Sliding mode control with continuous switching function and adaptive compensation of hysteresis and disturbances for a piezoelectric flexure-stage

Abstract

Flexible stages actuated by piezoelectrics offer high resolution for nanopositioning, but they exhibit nonlinear dynamics, such as hysteresis and creep, as well as disturbances that degrade control accuracy. In this work, an adaptive Sliding Mode Control is proposed to be implemented in nanopositioning stages. The nonmeasurable hysteresis is compensated by an estimator based on the Bouc-Wen model. The proposed control algorithm allows online adjustment of the controlgain of the robust term, taking into account the effects of bounded dynamic uncertainties and disturbances whose bounds are unknown. To avoid chattering during real-time applications, a continuous saturation-type function is used in the robust term, keeping the estimated variables bounded through the incorporation of a stabilizing term in the adaptive rules. The Lyapunov techniques guarantees global stability of the system. Experimental validation of the proposed control strategy was performed on a piezoelectric actuated nanopositioning stage, showing superior performance compared to conventional sliding mode controller.