Modeling and Compensation Algorithms of Asymmetric Nonlinearity for Piezoelectric Actuators Based on Madelung's Rules

This article presents a hysteresis modeling algorithm to describe the asymmetric nonlinearity in piezoelectric actuators (PEAs). The proposed algorithm primarily consists of two parts: 1) the wiping-out mechanism, and 2) the description method for the current hysteresis curve (CHC). The first part is associated with the realization of the wiping-out mechanism. It is used to determine the hysteresis curve where the hysteresis trajectory moves along, and this curve represents the CHC. In the second part, the information of the major ascending or descending curve is used to describe the CHC, and meanwhile, the trajectory is also described. The proposed algorithm works in real-time, which provides an intuitive mechanism to understand and investigate the asymmetric hysteresis nonlinearity in PEAs. Furthermore, the analytical inverse modeling algorithm is proposed to reduce the hysteresis effect. Experiments are conducted to validate the effectiveness of the proposed algorithms.