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

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.