Este trabalho apresenta um método alternativo para sintonia de múltiplos controladores ressonantes aplicados aos sistemas ininterruptos de energia. A proposta do método é fornecer um conjunto de equações algébricas de simples aplicação que possibilite aos projetistas destes sistemas determinar os parâmetros dos controladores ressonantes com múltiplos modos. As equações apresentadas para determinação dos parâmetros do controlador foram obtidas diretamente com base nos parâmetros e nas características funcionais do inversor. Também nestas equações estão presentes constantes as quais garantem que todo o inversor cujo controlador for sintonizado pelo método atenda as especificações estabelecidas pela norma 60240-3. As constantes são determinadas através da formulação do problema por desigualdades matriciais lineares (LMI - Linear Matrix Inequalities) que levam em conta o equacionamento dinâmico do inversor e dos múltiplos controladores ressonantes. A solução do problema satisfaz simultaneamente a minimização do esforço de controle, onde foi empregada a formulação de custo garantido, juntamente com a localização dos polos de malha-fechada para toda a variação admissível de carga, formulada através do procedimento de D-Estabilidade. / This master thesis shows an alternative method for tuning multiple resonant controllers applied to uninterrupted power supply. The method is intended to provide a set of simple algebraic equations that enable designers of those systems to determine the parameters of the resonant controllers through multiple modes. The equations presented for determining the controller’s parameters were obtained directly based on the parameters and functional characteristics of the inverter. Additionally, constants that ensure that every inverter whose controller is attuned by the method meets the 60240-3 specifications norms can be found in these equations. The constants are determined based on the formulation of the problem through linear matrix inequalities (LMI) that take in consideration the dynamic of the inverter and of the multiple resonant controllers. The solution of the problem ensures both the needs for minimization of control efforts at guaranteed cost, along with the location of close-loop poles for every permissible load variation, formulated through the D-Stability procedure.

Este trabalho apresenta um método alternativo para sintonia de múltiplos controladores ressonantes aplicados aos sistemas ininterruptos de energia. A proposta do método é fornecer um conjunto de equações algébricas de simples aplicação que possibilite aos projetistas destes sistemas determinar os parâmetros dos controladores ressonantes com múltiplos modos. As equações apresentadas para determinação dos parâmetros do controlador foram obtidas diretamente com base nos parâmetros e nas características funcionais do inversor. Também nestas equações estão presentes constantes as quais garantem que todo o inversor cujo controlador for sintonizado pelo método atenda as especificações estabelecidas pela norma 60240-3. As constantes são determinadas através da formulação do problema por desigualdades matriciais lineares (LMI - Linear Matrix Inequalities) que levam em conta o equacionamento dinâmico do inversor e dos múltiplos controladores ressonantes. A solução do problema satisfaz simultaneamente a minimização do esforço de controle, onde foi empregada a formulação de custo garantido, juntamente com a localização dos polos de malha-fechada para toda a variação admissível de carga, formulada através do procedimento de D-Estabilidade. / This master thesis shows an alternative method for tuning multiple resonant controllers applied to uninterrupted power supply. The method is intended to provide a set of simple algebraic equations that enable designers of those systems to determine the parameters of the resonant controllers through multiple modes. The equations presented for determining the controller’s parameters were obtained directly based on the parameters and functional characteristics of the inverter. Additionally, constants that ensure that every inverter whose controller is attuned by the method meets the 60240-3 specifications norms can be found in these equations. The constants are determined based on the formulation of the problem through linear matrix inequalities (LMI) that take in consideration the dynamic of the inverter and of the multiple resonant controllers. The solution of the problem ensures both the needs for minimization of control efforts at guaranteed cost, along with the location of close-loop poles for every permissible load variation, formulated through the D-Stability procedure.

Este trabalho apresenta um método alternativo para sintonia de múltiplos controladores ressonantes aplicados aos sistemas ininterruptos de energia. A proposta do método é fornecer um conjunto de equações algébricas de simples aplicação que possibilite aos projetistas destes sistemas determinar os parâmetros dos controladores ressonantes com múltiplos modos. As equações apresentadas para determinação dos parâmetros do controlador foram obtidas diretamente com base nos parâmetros e nas características funcionais do inversor. Também nestas equações estão presentes constantes as quais garantem que todo o inversor cujo controlador for sintonizado pelo método atenda as especificações estabelecidas pela norma 60240-3. As constantes são determinadas através da formulação do problema por desigualdades matriciais lineares (LMI - Linear Matrix Inequalities) que levam em conta o equacionamento dinâmico do inversor e dos múltiplos controladores ressonantes. A solução do problema satisfaz simultaneamente a minimização do esforço de controle, onde foi empregada a formulação de custo garantido, juntamente com a localização dos polos de malha-fechada para toda a variação admissível de carga, formulada através do procedimento de D-Estabilidade. / This master thesis shows an alternative method for tuning multiple resonant controllers applied to uninterrupted power supply. The method is intended to provide a set of simple algebraic equations that enable designers of those systems to determine the parameters of the resonant controllers through multiple modes. The equations presented for determining the controller’s parameters were obtained directly based on the parameters and functional characteristics of the inverter. Additionally, constants that ensure that every inverter whose controller is attuned by the method meets the 60240-3 specifications norms can be found in these equations. The constants are determined based on the formulation of the problem through linear matrix inequalities (LMI) that take in consideration the dynamic of the inverter and of the multiple resonant controllers. The solution of the problem ensures both the needs for minimization of control efforts at guaranteed cost, along with the location of close-loop poles for every permissible load variation, formulated through the D-Stability procedure.

Este trabalho apresenta um estudo de controladores repetitivos e ressonantes-repetitivos aplicados a fontes ininterruptas de energia (UPSs, do termo em inglês, Uninterruptible Power Supplies). Primeiramente, o desempenho dos controladores repetitivos é analisado a partir das exigências e dos procedimentos de testes definidos pela norma IEC 62040-3. A partir destes resultados, são discutidas as principais causas para o erro de seguimento de um sinal de referência e é avaliado o impacto de metodologias de correção aplicadas na função de transferência do controlador repetitivo. No contexto dos controladores ressonantes-repetitivos duas topologias são analisadas: a primeira é composta por um controlador ressonante sintonizado na frequência fundamental do sinal a ser seguido em paralelo com um controlador repetitivo sintonizado na mesma frequência; a segunda topologia é composta pelo mesmo paralelo entre os controladores ressonante e repetitivo, mas um filtro complementar é adicionado em série com o controlador repetitivo visando alocar a operação de cada controlador em faixas de frequências distintas. Então uma variação do controlador ressonante-repetitivo com filtro é proposta, na qual o filtro é utilizado para corrigir a fase do laço do controlador repetitivo e consequentemente aumentar a magnitude nas frequências de interesse. A partir desta estrutura proposta, uma representação no espaço de estados do sistema em malha fechada é obtida e o projeto do controlador é realizado através da solução de um problema de otimização com restrições na forma de Desigualdades Matriciais Lineares (do inglês, Linear Matrix Inequalities - LMIs). Resultados de simulação utilizando Matlab/PSIM são apresentados para demostrar a melhoria de desempenho do sistema com o controlador proposto. / This work presents a study of repetitive and resonant-repetitive controllers applied to Uninterruptible Power Supplies (UPSs). First, the performance of repetitive controllers is analyzed in terms of requirements and test procedures defined in the IEC 62040-3 standard. From these results the main causes of the reference tracking error are discussed and the impact of correction methodologies applied to repetitive controller transfer function is evaluated. In the context of the resonant-repetitive controllers two topologies are analyzed: the first is composed of a resonant controller tuned to the fundamental frequency of the signal to be followed in parallel with a repetitive controller tuned to the same frequency; the second topology is composed of the same parallel connection between the resonant and the repetitive controllers but a complementary filter is added in series with the repetitive controller aiming to restrict each controller action to different frequency bands. Then a variation of the resonant-repetitive controller with a filter is proposed, in which the filter is used to correct the phase of the repetitive controller loop and consequently increase the magnitude at the frequencies of interest. From this proposed structure, a state space model representing the closed loop system is obtained and the controller design is carried out by the solution of an optimization problem based on LMI (Linear Matrix Inequality) constraints. Simulation results in Matlab/PSIM are presented to demonstrate the improvement on system performance with the proposed controller.

Este trabalho apresenta um estudo de controladores repetitivos e ressonantes-repetitivos aplicados a fontes ininterruptas de energia (UPSs, do termo em inglês, Uninterruptible Power Supplies). Primeiramente, o desempenho dos controladores repetitivos é analisado a partir das exigências e dos procedimentos de testes definidos pela norma IEC 62040-3. A partir destes resultados, são discutidas as principais causas para o erro de seguimento de um sinal de referência e é avaliado o impacto de metodologias de correção aplicadas na função de transferência do controlador repetitivo. No contexto dos controladores ressonantes-repetitivos duas topologias são analisadas: a primeira é composta por um controlador ressonante sintonizado na frequência fundamental do sinal a ser seguido em paralelo com um controlador repetitivo sintonizado na mesma frequência; a segunda topologia é composta pelo mesmo paralelo entre os controladores ressonante e repetitivo, mas um filtro complementar é adicionado em série com o controlador repetitivo visando alocar a operação de cada controlador em faixas de frequências distintas. Então uma variação do controlador ressonante-repetitivo com filtro é proposta, na qual o filtro é utilizado para corrigir a fase do laço do controlador repetitivo e consequentemente aumentar a magnitude nas frequências de interesse. A partir desta estrutura proposta, uma representação no espaço de estados do sistema em malha fechada é obtida e o projeto do controlador é realizado através da solução de um problema de otimização com restrições na forma de Desigualdades Matriciais Lineares (do inglês, Linear Matrix Inequalities - LMIs). Resultados de simulação utilizando Matlab/PSIM são apresentados para demostrar a melhoria de desempenho do sistema com o controlador proposto. / This work presents a study of repetitive and resonant-repetitive controllers applied to Uninterruptible Power Supplies (UPSs). First, the performance of repetitive controllers is analyzed in terms of requirements and test procedures defined in the IEC 62040-3 standard. From these results the main causes of the reference tracking error are discussed and the impact of correction methodologies applied to repetitive controller transfer function is evaluated. In the context of the resonant-repetitive controllers two topologies are analyzed: the first is composed of a resonant controller tuned to the fundamental frequency of the signal to be followed in parallel with a repetitive controller tuned to the same frequency; the second topology is composed of the same parallel connection between the resonant and the repetitive controllers but a complementary filter is added in series with the repetitive controller aiming to restrict each controller action to different frequency bands. Then a variation of the resonant-repetitive controller with a filter is proposed, in which the filter is used to correct the phase of the repetitive controller loop and consequently increase the magnitude at the frequencies of interest. From this proposed structure, a state space model representing the closed loop system is obtained and the controller design is carried out by the solution of an optimization problem based on LMI (Linear Matrix Inequality) constraints. Simulation results in Matlab/PSIM are presented to demonstrate the improvement on system performance with the proposed controller.

Este trabalho apresenta um estudo de controladores repetitivos e ressonantes-repetitivos aplicados a fontes ininterruptas de energia (UPSs, do termo em inglês, Uninterruptible Power Supplies). Primeiramente, o desempenho dos controladores repetitivos é analisado a partir das exigências e dos procedimentos de testes definidos pela norma IEC 62040-3. A partir destes resultados, são discutidas as principais causas para o erro de seguimento de um sinal de referência e é avaliado o impacto de metodologias de correção aplicadas na função de transferência do controlador repetitivo. No contexto dos controladores ressonantes-repetitivos duas topologias são analisadas: a primeira é composta por um controlador ressonante sintonizado na frequência fundamental do sinal a ser seguido em paralelo com um controlador repetitivo sintonizado na mesma frequência; a segunda topologia é composta pelo mesmo paralelo entre os controladores ressonante e repetitivo, mas um filtro complementar é adicionado em série com o controlador repetitivo visando alocar a operação de cada controlador em faixas de frequências distintas. Então uma variação do controlador ressonante-repetitivo com filtro é proposta, na qual o filtro é utilizado para corrigir a fase do laço do controlador repetitivo e consequentemente aumentar a magnitude nas frequências de interesse. A partir desta estrutura proposta, uma representação no espaço de estados do sistema em malha fechada é obtida e o projeto do controlador é realizado através da solução de um problema de otimização com restrições na forma de Desigualdades Matriciais Lineares (do inglês, Linear Matrix Inequalities - LMIs). Resultados de simulação utilizando Matlab/PSIM são apresentados para demostrar a melhoria de desempenho do sistema com o controlador proposto. / This work presents a study of repetitive and resonant-repetitive controllers applied to Uninterruptible Power Supplies (UPSs). First, the performance of repetitive controllers is analyzed in terms of requirements and test procedures defined in the IEC 62040-3 standard. From these results the main causes of the reference tracking error are discussed and the impact of correction methodologies applied to repetitive controller transfer function is evaluated. In the context of the resonant-repetitive controllers two topologies are analyzed: the first is composed of a resonant controller tuned to the fundamental frequency of the signal to be followed in parallel with a repetitive controller tuned to the same frequency; the second topology is composed of the same parallel connection between the resonant and the repetitive controllers but a complementary filter is added in series with the repetitive controller aiming to restrict each controller action to different frequency bands. Then a variation of the resonant-repetitive controller with a filter is proposed, in which the filter is used to correct the phase of the repetitive controller loop and consequently increase the magnitude at the frequencies of interest. From this proposed structure, a state space model representing the closed loop system is obtained and the controller design is carried out by the solution of an optimization problem based on LMI (Linear Matrix Inequality) constraints. Simulation results in Matlab/PSIM are presented to demonstrate the improvement on system performance with the proposed controller.

Le travail proposé dans cette thèse porte sur l’amélioration de l’efficacité énergétique et de la sûreté de fonctionnement de la Machine à Réluctance Variable (MRV). D’abord, nous avons présenté la commande de la MRV en modes moteur et générateur débitant sur bus continu. Pour le mode moteur, on cherche à réguler la vitesse de rotation et le couple, alors qu’en mode générateur, l’objectif de la commande est de maintenir constante la tension du bus malgré les fluctuations de la vitesse et de la charge. Une démarche itérative est proposée pour la maximisation du rendement global. Trois paramètres de réglage ont été choisis : L’angle d’amorçage (Ψ), l’angle de conduction (Θp) et le courant de référence des phases (Iref). L’efficacité de l’algorithme est évaluée à travers des simulations et des tests expérimentaux. Un rendement global maximal de 70% est atteint pour des vitesses et couples élevés. Ensuite, on s’est intéressé à la connexion de la Génératrice à Réluctance Variable (GRV) au réseau alternatif monophasé ou triphasé dans le cadre d’une application éolienne. La tension continue à la sortie de la GRV est convertie en une tension alternative par un convertisseur DC-AC. Le premier objectif est de maintenir la tension du bus continu à sa valeur nominale; le second est de contrôler la qualité du courant injecté dans le réseau. En monophasé, trois types de correcteur sont testés pour réguler le courant sinusoïdal (un correcteur PI, un correcteur Résonant et un correcteur Proportionnel-Résonant). En triphasé, une commande VQ dans le référentiel de Park est adoptée: La tension du bus continu est contrôlée à travers le courant id et la puissance réactive est contrôlée par le courant iq. Les résultats de simulation montrent qu’on obtient des courants quasi-sinusoïdaux avec un taux de distorsion harmonique inférieur à 1% aussi bien en monophasé qu’en triphasé. Enfin, pour améliorer la sûreté de fonctionnement de l’actionneur et réduire les coûts liés à l’utilisation de capteurs mécaniques, trois stratégies de commande sans capteur de position sont présentées. La première est basée sur la technique d’injection. La deuxième repose sur l’estimation du flux. La troisième s’appuie sur les observateurs adaptatifs. On trouve que la technique d’injection et la méthode basée sur la mesure du flux fonctionnent de façon complémentaire. La première est efficace en basses vitesses et ne dépend pas de la charge, la deuxième est performante en hautes vitesses et pour des charges élevées. L’observateur adaptatif proposé assure une convergence exponentielle de la position malgré le modèle analytique simplifié de l’inductance utilisé pour la synthèse. Son principal avantage réside dans sa robustesse aux variations paramétriques et au couple de charge qui est estimé. / The work proposed here focuses on the improvement of the energy efficiency and the safety of the Switched Reluctance Machine (SRM). First, the control of the SRM in motor and generator modes is presented. In motor mode, the speed and the torque are regulated, while in generator mode, the objective is to keep constant the DC bus voltage. An iterative optimization algorithm is proposed formaximizing the global efficiency. The analysis of the electromechanical energy conversion has shown that there is an optimal combination of the control variables - turn on angle (Ψ), conduction angle (Θp) and reference current (Iref) – to maximize the efficiency. The strategy is evaluated using intensive numerical simulations and experimental validation. Thanks to the optimization, the global efficiency reaches 70% almost from half the nominal speed to the maximum speed. Then, the Switched Reluctance Generator (SRG) is used as an AC generator for a Wind Energy Conversion (WEC) application. The produced DC power is converted into AC power by means of voltage inverter and delivered to the AC grid. The first issue of the WEC control is to maintain constant the output DC voltage despite the wind speed variations and the load uncertainty. The second issue is to control the quality of the current. In single-phase AC network, three controllers are tested to regulate the AC current (PI controller, Resonant controller, Proportional-Resonant controller). In three-phase AC network, a VQ control in Park’s frame is adopted: The DC bus voltage is controlled through the direct current and the reactive power injected into the grid is controlled through the quadrature current. Simulation results show that quasi-sinusoidal currents with a harmonic distortion rate less than 1% are obtained in both cases. Finally, we address the problem of sensorless control. In fact, the control of the SRM requires that the rotor position is known. A mechanical encoder is used generally to measure the position. The elimination of this position sensor would reduce the cost and packaging requirements of the drive. Three methods to estimate the rotor position are presented. The first one named inductance-method is an active as it is based on the pulse injection technique. The second one named flux-method is a passive one as it used the current measurement. The third one is based on the state observers for the flux, position, and velocity and load torque estimation. The simulations results have shown that the inductance-based method is efficient in low speed region and the flux-based one is more efficient in high-speed region. It is also shown that, observers are exponentially convergent even when a simple analytical modelling, that neglects saturation effect, is used to design the observer.

Este trabalho apresenta um estudo da discretização de controladores ressonantes aplicados a fontes ininterruptas de energia (UPSs, do termo em inglês, Uninterruptible Power Suppllies). Primeiramente, diferentes métodos de discretização serão considerados na obtenção de um modelo em tempo discreto da UPS. Além disso, estes métodos serão comparados do ponto de vista frequencial para a definição da formulação do controlador ressonante a ser utilizado. Então, uma metodologia de projeto robusto do controlador ressonante em tempo discreto é proposta a partir de uma representação em espaço de estados do sistema em malha fechada e os parâmetros do controlador são obtidos através da solução de um problema de otimização convexa sujeito a restrições na forma de Desigualdades Matriciais Lineares (do inglês, Linear Matrix Inequalities - LMIs). A estratégia proposta foi validada por meio de resultados de simulação e experimentais obtidos com um inversor comercial de 3,5 kVA considerando os critérios estabelecidos na norma IEC 62040-3. Nestas condições, demonstrara-se um desempenho melhor do que os obtidos com a discretização do controlador projetado em tempo contínuo, sobretudo quando consideradas frequências de amostragem menores. / This work presents a study about discrete-time resonant controllers applied to uninterruptible power supplies (UPSs). First, different discretization methods are considered to obtain an equivalent UPS discrete-time model. Moreover, these methods are compared in the frequency domain in order to define the resonant controller structure to be employed. Then, a robust design methodology to the discrete-time resonant controller is proposed using a state-space representation of the closed-loop system and the controller parameters are obtained by solving a convex optimization problem subject to constraints in the form of Linear Matrix Inequalities (LMIs). The proposed strategy was validated by means of simulation and experimental results obtained with a 3.5 kVA commercial inverter taking into account the IEC 62040-3 norm requirements. In this conditions, a better performance was achieved than those obtained through discretization of a continuous-time controller, especially when considering smaller sampling frequencies.

Este trabalho aborda o problema de seguimento e rejeição de sinais periódicos em sistemas lineares sujeitos a saturação nos atuadores. Para garantir o seguimento/rejeição, dois controladores baseados no princípio do modelo interno são considerados: o primeiro baseia-se no modelo interno em sua formulação clássica, isto é, um controlador dinâmico contendo um número finito de modos (marginalmente) instáveis da referência/perturbação é introduzido na malha de controle, em uma abordagem chamada de controladores ressonantes; a segunda abordagem considera o controlador repetitivo, onde um elemento de atraso é inserido namalha de controle emumlaço de realimentação positiva, fazendo o papel do modelo interno de ordem infinita. Nos dois casos, o objetivo principal é a obtenção de condições na forma de inequações matriciais lineares (do inglês, Linear Matrix Inequalities - LMIs) para a síntese simultânea de uma realimentação de estados estabilizante e do ganho do laço estático de anti-windup. Partindo do pressuposto que as referências e perturbações pertencem a um certo conjunto admissível, estes ganhos garantem que as trajetórias do sistema em malha fechada inciadas em um certo conjunto elipsoidal convergem para outro conjunto elipsoidal invariante contido na região de operação linear do sistema. Nesta região, a presença do modelo interno na malha de controle garante o seguimento e a rejeição dos sinais de interesse. Nas duas abordagens são propostos problemas de otimização visando a maximização do conjunto invariante de estados admissíveis e/ou a maximização do conjunto de referências/perturbações admissíveis. Extensões da metodologia para sistemas de tempo discreto também são apresentadas. / This work addresses the tracking/rejection problem of periodic signals for linear systems subject to control saturation. To ensure the tracking/rejection, two internal model based controllers are considered: the first one considers the internal model in a classical framework, i.e. a dynamic controller containing a finite number of (marginally) unstable modes of the reference/disturbance signal is introduced in the control loop. In this work, this approach is called resonant controller. The second approach considers the repetitive controller, where a delay element is introduced in the control loop in a positive feedback loop, playing the role of an infinite order internal model. In both cases, the main objective is to obtain conditions in the form of LMIs to simultaneously compute a stabilizing state feedback gain and an anti-windup gain. Assuming that the references and disturbances signals belong to a certain admissible set, these gains guarantee that the trajectories of the closed-loop system starting in a certain ellipsoidal set contract to another invariant ellipsoidal set inside the linearity region of the closed-loop system. In this region the presence of the internal model ensures tracking/rejection of the considered periodic signals. In both frameworks, optimization problems aiming at the maximization of the invariant set of admissible states and/or the maximization of the set of admissible references/disturbances are proposed. Extensions of the proposed framework to discrete-time systems are also presented.

Dans un contexte de réduction des émissions de CO2 dans les systèmes industriels et d’amélioration de leur efficacité énergétique, les chauffages par induction répondent à ces critères. Le procédé consiste à plonger un corps conducteur d’électricité dans un champ magnétique variable, induisant ainsi des courants au sein de la pièce qui se met alors à chauffer par effet Joule. Cette technologie présente l’avantage d’atteindre des températures élevées de manière précise et rapide, sans contact avec la source d’énergie. Si aujourd’hui le contrôle de tels procédés passe par la structure mécanique du chauffage, de nombreuses études ont montré que l’association de plusieurs bobines alimentées par des systèmes d’électronique de puissance fournit une souplesse dans le contrôle des profils de température et une flexibilité vis-à-vis des pièces traitées. Ce travail présente deux systèmes de chauffage par induction. Le premier est un prototype réalisé par EDF considérant trois inducteurs alimentés par trois onduleurs à résonance. Nous nous y intéresserons plus particulièrement par la suite. Le second, en cours de réalisation, met en jeu six inducteurs pour du chauffage au défilé. Leurs caractéristiques, leurs alimentations et leurs fonctionnements sont abordés pour ensuite mettre en place deux modélisations des phénomènes électriques, l’une sous forme de fonctions de transfert, la seconde dans l’espace d’état. L’objectif final est le développement d’une alimentation auto-adaptative capable de contrôler en temps réel le profil de puissance injecté dans les pièces à chauffer afin d’atteindre un profil de température requis avec le minimum d’énergie consommée. L’étude se poursuit avec un inventaire des solutions existantes en termes de commande en boucle ouverte et en boucle fermée des systèmes mono-inducteurs, ainsi que des travaux, plus rares, pour les chauffages multi-inducteurs. De plus, des études ont montré que le contrôle de la température à la surface d’une pièce à chauffer passait par le contrôle des courants dans les inducteurs, en amplitude mais également en phase. C’est pourquoi nous proposons des lois de commande pour asservir les courants dans les inducteurs. Une routine d’optimisation fournit les amplitudes et les phases des courants dans les trois inducteurs permettant d’obtenir le profil de température le plus proche d’un profil de référence. Nous l’avons modifiée de façon à tenir compte de solutions énergétiquement optimisées en intégrant les pertes dans les interrupteurs et les inducteurs. Deux lois de commande originales sont proposées. La première étudie une commande robuste dans l’espace d’état par placement de vecteurs propres. La seconde met en jeu des correcteurs résonants qui confèrent à la boucle du système un module de gain infiniment grand à la fréquence de résonance de sorte qu’ils effacent les effets des perturbations agissant à cette même fréquence. Les méthodes de synthèse de ces correcteurs sont échantillonnées avec un très faible rapport fréquence d’échantillonnage/fréquence de résonance ; les performances sont détaillées et analysées pour le prototype à trois inducteurs. Pour tester plus facilement et valider en partie les lois mises en place, un simulateur analogique a été conçu, sorte d’émulateur reproduisant le comportement des courants dans les inducteurs et des tensions à leurs bornes. Il se base sur la modélisation sous forme de fonctions de transfert et ne comprend donc pas d’onduleur. Par l’intermédiaire d’une carte dSPACE intégrant un DSP, nous avons implanté et validé les deux lois de commande robustes sur le simulateur analogique. Par la suite, pour se rapprocher du système réel, nous avons mis en place une commande rapprochée transformant les trois signaux de commande en sortie des correcteurs vers les rapports cycliques des douze interrupteurs des convertisseurs alimentant les inducteurs. Cette étape a été validée par des essais expérimentaux réalisés en parallèle de nos études. / In the context of reducing carbon dioxide emissions in industrial systems and improving their energy efficiency, induction heaters meet these criteria. The method consists in immersing an electrically conductive body in a variable magnetic field, inducing currents within the piece which then begins to heat by Joule effect. This technology has the advantage of reaching high temperatures accurately and quickly, without contact with the power source. Today the control of such works with mechanical structures. But many studies have shown that the combination of several coils supplied by electronic power systems provides flexibility in controlling temperature profiles and flexibility towards the treated parts. This paper presents two systems of induction heating. The first is a prototype made by EDF considering three inductors supplied by three resonant inverters. We will focus more specifically later on this prototype. The second one, in progress, involves six inductors for scrolling heating. Their characteristics, their power supplies and their functions are discussed and then set up two models of electric phenomena, one form of transfer functions and one form in the state space. The final objective is the development of a self-adaptive power able to control real-time power profile injected into parts of heating to achieve a temperature profile required with minimum energy consumption. The study goes on with a list of existing solutions in terms of open-loop control and closed-loop control for single inductor system, as well as few rarer works for multi-inductors heaters. In addition, studies have shown that control of the surface temperature of the piece to be heated passes by the control of currents in the inductors, in magnitude but also in phase. That is why we propose control laws for controlling inductor currents. An optimization routine provides the magnitudes and phases of the currents in the three inductors to obtain the temperature profile closer to a reference profile. We modified it to take into account energy optimized solutions by integrating the losses in the switches and inductors. Two original control laws are proposed. The first one studies a robust control in the state space by placing eigenvalues and eigenvectors. The second one involves resonant markers that give the system loop gain module infinitely large at the resonant frequency so that they erase the effects of disturbances acting at the same frequency. The methods of synthesis of these markers are sampled with a very low sampling frequency / resonant frequency ratio; performance are detailed and analyzed for the prototype with three inductors. So as to test and validate easily some of the studied laws, an analog simulator was designed, a kind of an emulator, which reproduces the behaviour of the currents in the coils and the voltages at their terminals. It is based on the transfer function model and therefore does not include inverters. Through a dSPACE card integrating a DSP, we have implemented and validated the two robust control laws on the analog simulator. Thereafter, in order to be closer to the real system, we have established a close control which turns the three control signals toward the duty cycles of the twelve switches of the converters supplying the inductors. This step was validated by experimental tests carried out in parallel with our studies.