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ISA Saint Louis Short Course Dec 6-8, 2010
Exceptional Process Control Opportunities - An Interactive Exploration of Process Control Improvements - Day 1
Welcome
• Gregory K. McMillan – Greg is a retired Senior Fellow from Solutia/Monsanto and an ISA Fellow.
Presently, Greg contracts as a consultant in DeltaV R&D via CDI Process & Industrial. Greg received the ISA “Kermit Fischer Environmental” Award for pH control in 1991, the Control Magazine “Engineer of the Year” Award for the Process Industry in 1994, was inducted into the Control “Process Automation Hall of Fame” in 2001, was honored by InTech Magazine in 2003 as one of the most influential innovators in automation, and received the ISA Life Achievement Award in 2010. Greg is the author of numerous books on process control, his most recent being Essentials of Modern Measurements and Final Elements for the Process Industry. Greg has been the monthly “Control Talk” columnist for Control magazine since 2002. Greg’s expertise is available on the web site: http://www.modelingandcontrol.com/
Top Ten Things You Don’t Want to Hear in a Project Definition Meeting
• (10) I don’t want any smart instrumentation talking back to me• (9) Let’s study each loop to see if the valve really needs a positioner• (8) Lets slap an actuator on our piping valves and use them for control
valves• (7) We just need to make sure the control valve spec requires the
tightest shutoff• (6) What is the big deal about process control, we just have to set the
flow per the PFD• (5) Cascade control seems awfully complex• (4) The operators can tune the loops• (3) Let’s do the project for half the money in half the time• (2) Let’s go with packaged equipment and let the equipment supplier
select and design the automation system• (1) Let’s go out for bids and have purchasing pick the best deal
• “Without deadtime I would be out of a job”• Fundamentals
– A more descriptive name would be total loop deadtime. The loop deadtime is the amount of time for the start of a change to completely circle the control loop and end up at the point of origin. For example, an unmeasured disturbance cannot be corrected until the change is seen and the correction arrives in the process at the same point as the disturbance.
– Process deadtime offers a continuous train of values whereas digital devices and analyzers offer non continuous data values at discrete intervals, these delays add a phase shift and increase the ultimate period (decrease natural frequency) like process deadtime.
• Goals– Minimize delay (the loop cannot do anything until it sees and enacts change)
• Sources – Pure delay from process deadtimes and discontinuous updates
– Piping, duct, plug flow reactor, conveyor, extruder, spin-line, and sheet transportation delays (process deadtimes set by mechanical design - remaining delays set by automation system design)
– Digital device scan, update, reporting, and execution times (0.5T)– Analyzer sample processing and analysis cycle time (1.5T)– Sensitivity-resolution limits– Backlash-deadband
– Equivalent delay from lags– Mixing, column trays, dip tube size and location, heat transfer surfaces, and volumes in series (process
lags set by mechanical design - remaining lags set by automation system design)– Thermowells– Electrodes – Transmitter damping – Signal filters
(1) - Delay
Top Ten Concepts
• “Speed kills - (high speed processes and disturbances and low speed control systems can kill performance)”
• Fundamentals– The rate of change in 4 deadtime intervals is most important. By the end of 4 deadtimes,
the control loop should have completed most of its correction. Thus, the short cut tuning method (near-integrator) is consistent with performance objectives.
• Goals– Make control systems faster and make processes and disturbances slower
• Sources– Control system
– PID tuning settings (gain, reset, and rate)– Slewing rate of control valves and velocity limits of variable speed drives
– Disturbances– Steps - Batch operations, on-off control, manual actions, SIS, startups, and shutdowns– Oscillations - limit cycles, interactions, and excessively fast PID tuning– Ramps - reset action in PID
– Process– Degree of mixing in volumes due to agitation, boiling, mass transfer, diffusion, and migration
(2)- Speed
Top Ten Concepts
• “All is lost if nothing is gained”• Fundamentals
– Gain is the change in output for a change in input to any part of the control system. Thus there is a gain for the PID, valve, disturbance, process, and measurement. Knowing the disturbance gain (e.g. change in manipulated flow per change in disturbance) is important for sizing valves and feedforward control.
• Goals– Maximize control system gains (maximize control system reaction to change) and
minimize process and disturbance gains (minimize process reaction to change).• Sources
– PID controller gain – Inferential measurements (e.g. temperature change for composition change in distillation
column) – Slope of control valve or variable speed drive installed characteristic (inherent
characteristic & system loss curve)– Measurement calibration (100% / span). Important where accuracy is % of span– Process design– Attenuation by upstream volumes (can be estimated)– Attenuation by upstream PID loops (transfer of PV variability to controller output)
• For a discussion of unifying concepts check out Deminar #9 “Process Control Improvement Primer” Sept 8, 2010 Recording:http://modelingandcontrol.com/
(3) - Gain
Top Ten Concepts
(4) - Resonance
• “Don’t make things worse than they already are”• Fundamentals
– Oscillation period close to ultimate period can be amplified by feedback control
• Goals– Make oscillation period slower or control loop faster
• Sources– Control loops in series with similar loop deadtimes (e.g. multiple stage pH
control)
– Control loops in series with similar tuning and valve sticktion and backlash
– Day to night ambient changes to slow loops (e.g. column temperature control)
Top Ten Concepts
(4) - Resonance
Top Ten Concepts
1
UltimatePeriod
1
1FasterTuning
Log of Ratio ofclosed loop amplitudeto open loop amplitude
Log of ratio ofdisturbance periodto ultimate period
no attenuationof disturbances
resonance (amplification) of disturbances
amplitude ratio isproportional to ratio ofbreak frequency lag to
disturbance period
1
no better than manual worse than manual improving control
For all of you frequency response and Bode Plot Fans
(5) Attenuation
• “If you had a blend tank big enough you would not need control”• Fundamentals
– Attenuation increases as the volume of the blend tank increases and the ultimate period of the control loop decreases.
• Goals– Maximize attenuation by increasing volume and mixing and making loops faster
• Sources– Mixed volume size and degree of mixing
– Control loop speed
Top Ten Concepts
f
oof
tAA
2*
The attenuation of oscillations can be estimated from the expression of the Bode plot
equation for the attenuation of oscillations slower than the break frequency where (f) is the filter time constant, electrode or thermowell lag, or a mixed volume residence time
Equation is also useful for estimating original process oscillation amplitude from filtered oscillation amplitude to better know actual process variability
(measurement lags and filters provide a attenuated view of real world)
(5) Attenuation
Top Ten Concepts
(6) Sensitivity- Resolution
• “You cannot control what you cannot see”• Fundamentals
– Minimum change measured or manipulated - once past sensitivity limit full change is seen or used but resolution limit will quantize the change (stair step where the step size is the resolution limit). Both will cause a limit cycle if there is an integrator in the process or control system.
• Goals– Improve sensitivity and resolution
• Sources– In measurements, minimum change detected and communicated (e.g. sensor
threshold and wireless update trigger level) and quantized change (A/D & D/A)
– Minimum change that can be manipulated (e.g. valve stick-slip sensitivity and speed resolution)
Top Ten Concepts
(6) Sensitivity- Resolution
Top Ten Concepts
o
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ActualTransmitter Response
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1.00%
Sensitivity
(6) Sensitivity- Resolution
Top Ten Concepts
Digital Updates
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0 1 2 3 4 5 6 7 8 9 100.00%
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Resolution
(7) Hysteresis-Backlash
• “No problem if you don’t ever change direction”• Fundamentals
– Hysteresis is the bow in a response curve between full scale traverses in both directions. Normally much smaller and less disruptive than backlash
– Backlash (deadband) is minimum change measured or manipulated once the direction is changed - once past backlash-deadband limit you get full change
– Both Hysteresis and backlash will cause a limit cycle if there are 2 or more integrators in the process or control system.
• Goals– Minimize backlash and deadband
• Sources– Pneumatic instrument flappers, links, and levers (hopefully these are long gone)
– Rotary valve and damper links, connections, and shaft windup
– Variable speed drive setup parameter to eliminate hunting and chasing noise
Top Ten Concepts
(7) Hysteresis-Backlash
Top Ten Concepts
Digital Updates
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ActualTransmitter Response
TrueProcess Variable
0%
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Hysteresis
Hysteresis
(7) Hysteresis-Backlash
Top Ten Concepts
Backlash (Deadband)
Deadband is 5% - 50%without a positioner !
Deadband
Signal (%)
0
Stroke (%)
Digital positionerwill force valve
shut at 0% signal
Pneumatic positionerrequires a negative % signal to close valve
(8) Repeatability-Noise
• “The best thing you can do is not react to noise”• Fundamentals
– Noise is extraneous fluctuations in measured or manipulated variables
– Repeatability is difference in readings for same true value in same direction
– Often repeatability is confused with noise
• Goals– Minimize size and frequency of noise and do not transfer noise to process
• Sources– Noise
– Bubbles– Concentration and temperature non-uniformity from imperfect mixing– Electromagnetic interference (EMI)– Ground loops– Interferences (e.g. sodium ion on pH electrode)– Velocity profile non-uniformity – Velocity impact on pressure sensors
– Repeatability– Sensitivity and resolution
Top Ten Concepts
(8) Repeatability-Noise
Top Ten Concepts
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Repeatability
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0Actual
Transmitter Response
TrueProcess Variable
Official definition of repeatabilityobtained from calibration tests
(8) Repeatability-Noise
Top Ten Concepts
Pro
cess
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Repeatability
0
x
0 0 0 0 0 0 0 0 0 0
xx
xxx
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x x xActual
Transmitter Response
TrueProcess Variable
Practical definition of repeatabilityas seen on trend charts
(8) Repeatability-Noise
Top Ten Concepts
Noise as seen on trend charts
Pro
cess
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0 0 0 0 0 0 0 0 0 0 0x
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xxNoise
ActualTransmitter Response
TrueProcess Variable
• There is always an offset and drift, it is matter of size and consequence• Fundamentals
– The deviation of the peak in the distribution of actual values from true value
– Drift shows up as a slowly changing offset
• Goals– Minimize offset and nonlinearity by smart transmitters and sensor matching and
smart tuned digital positioners with accurate internal closure member feedback
• Sources– Manufacturing tolerance, degradation, de-calibration, and installation effects
(process and ambient conditions and installation methods and location)
(9) Offset-Drift
Top Ten Concepts
(9) Offset-Drift
Top Ten Concepts
0%
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Bias
ActualTransmitter Response
TrueProcess Variable
x
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x0
Offset (Bias)
(9) Offset-Drift
Top Ten Concepts
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xDrift = 1% per month
xxxxxx xxxx
Drift (Shifting Bias)
(10) Nonlinearity
• “Not a problem if the process is constant, but then again if the process is constant, you do not need a control system”
• Fundamentals– While normally associated with a process gain that is not constant, in a broader
concept, a nonlinear system occurs if a gain, time constant, or delay changes anywhere in the loop. All process control systems are nonlinear to some degree.
• Goals– Minimize nonlinearity by process and equipment design (e.g. reagents and heat
transfer coefficients), smart transmitters and sensor matching, valve selection, signal characterization, and adaptive control
• Sources– Control valve and variable speed drive installed characteristics (flat at high flows)– Process transportation delays (inversely proportional to flow)– Digital and analyzer delays (loop delay depends upon when change arrives in
discontinuous data value update interval)– Inferred measurement (conductivity or temperature vs. composition plot is a curve)– Logarithmic relationship (glass pH electrode and zirconium oxide oxygen probe)– Process time constants (proportional to volume and density)
Top Ten Concepts
(10) Nonlinearity
Top Ten Concepts
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Good Accuracy and Good Precision2-Sigma
Bias
2-SigmaTrue and
Measured Values
Fre
quen
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s
TrueValue
Measured Values
Good Accuracy and Poor Precision
2-Sigma 2-Sigma
Bias
True andMeasured
Values
True Value
Measured ValuesF
requ
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of
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Poor Accuracy and Good Precision2-Sigma
Bias
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Measured Values
True ValueMeasured
Values
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2-Sigma 2-Sigma
Bias
True andMeasured
Values
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Accuracy and PrecisionAccuracy and Precision
Top Ten Concepts
Time (seconds)
% Controlled Variable (CV) or
% Controller Output (CO)
CO
CV
o p2
Kp = CV CO
CV
CO
CV
Self-regulating processopen loop
negative feedback time constant
Self-regulating process gain (%/%)
Response to change in controller output with controller in manual
observed total loopdeadtime
oor
Maximum speedin 4 deadtimes
is critical speed
Self-Regulating Process Open Loop Response
Improving Dynamics
Time (seconds)o
Ki = { [ CV2 t2 ] CV1 t1 ] } CO
CO
ramp rate isCV1 t1
ramp rate isCV2 t2
CO
CV
Integrating process gain (%/sec/%)
Response to change in controller output with controller in manual% Controlled Variable (CV)
or% Controller Output (CO)
observed total loopdeadtime
Maximum speedin 4 deadtimes
is critical speed
Integrating Process Open Loop Response
Improving Dynamics
Response to change in controller output with controller in manual
o ’p2
Noise Band
Acceleration
CV
CO
CV
Kp = CV CO
Runaway process gain (%/%)
% Controlled Variable (CV) or
% Controller Output (CO)
Time (seconds)observed total loopdeadtime
runaway processopen loop
positive feedback time constant
For safety reasons, tests are terminated after 4 deadtimes
’oor
Maximum speedin 4 deadtimes
is critical speed
Runaway Process Open Loop Response
Improving Dynamics
CV change in controlled variable (%) CO change in controller output (%) Kc controller gain (dimensionless) Ki integrating process gain (%/sec/% or 1/sec) Kp process gain (dimensionless) also known as open loop gain DV = disturbance variable (engineering units) MV manipulated variable (engineering units) PV process variable (engineering units) t change in time (sec) tx execution or update time (sec) ototal loop dead time (sec) ffilter time constant or well mixed volume residence time (sec) mmeasurement time constant (sec) p2primary (large) self-regulating process time constant (sec) ’p2primary (large) runaway process time constant (sec) p1secondary (small) process time constant (sec) Ti integral (reset) time setting (sec/repeat) Td derivative (rate) time setting (sec) to oscillation period (sec) Lambda (closed loop time constant or arrest time) (sec) fLambda factor (ratio of closed to open loop time constant or arrest time)
Nomenclature
Improving Dynamics
Phase Shift () and Amplitude Ratio (B/A)
A B
time
phaseshift
oscillationperiod To
If the phase shift is -180o between the process input A and output B, then the total shift for a control loop is -360o and the output is in phase with the input (resonance) sincethere is a -180o from negative feedback (control error = set point – process variable).This point sets the ultimate gain and period that is important for controller tuning.
Improving Dynamics
For frequency response and Bode plot fans
Basis of First Order Approximation
=Tan-1() negative phase shift(as approaches infinity, approaches -90o phase shift)
t = (-360 To time shift
B 1AR = ---- = ----------------------- amplitude ratio A [1 + (] 1/2
Amplitude ratios are multiplicative (AR = AR1AR2) and phase shifts are additive ()asis of first order approx method where gains are multiplicative and dead times are additive
Improving Dynamics
For a self-regulating process
p1 p2 p2 Kpvp1
c1 m2 m2 m1 m1Kcvcc2
Kc Ti Td
Valve Process
Controller Measurement
Kmvvv
KLLL
Load Upset
CV
CO
MVPV
PID
Delay Lag
Delay Delay Delay
Delay
Delay
Delay
Lag Lag Lag
LagLagLag
Lag
Gain
Gain
Gain
Gain
LocalSet Point
DV
First Order Approximation: ov p1 p2 m1 m2 c
vp1m1m2c1 c2
(set by automation system design for flow, pressure, level, speed, surge, and static mixer pH control)
%
%
%
Delay <=> Dead TimeLag <=>Time Constant
For integrating processes: Ki = Kmv(Kpv / p2 ) Kcv
100% / span
Loop Block Diagram (First Order Approximation)
Hopefully p2 is the largest lag in the loop
Improving Dynamics
CV change in controlled variable (%) CO change in controller output (%) Kc controller gain (dimensionless) Ki integrating process gain (%/sec/% or 1/sec) Kp process gain (dimensionless) also known as open loop gain DV = disturbance variable (engineering units) MV manipulated variable (engineering units) PV process variable (engineering units) t change in time (sec) tx execution or update time (sec) ototal loop dead time (sec) ffilter time constant or well mixed volume residence time (sec) mmeasurement time constant (sec) p2primary (large) self-regulating process time constant (sec) ’p2primary (large) runaway process time constant (sec) p1secondary (small) process time constant (sec) Ti integral (reset) time setting (sec/repeat) Td derivative (rate) time setting (sec) to oscillation period (sec) Lambda (closed loop time constant or arrest time) (sec) fLambda factor (ratio of closed to open loop time constant or arrest time)
Nomenclature
Improving Dynamics
opo
ox EE
)(
opo
oi EE
)(
2
Peak error is proportional to the ratio of loop deadtime to 63% response time(Important to prevent SIS trips, relief device activation, surge prevention, and RCRA pH violations)
Integrated error is proportional to the ratio of loop deadtime squared to 63% response time(Important to minimize quantity of product off-spec and total energy and raw material use)
For a sensor lag (e.g. electrode or thermowell lag) or signal filter that is much largerthan the process time constant, the unfiltered actual process variable error can be
found from the equation for attenuation
Ultimate Limit to Loop Performance
Total loop deadtimethat is often set byautomation design
Largest lag in loopthat is ideally set bylarge process volume
Improving Dynamics
oL EeE Lo )1( /
Effect of load disturbance lag (L) on peak error can be estimated by replacing the open loop error with the exponential response of the disturbance during the loop deadtime
Disturbance Speed and Attenuation
For Ei (integrated error), use closed loop time constant instead of deadtime
Improving Dynamics
Effect of Disturbance Lag on Integrating Process
Periodic load disturbance time constant increased by factor of 10
Adaptive loop
Baseline loopAdaptive loop
Baseline loop
Primary reason why bioreactor control looptuning and performance for load upsets is anon issue!
Improving Dynamics
Accessing On-Demand and Adaptive Tuning
Click on magnifying glass to getdetail view of limits and tuning
Click on Duncan to get DeltaV Insight for “On-Demand” and “Adaptive” tuning
Improving Dynamics
Effect of Dynamics LabEffect of Dynamics Lab• Objective – Show the effect of deadtime on ultimate period and tuning
• Activities:1. Go to Main Display, select Single Loop Lab01, 2. Click on AC1-1 PID Faceplate and Click on magnifying glass icon to get Detail display 3. Click on Duncan icon for “Tune with Insight” and click on top tab “On Demand Tuning”4. Verify expert option is checked and click on “Test” for “On Demand Tuning”5. Note ultimate period and “Ziegler-Nichols - PI” tuning settings6. Update PID tuning settings and change mode from Explore to Run7. After run is finished, note metrics, and then click on any block in block diagram of loop8. Click on top tab for Process detail and increase Primary Delay from 1 to 5 sec9. Click on “Test” for “On Demand Tuning”10. Note ultimate period and “Ziegler-Nichols - PI” tuning settings11. Update PID tuning settings and change mode from Explore to Run12. After run is finished, note metrics, and decrease Primary Delay from 5 to 1 sec13. Click on top tab for Measurements detail and increase Delay from 0 to 4 sec14. Click on “Test” for “On Demand Tuning”15. Note ultimate period and “Ziegler-Nichols - PI” tuning settings16. Update PID tuning settings and change mode from Explore to Run17. After run is finished, note metrics, and decrease Measurement Delay from 4 to 0 sec18. Restore PID gain to 1.0 and reset time to 10 sec
Improving Dynamics
Top Ten Things Missing in University Courses on Process Control
• (10) Control valves with stick-slip and deadband• (9) Measurements with repeatability errors and turndown limits• (8) Volumes with variable mixing and transportation delays• (7) Process input load disturbance• (6) Control action (direct & reverse) & valve action (inc-open & inc-close)• (5) PID algorithms using percent • (4) PID structure, anti-reset windup, output limits, and dynamic reset• (3) Industry standards for function blocks and communication• (2) “Control Talk”• (1) My books
Improving Tuning - Part 1
Contribution of Each PID Mode
Improving Tuning - Part 1
• Proportional (P mode) - increase in gain increases P mode contribution– Provides an immediate reaction to magnitude of measurement change to minimize
peak error and integrated error for a disturbance– Too much gain action causes fast oscillations (close to ultimate period) and can make
noise and interactions worse– Provides an immediate reaction to magnitude of setpoint change for P action on Error to
minimize rise time (time to reach setpoint)– Too much gain causes falter in approach to setpoint
• Integral (I mode) - increase in reset time decreases I mode contribution– Provides a ramping reaction to error (SP-PV) to minimize integrated error if stable (since
error is hardly ever exactly zero, integral action is always ramping the controller output)– Too much integral action causes slow oscillations (slower than ultimate period)– Too much integral action causes an overshoot of setpoint (no sense of direction)
• Derivative (D mode) - increase in rate time increases D mode contribution– Provides an immediate reaction to rate of change of measurement change to minimize
peak error and integrated error for a disturbance– Too much rate action causes fast oscillations (faster than ultimate period) and can make
noise and interactions worse– Provides an immediate reaction to rate of change of setpoint change for D action on
Error to minimize rise time (time to reach setpoint)– Too much rate causes oscillation in approach to setpoint
Contribution of Each PID Mode
Improving Tuning - Part 1
CO2 = CO1
SP
seconds/repeatCO1
Time(seconds)
Signal (%)
0
kick fromproportional
mode
bump fromfiltered
derivativemode
repeat from integralmode
Contribution of Each PID Mode for a Step Change in the Set Point
( and )
SPPVIVP
52 48 ?
TC-100Reactor Temperature
steam valveopens
watervalveopens
50%
set point
temperature
time
PV
Should steam or water valve be open ?
Reset Gives Operations What They Want
Improving Tuning - Part 1
Open Loop Time Constant (controller in manual)
CO
Time(seconds)
Signal (%)
0 o
Dead Time (Time Delay)
p
Open Loop(process)
Time Constant (Time Lag)
CVSP
Controller is in Manual
Open LoopError Eo (%)
0.63Eo
Improving Tuning - Part 1
Closed Loop Time Constant (controller in auto)
CO
Time(seconds)
Signal (%)
0 o
Dead Time (Time Delay)
c
Closed Loop Time Constant
(Time Lag)Lambda ()
CV
SP
Controller is in Automatic
SP (%)
0.63SP
Improving Tuning - Part 1
Conversion of Signals for PID Algorithm
SensingElement
ControlValve
AOPIDSCLR
AI
SCLR
SCLR%
% %SUB
CVSP
%
CO OUT(e.u.)
ProcessEquipment
SmartTransmitterPV - Primary Variable
SV - Second Variable*TV - Third Variable*FV - Fourth Variable*
PV(e.u.)
PID
DCS
MV(e.u.)
The scaler block (SCLR) that convert between engineering units of application and % of scaleused in PID algorithm is embedded hidden part of the Proportional-Integral-Derivative block (PID)
Final Element
Measurement* - additional HART variables
PV(e.u.)
To compute controller tuning settings, the process variable and controller outputmust be converted to % of scale and time units of deadtimes and time constantsmust be same as time units of reset time and rate time settings!
Improving Tuning - Part 1
ocp
x EKK
E
)1(
1
ocp
fxii E
KK
tTE
Peak error decreases as the controller gain increases but is essentially the open loop error for systems when total deadtime >> process time constant
Integrated error decreases as the controller gain increases and reset time decreases but is essentially the open loop error multiplied by the reset time plus signal delays and lags for systems when total deadtime >> process time constant
Peak and integrated errors cannot be better than ultimate limit - The errors predictedby these equations for the PIDPlus and deadtime compensators cannot be better
than the ultimate limit set by the loop deadtime and process time constant
Practical Limit to Loop Performance
Open loop error forfastest and largestload disturbance
Improving Tuning - Part 1
)(5.0 oi
Slow tuning (large Lambda) creates an implied deadtime where the loop performsabout the same as a loop with fast tuning and an actual deadtime equal to the
implied deadtime (i)
Implied Deadtime from Slow Tuning
For most aggressive tuning Lambda is set equal to observed deadtime(implied deadtime is equal to observed deadtime)
Money spent on improving measurement and process dynamics(e.g. reducing measurement delays and process deadtimes)
will be wasted if the controller is not tuned faster to take advantage of the faster dynamics
You can prove most any point you want to make in a comparisonof control system performance, by how you tune the PID.Inventors of special algorithms as alternatives to the PID
naturally tend to tune the PID to prove their case. For example Ziegler-Nichols tuning is often used to show excessive
oscillations that could have be eliminated by cutting gain in half
Improving Tuning - Part 1
In this self-regulating process the original process delay (dead time) was 10 sec. Lambda was 20 sec and the sample time was set at 0, 5, 10, 20, 30, and 80 sec (Loops 1 - 6)
The loop integrated error increased slightly by 1%*sec for a sample time of 10 sec which corresponded to atotal deadtime (original process deadtime + 1/2 sample time) equal to the implied deadtime of 15 seconds.
http://www.modelingandcontrol.com/repository/AdvancedApplicationNote005.pdf
sample time = 0 sec
sample time = 5 sec
sample time = 10 sec
sample time = 20 sec
sample time = 30 sec
sample time = 80 sec
Effect depends on tuning, which leads to miss-guided generalities based on process dynamics
Effect of Implied Deadtime on Allowable Digital or Analyzer Delay
Improving Tuning - Part 1
Lambda Tuning for Self-Regulating ProcessesLambda Tuning for Self-Regulating Processes
CO
CVK p
)( opfp
ic K
TK
piT
Self-Regulation Process Gain:
Controller Gain
Controller Integral Time
pf Lambda (Closed Loop Time Constant)
Lambda tuning excels at coordinating loops for blending,fixing lower loop dynamics for model predictive control,
and reducing loop interaction and resonance
Improving Tuning - Part 1
Lambda Tuning for Integrating ProcessesLambda Tuning for Integrating Processes
Integrating Process Gain:
Controller Gain:
Controller Integral (Reset) Time:
Lambda (closed loop arrest time) is defined in terms of a Lambda factor (f):
if K/ Closed loop arrest timefor load disturbance
CO
tCVtCVKi %
/%/% 1122
2])/[( oifi
ic KK
TK
oifi KT )/(2
Controller Derivative (Rate) Time:
pdT
To prevent slow rolling oscillations:
iic K
TK2
*
secondary lag
Improving Tuning - Part 1
Fastest Possible Tuning (Lambda Tuning Method)
oic K
K
1
5.0
opf For max load rejection set lambda equal to deadtime
piT o
p
pi
KK
Substitute
)( op
ic K
TK
Into
Tuning for max disturbance rejection(Ziegler Nichols reaction curve method gain factor would be 1.0 instead of 0.5)
oiT 4
oiT 10
For setpoint response to minimize overshoot
Improving Tuning - Part 1
Near Integrator Approximation (Short Cut Tuning Method)
COtCVMaxK
Kp
pi /)/(
For “Near Integrating” gain approximation use maximum ramp rate divided by change in controller output
The above equation can be solved for the process time constant by taking the process gain to be 1.0 or for more sophistication as the
average ratio of the controlled variable to controller output
Tuning test can be done for a setpoint change if the PID gain is > 2 and the PID structure is
“PI on Error D on PV” so you see a step change in controller output from the proportional mode
Improving Tuning - Part 1
Fastest Controller Tuning (ultimate oscillation method*)
Kc Ku
Ti = 1.0 * u
Td = 0.1 u
For integrating processes or for self-regulating processes where p >> o,
double the factor for reset time (0.5 => 1.0) and add rate time if the process noise is negligible.
The oscillations associated with quarter amplitude decay is about ½ the ultimate gain. Thus if we use quarter amplitude decaying oscillations for the test, we take ½ of the controller gain that caused these oscillations to get ¼ of the ultimate gain
These tuning equations provide maximumdisturbance rejection but will cause
some overshoot of setpoint response
Improving Tuning - Part 1
* - Ziegler Nichols method closed loop modifiedto be more robust and less oscillatory
op
pc K
K
24.0oiT 4 1d pT
For runaway processes:
For self-regulating processes:
oic K
K
1
5.0oiT 4 1d pT
oic K
K
1
6.0
oiT 40 1d 2 pT
For integrating processes:
op
pc K
K
2'6.0
oic K
K
1
4.0
Near integrator (p2 >> o):
oiT 5.0
Near integrator (’p2 >> o):
Deadtime dominant (p2 << o):
0d Tp
c KK
14.0
Improving Tuning - Part 1
Fastest Controller Tuning (reaction curve method*)
These tuning equations provide maximumdisturbance rejection but will cause
some overshoot of setpoint response
* - Ziegler Nichols method closed loop modifiedto be more robust and less oscillatory
Ultimate Period and Ultimate Gain
Time(min)
Measurement (%)
Ultimate Gain is Controller Gain that Causedthese Nearly Equal Amplitude Oscillations (Ku)
Set Point
Ultimate Period Tu
0
If po then Tu If po then u
Improving Tuning - Part 1
Set Point
Time(min)
Measurement (%)
Offset
110% of o
Quarter Amplitude Period Tq
0
Damped Oscillation - (Proportional Only Control)
Improving Tuning - Part 1
1. Put the controller in auto at normal setpoint. 2. Choose largest step change in controller setpoint that is safe. Increase the reset
time by a factor of 10x for test.3. Add a PV filter to keep the controller output fluctuations from noise within the valve
deadband.4. Step the controller setpoint. If the response is non-oscillatory, increase the
controller gain and step the controller setpoint in opposite direction. Repeat until you get a slight oscillation (ideally ¼ amplitude decay). Make sure the controller output is not hitting the controller output limits and is on the sensitive part of the control valve’s installed characteristic.
5. Estimate the period of the oscillation. Reduce the controller gain until the oscillation disappears (½ current gain), set the reset time equal to ½ the period, and the rate time equal to ¼ of the reset time. If the oscillation is noisy or resembles a square wave or the controller gain is high (e.g. > 10), set the rate time to zero. The factors are ½ the ultimate period and twice the ultimate gain factors because the controller gain that triggered the ¼ amplitude oscillation is about ½ the ultimate gain and the ¼ amplitude period is larger than the ultimate period.
6. If a high controller gain is used (e.g. > 10) use setpoint rate of change (velocity) limits if a big kick in the controller output for setpoint changes from proportional action on error ( > 0) is disruptive to operations.
7. Make setpoint changes across the range of operation to make sure an operating point with a higher controller gain or larger process deadtime does not cause oscillations. Monitor the loop closely over several days of operation.
Damped Oscillation Tuning Method
Improving Tuning - Part 1
Traditional Open Loop Tuning Method 1. Choose largest step change in controller output that is safe.
2. Add a PV filter to keep the controller output fluctuations from noise within the valve deadband.
3. Make a change in controller output in manual.
4. Note the time it take for the process variable to get out of the noise band as the loop deadtime.
5. Estimate the process time constant as the time to reach 63% of the final value.
6. Estimate the process gain as final change in the process variable (%) after it reaches a steady state divided by change in the controller output (%).
7. To use reaction curve tuning, set the controller gain equal to ½ the process time constant divided by the product of the process gain and deadtime.
8. If the process lag is much larger than the loop deadtime, set the reset time setting equal to 4x the deadtime and set the rate time setting equal to the deadtime. If process lag is much smaller than the loop deadtime, set the reset time to 0.5x the loop deadtime and the rate time to zero.
9. If a high controller gain is used (e.g. > 10) use setpoint rate of change (velocity) limits if a big kick in the controller output for setpoint changes is disruptive to operations (for PID structures with > 0).
10. Make setpoint changes across the range of operation to make sure an operating point with a higher controller gain or larger process deadtime does not cause oscillations. Monitor the loop closely over several days of operation.
Improving Tuning - Part 1
Short Cut Ramp Rate Tuning Method
1. Choose largest step change in controller output and setpoint that is safe. If the test is to be made in auto, increase the reset time by factor of 10x for test.
2. Add a PV filter to keep the controller output fluctuations from noise within the valve deadband. Measure the initial rate of change of the process variable (PV1/t).
3. Make a either a change in controller output in manual or change in set point in auto4. Note the time it take for the for the process variable to get out of the noise band as
the loop deadtime.
5. Estimate the rate of change of the process variable (PV2/t) over successive deadtime intervals (at least two). Choose the largest rate of change. Subtract this from initial rate of change of the process variable and divide the result by the step change in controller output to get the integrating process gain.
6. To use reaction curve tuning, set the controller gain equal to 0.4 the inverse of the product of integrating process gain and loop deadtime (Equation 7). • If the inverse of the integrating gain is much larger than the loop deadtime, set the reset time
setting equal to 4x the process deadtime and set the rate time setting equal to the process deadtime, otherwise set the reset time to 0.5x the process deadtime and the rate time to zero
7. If a high controller gain is used (e.g. > 10) use setpoint rate of change (velocity) limits if a big kick in the controller output for setpoint changes is disruptive to operations (for PID structures with > 0)
8. Make setpoint changes across the range of operation to make sure an operating point with a higher controller gain or larger process deadtime does not cause oscillations. Monitor the loop closely over several days of operation.
Improving Tuning - Part 1
Manual Tuning LabManual Tuning Lab
• Objective – Gain experience with manual tuning methods to appreciate auto tuning
• Activities:1. Go to Main Display, and select Single Loop Lab01
2. Click on any block in block diagram
3. In Process detail, set Primary Process Lag 2 = 30 sec for Inc and Dec
4. Click on AC1-1 PID Faceplate and Click on magnifying glass icon to get Detail display
5. Tune PID with damped oscillation method and note tuning settings
6. Tune PID with traditional open loop method and note tuning settings
7. Tune PID with short cut tuning method and note tuning settings
Improving Tuning - Part 1
On-Demand Tuning Algorithm
Time(min)
Ultimate Period Tu
0
Set Point
d
a
Ultimate Gain 4 d Ku = e
n
e = sq rt (a2 - n2) If n = 0, then e = aalternative to n is a filter to smooth PV
Signal (%)
Improving Tuning - Part 2
Adaptive Tuning Algorithm
Improving Tuning - Part 2
Pure Gain Process
K
Estimated Gain
Multiple Model Interpolation with Re-centering
K
Estimated Gain
Multiple Model Interpolation with Re-centering
Changing Process Input
2( ) ( ( ) ( ) ) iE t y t Yi t
For each iteration, the squared error is computed for every model I each scan
Where:is the process output at the time tis i-th model output
A norm is assigned to each parameter value k = 1,2,….,m in models l = 1,2,…,n.
if parameter value is used inthe model, otherwise is 0
For an adaptation cycle of M scans
( ) y t( ) Yi t
1
( ) ( ) N
klkl i
i
Ep t E t
= 1kl
klp
1
( )M
kl kl
t
sumEp Ep t
1kl
kk
Ff sumF
1kl kl
FsumEp
11( ) ... ...k k kl kn
k kl knp a p f p f p f
Initial Model Gain = G1
G2-Δ G2 G2+ΔG2-Δ G2 G2+Δ
G3-Δ G3 G3+ΔG3-Δ G3 G3+Δ
Multiple iterations per
adaptation cycle
The interpolated parameter value is
Improving Tuning - Part 2
TC 1-4aTC
1-4a
TT 1-4a
AC 1-1AC 1-1
AT 1-1
LT 1-2
LC 1-2LC 1-2
TT 1-3
TC 1-3TC 1-3
RSP
Reactor
Coolant
Discharge
FC 1-5FC 1-5
FT 1-5
Slurry
Base
HeatExchanger A
RSP
FF 1-1FF 1-1
FF 1-2FF 1-2
FF 1-3FF 1-3
HydrocloneFeed Flow
Multiplied byFractional
Splitter Time
Feedforward
Feedforward
Feedforward
Dryer
Centrifuge
Splitter
HydrocloneFeed Flow
Multiplied byFractional
Splitter TimepH
ReactorTemperature
Level
Product Flow
RecirculationTemperature
Pensacola Reactor Adaptive Control Beta Test
Improving Tuning - Part 2
Pensacola Reactor Adaptive Control Beta Test
pH
Level
Temperature
Slurry Feed
Reactor Control “Before”
pH
LevelTemperature
Slurry Feed
Reactor Control “After”
Broadley-James Corporation Bioreactor Setup
Improving Tuning - Part 2
• Hyclone 100 liter Single Use Bioreactor (SUB)
• Rosemount WirelessHART gateway and transmitters for measurement and control of pH and temperature. (pressure monitored)
• BioNet lab optimized control system based on DeltaV
Bioreactor Adaptive Control Performance
Improving Tuning - Part 2
Bioreactor Adaptive Tuning Setup
Improving Tuning - Part 2
Bioreactor Adaptive Model Viewing
Improving Tuning - Part 2
Bioreactor Adaptive Learning Setup
Improving Tuning - Part 2
Output comes off high limit at 36.8 oC
0.30 oC overshoot
Bioreactor Adaptive Tuning Gain 40 Reset 500
Improving Tuning - Part 2
Output comes off high limit at 35.9 oC
0.12 oC overshoot
Bioreactor Adaptive Tuning Gain 40 Reset 5,000
Improving Tuning - Part 2
0.13 oC overshoot
Output comes off high limit at 36.1 oC
Bioreactor Adaptive Tuning Gain 40 Reset 10,000
Improving Tuning - Part 2
0.20 oC overshoot
Output comes off high limit at 36.4 oC
Bioreactor Adaptive Tuning Gain 40 Reset 15,000
Improving Tuning - Part 2
0.11 oC overshoot
Output comes off high limit at 36.1 oC
Bioreactor Adaptive Tuning Gain 80 Reset 15,000
Improving Tuning - Part 2
Integrating and Runaway Process Tuning
• It is difficult to prevent overshoot in processes without self-regulation• Controller gain adds self-regulation via closed loop response• Examples of integrating processes (ramping response) are
– Liquid and solids level – furnace, column, or vessel pressure – batch composition, pH, or temperature
• Examples of runaway processes (accelerating response) are – exothermic reactor temperature– strong acid - strong base pH– exponential growth phase biomass– compressor speed during surge
• An overdrive of the controller output beyond its resting value is needed to reach a set point or compensate for a disturbance (achieved by high controller gain)
• The maximum allowable controller gain for many integrating processes is well beyond the comfort level of most users. Measurement noise and resolution often sets the practical high limit to the controller gain rather than process dynamics
• Too much reset action (too small of a reset time) cause severe overshoot• A higher controller gain creates more overdrive for small setpoint changes and gets
controller off it’s output limit sooner for large setpoint changes• There is a window of allowable controller gains.
– Instability from too high of a controller gain (not likely for industrial processes)– Slow rolling oscillations from too low of a controller gain (common case) that slowly decay for
integrating processes but can grow for runaway processes till it hits physical limits
Improving Tuning - Part 2
MIT Anna India University Lab MIT Anna India University Lab Setup
Improving Tuning - Part 2
http://www.controlglobal.com/articles/2010/LevelControl1002.html
Improving Tuning - Part 2
Gravity discharge flow makes the level response self-regulating (increase in level head increases flow through discharge valve)
Increase in cross sectional area with level increases process time constantmaking process response slower
Conical Tank Detail
Improving Tuning - Part 2
Conical Tank Linear Level Controller Performance
Improving Tuning - Part 2
Conical Tank Adaptive Level Controller Models
Improving Tuning - Part 2
Conical Tank Adaptive Level Controller Performance
Nonlinear Control Valve LabNonlinear Control Valve Lab
Improving Tuning - Part 2
Equal PercentageFlow Characteristic
Nonlinear Control Valve LabNonlinear Control Valve Lab
Improving Tuning - Part 2
click on PID tagand then Tune
Nonlinear Control Valve LabNonlinear Control Valve Lab
Improving Tuning - Part 2
click on PID tagand then Tune
Nonlinear Control Valve LabNonlinear Control Valve Lab
Improving Tuning - Part 2
Process gain isapproximatelyproportionalto flow for
equal percentageflow characteristic
Nonlinear Control Valve LabNonlinear Control Valve Lab
Improving Tuning - Part 2
IdentificationOut Limit thatsets deadzoneshould be setapproximatelyequal to valvedeadband and stick-slip near
closed position
Nonlinear Control Valve LabNonlinear Control Valve Lab
Improving Tuning - Part 2
• Objective - Show adaptive control of fast nonlinear self-regulating processes (fast loop with equal percentage valve)
• Activities:1. Go to Main Display, select Cascade Loop Lab022. Click on any block, in Control Valve detail set Equal % Characteristic in Table3. Click on secondary loop AC1-2 PID Faceplate and put PID in Auto 4. Click on magnifying glass icon to get Detail display 5. Click on Duncan icon for “Tune with Insight” 6. Run “On-Demand Tuner” (set Ziegler-Nichols - PI factors: 0.2*Ku and 0.6*Tu)7. In “Models Viewing”, set number of regions = 5 and state parameter as “OUT”8. Go to settings, and set boundaries for each region
1. Region 1 0 => 35%2. Region 2 35 => 60%3. Region 3 60 => 75%4. Region 3 75 => 90%5. Region 3 90 => 100%
9. In “Adaptive Tuner”, set Lambda time = reset time10.With Adaptive Mode “Off” make 2 setpoint changes in each region11.Review “Adaptive Control” screen12.Review “Model Viewing” screen13.Review “Simulate” screen14.With Adaptive Mode “Partial” make same setpoint changes in each region
Nonlinear Control Valve LabNonlinear Control Valve Lab
Improving Tuning - Part 2
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