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Contrôle robuste des systèmes variant dans le temps : Application au contrôle d’attitude modélisée par quaternion

Thomas Conord 1
1 LAAS-MAC - Équipe Méthodes et Algorithmes en Commande
LAAS - Laboratoire d'analyse et d'architecture des systèmes
Abstract : This PhD thesis brings two contributions to the field of System Control: the first one deals with the attitude control of a generic fully actuated rigid object rotating in space; the second one concerns methods of analysis and synthesis of controllers for Linear Time Varying systems. The first contribution develops in detail the modeling of the tracking of a theoretically feasible attitude trajectory performed by this generic rotating object, using the unit quaternion to model the attitude. The rotational motion is intrinsically nonlinear (trigonometric), with singularities related to its periodicity, implying the non existence of a Linear Time Invariant controller able to make the closed loop system globally stable. By taking into account these specificities, the synthesis of nonlinear controllers enabling to obtain an almost global asymptotic stability of the closed loop system is then developed. Perspectives to improve this result with integrators to cancel out static and drag errors are finally proposed. The question of tuning these non-linear controllers to simultaneously meet several performance criteria leads to the second contribution: the opportunity to extend to Linear Time Varying systems the notions of pole placement and input/output performances analysis of Linear Time Invariant systems. The proposed method concerns systems with time varying parameters bounded in a convex set described by a polytope. It allows to write the performance analysis problems in the form of Differential Linear Matrix Inequalities, then to convert them into Linear Matrix Inequalities for the static state feedback synthesis. For this last result, two formulations are proposed: the first one with a Lyapunov certificate common to all the requirements; the second one with an added S-variable which allows to simultaneously search for several Lyapunov certificates, one for each performance requirement of the multi-objective problem. This synthesis result is eventually applied to the attitude control problem.
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Submitted on : Thursday, October 21, 2021 - 3:06:06 PM
Last modification on : Monday, November 29, 2021 - 4:30:59 PM

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Thomas Conord. Contrôle robuste des systèmes variant dans le temps : Application au contrôle d’attitude modélisée par quaternion. Automatique. UPS Toulouse - Université Toulouse 3 Paul Sabatier, 2021. Français. ⟨NNT : 2021TOU30081⟩. ⟨tel-03448843v1⟩

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