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

Hamed Kharrati,Witold Pedrycz,Sohrab Khanmohammadi,Ghasem Alizadeh

doi:10.1155/2012/273631

Hamed Kharrati, Witold Pedrycz + Show 2 more

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https://doi.org/10.1155/2012/273631

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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.

Highlights

Due to general and systematic platforms to deal with nonlinear control problems and various applications, research on Fuzzy Model-Based FMB control methodology has received significant attention in the last decade 1–3
To form the FMB control system, a controller is designed based on the fuzzy PDC concept to close the feedback loop
We present a methodology, which leads to the improved FMB control system including stability analysis

Summary

Introduction

Due to general and systematic platforms to deal with nonlinear control problems and various applications, research on Fuzzy Model-Based FMB control methodology has received significant attention in the last decade 1–3. The fuzzy logic strategy is one of the most popular tools for modeling and control of ill-defined and complex nonlinear plants. This line of research is motivated by the attractive properties of fuzzy logic control including robustness to disturbances, model parameter uncertainties, and sensor noise. Numerous FMB techniques have been applied to modeling, control, and stability analysis of nonlinear dynamical plants. The Lyapunov stability theory is the most common approach which is used to derive stability conditions for nonlinear plants under the FMB control systems 12–17. Achieving sound results acquired in the FMB control framework is the fundamental objective of this study

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