Piecewise modified Prandtl-Ishlinskii model for precise nano-positioning

Abstract

Piezoelectric ceramic, an indispensable micro-nano actuator, has advantages of small size, high sensitivity and strong controllability, which is widely applied in various fields like micro-nano processing, medicine, chemistry and materials. However, its nonlinear and asymmetric hysteresis features directly affect its positioning accuracy. The classical and generalized Prandtl-Ishlinskii models with linear symmetry operators are commonly used to deal with these issues, but they still face difficulties in asymmetric systems. Therefore, a piecewise modified Prandtl-Ishlinskii (PMPI) model is proposed to compensate nonlinear and asymmetric hysteresis in this paper. The new nonlinear operator and piecewise nonlinear envelope function are introduced into the PMPI model. Independent right and left parts are adopted to describe hysteresis increasing and decreasing stages, while the threshold and weight vectors correspond to them. Weight vectors are extended and a new diagonal matrix is constructed for avoiding excessive parameters and computation. Simulations and experiments are shown that the PMPI model has good compensation performance and effectiveness, which has better fitting, higher accuracy, fewer parameters and computation, and can be well applied to the precise nano-positioning systems with less nonlinear and asymmetric errors.