Control design based on novel parabolic sliding surfaces

This paper introduces novel parabolic sliding surfaces which inherently display finite time convergence to origin or from any point on surface to any other point. A control scheme which eliminates reaching phase is then proposed such that the system from given initial condition is driven to origin in finite time traversing two such surfaces. The proposed control scheme is shown to exhibit faster convergence than those based on linear sliding surfaces. The surface is further made globally attractive using switching term to take care of practical deviations from ideal surface. Application to a 2DOF robotic manipulator system shows enhanced performance (fast response and chatter free input) as compared to classic linear surface design.