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Model Based Control Strategies (Motor Learning)

Model Based Control Strategies (Motor Learning). 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.

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Model Based Control Strategies (Motor Learning)

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  1. Model Based Control Strategies(Motor Learning)

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

  6. History • 1- Feedback-Error-Learning (Kawato et al, 1987) • 2- Smith Predictor (Mial et al, 1993) • 3- Internal Model • 3- Model Predictive Control (Towhidkhah, 1993, 1996)

  7. Feedback Error Learning

  8. Granule cell axons ascend to the molecular layer, bifurcate and form parallel fibers that run parallel to folia forming excitatory synapses on Purkinje cell dendrites. Cerebellar cortex also has several types of inhibitory interneurons: basket cells, Golgi cells, and stellate cells. Purkinje cell axon is only output of cerebellar cortex, is inhibitory and projects to the deep nuclei and vestibular nuclei. Deep nuclei axons are the most common outputs of the cerebellum.

  9. Feedback Error Learning (cont.)

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

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

  12. 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.

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

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

  15. Model Predictive Control Basis

  16. Smith Predictor & MPC Comparison

  17. 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.

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

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

  20. 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 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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