Model Based Control Strategies Motor Learning

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Model Based Control Strategies(Motor Learning)
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Model Based Control

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

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Inverse Model (Dynamic)
Reference
Output
G(s)
G-1(s)
Plant
Controller
Control Signal
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Forward Model
qd
b
q
Plant G(s)
Controller Gc(s)
Plant Model
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Output
Reference
Plant
Controller
Control Signal
a)
Delay
Output
Reference
Plant
Delay
Controller
Control Signal
b)
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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)

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Feedback Error Learning
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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.
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Feedback Error Learning (cont.)
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Smith Predictor, 1958
qd
b
q
Plant G(s)
Controller Gc(s)
G(s)
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Smith Predictor (cont.)
qd
b
q
Plant G(s)
Controller Gc(s)
Gm(s) - G(s)
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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.
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(No Transcript)
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Model Predictive Control (MPC)

• Receding (Finite) Horizon Control
• Using Time (Impulse/Step) Response
• Based on Optimal Control with Constraints

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Model Predictive Control
q
b
qd
Plant
Controller
Td
Optimizer
qm
Plant Disturbance Model
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Model Predictive Control Basis
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Smith Predictor MPC Comparison
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Comparison of MPC Smith Predictor
Case Plant
Plant Model Plant Model
Delay Delay
I 1/s(swc) 1/s(swc) 150
150 II 1/s(swc) 1/s(swc)
150 250 III 1/s(swc)
1/s(swm) 150 150 IV 1/s(swc)
1/s(swm) 150 250 V (s-0.5)/s(swc)
(s-0.5)/s(swc) 150 150
wc 2pi(0.9), wm 2pi(0.54), Gc20, time
delay is in ms.
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Time (s)
Smith Predictor and MPC Outputs for Perfect Model
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Time (s)
Smith Predictor and MPC Outputs for Time Delay
Mismatch
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Time (s)
Smith Predictor and MPC Outputs for Non-Minimum
Phase System
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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).