Discrete-Time Multivariable Super-Twisting Algorithm With Semi-Implicit Euler Method

Abstract

The classical super-twisting algorithm (STA) has many advantages, such as the simplicity, finite-time convergence, high accuracy, and robustness. However, its scalar input and output may hinder its applications in affine systems with multiple inputs and multiple outputs (MIMO). Therefore, the classical STA has been extended into multivariable versions in the literature to overcome such a limitation. The problem is that, the multivariable STA inherits another downside of the classical STA during implementation, that is, the numerical chattering for large sizes of the sampling period or gains of the STA, which deteriorates the control performance in MIMO systems. This brief proposes a new discrete-time implementation scheme for the multivariable STA with a semi-implicit Euler discretization approach. It attenuates the numerical chattering while reserving the robustness of the multivariable STA. The advantages of the proposed scheme are demonstrated numerically with comparisons with the classical STA and the multivariable STA implementation method through simulations. © 2004-2012 IEEE.