Les systèmes électroniques commutés sont de plus en plus utilisés dans plusieurs domaines domestiques ou industriels: les écrans à cristaux liquides, les appareils électroménagers, l'éclairage, les ordinateurs personnels, les centrales électriques, les véhicules de transport et ainsi de suite. L'efficacité des opérations de toutes les applications dépend du travail essentiel réalisé par des systèmes électroniques à commutation, dont le comportement est déterminé par une interconnexion et un contrôle appropriés des dispositifs analogiques et numériques. Comme motivation de ce travail, nous considérons les convertisseurs DC-DC de puissance. Cette thèse contribue à fournir des solutions aux problèmes de contrôle hybrides et non linéaires des plusieurs types de convertisseurs de puissance. Dans la première partie nous intéressons au problème de la régulation de la tension des convertisseurs de puissance fonctionnant dans le mode de conduction discontinue. Deux convertisseurs de puissance sont considérés: le convertisseur boost et le convertisseur buck-boost. L'objectif de commande est la génération d'une orbite périodique. Notre principale contribution est un algorithme simple et robuste qui donne des formules explicites pour les temps de commutation sans approximations. Les résultats de simulation et expérimentaux sont présentés. Dans la deuxième partie une classe de convertisseurs de puissance qui peut être globalement stabilisé avec un contrôleur PI a été identifiée. Par ailleurs, nous allons prouver que l'observateur I&I peut être combiné avec le contrôleur PI tout en préservant les propriétés de stabilité asymptotique globale de la boucle fermé. La classe se caractérise par une inégalité matricielle linéaire simple. Le nouveau contrôleur est illustré avec le convertisseur très - populaire, et difficile à contrôler, le SEPIC, pour lequel les résultats de simulation et expérimentaux sont présentés. / Switched electronic systems are used in a huge number of everyday domestic and industrial utilities: liquid crystal displays, home appliances, lighting, personal computers, power plants, transportation vehicles and so on. Efficient operations of all such applications depend on the essential “hidden work" done by switched electronic systems, whose behavior is determined by a suitable interconnection and control of analog and digital devices. As a motivation of this work, we consider the DC-DC power converters. This thesis contributes to provide hybrid and nonlinear control problem solutions to several types of power converters. In the first part we are interested in the problem of voltage regulation of power converters operating in discontinuous conducting mode. Two power converters are considered: the boost converter and the buck-boost converter. The system does not admit a (continuous--time) average model approximation, hence is a hybrid system where the control objective is the generation of a periodic orbit and the actuator commands are switching times. Our main contribution is a simple robust algorithm that gives explicit formulas for the switching times without approximations. Simulation and experimental results that illustrate the robustness of the scheme to parameter uncertainty, as well as performance comparisons with current practice, are presented. In the second part a class of power converters that can be globally stabilized with an output-feedback PI controller has been identified. Moreover, we will prove that the I&I observer can be combined with the PI controller preserving the GAS properties of the closed-loop. The class is characterized by a simple linear matrix inequality. The new controller is illustrated with the widely-popular, and difficult to control, single-ended primary inductor converter, for which simulation and experimental results are presented.

A aeroelasticidade estuda a interação mútua entre os efeitos aerodinâmicos e estruturais. É sabido que essa relação muitas vezes se comporta de maneira não linear, causando diversos problemas, tais como flutter, oscilações em ciclo limite, bifurcações e caos. Tais fenômenos são difíceis de serem diagnosticados, podendo causar problemas graves à estrutura das aeronaves e também inviabilizar as suas operações. Dentre as principais fontes de não linearidades em sistemas aeroelásticos, pode-se citar as de origem aerodinâmica e estrutural. As de origem estrutural, por sua vez, podem ter caráter distribuído ou concentrado. Sabe-se que os efeitos estruturais concentrados denominados enrijecimento e folga são os de maior impacto na aeroelasticidade não linear. Desse modo, o objetivo desse trabalho é estudar a interação não linear entre duas não linearidades estruturais, ou seja, o enrijecimento associado à rigidez em torção e a folga presente nas articulações das superfícies de controle de seções típicas aeroelásticas. Experimentos em túnel de vento são realizados utilizando um dispositivo que permite variar a intensidade do efeito de enrijecimento e do tamanho da folga na articulação da superfície de comando. O modelo numérico de seção típica aeroelástica também é utilizado e validado com dados experimentais. Análises por meio de diagramas de bifurcação de Hopf e técnicas baseadas em espectros de potência são utilizadas. Todas as respostas aeroelásticas foram caracterizadas através de ferramentas de análise nos domínios do tempo e da frequência, como técnica de reconstrução de espaço de estados e os espectros de alta ordem (HOS), os quais são importantes na identificação dos tipos de acoplamentos não lineares. Resultados indicam que a combinação dos efeitos de enrijecimento e folga são responsáveis pelo comportamento subcrítico das bifurcações de Hopf e que a intensidade do enrijecimento tem influência direta nas amplitudes de ciclo limite. / Aeroelasticity is the field of engineering that deals with the mutual interaction between the aerodynamic and structural dynamics effects. It is known that this relationship often shows nonlinear behavior, causing various problems such as flutter, limit cycle oscillations, bifurcations and chaos. Such phenomena are difficult to predict and can cause serious problems to the aircraft structure and also they can jeopardize their operations. The unsteady aerodynamic and structural dynamics provide the main sources of nonlinearities in aeroelastic systems. Structural nonlinearities can be treated as distributed or concentrated effects. It is know that the nonlinear concentrated structural effects referred as hardening and freeplay have a significant impact on nonlinear aeroelasticity. The objective of this work is to analyze an aeroelastic system under the influence of combined structural nonlinearities, i.e., the hardening nonlinearity in the pitch airfoil motion and the freeplay nonlinearity in the control surface hinge. Wind tunnel experiments are carried out using one device that allows to vary the intensity of the hardening effect and the size of the freeplay gap in the control surface hinge. The numerical model of the typical aeroelastic section is also used and validated with experimental data. All aeroelastic responses are characterized by analytical tools in time and frequency domains. It was used the state space reconstruction technique and the higher order spectral analysis (HOS) to identify types of nonlinear couplings. The results indicate that the combination of hardening and freeplay effects are responsible for inducing the subcritical behavior on the Hopf bifurcations and that the intensity of the stiffness has a direct influence on the limit cycle amplitudes.

A aeroelasticidade estuda a interação mútua entre os efeitos aerodinâmicos e estruturais. É sabido que essa relação muitas vezes se comporta de maneira não linear, causando diversos problemas, tais como flutter, oscilações em ciclo limite, bifurcações e caos. Tais fenômenos são difíceis de serem diagnosticados, podendo causar problemas graves à estrutura das aeronaves e também inviabilizar as suas operações. Dentre as principais fontes de não linearidades em sistemas aeroelásticos, pode-se citar as de origem aerodinâmica e estrutural. As de origem estrutural, por sua vez, podem ter caráter distribuído ou concentrado. Sabe-se que os efeitos estruturais concentrados denominados enrijecimento e folga são os de maior impacto na aeroelasticidade não linear. Desse modo, o objetivo desse trabalho é estudar a interação não linear entre duas não linearidades estruturais, ou seja, o enrijecimento associado à rigidez em torção e a folga presente nas articulações das superfícies de controle de seções típicas aeroelásticas. Experimentos em túnel de vento são realizados utilizando um dispositivo que permite variar a intensidade do efeito de enrijecimento e do tamanho da folga na articulação da superfície de comando. O modelo numérico de seção típica aeroelástica também é utilizado e validado com dados experimentais. Análises por meio de diagramas de bifurcação de Hopf e técnicas baseadas em espectros de potência são utilizadas. Todas as respostas aeroelásticas foram caracterizadas através de ferramentas de análise nos domínios do tempo e da frequência, como técnica de reconstrução de espaço de estados e os espectros de alta ordem (HOS), os quais são importantes na identificação dos tipos de acoplamentos não lineares. Resultados indicam que a combinação dos efeitos de enrijecimento e folga são responsáveis pelo comportamento subcrítico das bifurcações de Hopf e que a intensidade do enrijecimento tem influência direta nas amplitudes de ciclo limite. / Aeroelasticity is the field of engineering that deals with the mutual interaction between the aerodynamic and structural dynamics effects. It is known that this relationship often shows nonlinear behavior, causing various problems such as flutter, limit cycle oscillations, bifurcations and chaos. Such phenomena are difficult to predict and can cause serious problems to the aircraft structure and also they can jeopardize their operations. The unsteady aerodynamic and structural dynamics provide the main sources of nonlinearities in aeroelastic systems. Structural nonlinearities can be treated as distributed or concentrated effects. It is know that the nonlinear concentrated structural effects referred as hardening and freeplay have a significant impact on nonlinear aeroelasticity. The objective of this work is to analyze an aeroelastic system under the influence of combined structural nonlinearities, i.e., the hardening nonlinearity in the pitch airfoil motion and the freeplay nonlinearity in the control surface hinge. Wind tunnel experiments are carried out using one device that allows to vary the intensity of the hardening effect and the size of the freeplay gap in the control surface hinge. The numerical model of the typical aeroelastic section is also used and validated with experimental data. All aeroelastic responses are characterized by analytical tools in time and frequency domains. It was used the state space reconstruction technique and the higher order spectral analysis (HOS) to identify types of nonlinear couplings. The results indicate that the combination of hardening and freeplay effects are responsible for inducing the subcritical behavior on the Hopf bifurcations and that the intensity of the stiffness has a direct influence on the limit cycle amplitudes.

Submitted by Cássia Santos (cassia.bcufg@gmail.com) on 2014-08-06T10:24:20Z No. of bitstreams: 2 license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) ciclos_limites_para_a_equacao_de_abel_generalizada.pdf: 641062 bytes, checksum: e4be39606562d4f6805c21c2cceb451c (MD5) / Made available in DSpace on 2014-08-06T10:24:20Z (GMT). No. of bitstreams: 2 license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) ciclos_limites_para_a_equacao_de_abel_generalizada.pdf: 641062 bytes, checksum: e4be39606562d4f6805c21c2cceb451c (MD5) Previous issue date: 2009-10-30 / Conselho Nacional de Pesquisa e Desenvolvimento Científico e Tecnológico - CNPq / In this work we conducted a study on the equations of the type dx dt = nå i=0 ai(t)xi; (A) where ai 2 C1, i = 0; ;n and 0 t 1. An equation of the form (A) is called a generalized Abel equation. Our study refers to the problem proposed by C. Pugh: There is a natural number N depending only on n, such that the equation (A) has at most N limit cycles? Initially we study the problem of C. Pugh for n = 1 and n = 2, for which the equation (A) has at most one and two limit cycles, respectively. For n = 3, A. Lins Neto shows that if a3(t) does not change sign on [0;1], then the equation (A) has at most three limit cycles. Also A. Lins Neto shows that, given a natural number l, it is possible to construct an equation of the form (A) with n = 3 that has at least l limit cycles. Still for n = 3, A. Gasull and J. Llibre study the problem of C. Pugh considering that a2(t) does not change sign on [0;1], and M. J. Alvarez, A. Gasull and H. Giacomini also study the problem of C. Pugh considering that there are real numbers a and b such that aa3(t)+ba2(t) does not change sign on [0;1] and a1(t) = a0(t) = 0. Besides this, we study some more general results studied by A. Gasull and A. Guillamon. / Neste trabalho realizamos um estudo sobre as equações do tipo dx dt = nå i=0 ai(t)xi; (A) onde ai 2 C1, i = 0; ;n e 0 t 1. Uma equação da forma (A) é denominada equação de Abel generalizada. Nosso estudo se refere ao problema proposto por C. Pugh: existe um número natural N dependendo apenas de n, tal que a equação (A) possui no máximo N ciclos limites? Inicialmente estudamos o problema de C. Pugh para n=1 e n=2, para os quais a equação (A) possui, no máximo, um e dois ciclos limite, respectivamente. Para n = 3, A. Lins Neto mostra que, se a3(t) não muda de sinal em [0;1], então a equação (A) possui no máximo três ciclos limite. Além disso A. Lins Neto mostra que, dado um número natural l, é possível construir uma equação da forma (A) com n = 3 que possui no mínimo l ciclos limites. Ainda para n = 3, A. Gasull e J. Llibre estudam o problema de C. Pugh considerando que a2(t) não muda de sinal em [0;1], e M. J. Álvarez, A. Gasull e H. Giacomini também estudam o problema de C. Pugh considerando que existem números reais a e b tais que aa3(t)+ba2(t) não muda de sinal em [0;1] e a1(t) = a0(t) = 0. Além destes resultados, estudamos alguns resultados mais gerais estudados por A. Gasull e A. Guillamon.

Cette étude est le résultat d’une thèse CIFRE de trois ans entre le bureau d’étude d’Airbus (domaine du contrôle de l’avion) et le laboratoire TéSA à Toulouse. L’objectif principal est de proposer, développer et valider une solution logicielle pour la détection et le diagnostic d’un type spécifique de vibrations des gouvernes de profondeur et direction, appelée oscillation en cycle limite (limit cycle oscillation ou LCO en anglais), basée sur les signaux existants dans les avions civils. LCO est un terme mathématique générique définissant un mode périodique indépendant de conditions initiales et se produisant dans des systèmes non linéaires non conservatifs. Dans cette étude, nous nous intéressons au phénomène de LCO induit par les jeux mécaniques dans les gouvernes d’un avion civil. Les conséquences du LCO sont l’augmentation locale de la charge structurelle, la dégradation des qualités de vol, la réduction de la durée de vie de l’actionneur, la dégradation du confort du poste de pilotage et de la cabine, ainsi que l’augmentation des coûts de maintenance. L’état de l’art en matière de détection et de diagnostic du LCO induit par le jeu mécanique est basé sur la sensibilité du pilote aux vibrations et sur le contrôle périodique du jeu sur les gouvernes. Cette étude propose une solution basée sur les données (issues de la boucle d’asservissement des actionneurs qui agissent sur les gouvernes) pour aider au diagnostic du LCO et à l’isolement du jeu mécanique. L’objectif est d’améliorer encore plus la disponibilité des avions et de réduire les coûts de maintenance en fournissant aux compagnies aériennes un signal de contrôle pour le LCO et les jeux mécaniques. Pour cette raison, deux solutions algorithmiques pour le diagnostic des vibrations et des jeux ont été proposées. Un détecteur en temps réel pour la détection du LCO est tout d’abord proposé basé sur la théorie du rapport de vraisemblance généralisé (generalized likelihood ratio test ou GLRT en anglais). Certaines variantes et simplifications sont également proposées pour satisfaire les contraintes industrielles. Un détecteur de jeu mécanique est introduit basé sur l’identification d’un modèle de Wiener. Des approches paramétrique (estimateur de maximum de vraisemblance) et non paramétrique (régression par noyau) sont explorées, ainsi que certaines variantes des méthodes non paramétriques. En particulier, le problème de l’estimation d’un cycle d’hystérésis (choisi comme la non-linéarité de sortie d’un modèle de Wiener) est abordé. Ainsi, les problèmes avec et sans contraintes sont étudiés. Une analyse théorique, numérique (sur simulateur) et expérimentale (données de vol et laboratoire) est réalisée pour étudier les performances des détecteurs proposés et pour identifier les limitations et la faisabilité industrielle. Les résultats numériques et expérimentaux obtenus confirment que le GLRT proposé (et ses variantes / simplifications) est une méthode très efficace pour le diagnostic du LCO en termes de performance, robustesse et coût calculatoire. D’autre part, l’algorithme de diagnostic des jeux mécaniques est capable de détecter des niveaux de jeu relativement importants, mais il ne fournit pas de résultats cohérents pour des niveaux de jeu relativement faibles. En outre, des types d’entrée spécifiques sont nécessaires pour garantir des résultats répétitifs et cohérents. Des études complémentaires pourraient être menées afin de comparer les résultats de GLRT avec une approche Bayésienne et pour approfondir les possibilités et les limites de la méthode paramétrique proposée pour l’identification du modèle de Wiener. / This research study is the result of a 3 years CIFRE PhD thesis between the Airbus design office(Aircraft Control domain) and TéSA laboratory in Toulouse. The main goal is to propose, developand validate a software solution for the detection and diagnosis of a specific type of elevator andrudder vibration, called limit cycle oscillation (LCO), based on existing signals available in flightcontrol computers on board in-series aircraft. LCO is a generic mathematical term defining aninitial condition-independent periodic mode occurring in nonconservative nonlinear systems. Thisstudy focuses on the LCO phenomenon induced by mechanical freeplays in the control surface ofa civil aircraft. The LCO consequences are local structural load augmentation, flight handlingqualities deterioration, actuator operational life reduction, cockpit and cabin comfort deteriorationand maintenance cost augmentation. The state-of-the-art for freeplay induced LCO detection anddiagnosis is based on the pilot sensitivity to vibration and to periodic freeplay check on the controlsurfaces. This study is thought to propose a data-driven solution to help LCO and freeplaydiagnosis. The goal is to improve even more aircraft availability and reduce the maintenance costsby providing to the airlines a condition monitoring signal for LCO and freeplays. For this reason,two algorithmic solutions for vibration and freeplay diagnosis are investigated in this PhD thesis. Areal time detector for LCO diagnosis is first proposed based on the theory of the generalized likeli hood ratio test (GLRT). Some variants and simplifications are also proposed to be compliantwith the industrial constraints. In a second part of this work, a mechanical freeplay detector isintroduced based on the theory of Wiener model identification. Parametric (maximum likelihoodestimator) and non parametric (kernel regression) approaches are investigated, as well as somevariants to well-known nonparametric methods. In particular, the problem of hysteresis cycleestimation (as the output nonlinearity of a Wiener model) is tackled. Moreover, the constrainedand unconstrained problems are studied. A theoretical, numerical (simulator) and experimental(flight data and laboratory) analysis is carried out to investigate the performance of the proposeddetectors and to identify limitations and industrial feasibility. The obtained numerical andexperimental results confirm that the proposed GLR test (and its variants/simplifications) is a very appealing method for LCO diagnostic in terms of performance, robustness and computationalcost. On the other hand, the proposed freeplay diagnostic algorithm is able to detect relativelylarge freeplay levels, but it does not provide consistent results for relatively small freeplay levels. Moreover, specific input types are needed to guarantee repetitive and consistent results. Further studies should be carried out in order to compare the GLRT results with a Bayesian approach and to investigate more deeply the possibilities and limitations of the proposed parametric method for Wiener model identification.

<p>A series of aeroelastic analyses is performed for a flexible high-aspect-ratio wing representative of a high altitude long endurance (HALE) aircraft. Such aircraft are susceptible to dynamic instabilities such as flutter, which can lead to large amplitude limit cycle oscillations. These structural motions are modeled by a representative linear typical section model and by Hodges-Dowell beam theory, which includes leading-order nonlinear elastic coupling. Aerodynamic forces are represented by the ONERA dynamic stall model with its coefficients calibrated to CFD data versus wind tunnel test data. Time marching computations of the coupled nonlinear beam and ONERA system highlight a number of features relevant to the aeroelastic response of HALE aircraft, including the influence of a tip store, the sensitivity of the flutter boundary and limit cycle oscillations to aerodynamic CFD or test data, and the roles of structural nonlinearity and nonlinear aerodynamic stall in the dynamic stability of high-aspect-ratio wings.</p> / Dissertation

Un de nos grands défis actuels est la décarbonisation du réseau électrique en éliminant les générateurs d'électricité à base de carburant, et de les remplacer de préférence par des ressources publiquement acceptés et qui respectent la nature de l'environnement. C'est où les ressources énergétiques renouvelables soulèvent comme une solution prometteuse. Les Systèmes de génération d'électricité à cycle de relaxation représentent notamment une classe intéressante des énergies renouvelables. Un tel système doit retrouver périodiquement un état qui permet la production d'énergie, ce qui entraîne un cycle à deux phases : une phase de génération et une phase de récupération qui consomme l'énergie. L'intérêt principal de cette thèse est focaliser sur le système de traction à base de cerf-volant, appelé par la suite le Kite Generator System (KGS). Il s'agit d'une solution proposée pour extraire l'énergie du vent stable et forte dans les hautes altitudes. Son principe de fonctionnement est d'entraîner mécaniquement un générateur électrique au sol en utilisant un ou plusieurs cerfs-volants captifs. La problématique est divisée en deux objectifs : 1 - L'optimisation et le contrôle du cycle de relaxation afin de maximiser la puissance moyenne produite par le système. Deux stratégies de contrôle sont proposées à cet effet : une basée sur un contrôle du modèle non linéaire prédictif (Nonlinear model predictive control - NMPC), et la deuxième basée sur l'application des contraintes virtuel (Virtual Constraints Control - VCC). 2 - L'Intégration du système sur le réseau électrique ou l'employer pour alimenter une charge isolée. Ces problèmes sont abordés dans cette thèse, réalisée au laboratoire de génie électrique de Grenoble (G2ELab) en collaboration avec le laboratoire d'Image Parole Signal Automatique de Grenoble (GIPSA-Lab). / One of our current major challenges is decarbonizing the electric grid by eliminating fuel based electricity generators, and replacing them preferably by nature-friendly publicly accepted resources. That is where renewable energy resources raise as a promising solution. Power relaxation-cycle systems represent an interesting and particular class of renewable. Such a system needs to regain periodically a state that allows energy production. Hence, it has two phases: A generation during which the system is working in its "power" region and is able to generate power and a recovery phase that starts when the system reaches its power region boundaries and resets the system's state to start a new generation phase, which results in power consumption. The main focus of this PhD dissertation is the kite-based traction system, named thereafter the kite generator system (KGS), which emerged as an important class of renewable energy systems that uses relaxation phases. It is a solution proposed to extract energy from the steady and strong wind found in high altitudes. Its operation principle is to mechanically drive a ground-based electric generator using one or several tethered kites. The problematic is divided into two objectives: 1 - Optimization and control of the relaxation cycle to maximize the system's average produced power. Two control strategies are proposed for this purpose: A nonlinear model predictive control (NMPC) based and virtual constraints control (VCC) based one. 2 - Integration of the system on the electric grid or employing it to supply an isolated load. These problems are addressed in this thesis, realized in Grenoble Electrical Engineering laboratory (G2ELab) with collaboration with Grenoble Image Parole Signal Automatique laboratory (GIPSA-Lab).

Cette thèse traite de l’analyse robuste du comportement dynamique des systèmes frottants. Ces derniers constituent une classe particulière des systèmes non linéaires et sont caractérisés par des comportements dynamiques très sensibles aux variations des paramètres de conception en particulier aux dispersions des lois de frottement. Cette sensibilité se traduit par des variations qualitatives importantes du comportement dynamique (stabilité, niveaux vibratoire) qui peuvent alors affecter négativement les performances des systèmes frottants. Il est ainsi important, voire indispensable, de pouvoir tenir compte de la dispersion des lois de frottement dans l’étude et l’analyse du comportement dynamique des systèmes frottants afin d’en garantir la robustesse et, dans une perspective plus générale, d’asseoir une démarche de conception robuste des systèmes frottants. Des méthodes spectrales basées sur le concept du chaos polynomial sont proposées dans cette thèse pour traiter de l’analyse robuste du comportement dynamique des systèmes frottants. Pouvant modéliser les fonctions et processus stochastiques, ces méthodes sont adaptées au problème en particulier à l’analyse de la stabilité et à la prédiction des niveaux vibratoires en tenant compte de la dispersion des lois de frottement. Différentes procédures sont proposées et développées pour traiter de ces deux questions. Une efficacité importante a été illustrée à travers l’évaluation des différentes méthodes proposées (chaos polynomial généralisé, chaos polynomial multi-éléments, chaos de Wiener-Haar) en les appliquant sur un exemple de système frottant. En effet, il est montré que ces méthodes offrent une alternative très intéressante à la méthode prohibitive, mais référentielle, de Monte Carlo puisque, pour des niveaux de précision et de confiance similaires, le coût en nombre, en volume et nécessairement en temps de calcul occasionné par les méthodes spectrales sur les différentes analyses (de la stabilité et des niveaux vibratoire) est largement inférieur à celui requis par la technique de Monte Carlo. / This thesis deals with the robust analysis of the dynamic behaviour of dry friction systems. These are a special class of nonlinear systems and are characterized by dynamic behaviors very sensitive to changes in design parameters in particular to dispersions of friction laws. This sensitivity results in important qualitative changes (stability, vibration levels) that can adversely affect the performances of friction systems. It is thus important, even essential, to take account of the dispersion laws of friction in the study and analysis of the dynamic behavior of friction systems in order to ensure robustness and, in a more general perspective, to establish a robust design approach for friction systems. Spectral methods based on the concept of polynomial chaos are proposed in this thesis to address these problems. The spectral methods can model random functions and stochastic processes so they have been adapted to deal with the robust analysis of the dynamic behavior of frictions systems subjected to random friction coefficient. Different procedures are proposed and developed to, analyze with robustness the stability of friction system in a first step and to predict and estimate the vibratory levels of the same systems. High efficiency is demonstrated by evaluating the various proposed methods (generalized polynomial chaos, multi-element polynomial chaos, Wiener-Haar chaos) on the two issues considered. Indeed, it is shown that these methods offer an attractive alternative to the prohibitive, but referential, Monte Carlo method since, for similar levels of accuracy and confidence, the cost in terms of number and volume of calculus and thus in time of computing occasioned by the spectral methods on the different problems (robust stability and vibration levels analysis) is well lower than the one occasioned by the Monte Carlo technique.

Cette thèse s'intéresse au pilotage des cycles limites pour une classe particulière de systèmes hybrides (SDH): les systèmes commutés cycliques. La thématique des SDH est née du constat d'insuffisance des modèles dynamiques classiques pour décrire les comportements lorsque des aspects évènementiels interviennent. Une classe particulièrement importante de SDH est formée par celle qui présente un régime permanent cyclique. Ces systèmes ont des points de fonctionnement non auto-maintenables: il n'existe pas de commande qui maintienne le système sur ce point. Le maintien n'est assuré qu'en valeur moyenne, en effectuant un cycle dans un voisinage du point par commutation des sous systèmes. L'établissement d'une loi de commutation pour cette classe de systèmes doit répondre aux objectifs de stabilité et de performance dynamique, mais doit également garantir la satisfaction de critères liés à la forme d'onde. A l'heure actuelle, peu de méthodes de commande prennent en compte le caractère cyclique du système. Les travaux de cette thèse ont pour objectif de développer des méthodes génériques et robustes pour piloter cette classe de systèmes. Les algorithmes proposés doivent également pouvoir être implémenté en temps réels. On modélise le système comme un système non - linéaire affine en la commande dont la loi de commande apparait dans le modèle. Ce type de modélisation permet d'envisager deux types de synthèse: l'une à base de commande prédictive et l'autre à base de commande optimale. Ce travail est validé par une partie applicative sur des manipulations dans le CRAN et dans des laboratoires du réseau d'excellence européenne HYCON dans le cadre duquel s'est déroulé cette étude / This work deals with limit cycle control for one particular class of hybrid dynamical systems (HDS): The cyclic switched systems. The HDS were born because the traditional dynamical models were not able to describe complex behaviors and most of all, behaviors with discontinuities. From an application point of view, one important class of HDS depicts a cyclic behavior in steady state. The main characteristic of these systems is that the operation point cannot be maintained: It does not exist a control that maintains the system on a desired operation point. However, this point can be obtained in average by turning into its neighborhood. Thus, a cycle is produced by switching among the system modes. A switched control law must satisfy stability and dynamic performance. Moreover, criteria related to the waveform must be verified. Nowadays, few methods take into account the cyclic behavior of the system. In this research, some generic methods are studied. They show good performance for controlling the cyclic switched systems. The proposed algorithms can be implemented in real-time. The approaches are based on an affine non-linear model of the system whose control explicitly appears. Two control methods are considered: i) A predictive control, ii) An optimal control. Since the predictive control is a good choice for tracking, it will be able to maintain the system in a cycle. The optimal control yields solutions that can be applied to the transients. Some experiments with both control methods applied to the power converters are shown. These tests were carried out not only in our laboratory (CRAN), but also in other laboratories as part of the HYCON excellence network

Ce mémoire s'intéresse à l'étude des comportements dynamiques dans les systèmes d'électronique de puissance. La nature des cycles définis par les variables d'état du système peut être établie soit grâce à un diagramme de bifurcation soit grâce aux multiplieurs de Floquet obtenus par le modèle discret du convertisseur. Cependant, pour certaines structures de convertisseur statique, un modèle discret ne peut être obtenu sans introduire de fortes hypothèses. Les bifurcations de type flip (à l'échelle des hautes fréquences) ne peuvent pas être prédites par le modèle moyen alors qu'elles apparaissent dans de nombreux convertisseurs statiques. Une nouvelle formulation d'un modèle moyen continu permettant d'estimer le premier point de bifurcation (flip, Hopf...) a été présentée. La méthodologie proposée a été appliquée à un convertisseur boost, en mode de conduction continu, contrôlé en courant par différents types de contrôleur à fréquence fixe de commutation. Ensuite, ce modèle moyen a été utilisé pour le dimensionnement des paramètres du régulateur de courant associé à un système de filtrage actif. Les résultats obtenus par le modèle proposé ont été validés par simulation numérique ainsi que par des résultats expérimentaux.Les méthodes d'analyse des cycles limites ont été étendues pour étudier la stabilité des réseaux DC lorsque la fréquence de coupure du filtre LC reliant la source de tension avec le convertisseur statique est proche de la fréquence apparente de commutation des convertisseurs utilisés. Différents modèles discrets ont été développés pour pouvoir considérer ou non le caractère échantillonné de la commande des convertisseurs / This thesis discusses the study of dynamic behavior in power electronics systems. The nature of cycles defined by the state variables of the system can be settled either by a bifurcation diagram or by Floquet multipliers obtained from the discrete model of the converter. However, for certain structures of static converters, a discrete model cannot be obtained without introducing large assumptions. The flip bifurcations (fast-scale) cannot be predicted by the averaged model whereas they appear in many statics converters. A new formulation of a continuous averaged model is presented to estimate the first bifurcation point (flip, Hopf ...). The proposed methodology is applied to a boost converter, operated in continuous conduction mode, controlled by different types of fixed frequency switching current controllers. Then, this averaged model is used for the design of the current controller parameters associated with an active filter system. The variables obtained by the proposed model have been validated by numerical simulation and experimental results. Methods of analysis of limit cycles are extended to study the stability of DC networks when the cutoff frequency of the LC filter between the voltage source and the converter is close to the switching frequency of converters. Different discrete-time models have been developed in order to consider whether to use sampled or no-sampled converter control