Study on second-order sliding mode control law for affine nonlinear system

The chattering and robustness issues of the existing sliding mode control especially second-order sliding mode (SOSM) control algorithms were analyzed. Aiming at the problems of slower convergence and stronger chattering in the nearly time-optimal SOSM control law, an improved control method was developed for the affine nonlinear systems through redesigning restrictive conditions and modifying reaching acceleration of sliding mode, which can effectively enhance responding speed of second-order sliding mode, as well as reduce the frequency and amplitude of chattering without losing the robustness of system. Taking a pendulum model as example, the simulation studies on the proposed algorithm were carried out, simultaneously comparing with the first-order exponential reaching law and the Lyapunov function-based SOSM control law. The simulative results demonstrate that the improved nearly time-optimal SOSM control law is appropriate for the uncertain nonlinear systems, and has the relative advantages on the aspects of chattering reduction and rapid response.