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Méthodes d'analyse et de synthèse robustes pour les systèmes linéaires périodiques

Christophe Farges 1
1 LAAS-MAC - Équipe Méthodes et Algorithmes en Commande
LAAS - Laboratoire d'analyse et d'architecture des systèmes
Abstract : This thesis addresses robustness problems for a linear periodic systems. These correspond to a special case of linear time-varying systems with periodic dynamics. Such periodic processes arise in numerous domains such as aeronautics, celestial mechanics or communication systems. Systematic procedures for robust analysis and synthesis are proposed. The adopted framework is based on the Lyapunov theory and uses the linear matrix inequalities (LMI) formalism. Uncertainties are supposed to affect not only the system but the controller itself. This last problem is treated by the synthesis of convex sets of controllers ensuring a given level of performances for the closed-loop system. The question of the time structure of the controller is formulated. Does the controller need to be of the same periodicity as the system? Is it possible to reduce the number of parameters to be stored inside the controller? The class of time-structured controller is defined and dedicated synthesis methods are developed. Theoretical results are illustrated on the problem of the stationkeeping for a spacecraft on a low earth orbit subject to different disturbance accelerations (atmospheric drag, effect of the non spheric mass repartition of the Earth). Different feedback control laws are computed with performance requirements such as minimizing the amount of maneuvering propellant or the effect of additional unknown disturbance accelerations. Their efficiency is evaluated by the mean of non linear simulations.
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Christophe Farges. Méthodes d'analyse et de synthèse robustes pour les systèmes linéaires périodiques. Mathématiques [math]. Université Paul Sabatier - Toulouse III, 2006. Français. ⟨tel-00132343⟩

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