185 research outputs found

    Implementação de lei de comutação restrita para controle de sistemas lineares comutado

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    A special class of switched linear systems with switching law constrained to logical state-input can be employed to model a wide range of different systems. The present paper presents a new stability analysis and controller design method for this class of hybrid systems. Proposed methods is based on the quadratic Lyapunov function. Stability analysis and design of these systems have resulted in solving a convex optimization problem of Linear Matrix Inequality type. The results of simulation on dc-dc buck converter confirm the effectiveness of proposed method.Se puede emplear una clase especial de sistemas lineales conmutados con ley de conmutación restringida a entrada de estado lógico para modelar una amplia gama de sistemas diferentes. El presente documento presenta un nuevo método de análisis de estabilidad y diseño de controlador para esta clase de sistemas híbridos. Los métodos propuestos se basan en la función cuadrática de Lyapunov. El análisis de estabilidad y el diseño de estos sistemas han dado como resultado la solución de un problema de optimización convexo de tipo de desigualdad de matriz lineal. Los resultados de la simulación en el convertidor dc-dc buck confirman la efectividad del método propuesto.Uma classe especial de sistemas lineares comutados com lei de comutação restrita a entrada de estado lógico pode ser empregada para modelar uma ampla gama de diferentes sistemas. O presente artigo apresenta um novo método de análise de estabilidade e design de controlador para esta classe de sistemas híbridos. Os métodos propostos são baseados na função quadrática de Lyapunov. A análise de estabilidade e o projeto desses sistemas resultaram na solução de um problema de otimização convexa do tipo Desigualdade de Matriz Linear. Os resultados da simulação no conversor dc-dc buck confirmam a eficácia do método proposto

    Contributions à la stabilisation des systèmes à commutation affine

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    Cette thèse porte sur la stabilisation des systèmes à commutation dont la commande, le signal de commutation, est échantillonné de manière périodique. Les difficultés liées à cette classe de systèmes non linéaires sont d'abord dues au fait que l'action de contrôle est effectuée aux instants de calcul en sélectionnant le mode de commutation à activer et, ensuite, au problème de fournir une caractérisation précise de l'ensemble vers lequel convergent les solutions du système, c'est-à-dire l'attracteur. Dans cette thèse, les contributions ont pour fil conducteur la réduction du conservatisme fait pendant la définition d'attracteurs, ce qui a mené à garantir la stabilisation du système à un cycle limite. Après une introduction générale où sont présentés le contexte et les principaux résultats de la littérature, le premier chapitre contributif introduit une nouvelle méthode basée sur une nouvelle classe de fonctions de Lyapunov contrôlées qui fournit une caractérisation plus précise des ensembles invariants pour les systèmes en boucle fermée. La contribution présentée comme un problème d'optimisation non convexe et faisant référence à une condition de Lyapunov-Metzler apparaît comme un résultat préliminaire et une étape clé pour les chapitres à suivre. La deuxième partie traite de la stabilisation des systèmes affines commutés vers des cycles limites. Après avoir présenté quelques préliminaires sur les cycles limites hybrides et les notions dérivées telles que les cycles au Chapitre 3, les lois de commutation stabilisantes sont introduites dans le Chapitre 4. Une approche par fonctions de Lyapunov contrôlées et une stratégie de min-switching sont utilisées pour garantir que les solutions du système nominal en boucle fermée convergent vers un cycle limite. Les conditions du théorème sont exprimées en termes d'Inégalités Matricielles Linéaires (dont l'abréviation anglaise est LMI) simples, dont les conditions nécessaires sous-jacentes relâchent les conditions habituelles dans cette littérature. Cette méthode est étendue au cas des systèmes incertains dans le Chapitre 5, pour lesquels la notion de cycles limites doit être adaptée. Enfin, le cas des systèmes dynamiques hybrides est exploré au Chapitre 6 et les attracteurs ne sont plus caractérisés par des régions éventuellement disjointes mais par des trajectoires fermées et isolées en temps continu. Tout au long de la thèse, les résultats théoriques sont évalués sur des exemples académiques et démontrent le potentiel de la méthode par rapport à la littérature récente sur le sujet.This thesis deals with the stabilization of switched affine systems with a periodic sampled-data switching control. The particularities of this class of nonlinear systems are first related to the fact that the control action is performed at the computation times by selecting the switching mode to be activated and, second, to the problem of providing an accurate characterization of the set where the solutions to the system converge to, i.e. the attractors. The contributions reported in this thesis have as common thread to reduce the conservatism made in the characterization of attractors, leading to guarantee the stabilization of the system at a limit cycle. After a brief introduction presenting the context and some main results, the first contributive chapter introduced a new method based on a new class of control Lyapunov functions that provides a more accurate characterization of the invariant set for a closed-loop system. The contribution presented as a nonconvex optimization problem and referring to a Lyapunov-Metzler condition appears to be a preliminary result and the milestone of the forthcoming chapters. The second part deals with the stabilization of switched affine systems to limit cycles. After presenting some preliminaries on hybrid limit cycles and derived notions such as cycles in Chapter 3, stabilizing switching control laws are developed in Chapter 4. A control Lyapunov approach and a min-switching strategy are used to guarantee that the solutions to a nominal closed-loop system converge to a limit cycle. The conditions of the theorem are expressed in terms of simple linear matrix inequalities (LMI), whose underlying necessary conditions relax the usual one in this literature. This method is then extended to the case of uncertain systems in Chapter 5, for which the notion of limit cycle needs to be adapted. Finally, the hybrid dynamical system framework is explored in Chapter 6 and the attractors are no longer characterized by possibly disjoint regions but as continuous-time closed and isolated trajectory. All along the dissertation, the theoretical results are evaluated on academic examples and demonstrate the potential of the method over the recent literature on this subject

    Nonlinear constrained and saturated control of power electronics and electromechanical systems

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    Power electronic converters are extensively adopted for the solution of timely issues, such as power quality improvement in industrial plants, energy management in hybrid electrical systems, and control of electrical generators for renewables. Beside nonlinearity, this systems are typically characterized by hard constraints on the control inputs, and sometimes the state variables. In this respect, control laws able to handle input saturation are crucial to formally characterize the systems stability and performance properties. From a practical viewpoint, a proper saturation management allows to extend the systems transient and steady-state operating ranges, improving their reliability and availability. The main topic of this thesis concern saturated control methodologies, based on modern approaches, applied to power electronics and electromechanical systems. The pursued objective is to provide formal results under any saturation scenario, overcoming the drawbacks of the classic solution commonly applied to cope with saturation of power converters, and enhancing performance. For this purpose two main approaches are exploited and extended to deal with power electronic applications: modern anti-windup strategies, providing formal results and systematic design rules for the anti-windup compensator, devoted to handle control saturation, and “one step” saturated feedback design techniques, relying on a suitable characterization of the saturation nonlinearity and less conservative extensions of standard absolute stability theory results. The first part of the thesis is devoted to present and develop a novel general anti-windup scheme, which is then specifically applied to a class of power converters adopted for power quality enhancement in industrial plants. In the second part a polytopic differential inclusion representation of saturation nonlinearity is presented and extended to deal with a class of multiple input power converters, used to manage hybrid electrical energy sources. The third part regards adaptive observers design for robust estimation of the parameters required for high performance control of power systems

    Design of switching strategies with applications in photovoltaic energy generation

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    Tese (doutorado) - Universidade Federal de Santa Catarina, Centro Tecnológico, Programa de Pós-Graduação em Engenharia de Automação e Sistemas, Florianópolis, 2014.Abstract : This work presents control strategies and stability analysis for switched systemswith a proposed application to photovoltaic energy generation systems.The conditions are based on Linear Matrix Inequalities (LMIs).Initially, a general description of the photovoltaic systems is presented coveringthe following aspects: the modeling of a photovoltaic array, some commonconnection topologies, the main objectives, techniques for maximizingthe generated power, among other informations. This content is necessary forthe control design method proposed in this work.Next, a design technique for the stabilization of affine switched systems isshown. The methodology used is based on the Lyapunov?s theory for stabilityof systems, describing sufficient conditions for the proposed switchingrule design in the form of LMIs and solving them using existing softwarepackages. In the sequel, the switching strategy is extended for a class ofnonlinear systems of great interest, especially for the control of photovoltaicsystems. This class is composed of systems containing sector-bounded nonlinearities.Furthermore, a method for stability analysis of switched systemsis proposed, extending the class of switched systems analyzed by the currentliterature. Numerical examples illustrate all the approaches developed.At the end, the application of the nonlinear control techniques to photovoltaicgeneration systems is presented. The main objectives considered are thetracking of the maximum power generation, with robustness to variations ofthe input parameters of the photovoltaic array, and the delivery of only activepower to the grid. Finally, simulation results demonstrate the applicabilityof the methodology for the control of this type of system, evidencing thecompliance of the stated objectives.Resumo expandido : Durante a última década, a tecnologia de sistemas fotovoltaicos tem mostrado potencial para se tornar uma das principais fontes de energia para o mundo, com crescimento contínuo e robusto, mesmo em tempos de crise econômica e financeira. Visando ampliar o aproveitamento da energia gerada e até mesmo reduzir os custos do sistema, o projeto de técnicas de controle eficientes apresenta grande importância para este tipo de sistema. Em sistemas fotovoltaicos o controle é realizado através de conversores de potência, que são sistemas chaveados. Por este motivo, o foco principal deste trabalho é a apresentação de estratégias de controle e análise de estabilidade para sistemas chaveados com uma proposta de aplicação para sistemas de geração de energia fotovoltaica. As condições de projeto e análise são todas baseadas em desigualdades matriciais lineares (LMIs). Inicialmente, uma descrição geral dos sistemas fotovoltaicos é apresentada, contendo a modelagem de um arranjo fotovoltaico, algumas topologias comuns de conexão, os principais objetivos, técnicas para a maximização da potência gerada, dentre outras informações necessárias para o projeto da técnica de controle proposta para este sistema. Na sequência é mostrada uma técnica de projeto de estratégias de chaveamento, cujo objetivo principal é garantir estabilidade e desempenho de sistemas comutados. A metodologia usada é baseada na teoria de estabilidade de Lyapunov, de modo a descrever condições suficientes para o projeto da lei de chaveamento em forma de LMIs e resolvê-las usando pacotes computacionais existentes. O método se aplica à classe de sistemas chaveados onde cada subsistema tem um campo vetorial afim e considera-se uma lei de chaveamento baseada no máximo entre funções auxiliares. A estabilidade do sistema em malha fechada é garantida mesmo se modos deslizantes ocorram em qualquer superfície de chaveamento resultante do projeto. Os resultados são apresentados para os casos de realimentação completa e realimentação parcial dos estados do sistema. Em seguida, uma das principais contribuições da tese, a proposta de uma extensão da lei de chaveamento para uma classe de sistemas chaveados não lineares é apresentada. O sistema pode conter não linearidades dependentes do estado limitadas em setor, como é o caso da não linearidade existente no modelo de painéis fotovoltaicos. As funções não lineares podem conter também parâmetros incertos, contanto que a função permaneça dentro dos limites do setor dado para toda a faixa de valores de interesse do parâmetro. Além disso, condições de projeto de leis de chaveamento independentes do equilíbrio são fornecidas e, portanto, neste caso a técnica se torna robusta a mudanças no ponto de operação desejado. Por fim, considerações sobre limitar a frequência de chaveamento são discutidas. A aplicação das técnicas descritas anteriormente para topologias comuns de conexão de sistemas fotovoltaicos é apresentada em seguida. Alguns dos desafios superados são a presença de referências variáveis, não linearidades limitadas em setor e medição parcial de estados no mesmo sistema. A aplicabilidade da metodologia para controlar o sistema fotovoltaico é ilustrada através de simulações baseadas em um exemplo numérico usando parâmetros de um sistema real. Como resultado requisitos importantes são satisfeitos, como o rastreamento do ponto de máxima potência e robustez com relação aos parâmetros incertos do painel fotovoltaico. Para a obtenção da robustez foram derivadas equações para determinar um setor que contem a não linearidade para quaisquer valores dos parâmetros. As dificuldades e perspectivas para o caso mais complexo (conexão com a rede elétrica) também são apresentadas. Motivado pela falta de técnicas de análise de estabilidade de sistemas seccionalmente afins contendo modos deslizantes na literatura atual, condições LMI suficientes para resolver este problema são propostas, resultando em outra importante contribuição da tese. As condições são baseadas em uma função de Lyapunov composta pela combinação convexa de funções quadráticas diferentes para cada região do sistema. As condições propostas incluem o importante caso onde o ponto de equilíbrio está localizado na fronteira entre subsistemas afim. Adicionalmente, condições suficientes para análise independentemente da parametrização das superfícies de chaveamento são derivadas, isto é, a superfície de chaveamento pode ser desconhecida neste caso. A nova técnica leva a uma metodologia unificada para a análise de estabilidade de sistemas seccionalmente afins e de sistemas chaveados afins com uma superfície de chaveamento previamente projetada. Esta tese é organizada em sete capítulos, quatro apêndices e referências. O Capítulo 1 tem o objetivo de contextualizar e motivar de forma breve o assunto da tese. O conhecimento básico sobre sistemas fotovoltaicos necessário para a aplicação proposta no documento é concentrado no Capítulo 2. O Capítulo 3 apresenta uma técnica de projeto de uma lei de chaveamento para o controle de sistemas chaveados com campos vetoriais afim. Esta técnica serve de base para as principais contribuições teóricas desta tese, apresentadas nos Capítulos 4, 5 e 6. No Capítulo 4, é apresentado o projeto de leis de chaveamento para sistemas chaveados contendo não linearidades limitadas em um setor, enquanto o Capítulo 5 apresenta a aplicação desta técnica para o controle de sistemas fotovoltaicos. No Capítulo 6, um método para análise de estabilidade de sistemas seccionalmente afins é introduzida. Exemplos numéricos são utilizados para ilustrar todas as contribuições da tese em seus respectivos capítulos. Algumas conclusões são discutidas no Capítulo 7, incluindo uma lista de sugestões para trabalhos futuros. Por fim, três apêndices demonstram o equacionamento de ferramentas de circuitos elétricos trifásicos utilizadas na tese e um apêndice apresenta resumos das publicações geradas pelo autor durante o período de doutorado

    Stability analysis and control of DC-DC converters using nonlinear methodologies

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    PhD ThesisSwitched mode DC-DC converters exhibit a variety of complex behaviours in power electronics systems, such as sudden changes in operating region, bifurcation and chaotic operation. These unexpected random-like behaviours lead the converter to function outside of the normal periodic operation, increasing the potential to generate electromagnetic interference degrading conversion efficiency and in the worst-case scenario a loss of control leading to catastrophic failure. The rapidly growing market for switched mode power DC-DC converters demands more functionality at lower cost. In order to achieve this, DC-DC converters must operate reliably at all load conditions including boundary conditions. Over the last decade researchers have focused on these boundary conditions as well as nonlinear phenomena in power switching converters, leading to different theoretical and analytical approaches. However, the most interesting results are based on abstract mathematical forms, which cannot be directly applied to the design of practical systems for industrial applications. In this thesis, an analytic methodology for DC-DC converters is used to fully determine the inherent nonlinear dynamics. System stability can be indicated by the derived Monodromy matrix which includes comprehensive information concerning converter parameters and the control loop. This methodology can be applied in further stability analysis, such as of the influence of parasitic parameters or the effect of constant power load, and can furthermore be extended to interleaved operating converters to study the interaction effect of switching operations. From this analysis, advanced control algorithms are also developed to guarantee the satisfactory performance of the converter, avoiding nonlinear behaviours such as fast- and slowscale bifurcations. The numerical and analytical results validate the theoretical analysis, and experimental results with an interleaved boost converter verify the effectiveness of the proposed approach.Engineering and Physical Sciences Research Council (EPSRC), China Scholarship Council (CSC), and school of Electrical and Electronic Engineerin

    H∞ Suboptimal Tracking Control for Bilinear Power Converter Systems with Dynamic Feedback - Theory and Experiment

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    In this thesis, bilinear power converters are considered that arise for state-averaged models in continuous conduction mode. Since such power converters are often not feedback linearizable with respect to the output to be controlled,they are an interesting and demanding class of control systems. One control objective for the considered system class is to include trajectory tracking in the system equations. With a state and input transformation into the so called error system representation, where the error between real variables and reference variables is considered, the error system equations show to be time-varying. Another objective is to cope with disturbances, noise, parameter uncertainties, etc. Therefore, integral feedback is included in the feedback strategy, which leads to input-affine systems with a special structure due to the originally bilinear system equations. A slightly different strategy is a disturbance feedback approach. It addresses the same control objectives, is structurally similar to integral feedback and allows for more freedom in choice of feedback design parameters. However, it is less general and requires online-replanning of the reference trajectory. For state feedback design, we choose H∞ control with a quadratic performance functional since we want to have low control effort and want to keep the error of the output to be controlled small in case of appearing disturbances. Finally, so as to address stability properties in the closed-loop, integral Input-to-State Stability (iISS) theory is a good choice to cope with nonzero disturbances. In order to guarantee stability for the closed-loop system in the presence of disturbances, we link the solution of the nonlinear H control problem with iISS. It is possible to derive conditions, when the suboptimal state feedback H∞ control problem for the bilinear power converter systems with integral feedback / disturbance feedback and trajectory tracking can be solved. At the same time, it can be shown that the closed-loop systems is iISS. To underline the generality of the approach, the obtained theory for bilinear power converter systems is extended to general bilinear systems and it is even possible to discuss the more demanding multiple-input case. Equipped with the required theory to solve the posed control problem, we address the experimental setup of a boost converter / DC motor system. Here, the control task is to track the angular velocity of the motor shaft and attenuate appearing load disturbances. Therefore, we implement disturbance feedback and proof boundedness of trajectories for the online-replanning of the approximate trajectory generation method. Various experiments are presented in order to investigate the applicability of the approach.In der vorliegenden Dissertation werden bilineare Leistungskonvertersysteme untersucht, wie sie für Modellgleichungen mit gemittelten Zuständen im kontinuierlichen Betrieb (engl. "continuous conduction mode")auftreten. Da eine große Zahl dieser Leistungskonverter nicht eingangs-zustandslinearisierbar hinsichtlich des Regelausgangs und dann oft sogar nicht-minimalphasig sind, zählen sie zur Klasse der schwierig zu regelnden Systeme. Ein Regelungsziel für die betrachtete Systemklasse ist die Berücksichtigung von Referenztrajektorien für einen Wunschausgang des Systemmodells. Dazu wird ein sogenanntes Fehlersystem eingeführt, das die Differenz zwischen tatsächlichen Größen und Referenzgrößen widerspiegelt. Aufgrund der Bilinearität der ursprünglichen Modellgleichung ist dieses Fehlersystem dann zeitvariant. Ein weiteres Ziel ist das Ausregeln von auftretenden Störungen, Messrauschen, Modellunsicherheiten, usw., was üblicherweise anhand eines Integratoranteils (kurz: I-Anteils) im Regelgesetz berücksichtigt wird. Ein I-Anteil ist eine dynamische Erweiterung der Zustandsgleichungen und führt zu einem zusätzlichen Zustand. Damit die zusätzliche Differentialgleichung nicht entkoppelt vorliegt, muss mit einer geeigneten Eingangstransformation dafür gesorgt werden, dass der Integriererzustand im Regelgesetz vorkommt. Dadurch wird jedoch die ursprüngliche Bilinearität der Gleichungen zerstört, so dass am Ende ein eingangsaffines System vorliegt, das aber natürlich aufgrund der Bilinearität der ursprünglichen Systemgleichungen eine spezifische Struktur aufweist. Eine ähnliche Herangehensweise wie beim I-Anteil ermöglicht die Schätzung und Rückführung der Störung, womit dieselben Regelungsziele verfolgt werden wie bei der Variante mit dem I-Anteil. Hier führt die dynamische Erweiterung mit dem Schätzer im Gegensatz zum I-Anteil allerdings wieder auf eine bilineare Systemgleichung. Allerdings ist dieser Ansatz weniger allgemein und erfordert eine Neuplanung der Referenztrajektorien in Echtzeit, birgt aber mehr Freiheiten in der Wahl der Reglerparameter für den geschlossenen Regelkreis. Als Rückführstrategie wird eine H∞-Zustandsregelung gewählt, um auftretenden Störungen mit möglichst minimalem Stellaufwand auszuregeln. Außerdem soll gleichzeitig der Fehler des Regelausgangs klein gehalten werden. Um schließlich die Stabilität des geschlossenen Regelkreises für nichtverschwindende Störungen untersuchen zu können, wird die sogenannten integral Input-to-State Stability (iISS) verwendet. Als Ergebnis der Arbeit können Bedingungen formuliert werden, wann eine suboptimale H∞-Zustandsregelung gefunden werden kann. Unter Annahme dieser Bedingungen folgt dann sofort die iISS-Eigenschaft des geschlossenen Regelkreises. Die Allgemeinheit des Verfahrens zeigt sich dadurch, dass es sogar möglich ist, den vorgestellten Ansatz auf allgemeine bilineare Systeme mit mehreren Eingängen zu erweitern. Das experimentelle Beispiel eines Hochsetzstellers in Kombination mit einem Gleichstrommotor wird dann zum Testen des Regelentwurfsverfahrens herangezogen. Dabei ist die Regelungsaufgabe, die Winkelgeschwindigkeit der Motorwelle einer vorgegeben Referenztrajektorie nachfahren zu lassen und auftretende Laststörungenauszuregeln. Dazu wurde die Variante der dynamischen Erweiterung anhand der Rückführung der Störung mit Trajektorienneuplanung verwendet. Mit einer suboptimalen H∞-Zustandsregelung wird der Regelkreis geschlossen, so dass iISS gewährleistet werden kann. Für die Echtzeitgenerierung der durch ein Approximationsverfahren ermöglichten Trajektorienneuplanung wird außerdem Beschränktheit gezeigt. Eine Vielzahl von Experimenten dient der genaueren Untersuchung des Verfahrens

    Comparison of LMI Solvers for Robust Control of a DC-DC Boost Converter

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    This work deals with a robust Fault-Tolerant Control (FTC) design for a class of uncertain systems. Fault resilience is associated with a robustness bound generated by a sufficient Linear Matrix Inequality (LMI) condition for static state feedback stabilization. This design control approach is based on solving an optimization problem expressed in terms of LMI with three different programming solvers which are mincx (Matlab), lmisolver (Scilab) and cvxopt (Python). Numerical validations were carried out, first on an academic model, then on the model of a PV energy conversion system connected to a DC-DC boost converter. Then, a robustness analysis for fault resilience associated with a control law gains, obtained using the three solvers, was realized to investigate the best performance. This approach was finally validated on an experimental test bench

    Aspects of Bifurcation Theory for Piecewise-Smooth, Continuous Systems

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    Systems that are not smooth can undergo bifurcations that are forbidden in smooth systems. We review some of the phenomena that can occur for piecewise-smooth, continuous maps and flows when a fixed point or an equilibrium collides with a surface on which the system is not smooth. Much of our understanding of these cases relies on a reduction to piecewise linearity near the border-collision. We also review a number of codimension-two bifurcations in which nonlinearity is important.Comment: pdfLaTeX, 9 figure

    Contributions to Control of Electronic Power Converters

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    This thesis deals with the control of electronic power converters. In its development two main parts have been differentiated. On the one hand, the problem of the voltage balance in the capacitors of the dc-link in a three-level NPC converter is addressed. On the other hand, given that the techniques used in the first part to model the converters need to make certain assumptions and, with the intention of avoiding averaged models, in the second part, switched affine models have been developed to design the control of the output voltage in DC-DC boost type converters. In this way, in the first part several control laws have been developed using an averaged model formulated by duty cycles for each level in each phase. This formulation allows to consider, in the controllers design stage, the degree of freedom associated with the homopolar voltage injection. Therefore, the controllers are designed as well as a part of the modulation, so that control and modulation are integrated in the same stage. In this way, three controllers have been designed where, apart from the objective of the voltage balance of the capacitors, other objectives such as the number of commutations or the quality of the output signal have also been improved. In the second part of the thesis, four methods have been developed for the design of control laws taking advantage of the modeling of converters as switched affine systems given their hybrid behaviour. Thus, the first two laws take advantage of this modeling using the delta operator to avoid numerical problems when using systems where the sampling time is very low. The first of these controllers is based on Lyapunov’s function while the second is independent of this function, thus obtaining less conservative results. The other two laws developed for switched affine systems use an alternative model to that performed in the first two controllers, so certain existing disadvantages are avoided using again a design not based on Lyapunov’s function. Thus, the first law presents a basic control but, even so, improves the results of other existing laws in the literature. Finally, a design method to deal with systems with variations in their parameters has been presented.La presente tesis trata sobre el control de convertidores electrónicos de potencia. En su desarrollo se han diferenciado dos partes principales. Por un lado, se trata el problema del balance de tensiones en los condensadores que forman el dc-link en un convertidor NPC de tres niveles. Por otro lado, dado que las técnicas utilizadas en la primera parte para modelar los convertidores necesitan realizar determinadas suposiciones y, con la intención de evitar modelos promediados, en la segunda parte se han desarrollado modelos afines conmutados para diseñar el control de la tensión de salida en convertidores DC-DC tipo boost. De esta forma, en la primera parte se han desarrollado varias leyes de control utilizando un modelo promediado formulado mediante ciclos de trabajo para cada nivel en cada fase. Esta formulación permite considerar en la fase de diseño de los controladores, un grado de libertad asociado a la inyección de tensión homopolar. Por lo tanto, se diseñan los controladores a la vez que una parte de la modulación, de forma que se integra control y modulación en una misma fase. De esta forma, se han diseñado tres controladores donde, a parte del objetivo de balancear la tensión de los condensadores, se ha ido buscando mejorar también otros objetivos como el número de conmutaciones o la calidad de la señal de salida. En la segunda parte de la tesis, se han desarrollado cuatro leyes de control aprovechando el modelado de convertidores como sistemas afines conmutados dada su naturaleza híbrida. De esta forma, las dos primeras leyes, aprovechan dicho modelado usando el operador delta para evitar problemas numéricos al utilizar sistemas donde el tiempo de muestreo es muy bajo. El primero de dichos controladores está basado en la función de Lyapunov mientras que el segundo es independiente de dicha función obteniendo así resultados menos conservadores. Las otras dos leyes desarrolladas para sistemas afines conmutados utilizan un modelado alternativo al realizado en las dos primeras, de forma que se evitan ciertas desventajas existentes y mantienen un diseño no basado en la función de Lyapunov. Así, la primera ley presenta un control más básico pero que, aun así, mejora los resultados de otras leyes existentes en la literatura. Por último, se ha presentado un procedimiento de diseño que hace frente a sistemas con variaciones en sus parámetros
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