Modeling and compensation for dynamic hysteresis of piezoelectric actuators based on Lissajous Curve

Abstract

Piezoelectric actuators, which are widely used in micro-positioning systems, have hysteresis characteristics between the input and output. In particular, the hysteresis loop is complicated and difficult to be described when the input amplitude and frequency change. Most existing dynamic models cannot describe the law of dynamic hysteresis accurately, such as describing the zero drift of the hysteresis loop. In this paper, a novel and accurate model based on the Lissajous Curve is proposed to describe and compensate the dynamic hysteresis. Firstly, the performance of the piezoelectric actuator is tested, and the experimental results are quantified to research the law of dynamic hysteresis. Secondly, the Lissajous Curve Prandtl-Ishlinskii (LC-PI) model is proposed and the influence of differential order on the operator and memoryless function is discussed. Thirdly, three experiments are designed to verify the LC-PI model. Compared with the existing models, the LC-PI model can describe different types of dynamic hysteresis loops more accurately under the same modeling conditions. Finally, the LC-PI model is used to compensate the dynamic hysteresis. Experimental results show that the compensator based on this model can effectively suppress the dynamic hysteresis of the piezoelectric actuator.