Proper Implicit Discretization of the Super-Twisting Controller -- without and with Actuator Saturation
Abstract
The discrete-time implementation of the super-twisting sliding mode controller for a plant with disturbances with bounded slope, zero-order hold actuation, and actuator constraints is considered. Motivated by restrictions of existing implicit or semi-implicit discretization variants, a new proper implicit discretization for the super-twisting controller is proposed. This discretization is then extended to the conditioned super-twisting controller, which mitigates windup in presence of actuator constraints by means of the conditioning technique. It is proven that the proposed controllers achieve best possible worst-case performance subject to similarly simple stability conditions as their continuous-time counterparts. Numerical simulations and comparisons demonstrate and illustrate the results.
Cite
@article{arxiv.2406.16094,
title = {Proper Implicit Discretization of the Super-Twisting Controller -- without and with Actuator Saturation},
author = {Richard Seeber and Benedikt Andritsch},
journal= {arXiv preprint arXiv:2406.16094},
year = {2024}
}