Discontinuous integral action for arbitrary relative degree in sliding-mode control

Abstract

For uncertain minimum phase systems with arbitrary and well-defined relative degree, we propose the implementation of a sliding-mode control through a homogeneous discontinuous integral action. The output (sliding) variable will track, exactly and in finite-time, any sufficiently smooth reference, while rejecting smooth perturbations with an absolutely continuous control signal. This controller generalizes the well-known super-twisting algorithm to arbitrary order. Continuous and homogeneous integral controllers are also proposed approximating the behaviour of the discontinuous controller. Smooth Lyapunov functions are derived to show the convergence and robustness properties of all controllers. The performance is illustrated by means of experimental results on a magnetic suspension system.