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

11

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

12

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]

13

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

14

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

15

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?