Journal of Applied Mathematics
Volume 2012 (2012), Article ID 639014, 22 pages
Research Article

Pareto Design of Decoupled Sliding-Mode Controllers for Nonlinear Systems Based on a Multiobjective Genetic Algorithm

1Department of Mechanical Engineering, Faculty of Engineering, University of Guilan, P.O. Box 3756, Rasht, Iran
2Intelligent-Based Experimental Mechanics Center of Excellence, School of Mechanical Engineering, Faculty of Engineering, University of Tehran, Tehran, Iran
3Department of Mechanical Engineering, Takestan Branch, Islamic Azad University, Takestan, Iran

Received 11 January 2012; Revised 4 April 2012; Accepted 8 April 2012

Academic Editor: Zhiwei Gao

Copyright © 2012 M. J. Mahmoodabadi et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper presents Pareto design of decoupled sliding-mode controllers based on a multiobjective genetic algorithm for several fourth-order coupled nonlinear systems. In order to achieve an optimum controller, at first, the decoupled sliding mode controller is applied to stablize the fourth-order coupled nonlinear systems at the equilibrium point. Then, the multiobjective genetic algorithm is applied to search the optimal coefficients of the decoupled sliding-mode control to improve the performance of the control system. Considered objective functions are the angle and distance errors. Finally, the simulation results implemented in the MATLAB software environment are presented for the inverted pendulum, ball and beam, and seesaw systems to assure the effectiveness of this technique.