Multi-Objective Optimal Feedback Controls for Under-Actuated Dynamical System

doi:10.1007/s12204-020-2211-2

Journal of Shanghai Jiao Tong University(Science) ›› 2020, Vol. 25 ›› Issue (5): 545-552.doi: 10.1007/s12204-020-2211-2

• • 下一篇

Multi-Objective Optimal Feedback Controls for Under-Actuated Dynamical System

QIN Zhichang (秦志昌), XIN Ying (辛英), SUN Jianqiao (孙建桥)

(1. School of Transportation and Vehicle Engineering, Shandong University of Technology, Zibo 255000, Shandong, China;
2. School of Mechanical Engineering, Tianjin University of Technology, Tianjin 300384, China; 3. Tianjin Key Laboratory
for Advanced Mechatronic System Design and Intelligent Control, Tianjin University of Technology, Tianjin 300384, China;
4. School of Engineering, University of California Merced, CA 95343, USA)

出版日期:2020-10-28 发布日期:2020-09-11
通讯作者: QIN Zhichang (秦志昌) E-mail:zcqin@sdut.edu.cn

Multi-Objective Optimal Feedback Controls for Under-Actuated Dynamical System

QIN Zhichang (秦志昌), XIN Ying (辛英), SUN Jianqiao (孙建桥)

(1. School of Transportation and Vehicle Engineering, Shandong University of Technology, Zibo 255000, Shandong, China;
2. School of Mechanical Engineering, Tianjin University of Technology, Tianjin 300384, China; 3. Tianjin Key Laboratory
for Advanced Mechatronic System Design and Intelligent Control, Tianjin University of Technology, Tianjin 300384, China;
4. School of Engineering, University of California Merced, CA 95343, USA)

Online:2020-10-28 Published:2020-09-11
Contact: QIN Zhichang (秦志昌) E-mail:zcqin@sdut.edu.cn

摘要/Abstract

摘要： This paper presents a study of optimal control design for a single-inverted pendulum (SIP) system with
the multi-objective particle swarm optimization (MOPSO) algorithm. The proportional derivative (PD) control
algorithm is utilized to control the system. Since the SIP system is nonlinear and the output (the pendulum angle)
cannot be directly controlled (it is under-actuated), the PD control gains are not tuned with classical approaches.
In this work, the MOPSO method is used to obtain the best PD gains. The use of multi-objective optimization
algorithm allows the control design of the system without the need of linearization, which is not provided by
using classical methods. The multi-objective optimal control design of the nonlinear system involves four design
parameters (PD gains) and six objective functions (time-domain performance indices). The Hausdorff distances of
consecutive Pareto sets, obtained in the MOPSO iterations, are computed to check the convergence of the MOPSO
algorithm. The MOPSO algorithm finds the Pareto set and the Pareto front efficiently. Numerical simulations
and experiments of the rotary inverted pendulum system are done to verify this design technique. Numerical and
experimental results show that the multi-objective optimal controls offer a wide range of choices including the
ones that have comparable performance to the linear quadratic regulator (LQR) control.

关键词: multi-objective optimal control, under-actuated system, particle swarm optimization (PSO), rotary
inverted pendulum

Abstract: This paper presents a study of optimal control design for a single-inverted pendulum (SIP) system with
the multi-objective particle swarm optimization (MOPSO) algorithm. The proportional derivative (PD) control
algorithm is utilized to control the system. Since the SIP system is nonlinear and the output (the pendulum angle)
cannot be directly controlled (it is under-actuated), the PD control gains are not tuned with classical approaches.
In this work, the MOPSO method is used to obtain the best PD gains. The use of multi-objective optimization
algorithm allows the control design of the system without the need of linearization, which is not provided by
using classical methods. The multi-objective optimal control design of the nonlinear system involves four design
parameters (PD gains) and six objective functions (time-domain performance indices). The Hausdorff distances of
consecutive Pareto sets, obtained in the MOPSO iterations, are computed to check the convergence of the MOPSO
algorithm. The MOPSO algorithm finds the Pareto set and the Pareto front efficiently. Numerical simulations
and experiments of the rotary inverted pendulum system are done to verify this design technique. Numerical and
experimental results show that the multi-objective optimal controls offer a wide range of choices including the
ones that have comparable performance to the linear quadratic regulator (LQR) control.

Key words: multi-objective optimal control, under-actuated system, particle swarm optimization (PSO), rotary
inverted pendulum

中图分类号:

O 232
TP 183

QIN Zhichang, XIN Ying, SUN Jianqiao . Multi-Objective Optimal Feedback Controls for Under-Actuated Dynamical System[J]. Journal of Shanghai Jiao Tong University(Science), 2020, 25(5): 545-552.

参考文献 25

[1]	HO W K, GAN O P, TAY E B, et al. Performance and gain and phase margins of well-known PID tuning formulas [J]. IEEE Transactions on Control Systems Technology, 1996, 4(4): 473-477.
[2]	WANG Q G, LEE T H, FUNG H W, et al. PID tuning for improved performance [J]. IEEE Transactions on Control Systems Technology, 1999, 7(4): 457-465.
[3]	ZIEGLER J G, NICHOLS N B. Optimum settings for automatic controllers [J]. Journal of Dynamic Systems,Measurement, and Control, 1993, 115 (2): 220-222.
[4]	NGATCHOU P, ZAREI A, EI-SHARKAWI M A. Pareto multi-objective optimization [C]//Proceedings of the 13th International Conference on Intelligent Systems Application to Power Systems. Arlington, VA,USA: IEEE, 2005: 84-91.
[5]	AYALA H V H, DOS SANTOS COELHO L. Tuning of PID controller based on a multiobjective genetic algorithm applied to a robotic manipulator [J]. Expert Systems with Applications, 2012, 39(10): 8968-8974.
[6]	XU Z H, LI S, CHEN Q W, et al. MOPSO based multi-objective trajectory planning for robot manipulators [C]//Proceedings of International Conference on Information Science and Control Engineering. Shanghai,China: IEEE, 2015: 824-828.
[7]	CENSOR Y. Pareto optimality in multiobjective problems[J]. Applied Mathematics & Optimization, 1977,4(4): 41-59.
[8]	DELLNITZ M, SCH¨UTZE O, HESTERMEYER T. Covering Pareto sets by multilevel subdivision techniques[J]. Journal of Optimization Theory and Applications,2005, 124(1): 113-136.
[9]	SRINIVAS M, PATNAIK L M. Genetic algorithms: A survey [J]. Computer, 1994, 27(6): 17-26.
[10]	KARABOGA D, BASTURK B. A powerful and efficient algorithm for numerical function optimization:Artificial bee colony (ABC) algorithm [J]. Journal of Global Optimization, 2007: 39(3): 459-471.
[11]	CHUN J S, KIM M K, JUNG H K, et al. Shape optimization of electromagnetic devices using immune algorithm[J]. IEEE Transactions on Magnetics, 1997,33(2): 1876-1879.
[12]	KENNEDY J, EBERHART R. Particle swarm optimization [C]//Proceedings of IEEE International Conference on Neural Networks. Perth, Australia: IEEE,1995: 1942-1948.
[13]	KENNEDY J, EBERHART R. Particle swarm optimization[M]//Encyclopedia of Machine Learning.Boston, MA, USA: Springer, 2011: 760-766.
[14]	ZHAO S Z, IRUTHAYARAJANM W, BASKAR S, et al. Multi-objective robust PID controller tuning using two lbests multi-objective particle swarm optimization[J]. Information Sciences, 2011, 181(16): 3323-3335.
[15]	GIRIRAJKUMAR S M, JAYARAJ D, KISHAN A R.PSO based tuning of a PID controller for a high performance drilling machine [J]. International Journal of Computer Applications, 2010, 1(19): 12-18.
[16]	HASSANZADEH I, MOBAYEN S. PSO-based controller design for rotary inverted pendulum system [J].Journal of Applied Sciences, 2008, 8(16): 2907-2912.
[17]	JAAFAR H I, SULAIMA M F, MOHAMED Z,et al. Optimal PID controller parameters for nonlinear gantry crane system via MOPSO technique[C]//Proceedings of IEEE International Conference on Sustainable Utilization and Development in Engineering and Technology. Selangor, Malaysia: IEEE, 2013:86-91.
[18]	ZHAO Q Q, QIN Z C, SUN J Q. Influence of design reference on tracking performance of feedback control[J]. Transactions of Tianjin University, 2018, 24(1):66-72.
[19]	PARSOPOULOS K E, VRAHATIS M N. Particle swarm optimization method in multiobjective problems [C]//Proceedings of ACM Symposium on Applied Computing. Madrid, Spain: ACM, 2002: 603-607.
[20]	COELLO C A C, LECHUGA M S. MOPSO: A proposal for multiple objective particle swarm optimization [C]//Proceedings of the Congress on Evolutionary Computation. Honolulu, HI, USA: IEEE, 2002: 1051-1056.
[21]	POLI R, KENNEDY J, BLACKWELL T. Particle swarm optimization: An overview [J], Swarm Intelligence,2007, 1(1): 33-57.
[22]	COELLO C A C, PULIDO G T, LECHUGA M S.Handling multiple objectives with particle swarm optimization[J]. IEEE Transactions on Evolutionary Computation, 2004, 8(3): 256-279.
[23]	COELLO C A C, LAMONT G B, VAN VELDHUIZEN D A. Evolutionary algorithms for solving multi-objective problems [M]. 2nd ed. New York, USA:Springer, 2007.
[24]	HUTTENLOCHER D P, KLANDERMAN G A, RUCKLIDGEWJ. Comparing images using the Hausdorff distance [J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 1993, 15(9): 850-863.
[25]	SCH¨UTZE O, ESQUIVEL X, LARA A, et al. Using the averaged Hausdorff distance as a performance measure in evolutionary multiobjective optimization[J]. IEEE Transactions on Evolutionary Computation,2012, 16(4): 504-522.

Multi-Objective Optimal Feedback Controls for Under-Actuated Dynamical System

Multi-Objective Optimal Feedback Controls for Under-Actuated Dynamical System

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