Stability analysis of networked dynamical systems has been of interest in many disciplines such as biology and physics and chemistry with applications such as LASER cooling and plasma stability. These large networks are often modeled to have a completely random (Erdös-Rényi) or semi-random (Small-World) topologies. The former model is often used due to mathematical tractability while the latter has been shown to be a better model for most real life networks. The recent emergence of cyber physical systems, and in particular the smart grid, has given rise to a number of engineering questions regarding the control and optimization of such networks. Some of the these questions are: How can the stability of a random network be characterized in probabilistic terms? Can the effects of network topology and system dynamics be separated? What does it take to control a large random network? Can decentralized (pinning) control be effective? If not, how large does the control network needs to be? How can decentralized or distributed controllers be designed? How the size of control network would scale with the size of networked system? Motivated by these questions, we began by studying the probability of stability of synchronization in random networks of oscillators. We developed a stability condition separating the effects of topology and node dynamics and evaluated bounds on the probability of stability for both Erdös-Rényi (ER) and Small-World (SW) network topology models. We then turned our attention to the more realistic scenario where the dynamics of the nodes and couplings are mismatched. Utilizing the concept of ε-synchronization, we have studied the probability of synchronization and showed that the synchronization error, ε, can be arbitrarily reduced using linear controllers. We have also considered the decentralized approach of pinning control to ensure stability in such complex networks. In the pinning method, decentralized controllers are used to control a fraction of the nodes in the network. This is different from traditional decentralized approaches where all the nodes have their own controllers. While the problem of selecting the minimum number of pinning nodes is known to be NP-hard and grows exponentially with the number of nodes in the network we have devised a suboptimal algorithm to select the pinning nodes which converges linearly with network size. We have also analyzed the effectiveness of the pinning approach for the synchronization of oscillators in the networks with fast switching, where the network links disconnect and reconnect quickly relative to the node dynamics. To address the scaling problem in the design of distributed control networks, we have employed a random control network to stabilize a random plant network. Our results show that for an ER plant network, the control network needs to grow linearly with the size of the plant network.

Applications of distributed-power systems are on the rise. They are already used in telecommunication power supplies, aircraft and shipboard power-distribution systems, motor drives, plasma applications, and they are being considered for numerous other applications. The successful operation of these multi-converter systems relies heavily on a stable design. Conventional analyses of power converters are based on averaged models, which ignore the fast-scale instability and analyze the stability on a reduced-order manifold. As such, validity of the averaged models varies with the switching frequency even for the same topological structure. The prevalent procedure for analyzing the stability of switching converters is based on linearized smooth averaged (small-signal) models. Yet there are systems (in active use) that yield a non-smooth averaged model. Even for systems for which smooth averaged models are realizable, small-signal analyses of the nominal solution/orbit do not provide anything about three important characteristics: region of attraction of the nominal solution, dependence of the converter dynamics on the initial conditions of the states, and the post-instability dynamics. As such, converters designed based on small-signal analyses may be conservative. In addition, linear controllers based on such analysis may not be robust and optimal. Clearly, there is a need to analyze the stability of power converters from a different perspective and design nonlinear controllers for such hybrid systems. In this Dissertation, using bifurcation analysis and Lyapunov's method, we analyze the stability and dynamics of some of the building blocks of distributed-power systems, namely standalone, integrated, and parallel converters. Using analytical and experimental results, we show some of the differences between the conventional and new approaches for stability analyses of switching converters and demonstrate the shortcomings of some of the existing results. Furthermore, using nonlinear analyses we attempt to answer three fundamental questions: when does an instability occur, what is the mechanism of the instability, and what happens after the instability? Subsequently, we develop nonlinear controllers to stabilize parallel dc-dc and parallel multi-phase converters. The proposed controllers for parallel dc-dc converters combine the concepts of multiple-sliding-surface and integral-variable-structure control. They are easy to design, robust, and have good transient and steady-state performances. Furthermore, they achieve a constant switching frequency within the boundary layer and hence can be operated in interleaving or synchronicity modes. The controllers developed for parallel multi-phase converters retain many of the above features. In addition, they do not require any communication between the modules; as such, they have high redundancy. One of these control schemes combines space-vector modulation and variable-structure control. It achieves constant switching frequency within the boundary layer and a good compromise between the transient and steady-state performances. / Ph. D.

These days, a wide range of autonomous systems, such as automobiles, delivery drones, and embedded household systems, are becoming more and more common in our society. This trend is projected to continue in the future. To effectively manage these dynamic systems, ensuring their safe operation is crucial for the well-being of our lives. Control of safety-critical systems has gained significant attention in recent years, particularly in the field of nonlinear control. While the mathematical tools for characterizing safety are well-established, there are still numerous challenges to be addressed when it comes to developing methodologies for synthesizing nonlinear control systems. This report investigates the similarity between the two control schemes, the prescribed performance control and control barrier function. Its purpose is to shed light on the development of control methodology in safetycritical systems. While both methods have been successfully constructed and developed recently, there is no existing report that clarifies their similarities. To gain a deeper understanding of the latest safety-critical control and investigate these similarities, this report aims to provide interesting insights and contribute to the further development of methodology. The key insight arises from the fact that the prescribed performance control can be considered a method based on barrier functions. Consequently, it can be regarded as a control barrier-based controller. In order to demonstrate the similarities and make a comparison between the two, a unified problem setting is presented. Once we have properly converted the problem, we can proceed with a comparison using numerical simulations. The results presented in this report demonstrate that the prescribed performance controller can be implemented using separate reciprocal CBF methods. Furthermore, it shows that the performance achieved is comparable to that of the CLF-CBF QP, which utilizes optimization techniques to ensure stability and safety requirements. These findings raise new questions regarding the relationship between these two approaches. Ultimately, the report delves into a deeper understanding of how model-free methods achieve superior performance compared to model-based methods that heavily rely on optimization. / Idag blir ett brett spektrum av autonoma system, som bilar, leveransdrönare och inbyggda hushållssystem, allt vanligare i vårt samhälle. Denna trend förväntas fortsätta i framtiden. För att effektivt hantera dessa dynamiska system är det avgörande att säkerställa att de fungerar på ett säkert sätt. Styrning av säkerhetskritiska system har fått stor uppmärksamhet under de senaste åren, särskilt inom området icke-linjär styrning. Även om de matematiska verktygen för att karakterisera säkerhet är väletablerade, finns det fortfarande många utmaningar att ta itu med när det gäller att utveckla metoder för att syntetisera olinjära styrsystem. Denna rapport undersöker likheten mellan de två kontrollsystemen, den föreskrivna prestandakontrollen och kontrollbarriärfunktionen. Syftet är att belysa utvecklingen av styrmetodik i säkerhetskritiska system. Även om båda metoderna har konstruerats och utvecklats framgångsrikt på senare tid, finns det ingen befintlig rapport som klargör deras likheter. För att få en djupare förståelse för den senaste säkerhetskritiska kontrollen och undersöka dessa likheter, syftar denna rapport till att ge intressanta insikter och bidra till den fortsatta utvecklingen av metodiken. Den viktigaste insikten härrör från det faktum att den föreskrivna prestandakontrollen kan betraktas som en metod baserad på barriärfunktioner. Följaktligen kan den betraktas som en styrbarriärbaserad styrenhet. För att visa på likheterna och göra en jämförelse mellan de två presenteras en enhetlig problemställning. När vi har omvandlat problemet på rätt sätt kan vi gå vidare med en jämförelse med hjälp av numeriska simuleringar. De resultat som presenteras i denna rapport visar att den föreskrivna prestandaregulatorn kan implementeras med separata reciproka CBF-metoder. Dessutom visar de att den uppnådda prestandan är jämförbar med den för CLFCBF QP, som använder optimeringstekniker för att säkerställa stabilitets- och säkerhetskrav. Dessa resultat väcker nya frågor om förhållandet mellan dessa två metoder. I slutändan ger rapporten en djupare förståelse för hur modellfria metoder uppnår överlägsen prestanda jämfört med modellbaserade metoder som i hög grad förlitar sig på optimering.

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[EN] This thesis deals with two characteristic problems in visual feedback robot control: 1) sensor latency; 2) providing suitable trajectories for the robot and for the measurement in the image. All the approaches presented in this work are analyzed and implemented on a 6 DOF industrial robot manipulator or/and a wheeled robot. Focusing on the sensor latency problem, this thesis proposes the use of dual-rate high order holds within the control loop of robots. In this sense, the main contributions are: - Dual-rate high order holds based on primitive functions for robot control (Chapter 3): analysis of the system performance with and without the use of this multi-rate technique from non-conventional control. In addition, as consequence of the use of dual-rate holds, this work obtains and validates multi-rate controllers, especially dual-rate PIDs. - Asynchronous dual-rate high order holds based on primitive functions with time delay compensation (Chapter 3): generalization of asynchronous dual-rate high order holds incorporating an input signal time delay compensation component, improving thus the inter-sampling estimations computed by the hold. It is provided an analysis of the properties of such dual-rate holds with time delay compensation, comparing them with estimations obtained by the equivalent dual-rate holds without this compensation, as well as their implementation and validation within the control loop of a 6 DOF industrial robot manipulator. - Multi-rate nonlinear high order holds (Chapter 4): generalization of the concept of dual-rate high order holds with nonlinear estimation models, which include information about the plant to be controlled, the controller(s) and sensor(s) used, obtained from machine learning techniques. Thus, in order to obtain such a nonlinear hold, it is described a methodology non dependent of the machine technique used, although validated using artificial neural networks. Finally, an analysis of the properties of these new holds is carried out, comparing them with their equivalents based on primitive functions, as well as their implementation and validation within the control loop of an industrial robot manipulator and a wheeled robot. With respect to the problem of providing suitable trajectories for the robot and for the measurement in the image, this thesis presents the novel reference features filtering control strategy and its generalization from a multi-rate point of view. The main contributions in this regard are: - Reference features filtering control strategy (Chapter 5): a new control strategy is proposed to enlarge significantly the solution task reachability of robot visual feedback control. The main idea is to use optimal trajectories proposed by a non-linear EKF predictor-smoother (ERTS), based on Rauch-Tung-Striebel (RTS) algorithm, as new feature references for an underlying visual feedback controller. In this work it is provided both the description of the implementation algorithm and its implementation and validation utilizing an industrial robot manipulator. - Dual-rate Reference features filtering control strategy (Chapter 5): a generalization of the reference features filtering approach from a multi-rate point of view, and a dual Kalman-smoother step based on the relation of the sensor and controller frequencies of the reference filtering control strategy is provided, reducing the computational cost of the former algorithm, as well as addressing the problem of the sensor latency. The implementation algorithms, as well as its analysis, are described. / [ES] La presente tesis propone soluciones para dos problemas característicos de los sistemas robóticos cuyo bucle de control se cierra únicamente empleando sensores de visión artificial: 1) la latencia del sensor; 2) la obtención de trayectorias factibles tanto para el robot así como para las medidas obtenidas en la imagen. Todos los métodos propuestos en este trabajo son analizados, validados e implementados utilizando brazo robot industrial de 6 grados de libertad y/o en un robot con ruedas. Atendiendo al problema de la latencia del sensor, esta tesis propone el uso de retenedores bi-frequencia de orden alto dentro de los lazos de control de robots. En este aspecto las principales contribuciones son: -Retenedores bi-frecuencia de orden alto basados en funciones primitivas dentro de lazos de control de robots (Capítulo 3): análisis del comportamiento del sistema con y sin el uso de esta técnica de control no convencional. Además, como consecuencia del empleo de los retenedores, obtención y validación de controladores multi-frequencia, concretamente de PIDs bi-frecuencia. -Retenedores bi-frecuencia asíncronos de orden alto basados en funciones primitivas con compensación de retardos (Capítulo 3): generalización de los retenedores bi-frecuencia asíncronos de orden alto incluyendo una componente de compensación del retardo en la señal de entrada, mejorando así las estimaciones inter-muestreo calculadas por el retenedor. Se proporciona un análisis de las propiedades de los retenedores con compensación del retardo, comparándolas con las obtenidas por sus predecesores sin compensación, así como su implementación y validación en un brazo robot de 6 grados de libertad. -Retenedores multi-frecuencia no lineales de orden alto (Capítulo 4): generalización del concepto de retenedor bi-frecuencia de orden alto con modelos de estimación no lineales, los cuales incluyen información tanto de la planta a controlar, como del controlador(es) y sensor(es) empleado(s), obtenida a partir de técnicas de aprendizaje. Así pues, para obtener dicho retenedor no lineal, se describe una metodología independiente de la herramienta de aprendizaje utilizada, aunque validada con el uso de redes neuronales artificiales. Finalmente se realiza un análisis de las propiedades de estos nuevos retenedores, comparándolos con sus predecesores basados en funciones primitivas, así como su implementación y validación en un brazo robot de 6 grados de libertad y en un robot móvil con ruedas. Por lo que respecta al problema de generación de trayectorias factibles para el robot y para la medida en la imagen, esta tesis propone la nueva estrategia de control basada en el filtrado de la referencia y su generalización desde el punto de vista multi-frecuencial. -Estrategia de control basada en el filtrado de la referencia (Capítulo 5): una nueva estrategia de control se propone para ampliar significativamente el espacio de soluciones de los sistemas robóticos realimentados con sensores de visión artificial. La principal idea es utilizar las trayectorias óptimas obtenidas por una trayectoria predicha por un filtro de Kalman seguido de un suavizado basado en el algoritmo Rauch-Tung-Striebel (RTS) como nuevas referencias para un controlador dado. En este trabajo se proporciona tanto la descripción del algoritmo como su implementación y validación empleando un brazo robótico industrial. -Estrategia de control bi-frecuencia basada en el filtrado de la referencia (Capítulo 5): generalización de la estrategia de control basada en filtrado de la referencia desde un punto de vista multi-frecuencial, con un filtro de Kalman multi-frecuencia y un Kalman-smoother dual basado en la relación existente entre las frecuencias del sensor y del controlador, reduciendo así el coste computacional del algoritmo y, al mismo tiempo, dando solución al problema de la latencia del sensor. La validación se realiza utilizando un barzo robot industria asi / [CA] La present tesis proposa solucions per a dos problemes característics dels sistemes robòtics el els que el bucle de control es tanca únicament utilitzant sensors de visió artificial: 1) la latència del sensor; 2) l'obtenció de trajectòries factibles tant per al robot com per les mesures en la imatge. Tots els mètodes proposats en aquest treball son analitzats, validats e implementats utilitzant un braç robot industrial de 6 graus de llibertat i/o un robot amb rodes. Atenent al problema de la latència del sensor, esta tesis proposa l'ús de retenidors bi-freqüència d'ordre alt a dins del llaços de control de robots. Al respecte, les principals contribucions son: - Retenidors bi-freqüència d'ordre alt basats en funcions primitives a dintre dels llaços de control de robots (Capítol 3): anàlisis del comportament del sistema amb i sense l'ús d'aquesta tècnica de control no convencional. A més a més, com a conseqüència de l'ús dels retenidors, obtenció i validació de controladors multi-freqüència, concretament de PIDs bi-freqüència. - Retenidors bi-freqüència asíncrons d'ordre alt basats en funcions primitives amb compensació de retards (Capítol 3): generalització dels retenidors bi-freqüència asíncrons d'ordre alt inclouen una component de compensació del retràs en la senyal d'entrada al retenidor, millorant així les estimacions inter-mostreig calculades per el retenidor. Es proporciona un anàlisis de les propietats dels retenidors amb compensació del retràs, comparant-les amb les obtingudes per el seus predecessors sense la compensació, així com la seua implementació i validació en un braç robot industrial de 6 graus de llibertat. - Retenidors multi-freqüència no-lineals d'ordre alt (Capítol 4): generalització del concepte de retenidor bi-freqüència d'ordre alt amb models d'estimació no lineals, incloent informació tant de la planta a controlar, com del controlador(s) i sensor(s) utilitzat(s), obtenint-la a partir de tècniques d'aprenentatge. Així doncs, per obtindre el retenidor no lineal, es descriu una metodologia independent de la ferramenta d'aprenentatge utilitzada, però validada amb l'ús de rets neuronals artificials. Finalment es realitza un anàlisis de les propietats d'aquestos nous retenidors, comparant-los amb els seus predecessors basats amb funcions primitives, així com la seua implementació i validació amb un braç robot de 6 graus de llibertat i amb un robot mòbil de rodes. Per el que respecta al problema de generació de trajectòries factibles per al robot i per la mesura en la imatge, aquesta tesis proposa la nova estratègia de control basada amb el filtrat de la referència i la seua generalització des de el punt de vista multi-freqüència. - Estratègia de control basada amb el filtrat de la referència (Capítol 5): una nova estratègia de control es proposada per ampliar significativament l'espai de solucions dels sistemes robòtics realimentats amb sensors de visió artificial. La principal idea es la d'utilitzar les trajectòries optimes obtingudes per una trajectòria predita per un filtre de Kalman seguit d'un suavitzat basat en l'algoritme Rauch-Tung-Striebel (RTS) com noves referències per a un control donat. En aquest treball es proporciona tant la descripció del algoritme així com la seua implementació i validació utilitzant un braç robòtic industrial de 6 graus de llibertat. - Estratègia de control bi-freqüència basada en el filtrat (Capítol 5): generalització de l'estratègia de control basada am filtrat de la referència des de un punt de vista multi freqüència, amb un filtre de Kalman multi freqüència i un Kalman-Smoother dual basat amb la relació existent entre les freqüències del sensor i del controlador, reduint així el cost computacional de l'algoritme i, al mateix temps, donant solució al problema de la latència del sensor. L'algoritme d'implementació d'aquesta tècnica, així com la seua validaci / Solanes Galbis, JE. (2015). MULTI-RATE VISUAL FEEDBACK ROBOT CONTROL [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/57951

Les observateurs et la régulation de sortie sont deux thèmes centraux de la théorie des système non linéaires. Bien que de nombreux chercheurs ont consacré leur attention à ces questions depuis plus de trente ans, il y a encore de nombreuses questions ouvertes. Dans la théorie des observateurs un rôle clé est joué par les observateurs à grand gain. Le but de la première partie de la thèse est d'etudier nouvelles techniques qui permettent de surmonter ou au moins d'atténuer les principaux problèmes qui caractérisent cette classe d'observateurs. Nous proposons une nouvelle classe d'observateurs à grand gain, appelé "low-power", qui permet de surmonter les problèmes numériques, d'éviter le phénomène de peaking et d'améliorer les propriétés de sensibilité aux bruit de mesure à haute fréquence. La deuxième partie de la thèse aborde du problème de la régulation de sortie, qui a été résolu pour les systèmes linéaires au cours des années 70, par Francis et Wonham qui ont énoncé le célèbre «principe de modèle interne". Des solutions constructives ont aussi été proposées dans le cadre non linéaire mais sous des hypothèses restrictives qui réduisent la classe des systèmes auxquels cette méthodologie peut être appliquée. Dans la thèse, nous nous concentrons sur le problème de la régulation de sortie en présence de perturbations périodiques, et nous proposons une nouvelle approche qui nous permet de considérer une classe plus large de systèmes non linéaires. La technique obtenué est robuste au sens défini par Francis et Wonham. / Observers and output regulation are two central topics in nonlinear control system theory. Although many researchers have devoted their attention to these issues for more than 30 years, there are still many open questions. In the observer theory a key role is played by the so called high-gain observers. The purpose of the first part of the thesis is to study novel techniques which allow to overcome or at least to mitigate some of the main drawbacks characterizing this class of observers. We propose a novel class of high-gain observers, denoted as ``low-power'', which allows to overcome numerical problems, to avoid the peaking phenomenon and to improve the sensitivity properties to high-frequency measurement noise. The second part of the thesis addresses the output regulation problem, solved for linear systems during the 70's by Francis and Wonham who coined the celebrated ``internal model principle''. Constructive solutions have also been proposed in the nonlinear framework but under restrictive assumptions that reduce the class of systems to which this methodology can be applied. In this thesis we focus on the output regulation problem in presence of periodic disturbances and we propose a novel approach which allows to consider a broader class of nonlinear systems. The resulting design is robust in the sense defined by Francis and Wonham.

Cette thèse a été consacrée à l'étude des réseaux multi-terminaux haute tension à courant continu (MTDC). Les principales contributions étaient dans le domaine du contrôle automatique non linéaire, appliquées aux systèmes électriques, électronique de puissance et les sources d'énergie renouvelables. Le travail de recherche a été lancé avec l'intention de combler certaines lacunes entre la théorie et la pratique, en particulier: 1) d'enquêter sur diverses approches de contrôle pour le but d'améliorer la performance des systèmes MTDC; 2) d'établir des connexions entre la conception du contrôle empiriques existantes et analyse théorique; 3) d'améliorer la compréhension du comportement multi-échelle de temps des systèmes MTDC caractérisés par la présence de transitoires lents et rapides en réponse aux perturbations externes. En conséquence, ce travail de thèse peut être mis en trois domaines, à savoir la conception non linéaire de commande de systèmes MTDC, analyse des comportements dynamiques de système MTDC et l'application de systèmes MTDC pour le contrôle de fréquence des systèmes de climatisation. / This dissertation was devoted to the study of multi-terminal high voltage direct current (MTDC) networks. The main contributions were in the field of nonlinear automatic control, applied to power systems, power electronics and renewable energy sources. The research work was started with the intention of filling some gaps between the theory and the practice, in particular: 1) to investigate various control approaches for the purpose of improving the performance of MTDC systems; 2) to establish connections between existing empirical control design and theoretical analysis; 3) to improve the understanding of the multi-time-scale behavior of MTDC systems characterized by the presence of slow and fast transients in response to external disturbances. As a consequence, this thesis work can be put into three areas, namely nonlinear control design of MTDC systems, analysis of MTDC system's dynamic behaviors and application of MTDC systems for frequency control of AC systems.

Nous nous intéressons aux méthodes de contrôle de vibrations de modèles réduits de structures à n degrés de liberté, sismiquement isolées au niveau de la base par des systèmes d'isolation mixte.Le mouvement provoqué par une sollicitation sismique horizontale a lieu dans le plan vertical.Nous avons construit un problème de contrôle semi-actif de systèmes incertains soumis à des perturbations inconnues, mais bornées. Dans le langage de l'automatique, il s'agit d'un problème d'atténuation de perturbations.Le résultat principal de cette thèse porte sur la construction d'une version modifiée des résultats de Leitmann et de ses collaborateurs sur la stabilisation de systèmes non linéaires incertains. Le théorème proposé repose sur une loi de commande par retour d'état qui assure en boucle fermée les propriétés de "uniform boundedness" et "uniform ultimate boundedness".En particulier, il peut être appliqué à la résolution de problèmes de contrôle semi-actif, qui sont actuellement traités en génie parasismique.L'objectif du contrôle est d'améliorer le comportement (i.e. la réponse) de structures isolées pour faire face aux perturbations externes, c'est-à-dire les séismes. Plusieurs points différencient notre problème de la majorité que l'on trouve dans la littérature: (i) on ne s'intéresse pas seulement à la protection de la structure isolée, mais aussi aux équipements situés à l'intérieur de la structure, et (ii) au lieu d'utiliser des indicateurs de performance habituels exprimés en termes de déplacement relatif de la base versus des accélérations absolues des planchers, nous utilisons uniquement le spectre de plancher en pseudo-accélération, comme il a été proposé dans des travaux précédents par Politopoulos et Pham. Ce travail est une tentative d'utiliser explicitement les spectres de plancher comme critère de performance.Concernant la procédure d'application, plusieurs étapes intermédiaires ont été détaillées:(i) modélisation de signaux sismiques;(ii) réglage des paramètres de la loi de commande utilisant la théorie des vibrations;(iii) validation et test du comportement en boucle fermée à travers des simulations numériques: pour des raisons de simplicité, on se limite au cas n=2.Cette procédure peut être utilisée sur des structures en industrie nucléaire, mais aussi en génie civil.D'autres sujets traités incluent une tentative d'utiliser les outils temps-fréquence, et en particulier la distribution de Wigner-Ville, pour la synthèse de lois de commande, en espérant pouvoir mieux contrôler les composants transitoires des signaux de perturbation (les entrées) et des variables d'état (les sorties). / Vibration attenuation control designs are proposed for reduced plant models consisting of n-degree-of-freedom base seismically-isolated structures (i.e., a specific type of earthquake-resistant design), modeled by uncertain nonlinear systems and subjected to one-dimensional horizontal ground acceleration (i.e. the earthquake signal), treated as unknown disturbance but assumed to be bounded.In control systems literature, this is a perturbation attenuation problem.The main result of this PhD is the development of a modified version of Leitmann and co-authors' classical result on the stabilization of uncertain nonlinear systems. The proposed theorem consists of a bounded nonlinear feedback control law that is capable of ensuring uniform boundedness and uniform ultimate boundedness in closed-loop. In particular, it can be applied to solving semi-active control design problems, which are currently dealt with in earthquake engineering.The control objective is to improve the behavior (i.e. response) of mixed base-isolated structures to external disturbance, namely earthquakes. What differentiates our problem from the majority to be found in the literature is that: (i) attention is being paid to the protection of equipment placed inside the structure an not only to the structure itself; (ii) instead of using regular performance indicators expressed in terms of relative base displacement versus floors accelerations, we use solely the pseudo-acceleration floor response spectra, as it was proposed in previous recent works by Politopoulos and Pham.Actually, this work is an attempt to explicitly use floor response spectra as performance criterion.Concerning the application procedure, some of the topics that were detailed are:(i) modeling of earthquake signals;(ii) tuning of control law parameters based on vibration theory;(iii) validation and testing of the closed-loop behavior using numerical simulations: for simplicity reasons, we take n=2.This procedure can be used on structures of both nuclear industry as well as civil engineering.Other topics include an attempt to using time-frequency concepts and in particular the Wigner-Ville distribution to the control law design procedure, in order to better control transitory components of both perturbation (the input) and state variables signals (the output).

O dispositivo TCSC vem sendo utilizado com grande eficiência em sistemas elétricos de potência para melhoriada estabilidade transitóriaa e para fornecer amortecimento às oscilações eletromecânicas.Diversos trabalhos vêm sendo desenvolvidos como intuito desintetizar leis de controle para estes dispositivos. A maioria das técnicas empregadas para o projeto de controle em sistemas elétricos de potência utilizam modelos linearizados. Controladores projetados com técnicas lineares podem perder eficiência quando este ponto de operação varia de forma significativa. Controladores não lineares podem oferecer maior robustez a estas variações. Dentre várias técnicas de projeto de controle não linear, os métodos baseado sem funções de Lyapunov e/ou funções energia têm sido amplamente utilizados em sistemas elétricos de potência. Estas técnicas requerem a existência de uma função de Lyapunov e/ou função energia para o projeto, entretanto, mostrou-se que não existem funções de Lyapunov e/ou funções energia gerais para modelos de sistemas elétricos mais complexos que consideram, por exemplo, as perdas do sistema.Funções energia generalizadas (FEG) surgiram como uma alternativa para lidar com estas classes de modelos que apresentam comportamento complexo. Apresentamos neste trabalho uma função energia generalizada para modelos de sistemas elétricos de potência preservando a estruturada rede elétrica, comum modelo de terceira ordem para os geradores síncronos e considerando as perdas no sistema de transmissão. Com a FEG proposta, sintetizamos leis de controle não lineares para dispositivos TCSC, que independe da topologia da rede, utilizando sinais de realimentação locais e/ou remotos. As leis de controle projetadas melhoram significativamente a dinâmica do sistema e aumentam consideravelmente a região de estabilidade do sistema. / The TCSC device has been used with great efficiency in electric power systems to improve transient stability and to provide damping to electromechanical oscillations. Several studies have been developed in order to synthesize control laws for these devices. Most of the techniques used to design controller in electric power systems use linearized models. Controllers designed with linear techniques can lose efficiency when the operating point varies significantly. Nonlinear controllers can provide robustness to these variations. Among various techniques for non linear control design, the ones based on Lyapunov functions and/or energy function shave been widely used in electric power systems. These techniques require the existence of a Lyapunov function and/or energy function for the design, however, it was shown the non existence of Lyapunov function and/or general energy function for comprehensive electrical power system models, such as,system with losses. Generalized energy functions emerged as an alternative to deal with these classes of models that exhibit complex behavior. Herewer develop a generalized energy function to electrical power system models preserving the structure of the network, with a third-order model for synchronous generators and considering losses in the transmission system. With the proposed generalized energy function, nonlinear control laws are synthesized for TCSC devices, which are independent of the network topology, employ local and/or remote feedback signals. The designed control laws significantly improve the system dynamics and greatly increase stability regions of electrical power system.