Predefined time quasi-sliding mode control with fast convergence based on a switchable exponent for nonlinear systems

Abstract

This paper proposed a new predefined time nonsingular sliding mode control (SMC) method for nonlinear systems. Firstly, based on the definition of predefined time stability (PTS), a new sufficient condition is designed to ensure that the system states converge to the origin within a predefined time. The design of a simple variable exponent not only guarantees PTS, but also enables adaptive adjustment when the system states are far away from and near the equilibrium point. And compared with traditional methods, the proposed Lemma 2 enhances the control effect and achieves faster convergence whether the system states are far from or near to the equilibrium point. Secondly, based on the proposed stability condition, a new nonsingular SMC method is designed to ensure that the tracking error converges to an arbitrarily small region within a predefined time. Finally, the proposed method is verified to have good performance through simulation and physical experiments.