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Model Based Control Strategies

Model Based Control Strategies. Model Based Control. 1- Inverse Model as a Forward Controller (Inverse Dynamics) 2- Forward Model in Feedback 3- Combination of above. Inverse Model (Dynamic). Reference. Output. G(s). G -1 (s). Controller. Plant. Control Signal. Forward Model. q d.

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Model Based Control Strategies

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  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) Reference Output G(s) G-1(s) Controller Plant Control Signal

  4. Forward Model qd b q Plant G(s) Controller Gc(s) Plant Model

  5. Model Reference b q Ref. Model Plant G(s) Controller Gc(s) qd

  6. Internal Model Control

  7. Smith Predictor (1958)

  8. Reference Output Plant Controller Control Signal a) Delay Output Reference Plant Delay Controller Control Signal b)

  9. Smith Predictor, 1958 qd b q Plant G(s) Controller Gc(s) G*(s)

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

  11. 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.

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

  13. Feedback Error Learning

  14. Feedback Error Learning (cont.)

  15. Model Predictive Control(1978)

  16. Model Predictive Control (MPC) • Receding (Finite) Horizon Control • Using Time (Impulse/Step) Response • Based on Optimal Control with Constraints

  17. Model Predictive Control q b qd Plant Controller Td Optimizer qm Plant & Disturbance Model

  18. Model Predictive Control Basis

  19. Smith Predictor & MPC Comparison

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

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

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

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

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

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