Anti-windup design with guaranteed regions of stability for discrete-time linear systems with saturating controls

Abstract

The purpose of this paper is to study the determination of stability regions for discrete-time linear systems with saturating controls through anti-windup schemes. Considering that a linear dynamic output feedback has been designed to stabilize the linear discrete-time system (without saturation), a method is proposed for designing an anti-windup gain that maximizes an estimate of the basin of attraction of the closed-loop system in the presence of saturation. It is shown that the closed-loop system obtained from the controller plus the anti-windup gain can be modeled by a linear system connected to a deadzone nonlinearity. From this model, stability conditions based on quadratic Lyapunov functions are stated. Algorithms based on LMI schemes are proposed for computing both the anti-windup gain and an associated stability region.KEYWORDS: Anti-windup, control saturation, discrete-time systems, regions of stability. RESUMOEste artigo tem por objetivo o estudo da determinação de regiões de estabilidade para sistemas lineares discretos no tempo com controles saturantes, através da utilização de laArtigo submetido em 05/12/02 1a. Revisão em 27/05/03; 2a. Revisão em 21/07/03 Aceito sob recomendação do Ed. Assoc. Prof. José R. C. Piqueira ços de anti-windup. Considerando que um compensador dinâmico de saída é previamente projetado para estabilizar o sistema linear em tempo discreto (i.e. desconsiderando-se a saturação), é proposto um método para projetar um ganho de anti-windup que maximize a região de atração do sistema em malha fechada na presença de saturação. É mostrado que o sistema em malha fechada, obtido a partir do controlador com o termo de anti-windup, pode ser modelado por um sistema linear em cascata com uma não-linearidade do tipo zona-morta. A partir deste modelamento, condições de estabilidade baseadas em funções de Lyapunov quadráticas são estabelecidas. Algortimos baseados na solução de LMIs são propostos para computar simultaneamente o ganho de antiwindup e a região de estabilidade associada. PALAVRAS-CHAVE:Anti-windup, saturação de controle, sistemas discretos no tempo, regiões de establidade.

Discrete-time control for variable speed wind turbine

“…Many rigorous design methods are available to provide guarantee proprieties on systems stability. Let us quote of these methods, the antiwindup design ([8]-- [10]), and many other methods which introduce conditions on systems containing saturation functions ( [11], [13] [24]…). In the actual systems, however, controllers are implemented in the discrete-time domain since they use microprocessors or computers in general.…”

Comparative study of the saturated sliding mode and anti-windup controllers

“…Used in early days, many rigorous design methods are available to provide guarantee properties on systems stability. Let us quote of these methods, the anti-windup design ( [1], [2]...), and many other methods which introduce conditions on systems containing saturation functions ( [1], [3], [4], [5], [6]...). In this paper, we are interested the problem of sliding mode control of linear system with saturation on the entries.…”