Design of a new incremental sliding mode controller

A new stable sliding mode control method for a class of underactuated mechanical systems with saturation is proposed in this paper. Two state variables of the underactuated system are chosen to construct the first-layer sliding surface. Then, the first-layer sliding surface and one of the left state variables are used to construct the second-layer sliding surface. This process continues till the last sliding surface is constructed. For an underactuated system, which consists of 2n state variables, the sliding surface has (2n-1)-layer structure. For guaranteeing every sliding surface can converge rapidly to zero, we design a new sliding mode control law. Using Lyapunov law, we prove the stability of all the sliding surfaces theoretically. On account of saturation nonlinearity of the control input, asymptotic stability of the control system is proven by nonlinear small gain theorem. The simulation results show the validity of this method for this class of underactuated mechanical systems.