Compensation method for complex hysteresis characteristics on piezoelectric actuator based on separated level-loop Prandtl–Ishlinskii model

Abstract

Piezoelectric ceramic actuators show nonlinear hysteresis characteristics due to material properties. In order to modify the inverse piezoelectric effect as an ideal linear execution, the classical Prandtl–Ishlinskii (PI) model is usually used on compensation by feedforward control. The PI model performs well on the simple hysteresis characteristics. However, when the output requirements are complex, the PI model has uneven compensation accuracy on the complex hysteresis characteristics and cannot achieve the accuracy as same as the simple hysteresis. This paper proposes a simplification of the complex hysteresis: Separated level-loop PI (SLPI) model. Firstly, use a loop separation logic algorithm simplification of the complex hysteresis characteristics to obtain hysteresis single loops with loop levels and vertexes. Secondly, hysteresis characteristics of each loop are independently modeled using the PI model. Finally, the inverse model is reconstructed by the rollback method to restore a positive sequence of the feedforward voltage and then input the feedforward voltage as a compensation to achieve higher and more uniform accuracy. Experiments and discussions show that the SLPI model can effectively improve the compensation results of complex hysteresis characteristics by 50.3%, and the average compensation accuracy difference between single hysteresis loops is reduced by 53.7%.