Second order sliding mode control using nonlinear dynamic sliding manifold: Lyapunov approach

In this paper a second order sliding mode controller (2-SMC) for systems of relative degree two is designed, using a dynamic sliding manifold. The proposed control algorithm does not depend on the derivative of the sliding variable, while the sliding set (the sliding variable and its derivative both equal to zero) is reached in finite time. The finite time convergence is proven using Lyapunov techniques. The theoretical results which have been obtained are illustrated on a tutorial example and on a case study of a DC motor control.