Intelligent controller design based on gain and phase margin specifications
-
Upload
reuben-bishop -
Category
Documents
-
view
26 -
download
1
description
Transcript of Intelligent controller design based on gain and phase margin specifications
![Page 1: Intelligent controller design based on gain and phase margin specifications](https://reader035.fdocuments.net/reader035/viewer/2022062421/56812af3550346895d8ed983/html5/thumbnails/1.jpg)
Intelligent controller design based on gain and phase margin specifications
Daniel Czarkowski and Tom O’Mahony*
Advanced Control Group,
Department of Electronics Engineering,
Cork Institute of Technology,
e-mails: [email protected] * [email protected]
![Page 2: Intelligent controller design based on gain and phase margin specifications](https://reader035.fdocuments.net/reader035/viewer/2022062421/56812af3550346895d8ed983/html5/thumbnails/2.jpg)
ISSC 2004, Belfast 2
Overview
• Do advanced control structures significantly outperform PID for SISO systems?
• Compare– PID– 2-DOF PID– GPC
![Page 3: Intelligent controller design based on gain and phase margin specifications](https://reader035.fdocuments.net/reader035/viewer/2022062421/56812af3550346895d8ed983/html5/thumbnails/3.jpg)
ISSC 2004, Belfast 3
Contents List
• Types of controllers
• Tuning– Gain and phase margin criteria– Non convex problem to be solved– Genetic Algorithms
• Models used in the evaluation
• Results
• Conclusions
![Page 4: Intelligent controller design based on gain and phase margin specifications](https://reader035.fdocuments.net/reader035/viewer/2022062421/56812af3550346895d8ed983/html5/thumbnails/4.jpg)
ISSC 2004, Belfast 4
PID controller
• Controller structure
• Control law
• 3 Variables to tune
R(s)
D(s)
G(s)C(s)Y(s)E(s) U(s)
( ) ( ) ip d
KU s E s K K s
s
, ,p i dK K K
![Page 5: Intelligent controller design based on gain and phase margin specifications](https://reader035.fdocuments.net/reader035/viewer/2022062421/56812af3550346895d8ed983/html5/thumbnails/5.jpg)
ISSC 2004, Belfast 5
2-DOF PID controller
• Controller structure
• Control law
• 6 variables to tune
D(s)
G(s)F(s)Y(s)
H(s)
U(s)R(s)
( ) ( )( ) ( ) ( ) ( ) ( )
1
dip
d
p
sK c R s Y sKU s K b R s Y s R s Y s
sKsK N
, , , , ,p i dK K K b c N
![Page 6: Intelligent controller design based on gain and phase margin specifications](https://reader035.fdocuments.net/reader035/viewer/2022062421/56812af3550346895d8ed983/html5/thumbnails/6.jpg)
ISSC 2004, Belfast 6
GPC controller
• Introduced by Clarke et al., 1987
• Two degree of freedom structure
• Digital controller was used
• Unconstrained control algorithm
• 7 tuning parameters1
1 2, , , , ( )uN N N T z
![Page 7: Intelligent controller design based on gain and phase margin specifications](https://reader035.fdocuments.net/reader035/viewer/2022062421/56812af3550346895d8ed983/html5/thumbnails/7.jpg)
ISSC 2004, Belfast 7
GPC properties
• Advantages– Two degree of freedom– Optimal controller– Can handle more complex systems– More flexible structure
• Disadvantages– No well developed tuning rules– More difficult to tune– Very few industrial implementations
![Page 8: Intelligent controller design based on gain and phase margin specifications](https://reader035.fdocuments.net/reader035/viewer/2022062421/56812af3550346895d8ed983/html5/thumbnails/8.jpg)
ISSC 2004, Belfast 8
Design strategy
• Performance & robustness
• Performance– IAE servo + regulator
• Robustness– Gain and phase margin
1 2
1
1
0
( ) ( )t t
k k t
IAE e k e k
6 , 45
14 , 45
m m
m m
A dB
A dB
![Page 9: Intelligent controller design based on gain and phase margin specifications](https://reader035.fdocuments.net/reader035/viewer/2022062421/56812af3550346895d8ed983/html5/thumbnails/9.jpg)
ISSC 2004, Belfast 9
Non-convex problem
• Inverse unstable system
00.2
0.40.6
0.81
0
0.1
0.2
0.3
0.410.5
11
11.5
12
KpKi
IAE
local minimum
global minimum
Avoid local minima!
3
1 2( )
( 1)
sG s
s
![Page 10: Intelligent controller design based on gain and phase margin specifications](https://reader035.fdocuments.net/reader035/viewer/2022062421/56812af3550346895d8ed983/html5/thumbnails/10.jpg)
ISSC 2004, Belfast 10
Genetic Algorithms
• Stochatistic optimisation method– Gray Coding– Stochatistic Universal Sampling, SUS– Single point crossover– Maximum number of generations, 300– Population size, 100– Constraints on the controller parameters
![Page 11: Intelligent controller design based on gain and phase margin specifications](https://reader035.fdocuments.net/reader035/viewer/2022062421/56812af3550346895d8ed983/html5/thumbnails/11.jpg)
ISSC 2004, Belfast 11
Direct the GA
• GA optimisation problem
• Penality factors on gain and phase margins
min . . 6 , 45Am m m mJ IAE s t A dB
0 2 4 6 80
2
4
6
8
10
Am (dB)
Am
0 10 20 30 40 50 600
2
4
6
8
10
m (deg)
m
![Page 12: Intelligent controller design based on gain and phase margin specifications](https://reader035.fdocuments.net/reader035/viewer/2022062421/56812af3550346895d8ed983/html5/thumbnails/12.jpg)
ISSC 2004, Belfast 12
Models
• Benchmark test– Inverse unstable system– Integrating systems– Underdamped system– Conditionally stable system– 3 models with time delay– First order model
• 12 models were evaluated
(K. J. Åström 1998, 2000)
![Page 13: Intelligent controller design based on gain and phase margin specifications](https://reader035.fdocuments.net/reader035/viewer/2022062421/56812af3550346895d8ed983/html5/thumbnails/13.jpg)
ISSC 2004, Belfast 13
Results
• Comparison of PID, 2-DOF PID and GPC, 6 , 45m mIAE A dB , 14 , 45m mIAE A dB
GPC outperforms the other two counterparts
1 2 3 4 5 6 7 8 9 10 11 120
2
4
6
8
10
12
IAE
Model number1 2 3 4 5 6 7 8 9 10 11 12
0
2
4
6
8
10
12
14
16
IAE
Model number
![Page 14: Intelligent controller design based on gain and phase margin specifications](https://reader035.fdocuments.net/reader035/viewer/2022062421/56812af3550346895d8ed983/html5/thumbnails/14.jpg)
ISSC 2004, Belfast 14
Results
• Design based on minimum Am=6dB– GPC vs PID, average IAE decreased by 43%– GPC vs 2-DOF PID, average IAE decreased by 25%– 2-DOF PID vs PID, average IAE decreased by 24%
• Design based on minimum Am=14dB– GPC vs PID, average IAE decreased by 37%– GPC vs 2-DOF PID, average IAE decreased by 22%– 2-DOF PID vs PID, average IAE decreased by 15%
![Page 15: Intelligent controller design based on gain and phase margin specifications](https://reader035.fdocuments.net/reader035/viewer/2022062421/56812af3550346895d8ed983/html5/thumbnails/15.jpg)
ISSC 2004, Belfast 15
Set-point following
• Model
• Design
• Results
0 5 10 15 200
0.5
1
1.5
y(t)
0 5 10 15 20-1
0
1
2
3
4
5
u(t)
Time (sec)
GPC
2-DOF PIDPID
, 6 , 45m mIAE A dB
3
1( )
( 1)G s
s
2.08 1.62 1.54
14.64
2
6.83
GPCPI
IAE
A
F
m
D DO
Better robustness achieved by PID controllers!
![Page 16: Intelligent controller design based on gain and phase margin specifications](https://reader035.fdocuments.net/reader035/viewer/2022062421/56812af3550346895d8ed983/html5/thumbnails/16.jpg)
ISSC 2004, Belfast 16
• Model
• Design
• Results
Set-point following
0 10 20 30 40 50 60 70 800
0.5
1
1.5
2
y(t)
0 10 20 30 40 50 60 70 80-0.5
0
0.5
1
1.5
u(t)
Time (sec)
GPC
PID
2-DOF PID
, 6 , 45m mIAE A dB
13
51( )
( 1)sG
ses
42.9 41 33.52
6.27 6.02 6.
2
00
IAE
A
GP POF
m
CID D
GPC performs 25% better than the PID controllers!
![Page 17: Intelligent controller design based on gain and phase margin specifications](https://reader035.fdocuments.net/reader035/viewer/2022062421/56812af3550346895d8ed983/html5/thumbnails/17.jpg)
ISSC 2004, Belfast 17
Set-point following
• Model
• Design
• Results
153
1( )
( 1)G s e
s
4, 451 ,m mdIAE A B
53.9 53.7 55.3
14.00 14.01 1
2
4.00
IAE
Am
PID GPCDOF
0 20 40 60 80 100 120 140 160 180 2000
0.5
1
1.5
2
y(t)
0 20 40 60 80 100 120 140 160 180 200-0.5
0
0.5
1
1.5
u(t)
Time (sec)
GPC
GPC does not perform better than the PID controllers!
![Page 18: Intelligent controller design based on gain and phase margin specifications](https://reader035.fdocuments.net/reader035/viewer/2022062421/56812af3550346895d8ed983/html5/thumbnails/18.jpg)
ISSC 2004, Belfast 18
Summary of work
• A GA approach to tuning controllers based on gain and phase margin was applied
• Novel optimisation function was proposed
• Twelve models were tuned
• Three controllers were evaluated
• The controllers were subsequently employed on a real time system
![Page 19: Intelligent controller design based on gain and phase margin specifications](https://reader035.fdocuments.net/reader035/viewer/2022062421/56812af3550346895d8ed983/html5/thumbnails/19.jpg)
ISSC 2004, Belfast 19
Conclusions
• GPC performance depends on the sampling period
• Tuning strategy works well, but...
• GPC performed better in simulation, but...
• Do advanced control algorithms perform better?
![Page 20: Intelligent controller design based on gain and phase margin specifications](https://reader035.fdocuments.net/reader035/viewer/2022062421/56812af3550346895d8ed983/html5/thumbnails/20.jpg)
Questions?