Multivariable Generalized Super-Twisting Algorithm Robust Control of Linear Time-Invariant Systems

TL;DR

This paper introduces a robust control method for linear systems using a Multivariable Generalized Super-Twisting Algorithm, ensuring stability and performance under uncertainties and disturbances, with practical application demonstrated on a mechanical system.

Contribution

It develops a novel LMI-based design procedure for MGSTA control that guarantees finite-time convergence and robustness against uncertainties and disturbances.

Findings

Effective control of a 3-DOF mechanical system demonstrated

LMI conditions ensure robust stability and performance

Finite-time convergence achieved with the proposed method

Abstract

This paper presents a novel procedure for robust control design of linear time-invariant systems using a Multivariable Generalized Super-Twisting Algorithm (MGSTA). The proposed approach addresses robust stability and performance conditions, considering convex bounded parameter uncertainty in all matrices of the plant state-space realization and Lipschitz exogenous disturbances. The primary characteristic of the closed-loop system, sliding mode finite-time convergence, is thoroughly examined and evaluated. The design conditions, obtained through the proposal of a novel max-type non-differentiable piecewise-continuous Lyapunov function are formulated as Linear Matrix Inequalities (LMIs), which can be efficiently solved using existing computational tools. A fault-tolerant MGSTA control is designed for a mechanical system with three degrees of freedom, illustrating the efficacy of the proposed LMI approach.