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arXiv · 2303.15273

Modified Implicit Discretization of the Super-Twisting Controller

Benedikt Andritsch·Lars Watermann·Stefan Koch·Markus Reichhartinger·Johann Reger·Martin Horn
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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.

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Benedikt Andritsch, Lars Watermann, Stefan Koch, Markus Reichhartinger, Johann Reger, Martin Horn. 2023-03-27. Modified Implicit Discretization of the Super-Twisting Controller. https://doi.org/10.1109/tac.2024.3370494

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