CoordenaÃÃo de AperfeÃoamento de Pessoal de NÃvel Superior / This study aims to develop a planning system on multiple spatial and temporal scales, and apply it to the Brazilian electric sector and Cearà State, Jaguaribe Metropolitan System. For realization of this proposal, we have been considered some temporal scales: short-term (up to 1 month), short term (up to one year) and medium to long term (1-10 years and 10-30 years, respectively). To obtain estimates of the flow of short-term rainfall forecasts from atmospheric models for later entry in the hydrological rainfall-runoff model are used. To short term scale were considered stochastic and statistical models, as the Periodic Autoregressive type (PAR), Periodic Autoregressive with exogenous variables (PARx) and K-nearest neighbor models, and the use of global atmospheric models as input to hydrological rainfall-runoff model Soil Moisture Accounting Procedure (SMAP). For the range of the medium term were considered auto regressive models (AR) and Fourier and wavelets. We used data from the Coupled Model Intercomparison Project Phase 5 (CMIP5) as input in hydrological rainfall-runoff model for long-term scale. For the weather forecast, as the rain threshold adopted in the construction of the contingency table increases, the quality of the forecasts decreases, except for the adjustment index. Thus, the system of numerical prediction proves efficient in detecting the occurrence of rainfall of less intensity, with most satisfactory results in the North and Northeast regions of Brazil. On seasonal scale the models feature up better than the climatology. Likewise, in the range of medium-term models based on Fourier series and wavelets have better likelihood than the weather. In multi-scale, there are differences in the future shown by the projections of the CMIP5 models that were analyzed for RCP8.5 and RCP4.5 the XXI century scenarios, but in the North sector of the National Interconnected System (SIN), most models indicate negative trend, diverging only in magnitude. / O presente trabalho visa elaborar um sistema de planejamento em mÃltiplas escalas temporais e espaciais e aplicÃ-lo ao setor elÃtrico brasileiro e ao sistema Jaguaribe-Metropolitano do Estado do CearÃ. Para realizaÃÃo desta proposta, foram consideradas algumas escalas temporais: curtÃssimo prazo (atà um mÃs), curto prazo (atà um ano) e mÃdio e longo prazo (1 a 10 anos e atà 30 anos, respectivamente). Para obtenÃÃo das previsÃes de vazÃes de curtÃssimo prazo sÃo utilizadas as previsÃes de precipitaÃÃo a partir de modelos atmosfÃricos, para posterior entrada no modelo hidrolÃgico chuva-vazÃo. Para escala de curto prazo foram considerados modelos estocÃsticos e estatÃsticos, como do tipo PeriÃdico Autorregressivo (PAR), PeriÃdico Autorregressivo com variÃveis exÃgenas (PARx) e K-vizinhos, e o uso de modelos atmosfÃricos globais como entrada do modelo hidrolÃgico chuva-vazÃo Soil Moisture Accounting Procedure (SMAP). Na escala de mÃdio prazo foram considerados modelos autorregressivos (AR) e as transformadas de Fourier e ondeletas. Para escala de longo prazo foram utilizados dados provenientes do Coupled Model Intercomparison Project Phase 5 (CMIP5) como dados de entrada no modelo hidrolÃgico chuva-vazÃo. Quanto à previsÃo de tempo, à medida que o limiar de chuva adotado na construÃÃo da tabela de contingÃncia aumenta, a qualidade das previsÃes diminui, exceto para o Ãndice acerto. Dessa forma, o sistema de previsÃo numÃrica mostra-se eficiente em detectar a ocorrÃncia de chuvas de menor intensidade, apresentando resultados mais satisfatÃrios nas regiÃes Norte e Nordeste do Brasil. Na escala sazonal, os modelos apresentam-se melhor que a climatologia. Da mesma forma, na escala de mÃdio prazo, os modelos baseados na sÃrie de Fourier e ondeletas apresentam melhor verossimilhanÃa do que a climatologia. Na escala plurianual, hà divergÃncias quanto ao futuro mostrado pelas projeÃÃes dos modelos do CMIP5 que foram analisados para os cenÃrios RCP8.5 e RCP4.5 do sÃculo XXI, porÃm no setor Norte do Sistema Interligado Nacional (SIN), a maioria dos modelos sinaliza tendÃncia negativa, divergindo apenas em magnitude.

Using data from the frequency disturbance recorders (FDRs) that comprise the nation-wide frequency monitoring network known as FNET, disturbances in the eastern interconnected system (EI) have been monitored and recorded over the past several years. Analysis of this and other data by a wide variety of research scientists and engineers has rendered the idea that frequency disturbances from generator trips, transmission line trips, load trips, and other events, travel with finite speed as electromechanical waves throughout any power system (in this case the EI). Using FNET data as a tool, it is possible to measure and output the arrival times of these disturbance waves with a time resolution of 100 ms. To observe with certainty the arrival time of the frequency disturbance waves, field data collected by the FDRs must first be conditioned in a robust manner. The current method that uses the moving mean of raw FDR data is analyzed and two computationally efficient robust methods are suggested in this report. These new methods that rely on robust statistics are more resistant to the effect of outliers contained within the raw FDR data. Furthermore, like the moving mean, these methods smooth the raw data without removing the general trend. Having recorded and conditioned the FDR data, three conventional triangulation techniques taken from the field of seismology are proposed and analyzed. This study reconfirms the fact that the EI is not a medium of continuous elasticity though which the frequency perturbations travel but rather a discontinuous patchwork of varying elasticities. Within this report, nine generator trip events are analyzed and the aforementioned triangulation methods are applied. The advantages and disadvantages of each method are discussed. To conclude, axioms of future research are proposed and delineated. / Master of Science

Les travaux de cette thèse portent sur l’estimation et la commande décentralisée des systèmes de grande dimension. L’objectif est de développer des capteurs logiciels pouvant produire une estimation fiable des variables nécessaires pour la stabilisation des systèmes non linéaires interconnectés. Une décomposition d’un tel système de grande dimension en un ensemble de n sous-systèmes interconnectés est primordiale. Ensuite, en tenant compte de la nature du sous-système ainsi que les fonctions d’interconnexions, des lois de commande décentralisées basées observateurs ont été synthétisées. Chaque loi de commande est associée à un sous-système qui permet de le stabiliser localement, ainsi la stabilité du système global est assurée. L’existence d’un observateur et d’un contrôleur stabilisant le système dépend de la faisabilité d’un problème d’optimisation LMI. La formulation LMI, basée sur l’approche de Lyapunov, est élaborée par l’utilisation de principe de DMVT sur la fonction d’interconnexion non linéaire supposée bornée et incertaine. Ainsi des conditions de synthèse non restrictives sont obtenues. Des méthodes de synthèse de loi de commande décentralisée basée observateur ont été proposées pour les systèmes non linéaires interconnectés dans le cas continu et dans le cas discret. Des lois de commande robuste H1 décentralisées sont élaborées pour les systèmes non linéaires interconnectés en présence de perturbations et des incertitudes paramétriques. L’efficacité et la validation des approches présentées sont testées sur un modèle de réseaux électriques composé de trois générateurs interconnectés / This thesis focuses on the decentralized estimation and control for large scale systems. The objective is to develop software sensors that can produce a reliable estimate of the variables necessary for the interconnected nonlinear systems stability analysis. A decomposition of a such large system into a set of n interconnected subsystems is paramount for model simplification. Then, taking into account the nature of the subsystem as well as the interconnected functions, observer-based decentralized control laws have been synthesized. Each control law is associated with a subsystem which allows it to be locally stable, thus the stability of the overall system is ensured. The existence of an observer and a controller gain matrix stabilizing the system depends on the feasibility of an LMI optimization problem. The LMI formulation, based on Lyapunov approach, is elaborated by applying the DMVT technique on the nonlinear interconnection function, assumed to be bounded and uncertain. Thus, non-restrictive synthesis conditions are obtained. Observer-based decentralized control schemes have been proposed for nonlinear interconnected systems in the continuous and discrete time. Robust Hinfini decentralized controllers are provided for interconnected nonlinear systems in the presence of perturbations and parametric uncertainties. Effectiveness of the proposed schemes are verified through simulation results on a power systems with interconnected machines

As características singulares da energia elétrica quanto a sua forma de produção, transporte, consumo e sua importância ao desenvolvimento nacional levaram ao desenvolvimento de estruturas de gestão caracterizadas pela intervenção do estado. A busca por modelos de gestão aprimorados e eficientes conduziram o setor elétrico nacional a experimentar diversas transformações. O modelo atual é oriundo da transformação de uma estrutura verticalizada onde praticamente todos os segmentos do setor eram de propriedade pública. E ele é caracterizado por ramos de atividades independentes contemplando a produção, o transporte, a distribuição e a comercialização de energia elétrica. Nesse contexto, o sistema de transmissão tem papel de destaque, pois propicia a otimização das interligações entre as diversas fontes energéticas, permitindo o aproveitamento dos recursos de geração instalados ao longo do território nacional e o atendimento às demandas energéticas dos grandes centros consumidores. Nesse sistema a receita das transmissoras é disponibilizada mensalmente às concessionárias por meio de seus respectivos pagamentos base. Como forma de fiscalizar e incentivar a qualidade dos serviços a agência reguladora estabeleceu a aplicação de penalidades mediante resoluções normativas. O objetivo desse trabalho consiste em apresentar as penalizações impostas às transmissoras, com foco na aplicação da Parcela Variável. Para atender a esse objetivo será necessário navegar por outras áreas relacionadas com o sistema de transmissão, entre elas: as diretrizes envolvidas no planejamento da expansão do sistema, os trâmites para o acesso a rede, a formação da receita das transmissoras, bem como a apresentação de dados que ilustram a atual situação desse segmento. / The unique characteristics of electric energy as to its form of production, transportation, consumption and its importance to national development led to the development of management structures characterized by state intervention. The search for improved and efficient management models has led the national electricity sector to undergo several transformations. The current model comes from the transformation of a vertical structure where practically all the segments of the sector were public property. And it is characterized by branches of independent activities contemplating the production, transportation, distribution and commercialization of electric energy. In this context, the transmission system plays an important role, as it facilitates the optimization of the interconnections between the different energy sources, allowing the use of the generation resources installed throughout the national territory and the energy demands of the large consumer centers. In this system, the transmissions' revenue is made available monthly to the concessionaires through their respective base payments. As a way of monitoring and encouraging the quality of services, the regulatory agency established the application of penalties through normative resolutions. The objective of this work is to present the penalties imposed on the transmission system, focusing on the application of the Variable Parcel over their respective monthly payments. In order to meet this objective, it will be necessary to navigate to other areas related to the transmission system, among them: the guidelines involved in planning the expansion of the system, the procedures for accessing the network, the formation of the transmission systems' revenue, as well as the presentation of information that illustrates the current situation of this segment. / Dissertação (Mestrado)

A comercialização de energia elétrica no Brasil e no mundo sofreu diversas modificações nos últimos 20 anos. Com o objetivo de alcançar o equilíbrio econômico entre oferta e demanda do bem chamado eletricidade, os agentes deste mercado seguem as regras definidas pela sociedade (governo, empresas e consumidores) e também as leis da natureza (hidrologia). Para tratar de problemas tão complexos, estudos são realizados na área da heurística computacional. O objetivo deste trabalho é elaborar um software de previsão de preços do mercado spot utilizando redes neurais artificiais (RNA). As RNA são muito utilizadas em diversas aplicações, principalmente em heurística computacional, nas quais sistemas não lineares apresentam desafios computacionais difíceis de serem superados devido ao efeito da maldição da dimensionalidade. Tal maldição se deve pelo fato do poder computacional atual não ser suficiente para processar problemas com elevada combinação de variáveis. O problema de prever os preços do mercado spot depende de fatores como: (a) a previsão de demanda (carga); (b) a previsão da oferta (reservatórios, regime de chuvas e clima), fator de capacidade; e (c) o equilíbrio da economia (precificação, leilões, influência de mercados externos, política econômica, orçamento governamental, política governamental). Estes fatores são utilizados na construção do sistema de previsão e os resultados de sua eficácia são testados e apresentados. / The commercialization of electricity in Brazil as well as in the world has undergone several changes over the past 20 years. In order to achieve an economic balance between supply and demand of the good called electricity, stakeholders in this market follow both rules set by society (government, companies and consumers) and set by the laws of nature (hydrology). To deal with such complex issues, various studies have been conducted in the area of computational heuristics. This work aims to develop a software to forecast spot market prices in using artificial neural networks (ANN). ANNs are widely used in various applications especially in computational heuristics, where non-linear systems have computational challenges difficult to overcome because of the effect named curse of dimensionality. This effect is due to the fact that the current computational power is not enough to handle problems with such a high combination of variables. The challenge of forecasting prices depends on factors such as: (a) foresee the demand evolution (electric load); (b) the forecast of supply (reservoirs, hydrology and climate), capacity factor; and (c) the balance of the economy (pricing, auctions, foreign markets influence, economic policy, government budget and government policy). These factors are considered be used in the forecasting model for spot market prices and the results of its effectiveness are tested and huge presented.

A comercialização de energia elétrica no Brasil e no mundo sofreu diversas modificações nos últimos 20 anos. Com o objetivo de alcançar o equilíbrio econômico entre oferta e demanda do bem chamado eletricidade, os agentes deste mercado seguem as regras definidas pela sociedade (governo, empresas e consumidores) e também as leis da natureza (hidrologia). Para tratar de problemas tão complexos, estudos são realizados na área da heurística computacional. O objetivo deste trabalho é elaborar um software de previsão de preços do mercado spot utilizando redes neurais artificiais (RNA). As RNA são muito utilizadas em diversas aplicações, principalmente em heurística computacional, nas quais sistemas não lineares apresentam desafios computacionais difíceis de serem superados devido ao efeito da maldição da dimensionalidade. Tal maldição se deve pelo fato do poder computacional atual não ser suficiente para processar problemas com elevada combinação de variáveis. O problema de prever os preços do mercado spot depende de fatores como: (a) a previsão de demanda (carga); (b) a previsão da oferta (reservatórios, regime de chuvas e clima), fator de capacidade; e (c) o equilíbrio da economia (precificação, leilões, influência de mercados externos, política econômica, orçamento governamental, política governamental). Estes fatores são utilizados na construção do sistema de previsão e os resultados de sua eficácia são testados e apresentados. / The commercialization of electricity in Brazil as well as in the world has undergone several changes over the past 20 years. In order to achieve an economic balance between supply and demand of the good called electricity, stakeholders in this market follow both rules set by society (government, companies and consumers) and set by the laws of nature (hydrology). To deal with such complex issues, various studies have been conducted in the area of computational heuristics. This work aims to develop a software to forecast spot market prices in using artificial neural networks (ANN). ANNs are widely used in various applications especially in computational heuristics, where non-linear systems have computational challenges difficult to overcome because of the effect named curse of dimensionality. This effect is due to the fact that the current computational power is not enough to handle problems with such a high combination of variables. The challenge of forecasting prices depends on factors such as: (a) foresee the demand evolution (electric load); (b) the forecast of supply (reservoirs, hydrology and climate), capacity factor; and (c) the balance of the economy (pricing, auctions, foreign markets influence, economic policy, government budget and government policy). These factors are considered be used in the forecasting model for spot market prices and the results of its effectiveness are tested and huge presented.

Beaucoup de services vitaux de la vie quotidienne dépendent de systèmes d'ingénierie hautement complexes et interconnectés; Ces systèmes sont constitués d'un grand nombre de capteurs interconnectés, d'actionneurs et de composants du système. L'étude des systèmes interconnectés joue un rôle important dans l'étude de la fiabilité des systèmes dynamiques; car elle permet d'étudier les propriétés d'un système interconnecté en analysant ses sous-composants moins complexes. Le diagnostic des pannes est essentiel pour assurer des opérations sûres et fiables des systèmes de contrôle interconnectés. Dans toutes les situations, le système global et / ou chaque sous-système peuvent être analysés à différents niveaux pour déterminer la fiabilité du système global. Dans certains cas, il est important de déterminer les informations anormales des variables internes du sous-système local, car ce sont les causes qui contribuent au fonctionnement anormal du processus global. Cette thèse porte sur les défis de l'application de la théorie inverse du système et des techniques FDD basées sur des modèles pour traiter le problème articulaire du diagnostic des fautes et de l'analyse des causes racines (FD et RCA). Nous étudions ensuite le problème de l'inversibilité de la gauche, de l'observabilité et de la diagnosticabilité des fauts du système interconnecté, formant un algorithme FD et RCA multi-niveaux basé sur un modèle. Ce système de diagnostic permet aux composants individuels de surveiller la dynamique interne localement afin d'améliorer l'efficacité du système et de diagnostiquer des ressources de fautes potentielles pour localiser un dysfonctionnement lorsque les performances du système global se dégradent. Par conséquent, un moyen d'une combinaison d'intelligence locale avec une capacité de diagnostic plus avancée pour effectuer des fonctions FDD à différents niveaux du système est fourni. En conséquence, on peut s'attendre à une amélioration de la localisation des fauts et à de meilleurs moyens de maintenance prédictive. La nouvelle structure du système, ainsi que l'algorithme de diagnostic des fautes, met l'accent sur l'importance de la RCA de défaut des dispositifs de terrain, ainsi que sur l'influence de la dynamique interne locale sur la dynamique globale. Les contributions de cette thèse sont les suivantes: Tout d'abord, nous proposons une structure de système non linéaire interconnecté inversible qui garantit le fauts dans le sous-système de périphérique de terrain affecte la sortie mesurée du système global de manière unique et distincte. Une condition nécessaire et suffisante est développée pour assurer l'inversibilité du système interconnecté qui nécessite l'inversibilité de sous-systèmes individuels. Deuxièmement, un observateur interconnecté à deux niveaux est développé; Il se compose de deux estimateurs d'état, vise à fournir des estimations précises des états de chaque sous-système, ainsi que l'interconnexion inconnue. En outre, il fournira également une condition initiale pour le reconstructeur de données et le filtre de fauts local une fois que la procédure FD et RCA est déclenchée par tout fauts. D'une part, la mesure utilisée dans l'estimateur de l'ancien sous-système est supposée non accessible; La solution est de la remplacer par l'estimation fournie par l'estimateur de ce dernier sous-système. / Many of the vital services of everyday life depend on highly complex and interconnected engineering systems; these systems consist of large number of interconnected sensors, actuators and system components. The study of interconnected systems plays a significant role in the study of reliability theory of dynamic systems, as it allows one to investigate the properties of an interconnected system by analyzing its less complicated subcomponents. Fault diagnosis is crucial in achieving safe and reliable operations of interconnected control systems. In all situations, the global system and/or each subsystem can be analyzed at different levels in investigating the reliability of the overall system; where different levels mean from system level down to the subcomponent level. In some cases, it is important to determine the abnormal information of the internal variables of local subsystem, in order to isolate the causes that contribute to the anomalous operation of the overall process. For example, if a certain fault appears in an actuator, the origin of that malfunction can have different causes: zero deviation, leakage, clogging etc. These origins can be represented as root cause of an actuator fault. This thesis concerns with the challenges of applying system inverse theory and model based FDD techniques to handle the joint problem of fault diagnosis & root cause analysis (FD & RCA) locally and performance monitoring globally. By considering actuator as individual dynamic subsystem connected with process dynamic subsystem in cascade, we propose an interconnected nonlinear system structure. We then investigate the problem of left invertibility, fault observability and fault diagnosability of the interconnected system, forming a novel model based multilevel FD & RCA algorithm. This diagnostic algorithm enables individual component to monitor internal dynamics locally to improve plant efficiency and diagnose potential fault resources to locate malfunction when operation performance of global system degrades. Hence, a means of acombination of local intelligence with a more advanceddiagnostic capability (combining fault monitoring anddiagnosis at both local and global levels) to performFDDfunctions on different levels of the plantis provided. As a result, improved fault localization and better predictive maintenance aids can be expected. The new system structure, together with the fault diagnosis algorithm, is the first to emphasize the importance of fault RCA of field devices, as well as the influences of local internal dynamics on the global dynamics. The developed model based multi-level FD & RCA algorithm is then a first effort to combine the strength of the system level model based fault diagnosis with the component level model based fault diagnosis. The contributions of this thesis include the following: Firstly, we propose a left invertible interconnected nonlinear system structure which guarantees that fault occurred in field device subsystem will affect the measured output of the global system uniquely and distinguishably. A necessary and sufficient condition is developed to ensure invertibility of the interconnected system which requires invertibility of individual subsystems. Second, a two level interconnected observer is developed which consists of two state estimators, aims at providing accurately estimates of states of each subsystem, as well as the unknown interconnection. In addition, it will also provide initial condition for the input reconstructor and local fault filter once FD & RCA procedure is triggered by any fault. Two underlyingissues are worth to be highlighted: for one hand, the measurement used in the estimator of the former subsystem is assumed not accessible; the solution is to replace it by the estimate provided by the estimator of the latter subsystem. In fact, this unknown output is the unknown interconnection of the interconnected system, and also the input of the latter subsystem.

Cette recherche vise à résoudre un problème particulier du contrôle de vibration des structures intelligentes. Notre objectif est de réduire les vibrations dans une zone spécifique de la structure intelligente avec une perturbation qui couvre une large gamme de fréquences. De plus, dans cette zone spécifique, ni l'actionnement ni la détection ne sont possibles.Ici, nous faisons face à plusieurs défis principaux. Premièrement, nous devons contrôler les vibrations d’une zone spécifique de la structure, alors que nous n’avons accès aux mesures que dans d’autres zones. Deuxièmement, la large bande passante de la perturbation implique que nombreux modes doivent être contrôlés au même temps, ce qui nécessite l'utilisation de plusieurs actionneurs et capteurs. Cela conduit à un contrôleur MIMO difficile à obtenir avec les méthodes classiques de conception de contrôleur. Troisièmement, il faut éviter le problème de propagation, qui consiste à garantir la stabilité en boucle fermée lorsque le contrôleur basé sur un modèle est appliqué à la configuration réelle. Pour relever ces défis, nous étudions deux stratégies de contrôle: le contrôle centralisé et le contrôle distribué.Pour le contrôle centralisé, nous proposons une méthodologie qui nous permet d’obtenir un contrôleur MIMO simple permettant de relever ces défis. Tout d'abord, plusieurs techniques de modélisation et d’identification sont appliquées pour obtenir un modèle précis d'ordre faible de la structure intelligente. Ensuite, une méthode de synthèse basée sur le contrôle H_∞ avec un critère H_∞ particulièrement proposé est appliquée. Ce critère H_∞ intègre plusieurs objectifs de contrôle, y compris les défis principaux. En particulier, le problème de débordement se transforme en un problème de stabilité robuste et sera garanti en utilisant ce critère. Le contrôleur H_∞ obtenu est une solution standard du problème H_∞. Le contrôleur final est obtenu en simplifiant ce contrôleur H_∞ sans perdre la stabilité en boucle fermée ni dégrader les performances. Cette méthodologie est validée sur une structure de poutre avec des transducteurs piézoélectriques et la zone centrale est celle où les vibrations devraient être réduites. L'efficacité du contrôleur obtenu est validée par des simulations et des expériences.Pour le contrôle distribué, on considère la même structure de poutre et les mêmes objectifs de contrôle. Il existe des méthodes visant à concevoir des contrôleurs distribués pour les systèmes spatialement interconnectés. Cette recherche propose une méthode basée sur la FEM, associée à plusieurs techniques de réduction de modèle, permettant de discrétiser spatialement la structure de poutre et d'en déduire les modèles d’espace d'état des sous-systèmes interconnectés. La conception des contrôleurs distribués ne sera pas abordée dans cette recherche. / This research aims at solving a particular vibration control problem of smart structures. We aim at reducing the vibration in a specific zone of the smart structure under the disturbance that covers a wide frequency band. Moreover, at this specific zone, neither actuation nor sensing is possible.Here we face several main challenges. First, we need to control the vibration of a specific zone of the structure while we only have access to measurements at other zones. Second, the wide bandwidth of the disturbance implies that numerous modes should be controlled at the same time which requires the use of multiple actuators and sensors. This leads to a MIMO controller which is difficult to obtain using classical controller design methods. Third, the so-called spillover problem must be avoided which is to guarantee the closed-loop stability when the model-based controller is applied on the actual setup. To tackle these challenges, we investigate two control strategies: the centralized control and the distributed control.For centralized control, we propose a methodology that allows us to obtain a simple MIMO controller that accomplishes these challenges. First, several modeling and identification techniques are applied to obtain an accurate low-order model of the smart structure. Then, an H_∞ control based synthesis method with a particularly proposed H_∞ criterion is applied. This H_∞ criterion integrates multiple control objectives, including the main challenges. In particular, the spillover problem is transformed into a robust stability problem and will be guaranteed using this criterion. The obtained H_∞ controller is a standard solution of the H_∞ problem. The final controller is obtained by further simplifying this H_∞ controller without losing the closed-loop stability and degrading the performance. This methodology is validated on a beam structure with piezoelectric transducers and the central zone is where the vibration should be reduced. The effectiveness of the obtained controller is validated by simulations and experiments.For distributed control, we consider the same beam structure and the same control objectives. There exist methods aiming at designing distributed controllers of spatially interconnected system. This research proposes a FEM based method, combined with several model reduction techniques, that allows to spatially discretize the beam structure and deduce the state-space models of interconnected subsystems. The design of distributed controllers will not be tackled in this research.