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 tracking control of a piezoelectric-actuated X-Y table. Due to nonlinear hysteretic behaviors associated with the system, control problems involving piezoelectric actuator (PA) are challenging. Moreover, universal and effective hysteresis model for the 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 nonlinear function. The latter is then approximated using a linear combination of orthogonal Haar wavelets. 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.