This paper presents a many-objective optimization (MaOO) approach to design control and observer gains simultaneously. The many-objective optimization (MaOO) approach finds trade-offs between different nonagreeable design goals. We report the MaOO results of a proportional-integral-derivative (PID) control with a state estimator applied to a second-order oscillator. The overall system is optimized to minimize the peak time, overshoot, tracking error, and control energy, and maximize the rejection of external disturbance and measurement noise, while the relative stability, which is defined by maximum real part of eigenvalues of the closed-loop system, is constrained to be less than or equal to −1. The numerical simulations show promising findings of the proposed method.

References

References
1.
Liu
,
G. P.
, and
Daley
,
S.
,
2000
, “
Optimal-Tuning Nonlinear PID Control of Hydraulic Systems
,”
Control Eng. Pract.
,
8
(
9
), pp.
1045
1053
.
2.
Kim
,
D. H.
,
2005
, “
Tuning of PID Controller Using Gain/Phase Margin and Immune Algorithm
,”
IEEE Mid-Summer Workshop on Soft Computing in Industrial Applications
, pp.
69
74
.
3.
Bryson
,
E.
, Jr.
,
1996
, “
Optimal Control—1950 to 1985
,”
IEEE Control Syst.
,
16
(
3
), pp.
26
33
.
4.
Gambier
,
A.
, and
Jipp
,
M.
,
2011
, “
Multi-Objective Optimal Control: An Introduction
,”
8th Asian Control Conference
, pp.
1084
1089
.http://ieeexplore.ieee.org/document/5899223/
5.
Liu
,
G. P.
,
Yang
,
J.-B.
, and
Whidborne
,
J. F.
,
2003
,
Multiobjective Optimisation and Control
(Engineering Systems Modelling and Control Series), Research Studies Press, Hertfordshire, UK.
6.
CoelloCoello
,
C. A.
,
Lamont
,
G.
, and
VanVeldhuizen
,
D. A.
,
2007
,
Evolutionary Algorithms for Solving Multi-Objective Problems
,
Springer
,
New York
.
7.
Hernández
,
C.
,
Naranjani
,
Y.
,
Sardahi
,
Y.
,
Liang
,
W.
,
Schütze
,
O.
, and
Sun
,
J.-Q.
,
2013
, “
Simple Cell Mapping Method for Multi-Objective Optimal Feedback Control Design
,”
Int. J. Dyn. Control
,
1
(
3
), pp.
231
238
.
8.
Rani
,
M.
,
Selamat
,
H.
,
Zamzuri
,
H.
, and
Ibrahim
,
Z.
,
2010
, “
Multi-Objective Optimization for PID Controller Tuning Using the Global Ranking Genetic Algorithm
,”
Int. J. Innovative Comput., Inf. Control
,
8
(
1A
), pp.
269
284
.http://www.ijicic.org/ijicic-10-08085.pdf
9.
Khoie
,
M.
,
Sedigh
,
A.
, and
Salahshoor
,
K.
,
2011
, “
PID Controller Tuning Using Multi-Objective Optimization Based on Fused Genetic-Immune Algorithm and Immune Feedback Mechanism
,”
International Conference on Mechatronics and Automation
, Zhengzhou, China, Aug. 11–14, pp.
267
276
.
10.
Kumar
,
C. A.
, and
Nair
,
N. K.
,
2010
, “
NSGA-II Based Multiobjective PID Controller Tuning for Speed Control of DC Motor Drives
,”
Int. J. Soft Comput.
,
5
(
3
), pp.
83
87
.
11.
Ibtissem
,
C.
,
Noureddine
,
L.
, and
Pierre
,
B.
,
2012
, “
Tuning PID Controller Using Multiobjective Ant Colony Optimization
,”
Appl. Comput. Intell. Soft Comput.
,
2012
, p.
536326
.
12.
Esmaeil
,
A.-G.
, and
Lucas
,
C.
,
2007
, “
Designing an Optimal PID Controller Using Imperialist Competitive Algorithm
,”
First Joint Congress on Fuzzy and Intelligent Systems
, Razavi Khorasan Province, Iran, Aug. 29–31.http://www.academia.edu/699381/Designing_an_optimal_PID_controller_using_Imperialist_Competitive_Algorithm
13.
Liu
,
G. P.
, and
Daley
,
S.
,
1999
, “
Optimal-Tuning PID Controller Design in the Frequency Domain With Application to a Rotary Hydraulic System
,”
Control Eng. Pract.
,
7
(
7
), pp.
821
830
.
14.
Dorf
,
R. C.
, and
Bishop
,
R. H.
,
2011
,
Modern Control Systems
.
Prentice Hall
, Upper Saddle River, NJ.
15.
Pareto
,
V.
,
1971
(original edition in French in
1927
),
Manual of Political Economy
,
The MacMillan Press
,
London
.
16.
Deb
,
K.
,
Pratap
,
A.
,
Agarwal
,
S.
, and
Meyarivan
,
T.
,
2002
, “
A Fast and Elitist Multiobjective Genetic Algorithm: NSGA-II
,”
IEEE Trans. Evol. Comput.
,
6
(
2
), pp.
182
197
.
17.
Sardahi
,
Y.
,
2016
, “
Multi-Objective Optimal Design of Control Systems
,” Ph.D. dissertation, University of California, Merced, CA.
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