On the behaviour of under-tuned super-twisting sliding mode control loops

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.