Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 273631, 21 pages
http://dx.doi.org/10.1155/2012/273631
Research Article

Improved Polynomial Fuzzy Modeling and Controller with Stability Analysis for Nonlinear Dynamical Systems

Hamed Kharrati,1,2 Sohrab Khanmohammadi,1 Witold Pedrycz,2 and Ghasem Alizadeh1

1Faculty of Electrical and Computer Engineering, University of Tabriz, P.O. Box 5166616471, Tabriz, Iran
2Department of Electrical and Computer Engineering, University of Alberta, Edmonton, AB, Canada T6G 2V4

Received 25 May 2012; Revised 30 September 2012; Accepted 4 October 2012

Academic Editor: Mohammed Chadli

Copyright © 2012 Hamed Kharrati 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.

Abstract

This study presents an improved model and controller for nonlinear plants using polynomial fuzzy model-based (FMB) systems. To minimize mismatch between the polynomial fuzzy model and nonlinear plant, the suitable parameters of membership functions are determined in a systematic way. Defining an appropriate fitness function and utilizing Taylor series expansion, a genetic algorithm (GA) is used to form the shape of membership functions in polynomial forms, which are afterwards used in fuzzy modeling. To validate the model, a controller based on proposed polynomial fuzzy systems is designed and then applied to both original nonlinear plant and fuzzy model for comparison. Additionally, stability analysis for the proposed polynomial FMB control system is investigated employing Lyapunov theory and a sum of squares (SOS) approach. Moreover, the form of the membership functions is considered in stability analysis. The SOS-based stability conditions are attained using SOSTOOLS. Simulation results are also given to demonstrate the effectiveness of the proposed method.