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Some Results on Reset Control systems

Loquen, Thomas. Some Results on Reset Control systems. PhD, Institut National Polytechnique de Toulouse, 2010

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Official URL: http://ethesis.inp-toulouse.fr/archive/00001245/

Abstract

Hybrid controllers are flexible tools for achieving system stabilization and/or performance improvement tasks. More particularly, hybrid controllers enrich the spectrum of achievable trade-offs. Indeed, the interaction of continuous- and discrete-time dynamics in a hybrid controller leads to rich dynamical behavior and phenomena not encountered in purely continuous-time system. Reset control systems are a class of hybrid controllers whose states are reset depending on an algebraic condition. In this thesis, we propose constructive conditions (Linear Matrix Inequalities) to analyze stability and performance level of a closed-loop system including a reset element. More particularly, we consider a magnitude saturation which could be the source of undesirable effects on these performances, including instability. Proposed results estimate the stability domain and a performance level of such a system, by using Lyapunov-like approaches. Constructive algorithms are obtained by exploiting properties of quadratic - or piecewise quadratic - Lyapunov functions. Beyond analysis results, we propose design methods to obtain a stability domain as large as possible. Design methods are based on both continuous-time approaches (anti-windup compensator) and hybrid-time approaches (design of adapted reset rules).

Item Type:PhD Thesis
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Institution: Université de Toulouse > Institut National Polytechnique de Toulouse - INPT
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Research Director:
Tarbouriech, Sophie and Prieur, Christophe
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