FAT-based adaptive sliding-mode control for a piezoelectric-actuated system

In this paper, a function approximation technique (FAT) based adaptive controller is proposed for the tracking control of a piezoelectric-actuated X-Y table. Owing to the highly nonlinear behavior associated with the actuator, control problems involving a piezoelectric-actuated system are challenging. Moreover, a universal and effective hysteresis model for the piezoelectric actuator (PA) is difficult, if not impossible, to obtain. Thus, a model-free method is proposed in this study to tackle the problem. The study formulates the dynamic equation of the system using an unknown time-varying function. The latter is then approximated using a linear combination of orthogonal Haar wavelets. Therefore, the time-varying nature of the system's dynamics and uncertainties is handled by the FAT levering on the Haar wavelet. The stability of the closed-loop system is assured by an updating law which is derived from Lyapunov stability theory. Experimental results demonstrate the effectiveness of the proposed design.