Tracking control of a 3-D piezoelectrically actuated system by using adaptive sliding mode controller

In this paper, a model-free adaptive sliding controller with fuzzy compensation is proposed for contour tracking control of a 3-D piezoelectrically actuated system due to the system's nonlinear and time-varying characteristics. This control strategy employs the functional approximation 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 augmented to compensate for the finite approximation error and facilitate the controller design. 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 Lyapunov direct method is applied to find adaptive laws for updating coefficients in the approximating series and tuning parameter in the fuzzy compensator to guarantee the control system stability. To validate the proposed scheme, control results obtained using the proposed adaptive sliding mode controller augmented with fuzzy compensator are compared with those obtained without fuzzy compensation.