FAT-based Adaptive Sliding-Mode Control for a Piezoelectric-actuated System

Abstract

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.

Keywords

Adaptive sliding mode control function approximation technique Haar wavelet piezoelectric actuated system sliding mode control

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