Proper Implicit Discretization of the Super-Twisting Controller -- without and with Actuator Saturation

TL;DR

This paper introduces a new proper implicit discretization method for the super-twisting sliding mode controller, including an extension to mitigate actuator windup, ensuring optimal worst-case performance under practical constraints.

Contribution

A novel implicit discretization approach for the super-twisting controller is proposed, along with a conditioned version to handle actuator saturation effectively.

Findings

The proposed discretization achieves optimal worst-case performance.

The conditioned controller mitigates windup under actuator constraints.

Numerical simulations validate the theoretical results.

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.