Second Order Sliding Mode Control for a Class of Underactuated Systems

This paper presents a second order sliding mode control method to stabilize a class of underactuated systems. In the controller design, the sliding manifold is designed by the nominal linear combination of position and velocity tracking errors of two system states, this can stabilize the indirectly controlled modes. The four coefficients of sliding manifold are obtained via Hurwitz condition in the system stability analysis process. In addition, simulation results are presented for a translator oscillator with rotational actuator (TORA) and an inverted pendulum as two examples of a class of underactuated systems. In both cases, the proposed control method is shown to be effective in the presence of stabilization and tracking control.