Fat based model-free adaptive controller for a piezoelectric-actuated system

In this paper, a function approximation technique (FAT) based adaptive controller is proposed for the tracking problem of a piezoelectric-actuated X-Y table. Control problems involving piezoelectric actuator (PA) are challenging due to the nonlinear hysteretic behaviors associated with the actuator. Moreover, universal and effective hysteresis model for the PA is difficult if not impossible to obtain. Thus, a model-free method is proposed here to tackle the problem. The study firstly formulates the dynamic equation of the system using nonlinear function. The latter is then approximated using a linear combination of orthogonal basis functions. Stability of the closed-loop system is assured by an updating law that is derived from Lyapunov stability theory. Experimental results demonstrate the effectiveness of the proposed design.