Research on parameter updating compensator for piezoelectric actuator based on modified dynamic Prandtl-Ishlinskii model

Piezoelectric actuators are widely used in the fields of micro-nano manufacturing and precision measurement, but the hysteresis nonlinearity will reduce their positioning accuracy. Researchers normally use the hysteresis model to build a feedforward inverse compensator to suppress the hysteresis nonlinearity. However, the existing compensator generally has the situation that the parameters do not match the reference trajectory, which cannot fully utilize the advantages of the high-precision hysteresis model. Therefore, this paper proposes a Modified Dynamic Prandtl-Ishlinskii (MDPI) model and establishes a feedback inverse compensator capable of parameter update. Firstly, in view of the problem that the Dynamic Delay Prandtl-Ishlinskii (DDPI) model does not have an analytical inverse, we modified it and derived the expression of the MDPI model. Secondly, the accuracy of the two models is compared through experiments. Although some approximations are used in deriving the MDPI model, it can still accurately describe different hysteresis loops. Thirdly, an Analytical Inverse (A-I) compensator based on the MDPI model was established and compared with the Direct Inverse compensator (D-I) based on the DDPI model by experiment. We found that the A-I compensator has obvious advantages in suppressing the singular hysteresis. Finally, the controller with parameter update function is designed to update the parameters of the compensator in real time. The simulation and experiment results show that the established feedback inverse compensator can change the internal parameters for different trajectories or external environments, and further improve the positioning accuracy of the piezoelectric actuator.