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

Piezoelectric ceramic actuators exhibit nonlinear hysteresis characteristics owing to their material properties. To modify the inverse piezoelectric effect as an ideal linear execution, the classical Prandtl–Ishlinskii (PI) model is usually used for compensation by feedforward control. The PI model compensates well on simple hysteresis characteristics. However, when the output requirements are complex, the PI model demonstrates uneven compensation accuracy on the complex hysteresis characteristics and cannot achieve an accuracy similar to that of simple hysteresis. This paper proposes a simplification of complex hysteresis: Separated Level-loop PI (SLPI) model. First, we use a loop-separation logic algorithm to simplify the complex hysteresis characteristics to obtain hysteresis in the form of single loops with loop levels and vertexes. Second, the hysteresis characteristics of each loop are independently modeled using the PI model. Finally, the inverse model is reconstructed using a rollback method to restore a positive sequence of the feedforward voltage; then, the feedforward voltage is input as a compensation value 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; moreover, the average compensation accuracy difference between single hysteresis loops was reduced.