On practical terminal sliding-mode control for systems with or without mismatched uncertainty

Abstract

This paper’s primary motivation is to construct a class of novel terminal sliding-mode (TSM) control to stabilize systems rapidly with reduced chattering. To this end, a novel sliding surface, coined as practical TSM (PTSM) manifold, is designed with the help of the logarithmic hyperbolic cosine function. Since the partial flatness, i.e. the Lipschitz continuity and the practical terminal attractiveness, of the proposed PTSM manifold results in its derivative nonsingularity, the super-twisting algorithm (STA) is employed to generate its finite-time reachability with reduced chattering. Once the proposed sliding surface is established, controlled states will quickly fall into a small neighborhood of the equilibrium and then asymptotically slide to zero with a local high gain. In addition, this method is extended to solve the control problem of systems with mismatched uncertainties. Several groups of simulations verify the superiority of proposed controllers.