Modified Implicit Discretization of the Super-Twisting Controller
Abstract
In this paper a novel discrete-time realization of the super-twisting controller is proposed. The closed-loop system is proven to converge to an invariant set around the origin in finite time. Furthermore, the steady-state error is shown to be independent of the controller gains. It only depends on the sampling time and the unknown disturbance. The proposed discrete-time controller is evaluated comparative to previously published discrete-time super-twisting controllers by means of the controller structure and in extensive simulation studies. The continuous-time super-twisting controller is capable of rejecting any unknown Lipschitz-continuous perturbation and converges in finite time. Furthermore, the convergence time decreases, if any of the gains is increased. The simulations demonstrate that the closed-loop systems with each of the known controllers lose one of these properties, introduce discretization-chattering, or do not yield the same accuracy level as with the proposed controller. The proposed controller, in contrast, is beneficial in terms of the above described properties.
Cite
@article{arxiv.2303.15273,
title = {Modified Implicit Discretization of the Super-Twisting Controller},
author = {Benedikt Andritsch and Lars Watermann and Stefan Koch and Markus Reichhartinger and Johann Reger and Martin Horn},
journal= {arXiv preprint arXiv:2303.15273},
year = {2024}
}