Discontinuous and continuous sliding mode motion control

Abstract

An advanced discrete-time chattering-free sliding mode control scheme is presented. The distinctive feature of the scheme is its robustness to different initial condition values and parameter mismatch. Nonlinear control principles will be used namely, the combined feedforward and the robust negative feedback part based on VSS controllers. In the discrete-time expression the discontinuous operation of controllers in the sliding mode has ben replaced by the continuous one. In this way the chattering of control input has been eliminated and the excitation of the dynamic system without high-frequency oscillations has been achieved. The proposed control solution is near an ideal control function in the sliding mode. Unlike other algorithms intended to avoid chattering, this nonmodel-based approach uses only the information about the distance from the sliding mode manifold to derive the control. The advantage of the proposed control scheme prevail over those conventional model-based control scheme since no precise knowledge of mathematical model is necessary. In order to implement the control it must be only known the structure of input matrix and the mean values of its parameters. The input-output linear behavior of the closed control loop is predominantly determined by the controller's gain matrix.