Adaptive Backstepping Time Delay Control for Precision Positioning Stage with Unknown Hysteresis

Piezoelectric-actuated precision positioning stages are widely used in high-precision instruments and high-end equipment due to their advantages of high resolution, fast response, and compact size. However, due to the strong nonlinearity of hysteresis, the presence of hysteresis in piezoelectric actuators seriously affects the positioning accuracy of the system. In addition, it is challenging to identify the model parameters for hysteresis. In this paper, an adaptive backstepping time delay control method is proposed for piezoelectric devices system with unknown hysteresis. Firstly, the Bouc–Wen model is used to describe the hysteresis characteristics, and the model is interpreted as a linear term and a bounded uncertain hysteresis term. Then, the time delay estimation technique is used to estimate the hysteresis term of the Bouc–Wen model online, and the unknown parameters of the system and hysteresis model are obtained through adaptive updating laws. Furthermore, the stability of the control scheme is proved based on Lyapunov stability theory. Finally, the effectiveness and superiority of the proposed control scheme are demonstrated by comparing it with two typical hysteresis compensation control algorithms through three different sets of input signals.