Adaptive Discrete-Time Estimated Inverse Control for Piezoelectric Positioning Stage

This article aims at designing an adaptive estimated inverse control scheme to realize precise tracking control for a class of discrete-time nonlinear system with hysteresis nonlinearities. To this end, firstly, the dynamic surface control technology with digital first-order low-pass filter is designed and the original control system does not need to be transformed into an unknown special form. Then, the procedures of the controller design are greatly simplified. Secondly, the hysteresis nonlinearity is mitigated by constructing an discrete-time estimated inverse hysteresis compensator. Finally, the validity of the proposed adaptive control scheme is verified by the computer control experiments on a hardware-in-the-loop simulation platform. It is proved that all the signals in the closed-loop system are semi-globally uniformly ultimately bounded (SUUB).