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) PlantController Control Signal Output Reference G(s) G -1 (s)

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

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

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)

Feedback Error Learning

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.

Feedback Error Learning (cont.)

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

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

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,

Model Predictive Control (MPC)

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

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

Model Predictive Control Basis

Smith Predictor & MPC Comparison

I 1/[s(s+w c )] 1/[s(s+w c )] I 1/[s(s+w c )] 1/[s(s+w c )] II 1/[s(s+w c )] 1/[s(s+w c )] II 1/[s(s+w c )] 1/[s(s+w c )] III 1/[s(s+w c )] 1/[s(s+w m )] IV 1/[s(s+w c )] 1/[s(s+w m )] V(s-0.5)/[s(s+w c )](s-0.5)/[s(s+w c )] V(s-0.5)/[s(s+w c )](s-0.5)/[s(s+w c )] 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.

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

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

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

SPC MPC 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