Eigenvalue Mapping-based Discretization of the Generalized Super-Twisting Algorithm

TL;DR

This paper introduces an advanced eigenvalue mapping-based discretization method for the generalized super-twisting algorithm, improving control accuracy and robustness while eliminating chattering.

Contribution

It extends eigenvalue mapping to the complex domain and proposes new hybrid and novel eigenvalue mapping functions for better discretization.

Findings

Eliminates discretization chattering.

Enhances control precision in steady-state.

Control gains overestimation has minimal impact.

Abstract

In this paper, an eigenvalue mapping-based discretization method is applied to discretize the generalized super-twisting algorithm. The existing eigenvalue mapping is extended to the complex domain which greatly enlarges the range of parameter selection. Furthermore, we present the clue to find new eigenvalue mapping functions (EMFs). One new hybrid EMF and three brand-new EMFs are proposed in this paper. In contrast to the conventional methods, the proposed discretization method totally avoids the discretization chattering and the control precision is enhanced in terms of the steady-state error. Besides, the control precision is insensitive to the overestimation of the control gains, which benefits the gain tuning of the controller in practice. Simulation examples verify the effectiveness and superiority of the proposed discretization methodology.