Controllers Tuning through Multi-objective Non-Dominated Sorting Genetic Algorithms

CHOURAQUI Samira^1, and BENZATER Habiba¹

¹Department of Computer Science, University of Sciences and Technology USTO’MB, El Mnouar, Algeria

Cite this paper:
CHOURAQUI Samira and BENZATER Habiba. Controllers Tuning through Multi-objective Non-Dominated Sorting Genetic Algorithms. World Journal Control Science and Engineering. 2013; 1(1):15-24. doi: 10.12691/wjcse-1-1-3

Abstract

In control system design there are often a number of design objectives to be considered. The objectives are sometimes connecting and no design exists which can be considered best with respect to all objectives. Hence, there is an inevitable tradeoff between design objectives, for example, between and output performance objective and stability robustness. These considerations have led to the study of multi objective optimization methods for control systems. In this paper a multi-objective Non-Dominated sorting genetic Algorithms NSGA-II is used to tuning of Proportional Derivative (PD) controller of a six freedom arm manipulator PUMA560. The NSGAII algorithm searches for the controller PD gains so that the six values of Integral Absolute Error (IAE) in joint space are minimized. Simulation numerical results of multivariable PD control and convergence of the NSGA-II are presented and discussed.

Keywords:
arm manipulator PD control Simulink NSGA-II

This work is licensed under a Creative Commons Attribution 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/

Figures

References:

[1]	Whidborne, J.F., G. Murad, D.-W. Gu and I. Postlethwaite Robust control of an unknown plant, the IFAC 93 benchmark. Int. J. Control, vol. 61, no. 3, pp. 589-640, 1995a.
[2]	Whidborne, J. F., I. Postlethwaite and D.-W. Gu A mixed optimization approach to multi-objective computer-aided control system design, In Proc. IEEE Symp. on Comp. Aided Contr. Syst. Design (CACSD'96). Dearborn, Michigan: pp. 309-314, 1996.
[3]	Liu, G. P. and R. J. Patton, Parametric state feedback controller design of multivariable systems, International Journal of Control, vol. 61, no. 6, pp. 1457-1464, 1995.
[4]	Liu, G. P. and R. J. Patton, Robust control design using eigenstructure assignment and multiobjective optimization, Int. Journal of Systems Science, vol. 27, no. 9, pp. 871-879, 1996.
[5]	Whidborne, J.F., I. Postlethwaite and D.-W. Gu, Multiobjective control system designs a mixed optimization approach, Recent Trends in Optimization Theory and Applications, R. P. Agarwal (ed.), vol. 5 of World Scientificc Series in Applicable Analysis Singapore: World Scientific pp. 467-482, 1995b.
[6]	Liu, G. P. and S. Daley, Stable dynamical controller designs for robust polynomial pole assignment,. IEE Proceedings, Part D, vol. 145, no. 3, pp. 259-264, 1998.
[7]	Liu, G. P. and S. Daley, Optimal-tuning PID control for industrial systems, Control Engineering Practice, vol. 9, 2001 (accepted).
[8]	Liu, G. P. and V. Kadirkamanathan, Multiobjective criteria for nonlinear model selection and identification with neural networks, IEE Proceedings, Part D, vol. 146, no. 5, pp. 373-382, 1999.
[9]	Chen, J., R. J. Patton and G. P. Liu, Optimal residual design for fault diagnosis using multi-objective optimisation and genetic algorithms, International Journal of Systems Science, vol. 27, no. 6, pp. 567-576, 1996.
[10]	Tabak, T., A. A. Schy, D. P. Giesy, and K. G. Johnson, Application of multiple objective optimization in aircraft control systems design,. Automatica, vol. 15, pp. 595-600. 1979.
[11]	Skelton, R. E. and M. DeLorenzo, Spacestructure control design by variance assignment, J, Guid., vol. 8, no. 4, pp. 454-462. 1985.
[12]	Koussoulas, N. T. and C. T. Leondes, The multiple linear quadratic Gaussian problems. International Journal of Control, vol. 43, no. 2, pp. 337-349. 1986.
[13]	Toivonen, H. T. and P. M. Makila, Computer-aided design procedure for multi-objective LQG control problems, International Journal of Control, vol. 49, no. 2, pp. 655-666. 1989.
[14]	Khargonekar, P. P. and M. A. Rotea, Multiple objective optimal control of linear systems: the quadratic norm case,IEEE Trans. Automat. Contr., vol. 36, no.1, pp. 14-24, 1991.
[15]	Jaimes A.L., Zapotecas Martinez S., C.A. C. Coello, Chapter 1 An Introduction To Multi-Objective Optimization Techniques, In: Book Title Editor: Editor Name, pp. 1-26, 2009 Nova Science Publishers, Inc.
[16]	Gambier A, MPC and PID Control Based on Multi-objective Optimization, American Control Conference Westin Seattle Hotel, Seattle, Washington, USA, June 11-13, 2008.
[17]	Zitzler E and Thiele L, Multiobjective evolutionary algorithms: a comparative case study and the strength Pareto approach. IEEE Transactions on Evolutionary Computation, 1999, 3(4):257-271.
[18]	J. Rutherford, Using the PUMA560 Robot, PUMA Unofficial User’s Guide, 2012.
[19]	J. J. Craig, Introduction to Robotics Mechanics and Control, Third Edition” 2005 Pearson Education, Inc.
[20]	B Armstrong, O Khatib, Joel Burdick, The Explicit Dynamic Model and Inertial Parameters of the PUMA 560 Arm, IEEE, 1986.
[21]	W. khalil, E. Dombre, Modélisation et commande des robots, Hermes Edition, Paris, 1988.
[22]	J. J. Craig, Introduction to Robotics Mechanics and Control, second Edition, 1989, 1986 by Addison-Wesley Publishing Company, Inc.
[23]	F. Piltan , M.H. Yarmahmoudi, M. Shamsodini, E. Mazlomian & A. Hosainpour, PUMA-560 Robot Manipulator Position Computed Torque Control Methods Using MATLAB/SIMULINK and Their Integration into Graduate Nonlinear Control and MATLAB Courses, International Journal of Robotics and Automation, (IJRA), Volume (3): Issue (3) : 2012.
[24]	D. Czarkowski, Identification And Optimization PID Parameters Using Matlab, report of the project for bachelor of engineering in electronics, Cork Institute of Technology Gdynia Maritime University, Cork 2002.
[25]	Sumathi S, Surekha P, Computational intelligence paradigms: theory & applications using MATLAB, © 2010 by Taylor and Francis Group, 2010.
[26]	N. Moreira , P. Alvito and P. Lima, First steps towards an open control architecture for a PUMA 560, Proc. 2nd Portuguese Conf. On Automatic Control, 1996.