Chap 05 Marlin 2002

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CHAPTER 5 : TYPICAL PROCESS

SYSTEMS

When I complete this chapter, I want to be

able to do the following.

Predict output for typical inputs forcommon dynamic systems

Derive the dynamics for important

structures of simple dynamic systems

Recognize the strong effects on process

dynamics caused by process structures

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Outline of the lesson.

Common simple dynamic systems

- First order -Second order- Dead time - (Non) Self-regulatory

Important structures of simple systems

- Series - Parallel- Recycle - Staged

Workshop


SYSTEMS

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SIMPLE PROCESS SYSTEMS: 1st ORDER

The basic equation is:

)t(XK)t(Ydt

)t(dY=+

0 20 40 60 80 100 120

0.8

1

1.2

1.4

1.6

1.8

time

tank

concentration

0 20 40 60 80 100 1200.5

1

1.5

2

time

inletconcentration

Maximum

slope at

t=0

Output changes immediately

Output is smooth, monotonic curve

At steady state

Y = K X

63% of steady-state CA

X = Step in inlet variable

Would this beeasy/difficult to

control?

K = s-s gain

= time constant

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SIMPLE PROCESS SYSTEMS: 1st ORDER

These are simplefirst order systems

from several

engineering

disciplines.

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SIMPLE PROCESS SYSTEMS: 2nd ORDER

The basic equation is:

)()()(

2)(

2

22 tXKtY

dt

tdY

dt

tYd=++

K = s-s gain , = time constant , = damping factor

0 10 20 30 40 50 60 70 800

0.2

0.4

0.6

0.8

1

Time

C

ontrolledVariable

0 10 20 30 40 50 60 70 800

0.2

0.4

0.6

0.8

1

Time

ManipulatedVariable

0 20 40 60 80 100 120 140 160 180 2000

0.5

1

1.5

Time

ControlledVariable

0 20 40 60 80 100 120 140 160 180 2000

0.2

0.4

0.6

0.8

1

Time

ManipulatedVariable

overdamped underdamped

Would this be

easy/difficult to

control?

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SIMPLE PROCESS SYSTEMS: 2nd ORDER

These are simple

second

order systems

from several

engineering

disciplines.

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SIMPLE PROCESS SYSTEMS: DEAD TIME

time

Xin

Xout

= dead time

Would this beeasy/difficult to

control?

)()(

)()(

sXesX

tXtX

in

s

out

inout

=

=

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SIMPLE PROCESS SYSTEMS: INTEGRATOR

pump valve

Level sensorLevel sensor

Liquid-filled

tank

Plants have many inventories whose flows in and out do

not depend on the inventory (when we apply no control

or manual correction).

These systems are often termed pure integrators

because they integrate the difference between in and outflows.

outin FFdt

dLA

dt

dV ==

)()(

)()(

LftF

LftF

out

in

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pump valve


Liquid-filled

tank

outin FFdt

dLA

dt

dV ==

Fout

Fin

Plot the level for this scenario

time

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pump valve


Liquid-filled

tank

outin FFdt

dLA

dt

dV ==

Fout

Fin

time

Level

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pump valve


Liquid-filled

tank

Non-self-regulatory variables

tend to drift far fromdesired values.

We must control these

variables.

Lets look ahead

to when we

apply control.

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STRUCTURES OF PROCESS SYSTEMS

T

NON-INTERACTING SERIES

The output from an elementdoes not influence the input to

the same element

Common example is tanks inseries with pumped flow

between

Block diagram as shown

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T


The output from an elementdoes not influence the input to

the same element

Common example is tanks inseries with pumped flow

between

Block diagram as shown

Gvalve(s) Gtank2(s)Gtank1(s) Gsensor(s)

v(s) F0(s) T1(s) T2(s) Tmeas(s)

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)()()( sGsXsY i

n

i==1

In general:

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)()()( sGsXsY i

n

i==1

In general:

With each

element a first

order system:

)()(

)(

11 +== s

K

sX

sY

i

in

i

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)()()( sGsXsY i

n

i==1

In general:

With each

element a first

order system:

)()(

)(

11 +== s

K

sX

sY

i

in

i

overall gain is

product of gains

no longer first order

system

slower than any

single element

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0 10 20 30 40 50 60 70-5

-4

-3

-2

-1

0

Time

Contro

lledVariable

0 10 20 30 40 50 60 700

2

4

6

8

10

Time

ManipulatedVariable

Step Response

Looks as though some

dead time occurs

Smooth, monotonic,

not first order Slower than any

element

K = (Ki)



0.10/(5s+1) 1/(5s+1)-1.2/(5s+1) 3.5/(5s+1)


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With each

element a first

order system

with dead time:

)()(

)( i

11 +

=

= s

eK

sX

sY

i

si

n

i

Guidelines on step response

Sigmoidal (S) shaped

t63% ( i + i) [not rigorous!] K = (Ki) [rigorous!]

Usually, some apparent dead

time occurs

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Class Exercise: Sketch the step response for the system

below.

= 2= 2

?

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Class Exercise: Sketch the step response for the system

below.

0 5 10 15 20 250

1

2

3

4

5DYNAMIC SIMULATION

Time

Controlle

dVariable

0 5 10 15 20 250

1

2

3

4

5

Time

ManipulatedVariable

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Class Exercise: Sketch the step response for each of the

systems below and compare the results.

Case 1

= 2 = 2 = 2 = 2

= 2 = 1 = 1= 2 & = 2

Case 2

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0 2 4 6 8 10 12 14 16 18 200

1

2

3

4

time

case1respons

es

0 2 4 6 8 10 12 14 16 18 200

1

2

3

4

time

case2respons

es

Two plants can have different intermediate variables and have

the same input-output behavior!

Step

Case1

Case2

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PARALLEL STRUCTURES result from more than one

causal path between the input and output. This can be a

flow split, but it can be from other process relationships.

G1(s)

G2(s)

X(s) Y(s)

A B C

Example process systems Block diagram

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PARALLEL STRUCTURES

G1(s)

G2(s)

X(s) Y(s)

))((

)(

)(

)(

11

1

21

3

++

+

= ss

sK

sX

sY p

If both elements are first order, the overall model is

Class exercise:

Derive this

transfer function

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PARALLEL STRUCTURES can experience complex

dynamics. Parameter is the zero in the transfer function.

G1(s)

G2(s)

X(s) Y(s)

0 1 2 3 4 5 6 7 8 9 10-0.5

0

0.5

1

1.5

time

outputvariable,Y

(t)

0

-2

1

2

3

4

-1

Which would

be difficult/easy

to control?

Sample step response at t=0

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PARALLEL STRUCTURE

Class exercise: Explain the dynamics of the outlet

temperature after a change to the flow ratio, with the totalflow rate constant.

T

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0 5 10 15 20 2589

90

91

92

93

time

m

ixingtemperature

0 5 10 15 20 250.4

0.5

0.6

0.7

time

fractionby-pass

0 5 10 15 20 2589

90

91

92

93

time

senoroutput

T

Why an overshoot?

PARALLEL STRUCTURES: Explain the dynamics of the

outlet temperature after a step change to the flow ratio.

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PARALLEL STRUCTURE


concentration after a step change to the solvent flow rate.

FA

CA0

V1CA1

V2CA2FS

CAS=0

reactant

solvent

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0 10 20 30 40 50 600.05

0.06

0.07

0.08

0.09

0.1

time

solventflow

0 10 20 30 40 50 600.39

0.4

0.41

0.42

0.43

tank2concentration

Why an inverse response?

PARALLEL STRUCTURE


concentration after a step change to the solvent flow rate.

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RECYCLE STRUCTURES result from recovery of

material and energy. They are essential for profitable

operation, but they strongly affect dynamics.

T0

T3

T4

Process example Block diagram

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RECYCLE STRUCTURES

GH1(s) GR(s)

GH2(s)

T0(s)

T1(s) T3(s)

T4(s)

T2(s)

)()(

)()(

)(

)(

sGsG

sGsG

sT

sT

HR

HR

2

1

10

4

=

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RECYCLE STRUCTURES

Class exercise: Determine the effect of recycle on the

dynamics of a chemical reactor (faster or slower?).

T0

T3

T4

Exothermic

reaction

feed/effluent

preheater

)/()(

/.)(

/.)(

1103

300

400

2

1

+=

=

=

ssG

KKsG

KKsG

R

H

H

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Class exercise: Determine the effect of recycle on the

dynamics of a chemical reactor (faster or slower?).

0 5 10 15 20 25 30 35 40 45 500

0.5

1

1.5

2

2.5

time

T

4withoutrecycle

T4 is a deviation variable

0 50 100 150 200 250 300 350 400 450 5000

5

10

15

20

25

time

T4

withrecycle

Without recycle,

faster and smaller

effect

With recycle, slower

and larger effect

Different

scales!

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STAGED STRUCTURES

FR

FV

xB

xD

Tray n

Liquid

Liquid Vapor

Vapor

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STAGED STRUCTURES

0 10 20 30 40 500.965

0.97

0.975

0.98

0.985

0.99

Time (min)

XD

(molfrac)

0 10 20 30 40 500.005

0.01

0.015

0.02

0.025

Time (min)

XB(molfrac)

0 10 20 30 40 508530

8530.5

8531

8531.5

8532

8532.5

Time (min)

R

(mol/min)

0 10 20 30 40 501.35

1.355

1.36

1.365

1.37x 10

4

Time (min)

V(mol/min)

Complex structure,

smooth dynamics

Steps because analyzer

provides new measurement

only every 2 mintes.

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OVERVIEW OF PROCESS SYSTEMS

Even simple elements can yield complex dynamics when

combined in typical process structures.

We can

Estimate the dynamic

response based on

elements and

structure

Recognize range of

effects possible

Apply analysis

methods to yield

dynamic model

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CHAPTER 5: PROCESS SYSTEMS WORKSHOP 1

Four systems experienced an impulse input at t=2. Explain what you can

learn about each system (dynamic model) from the figures below.

0 5 10 15 20 25 300

1

2

3

output

(a)

0 5 10 15 20 25 30-1

0

1

2

3

output

(b)

0 5 10 15 20 25 30-1

0

1

2

3

time

output

(c)

0 5 10 15 20 25 300

0.5

1

1.5

2

2.5

time

output

(d)

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Using the guidelines in this chapter, sketch the response of

the measured temperature below to a +5% step to the valve.

T

% openmin/m.

)s(v

)s(F)s(G valve30 10==

1250

21 3

0

1+

==s

min)/m/(K.

)s(F

)s(T)s(G tank1

1300

01

1

2

+==

s

KK

sT

sTsG

/.

)(

)()(tank2 110

01

2

+=

=

s

KK

sTsTsG measuredsensor

/.

)()()(

(Time in seconds)

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Sensors provide an estimate of the true process variablebecause the measurement is corrupted by errors.

Discuss sources of noise in a measurement.

Define the following terms for a sensor

- Accuracy- Reproducibility

Explain some process measurements needing (a) good

accuracy and (b) good reproducibility

Suggest an approach for operating a process when a key

material property (composition, etc.) cannot be

measured using an onstream analyzer.

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We are designing the following reactor with recycle. Wehave two choices for the conversion in the reactor. Will the

plant dynamics be affected by the selection?

Freshfeed

flow is

constant

Pure,

unreacted

feed

Pure

product

X = 50%

X = 95%

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SYSTEMS

When I complete this chapter, I want to be

able to do the following.

Predict output for typical inputs for common

dynamic systems

Derive the dynamics for important structures ofsimple dynamic systems

Recognize the strong effects on process dynamics

caused by process structures

Lots of improvement, but we need some more study!

Read the textbook

Review the notes, especially learning goals and workshop

Try out the self-study suggestions Naturally, well have an assignment!

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CHAPTER 5: LEARNING RESOURCES

SITE PC-EDUCATION WEB

- Instrumentation Notes

- Interactive Learning Module (Chapter 5)

- Tutorials (Chapter 5)

Software Laboratory- S_LOOP program

Textbook

- Chapter 18 on level modelling and control- Appendix I on parallel structures

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CHAPTER 5: SUGGESTIONS FOR SELF-STUDY

1. Extend textbook Figure 5.1 for new input functions

(additional rows): impulse and ramp.

2. Determine which of the systems in textbook Figure 5.3

can be underdamped.

3. Explain the shape of the amplitude ratio as frequencyincreases for each system in textbook Figure 5.1.

4. Discuss the similarity/dissimilarity between self

regulation and feedback.

5. Explain textbook Figure 5.5.

6. Discuss the similarity between recycle and feedback.

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CHAPTER 5: SUGGESTIONS FOR SELF-STUDY

7. Discuss how the dynamics of the typical process

elements and structures would affect our ability to

control a process. Think about driving an automobilewith each of the dynamics between the steering wheel

and the direction that the auto travels.

8. Formulate one question in each of three categories (T/F,multiple choice, and modelling) with solution and

exchange them with friends in your study group.

Chap 05 Marlin 2002

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