1. Model Predictive Control

2. Review

3. Miall, R. C., Weir, D. J., Wolpert, D. M., and Stein, J. F., (1993),
"Is the Cerebellum a Smith Predictor ?", Journal of Motor Behavior, 25,

4. Miall et al

7. Smith Predictor qd b
Plant
G(s) q
Controller
Gc(s)
Gm(s) - G*(s)

10. Model Predictive Control

11. Model Predictive Control Originated in 1980s
Techniques developed by industry:
1. Dynamic Matrix Control (DMC)
Shell Development Co.: Cutler and Ramaker (1980),
Cutler later formed DMC, Inc.
DMC acquired by Aspentech in 1997.
2. Model Algorithmic Control (MAC)
• ADERSA/GERBIOS, Richalet et al. (1978) in France.
• Over 5000 applications of MPC since 1980

12. MPC Features Receding (Finite) Horizon Control
Using Time (Impulse/Step) Response
Based on Optimal Control with Constraints
Suitable for MIMO system

13. Model Predictive Control Basis

14. Model Predictive Controlb q qd
Controller
Plant Td
Optimizer qm
Plant & Disturbance
Model

15. Prediction for SISO Models:
Example: Step response model
Si = the i-th step response coefficient
N = an integer (the model horizon)
y0 = initial value at k=0
Unit Step Response

16. Smith Predictor & MPC Comparison

17. Comparison of MPC & Smith Predictor
Case Plant Plant Model Plant Model Delay Delay
I /[s(s+wc)] /[s(s+wc)]
II /[s(s+wc)] /[s(s+wc)]
III /[s(s+wc)] /[s(s+wm)]
IV /[s(s+wc)] /[s(s+wm)]
V (s-0.5)/[s(s+wc)] (s-0.5)/[s(s+wc)]
wc = 2*pi*(0.9), wm = 2*pi*(0.54), Gc=20, time delay is in ms.

18. Smith Predictor and MPC Outputs for Perfect Model
Time (s)
Smith Predictor and MPC Outputs for Perfect Model

19. Smith Predictor and MPC Outputs for Time Delay Mismatch
Time (s)
Smith Predictor and MPC Outputs for Time Delay Mismatch

20. Smith Predictor and MPC Outputs for Non-Minimum Phase System
Time (s)
Smith Predictor and MPC Outputs for Non-Minimum Phase System

21. Comparison of MPC & Smith Predictor ( Cont. )
Error Case I Case II Case III Case IV Case V
SPC
MPC
SPC = Smith Predcitor Controller,
MPC = Model Predictive Controller,
Error is root mean square errors (rad).