Download - Evaluation of model-based predictive control
Student: Daniel Czarkowski
Supervisor: Tom O’Mahony
date 25/03/2003
Evaluation of model-based predictive control
Overview
• Background Model Based – Predictive Control
• Generalised Predictive control
• Models
• Benchmarks: GPC versus PI
3
MBPC
• Features of MBPC– All of them use a process model– The optimum control sequence is obtained
through the minimization of a cost index– Only the first element of this sequence is
transmitted to the plant as the current control u(t) (receding horizon)
4
MBPC
• Model Based Predictive Control can be achieved according to:– The type of model used– The type of cost function used– The optimization method applied
5
Model - based control
yProcess
uwController
ControllerDesign
Controllerparameters
DesignParameters
Model
6
• CARIMA model
• Cost function
GPC
)(
)()()1()()()( 1
111
z
tzCtuzBtyzA
2
1 1
2221 )1()()()(ˆ),(
N
Nj
N
j
u
jtujjtwjtyNNJ
7
GPC
• Implementation of a Genetic Algorithm for minimization IAE:– Servo response– Regulatory disturbance– Combined
8
Models
• The models of benchmarked plant were taken from Astrom
3)1(
1)(
s
sG
)008.01)(04.01)(2.01)(1(
1)(
sssssG
3)1(
21)(
s
ssG
9
PI controller
IAE
ZN: 6.25
Lambda:13.79
Non-Convex:5.07
3)1(
1)(
s
sG
10
PI vs. GPC
• GPCn1=1 n2=2 nu=1 λ=1*10-6
T-polynomial=(1-0.63*z-1)
Sampling Period = 0.7 (sec.)
IAE=0.91
• PI controllerk=0.862 ki=0.461
IAE=5.07
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Sampling Period
n1=2 n2=3 nu=1 λ=1*10-6
T-polynomial=1+0.9*z-1
• Ts=0.7sec. IAE=0.81• Ts=0.1sec. IAE=0.3
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Searching area
010
2030
40
0
20
400
0.5
1
1.5
n2n1
IAE
010
2030
40
0
10
20
30
402
4
6
8
10
n2n1
Gai
n M
arg
in [
db
]
010
2030
40
0
10
20
30
4010
20
30
40
50
60
70
n2n1
Ph
ase
Mar
gin
[d
eg]
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Benchmark of GPC
)008.01)(04.01)(2.01)(1(
1)(
sssssG
• Fourth Order System:
GPCn1=2 n2=3 nu=1 λ=1*10-6 Tpoly=1+0.293*z-1
IAE=0.23
PI controllerk=2.74 ki=4.08
IAE=0.82
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Benchmark of GPC
Nonminimum-phase model3)1(
21)(
s
ssG
GPC
n1=4 n2=4 nu=1 Ts=0.83
Tpoly=(1-0.224*z-1)3
IAE=8.10
PI controller
k=0.294 ki=0.184
IAE=14,4
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Conclusions
• The Åström benchmark test was developed for PI controller
• A Genetic Algorithm was implemented for tuning GPC controller
• Part of comparison has been done
Questions?