1. Model Based Control Strategies

2. Model Based Control 1- Inverse Model as a Forward Controller (Inverse Dynamics) 2- Forward Model in Feedback 3- Combination of above

3. Inverse Model (Dynamic) PlantController Control Signal Output Reference G(s) G -1 (s)

4. Forward Model Plant G(s) Controller Gc(s) Gc(s) Plant Model   dddd

5. Model Reference Plant G(s) Controller Gc(s) Gc(s) Ref. Model   dddd

6. Internal Model Control

9. Smith Predictor (1958)

10. Plant Controller Delay Control Signal OutputReference Plant Controller Delay Control Signal Output Reference a) b)

11. Smith Predictor, 1958 Plant G(s) Controller Gc(s) Gc(s) G * (s)   dddd

12. Smith Predictor (cont.) Plant G(s) Controller Gc(s) Gc(s) G m (s) - G * (s)   dddd

13. 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, 203-216.

17. Feedback Error Learning (Kawato et al, 1987)

18. Feedback Error Learning

19. Feedback Error Learning (cont.)

20. Model Predictive Control (1978)

21. Model Predictive Control (MPC) 1.Receding (Finite) Horizon Control 2.Using Time (Impulse/Step) Response 3.Based on Optimal Control with Constraints

23. Model Predictive Control Plant Controller Plant & Disturbance Model Optimizer TdTdTdTd   mmmm dddd

24. Model Predictive Control Basis

25. Smith Predictor & MPC Comparison

26. I 1/[s(s+w c )] 1/[s(s+w c )] 150 150 I 1/[s(s+w c )] 1/[s(s+w c )] 150 150 II 1/[s(s+w c )] 1/[s(s+w c )] 150 250 II 1/[s(s+w c )] 1/[s(s+w c )] 150 250 III 1/[s(s+w c )] 1/[s(s+w m )] 150 150 IV 1/[s(s+w c )] 1/[s(s+w m )] 150 250 V(s-0.5)/[s(s+w c )](s-0.5)/[s(s+w c )] 150 150 V(s-0.5)/[s(s+w c )](s-0.5)/[s(s+w c )] 150 150 Comparison of MPC & Smith Predictor Case Plant Plant Model Plant Model Delay Delay w c = 2*pi*(0.9), w m = 2*pi*(0.54), G c =20, time delay is in ms.

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

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

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

30. SPC 0.2664 0.3096 0.3271 0.3830 0.2485 MPC 0.0519 0.1363 0.1428 0.2525 0.0303 Comparison of MPC & Smith Predictor ( Cont. ) SPC = Smith Predcitor Controller, MPC = Model Predictive Controller, Error is root mean square errors (rad). Error Case I Case II Case III Case IV Case V