Practical Terminal Sliding-Mode Control and Its Applications in Servo Systems

This article’s primary motivation is to propose a nonsingular and continuous terminal sliding-mode (TSM) control with reduced chattering, which is able to rapidly stabilize the second-order plant with high precision. To this end, a novel sliding-mode manifold, coined as practical TSM (PTSM) one, is first constructed. Once the proposed sliding surface is reached, a Lipschitz-continuous but slope-steep generalized velocity will be established at the origin such that the global nonsingularity of the equivalent control is ensured. The fast dynamic response with local high gain characterizes the sliding behavior inside the unit neighborhood of the origin. Importantly, the analytical solution of the proposed sliding-mode reduced-order system is deduced, which indicates that the finite time taken to slide into a preset small neighborhood of the origin can be calculated. The above designability of convergence time is necessary for control practices with accurate time sequence planning. Further, the corresponding globally singular-free PTSM reaching law with reduced chattering is designed based on the super-twisting algorithm. Finally, several groups of linear-motor-based control experiments verify the superiorities of proposed controllers.