Modeling and sliding mode control based on inverse compensation of piezo-positioning system

In order to enhance the control performance of piezo-positioning system, the influence of hysteresis characteristics and its compensation method are studied. Hammerstein model is used to represent the dynamic hysteresis nonlinear characteristics of piezo-positioning actuator. The static nonlinear part and dynamic linear part of the Hammerstein model are represented by models obtained through the Prandtl-Ishlinskii (PI) model and Hankel matrix system identification method, respectively. This model demonstrates good generalization capability for typical input frequencies below 200 Hz. A sliding mode inverse compensation tracking control strategy based on P-I inverse model and integral augmentation is proposed. Experimental results show that compared with PID inverse compensation control and sliding mode control without inverse compensation, the sliding mode inverse compensation control has a more ideal step response and no overshoot, moreover, the settling time is only 6.2 ms. In the frequency domain, the system closed-loop tracking bandwidth reaches 119.9 Hz, and the disturbance rejection bandwidth reaches 86.2 Hz. The proposed control strategy can effectively compensate the hysteresis nonlinearity, and improve the tracking accuracy and anti- disturbance capability of piezo-positioning system.