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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
Model Based Control
  • 1- Inverse Model as a Forward Controller

(Inverse Dynamics)

  • 2- Forward Model in Feedback
  • 3- Combination of above
inverse model dynamic
Inverse Model (Dynamic)

Reference

Output

G(s)

G-1(s)

Controller

Plant

Control Signal

forward model
Forward Model

qd

b

q

Plant

G(s)

Controller

Gc(s)

Plant Model

slide5

Reference

Output

Plant

Controller

Control Signal

a)

Delay

Output

Reference

Plant

Delay

Controller

Control Signal

b)

smith predictor 1958
Smith Predictor, 1958

qd

b

q

Plant

G(s)

Controller

Gc(s)

G*(s)

smith predictor cont
Smith Predictor (cont.)

qd

b

q

Plant

G(s)

Controller

Gc(s)

Gm(s) - G*(s)

slide8

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.

model predictive control mpc
Model Predictive Control (MPC)
  • Receding (Finite) Horizon Control
  • Using Time (Impulse/Step) Response
  • Based on Optimal Control with Constraints
model predictive control
Model Predictive Control

q

b

qd

Plant

Controller

Td

Optimizer

qm

Plant & Disturbance

Model

slide19

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.

slide20

Time (s)

Smith Predictor and MPC Outputs for Perfect Model

slide21

Time (s)

Smith Predictor and MPC Outputs for Time Delay Mismatch

slide22

Time (s)

Smith Predictor and MPC Outputs for Non-Minimum Phase System

slide23

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).