Adaptive sliding control with self-tuning fuzzy compensation for a piezoelectrically actuated X–Y table

The piezoelectrically actuated system has non-linear and time-varying behaviour, hence it is difficult to establish an accurate dynamic model for a model-based sliding-mode control design. In this study, a model-free adaptive sliding controller is proposed to control the piezoelectrically actuated system. This control strategy uses the functional approximation (FA) technique to establish the unknown function for releasing the model-based requirement of the sliding-mode control. In addition, a fuzzy scheme with online learning ability is introduced to compensate the FA error for improving the control performance and reducing the implementation difficulty. The important advantages of this approach are to achieve the sliding-mode controller design without the system dynamic model requirement and release the trial-and-error work of selecting approximation function. The update laws for the coefficients of the Fourier series functions 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.