Model Predictive Control for Integrating ProcessesModel Predictive Control for Integrating Processes

Lou Heavner – Consultant, APC

PresenterPresenter

Lou Heavner

IntroductionIntroduction

Historically, APC project engineers and consultants have tried to keep level control outside of the MPC solution. Level control and control of other integrating processes are poorly understood by many control engineers. This presentation will attempt to answer the following questions:– Can you control level with MPC?– How do you control level with MPC?– When should you control level with MPC?

Integrating ProcessesIntegrating Processes

Non-Self-Regulating – No natural equilibrium or steady-state– Must be controlled– Includes most liquid levels, many gas pressure systems, and

some other processes• Over a short enough time horizon, most processes appear to

be integrating

– Deadtime may be present, but no 1st order or higher order time constants in open loop response

Integrating Process - Open Loop ResponseIntegrating Process - Open Loop Response

Controller Output

Process

Variable

Process ExamplesProcess Examples

Hopper w/ Loss-in-Weight Feeder and Conveyor– Large Deadtime Dynamic

Distillation Column Bottom Level and Reflux Accumulator Level– Multi-variable Interaction

Evaporator Level– Multi-variable Interaction– Large Deadtime Dynamic

Oil & Gas Production Separator Level– Multi-variable Interaction– Slug Control

Conventional Control of Integrating ProcessesConventional Control of Integrating Processes

PI control is recommended– Closed Loop Time Constant (lambda)

• Lambda - (setpoint change) - time for PV to reach setpoint after a setpoint change

• Lambda - (load change) - the time required to stop the change in the PV due to a step load change. The level will return to setpoint in about 6 x Lambda.

• Beall reference describes in great detail

Lambda Tuning Rules (Integrating Process)Lambda Tuning Rules (Integrating Process)

Choose Lambda (λ)– Small Lambda reduces process overshoot and shortens

process response– Small Lambda passes more of the variability “downstream”– Rule of thumb: select Lambda as large as possible to

attenuate process variability

Tr = (2* λ) + Td or if Td<< λ, Tr = 2 *λ Kc = ____Tr____ or if Td<< λ, Kc = ___2____

Kp(λ + Td)2 Kp* λ

Model Predictive ControlModel Predictive Control

●Handles difficult process dynamics, reduces

variability and protects constraints

●Easy, Fast, Implementation

●Fully embedded, no integration required

-Configuration

-Operator Displays

-Historian

●Scaleable, Practical Model Predictive Control

●PredictPro

-LP Optimization

-Large Problems (80x40)

Model Predictive ControlModel Predictive Control

Learns From The Past

To Predict The Future

Learns From The Past

To Predict The Future

Past Present Future

Modeled

Relationship

Multivariable Dynamic Process ModelsMultivariable Dynamic Process Models

The Model Consists Of Step Responses That Show The

Relationship Between Every Process Input And Output

The Model Consists Of Step Responses That Show The

Relationship Between Every Process Input And Output

Model Predictive Control of Integrating ProcessesModel Predictive Control of Integrating Processes

Factors considered:– Feedback mechanism

• Model Correction Factor

• Rotation Factor

– TSS selection– MPC Controller “Tuning”

• POM

• POE

– Multivariable Interaction– Deadtime

Prediction ErrorPrediction Error

Model Correction Factor & Rotation Factor– Consider a prediction vector P whose elements are indexed by j. That

is j= 0 to 119 since in MPC-PRO the prediction horizon is 120 elements long.

– The equation for the update of the prediction vector is:P(j) = P(j) + {(1 – R) + j*R}*F Where R is the ROTATION FACTOR and F is the filtered shift measured as

the error (i.e. the difference between the first element of the last prediction vector and the feedback measurement) multiplied by the MODEL CORRECTION FACTOR

 Parameter Names & Default Values– Predict Pro: ROTATION_FACTOR[x] = 0.05– Predict: ROT_FACTOR[x] = 0.001– MOD_CORR_FACTOR[x] = 0.75 v10.0+ or 0.4 in earlier versions– [x] is the number of the process output– Tunable w/o download

MPC TuningMPC Tuning

Time to Steady-State (TSS)– Defines Prediction Horizon– Sets Controller execution speed– Requires Download

Penalty on Move (POM)– Slows the control action of MVs (Process Inputs)– Makes the controller more robust– Powerful, but requires a download to change

Penalty on Error (POE)– Works on Process Outputs– Fine tuning and usually not altered– Requires Download

MPC Pro OperateMPC Pro Operate

SP and Load Response

Effect of TSS SP changesEffect of TSS SP changes

Increasing TSS stabilizes the level control reducing both overshoot and MV moves

CaseTSS

(Configured) "Lambda"Max CV

OvershootMax MV

MoveApparent

TSS

sec min % % min

1 240 9 2.19 5.64 44

2 360 9 0.77 5.17 28

3 600 15 0.38 2.99 33

4 1080 n/a 0 0.36 27

POM = 39.5MCF = 0.75ROT = 0.05

Effect of TSS on load disturbancesEffect of TSS on load disturbances

CaseTSS

(Configured) "Lambda"Max CV

OvershootApparent

TSS

sec min % min

1 240 5 2.44 31

2 360 4 2.03 30

3 600 6 2.99 27

4 1080 6 2.42 32

Setting TSS = 6* Deadtime gives good results approximating 1st

order response

Setting TSS = 10 x Deadtime approaches critically damped response

POM = 39.5MCF = 0.75ROT = 0.05

Load Response with 2 different TSSLoad Response with 2 different TSS

Effect of POEEffect of POE

TSS = 240 secMCF = 0.75ROT = 0.05

Reducing POM improves performance

Case POM "Lambda"Max CV Overshoot

Max MV Move

Apparent TSS

min % % min

1 22 6 1.17 1.82 21

2 39.5 9 2.19 5.64 44

3 55.5 11 2.76 4.44 44

Effect of Model Correction FactorEffect of Model Correction Factor

TSS = 240 secPOM = 39.5ROT = 0.05

Case MCF "Lambda"Max CV Overshoot

Max MV Move

Apparent TSS

min % % min

1 0.5 5 2.11 5.63 33

2 0.75 9 2.19 5.64 44

3 0.9 8 2.12 5.45 32.5

Effect of Rotation FactorEffect of Rotation Factor

Case ROT "Lambda"Max CV Overshoot

Max MV Move

Apparent TSS

min % % min

1 0.01 8 2.22 5.78 44

2 0.05 9 2.19 5.64 44

3 0.1 8 2.18 5.65 32.5

4 0.5 8 2.11 5.47 33

TSS = 240 secPOM = 39.5MCF = 0.75

Lessons LearnedLessons Learned

Select TSS– Limited by Deadtime– Dependant on Self-Regulating responses in multi-variable

application– Nature of desired “closed-loop” response – Tight Response vs

Attenuate Variability– Increase TSS to reduce overshoot

• Start with 6 x deadtime if possible Select Penalty on Move

– Counter-intuitive for integrating processes– Smaller POM reduces overshoot and shortens response

Select Model Correction Factor– Relatively weak handle

Select Rotation Factor– Relatively weak handle

Where To Get More InformationWhere To Get More Information

Author:– Lou.Heavner@Emerson.com– (512) 834-7262

References:– Beall, James F., Base Process Control Diagnostics and

Optimization, Internal Emerson document, 2002.

Consulting services– Contact your local sales office