Second-Order Sliding Mode Controller Design with a Larger Domain of Attraction

In this paper, by combining a second-order sliding mode (SOSM) algorithm with the saturation technique, a novel SOSM control scheme has been presented. The feature of the proposed SOSM controller lies that there is a saturation function imposed on the sliding variable, which could significantly enlarge the domain of attraction for the closed-loop system. The geometric method has been utilized to prove that all the sliding variables will be steered to the origin in a finite time. Meanwhile, the relation between the control parameters and the shape of the phase trajectory has also been discussed. Finally, the proposed method has been applied to the tracking control problem for a robotic manipulator.