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Introduction to Model Predictive Control Technology

Introduction to Model Predictive Control Technology. Hao-Yeh Lee P rocess S ystem E ngineering Laboratory Department of Chemical Engineering National Taiwan University May 12, 2005. Outline. Introduction Model Forms for MPC Dynamic Matrix Control (DMC) SISO formulation MIMO formulation

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Introduction to Model Predictive Control Technology

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  1. Introduction to Model Predictive Control Technology Hao-Yeh Lee Process System Engineering Laboratory Department of Chemical Engineering National Taiwan University May 12, 2005

  2. Outline • Introduction • Model Forms for MPC • Dynamic Matrix Control (DMC) • SISO formulation • MIMO formulation • Quadratic Dynamic Matrix Control (QDMC) • MATLAB tools for MPC • Case Study • Future work

  3. Introduction • The main idea of model predictive control (MPC) is to choose the control action by repeatedly solving on line an optimal control problem. • This aims at minimizing a performance criterion over a future horizon, possibly subject to constraints on the manipulated inputs and outputs, where the future behavior is computed according to a model of the plant.

  4. Advantages of MPC • Easy to use for MIMO system and easy to handle process interactions • Easy to handle time delays, inverse response, as well as other difficult process dynamics. • Only few tuning parameters are needed.

  5. A History of MPC • MAC, IDCOM (Richalet et al. , 1976, 1978) • using a discrete-time Finite Impulse Response (FIR) model. • Dynamic Matrix Control (DMC), (Cutler and Ramaker, 1979) • linear step response model for the plant • quadratic performance objective over a finite prediction horizon • future plant output behavior specified by trying to follow the setpoint as closely as possible • optimal inputs computed as the solution to a least-squares problem

  6. A History of MPC (cont’d) • Quadratic Dynamic Matrix Control (QDMC), (García and Morshedi, 1984) • linear step response model for the plant • quadratic performance objective over a finite prediction horizon • future plant output behavior specified by trying to follow the setpoint as closely as possible subject to process constraints • optimal inputs computed as the solution to a quadratic program • Generalized Predictive Control (GPC) (Clarke et al., 1987) • Transfer function model for the plant • Nonlinear Model Predictive Control (NMPC)

  7. Basic Elements of MPC • Reference Trajectory Specification • Process Output Prediction • Control Action Sequence Computation • Error Prediction Update

  8. Model Forms for MPC • Convolution model • Step response model • Impulse response model • Discrete state-space model • Discrete transfer function model  finite step response (FSR)  finite impulse response (FIR)

  9. Dynamic Matrix Control • Unconstrained Model Predictive Control

  10. Step Response Model • For SISO system

  11. Finite Step Response Model • ：process output at time k • ：step response coefficient at time i • ：controller output at time k • ：Model horizon

  12. Finite Step Response Model (cont’d) • If the Hm is large enough, the process output will be approached to steady state for the stable process • The finite step response model (FSR)

  13. Impulse response model • It is easy to convert the impulse response model as step response model

  14. The Concept of Moving Horizon

  15. After Hcsteps, the manipulating variable rates are all the same, then

  16. Process Output Prediction • Define the past input effect term: Dynamic matrix

  17. Process Output Prediction (cont’d) • Define error prediction update term Future input effect past input effect Future output

  18. Control Action Sequence Computation • DMC control law

  19. Control Action Sequence Computation(cont’d)

  20. Control Action Sequence Computation(cont’d) • To apply the concept of moving horizon

  21. MIMO system formulation • For nu × ny MIMO system • Step response model

  22. MIMO system formulation (cont’d)

  23. Selection of Tuning Parameters • Systematic parameters • Sampling interval (Ts) • Ts should be small enough to capture the dynamics of the process, large enough to permit the on-line computations necessary for implementation • Model horizon (Hm) • Major tuning parameters • Prediction horizon (Hp) • Longer Hp tends to produce more aggressive control action, more overshoot, faster response and moresensitive to disturbances • Control horizon (Hc) • Control horizon should be less or equal to prediction horizon • The effect of increasing is very similar to prediction horizon

  24. Selection of Tuning Parameters(cont’d) • Weighting parameters • Penalty factor ( f ) • A input weighting factor usually is set less than 10% of the output penalty to achieve good closed-loop performance. • Weighting matrix (G) • Output penalty matrix

  25. Quadratic Dynamic Matrix Control • QDMC is the DMC extended to concern the system constraints • It uses quadratic programming technique to solve the optimization problem. • Quadratic programming form:

  26. Process constraints • Manipulated variable constraints

  27. Process constraints (cont’d) • Manipulated variable rate constraints

  28. Process constraints (cont’d) • Output variable constraints

  29. Quadratic Programming Control law:

  30. Limitations of Existing Technology • impulse and step response models are limit application of the algorithm to strictly stable processes • sub-optimal solution of the dynamic optimization • constant output disturbance assumption • tuning is required to achieve nominal stability • model uncertainty is not addressed adequately

  31. MATLAB Tools for MPC • MATLAB code for DMC • [yp,u,ym] = mpcsim(plant,model,Kmpc,tend,r,usat,... tfilter,dplant,dmodel,dstep) • Kmpc = mpccon(model,ywt,uwt,M,P) • plant = tfd2step(tfinal,delt2,nout,g1,...,g25) • plant = ss2step(phi, gam, c, d, tfinal) • MATLAB code for QDMC • [yp,u,ym] = cmpc(plant,model,ywt,uwt,M,P,tend,... r,ulim,ylim,tfilter,dplant,dmodel,dstep)

  32. Case Study • 2x2 Example • Wood and Berry process

  33. MATLAB Code for MPC • Setpoint change g11=poly2tfd(12.8,[16.7 1],0,1); g21=poly2tfd(6.6,[10.9 1],0,7); g12=poly2tfd(-18.9,[21.0 1],0,3); g22=poly2tfd(-19.4,[14.4 1],0,3); delt=3; ny=2; tfinal=90; model=tfd2step(tfinal,delt,ny,g11,g21,g12,g22); plant=model; P=6; M=2; ywt=[ ]; uwt=[1 1]; tend=30; r=[0 1]; ulim=[-inf -0.15 inf inf 0.1 100]; ylim=[ ]; [y,u]=cmpc(plant,model,ywt,uwt,M,P,tend,r,ulim,ylim); plotall(y,u,delt)

  34. Disturbance rejection gd11=poly2tfd(3.8,[14.9 1],0,8.1); gd21=poly2tfd(4.9,[13.2 1],0,3.4); dmodel=tfd2step(tfinal,delt,ny,gd11,gd21); dplant=dmodel; r=[0 0]; dstep=1; tfilter = []; [y,u]=cmpc(plant,model,ywt,uwt,M,P,tend,r,ulim,ylim, tfilter,dplant,dmodel,dstep); plotall(y,u,delt)

  35. Conclusion • The major advantage of the MPC algorithm is easy to handle multivariable system. • Quadratic dynamic matrix control can concern the system constraints and the optimization problem can be solved by quadratic programming. • MATLAB tools for MPC is easy to use for process simulation.

  36. Future work • Apply MPC to EtAc reactive distillation process • DMC • QDMC • NMPC • …

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