Optimal control of a nano-positioning stage using linear matrix inequality and hierarchical genetic algorithms

Author

Yu, Gwo-Ruey ; Haung, Lun-Wei

Author_Institution

Electr. Eng. Dept., Nat. Ilan Univ., Ilan

fYear

2008

fDate

12-15 Oct. 2008

Firstpage

2834

Lastpage

2839

Abstract

This paper presents optimal fuzzy control of a nano-positioning system by linear matrix inequality (LMI) and hierarchical genetic algorithms (HGAs). First, the Bouc-Wen model describes the nonlinear hysteresis curve of a piezoelectric actuator. Then, the Takagi-Sugeno (T-S) fuzzy model approximates the Bouc-Wen equation. The parallel distributed compensation (PDC) is designed to control the nonlinear nano-positioning system. The HGAs are applied to search the optimal membership functions, state feedback gains, and rulebase of T-S fuzzy model. The stability of the nonlinear nano-positioning system is guaranteed based on the positive-definite solution of LMI.

Keywords

fuzzy control; genetic algorithms; linear matrix inequalities; nanopositioning; nonlinear control systems; optimal control; piezoelectric actuators; stability; state feedback; Bouc-Wen model; Takagi-Sugeno fuzzy model; hierarchical genetic algorithm; linear matrix inequality; nanopositioning system; nonlinear hysteresis curve; optimal fuzzy control; parallel distributed compensation; piezoelectric actuator; state feedback gain; Fuzzy control; Genetic algorithms; Hysteresis; Linear matrix inequalities; Nanopositioning; Nonlinear control systems; Nonlinear equations; Optimal control; Piezoelectric actuators; Takagi-Sugeno model; hierarchical genetic algorithms; linear matrix inequality; nano-positioning system;

fLanguage

English

Publisher

ieee

Conference_Titel

Systems, Man and Cybernetics, 2008. SMC 2008. IEEE International Conference on

Conference_Location

Singapore

ISSN

1062-922X

Print_ISBN

978-1-4244-2383-5

Electronic_ISBN

1062-922X

Type

conf

DOI

10.1109/ICSMC.2008.4811726

Filename

4811726