Tracking of a piezo-actuated system using adaptive sliding-mode control and function-approximation technique

A novel adaptive sliding-mode controller integrated with Haar-function-approximation technique is proposed to attack tracking problems of a piezo-actuated system. Unlike conventional model-based approaches, the method proposed here can achieve sliding-mode controller design without the knowledge of the hysteresis model. To design the adaptive sliding controller, nonlinear hysteretic behaviour is treated as a time-varying uncertainty of the system. Then, Haar-wavelet function approximation technique is applied to dynamically approximate the hysteretic behaviours of the system. Based on the information gained from Haar-wavelet expansion, Lyapunov stability theory is used to develop adaptive control law and to assure the system's stability. Numerical studies indicate that the proposed method can eliminate the undesired tracking errors caused by the nonlinear hysteresis. Experimental validations of the proposed method are undergoing.