Modeling, identification and compensation of hysteresis nonlinearity for a piezoelectric nano-manipulator

Abstract

Hysteresis nonlinearity widely exists in piezoelectric actuated nano-positioning applications, which degrades their tracking accuracy and limits their precision positioning applications. This paper presents a novel hysteresis modeling and compensation approach to alleviate the adverse effect of the asymmetric and rate-dependent hysteresis nonlinearity for a piezoelectric transducer actuated servo stage. By integrating a generalized input function with the play operator of the classical Prandtl–Ishlinskii model, a novel polynomial-based rate-dependent Prandtl–Ishlinskii (PRPI) model is proposed to capture the hysteresis behavior of the piezoelectric positioning stage, where a polynomial function of input and a time rate function of input are introduced to formulate the generalized input function. Meanwhile, a new adaptive differential evolution optimization algorithm is developed to identify the parameters of the proposed PRPI hysteresis model. Based on the PRPI hysteresis model with the identified parameters, an inverse feedforward controller is constructed to achieve the accurate tracking motion. Furthermore, the hysteresis compensation error of the proposed PRPI model is theoretically analyzed. Finally, comparative experiments are conducted, and the experimental results provided in this paper demonstrate the effectiveness and superiority of the proposed inverse PRPI model compensation approach.