Proper Implicit Discretization of the Super-Twisting Controller -- without and with Actuator Saturation
<|reference_start|>Proper Implicit Discretization of the Super-Twisting Controller -- without and with Actuator Saturation: 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 similarily simple stability conditions as their continuous-time counterparts. Numerical simulations and comparisons demonstrate and illustrate the results.<|reference_end|>
@article{seeber2024proper,
    title={Proper Implicit Discretization of the Super-Twisting Controller --
  without and with Actuator Saturation},
    author={Richard Seeber, Benedikt Andritsch},
    journal={arXiv preprint arXiv:2406.16094},
    year={2024},
    archivePrefix={arXiv},
    eprint={2406.16094},
    primaryClass={eess.SY cs.SY}
}