Discrete‐time adaptive fuzzy control with hysteresis observer for a three‐axis flexure stage

Abstract

This paper first derives the discrete‐time dynamic model, including hysteresis effect, for a three‐axis piezoactuated micro/nano flexure stage. Based on the discrete‐time model, an adaptive controller with hysteresis variables observer is designed via Lyapunov stability theory. In the stable adaptive controller, a fuzzy function approximator with normalized gradient parameters update law is included to compensate for the identification inaccuracy, model uncertainty, and flexure coupling effects. Simulation results are used for illustrating control performance.