pid control of true integrating processes - greg mcmillan deminar

Interactive Opportunity Interactive Opportunity AssessmentAssessmentInteractive Opportunity Interactive Opportunity AssessmentAssessment

Demo and Seminar (Deminar) Series for Web Labs –

PID Control of True Integrating PID Control of True Integrating Processes Processes

Aug 11, 2010Sponsored by Emerson, Experitec, and Mynah

Created byGreg McMillan and Jack Ahlers

www.processcontrollab.com Website - Charlie Schliesser (csdesignco.com)

[File Name or Event]Emerson Confidential27-Jun-01, Slide 2 Slide 2

WelcomeWelcome WelcomeWelcome 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 Reasons to Elect a Control Top Ten Reasons to Elect a Control Engineer as a PresidentEngineer as a President


(10) Completely automated and remotely controlled combat (9) Dynamic programs (8) Models of the economy (7) No overshoot of the budget (6) Real time optimization of manufacturing (5) Regulatory control of financial markets (4) Feedforward control of Congress (3) Model predictive control of energy (2) A nuclear reactor in every home

And the Number 1 Reason:




(1) A computer in every pocket


Demos of Control Loop OpportunitiesDemos of Control Loop Opportunitiesto Reduce Fed-Batch and Startup Timeto Reduce Fed-Batch and Startup TimeDemos of Control Loop OpportunitiesDemos of Control Loop Opportunitiesto Reduce Fed-Batch and Startup Timeto Reduce Fed-Batch and Startup Time

PID on Error Structure– Maximizes the kick and bump of the controller output for a setpoint change. – Overdrive (driving of output past resting point) is essential for getting slow loops,

such as vessel temperature and pH, to the optimum setpoint as fast as possible.– The setpoint change must be made with the PID in Auto mode.– “SP track PV” will generally maximize the setpoint change and hence the kick

and bump (retaining SP from last batch or startup minimizes kick and bump) SP Feedforward

– For low controller gains (controller gain less than inverse of process gain), a setpoint feedforward is particularly useful. For this case, the setpoint feedforward gain is the inverse of the dimensionless process gain minus the controller gain.

– For slow self-regulating (e.g. continuous) processes and slow integrating (e.g. batch) processes, even if the controller gain is high, the additional overdrive can be beneficial for small setpoint changes that normally would not cause the PID output to hit a limit.

– If the setpoint and controller output are in engineering units the feedforward gain must be adjusted accordingly.

– The feedforward action is the process action, which is the opposite of the control action, taking into account valve action. In other words for a reverse control action, the feedforward action is direct provided the valve action is inc-open or the analog output block, I/P, or positioner reverses the signal for a inc-close.


Demos of Control Loop OpportunitiesDemos of Control Loop Opportunitiesto Reduce Fed-Batch and Startup Timeto Reduce Fed-Batch and Startup TimeDemos of Control Loop OpportunitiesDemos of Control Loop Opportunitiesto Reduce Fed-Batch and Startup Timeto Reduce Fed-Batch and Startup Time

Full Throttle (Bang-Bang Control) - The controller output is stepped to it output limit to maximize the rate of approach to setpoint and when the projected PV equals the setpoint less a bias, the controller output is repositioned to the final resting value. The output is held at the resting value for one deadtime. For more details, check out the Control magazine article “Full Throttle Batch and Startup Response.” http://www.controlglobal.com/articles/2006/096.html

– A deadtime (DT) block must be used to compute the rate of change so that new values of the PV are seen immediately as a change in the rate of approach.

– If the total loop deadtime (o) is used in the DT block, the projected PV is simply the current PV minus the output of the DT block (PV) plus the current PV.

• If the PV rate of change (PV/t) is useful for other reasons (e.g. near integrator or true integrating process tuning), then PV/t = PV/o can be computed.

– If the process changes during the setpoint response (e.g. reaction or evaporation), the resting value can be captured from the last batch or startup

– If the process changes are negligible during the setpoint response, the resting value can be estimated as:

• the PID output just before the setpoint change for an integrating (e.g. batch) process• the PID output just before the setpoint change plus the setpoint change divided by the

process gain for a self-regulating (e.g. continuous) process

– For self-regulating processes such as flow with the loop deadtime (o) approaching or less than the largest process time constant (p ), the logic is revised to step the PID output immediately to the resting value. The PID output is held at the resting value for the T98 process response time (T98 o p ).


Integrating ResponseIntegrating ResponseIntegrating ResponseIntegrating Response

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 processdeadtime


Loop Block DiagramLoop Block DiagramLoop Block DiagramLoop Block Diagram

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

Total Observed Dead Time: ov p1 p2 m1 m2 c

vp1m1m2c1 c2

%

%

%

Delay => Dead TimeLag =>Time Constant

Ki = Kmv(Kpv / p2 ) Kcv

100% / span


CV change in controlled variable (%) CO change in controller output (%) Kc controller gain (dimensionless)

Ki integrating gain (%/sec/% or 1/sec)

Kp process gain (dimensionless) also known as open loop gain MV manipulated variable (engineering units) PV process variable (engineering units) t change in time (sec)

ototal loop dead time (sec)

mmeasurement time constant (sec)

pprocess time constant (sec) also known as open loop time constant

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)

NomenclatureNomenclature NomenclatureNomenclature


PID StructurePID StructurePID StructurePID Structure

ER is external reset(e.g. secondary PV)Dynamic Reset Limit

SP

proportional

derivative

Gain

Rate

CO

filter

filter

CV filterFilter Time Rate Time

filter

Filter Time = Reset Time

ER

PositiveFeedback


PID Structure ChoicesPID Structure ChoicesPID Structure ChoicesPID Structure Choices

1. PID action on error (= 1 and = 1)

2. PI action on error, D action on PV (= 1 and = 0)

3. I action on error, PD action on PV (= 0 and = 0)

4. PD action on error (= 1 and = 1) (no I action)

5. P action on error, D action on PV (= 1 and = 0) (no I action)

6. ID action on error ( = 1) (no P action)

7. I action on error, D action on PV ( = 0) (no P action)

8. Two degrees of freedom controller (and adjustable 0 to 1)

The and factors do not affect the load response of a control loop


Contribution of Each PID Mode Contribution of Each PID Mode (Step Change in the Set Point)(Step Change in the Set Point)

Contribution of Each PID Mode Contribution of Each PID Mode (Step Change in the Set Point)(Step Change in the Set Point)

CO2 = CO1

SP

seconds/repeatCO1

Time(seconds)

Signal (%)

0

kick fromproportional

mode

bump fromfiltered

derivativemode

repeat from integralmode

For fastest setpoint response we want to maximize kick from proportional mode bump from derivative mode, and setpoint weighting factors (= 1 and = 1)


Lambda Tuning for Lambda Tuning for Integrating ProcessesIntegrating ProcessesLambda Tuning for Lambda Tuning for

Integrating ProcessesIntegrating 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 KTK

2*

secondary lag


Primary and secondary Kp secondary p primary p totalo

Ki Kp p

2 pdT

Tuning for Today’s ExampleTuning for Today’s ExampleTuning for Today’s ExampleTuning for Today’s Example

1f

21010)01.0/1(2)/(2 oifi KT

7.1]10)01.0/1[(01.0

210

])/[( 22

oifi

ic KK

TK

01.0

2210*7.1


Demo of Effect of PID Structure 3Demo of Effect of PID Structure 3on Setpoint Responseon Setpoint Response


Objective – Show slow setpoint response from just integral action

Activities:– For Single Integrating Loop:

• Enter tuning settings, Gain = 1.7, Reset = 210 sec, Rate = 2 sec

• Set Primary Process Delay = 9 sec, Lag 2 Inc & Lag 2 Dec = 100 sec

• Set Primary Process Type = Integrating

• Choose controller structure 3 (I action on error, PD action on PV (= 0 and = 0))

• Make setpoint change from 50% to 60%


Other Control Loop OpportunitiesOther Control Loop Opportunitiesto Reduce Fed-Batch and Startup Timeto Reduce Fed-Batch and Startup Time


Output Lead-Lag – A lead-lag on the controller output or in the digital positioner can kick the signal

though the valve deadband and sticktion, get past split range points, and make faster transitions from heating to cooling and vice versa.

– A lead-lag can potentially provide a faster setpoint response with less overshoot when analyzers are used for closed loop control of integrating processes When combined with the enhanced PID algorithm (PIDPlus) described in:

• Deminar #1 http://www.screencast.com/users/JimCahill/folders/Public/media/5acf2135-38c9-422e-9eb9-33ee844825d3

• White paper http://www.modelingandcontrol.com/DeltaV-v11-PID-Enhancements-for-Wireless.pdf

Deadtime Compensation– The simple addition of a delay block with the deadtime set equal to the total loop

deadtime to the external reset signal for the positive feedback implementation of integral action described in Deminar #3 for the dynamic reset limit option http://www.screencast.com/users/JimCahill/folders/Public/media/f093eca1-958f-4d9c-96b7-9229e4a6b5ba .

– The controller reset time can be significantly reduced and the controller gain increased if the delay block deadtime is equal or slightly less than the process deadtime as studied in Advanced Application Note 3 http://www.modelingandcontrol.com/repository/AdvancedApplicationNote003.pdf




Feed Maximization– Model Predictive Control described in Application Note 1

http://www.modelingandcontrol.com/repository/AdvancedApplicationNote001.pdf – Override control (next slide) is used to maximize feeds to limits of operating

constraints via valve position control (e.g. maximum vent, overhead condenser, or jacket valve position with sufficient sensitivity per installed characteristic).

– Alternatively, the limiting valve can be set wide open and the feeds throttled for temperature or pressure control. For pressure control of gaseous reactants, this strategy can be quite effective.

– For temperature control of liquid reactants, the user needs to confirm that inverse response from the addition of cold reactants to an exothermic reactor and the lag from the concentration response does not cause temperature control problems.

– All of these methods require tuning and may not be particularly adept at dealing with fast disturbances unless some feedforward is added. Fortunately the prevalent disturbance that is a feed concentration change is often slow enough due to raw material storage volume to be corrected by temperature feedback.

Profile Control– If you have a have batch measurement that should increase to a maximum at the

batch end point (e.g. maximum reaction temperature or product concentration), the slope of the batch profile of this measurement can be maximized to reduce batch cycle time. For application examples checkout “Direct Temperature Rate of Change Control Improves Reactor Yield” in a Funny Thing Happened on the Way to the Control Room http://www.modelingandcontrol.com/FunnyThing/ and the Control magazine article “Unlocking the Secret Profiles of Batch Reactors” http://www.controlglobal.com/articles/2008/230.html .

04/13/23 18

feed A

feed B

coolantmakeup

CAS

ratio

CAS

Example of Advanced Regulatory ControlExample of Advanced Regulatory Control(reduced batch cycle time by 25%)(reduced batch cycle time by 25%)

reactor

vent

product

maximum productionrate

condenser

CTW

PT

PC-1

TT

TT

TC-2

TC-1

FC-1

FT

FT

FC-2

<

TC-3

RC-1

TT

ZC-1

ZC-2CAS

CAS

CAS

ZC-3 ZC-4<

Override Control

override control

ZC-1, ZC-3, and ZC-4 work to keep their respective

control valves at a max throttle position with good

sensitivity and room for loop to maneuver. ZC-2

will raise TC-1 SP if FC-1 feed rate is maxed out


Sequence Opportunities Sequence Opportunities to Reduce Pure-Batch and Startup Timeto Reduce Pure-Batch and Startup Time

Sequence Opportunities Sequence Opportunities to Reduce Pure-Batch and Startup Timeto Reduce Pure-Batch and Startup Time

Reduce wait times, operator attention requests, and manual actions by automation.

Reduce excess hold times (e.g. heat release can confirm reaction start/end). Improve charge times and accuracy by better sensor design (e.g. mass flow

meters and valve location (e.g. minimize dribble time and holdup). Minimize acquire time by improved prioritization of users (e.g. unit operation

with biggest effect on production rate gets access to feeds and utilities). Reduce failure expression activation by better instruments, redundancy and

signal selection, and more realistic expectations of instrument performance. Improve failure expression recovery by configuration and displays. Eliminate steps by simultaneous actions (e.g. heat-up and pressurization). Increase feed and heat transfer rate by an increase in pump impeller size. Minimize non constrained processing time by all out run, cutoff, and coast. Minimize processing time by better end point detection (inferential

measurements by neural networks and online or at-line analyzers). Mid batch correction based on adapted online virtual plant model or batch

analytics projection to latent structures (PLS) and first principle relationships.




Objective – Show faster setpoint response from addition of kick from proportional mode and bump derivative mode


• Look at setpoint response for structure 3

• Choose controller structure 1 (PID action on error (= 1 and = 1))



Identified Responses for Identified Responses for Batch Profile ControlBatch Profile Control


Product Formation Rate

Biomass Growth rate

Substrate

Dissolved Oxygen

Model Predictive Control (MPC) of Model Predictive Control (MPC) of Growth Rate and Product Formation RateGrowth Rate and Product Formation Rate


Demo of Effect of SP FeedforwardDemo of Effect of SP Feedforwardon Setpoint Responseon Setpoint Response

Demo of Effect of SP FeedforwardDemo of Effect of SP Feedforwardon Setpoint Responseon Setpoint Response

Objective – Show how reduce batch cycle time by use of setpoint feedforward


• Look at setpoint response for structure 1

• Set SP FF Gain = 2



Batch Basic Fed-Batch APC Fed-BatchBatch

Inoculation Inoculation

Dissolved Oxygen (AT6-2)

pH (AT6-1)

Estimated Substrate Concentration (AT6-4)

Estimated Biomass Concentration (AT6-5)

Estimated Product Concentration (AT6-6)

Estimated Net Production Rate (AY6-12)

Estimated Biomass Growth Rate (AY6-11)

MPC in Auto

Model Predictive Control (MPC) Model Predictive Control (MPC) Reduces Batch Cycle TimeReduces Batch Cycle Time


Current Product Yield (AY6-10D)

Current Batch Time (AY6-10A)

Predicted Batch Cycle Time (AY6-10B)

Predicted Cycle Time Improvement (AY6-10C)

Predicted Final Product Yield (AY6-10E)

Predicted YieldImprovement (AY6-10F)

Batch Basic Fed-Batch APC Fed-BatchBatchInoculation

Inoculation

MPC in Auto

Predicted Final Product Yield (AY6-10E)

Predicted Batch Cycle Time (AY6-10B)

Model Predictive Control (MPC) Model Predictive Control (MPC) Improves Batch PredictionsImproves Batch Predictions


Demo of Effect of Bang-Bang ControlDemo of Effect of Bang-Bang Controlon Setpoint Responseon Setpoint Response

Demo of Effect of Bang-Bang ControlDemo of Effect of Bang-Bang Controlon Setpoint Responseon Setpoint Response

Objective – Show how to reduce batch and startup time by a full throttle setpoint response (bang-bang control)


• Look at setpoint response for setpoint feedforward

• Set SP FF Gain = 0

• Set Bang-Bang Bias = 4%



Structure 3Rise Time = 8.5 min

Settling Time = 8.5 minOvershoot = 0%

Structure 1Rise Time = 1.6 min

Settling Time = 7.5 minOvershoot = 1.7%

Structure 1 + SP FFRise Time = 1.2 min


Structure 1 + Bang-BangRise Time = 0.5 min


Summary of Demo ResultsSummary of Demo ResultsSummary of Demo ResultsSummary of Demo Results


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PID Control of Runaway Processes PID Control of Runaway Processes (How to Improve the Performance of Exothermic Reactor Temperature Loops)

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QUESTIONS? QUESTIONS? QUESTIONS? QUESTIONS?

pid control of true integrating processes - greg mcmillan deminar

Education

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