Constructive nonlinear sliding mode surfaces for a class of underactuated systems with parametric uncertainties

This paper presents a constructive methodology to design sliding mode surfaces for a class of underactuated mechanical systems. The surfaces are designed taking advantage of a fictitious output and the Lyapunov theory. The fictitious output is chosen in such a way that the system is minimum-phase. The technique is developed for a class of underactuated mechanical systems with uncertainty in their physical parameters, mainly in the inertial terms. Two examples in the class, the pendulum on a cart and the inertia wheel pendulum are thoroughly analyzed. Simulations show the good performance, namely, time response and parametric robustness, of the controller.