Double layer sliding mode control for second-order underactuated mechanical systems

A new stable sliding mode control method for a class of underactuated mechanical systems is proposed in this paper. The controller has the double-layer structure. Firstly, the system states are divided into several different subsystems. For each of these subsystems, a first-layer sliding plane is constructed. From these first-layer sliding planes, then we further construct a second-layer sliding plane. By analyzing the features of the mathematical model of the underactuated mechanical systems, we derive the sliding-mode control law and indicate the ranges of the controller parameters. Using Lyapunov law, the paper proves the stability of all the sliding planes theoretically. The simulation results show the validity of this method for this class of underactuated mechanical systems.