This work describes the modeling, control design, and experimental verification of an electromagnetic suspension system with position feedback using infrared sensors. A nonlinear model is obtained by fitting a first principle analytical model of the system to experimental data. A sliding control strategy is designed using a sliding surface derived from the model to achieve robust stabilization for the closed-loop system. The control is then implemented on an embedded commercial DSP system for experimental verification of the designed control on a laboratory scale electromagnetic suspension system. To compensate for the steady-state tracking error, two modifications are considered. In the first method, a small magnitude integral term is added to the error feedback, equivalently adjusting the reference signal and eliminating the constant bias. In the second method, an integral sliding control is considered, using a higher-order sliding surface, which also eliminates the constant bias. The experimental results show the efficacy of all designed control techniques. The modified techniques, unlike the original design, effectively eliminate the constant position error.

When faced with death counts strati ed by age, analysts often calculate a crude mortality rate (CMR) as a single summary measure. This is done by simply dividing total death counts by total population counts. However, the crude mortality rate is not appropriate for comparing different populations due to the significant impact of age on mortality and the possibility of having different age structures for different populations. While a set of age-adjustment methods seeks to collapse age-specific mortality rates into a single measure that is free from the confounding effect of age structure, we focus on one of these methods called "direct age-standardization" method which summarizes and compares age-specific mortality rates by adopting a reference population. While qualitative insights in relation to age-standardization are often discussed, we seek to approximate age-standardized mortality rate of a population based on the corresponding CMR and the 90th quantile of its population distribution. This approximation is most useful when age-specific mortality data is unavailable. In addition, we provide quantitative insights related to age-standardization. We derive our model based on mathematical insights drawn from the explication of exact calculations and validate our model by using empirical data for a large number of countries under a large number of circumstances. We also extend the application of our approximation model to other age-standardized mortality indicators such as cause-specific mortality rate and potential years of life lost. In the second part of the thesis, we consider the formulation of a general risk management procedure, where risk needs to be measured and further mitigated. The formulation admits an optimization representation and requires as input the distributional information about the underlying risk factors. Unfortunately, for most risk factors it is known to be difficult to identify their distribution in full details, and more problematically the risk management procedure can be prone to errors in the input distribution. In particular, one of the most important distribution information is the covariance hat captures the spread and correlation among risk factors. We study the issue of covariance uncertainty in the problem of mitigating tail risk and by admitting an uncertainty set of covariance of risk factors, we propose a robust optimization model which minimizes risk for the worst scenario especially when data is insufficient and the number of risk factors is large. We will then transform our model into a computationally solvable one and test the model using real-world data.

Made available in DSpace on 2014-11-10T11:09:48Z (GMT). No. of bitstreams: 0 Previous issue date: 2014-04-25Bitstream added on 2014-11-10T11:58:01Z : No. of bitstreams: 1 000794484.pdf: 4606369 bytes, checksum: 3b03f3088fb54f098f7565bc5b9ad8da (MD5) / Nesta tese apresentam-se resultados para a estabilidade robusta de sistemas lineares sujeitos a incertezas paramétricas do tipo politópicas, variantes no tempo (do inglês Linear Parameter Varying - LPV). De início, expõe-se um método aprimorado para o projeto com otimização da norma de controladores robustos via desigualdades matriciais lineares (do inglês Linear Matrix Inequalitites - LMIs), com base na teoria de estabilidade segundo Lyapunov. Esta nova formulação foi manipulada utilizando o lema de Finsler, e permitiu encontrar melhores resultados de factibilidade com o acréscimo de matrizes extras e redução do número de LMIs. Neste novo equacionamento houve a inclusão do índice de desempenho da taxa de decaimento, responsável por diminuir o tempo de duração do período transitório, e também da otimização da norma dos controladores, responsável por menores ganhos mantendo a mesma eficiência dos requisitos de projeto. Devido a importantes resultados da literatura para o projeto de controladores robustos com incertezas variantes no tempo, optou-se por explorar o projeto de controladores dinâmicos chaveados, inovando-se no tocante ao acréscimo da taxa de decaimento e à otimização da norma dos controladores chaveados, o que possibilitou encontrar melhores resultados de implementação. Por fim, foram propostos critérios menos conservadores para a análise de estabilidade e projeto de controladores chaveados, utilizando funções de Lyapunov quadráticas por partes do tipo mínimo. A vantagem desse procedimento está no aumento dos parâmetros de relaxação porém, concebido através de formulações baseadas em desigualdades matriciais bilineares (do inglês Bilinear Matrix Inequalitites - BMIs), nos quais os termos e se encontram no produto entre variáveis escalares de otimização e matrizes, que também são variáveis do procedimento de otimização. Apresentam-se, no corpo do texto, exemplos numéricos e ... / This thesis presents results for robust stability of linear systems subject to polytopic timevarying parametric uncertainties (LPV). To start with, an improved method for the optimal gain design of robust controllers via Linear Matrix Inequalities (LMI), based on Lyapunov stability theory is presented. This new formulation was manipulated using the Finsler lemma, which enabled finding better feasibility results with the addition of extra matrices and reducing the number of LMIs. In this new equation it was included the decay rate performance index, responsible for reducing the transitional period time, as well as the controllers norm optimization, responsible for lower gains while maintaining the same project requirements efficiency. Then, due to important results in literature regarding the design of robust controllers with time-varying uncertainties, the design of switched dynamic controllers was explored by including the decay rate index and the optimization of the switched controllers norm in the equation, which allowed finding better implementation results. Finally, less conservative criteria were proposed for stability analysis and design of switched controllers using minimum-type piecewise quadratic Lyapunov functions. The advantage of this procedure lies in the increase of relaxation parameters, however, designed through formulations based on Bilinear Matrix Inequalities (BMIs), where the bilinear terms are in the product between optimization scalar variables and matrices, which are also variables on the optimization procedure. Numerical examples are presented and simulated to illustrate the efficiency of the proposed methodologies in relation to other existing throughout the text. The designed controllers were implemented using these new proposals in a Three Degrees Of Freedom (3-DOF) helicopter or in the Shake Table II (STII) + Active Mass Dumper - One Floor (AMD-1) system, in order to validate in practice the proposed theories

Les travaux de recherche développés dans cette thèse portent sur l'estimation robuste dans un contexte de population finie et infinie. Cette thèse comporte cinq chapitres, une introduction et une conclusion. Le chapitre 2 passe en revue la littérature portant sur plusieurs sujets tels que : l'inférence en population finie, l'estimation pour des petits domaines, l'estimation robuste dans un contexte de populations finies mais également de populations infinies. Dans le chapitre 3, le problème du choix du seuil dans le cas des estimateurs winzorisés est abordé. Nous avons montré que ces estimateurs appartiennent à une classe plus large, ce qui a permis de déterminer la valeur du seuil qui minimise le plus grand biais conditionnel estimé de l'échantillon (en valeur absolue) par rapport à l'estimateur winzorisé. Sous certaines conditions, nous avons montré que le seuil optimal existe et qu'il est unique dans certaines situations. Nous avons également proposé une méthode de calage permettant d'assurer la cohérence externe, qui est un problème très important en pratique. Les résultats d'une étude par simulation montrent que la méthode proposée fonctionne très bien en termes de biais et d'efficacité relative. Dans le chapitre 4, nous avons généralisé les résultats obtenus par Beaumont, Haziza et Ruiz-Gazen (2013, Biometrika) au cas de l'échantillonnage à deux-phases avec application au problème de la non-réponse totale. À notre connaissance, c'est le premier article portant sur l'estimation robuste en présence de données manquantes. Nous avons développé une version robuste des estimateurs par double dilatation et des estimateurs de calage. Dans le chapitre 5, nous nous sommes intéressés à l'estimation robuste dans un contexte de statistique classique (ou de populations infinies). Nous avons proposé une alternative robuste à la moyenne empirique. En particulier, nous avons développé une expression approximative de l'erreur quadratique moyenne pour des distributions appartenant aux domaines d'attraction de Gumbel et à celui de Frechet, ce qui nous a permis de comparer l'efficacité de l'estimateur proposé à celle de l'estimateur winzorisé une fois proposé par Rivest (1994, Biometrika). Dans le chapitre 6, nous avons traité du problème de l'estimation robuste dans un contexte d'estimation pour petits domaines, qui est un sujet qui a suscité beaucoup d'intérêt dans les dernières années. Nous avons proposé une approche unifiée d'estimation robuste à la présence de valeurs influentes dans le cas d'un modèle linéaire mixte généralisé. Lorsque le modèle sous-jacent est un modèle linéaire mixte, la méthode proposée est équivalente à la méthode de Dongmo Jiongo, Haziza et Duchesne (2013, Biometrika). Nous avons effectué des simulations dans le cas d'une variable d'intérêt continue, d'une variable binaire et d'une variable de comptage et avons montré empiriquement que la méthode proposée a de bonnes propriétés en termes d'erreur quadratique moyenne. / The main topic of this thesis is the robust estimation in finite or infinite population. The thesis is divided in five chapters, an introduction and a conclusion. The chapter 2 is a literature review focus on several topics as: inference in finite population, small area estimation, robust estimation in finite and infinite population. In chapter 3, we deal with the winsorization, which is often used to treat the problem of influential values. This technique requires the determination of a constant that corresponds to the threshold above which large values are reduced. We consider a method of determining the constant which involves minimizing the sample's largest estimated conditional bias. In the context of domain estimation, we also propose a method of ensuring consistency between the domain-level winsorized estimates and the population-level winsorized estimate. The results of two simulation studies suggest that the proposed methods lead to winsorized estimators that have good bias and relative efficiency properties. In chapter 4, we extend the results of Beaumont et al. (2013) to the case of two-phase sampling designs. We extend the concept of conditional bias attached to a unit with respect to both phases and propose a robust version of the double expansion estimator. Our results can be naturally extended to the case of unit nonresponse, since the set of respondents often being viewed as a second phase sample. A robust version of calibration estimators, based on auxiliary information available at both phases, is also constructed. In chapter 5, we focus on the estimation of the population mean of a skewed population. We propose a robust version of the empirical mean, develop some mean square error approximations for the max-domain of attraction of Gumbel and Fréchet, and compare the efficiency of the proposed estimator to the one-winsorized estimator proposed by Rivest (1994, Biometrika). We also extend the result to the case of a regression coefficient for a linear model. In chapter 6, we focus on the robust estimation for small areas. We first propose a robust predictor in a general model-based framework with the use of generalized linear models and then we propose a unified framework for robust small area prediction in the context of generalized LMMs. We conduct a Monte Carlo study in the case where the variable of interest is continuous, binary or count data and we show empirically that the estimator derived from the proposed method have good bias and relative efficiency properties.

Ce travail concerne le développement de méthodes de commandes avancées pour les suspensions automobiles afin d'améliorer la tenue de route des véhicules et le confort des passagers, tout en respectant les contraintes technologiques liées aux actionneurs de suspension (passivité, non-linéarités, limite structurelle). Dans la 1ère partie, nous proposons deux schémas de commande par approche LPV polytopique (Linéaire à Paramètre Variant) et Stabilisation Forte (Strong Stabilization) avec optimisation par algorithme génétique pour résoudre les conflits confort/tenue de route et confort/débattement de suspension. Dans la 2ème partie, pour résoudre le problème complet de commande de suspensions semi-actives, nous développons d'abord une stratégie générique pour les systèmes LPV généraux soumis à la saturation des actionneurs et à des contraintes d'état. Le problème est étudié sous la forme de résolution d'inégalités linéaires matricielles (LMI) qui permettent de synthétiser un contrôleur LPV et un gain anti wind-up garantissant la stabilité et la performance du système en boucle fermée. Ensuite, cette stratégie est appliquée au cas de la commande des suspensions semi-actives. Les méthodes proposées sont validées par une évaluation basée sur un critère industriel et des simulations effectuées sur un modèle non-linéaire de quart de véhicule. / This work concerns the development of advanced control methods for automotive suspensions to improve road holding and passenger comfort, while satisfying the technological constraints related to the suspension actuators (passivity, nonlinearity, structural limit). In the first part, we propose two control schemes by polytopic LPV (Linear Parameter Varying) approach and by Strong Stabilization with genetic algorithm optimization to solve the comfort/handling and comfort/suspension travel conflits. In the second part, to solve the full semi-active suspension problem, we develop first a generic strategy for general LPV systems subject to actuator saturation and state constraints. The problem is studied in the form of resolution matrix of linear inequalities (LMI) that allows synthesizing an LPV controller and an anti-windup gain to ensure the stability and performance of the closed-loop system. Second, the theoretical result is applied to the case of semi-active suspension control. The proposed methods are validated by an evaluation based on an industrial standard and simulations on a nonlinear quarter vehicle model.

Made available in DSpace on 2014-06-11T19:22:31Z (GMT). No. of bitstreams: 0 Previous issue date: 2013-05-24Bitstream added on 2014-06-13T18:49:29Z : No. of bitstreams: 1 manesco_rm_me_ilha.pdf: 1114845 bytes, checksum: 86414a871a4a2dd233af7709965f2bb3 (MD5) / Este trabalho trata do problema de estabilização robusta e de novas técnicas de otimização robusta de sistemas lineares contínuos no tempo sujeitos a incertezas politópicas no modelo. Todo trabalho é fundamentado em leis de controle por realimentação estática de saída. As técnicas de projetos apresentam condições suficientes na forma de desigualdades matriciais lineares (LMIs, acrônimo inglês para Linear Matrix Inequalities), formuladas com base na teoria de estabilidade segundo Lyapunov. Além do mais, índices de desempenho como a taxa de decaimento também são considerados no modelo, visto que, garantir apenas a estabilidade nem sempre é suficiente para fins de engenharia. As modelagens LMIs são realizadas através de lemas largamente utilizados em diversas áreas de sistema de controle, como, por exemplo, o lema de Finsler, que permite o uso tanto de uma função de Lyapunov dependente de parâmetros (PDLF, acrônimo inglês para Parameter-Dependent Lyapunov Function) quanto o uso de LMIs clássicas baseadas na existência de uma função de Lyapunov quadrática comum (CQLF, acrônimo inglês para Common Quadratic Lyapunov Function) para assegurar a estabilidade assintótica dos sistemas. Comparações entre ambos os métodos de projeto foram realizadas, e o presente trabalho apresenta resultados menos conservadores na maior parte das ocasiões, isto é, na maioria das vezes os problemas podem ser solucionados com PDLFs e não com CQLFs. Ainda, é proposta neste trabalho uma nova técnica para otimização da norma de controladores de saída e comparações são realizadas entre os métodos como forma de verificar a sua eficácia. O desafio deste trabalho consiste em realizar projetos de controladores robustos via LMIs através da realimentação estática de saída que fossem passíveis de implementação... / This thesis addresses the problem of robust stabilization and robust new optimization techniques for continuous-time linear systems subject to polytopic uncertainties in the model. All work is based on static output feedback control laws. The text presents sufficient conditions for control projects in the form of Linear Matrix Inequalities (LMIs), formulated in terms of the Lyapunov stability theory. Moreover, performance indices as decay rate are also considered in the model, since only ensure stability is not always sufficient for engineering purposes. The modeling is performed using LMIs widely used lemmas in several areas of control systems , such as, for example, the Lemma of Finsler, which allows the use of Parameters Dependent Lyapunov Functions (PDLFs) as the use of classic LMIs based on the existence of a Common Quadratic Lyapunov Functions (CQLFs) to ensure asymptotic stability of the systems. Comparisons between the two design methods were performed, and the present work shows less conservative results on most occasions, in other words, the problems can be solved with PDLFs and not with CQLFs in most cases. Still, this work proposes a new technique for optimizing the norm of output controllers and comparisons are made between the methods as a way to verify its effectiveness. The challenge of this work was to carry out robust controllers designs based on LMIs through static output feedback that could be implemented on a real physical system subject to failure. Thus, simulations were made and the designed output controllers were implemented in a 3-DOF (Degrees Of Freedom) helicopter bench of Quanserr trademark, always seeking alternative controllers with better performance and lower norm that... (Complete abstract click electronic access below)

Made available in DSpace on 2014-06-11T19:22:32Z (GMT). No. of bitstreams: 0 Previous issue date: 2013-03-08Bitstream added on 2014-06-13T19:48:53Z : No. of bitstreams: 1 silva_jhp_me_ilha.pdf: 1343237 bytes, checksum: 23b5f5f368f8d9c7eb211e7c5d1826a7 (MD5) / Neste trabalho são propostas condições suficientes para o controle H∞ chaveado de sistemas lineares incertos contínuos no tempo. A técnica abordada para este estudo consiste na utilização de uma função quadrática de Lyapunov e em um caso mais específico, uma função quadrática de Lyapunov por partes. A análise de estabilidade é descrita por meio de Desigualdades Matriciais Lineares (em inglês: Linear Matrix Inequalities), LMIs, que, quando factíveis, são facilmente resolvidas por meio de ferramentas disponíveis na literatura de programação convexa. Assim é apresentada uma metodologia de chaveamento do ganho de realimentação do vetor de estado, que assegura também o critério de desempenho H∞, cuja estratégia busca a obtenção do mínimo valor da derivada de uma função de Lyapunov quadrática. O método foi estendido com o emprego de uma função de Lyapunov quadrática por partes, cujo projeto é baseado nas desigualdades de Lyapunov-Metzler. É demonstrado que esta nova estratégia de chaveamento, além de uma implementação simples, oferece uma flexibilização das LMIs em comparação com os métodos convencionais que também utilizam o controle H∞. A teoria é ilustrada através de exemplos, que permitem comprovar o bom desempenho dos métodos propostos, incluindo a implementação em laboratório do controle de um helicóptero 3-DOF de bancada da QUANSER, sujeito a falhas estruturais. / Sufficient conditions for the switched H∞ control of continuous-time uncertain linear systems are proposed. The technique discussed in this study is based on quadratic Lyapunov functions and a piecewise quadratic Lyapunov functions. The stability analysis is described by LMIs that, when feasible, are easily solved by available tools in the convex programming literature. Thus, a methodology for designing the switching of state vector feedback gains, which also ensures H∞ performance criterion, is presented. This new procedure chooses the state feedback gain that returns the minimum value of the time derivative of the Lyapunov function. The method was extended to a piecewise quadratic Lyapunov function and is designed from the solution of Lyapunov-Metzler inequalities. It is shown that this switching strategy, beyond a simple implementation, offers a relaxation in the LMIs, when compared with the conventional methods used in H∞ control. The procedure are illustrated by means of examples, including an implementation in the control of a 3-DOF helicopter, subject to structural failures.

Made available in DSpace on 2014-06-11T19:22:32Z (GMT). No. of bitstreams: 0 Previous issue date: 2011-02-16Bitstream added on 2014-06-13T18:49:31Z : No. of bitstreams: 1 silva_jl_me_ilha.pdf: 4436511 bytes, checksum: a3ef3dcb55e4a2eca8bbc6e79470f5cc (MD5) / Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) / O principal objetivo do trabalho é explorar a técnica de controle robusto com Modos Deslizantes para a acomodação e atenuação de uma falha no sinal de controle de um helicóptero. Foram projetados dois controladores, o Controle com Estrutura Variável e Modos Deslizantes contínuo no tempo (CEV/MD), e o segundo é o Controle Discreto com Modos Deslizantes (CDMD). Foi usado um modelo matemático não linear que representa um simulador de voo (Helicóptero 3-DOF da Quanser R ), que é um equipamento útil para o ensino, aplicação e desenvolvimento de técnicas de controle robusto. Os resultados experimentais obtidos, fazem uma comparação entre o controle contínuo e o controle discreto. Para que essa comparação seja feita foi inserida uma falha no sinal de controle. Mesmo diante das diferenças na resposta do sinal de controle, entre os controladores, o sistema teve um bom desempenho quando controlado pelo CEV/MD e CDMD, mostrando assim a eficiência da técnica de controle com Modos Deslizantes / The main objective of this work is the exploration of the robust control technique with Sliding Mode (VSC-SM) for fault accommodation and attenuation in an aircraft’s propulsion system. Two controllers were designed, Variable Structure Control with Sliding Mode (VSCSM) and Discrete Control with Sliding Modes (DCSM). For that, it was used a mathematical model of a flight Simulator of a Quanser’s helicopter, named as 3-DOF Helicopter, which is an excellent module for teaching, application and development of robust control techniques. The results obtained in digital simulations show great performance of the system in fault when controlled by VSC-SM and DCSM

Orientador: Marcelo Carvalho Minhoto Teixeira / Banca: Jean Marcos de Souza Ribeiro / Banca: Cristiano Quevedo Andrea / Resumo: Nesta dissertação apresentam-se o princípio de funcionamento do motor de indução trifásico em regime permanente abordando os ensaios necessários para obtenção de seus parâmetros e as diferentes possibilidades de variação de velocidade. A partir disso, efetuou-se uma análise da modelagem dinâmica do motor, enfocando nas transformações de eixos, além de analisar os tipos de controle, escalar, vetorial direto e indireto (orientado pelo fluxo do rotor, pelo fluxo do estator e pelo fluxo do entreferro) e o controle direto de torque. Também se abordou os conversores CC - CA utilizados para o acionamento do motor de indução trifásico, juntamente com suas principais metodologias de modulação. Fez-se uma revisão do estado da arte dos sistemas de acionamento e controle mais estudados nos últimos anos sobre o assunto. Após, estudou-se os conceitos de estabilidade quadrática proposto por Lyapunov, juntamente com o controle H∞, os quais foram a base para o desenvolvimento de controladores robustos projetados no trabalho com desigualdade matriciais lineares (em inglês Linear Matrix Inequalities (LMIs)). Desenvolveram-se cinco tipos de controladores robustos com LMIs: o robusto, com taxa de decaimento (para sigma 1 e 10), H∞, H∞ com D-Estabilidade e H∞ com D-Estabilidade e realimentação da integral do erro de saída sendo que em todos o motor de indução trifásico foi orientado pelo fluxo do rotor. Os controladores foram projetados para quatro diferentes configurações, sendo considerados, primeiro caso - variação da velocidade (5 rad/s até a nominal); segundo caso - variação da velocidade e incerteza na resistência rotórica (3%); terceiro caso - variação na velocidade e incerteza na constante de tempo do rotor (5%); quarto caso - variação na velocidade e incertezas na constante de tempo do rotor (15%) e do estator (10%). Em todos os controladores projetados foram... / Abstract: This research shows the steady state operating principle of triphasic induction motors to approach the tests necessary to obtain their parameters and different speed variation possibilities. After were performed an analysis of the dynamics of motor modeling, focusing on the transformation of axes, and analyzing the types of control, scalar, direct and indirect vector (guided by the rotor flux at the stator flux and flux air gap) and direct torque control. The converters CC - AC used to drive the induction motor are also aborded, along with their main methods of modulation. A review of the state of the art regarding the drives and control systems most studied in recent years on the subject is presented. After were studied the concepts of quadratic stability proposed by Lyapunov, together with the H∞ control, which were the basis for the development of robust controllers based on Linear Matrix Inequality (LMI). In this research were developed five types of robust controllers with LMI: the robust controller, the controller with decay rate (for sigma 1 and 10), H∞ controller, H∞ controller with D- Stability and H∞ controller with D- Stability and feedback the integral of output error, considering in all cases that the triphasic induction motor is driven by rotor flux. The controllers were designed for four different configurations and were considered the first case - the speed variation (5 rad/s up to the rated); second case - the speed variation and uncertainty in the rotor resistance (3%); third case - variations in speed and uncertainty in the rotor time constant (5%); fourth case - variations in speed and uncertainties in the rotor time constant (15%) and the stator (10%). In all researched controllers were analyzed the response time of the outputs for a unit step input load torque disturbance. This analysis aimed to evaluate system behavior, however, for a complete and rigorous analysis ... / Mestre

This dissertation deals with frequency domain identification of linear dynamic systems in a deterministic set-up. Various untuned algorithms are suggested, including one which is robustly convergent and asymptotically optimal (in n-width sense) for a finite model order. The suggested algorithms can easily be implemented in commercially available software for convex optimization.