**Research on Asymmetric Hysteresis Modeling and Compensation of Piezoelectric Actuators with PMPI Model**

**Wen Wang 1, Jian Wang 1, Zhanfeng Chen 1,\*, Ruijin Wang 1, Keqing Lu 1, Zhiqian Sang 1 and Bingfeng Ju 2**


Received: 31 January 2020; Accepted: 27 March 2020; Published: 30 March 2020

**Abstract:** Because of fast frequency response, high stiffness, and displacement resolution, the piezoelectric actuators (PEAs) are widely used in micro/nano driving field. However, the hysteresis nonlinearity behavior of the PEAs affects seriously the further improvement of manufacturing accuracy. In this paper, we focus on the modeling of asymmetric hysteresis behavior and compensation of PEAs. First, a polynomial-modified Prandtl–Ishlinskii (PMPI) model is proposed for the asymmetric hysteresis behavior. Compared with classical Prandtl–Ishlinskii (PI) model, the PMPI model can be used to describe both symmetric and asymmetric hysteresis. Then, the congruency property of PMPI model is analyzed and verified. Next, based on the PMPI model, the inverse model (I-M) compensator is designed for hysteresis compensation. The stability of the I-M compensator is analyzed. Finally, the simulation and experiment are carried out to verify the accuracy of the PMPI model and the I-M compensator. The results implied that the PMPI model can effectively describe the asymmetric hysteresis, and the I-M compensator can well suppress the hysteresis characteristics of PEAs.

**Keywords:** piezoelectric actuators (PEAs); asymmetric hysteresis; Prandtl–Ishlinskii (PI) model; polynomial-modified PI (PMPI) model; feedforward hysteresis compensation
