Adaptive compound control based on generalized Bouc–Wen inverse hysteresis modeling in piezoelectric actuators

Abstract

This paper focuses on the study of the dynamic hysteresis compensation and control of piezoelectric actuators so as to improve the swing accuracy of the piezoelectric fast steering mirror mechanism in the photoelectric compound-axis control system. Moreover, in view of the rate dependence and asymmetry of piezoelectric hysteresis, and the complex inversion process of the generalized Bouc-Wen hysteresis model, the Hammerstein dynamic inverse hysteresis model of the piezoelectric actuator is established. To be specific, the static nonlinearity and rate dependence of the piezoelectric inverse hysteresis are represented by the generalized Bouc-Wen inverse model and the auto-regressive exogenous model, respectively, and the parameters of the model are identified by the adaptive beetle swarm optimization algorithm. In the process of the open-loop feedforward compensation, the dynamic positioning accuracy of the piezoelectric actuator is greatly affected by various disturbances and the uncertainty of the hysteresis compensation model. In this context, a compound control strategy that combines the feedforward compensation with the single-neuron adaptive proportion-integration-differentiation control is proposed based on the Hammerstein dynamic inverse hysteresis model of the piezoelectric actuator. The experimental results verify the effectiveness and superiority of the proposed control strategy.