On the Behaviour of Under-tuned Super-Twisting Sliding Mode Control Loops

TL;DR

This paper analyzes the stability and performance of under-tuned super-twisting sliding mode control loops under periodic perturbations, revealing convergence to a stable limit cycle and offering practical gain selection guidelines.

Contribution

It introduces milder gain conditions ensuring system stability and convergence, expanding practical applicability of super-twisting control loops.

Findings

Trajectories converge to a stable limit cycle under milder gain conditions.

Guidelines for selecting control gains based on system state bounds.

Simulation results validate the theoretical analysis.

Abstract

This paper investigates the stability properties and performance of super-twisting sliding-mode control loops subject to periodic perturbations. Although there exist conditions on the control gains that guarantee finite-time stability of the closed-loop system, such conditions are often too restrictive from a practical standpoint, especially in relation to actuator limitations and induced chatter. Using regularisation and averaging theory, it is proven that under milder conditions for the control gains, the trajectories of the periodically perturbed closed-loop system converge to a stable limit cycle of the same period containing the origin. Additionally, guidelines for selecting the controller gains are provided based on bounds of the closed-loop system states. Finally, the theoretical findings are validated through simulations.