Adaptive second-order sliding mode control: A unified method

This paper develops a unified adaptive second order sliding mode (ASOSM) control method. By using the proposed control structure, the upper bounds of uncertainties are not required, the over-estimation of the control gains are avoided, and the chattering of the conventional sliding mode controllers can be attenuated. It should be noted that the adaptive gains are obtained based on the switching function and its derivative; as a result, the gains keep updating before and after the practical sliding mode is established. Meanwhile, the finite time convergence is proved based on a quadratic Lyapunov approach. Finally, to illustrate the performance of the presented method, an ASOSM controller is designed for a pendulum system and several simulations are performed.