model based control strategies
DESCRIPTION
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. - PowerPoint PPT PresentationTRANSCRIPT
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)
PlantController
Control Signal
OutputReference G(s)G-1(s)
Forward Model
Plant G(s)
Controller Gc(s)
Plant Model
qbqd
Model Reference
Plant G(s)
Controller Gc(s)
Ref. Model
qbqd
Internal Model Control
Smith Predictor (1958)
PlantController
Delay
Control Signal
OutputReference
PlantController Delay
Control Signal
OutputReference
a)
b)
Smith Predictor, 1958
Plant G(s)
Controller Gc(s)
G*(s)
qbqd
Smith Predictor (cont.)
Plant G(s)
Controller Gc(s)
Gm(s) - G*(s)
qbqd
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.
Feedback Error Learning(Kawato et al, 1987)
Feedback Error Learning
Feedback Error Learning (cont.)
Model Predictive Control(1978)
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
PlantController
Plant & Disturbance Model
Optimizer Td
qb
qm
qd
Model Predictive Control Basis
Smith Predictor & MPC Comparison
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
Comparison of MPC & Smith Predictor
Case Plant Plant Model Plant Model
Delay Delay
wc = 2*pi*(0.9), wm = 2*pi*(0.54), Gc=20, time delay is in ms.
-1.2
-0.6
0
0.6
1.2
0 1 2 3 4 5 6 7
Am
plitu
de
Ref. S. P. MPC
Time (s)
-0.4
0
0.4
0 1 2 3 4 5 6 7
Err
or
S.P. MPC
Smith Predictor and MPC Outputs for Perfect Model
-0.7
-0.3
0.1
0.5
0 1 2 3 4 5 6 7
Erro
r
S.P. MPC
Smith Predictor and MPC Outputs for Time Delay Mismatch
Time (s)
-1.2
-0.4
0.4
1.2
0 1 2 3 4 5 6 7 8
Am
plitu
de
Ref. S. P. MPC
-1.4
-0.7
0
0.7
1.4
0 1 2 3 4 5 6 7
Am
plitu
deRef. S. P. MPC
-0.5
-0.1
0.3
0.7
0 1 2 3 4 5 6 7
Erro
r
S.P. MPC
Smith Predictor and MPC Outputs for Non-Minimum Phase System
Time (s)
SPC 0.2664 0.3096 0.3271 0.3830 0.2485
MPC 0.0519 0.1363 0.1428 0.2525 0.0303
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