abstract: Traditional approaches to modeling microgrids include the behavior of each inverter operating in a particular network configuration and at a particular operating point. Such models quickly become computationally intensive for large systems. Similarly, traditional approaches to control do not use advanced methodologies and suffer from poor performance and limited operating range. In this document a linear model is derived for an inverter connected to the Thevenin equivalent of a microgrid. This model is then compared to a nonlinear simulation model and analyzed using the open and closed loop systems in both the time and frequency domains. The modeling error is quantified with emphasis on its use for controller design purposes. Control design examples are given using a Glover McFarlane controller, gain sched- uled Glover McFarlane controller, and bumpless transfer controller which are compared to the standard droop control approach. These examples serve as a guide to illustrate the use of multi-variable modeling techniques in the context of robust controller design and show that gain scheduled MIMO control techniques can extend the operating range of a microgrid. A hardware implementation is used to compare constant gain droop controllers with Glover McFarlane controllers and shows a clear advantage of the Glover McFarlane approach. / Dissertation/Thesis / Ph.D. Electrical Engineering 2013

Estuda-se o problema de sintonia de controladores, objetivando-se a formulação do problema de sintonia ótima de controladores. Busca-se uma formulação que seja geral, ou seja, válida para qualquer estrutura de controlador e qualquer conjunto de especificações. São abordados dois temas principais: especificação de controladores e sintonia ótima de controladores. São compiladas as principais formas de especificação e avaliação de controladores e é feita a formulação do problema de sintonia de controladores como um problema padrão de otimização. A abordagem proposta e os conceitos apresentados são então aplicados em um conjunto de exemplos. / The problem of control tuning is studied, aiming the formulation of the optimal control tuning problem. A general formulation, valid for any controller structure and any set of specifications, is sought. Two main themes are addressed: controller specification and optimal controller tuning. The main ways of controller specification and assessment are compiled and the optimal controller tuning problem is formulated as a standard optimization problem. The proposed approach and the presented concepts are then applied in a set of examples.

Em metalurgia, a busca pela qualidade, baixo custo e alta produtividade têm feito empresas e institutos de pesquisa trabalharem juntos, procurando novas tecnologias que supram as necessidades do mercado. Dentre essas novas tecnologias, se destaca o processo de lingotamento contínuo de tiras de aço, utilizando o conceito de twin roll, cuja proposição inicial foi sugerida no século XIX por Henry Bessemer. Este trabalho apresenta a modelagem, análise e controle de um sistema de bobinamento de tiras de aço produzidas através de lingotamento contínuo do tipo twin roll , em uma planta localizada no Instituto de Pesquisas Tecnológicas de São Paulo. As características do processo foram primeiramente apresentadas. A modelagem matemática do sistema de bobinamento foi realizada, levando-se em consideração os componentes envolvidos no sistema. As variações paramétricas foram então evidenciadas. O sistema de controle foi primeiramente implementado utilizando-se um controlador do tipo PID, pelo fato desse tipo de controle ser altamente difundido industrialmente. Para maior precisão do sistema de controle, propôs-se a introdução de um sensor ultrasônico para medição das variações do raio de bobinamento. Por último realizou-se o projeto de um compensador robusto utilizando a metodologia LQG/LTR. Para a realização das simulações utilizou-se o programa Matlab/simulink. / In metallurgy, the quest for quality, low cost, and high productivity have resulted in companies and research institutes working together to find new technologies to satisfy the customer demand. Among these new technologies is the direct steel strip casting, using the twin roll concept suggested in the 19th century by Henry Bessemer. This work presents the modelling, analysis and control of a steel strip coiling system using twin roll direct casting, in a plant installed at the Technological Research Institute of Sao Paulo. The characteristics of the process are first introduced. The mathematic modelling of the coiling system used, take into account the system components. The parametric changes were adressed. The control system was first implemented using a PID controller as this kind of control is highly used in the industry. An ultrasonic sensor was introduced in the system to improve the control precision by coiling radius measurement. Last a robust compensator using the LQG/LTR method was designed. The simulations were done using Matlab/Simulink software.

Nesta dissertação é realizado um estudo comparativo entre controladores robustos projetados para sistemas lineares em espaço de estado sujeitos a incertezas paramétricas. O objetivo é resolver problemas de acompanhamento de trajetória de robôs. O estudo é realizado em um robô móvel com tração diferencial e em um quadricóptero. Para tal, é aplicado um Regulador Linear Quadrático Robusto no qual engloba em uma estrutura unificada todos os parâmetros de incerteza de entrada e saída de maneira recursiva, útil em aplicações em tempo real. A fim de demonstrar a eficiência do Regulador Robusto, resultados de simulações e de experimentos são empregados comparando-o com controle Η∞ não linear via teoria dos jogos e com um controle Proporcional-Derivativo mais torque calculado. / This work provides a comparative study between robust controllers for linear statespace systems subject to parametric uncertainties to solve trajectory tracking problems. The study is developed in a mobile robot with differential traction and in a quadricopter. A Robust Linear Quadratic Regulator is applied, which encompasses in a unified framework all input and output uncertain parameters, useful in online applications. In order to show the effectiveness of the robust regulator, simulations and experiments results allow the comparison with nonlinear Η∞ control via game theory and with a Proportional- Derivative control plus computed torque.

[pt] Esta tese teve como objetivo o estudo do problema de Desempenho H2 Robusto, com enfase para o caso de perturbações lineares não estruturadas nos fatores coprimos normalizados da função de transferência que representa uma determinada planta nominal. A primeira parte desta tese foi dedicada à determinação de um novo índice de Desempenho H2 Robusto pela utilização de limitantes superiores, levando em conta dois fatores: melhoria destes limitantes com relação aos limitantes propostos na literatura e viabilidade de sua implementação numérica. A parte seguinte da tese foi dedicada à determinação de elementos que influenciam no Desempenho H2 Robusto. Estes elementos serviram de base para a definição de problemas de controle multiobjetivos que, por sua vez, geraram uma classe de controladores sobre a qual foi otimizado o índice de Desempenho H2 Robusto proposto nesta tese. / [en] The objective of this thesis was the study of the Robust H2 Performance problem, with emphasis on the case of linear and unstructured perturbations on the normalized coprime factors of the transfer function that represents the nominal plant. The first was dedicated to the determination of a new Robust H2 Performance index, by the utilization of upper bounds, taking into accunt two factors: better upper bounds, with relation to upper bonds proposed in the literature, and numerical implementation viability. The second part was dedicated to the determination of elements that have influence in the Robust H2 Performance. These elements became a basis for the definition of multiobjetive control problems, that generate a class of controllers, over which the Robust H2 Performance index, proposed in the first part of this thesis, was optimizated.

[pt] Esta tese apresenta um estudo na área de controle robusto não paramétrico, mais precisamente relacionado ao Problema H2/Hinf. O Principal objetivo deste trabalho consiste no projeto de controladores por uma abordagem direta sobre o problema mencionado, baseada em método de Gallerkin. Dois métodos foram propostos, sendo denominados Expansão em Base Pré-Estabelecida (EBPE) e Expansão em Base Otimizada (EBO). Para a aplicação destes métodos, os controladores estabilizantes do sistema em estudo devem ser explicitados por intermédio da parametrização de Youla. Em seguida, uma nova parametrização é realizada a fim de colocar o problema resultante em um formato padrão, com a norma Hinf sob a forma do problema de Nehari. Um controlador calculado por EBO ou EBPE possui ordem previamente determinada, estabiliza internamente a planta, minimiza um funcional de desempenho e satisfaz a um nível pré- especificado de robustez em estabilidade. Em EBPE, uma base é escolhida para o espaço solução e o ajuste dos coeficientes de seus vetores é realizado minimizando o critério proposto. A vantagem deste método é resolver um problema de otimização convexo. Por outro lado, a escolha dos vetores que participarão da base truncada já estará definida, levando a uma solução com ordem superior àquela obtida por EBO e um mesmo nível de desempenho. No método EBO, as tarefas de escolha dos vetores que participarão da base e seus respectivos ajustes de coeficientes são realizados simultaneamente. Embora este problema seja não convexo, sua vantagem reside na possibilidade de encontrar soluções com ordens relativamente menores em comparação com aquelas por EBPE para um mesmo nível de desempenho. Adicionalmente, discute-se alguns resultados teóricos, onde a existência e a unicidade da solução do Problema H2/Hinf são demonstradas. Mostra-se também que a sequência de controladores calculados pelos métodos propostos, à medida que a ordem aumenta, converge para a solução ótima do problema original. / [en] This thesis presents a study on the subject of robust and non parametrical control, more precisely related to the Mixed H2/Hinf problem. The main purpose of this work consists in the controllers design by a direct approach over the mentioned problem, using Galerkin`s method. Two numerical methods were proposed, being known as Pre- Established Basis Expansion (EBPE) and Optimized Basis Expansion (EBO). For the application of these methods, the stabilizing controllers of the system under analisys must be explicated by Youla`s parametrization. After this, a new parametrization is performed in order to set the problem in a standard format, with the Hinf-norm in the Nehari problem. A controller computed by EBO or EBPE has a previously specified order, internally stabilizes the plant, minimizes a performance functional and satisfies a pre- established robustness stability margin. In the EBPE method, a basis is chosen from space solution and the adjustment of the vectors` coefficients is performed minimizing the proposed criterion. The advantage is solve a convex optimization problem. By the other side, the choice of vectors in the truncated basis will be defined, leading to a solution with a higher order than the one obtained by the EBO approach, for the same performance level In the EBO method, both the vectors` choice in the truncated basis and their respective coefficient adjustment are performed simultaneously. The Youla`s parameter is approximated by the class of real, rational, proper and stable transfer function and the project variables are the coefficients of the numerator and denominator polynomials. Although this problem is a non- convex one, its main advantage lies in the possibility of finding controllers of relatively lower orders than ones by EBPE at the same level of performance. In addition, some theoretical results are discussed, where the existence and uniqueness of Mixid H2/Hinf problem solution are proved. It is also shown that the sequence of controllers computed by the proposed methods, as order increase, converges to the solution of the original problem.

Le contexte général des travaux de recherche de cette thèse concerne les problématiques liées à l’optimisation glob-ale liée à la conception des futurs satellites d’observation terrestre et de missions scientifiques, nécessitantune très haute stabilité en pointage (capacité du satellite à garder son point de visée). Plus particulièrement,les travaux concernent le contrôle actif des modes micro-vibratoires.Dans une mission satellitaire d’observation terrestre, la qualité des images dépend bien évidemmentdes instruments de mesure optique (diamètre du miroir, aberrations optiques et qualité du polissage)mais également des performances de la stabilité de la ligne de visée du satellite qui peut s’avérer dégradéepour cause de micro-vibrations. La présence de ces micro-vibrations est liée aux divers éléments tournantdu satellite tels que les mécanismes de rotation des panneaux solaires ou de contrôle d’orientation dusatellite (on parle de contrôle d’attitude réalisé au moyen de roues inertielles).Le contrôle des micro-vibrations représentent ainsi un défit technologique, conduisant l’ESA et les ac-teurs industriels du monde spatial, a considéré cette problématique comme hautement prioritaire pour ledéveloppement des satellites d’observation terrestre nouvelle génération.Il existe à l’heure actuelle deux principes fondamentaux de contrôle des micro-vibrations :• le contrôle dit passif: la stratégie consiste à introduire des dispositions constructives et des matériauxparticuliers permettant de minimiser la transmission des vibrations à l’environnement.• le contrôle dit actif : le concept de contrôle actif des vibrations est tout autre : l’idée est cette fois-ci,de bloquer la micro-vibration en exerçant une vibration antagoniste créée artificiellement avec despropriétés en opposition, à tout instant, relativement à la vibration indésirable, pour rendre nulleleur somme.L’industrie spatiale aborde cette problématique en plaçant des isolateurs en élastomère au voisinage dechaque source de micro-vibrations. Cette solution, qui a fait ses preuves puisqu’elle équipe actuelle-ment nombre de satellites en orbite, permet de rejeter nombre de micro-vibrations. Malheureusement,la demande de plus en plus importante de grande stabilité de la ligne de visée pour les futures missionsd’observation terrestres telles que les missions GAIA rend l’approche passive insuffisante.L’ESA et Airbus Defence and Space, ont donc collaborer conjointement avec l’équipe ARIA au travers decette thèse, dans des travaux de recherche dans le domaine du contrôle actif pour palier ces problèmes.L’objectif visé est de coupler les approches passives et actives afin de rejeter à la fois les micro-vibrations enhautes fréquences (approche passive existant) et en basses fréquences (approche active objet des travauxde la thèse) / Next generation satellite missions will have to meet extremely challenging pointing stability requirements. Even low levels of vibration can introduce enough jitter in the optical elements to cause a significant reduction in image quality. The success of these projects is therefore constrained by the ability of on-board vibration isolation and optical control techniques to keep stable the structural elements of the spacecraft in the presence of external and internal disturbances.In this context, the research work presented in this thesis combines the expertise of the European Space Agency (ESA), the industry (Airbus Defence and Space) and the IMS laboratory (laboratoire de l’Intégration du Matériau au Système) with the aim of developing new generation of robust microvibration isolation systems for future space observation missions. More precisely, the thesis presents the development of an Integrated Modeling, Control and Analysis framework in which to conduct advanced studies related to reaction wheel microvibration mitigation.The thesis builds upon the previous research conducted by Airbus Defence and Space and ESA on the use of mixed active/passive microvibration mitigation techniques and provides a complete methodology for the uncertainty modeling, robust control system design and worst-case analysis of such systems for a typical satellite observation mission. It is shown how disturbances produced by mechanical spinning devices such as reaction wheels can be significantly attenuated in order to improve the pointing stability of the spacecraft even in the presence of model uncertainty and other nonlinear phenomenon.Finally, the work introduces a new disturbance model for the multi harmonic perturbation spectrum produced by spinning reaction wheels that is suitable for both controller synthesis and worst-case analysis using modern robust control tools. This model is exploited to provide new ways of simulating the image distortions induced by such disturbances.

The primary objective of this thesis is to leverage on the framework of H∞ loop-shaping control to formulate efficient and powerful optimization algorithms in LMI framework for the synthesis of performance loop-shaping weights. The H∞ loop-shaping design procedure is an efficient controller synthesis technique that combines classical loop-shaping concepts with H∞ synthesis. This procedure establishes a good tradeoff between robust stability and robust performance of a closed-loop system in a systematic manner. However, the selection of pre- and/or post-compensators, a crucial step in the design procedure, is nontrivial as factors such as the right half plane poles/zeros of the nominal plant, roll-off rate around the crossover frequency, strength of cross-coupling in multi-input multi-output systems, expected bandwidth, etc. must be adequately considered.Firstly, a frequency-dependent weight optimization framework is formulated in state-space form in order to remove the dependency on frequency while retaining the objective of maximizing the robust stability margin of a closed-loop system. This formulation facilitates the synthesis of low-order controllers, which is desirable from an implementation perspective.A weight optimization framework that incorporates smoothness constraints in order to prevent the cancellation of important modes of the system, for example, lightly damped poles/zeros of flexible structures, is subsequently formulated. The proposed formulation is intuitive from a design perspective as the smoothness constraints are expressed as gradient constraints on a log-log scale in dB/decade, consistent with the notation used in Bode plot for single-input single-output systems and singular value plots for multi-input multi-output systems.Thereafter, an optimization framework that maximizes the robust performance of a closed-loop system is presented. The philosophy in this framework is in line with practical design objectives that give the best achievable robust performance on a particular problem once a level of robust stability margin is demanded.Lastly, a novel unmanned vehicle is proposed. The vehicle uses a full six-degree-of-freedom tri-rotor actuation, capable of fully decoupled thrust and torque vectoring in all the 3D space. This vehicle can act as an unmanned ground vehicle or unmanned aerial vehicle, but the objective herein is restricted to the upright stability of the vehicle while operating on the ground as this is a precursor to rolling motion. The full nonlinear model of the vehicle is derived and linearized for subsequent controller synthesis, and this is thereafter validated by means of numerical simulations.

Main steam temperatures play a significant role in large coal fired power plant operation. Ideally, main steam temperatures should be accurately controlled to protect the thick wall components against long term overheating and thermal stress while meeting the design conditions at the steam turbine inlet. Although high steam temperatures are beneficial for thermal efficiency, it accelerates creep damage in high temperature components which is detrimental to the life of components. Alternatively, low steam temperatures increase the moisture content at the last stage blades of the turbine, causing the blades to deteriorate and fail. Control of the outlet steam temperature according to design conditions at variable loads is maintained via a balance between heat input (flue gas temperature and mass flow rate), evaporator outlet steam mass flow and spray water. The present control philosophy accuracy of main steam temperatures at an Eskom coal fired power plant was evaluated and compared to the latest technology and control strategies. Improving and optimizing steam temperature controls ensures design efficiency while maintaining long term plant health. The level of spatial discretization applied in simplifying the real boiler for modelling purposes was approached at a relatively high level. The intention was to model normal operating conditions and certain transients such as variable heat input and load changes to see its effect on steam temperatures and to be able to evaluate the performance of different temperature control techniques. The main outcome of this project was to design a robust control system for a dynamic model of the boiler using sets of low order linear models to account for uncertainty. The main concepts, models and theories used in the development of this dissertation include: 1) A detailed thermo-fluid model developed using Flownex to have high fidelity models of the process under varying operating conditions. This model was used to test and evaluate the robust controller design. 2) System Identification in Matlab to construct mathematical models of dynamic systems from measured inputoutput data and identify linear continuous time transfer functions under all operating conditions [1]. 3) Quantitative Feedback Theory (QFT) to design controllers for an attemperator control system at various onload operating conditions. This design was used understand the engineering requirements and seeks to design fixed gain controllers that will give desired performance under all operating conditions. 4) The design of a valve position controller to increase the heat uptake in a convective pass, thereby improving efficiency: Excessive attemperation in the superheater passes is generally associated with high flue gas temperatures which decrease thermal efficiency. Therefore, robust control of the attemperation system leads to an increase in heat uptake between the flue gas and steam in the boiler, resulting in a reduction in the flue gas temperature leaving the boiler, thus improving efficiency. The robust QFT controllers were set up using the valve position control technique and were used to confirm the improvement of control performance. The theories mentioned above were used to understand the control performance under varying plant conditions using a standard cascaded arrangement. It incorporated robust control design and engineering requirements such as bandwidth, plant life, spray water and thermodynamic efficiency. The control effort allocated to each superheaterattemperator subsystem in the convective pass was designed as a multi-loop problem.

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