Multi-layer barrier adaptation of the discrete-time super-twisting controller

TL;DR

This paper develops a multi-layer barrier adaptation for discrete-time super-twisting sliding mode control, improving robustness and stability in digital implementations under fast perturbations.

Contribution

It introduces a nested barrier architecture discretized with an eigenvalue-based exact matching approach, preserving continuous-time properties in digital control.

Findings

The proposed controller maintains stability at the sampling level.

Numerical simulations validate the effectiveness of multi-layer barrier adaptation.

The approach enhances robustness against fast perturbations in digital control.

Abstract

In digital sliding mode control implementations, discretization-induced chattering and inter-sample blindness can severely degrade the closed-loop performance, especially in case of fast perturbations. This paper addresses these challenges for a discrete-time implementation of the super-twisting sliding mode controller. Building upon recent results on barrier-function-modulated super-twisting algorithms, a nested architecture employing multiple barriers is discretized using an eigenvalue-based exact matching approach. The resulting discrete-time controller preserves the adaptive and robustness properties established in continuous time, while ensuring consistent stability behavior at the sampling level. The proposed framework is validated through numerical simulations. The results highlight the effectiveness of multi-layer barrier adaptation for discrete-time sliding mode control applications.