Derivative and integral terminal sliding mode control for a class of MIMO nonlinear systems

This paper presents derivative and integral terminal sliding mode control (TSMC) for a class of MIMO nonlinear systems in a unified viewpoint. First, integral TSMC is developed for robust output tracking of uncertain relative-degree-one systems by introducing sign and fractional integral terminal sliding modes. Next, by combining derivative and integral terminal sliding modes in a recursive structure, two derivative-integral terminal sliding mode control (DI-TMSC) methods are proposed to achieve exact or approximate finite-time convergence for the output tracking of higher order nonlinear systems. Different from traditional TSMC, this paper accomplishes finite convergence time for more general high-order MIMO systems and avoids the singular problem in the controller design. Furthermore, the control system is forced to start on the terminal sliding hyperplane, so that the reaching time of the sliding modes is eliminated. In other words, the transient response is improved under more relaxed stability conditions. Finally, several numerical simulations and experiments show the expected control performance.