Sliding mode control for a class of second-order nonlinear systems with unmatched disturbances

This paper presents a novel sliding mode control method for a class of second-order systems subject to unmatched disturbances to ensure finite-time exact tracking and disturbance rejection. Firstly, a feedback domination approach with a dynamic disturbance compensation is developed based on a finite-time disturbance observer. Secondly, a new nonlinear sliding manifold is proposed by virtue of a virtual dynamic compensator. Finally, a new family of second-order sliding mode controller with a very simple form is constructed. Stability analysis of the closed-loop system is established by means of Lyapunov functions. The time taken to reach the desired reference signal from any initial state in the presence of disturbances is guaranteed to be finite time under the proposed controller. A simulation example is presented to validate the control performance of the proposed method.