend that feed

forward be implemented external to predicted algorithm. It becomes difficult to suppress the

compensating action based on the feed forward signal, rather it is better to move the valve some

amount and not try to allow the compensating algorithm to adjust for the change. The algorithm

will correct for model errors as designed.

The following block diagram shows the simulation tested. The process dead time is simulated as

6 one-minute first order lags while the process time constants are simulated as 2 first orders, one

at 2 minutes and the second as 3 minutes. The compensation blocks are simulated as 5 one-

minute lags while the compensating algorithm was simulated as a 3 minute and a 4 minute lags.

Smith Predictor Disturbance

30

35

40

45

50

55

60

9:21 9:36 9:50 10:04 10:19 10:33

Time

Perc

ent



133

The compensation algorithm was reduced by 80%. The process was given a non-linear behavior

through the math block.


134

Potential Problems

The main difficulty with this algorithm is that the control is good as long as the process model

remains reasonable. If the process dead time and time constants change significantly, the control

loop will operate with choppy behavior and not stabilize. The compensating algorithm will shift in

and cause control instability. Because the algorithm compensates for the actual magnitude of the

process variable, process non–linearity can be compensated. However, the model cannot

compensate for process changes that modify either the process dead time or time constants.

Consider as an example the plug flow reactor previously mentioned. As long as the production

rate remains the same, the dead time will remain the same. It the rate is increased, the dead time

will be lower. This lower value may become lower than the compensated dead time. In that case,

the control will become erratic and never become stable. Similar circumstances can occur with

the time constants. For these cases, the non-linear adaptive controllers appear to have an

advantage because the controller can change as the process conditions change.

Integral Delay

Another way to provide improved control to a process with dead time is to configure a delay

before the integral function. In this way a change in the error value will result in an immediate

change in the proportional action, however the reset or integral behavior will be delayed. The


135

integral delay time should be equal to the process dead time. This prevents excessive integral

action. The simulation was written in ACSL. The delayed integral reset term was written as:

e = Tsp - TwF ed = DELAY(e,0.0,c_td,10000) a = INTEG(ed , 20) + K*e a1 = LEDLAG(T1, Tf, a+ff, 20) a2 = LEDLAG(T2, alpha*T2, a1, 20) Pcntout1 = BOUND(5.0, 100.0, a2)

The lead lag elements provide the rate term. The proportional gain is the K value. The ff term is a

feed forward term that was not used in this simulation. A change in set point was used to simulate

dynamic behavior.

A simulation of this control behavior is shown below. The compensated or delayed response is

shown as TwF comp, the solid line. The dashed line is the same process without the integral

delayed, TwF. In this simulation, the dead time was set at one minute. Most commercially

available controllers will not allow the user to configure the controller’s internal elements. Many do

not offer delay or dead time function blocks. A delay function block requires the controller

manufacture to use more dynamic memory, which increases the cost.

Integral Delay

100

120

140

160

180

200

220

15 20 25 30 35

Time

Tem

p D

egF

TspTwF compTwF


136

References:



Gallier, P. W., Otto, R. E., “Self-tuning Computer Adapts DDC Algorithms”, Instrumentation

Technology, 65-70, Feb. 1968.

Blevins, T. L., “Modifying the Smith Predictor for an Application Software Package”, Advances in

Instrumentation, Instrument Society of America, Research Triangle Park, NC, Volume 34 Part 2,

1979.

McMillan, G. K., Process/Industrial Instruments and Controls Handbook, 5th edition, McGraw-Hill,

pp.10.183, 1999

Tan, K. K., Wang, Q. G., “New Approach to Analysis and Design of Smith-Predictor Controllers”,

AIChE Journal, June 1996, Vol. 42, No. 6, pp. 1793-1797.


137

Chapter 16 Statistical Process Control

Controller in a Spreadsheet

Frequently a process will require control for a variable that has a lot of noise or variability in the

signal. This variability can come from a number sources, if the signal is the result of a laboratory

analysis, there are sampling errors. Because of this variability, the true value of the variable at

any given time is not known exactly. In these cases, it is best to control this variable through

statistics. The use of a statistical process control single input, single output is described below.

An EXCEL spreadsheet that performs the control will be described. The controller spreadsheet

has three features. The first is the use of a cumulative sum or CUSUM to trigger control actions.

The second is the use of a self-tuning filter used to filter the controlled variable. The third is the

use of a proportional plus integral, PI, velocity controller.

CUSUM

Because of analytical and sampling errors, there is variability in the process variable or PV. This

means that even with a prefect plant, there will be some variability in the analytical results for a

control sample. This data's variability is assumed to have a statistical normal distribution. The

reasons for the data's variability are instrument error, analyst error, which is the sample

preparation, requires a lab technique that will produce different results between the analyst, and

field sampling errors.

Small changes in the control output only add additional noise to the process. The objective of the

CUSUM is to only make process changes when the controlled variable exceed a certain threshold

and not make any changes if the process is operating within the normal variability. This is based

on the sample standard deviation, σx.

Calculating the standard deviation can require many past samples. A technique employed by this

controller is to calculate this based on an exponentially weighted moving average or EWMA of the

sample variance, the square of the sample standard deviation, or (σx)2. This technique is also

employed for the digital filter.

Define the sample mean for a population on N samples as:

x Xi

N

i==∑1

1N (1)

The sample standard deviation of this population is defined as:


138

σxi

Ni

Nx x=

− =−∑1

1 1

2( ) (2)

This equation is not practical to implement for process control because of the large number of

points required calculating σ. If we define another variable, ρ, as:

ρxi

Ni i

Nx x=

− =− −∑1

1 11

2( ) (3)

This variable, ρ, is related to the sample standard deviation by:

σ ρx = 2

2 (4)

Since ρ is based on the limited information of two samples, an EWMA of this value is calculated.

This is defined as deltaf in the program where deltaf = ρ2 = 2σ2. For each sampled value deltaf

becomes:

deltaf deltaf x xi i= + − −09 01 1 2. * . *( ) (5)

Deltaf, a calculated value related to the standard deviation, is used in both the digital filter and the

CUSUM calculation. In order to prove this calculation, A MATLAB program that performs these

calculations for 2000 random points demonstrates the accuracy of the above relationships within

a couple of percent.

CUSUM is the accumulative sum of the error, where the error is the difference between the

process variable and the set point:

cusum cusum pv pisp= + −( ) (6)

Control is signaled when the cusum exceeds a trigger, trigger_cs, that is related to the EWMA of

the standard deviation:

IF ( abs cusum trigger cs deltaf( ) _ * /> 2 ) (7)

THEN take control action.


139

The size of trigger_cs is a function of the width of control band, for a 95% confidence interval or 2

σ, the value is 2.

An advantage of this technique is that changes in the process are only made it the process

variable extends outside the normal variability.

Digital Filter

The spreadsheet controller equation uses a filtered value of the process variable. ACSL

simulations show that an unfiltered variable causes poorer control. The filtered signal is an

EWMA of the current variable and the past filtered signal:

PV st PV st PVf current f= + −λ λ* ( ) *1 (8)

The calculation of the filter factor, λst, is based on deltaf from the CUSUM calculation. This filter

will automatically adjust the filter factor to keep the filter value within a predefined confidence

interval.

λst t stat deltaf E= + −[0. ( _ * ) / ( * )]5 42 2 1 (9)

t stat_ .. ,0 025 13 21604= , is the t statistic for a 95% confidence interval for a sample size of 13. E

is defined as the 95% confidence half interval of the filtered value. The size of E should be based

on the plants sample variability. A good estimate is based on the analytical variability:

E analytical= 2*σ (10)

In actual practice, this calculated filter factor is clamped between 0.05 and 1.0. This prevents

saturation of the filtered variable. The advantage of this filter is that the degree of filtering is

adjusted to keep the confidence interval within this band. From a control viewpoint, filtering

introduces a signal lag and can be detrimental to good control. This filter will regulate itself to

keep the variability within the band, only allowing the degree of filtering required for good control.

This filtered signal is the input signal to the controller equation.


140

The above plot demonstrates the response of a step input noise induced signal, x trace, a self

tuning filter, xf trace, and a conventional or weighted filter, xf1 trace. A weighted filter has a

constant filter factor.

Velocity PI Controller

The spreadsheet controller implements a simple velocity PI or proportional plus integral controller.

This controller calculates the change in output based on the controller tuning settings and the

magnitude of the error, which is the difference between the filtered process variable and the set

point. The advantage using this control algorithm is that prior knowledge of the absolute output is

not necessary. The controller does need to keep the last previous iteration values. The actual

control calculation is made with the gain term acting with the change in error and the reset term

acting with the error. The control equations are as follows:

Self Tuned filter

0

10

20

30

40

50

60

70

80

0 50 100 150 200 250

Samples

Varia

ble x red

xf self tuned greenxf1 weighted blue


141

Calculate the new error term:

pierr pvf pisp1 = − (11)

Where pisp the desired set point and pvf is the filtered value of the process variable.

The PI velocity control algorithm then becomes:

delu pigain pierr pierr pii pierr ctrli= − +*( ) * /1 2 1 (12)

Where pierr2 is the value of the previous control calculation's error, pigain is the proportional

gain, pii is the reset gain and ctrli it the controller iteration time in minutes. The reason for the

division is to make the value of the integral time reasonable.

References

R. Bibbero, Microprocessors in Instruments and Control, John Wiley & Sons, New York, 1977, pp.

160 to 162.

R. Russell Rhinehart, Songling Cao, "A Self-tuning Filter", ACOS Newsletter, Instrument Society

of America, Research Triangle Park, NC, Summer 1997, pp. 3 to 8.

R. Russell Rhinehart, "An on-line SPC-based trigger for control action", Proceedings SPIE - The

International Society for Optical Engineering, October 20-21, 1994, Austin, TX, SPIE Vol. 2336,

pp. 50 to 58.


142

Chapter 17 Robust Statistics

Hampel Filter

There is a growing field of “robust” statistics. This field has some different ideas about what to do

with outliers. As we all are told, most signals are assumed to have a normal distribution. In the

real world of process industries, process variable noise may at times have spikes impressed on

the signal, which becomes the outliers. This is because the instruments are sometimes

measuring process conditions that are not “normal”. Perhaps the flow meter is measuring a gas

and a slug of liquid strikes a sensing element. Or the liquid flow has some entrained gas or vapor.

In these cases, the process variable response is not “normal”; rather there is a spike. Most

engineers would just add a filter to the signal. The problem with that is the resulting signal still has

a spike, just one that is smaller than the disturbance, and worse yet, the signal takes time to

recover. Exponentially weighted moving average or EWMA filters compute a filtered value based

on a fraction of the current signal plus one minus the fraction times the previous filtered value.

The robust filter takes a "reality check" of the point, that is, does the point lie outside the range

where it is considered reasonable.

A filter that can correct this problem is called a Hampel filter. This filter places the variable in a

series of pervious variables, seven is a common number, and calculates the median value of the

series. This is where this statistic is different from most statistical filters, which use the mean

value. In process control, a frequent use of the median value is in pH, where three transmitters

are used and the control signal is the median of the three. Once the median value is calculated,

the current value is compared with the median value of the series. This statistic is based on a

factor of the median absolute deviation or MAD. A comparison of this is the range in the normal

statistical domain is sigma, or standard deviation. The value of the MAD factor is 1.4826. Note

that this unit is scaling invariant. The equivalent for 3σσσσ is 3*MAD. If the test point is greater than

or equal to 3*MAD, the filtered value is taken as the median value of the sample series. If it is

below 3*MAD, the filtered value is taken directly as the value of the point. Three is the normal

factor used; however it can be changed depending on the desired performance.

There are trade offs when using filters, and this filter is exception. There are two problems with

this filter. One is the apparent dead time due to step changes. The filtered value will not change

until the median value in the series becomes high enough to shift the median value. For seven

points, the filter has an apparent dead time of four sample scans. This might become a problem

in some applications. The user should take in to consideration the scan frequency of the analog

input hardware as well as any input electronic filters. The second problem is the end effect. The

filter needs to be seeded and cannot work unless the series can be established.

The MATLAB code for this filter is the following: % x is the process variable signal.


143

% xh is the Hampel sample series. % yh is the Hampel filtered value. % i is an index of points in the signal series. % Hampel filter constants MAD = 1.4826; K = 3; % For 7 data points in the series % Hampel filter calculation if i<2*K+1 yh(i) = x(i); % the end effects else % Begin the Hampel filter calculation % locate the sample series kk=1; for jj = i:-1:i-2*K+1 xh(kk) = x(jj); kk=kk+1; end Z = median (xh); if abs(x(i)-Z)<3*MAD yh(i) = x(i); else yh(i) = Z; end end


144

The following plot shows the response of this simulated filter compared to a weighted filter.

The bottom trace is the unfiltered process variable while the top traces are the EWMA weighted

filter and the Hampel filter. Note the spikes generated by the EWMA filter. The Hampel filter

removes the spikes, but does experience some dead time in order to see the median value

change.

The Hampel filter can also serve as a pre-filter to other filters. The following plot shows a Hampel

filter together with a self-tuning filter. The self-tuning filter adjusts the weight factor to an EWMA to

keep the resulting noise within an expected value. Increasing the controller’s rate setting can

compensate the added lag.


145

This plot shows a Hampel filter together with a CUSUM filter. In this case signals are tested

against the Hampel filter "reality check” before they are applied to the CUSUM filter algorithm.


146

The same test data set when applied to a CUSUM filter without the Hampel filter shows these

results. Note the step shifts in the CUSUM output when a spike is sensed, rendering the CUSUM

filter almost useless under these conditions.


147

Experimental Data

Another use of the Hampel filter is data conditioning. In this case a series of experimental data

points, say those taken form a pilot plant experiment, that may be used to fit equations. If the

number of data points is small, frequently the experimenter will just remove those points before

the data is applied to the regression. For large data sets, this filter would be a good choice to

remove those points and replace them with ones more representatives of the series. This would

help improve the precision of the regression because most regression counts each data point

with the same weight.

For anyone doing this type of test, an improvement could be made if the outlier point could be fit

within a Taylor series of values around the tested data point. This would be more representative

value than the median value previously discussed.


148

References:

Jörg W. Müller, “Possible Advantages of a Robust Evaluation of Comparisons”, Journal of

Research of the National Institute of Standards and Technology”, Volume 105, Number 4, July-

August 2000, pp. 551 to 555.

Ron Pearson, “Scrub data with scale-invariant nonlinear digital filters”, EDN, January 24, 2002,

pp. 71 to 78.

R. Russell Rhinehart, Songling Cao, "A Self-tuning Filter", ACOS Newsletter, Instrument Society

of America, Research Triangle Park, NC, Summer 1997, pp. 3 to 8.

R. Russell Rhinehart, "An on-line SPC-based trigger for control action", Proceedings SPIE - The

International Society for Optical Engineering, October 20-21, 1994, Austin, TX, SPIE Vol. 2336,

pp. 50 to 58.


149

Chapter 18 Process Simulators

Classes and Divisions

There are two classes of simulators, ones that require the user to program in FORTRAN, C++,

Visual Basic etc. and ones that advertise that these skills are not required. Most of these

programs never work the way they should with your process, but usually work well with the

sample problems, which are usually very simple or elementary.

Why simulate at all? From a control systems engineer's viewpoint, it is helpful to be able to

predict the dynamics thereby gaining the knowledge of how loops may behave as well as allowing

the simulation to be used as a training tool. The chemical engineers want to have some data to

support the plant design and a simulator will help justify equipment design and sizes.

I have been asked to sit in on many discussions and vendor presentations about simulators. The

subject comes up about what type of physical property database to use or how their product

interfaces to the users database or how to enter physical and chemical properties of compounds

not in their database. Clearly, this is the single most important factor from the chemical

engineering simulation viewpoint. They usually divert their discussion to the DIPPR database

while my mind keeps wondering about the dynamics that they say they have, usually as an

option. Most of these products require a large cash outlet as well as ongoing customer support

from some hot line or email service.

Control Deficiencies

When you use one of these simulators for control, there are some watchouts; does you simulator

actually simulate the following:

Can the dynamics simulate true deadtime? This is important because if it weren't for deadtime,

most process control engineers would be out of a job. The control blocks should emulate real

time as much as possible and therefore need deadtime. If your simulator does not do deadtimes,

do not give up, it must do first order filtering. Just add multiple first orders in series, which looks

like a first order with deadtime. This may not be sufficient, as I will explain later.

Noise simulation: This is necessary where analytical control is being implemented, noise needs to

be filtered which adds lag to the process. The simulator should be able to add Gaussian noise

with an adjustable standard deviation. This is very important for analytical data.

Remember if the process model is only 85% accurate, it is good enough for process control.

Frequently other engineers are very possessive and not willing to let others see the model

because if is not accurate enough. For control purposes, accuracy is not required, just some

overall dynamic behavior. The difference of 10% one way or another usually doesn't effect control

simulations. Remember the objective of the simulator is to show the approximate behavior, and

test various control strategies.


150

Simulated Physical Properties

This is the major watch out one should have with commercial packages. In order for the simulator

to produce good results, you need a good estimate of the physical properties. How do they get

these properties in their database? They perform regressions on experimental data or they use

some equations based on molecular structure. If the data is experimental, what data did they

use? Over what range was the data regressed? Frequently the data entered is only based on a

few points and well outside the range where you may want to run your simulation. A good

example of this is formaldehyde and water solutions.

An Actual Example

In order to minimize the size of a surge tank, a commercial package, with dynamic properties,

was used to simulate a process chilled cooling system using a 50-50 mixture of ethylene glycol

and water as the cooling medium. Forty percent of the system capacity is a batch process so

there was some concern that a large surge tank is in place in order to allow the chiller to maintain

the utility at the desired temperature.

HEATEXCHANGER

COMPRESSOR

FREONCONDENSER

tower water

Figure 1 Chilled Water System

TC

LOADS

Specifications:


151

Outlet Temperature -4 degF Cooling Media 50-50 EG-H2O solution Flow Rate 600 GPM Cooling capacity 146 Tons Piping 1000 feet 6" SCH40

A commercial simulator was used to test the effect of various size surge tanks on dynamic

response of the chiller's outlet temperature controller.

The first problem was the apparent inability of the simulator to calculate the viscosity of the glycol

and water mixture. The simulator gave a viscosity several times the viscosity given by the vendor

of the ethylene glycol and water solution. The density given was also in error. I question how

these packages simulate liquid mixtures.

Once the simulation was configured, it showed that there was no control problem and that the

return temperature changed instantaneously and as a result no surge capacity was required!

This, of course, cannot be. The simulation failed to show the effect of the installed deadtime due

to the piping. This turned out to be a very important criterion, because the liquid in the piping

acted as surge capacity.

Piping should be considered both as a delay line and as surge. Consider the following:

The pipeline, 1000 feet in length (500-foot supply and return branches) of 6" SCH40 pipe

contains 1.5 gal/foot. When flowing at 600 GPM or 6.6 feet/second, the total delay per branch

would be 500/6.6 or about 75 seconds. With a sample time of 5 seconds this would be

75/5 = 15 pipe segments with 500/15 = 33 feet/segment which is 33.33 feet/segment * 1.5

gal/foot = 50 gal/ segment.

In this case, it became necessary to simulate the pipeline as a series of 50 gallon tanks, the idea

that deadtime can be simulated as a series of first order lags. Once this change was made, to the

simulation, the simulator showed the first order effect, but still failed to show the effect of true

deadtime. The system was finally simulated in EXCEL to control the integration scan time,

which was necessary to see the effect of the piping deadtime. Once the simulation was complete,

it demonstrated that there is sufficient reserve of coolant in the supply and return piping to

eliminate the surge tank. The following plots show the correct results of the simulation. Notice the

dead time between the load temperatures.


152

EG-H2O Chiller Temperatures

-5

-4

-3

-2

-1

0

1

0 10 20 30 40 50 60 70

Time, min

Deg

F

TspT loadT returnT chiller

Process and Chiller Loads

0

10

20

30

40

50

60

70

0 10 20 30 40 50 60 70

Time, min

Pcnt p load

c load

This simple simulation demonstrates the potential problems with commercial process simulator

packages.


153

Integration Algorithms

So how can you integrate with a spreadsheet? I’ll bet it is too complicated.

Writing differential equations is not a very complicated exercise. The integration algorithms are

found in most college math texts or on the Internet. Writing a differential equation is just a matter

of writing a difference equation and solving it with an algorithm. Remember, difference equations

first, then given to solve through the algorithm.

Integrators come in two varieties, relative to step size, variable or fixed. Examples of variable

sized are Gear’s Stiff and Runge-Kutta-Fehlberg. These algorithms reduce the integration interval

to minimize the error. There is the Simpson’s rule that states that the error in an algorithm is

related to the size of the integration interval raised to the power of the number of evaluations.

Variable size algorithms keep reducing the interval until the error is less than that specified by the

user. These algorithms are frequently used by those who are making a space shot or in

determining the reaction rate constants for some process chemistry. They are of little use for

control simulations because in control, fixed intervals are required. Even if the process is static,

control must continue and mixing different algorithms is seldom worth the effort. The Runge-Kutta

level 4, meaning four levels or intermediate solutions per iteration, is the best for most control

purposes. Even a simple Euler algorithm can give good results.

To write a differential equation, just remember you only need to write the difference, which is the

input minus the output. Just remember solving a differential equation required the initial value, so

you have to start somewhere. The following is a Visual Basic code for a differential equation

program solving a simple pressure control loop using the ideal gas law and the Universal Gas

Sizing Equations. In this case, a tank is blanketed with nitrogen. The nitrogen is supplied through

a regulator upstream of an orifice plate. The tank is vented through a control valve. x is a three

element array, x(1) = mass in the tank, x(2) = valve time constant, x(3) = integrated error term. x

is set to the initial condition values. The differential equations solve for a new x term based on the

differences. In this example, it is best to determine the mass in the tank by assuming an initial

pressure.

Runge-Kutta level 4 integration example

‘ first set the existing variables to a xnew For j = 1 To ssv xnew(j) = x(j) Next ' begin the four step process For j = 1 To 4 ' calculate the initial mass in tank p=nRT/V P_tank = (xnew(1) / MW) * R_gas * t / vol ' calculate the change in pressure ' first we need the outlet flow, n_out dP = P_tank - p_atm If (dP > P1_orifice - p_atm) Then dP = P1_orifice - p_atm


154

End If If (dP < 0#) Then dP = 0# End If Qout = Cg_valve(Index) * P_tank * _ ((520 / (spgr * t)) ^ 0.5) * _ Sin((59.64 / C1_valve) * ((dP / P_tank) ^ 0.5)) Qout = Qout / minperhr n_out = Qout * spgr / 13.1 ' then calculate the flow across the orifice plate, n_in dP = P1_orifice - P_tank If (dP > P1_orifice - p_atm) Then dP = P1_orifice - p_atm End If If (dP < 0#) Then dP = 0# End If Qin = Cg_orifice * P1_orifice * _ ((520 / (spgr * t)) ^ 0.5) * _ Sin((59.64 / C1_orifice) * ((dP / P1_orifice) ^ 0.5)) Qin = Qin / minperhr n_in = Qin * spgr / 13.1 ‘ for x(1), the mass difference is the inlet minus the outlet ‘ for x(2), the first order lag simulating valve travel ‘ for x(3), the integration of the control error x_dot(1) = n_in - n_out x_dot(2) = (1 / tau_v) * (u(Index) - xnew(2)) x_dot(3) = (Psp(Index) - P_tank) ‘ These are the integration equations If j = 1 Then For i = 1 To ssv k1(i) = step * x_dot(i) xnew(i) = x(i) + k1(i) / 2 Next End If If j = 2 Then For i = 1 To ssv k2(i) = step * x_dot(i) xnew(i) = x(i) + k2(i) / 2 Next End If If j = 3 Then For i = 1 To ssv k3(i) = step * x_dot(i) xnew(i) = x(i) + k3(i) Next End If

If j = 4 Then For i = 1 To ssv k4(i) = step * x_dot(i) x(i) = x(i) + (1 / 6) * (k1(i) + 2 * k2(i) + 2 * k3(i) + k4(i)) ' Calculated next state Next End If Next ' calculate the new outlet pressure by calculating the mass in tank p=nRT/V P_tank = (x(1) / MW) * R_gas * t / vol


155

Using the Control System as a Simulator

In many cases where the user is only interested in simulating hydraulic or thermal systems, or

where chemical reactions are simplified or ignored, the control system itself can be modified to

provide the simulated process. The following example illustrates this. Assume a heat-jacketed

vessel is cooled by using an internal cooling coil. The temperature is controlled by the amount of

cooling water through the coil and the heat is controlled to keep the flow it a high enough value it

facilitate good heat transfer.

Modifying the control program can simply be done adding the required function blocks to

calculate the heat transfer. The cooling heat value can be subtracted from the heating heat value

and be totalized. The resultant total functions as an integrator, which is the heat value in

BTU/minute, This can be converted to a temperature reading.

In the simulation blocks the following functions are simply calculated:

The cooling flow, F_COIL, is equal to K*(TV-104) where TV-104 in percent.

The heat transfer coefficient, U_COIL, is equal to a K0 + K1*(TV-104).

The coil outlet temperature is calculated by a heat balance across the coil is equal to the heat

flowing through the coil:

Q_COIL1 = U_COIL * A *( (TI-104R) – (TOUTCOIL + Tincoil) /2 ) =

F_COIL * (TOUTCOIL – Tincoil)

Solving the above for TOUTCOIL:

TOUTCOIL =

(U_COIL * A ((TI-104R) – (Tincoil/2) + F_COIL*Tincoil) / (F_COIL + U_COIL*A/2)

The heat transferred through the coil, Q_COIL1, is equal to F_COIL*(TCOILOUT – Tincoil) / 60.

Tincoil is a constant of 529.7 DegR.

The electrical power percentage, P-104, is converted to heat in BTUs. This value is as lagged by

a first order lag equal to the thermal time constant across the jacket, tau.

Q_ELECT = K*(P-104)* (1.0 - e-t/tau )

The Q_COIL is a lagged value of the calculated Q_COIL1.

Once the electrical heat and cooling heat values are calculated, the subtracted element, ∆∆∆∆,

subtracts the cooling heat from the electrical heat. This heat value is then totalized. The

controlled variable, TI-104, is finally calculated in degrees C. The temperature in degrees R, TI-

104R, is calculated also.


156

Figure 2 Controller for Simulation


157

Figure 3 Simulation Equations Developed form the Control System’s tool kit


158

Chapter 19 Environmental Temperature and Humidity Control

There appears to be renewed interest in temperature and humidity control for plant sciences. This

chapter will address some techniques for good control of the growth environment. Many of the

techniques described in this report can be used in dryer control.

In order to gain a clear understanding of some techniques, the user is encouraged to consult the

psychometric chart. The chart displays the phase conditions of water vapor in air. The chart will

provide visibility of underlying phase changes. An understanding of the unit operations occurring

on the processed air as well as units of measurement is articulated on the chart.

The air temperature is the also called dry bulb temperature. This is the temperature of the stable

air water vapor mixture.

The dew point temperature is a measurement of the temperature where condensation begins to

form as the water is condensed from the wet air.

The wet bulb temperature is the temperature at which adiabatic heat is transferred during the

drying of a solid or humidification of air. For a dryer, moisture in the solid is transferred to the air.

The air will gain moisture while the solid looses moisture, therefore or humidification of the air

occurs. This is the same effect if water is sprayed into the air stream. This process will occur at a

constant wet bulb temperature. The dry bulb air temperature will decrease during this process

and be lower exiting the dryer or chamber.

Relative humidity is the ratio of the water vapor pressure at the dew point to the water vapor

pressure at the dry bulb temperature. This ratio is usually expressed as a percent. This ratio is

multiplied by 100 to obtain the percentage reading.

The first step is to consider what type of inlet air is required. In many applications, cool dry air is

supplied to a test growth chamber. This can serve as an entry point in the system. The air will

enter the system at a given temperature and humidity.

Energy sources – Heating the air can be accomplished by using an electric heater. In this case,

the heated air will exit the heating plenum at a lower relative humidity, because increasing the

temperature non- adiabatic will not change the moisture in the air.

If steam is used to humidify the air, the temperature will increase as well as the humidity. If, on

the other hand, water is injected in the air stream, the temperature will decrease while the

humidity will increase. This will occur along the constant wet bulb temperature.

Temperature Instruments

The preferred method of temperature measurement is with either a thermocouple or an RTD.

Many years of experience showing the superiority of the RTD compared to thermocouples. The

RTD based on nickel wire resistance, detects temperature on the sheath and is accurate within +

- 0.1 degree C.


159

A thermocouple on the other hand is a tip sensitive element. It is accurate within + - 1.1 degree C.

In areas that are close to heat or light sources, make sure the element is not placed in a dead

spot in the chamber or zone. Shade the element from the sun.

Humidity Instruments

Several years ago, the only type of humidity instrument available was a coil that changed shape

as the humidity changed. These were very unreliable. Another humidity instrument used P2O5

conductivity, as the humidity in the air increased; the P2O5 would become phosphoric acid and

increase conductivity. This probe is subject to frequent regeneration. Sometimes the P2O5 would

dissolve away from the electrodes.

Chilled mirror dew point sensors measure the dew point by controlling the temperature where it a

reflective surface begins to fog, by definition this is the dew point. These instruments needs

frequent cleaning in dusty environments.

Within the last few years a new design a new design has emerged. This is based on solid-state

thin film polymer, a capacitive element, moisture absorbs in the polymer and the electrical

capacitance changes, which is measured by the electronic circuits. This instrument has an

accuracy of + - 2%. These instruments are quite reliable in dusty environments, however they can

be permanently damaged if operated at sustained humidity above the rated specification, typically

95%.

Another early method of measuring the amount of moisture in air is the wet bulb temperature. A

sling psychomotor can measure this temperature. A small cloth sock is placed on the end of a

mercury thermometer. This device is slung through the air and the temperature is reduced due to

the water evaporative cooling. An inexpensive wet bulb temperature device can be fabricated by

using a thermocouple mounted above a cup of water. A paper towel can be folded around the tip

of the thermocouple and allowed to form a wicking action with the water. A small fan can move

the air around the wetted element. This design was tested and worked for several hours. The

water needs to be replenished periodically.


160

The water temperature should be equal to or higher than the ambient temperature. If the water

temperature is colder than the dew point temperature, then this method will measure the dew

point temperature because moisture in the air will condense on the wick.

Sensor and Moisture Injection Location

Make sure that there is adequate airflow around the temperature and humidity elements that they

are not in a dead volume in the chamber. Follow the humidity or dew point temperature’s

operational manual. If the instrument is not mounted in a flowing stream, it will not be responsive

to the surrounding conditions. One way to avoid this problem is to mount the temperature and

moisture measurement probes in a small white box that has a small electrical enclosure fan to

move enough air to insure good response. The box should be white and insulated to avoid

heating.

Atomization of water in a flowing stream is a complex process. While the overall mass and energy

balances follow simple engineering calculations, the transport of water mist to vapor is not trivial.

It is recommended that the user seeks out spray vendors and work closely with them for the

3/8" wide paper towel strip;1" from water surface

060

4" desk fanPARAGON Industrieslow speed

Cup of water

Paper towel;Coronet Dura Fiber

Other materials tested:Surgical gause did notsupport the capullaryaction Cotton strip is to heavy.

Williams - SonamaRoasting Thermometer

Wet Bulb Temperature Measurement

ambient air at 69 degFWet Bulb experimentThis set up was run forseveral hours, thecapullary action in thepaper towel allowed thewet bulb temperature tostabilize.


161

design in question. One way to improve the mass transfer of water into air is to heat the water

before it is injected.

Plant Physiology

For environmental chambers used to grow plants, light becomes an important variable. Biologists

are concerned about the spectral response of plants. Special lights have to be used to

accommodate the correct spectrum. Different types of lights, incandescent as well as high

intensity discharge or special fluorescent lights may be required. The lights should be timed to

correspond to day night 24 hour cycle. The plant’s DNA will trigger premature flowering if the

lights are turned on even for a short period of time during the “night” cycle.

When light is turned on a plant, it begins its transpiration cycle. The plant will begin to release

water from its leaves. It is important to operate the chamber at the proper humidity to avoid

having the water remain on the leaves. Because of the transpiration process, the plant variability

makes it is very difficult to apply feed forward control to the temperature and humidity control

loops.

Temperature and Humidity Control Interaction

As can be seen with the aid of psychometric chart, temperature and humidity are interactive

variables. Increasing the temperature will cause a decrease in humidity. For most enclosures,

modulating the heat input controls the temperature. Humidity is controlled while adding steam or

water in the fan box.

Assume electrical heat is used. Refer to the chart below, assume the air enters at 60 degrees F

and 50% relative humidity, point 1 and is heated by an electrical heater to 95 degrees F the

relative humidity will be reduced to 15%, point 2. However the dew point temperature will remain

constant at 41.3 degrees F.


162

In the drying or the air humidification with water vapor processes, the wet bulb temperature

remains constant while the humidity increases and the temperature decreases. This process is

shown as the line between points 2 and 3.

On the other hand, if steam is used to humidify the air, the temperature is increased instead of

decreased. This is because the steam has higher heat content than the air. This is shown in the

following diagram.


163

If electrical heat is employed to increase the temperature, there is no change in the dew point

temperature. That is, the dew point temperature is the same at point 1 as it is at point 2. One way

to decouple the interaction between temperature and humidity is to control the dew point

temperature instead of the humidity. The dew point temperature set point can be calculated by

knowing the humidity and the temperature. In most cases the users are interested in controlling

humidity rather than dew point. The humidity is calculated as a ratio of partial pressures:

ow

w

pp

RH *100= (1)

wp is the water vapor pressure at the dew point temperature and owp is the water vapor

pressure at the dry bulb temperature.

The water vapor pressure can be calculated through the exponential equation:

+−=

0.3853.7071exp*10*04466.2 6

tp (2)

Where t is in degrees F and p is in psia. Since the humidity is a ratio of the partial pressures, the

dew point controller set point can be calculated as a fraction of the above equation solved in


164

reverse. The above equation was solved in reverse by using the Excel solver routine. The dew

point temperature equation can then be calculated as:

)5082.0/)))0.385/(3.7071exp(*6.20446*exp(((*5.9439.115 +−−= dbdp tRHt (3)

Where RH is the relative humidity set point and tdb is the dry bulb temperature. The dry bulb

temperature set point should be the actual dry bulb temperature. This calculation is valid between

the range of 35 and 110 degrees F. In this manor, the humidity is controlled at the actual

temperature. The temperature controller will then control at the proper set point which will control

be an input to the humidity controller’s set point. Both loops need to be in automatic for this

method to work properly. Attempting to operate either loop in manual will result in an unstable

system.

If the user has employed a humidity instrument instead of a dew point temperature, the above

equation can be used to calculate the dew point signal except the relative humidity term in the

above equation is the normalized ( 0 to 1.0) relative humidity signal. Controlling dew point in

either case will result in decoupling the interaction and will result in more stable control.

A diagram of the resulting control system is shown below. The linearization function block is used

to compensate for the non-linear characteristics of the electrical heater. The low signal selector is

used to prevent setting the dew point temperature controller’s set point above the required set

point. The purpose of this control design is to control the humidity at the correct value

independent of the temperature. A change in heat will not affect the absolute moisture value. If a

disturbance to the system increases the moisture, the temperature will be reduced. This reduced

temperature will lower the dew point controller’s set point, which will lower the water flow to the

system. In this way the control technique will decouple the temperature and humidity interaction.


165

In the above case, it is assumed that any make up air be dry. Frequently this is not the case it

may be desired to control the temperature and humidity in an enclosure by re-circulating a portion

of the wet air in the system. Because the re-circulated air has high humidity, it is not possible to

have exact humidity control with that design. As a result, reset should not be used in the humidity

or dew point controller. An example of this is shown below.

By controlling inlet airflow and humidity by venting a portion of the outlet air and mixing the

remaining air with fresh air will result in an unstable control system. This is shown through the use

of a psychometric chart program from Akton Associates, Martinez, CA 94553. Because some of

the values are close to others, not all point numbers are displayed on the chart.

The results of two of these simulations is shown below:

Dry Bulb Temp SP

RH SP

Dry Bulb Temp

RH

f(RH,t)

Calculated Dew PointController SP

f(RH,t)

Calculated Dew PointController PV

Water Spray valve orpump

∆

P I

f(x)

Dew PointTemperature

Controller

Temperature Controller

Linearization

Electrical Heater

∆

P I

)5082.0/)))0.385/(3.7071exp(*6.20446*exp(((*5.9439.115 +−−= dbdp tRHt

Humidity Control by Dew Point Temperature

Equation in function block

<low

select


166

Process Report 1 W t rh v h td tw Vtot m ma mw lbm/lbm F % ft^3/lb Btu/lb F F ft^3/hr lbm/hr lbm/hr lbm/hr 1 0.0324 105* 65* 15.32 53.33 90.8 93.2 9936* 669.5 648.5 20.99 2 0.0338 98.6 82* 15.18 53.29 92.1 93.2* 9845* 670.5 648.5 21.93 3 0.0338 98.6* 82* 15.18 53.31 92.1 93.2 -466.7 -31.78 -30.74 -1.04* 4 0.0338 98.6* 82* 15.18 53.29 92.1 93.2 9378* 638.7 617.8 20.89 5 0.00387 50* 50* 13.23 8.48 32.1 41.8 405.8 30.8* 30.68 0.1186 6 0.0324 96.4* 84.1* 15.09 51.17 90.8 91.8 9784* 669.5 648.5 21.01 7 0.0324* 105* 65.1 15.32 53.36 90.8 93.2 9936* 669.5 648.5 21.01 Process Report 2 W t rh v h td tw Vtot m ma mw lbm/lbm F % ft^3/lb Btu/lb F F ft^3/hr lbm/hr lbm/hr lbm/hr 1 0.0324 105* 65* 15.32 53.33 90.8 93.2 9936* 669.5 648.5 20.99 2 0.0338 98.6 82* 15.18 53.29 92.1 93.2* 9845* 670.5 648.5 21.93 3 0.0338 98.6* 82* 15.18 53.31 92.1 93.2 -269.2 -18.34 -17.74 -0.6* 4 0.0338 98.6* 82* 15.18 53.29 92.1 93.2 9575* 652.1 630.8 21.33 5 0.00387 50* 50* 13.23 8.48 32.1 41.8 408.4 31* 30.88 0.1194 6 0.0324 96.4* 84.1* 15.09 51.2 90.8 91.8 9984* 683.1 661.7 21.45 7 0.0324* 105* 65.1 15.32 53.36 90.8 93.2 10140* 683.1 661.7 21.44

Air properties are shown as points on the chart. In the case of Process Report 1: Point 1 is the hot air entry point.

Point 2 is the air outlet point and assumes that the inlet conditions cause a water addition of 1.04 pounds per hour. Point 3 shows this water loss leaving the system. Any more or less water leaving would result in an imbalance of the drying conditions. Point 4 is the portion of the outlet air re circulated. Point 5 is shows the properties of the fresh air make up stream. Point 6 shows the fresh air makeup mixed with the re circulated air. Point 7 shows the properties of the heated air stream. Note that for all practical purposes, this system results in a balanced design for Process Report 1. For Process Report 2, assume that the inlet conditions will only release 0.6 pounds per hour to the air instead of the 1.04 pounds per hour in report 1. As previously stated, from a mass balance viewpoint, 0.6 pounds per our must leave the system. For this case, in order to obtain 105 degF air at 65% relative humidity, more total air flow is required. The control structure has conditional stability. There is only one stable point of operation. This is

quite different from a stable multivariable control system. In that case, there is structural stability.

In this case, the volume flow rate of the recycled air is defined because the exhausted air is

defined by the amount of moisture added to the air. This fixes the amount of fresh air mixed in the

inlet to obtain the desired humidity. The total mixed rate will most probably not be that set by the

airflow control, which will cause instability.

Even though this will occur, using this system will result in an oscillation of the inlet humidity. With

mild tuning settings, this oscillation should be small and not affect the process.


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Wet Bulb Temperature Regressions

If the wet bulb temperature is used to measure humidity instead of a humidity or dew point

sensor, the dew point temperature can be calculated from the wet bulb and dry bulb

temperatures. This can be accomplished by linear regression techniques. The relative humidity

can be calculated as:

ttwtwtttwrh **093.0*027.0*061.0*385.6*296.7969.62 22 −++−+= (4)

Where rh is the relative humidity, tw is the wet bulb temperature and t is the dry bulb temperature

in degrees F.

The dew point temperature can be calculated by modification of the exponential relationship as

shown in equation 3 from the previous section.

)5082.0/)))0.385/(3.7071exp(*6.20446*exp(((*5.9439.115 +−−= dbdp tRHt


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Chapter 20 Neural Networks

When neural networks came on the industrial scene in the 1980s, they were viewed as a

panacea for all the difficult on unsolvable control problems through the ages. However, when

these problems were undertaken, few successes occurred. This gave them a bad name, and they

still suffer the effects of this initial trial. The objective of this chapter is to give the reader a brief

understanding of what they are, how to developing a network as well as a perspective in the form

of an anatomy of an application.

There are many excellent references describing the detailed network structure and mathematics.

I strongly advise the user to study these.

Just what is a neural network?

Neural networks are computer programs that model the functionality of the brain. As with other

programs they have inputs and outputs however they process the data differently. They have an

analog to the operation of the fundamental cellular unit in the brain called the neuron. There are

estimates of as many as 100 billion neurons in the human brain. They are often less than 100

microns in diameter and have as many as 10,000 connections to other neurons. Each neuron has

an axon that acts as a wire for all connections to the other cell's neurons. The neurons have input

paths that are called dendrites that gather information from these axons. The connection between

the dendrites and the axon is called a synapse. The transmission of signals across the synapse is

chemical in nature and the magnitude of the signal depends on the amount of chemicals (called

neurotransmitter) released by the axon. Many drugs work on the basis of changing those natural

chemicals. The synapse combined with the processing of information in the neuron is how the

brain's memory process functions.

In computers or artificial neural networks, the neuron's analogy is called the processing element

or PE. The PE has many inputs either from input data or other PE elements. The inputs to the PE

are weighted similar to the synaptic strength and are summed. The result of this summation is

processed by a transfer function or a threshold function before it is passed to the output path. The

output path is then passed to other inputs or to an output node. These PEs are organized in

layers. These layers are grouped into input, output and hidden.

Neural networks are different from artificial intelligent or AI systems. AI systems are rule based

and as a result need a human expert to work with the system to input the rules. Neural networks

learn by processing the data without rules. This input process is called training. Examples of

known behavior are presented to the system and computations adjust its junction weights to the

required behavior. Obviously someone knowledgeable in the simulated process is necessary to

input the data. The compilation of this data is called learning or training instead of programming.

The network converges to a point. Testing this network against known data is called recall.

Because neural networks do not have rules i.e. not rule based, they cannot explain how they


169

arrived at a stated answer. There is a hidden danger in applying bad data to a system that has

learned good behavior; it can unlearn. It has no way of knowing that the data it is learning with is

bad or not as accurate or valid as it learned before.

Perhaps another way to describe a neural network is that it is a non-linear regression. Input data

values are applied to a series of functions. The weights of these functions are adjusted to

minimize the error between the network’s output value and the output data corresponding the

input data. Each data input and output point is scaled, that is it is normalized and centered on

zero with a standard deviation of one. This is done to insure that each data point is compared to

the other data points with the same reference.

Types of Networks and Uses

The topology of the inputs outputs, and PEs, their connection weights and learning rules are what

defines the network. The network is the collection of inputs, outputs and PEs. They are defined as

layers, the input and output layers are the points where data is entered and outputs leave. The

processing elements or PEs are layered in what is called hidden elements. These are layered

parallel to the input and output elements. The connections between the elements have varied

strength and form the analogy to the synapse strength in the brain. The network structure actually

describes a complex matrix mathematical equation. An example of the “network” is shown below

in figure 1. The u values are the scaled input values. Yhat is the scaled output value. The circles

are nodes. The loan node in the upper middle is a constant of one. Single constant values are

used to bias the results if necessary.


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Figure 1 Example of a Neural Network

The inner connecting lines correspond to weights or values that are multiplied by the input value

or the intermediate node value. Solid lines are positive while negative values are dotted. The sum

of these weights times the input values (or hidden values) are then processed through a transfer

function, commonly some exponential function. This function can even be a linear. In that case

the network becomes a linear regression. So for the above example, there are a total of 19

weights that have to be selected.

A never-ending amount of the literature on neural networks describes the mathematical way

these weights are selected, the number of network layers, as well as the type of function used for

each node. There is a great deal of similarity between training neural networks and optimization

problems. After all, the design of the neural network is an optimization problem, searching for the

best design to minimize the error between the actual value and the output.

The literature contains examples of many different applications in a wide variety of uses. Some

of these are electrocardiograms (EKG) noise cancellation, speech recognition, sonar signal

processing. There has even been an application of a stock market predictor.

In the process industries, one of the frequent applications is “soft sensors”. The concept is that if

many physical measurements about the process are known the value of an unmeasured variable


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can be computed with a neural network. This unmeasured value can be an analytical

measurement, such as the chemical analysis of a power plant stack.

There are many documented applications of successful soft sensor applications. The analytical

instrument is rented, installed on the plant stack. Next a large amount of data is taken over

several operational conditions. This data is then used to develop and train a neural network to

model the analytical instrument.

Back Propagation Network

Back propagation is a calculation method made to select the size of the weights in the network. It

is just one of several, but the one frequently described in control literature for network training.

This network works on the basis of updating the weights between the inputs, PEs and outputs by

the error; the difference between the output of the network and the desired output. It assumes

that all PEs are responsible for the error. This error is then propagated backward through the

network and new weights are calculated. There can be several hidden layers, but in most cases

one or two are used.

A summary of the calculations is presented here. Detailed discussion is available in several of the

sources in the bibliography.

The output of an element x in layer s with weight w is given the sum of the input elements:

∑ == − )())*(( 1 IfUWfX SSS

Where s-1 is the output of the layer before s. I is the input to the PE. The PE processes the input

to some function such as a hyperbolic tangent:

1)*2exp(21)(

+−=

xxf

Processing the changes in weights depends on a global error E:

∑ −= 2)(*5.0 odE

Where d is the desired output and o the actual output.

The error passed back through the network at a particular element is:

)()(

IdEde −=

Where d is the partial derivative.

The new weight of each PE is calculated as:


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)(*)**(][][ WdeltaaxelcoefoldWnewW ++=

Where lcoef is the learning coefficient for that particular element, delta(W) is the past change in

weight, and a is an acceleration term. a and lcoef are values less then one.

When designing these networks using back propagation method, the size of the step taken to get

to the minimum point is important. If it is too large, the network will not find the lowest error point.

It is too small, the search will take a very long time to execute.

There are several variations to this network. One is to implement different error function. Another

is to use different transfer functions within the PEs. These are hyperbolic tangent; tanH and the

sin function. There are several different learning rules that can be selected. The delta rule is

based on reducing the error of the net's output based on the desired output by variation of the

input weights as just described. Hebbian learning rule works on the basis that the input weight is

increased if that input produces the desired output. This is analogous to how the brain learns.

While I can find no reference to this in the literature, it appears that the delta rule with

acceleration method is similar to the Wegstein method used to solve recycle problems in

chemical engineering problems.

Other Learning Methods

One of the most frequent methods to “train”, another way to say regress, a neural network, is the

Marquardt method. This method makes use of two other methods to optimize data sets, the

steepest descent and the Newton method. Both these methods are considered classical

mathematical methods for data regression and optimization.

The steepest decent method uses the first order derivative of the transfer function to determine

the direction to move.

The Newton method uses the second derivative function to calculate the change in weights.

The Marquardt method takes advantage of both these methods. The farther away the solution is

from the solution the steepest decent method will perform fastest. Yet when the weights are

closest to the point, the Newton method will approach the solution the fastest. Marquardt’s

method computes the change in weight values based on a combination of these factors.

Using both these methods for neural network training in concert, Marquardt method will compute

the network much faster than the back propagation method.

Marquardt is mentioned in many texts on design optimization. The author recommends the reader

to become familiar with the Marquardt method if they will be involved in any optimization

problems.

Network Pruning

The use of a minimum amount of weights to describe a functional relationship is the same

principal that applies to neural networks as it does to linear regression techniques. This concept


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should definitely be considered if the data set is small. If a large network is used to train a small

data set, the network just “learns” the data set and not the underlying mathematical relationship.

In neural network lexicon this is called “over training”.

Pruning methods start with a trained network and remove a weight and retrain the remaining

network, usually with a second data set that is different than the first set. The pruned and

retrained network is then checks the change in error due to removed weight. This sequence is

repeated until the error begins to increase, at which time the pruning algorithm stops.

I recommend that pruning be done on all data sets taken from experimental data. For networks

derived from computational methods, that is where a neural network is used to describe the

results form a complex simulation or calculation, pruning may not reduce the size of the network

since all input variables are used to define the network.

Network Development

Just how do you go about developing a network?

The first step is to organize the data, usually in an EXCEL spreadsheet. I then visually remove

entries that have empty data variables. Next I check the minimum, maximum and mean of each

data variable. It is important to train the network with the data set that contains the full range of

each variable. The network will not be accurate if the tested variables lay outside the training data

envelope.

One of the main points of opposition is that they dismiss known first principal methods. This

statement is true when considering the network itself, which is a mathematical relationship that

would precisely resemble the scientifically derived equations only by accident. However the user

should consider known principals when selecting the inputs to the network. Do not use variables

that contain redundant information. As an example, assume the user is developing a network to

model a drying process of a complex solid. Input variables such as air temperature and humidity

should be incorporated, as they are logical variables that are known to affect the drying process.

Adding wet bulb temperature as an input would serve no useful purpose since the wet bulb

temperature has a known relationship to the air temperature and humidity.

Once all the data have been checked and measured separate the data in two or three groups. I

use two groups if the data set is small compared to size of the network. Three sets are generally

used if you use one of the pruning algorithms.

One set, the largest, perhaps two-thirds to three-quarters the size of all the data, is used to train

the network. The other two sets are used to test and prune the network.

It is very important that the data points in test sets are within the values used to train the network. The training set must contain the minimum and maximum points! Before I begin the training, I check the population of the data variables. This can be accomplished

by plotting a histogram for each input variable over the trained set. If too many data points are the


174

same, the network will do a great job learning that one point. This is because the least error

squared is weighted heavily at the one point, repeated many times.

Next each data input and output point is scaled, that is it is normalized and centered on zero with

a standard deviation of one. This is done to insure that each data point is compared to the other

data points with the same reference. This is true on matter what algorithm is used to train the

network.

Rule one in applying neural networks is a simple one. Develop a linear regression first. In many

applications, the linear relationship will produce a better correlation that a neural network. One

can easily test this by using a simple regression equation of the data and examining the

correlation coefficient.

If the linear relationship does not produce a good fit, then a neural network should be developed.

For large data sets with many inputs, I generally use the back propagation algorithm. If the data is

taken from a simulation or a small data set, I use the Marquardt algorithm.

Another problem that can prevent the network from providing a reasonable relationship is the

inclusion of an outlier in the data set. The training including outliers will force the network to a

point not properly representing the behavior.

One technique I use to remove the outlier is to provide a “reality check” part way through the

training. This should be done about one third into the training iterations. The check is to examine

the residuals, or differences in error between the training results and the actual data. Data points

are removed from the data set if they are outside some bound, usually three standard deviations.

I personally believe this is important for large data sets, several thousand points or more, of

experimental data. Manually generated data numbers can frequently be entered wrong. Some

data points are abnormal for an infinite number of reasons. Within some uses of statistics, the

outliers become a major concern. Drug discovery is very interested in outliers. Outliers are

studied more intensively that the normal cases. For industrial applications I do not believe there

is a problem with discarding outliers from a training set. Concept can be used for linear

regression techniques also.

Once the training is done, I check the network with the test data. If the network appears

reasonable it should be pruned if there is enough data points to do this if there are an excessive

number of weights.

The Anatomy of a Neural Network

A given laboratory process uses a non-specific analyzer to analyze the concentration of one of

the impurities. For high values of the impurity, a simple graph was used to correlate the

instrument signal to the concentration. However at lower concentrations, this relationship did not

correlate. Because the process is very complex it was postulated that a neural network could be

developed to improve the correlation by adding other process input signals, such as temperature,


175

pressure, level flow rates etc. together with the analyzer signal to develop the model. This

example is an example of a “soft sensor” application.

In this particular case the number of data points was limited. The data was separated into two

groups, a training set and a test set. This training data set consists of 137 entries while the test

set consisted of only 8 data entries. There were 5 process data points plus a constant to make a

total of 6 input points to the network. The output is the impurity concentration in parts per million

exiting the process. The test set was not part of the training data set in order to preserve the

validity of the test. The data points were recorded when the process reached steady state. This is

very important if when the network is used to train a dynamic system, otherwise historical data

should also be included, which can result in a large model.

The data was regressed to a single hidden layer hyperbolic nodes neural network using the

Levenberg-Marquardt method. The data was regressed using an algorithm available over the

Internet and written in MATLAB .

Figure 2 shows the test result of the first regression and figure 3 shows the result of the training

set. The initial training gave poor results because there were two points where the impurity

analysis was zero. These points were deleted from the data set. While the results from that set

appear to be good, R-squared over 0.9, the network was over trained that explains the poor

performance in estimating the high concentration. Figure 4 shows the diagram of the network,

consisting of 28 weights. This is far to many weights for such a small data set.

An algorithm provided in the neural network package that "prunes" the network was then used on

the first network. This method trims the size of the network and tests it against both the training

and test set to obtain the best fit. The results of this pruning session are shown in figures 5, 6 and

7. The network did have difficulty determining the exact concentration at very high levels. This is

because there are not many points at this level to train. The final algorithm only uses the non-

specific analyzer signal and one other process signal. The other node is a constant. A way to

obtain the confidence of the network is to prepare an EXCEL spreadsheet that performs the

same calculation as the neural network. This way the user can input several “what if” scenarios

and observe the behavior.

In actual practice, once the users began to be aware of the effect of the other signal, they

recalibrated the non-specific analyzer. This required the data gathered after the calibration

change could not be combined with the old data. When the new data was analyzed, a simple

linear regression was used to calculate the impurity concentration. One way the old data may

have been used with the new data would be to introduce an input to the network –1 for the old

data and +1 for the new data. The network would be able to train with both sets.

Automatic Control Method

Caution should be exercised if this regression network is used to control the impurity

concentration in the process. This is because the other process signal is used as input in the


176

concentration equation. Before this signal is introduced to the regression equation, a series of

first order lags should be applied to the signal. These lags are equivalent to the residence time of

the equipment and the non-specific analyzer signal lag. The neural network impurity

concentration output would serve as the input to a controller. That controller's reset setting would

be equivalent to the total contributed lag of the process input lags. Shinskey describes this

technique for inferential moisture controls where the implied moisture is a calculation based on

the inlet temperature, which is manipulated to control the moisture. A diagram showing the

control function blocks is shown in figure 8.

Figure 2 Test Result of the First Regression


177

Figure 3 Training Set Results


178

Figure 4 Diagram of the Network


179

Figure 5 Test Data Results from Pruned Network


180

Figure 6 Pruned Network


181

Figure 7 Result of the Training Set with the Pruned Network


182

f(t) f(t) f(t)

∆Impurity Setpoint

f(x)

Neural Network

non-specific analyzersignal

Process Signal

P I

Manipulated Variable

Process Lags Instrument Lag

PI Controller,I term equal to three input lags

Impurity Controller Using Neural Network

Figure 8 Neural Network Connections to PI Controller

References:

B. Soucek, Neural and Concurrent Real-Time Systems, The Sixth Generation, New York, New

York: John Wiley & Sons, 1989

R. Colin Johnson, Chappel Brown, Cognizers Neural Networks and Machines That Think, New

York, New York: John Wiley & Sons, 1988

Steven F. Zornetzer, An Introduction to Neural and Electronic Networks, Academic Press,

Inc.,San Diego, CA., 1990

John Hertz, Anders Krogh, Richard G. Palmer, Introduction To The Theory of Neural

Computation, Redwood City, CA: Addison-Wesley,1991

Russell Eberhart, Roy W. Dobbins, Neural Network PC Tools; A Practical Guide, San Diego, CA.:

Academic Press, Inc.,1990


183

Neural Computing,Reference Guide, Using NWorks, NeuralWare, Inc. Pittsburgh, PA, 1991

(Technical Manuals With NeuralWare Explorer Program)

Eugene L. Zurch, Data Acquisition and Conversion Handbook, Mansfield, MA: Datel Intersil, 1979

Ramchandran, S; Rhinehart, R. R., "Do neural networks offer something for you?" InTech

November 1995, p 59.

MATLAB Neural Network Toolkit, Technical University of Denmark, Department of Automation,

1997.

Marquardt, Donald W., "An Algorithm For Least-Squared Estimation of Nonlinear Parameters", J.

Soc. Industrial Math. Vol. 11, No. 2, June, 1963.

Hassibi, B., Stork, D. G., "Second Order Derivatives for Neural Network Pruning: Optimal Brain

Surgeon", NIPS 5, Eds. S. J. Hansen et al., San Mateo, Morgan Kaufmann, 1993.

Shinskey, F. G., Energy Conservation Through Control, Academic Press, New York, 1978.

Reed, Russell D.; Marks II, Robert J., Neural Smithing, A Bradford Book, MIT Press, Cambridge,

Massachusetts, 1999.


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Chapter 21 Notes on Instrument Design

Introduction

This chapter presents some of the watch outs and problems I have experienced with instrument

design. There are many handbooks on instrument design that contain a variety of notes and

descriptions of various instrument. The following comments are referenced to the author’s

experiences.

Rule one – Make sure you know your process. Communicate this information accurately and

effectively to the manufacture or their representative. Remember they want to see you succeed

with their instrument just as much as you do. They do not want to sell you an instrument that is

not right for the application. They know if it doesn’t work you will be dissatisfied and not want to

use their instrument again. I have found that when I spend the time and effort to communicate the

process conditions to an instrument manufacture, I am rewarded for my efforts.

Following the installation instructions will also help with a successful startup. The author has

spent many nights in far away places simply following the instructions on startups where they

were not done in the first place.

Power and Current Sensors

Give consideration to the frequency response of current and power sensors. They will not read

accurately outside their advertised range. This becomes a problem when measuring the current

to adjustable speed drives. These drives vary the frequency to adjust the speed of the motor and

can operate outside the envelope of many current and voltage sensors. The typical frequency

range of these sensors is 47 to 63 Hz while the range of the adjustable drive may be 10 to 80 Hz.

A frequent application of these sensors is on pump motors to detect a no flow condition. For small

power motors, current sensors may not be sensitive to detect the no flow point. Electrical power is

proportional to the square of the applied voltage and as a result, the no load point can be difficult

to repeat. Another reason may be that the pump is too large for the application. In these cases, a

power sensor is required. Before installing a three-phase transmitting wattmeter, one should

consider the cost of installing two single-phase wattmeters. The circuit measures the current

through two legs and measures the voltage relative to a common phase, C phase as shown

below. This design may be cheaper to install.


185

MCT1

CT2

A phase

B phase

C phase

V1

V2

Two Single Phase Watt MetersMeasurement of Three Phase Circuit

The two-watt meters measure power of phase A and B relative to phase C.

Adjustable Speed Drives

There is a misconception with adjustable frequency drives that they provide better resolution than

control valves. This is not always the case. The digital to analog converter in the drive electronics

has a quantiziation error, which is proportional to the number of bits in the converter. An actual

application of this is shown below. The histogram shows effect of quanitization error. This plot has

two nodes because of the resolution on the circuitry.

The positive displacement pump curve has a slope of 0.1 gal/rpm flow. The motor synchronous

speed is 1800 rpm. The adjustable frequency AC drive specification has 514 frequency divisions

for the published resolution. The following MATLAB calculation shows this effect. resolution=514; f=60; Hz poles=2; speed_reducer=7.65; density=9.25; lb./gal The two nodes have peaks at: delta_mass=127.8-127.4; delta_mass delta_mass = 0.4000 delta_flow=delta_mass/density delta_flow = 0.0432 delta_speed_pump=delta_flow/0.1 delta_speed_pump = 0.4324 rpm delta_speed_motor=delta_speed_pump*speed_reducer delta_speed_motor = 3.3081 rpm Assume drive is calibrated for 0 to 60 Hz. Speed resolution is: sync_speed=f*60/poles;


186

sync_speed/resolution ans = 3.5019 rpm Which agrees with data histogram plot. Much better resolution could be accomplished with a

control valve with positioner and a centrifugal pump.

Histogram Of Flow Controlled by a Variable Speed Controller

Filled System Pressure Transmitters

Filled system diaphragm transmitters are used for corrosive and slurry applications. These

diaphragms are connected to the transmitter by capillary tubing. The whole volume is filled with a

liquid fill, usually a silicone or fluorinated chemical. This chemical must be compatible with the

process fluid. For oxygen or chlorine service, the fill must not contain any oil or oil based

chemicals. Consideration should be made to the internal displaced volume of the transmitter as

well as the diaphragm. Every pressure transmitter has some volume displacement, however

small. The diaphragm must be capable of flexing this volume. If the transmitter company

fabricates the filled system, they have most likely seen the problem. Teflon diaphragms flex more

and should be considered if the volume displacement is high, common on older transmitters.

Newly designed transmitters use silicon piezoelectric technology which require approx. 0.01 in3

displacement, rather than bourbon tube and bellows force balance methods which have volume

displacements, around 0.5 in3. An alternate is to fabricate a short length of pipe between the

instrument and the process filled with the chemical fill material, which would be inert to the


187

process material. Many years ago this is how standard brass tube instruments were used for

chemical service. Temperature differences between the high and low side capillary tube can

cause the instrument to read incorrectly.

Purge Pipe Level Transmitters

Perhaps the most common level transmitter is a purge pipe. This instrument makes use of a

differential pressure transmitter measuring the difference between the back pressure created

through a gas bubbling out of a pipe inserted in the tank and the tank’s head space.

Most of the problems with these instruments are as a result of improper installation. Many newer

types of level instruments, such as radar and ultrasonic, are used where purge instruments fail to

perform. Many of these installations are not necessary. Proper installation requires that:

The pipe, typically 1-inch schedule 40, must have a slot, or preferably several slots, at the end of

the pipe. The idea is to sparge or create small bubbles of gas at the end of the pipe. If a large

bubble occurs, the pipe will tend to plug because when the bubble collapses, the liquid enters the

inside of the pipe and solids build up there. An older instrument publication detailed a short length

of a larger diameter pipe at the end of the purge pipe with several ¼-inch slots.

The gas flow should be flow controlled to the pipe. This should be done with a constant flow

controller or regulator rather than a needle valve. Without a flow controller, the needle valve will

act as the only restriction and as the level increases, the flow will be reduced. Make sure the flow

regulator can compensate for variable downstream pressure variations. This is what will be

measured.

For aqueous slurry applications, a dry purge gas will cause caking across the end of the purge

pipe. This is because the gas will dry out the slurry at that point. One way to prevent this is to

purge a small quantity of water and mix it in with the purge gas. The moist gas will prevent the

caking.

Placement of the low-pressure port is important too. It must measure the head space and not the

outlet pressure piping. Frequently the off gas line pressure is made because no nozzles are

available on the tank. This example shows the problem with this method. Assume a 6-inch

schedule 10 pipe with a vapor flowing at 100 feet per second outlet velocity. A sudden contraction

is assumed to be the only restriction.

From the CRANE manual: Y=1; d=6.357; K=0.78; V=5; vel=100; A=0.2204; w=vel*A/V

w = 4.4080 dP=27.67*K*V*(w/(0.525*Y*(d^2)))^2 dP = 4.6583 inches of water This difference is enough to cause false readings, premature alarms and interlock trips.


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Temperature Measurement

Elements: For most process measurements, RTD (Resistance Temperature Detector) or TC

(Thermocouples) elements are used. These are installed with thermowells and mounted on

process vessels or piping. In general, thermocouples are more rugged and less accurate than

RTD elements. An ANSI standard details thermocouples and their errors.

Thermowells: Thermal elements of both types use thermowells to protect the element from the

process stream. Thermowells contribute the major time lag in the temperature control system, on

the order of minutes in some cases. To improve the heat transfer, the recommended bore of the

element is 0.260 inches for RTDs and 0.385 inches for thermocouples. Thermocouples are tip

sensitive, therefore important that the element be in contact with the bottom of the well, usually

spring loaded. RTD elements are stem sensitive and therefore they should be as close as

possible to the side of the well. Tapered or step down type thermowells improve response time. It

is generally practiced that the element and the well be purchased as a prefabricated assembly.

Thermocouples generally have a faster time constant than RTD elements, however newer

designed thin film RTDs have improved the response time.

Metal sheathed elements are a design of thermoelements that incorporate a thin walled metal

tube, less than ½-inch diameter, around the RTD or TC. These elements screw directly into a

pipefitting. These elements have rapid thermal response and little heat conduction error.

Errors: The errors resulting from installation effects accumulate in a square root of the sum of

squares of each error can reach five times the error of the element itself. A summary of these

errors is as follows:

Heat Conduction: Heat conduction is the error due to the temperature at the tip of the well being

different than the mounting surface, usually the ambient. Heat then travels through the well to the

ambient. This error is a function of the thermodynamic properties of the material measured as

well as the well construction. In general, the thinner the element, the more accurate the

measurement. An Excel spread sheet is included to show the conductive error with the dryer

elements in question. This spreadsheet also calculates the time constant. The well should be in a

free flowing stream and not coated with material.

Heat Radiation: In combustion heat sources, radiation error can contribute several degrees. For

combustion heat sources, it is best not to allow the element to be within direct sight of the flame.

Velocity Error: If the velocity becomes very high, approaching Mach one, the velocity causes an

increase in temperature due to compression heating.

Recommendations: A thermocouple transmitter acts as an electrical isolator as well as linearizes

the thermocouple signals and generates a control signal, 4 to 20 MA, to A/D (analog to digital)

converter. A transmitter should be used if the input accuracy of the thermocouple input is as poor

as specified in the control system’s documentation.

Single Point Ultrasonic Level Instruments


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Be sure to pay attention to the temperature when specifying these types of instruments. Many of

these use sensitive crystals to generate and detect the ultrasonic signal. It has been my

experience that sometimes the upper temperature limit may be lower than the normal process

operating temperature. I was once asked to investigate why one of these instruments failed. After

interviewing the operators I learned that it failed after the first time the probe sensed the level.

After consulting the instrument data sheet I also learned that the temperature was well above the

maximum specified temperature. The diaphragms are usually thin, so material of construction

sould be given extra consideration.

Pressure Transmitters

There are some notable application problems I have frequently observed with these instruments.

The first is over pressure due to transient pressure surges. Differential pressure transmitters

specify a static over pressure value which may be exceeded if the instrument is not piped

properly.

The second is the material of construction of the oil fill. If the instrument is used in an oxidizing

environment the liquid fill must not react with the process material. This reaction can cause an

internal process fire.

Other problems with differential pressure transmitters have been:

With filled systems the static pressure difference must take into account the density of the fill.

Make sure the oil fill will operate properly over the temperature range.

When measuring a vapor or gaseous and vapor mixture stream, mount the pressure transmitter

above the process connection. If the transmitter is mounted below the take off point the vapor

may condense in the sensing line. In many cases this additional head of condensed liquid is

greater than the maximum calibrated span of the instrument. In many cases it may requiring

mounting the transmitter on the next floor level. I have personally observed this problem in many

plants.


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An alternate way to avoid the problem is to purge the sensing line. Purge gasses are not well

accepted by environmentally conscious chemical engineers. Purge gasses are very often a

source of vapor losses and must be reported to the EPA as part of the permitting process. Some

companies prohibit the use of purge gasses and invent very cleaver ways to keep the level of

inerts low exiting the process.

Vacuum Applications

Instruments installed in vacuum applications should by piped with piping systems designed for

vacuum service. Certain types of compression tubing fittings only work under pressure and not

vacuum.

Electrical Noise

Instrument engineers frequently come across the problem of electrical noise in the instrument

control system. The following example is typical of the problem.

The problem occurred when attempting to start up a small humidity controlled dryer. Water was

pumped to a spray nozzle, the speed of the pump controlled the amount of water added. The

humidity probe had a dual sensor, temperature and humidity elements in one device. The sensor

used one of the newer capacitive polymer elements. A frequent problem with these elements is

should the element become saturated with water, the signal will hold its value for some time. In

several cases, the probe never dried out and was discarded.

The problem became evident when the motor speed increased; the humidity increased and finally

held at a steady value even though it was obvious that much more moisture had been added to

the air. A quick call the manufacture’s hot line advised me to move the sensor downstream and

avoid a sample directly in the spray path. This advice was tried and the sensor increased slowly

and then held value at some point after startup.

“Is there any other way this could happen?” Yes, there is. Electrical noise could cause the

instrument to read in error, or in severe cases, cause the signal to drive full scale in either

direction. I started up the system again and this time when the probe froze, I removed it from the

sample line and waved it in the air. The probe did not respond to ambient conditions. Then I shut

PressureTransmitter

Mount above the processconnection


191

the pump off and it responded correctly. The culprit was electrical noise from a very small

adjustable speed drive.

Electrical noise from adjustable speed drives is very common in industrial plants. Many

manufactures recommend that transformers be installed. The following instruction is taken from a

Rockwell Automation manual for a ¼ to 2 HP 115/230 VAC DC3E adjustable speed drive:

A good reference on proper wiring and shielding techniques appeared in the IEEE transactions

several years ago. I highly recommend it for your reference.

Klipec, Bruce E., “Reducing Electrical Noise in Instrument Circuits”, IEEE Transactions on

Industry and General Applications Vol. IGA-3, No. 2, March/April 1967.

Klipec’s recommendation is to use twisted shielded cable, use aluminum Mylar shields, run

instrument and power cables at right angles. Even in these times when good design practices are

taken by instrument and control manufactures, it still takes a vigilant effort on the part of a control

engineer it insure proper wiring techniques.

Sensor Placement

Where should I place process sensors?

Where sensors are placed relative to the process is very critical because it can effect the

dynamics. There are two dynamic effects, process dead time and process time constant. Sensors

should be placed so as to minimize these two effects.

Dead time is generally referenced to transportation time. There is dead time if the sensor is

located downstream of the process, which is transportation dead time. This could be as simple as

the time it takes for the process to flow to the sensor, or it could be a rather complex dead time as

is present in a stirred tank reactor. The sensor should be placed as close to the process as

possible. This is not a hard fast rule; there are times that this may be a poor location if the sensor

would not represent the true reading because of interference. In a large tank, the sensor should

be located close to the heating element. This is to minimize overshoot due to the long time

constant.

Time constant is the first order effect, as an example volume divided by flow. This is also called

lag. There is some misunderstanding within the process community about these terms. In

general, lag can be controlled easier than dead time; it is best to minimize process lag so that the

dynamics will be faster. However, if the process has a lot of dead time, introduction of process lag

will actually help the process. An example of this is pH control. There the ratio of dead time to


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time constant should be 0.05. So if the dead time is excessive, one way to improve the control is

to increase the lag. This frequently results in a larger tank; a major problem for control engineers

is convincing process engineers that a larger tank is necessary for better control. What they need

to educate their coworkers about is this important ratio.

How can I begin to understand this concept?

To begin, think of the process at a steady state condition. Most engineers don't have a problem

with this. If they do, they usually have left the profession some time ago and went into something

else. I knew a chemical engineer that became a lawyer because they said they just couldn't put it

all together. Once you understand this, then ask yourself the question; "What if variable (flow,

temperature, catalyst activity etc.) increased by 5%?" How would the process behave? How long

before the sensor will measure the effect? How long will it take the process to see the effect of

the new plus 5% value? Sometimes these answers require the solution of; I hate to say it but

differential equations. But usually the process behaves like a first order or exponential

relationship. Many processes have several first orders involved. Multiple first orders introduce that

dreaded dead time again. As a general rule, for continuous processes, try to control the product

leaving a process rather than the whole process. As an example, control the outlet composition of

a reactor by controlling the composition in the stream leaving the reactor rather than in the

reactor. If you can introduce the controlling stream in a circulating system, this will reduce the

process lag. This may not be possible because the dynamics of the process dictate that you need

the reactants in contact for a certain time, residence time or time constant. For dilution systems

and temperature, it is better to control the outlet stream in an inline method. The idea is to

engineer the process with as little dead time and time constant as possible. Life would be great if

all loops behaved like flow loops. You have the ability to make that goal a reality with proper

sensor placement.

References:

American National Standard for Temperature Measurement Thermocouples ANSI - MC96.1-19xx, Instrument Society of America, ThermoElectric Co Technical Reference Richmond, D. W. "Selecting Thermowells for Accuracy and Endurance." InTech, February, 1980 Klipec, Bruce E., “Reducing Electrical Noise in Instrument Circuits”, IEEE Transactions on Industry and General Applications Vol. IGA-3, No. 2, March/April 1967.


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Chapter 22 Human Relations in Engineering

In this section, I will not quote any human behavior psychologists or any academic figures as I

have done before. This is my own experience on human behavior in the engineering workplace.

Work the problem, not the people.

This quote embodies a very important principal, where should you place your energy and efforts?

There are only 24 hours in one day and the average human consumes 3 k calories during that

day. So how are you going to expend all that energy, in working the problem or finding fault and

trying to build a case to support subverting your non-performing coworker? So engineer X never

gives you the right information or you always have to do some extra legwork? Just remember that

management could care less about it, they just want the job done and don’t want to listen to "As

the World Turns". If you find that, during some project, some one upset you a lot, just walk it off,

and work around it. Remember the objective is to complete the job on time and under budget and

even if you complain, you will still have to do the work anyway. Who else do they have to do the

work?

Remember that there are two types of people on the job, those who are part of the problem and

those who are part of the solution. There is no in between. You always want to be part of the

solution.

Culture

All companies have a culture. They don't publish a book of culture, but they have one. It is the

unwritten rules, the "soft issues". In my experience, more people have lost their jobs because of

violating the "soft issues" than breaking the obvious rules. Just try to cross one of these cultural

beliefs and you soon will run into more resistance than a brick wall. They will fire you before they

change their culture.

In this country we embrace diversity, yet we contradict this when someone form some particular

background conducts him or herself in such a way that is counter to the company culture. What

companies mean to say is that they accept other minorities as long as they conform to their

culture. What is that culture? The culture is ruthless capitalism and a high work ethic. The

company could care less about your ethnic background. It cares that it can get the most value

from your work. Cost and schedule are usually more important than elevating of technology.

Markets are capital driven these days and no one is interested in building the future. Management

only has a quarter-to-quarter mentality.

Every company has its sacred cows. Never try to change the cows or kill the cows.

Then when and how should I pick my battles?

Pick your battles very carefully, one at a time. Always make your boss look good. Convince him

that your idea is good, that is the first step. Never try to sell anything your boss doesn’t like. As an

example, suppose you want to change a process from batch to continuous operation. You know


194

this is a major undertaking. You need to sell the idea by simulating why continuous controls are

better. Compare the operational errors. Begin to develop alliances and sell your ideas to others,

one engineer at a time. How was Rome built? One brick at a time. Changing technology takes

time and cannot be done by one person. You absolutely must build alliances. If you can work with

someone from the plant, take some of their thoughts in the concept, they begin to take ownership

and you will find you have the best sales person you need. Not invented here (NIH) factors are

real and in some cultures can never be overcome. Fold up your tent and move on. There are

some sights that view anything from the outside their organization is useless.

Warm Bunnies to Stroke

Frequently a plant or engineering group will request something that you think may not be

required, maybe useless or perhaps not very productive. This might be some on line analytical

instrument, a new type of control system etc. Rather than fight them on this, it might be best for

you to just cave in and let them have their warm bunny to stroke. This extra cost will help the

whole project because they will feel more involved. Plus you can use this as a bargaining chip for

future favors. There is a watch out. They may actually spend all their time on the bunny and loose

sight of the total picture, failing to see the forest through the trees.

Bile Venting

Occasionally you may find someone from another organization that will be very upset that you

were even born. They will carry on about your family as well as some past wrong that your plant

or organization did. Many times the incident happened years ago. Do not try to interrupt them. Let

them vent the bile. View this as a rupture disk on a tank. You have to let it go. After the incident,

talk calmly and assure the individual that you support him, are interested in his viewpoint and

welcome his opinion. But you must remain firm that you will remain on the project and that is

beyond the control of both of you.

Empowerment

Forget it, you are not empowered to do what you want rather you are empowered to do what they

think you should do. If you want to test the empowerment issue, just try to do something relating

to money. Money is the root of it all. The test of empowerment is just how much authority you

have when it comes to financial decisions. You will find you don't have much unless you own the

company. So don't push empowerment issue, even if they want you to. Management tells you

that you are empowered to make you feel important so you will be a more productive worker.

Professional Engineering License

Should I take the time and expend the energy to get my PE?


195

Yes. You are the only one looking out for your carrier. Don’t think the company is, not in this day

and age. You alone are responsible for it. One of the best ways to improve your standing in our

profession is the PE. I know it is not emphasized in some companies, but it is in other

organizations. Think of it this way: There are two engineers interviewing for the same job. Both

have the same experience and educational background but one has the PE. The PE will usually

get the job because it shows professionalism. I recommend that an engineer obtain their PE

before they even think of graduate school.

On a related matter, I recommend that engineers spend some time in some capacity with their

professional society. This might be in a membership campaign. I worked in ISA as a program

coordinator many years ago. I believe this is your duty and obligation to your profession. I don’t

believe that you should be a society groupie, but everybody should volunteer some of their time

to their professional society.

Conventional Wisdom

This term is used frequently in the engineering profession. When a new project is developed, the

engineers will frequently estimate the task at hand based on “conventional wisdom”. I worked for

a large engineering organization whose estimating department always estimated a project based

on an “ideal project”. When I asked them which project that was, they told me that an ideal project

never existed. This was another way of saying that conventional wisdom was used to estimate

the costs.

When a problem occurs in a plant that has run for several years, the operational management will

frequently say that conventional wisdom says that the problem is such and such.

Conventional wisdom is also considered experience or heavily influenced by experience.

Management is usually not interested in conventional wisdom. I highly recommend that you not

use this term with management. It is my experience that they do not like the term and will

challenge you on its use of it. If you make a simplifying assumption based on experience, explain

what that is and why it should be done that way. An engineer should always make a decision if

the design can follow past practices or standards. Conventional wisdom is not a substitute for

good design or operational technique. If you are asked a question you don’t know the answer, tell

them you do not know the answer. Do not try to give a conventional wisdom answer. Admitting

you don’t know is not wrong, just smart on your part. No one is expected to be a storehouse of all

knowledge.

Production Engineer's Rule One

The number one rule for any production engineer, or anyone involved in plant operations is:

Never show a capacity increase without a capital expenditure. Why should I do that? I have a great idea that will cost nothing!


196

Because if you increase capacity without any money spent, the next year your management will

expect the same level of performance. You may not be able to do a repeat performance and this

will hurt your future. They will be even more disappointed with this than if you just ran the unit at

design rate in the first place. Supermen and water walkers remind me of the fireworks you see on

the fourth of July, a big flash and noise, then nothing but darkness. Sustained performance is

what is required for your personal growth. Never think that you can "get there" with one good

assignment. It takes many successes to prove your worth to management. One swallow doesn't

make a summer. And politics always prevents many good people from getting noticed.

Advice to Promising Engineers

I cannot emphasize the importance of a well-rounded primary education. When I applied to MIT

they told me I had too many technical courses and that students would be better off with

a general liberal arts background. They would make engineers of them. When I started my

freshman year at University of Missouri, Rolla my first EE professor told us English was our most

important first semester course. No matter what assignment you may have in the future,

communications is necessary. A well-rounded education is required to be able to communicate

with the outside world. Always remember that.

The Future is Now

This is a chapter title from a book by George Allen, the former coach of the Washington

Redskins. George thought that he could take a problem player and get him on the right track

faster than he could build up a squad over time. As an aside, he thought that the player wanted

recognition as much as money. Boy was he wrong in this day and age!

In my professional life of over thirty years in various organizations, I have been exposed to all

sorts of goals, vision statements, six sigma, 5 and 10-year plans etc. What I have observed about

management and these programs is the following:

No major change in any organization can be made from within. This is because the organization

cannot usually see itself outside its own box. It will tend to engineer the effect rather than the

cause. As an example, assume the plant has continually had a problem with a fouled heat

exchanger. When asked to fix the problem it will go through some sort of Kepner-Tregoe problem

analysis and come to some solution. This solution frequently has such items as profiling the

temperature control pattern, shocking the tubes etc. But it has been my experience that the team

fails to ask itself if the exchanger is needed in the first place. They just miss this because, after

all, the problem is the exchanger fouling, right? Wrong. The problem is the costs associated with

the fouled exchanger, repair costs, downtime etc.

Vision statements, 5 and 10 year plans are frequently made, sometimes at great expense to the

company, are detrimental to getting immediate results. I believe that plans and statements such

as these get in the way of picking the key problems in a unit that can usually yield payouts in less


197

than a year. These plans take valuable time away from the trained personal needed to solve the

immediate problems, where the quickest payout occurs. Instead they are busy attending

meetings about the company plan.

I believe in the chapter title, the future is now. I believe that with the correct process controls in

place, using SPC and sampling schedules correctly, any production unit in the US today can gain

4% improvement in cost of goods with little to no capital investment. Time after time I have seen

too many controls operating improperly and know this is true. Typical Example: Once I had a

problem column in Texas. The column pressures and temperatures were cycling. I made a

telephone call to a company column expert. After about 30 minutes, he recommended a very

simple configuration change that cut the cycling down. I was later told that that was worth about

$10,000 per year. That was 1980s money. Just remember, you do need some expenditure to

gain the recognition.

If you fail to take stock of the present problems, there will not be a tomorrow.

References:

Allen, George, Strategies for Winning, New York, New York: McGraw-Hill, 1990.

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