Passivity-based second-order sliding mode control for mechanical port-Hamiltonian systems

In this paper, we propose a new second-order sliding mode controller for mechanical port-Hamiltonian systems. This paper proposes a passivity-based sliding mode controller based on kinetic-potential energy shaping (KPES). So far this type of controller was only able to achieve first-order sliding mode control, since the KPES allows one to embed a subsystem whose dimension is the same as that of the input into the closed-loop system. This paper extends the KPES to incorporate a higher-order subsystem in the closed-loop system, which enables us to obtain the subsystem that can realize second-order sliding mode control. The proposed controller is integration of a passivity-based controller and a second-order sliding mode controller which does not cause undesirable chattering phenomena. It ensures finite-time convergence of the subsystem and asymptotic stability of the entire closed-loop system by utilizing two Lyapunov functions. Moreover, due to the design freedom in selecting a Lyapunov function candidate of the KPES, it can deal with several control objectives including trajectory tracking control. A numerical example demonstrates the effectiveness of the proposed method.