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
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.
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 PredictorComparison 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
pli
tu
de
Ref. S. P. MPC
Time (s)
-0.4
0
0.4
0 1 2 3 4 5 6 7
Erro
r
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 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
pli
tud
e
Ref. S. P. MPC
-1.4
-0.7
0
0.7
1.4
0 1 2 3 4 5 6 7
Am
pli
tu
de Ref. 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 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. )
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