Haar wavelet FAT-based adaptive controller for a piezoelectrically actuated system control

In this paper, a model-free intelligent controller is proposed to control the piezoelectrically actuated system. This control strategy employs the Haar wavelet functional approximation technique (FAT) to establish the unknown function for releasing the model-based requirement of the sliding mode control. In addition, an adaptive fuzzy scheme with online learning ability is introduced to compensate the functional approximation error for improving the control performance and reducing the implementation difficulty. The update laws for the coefficients of the Haar wavelet and the fuzzy tuning parameters are derived from a Lyapunov function to guarantee the control system stability. This proposed controller is implemented on a piezoelectrically actuated X-Y table. To verify the dynamic performance improvement of inducing a fuzzy compensation in this model-free controller, the dynamic responses of the proposed controller are compared with those of the adaptive sliding controller without fuzzy compensation.