Cette thèse est construite autour de deux types d'estimation de l'état d'un système, traités séparément. Le premier problème abordé concerne la construction d'observateurs positifs basés sur la métrique de Hilbert. Le second traite de la synthèse d'observateurs par intervalles pour différentes familles de systèmes dynamiques et la construction de lois de commande robustes qui stabilisent ces systèmes.Un système positif est un système dont les variables d'état sont toujours positives ou nulles lorsque celles-ci ont des conditions initiales qui le sont. Les systèmes positifs apparaissent souvent de façon naturelle dans des applications pratiques où les variables d'état représentent des quantités qui n'ont pas de signification si elles ont des valeurs négatives. Dans ce contexte, il parait naturel de rechercher des observateurs fournissant des estimées elles aussi positives ou nulles. Dans un premier temps, notre contribution réside dans la mise au point d'une nouvelle méthode de construction d'observateurs positifs sur l'orthant positif. L'analyse de convergence est basée sur la métrique de Hilbert. L'avantage concurrentiel de notre méthode est que la vitesse de convergence peut être contrôlée.Notre étude concernant la synthèse d'observateurs par intervalles est basée sur la théorie des systèmes dynamiques positifs. Les observateurs par intervalles constituent un type d'observateurs très particuliers. Ce sont des outils développés depuis moins de 15 ans seulement : ils trouvent leur origine dans les travaux de Gouzé et al. en 2000 et se développent très rapidement dans de nombreuses directions. Un observateur par intervalles consiste en un système dynamique auxiliaire fournissant un intervalle dans lequel se trouve l'état, en considérant que l'on connait des bornes pour la condition initiale et pour les quantités incertaines. Les observateurs par intervalles donnent la possibilité de considérer le cas où des perturbations importantes sont présentes et fournissent certaines informations à tout instant. / This thesis presents new results in the field of state estimation based on the theory of positive systems. It is composed of two separate parts. The first one studies the problem of positive observer design for positive systems. The second one which deals with robust state estimation through the design of interval observers, is at the core of our work.We begin our thesis by proposing the design of a nonlinear positive observer for discrete-time positive time-varying linear systems based on the use of generalized polar coordinates in the positive orthant. For positive systems, a natural requirement is that the observers should provide state estimates that are also non-negative so they can be given a physical meaning at all times. The idea underlying the method is that first, the direction of the true state is correctly estimated in the projective space thanks to the Hilbert metric and then very mild assumptions on the output map allow to reconstruct the norm of the state. The convergence rate can be controlled.Later, the thesis is continued by studying the so-called interval observers for different families of dynamic systems in continuous-time, in discrete-time and also in a context "continuous-discrete" (i.e. a class of continuous-time systems with discrete-time measurements). Interval observers are dynamic extensions giving estimates of the solution of a system in the presence of various type of disturbances through two outputs giving an upper and a lower bound for the solution. Thanks to interval observers, one can construct control laws which stabilize the considered systems.

La thèse porte sur le développement des techniques non linéaires robustes de stabilisation et commande des systèmes avec perturbations de model. D’abord, on introduit les concepts de base de stabilité et stabilisabilité robuste dans le contexte des systèmes non linéaires. Ensuite, on présente une méthodologie de stabilisation par retour d’état en présence d’incertitudes qui ne sont pas dans l’image de la commande («unmatched»). L’approche récursive du «backstepping» permet de compenser les perturbations «unmatched» et de construire une fonction de Lyapunov contrôlée robuste, utilisable pour le calcul ultérieur d’un compensateur des incertitudes dans l’image de la commande («matched»). Le contrôleur obtenu est appelé «recursive Lyapunov redesign». Ensuite, on introduit la technique de stabilisation par «Immersion & Invariance» comme outil pour rendre un donné contrôleur non linéaire, robuste par rapport à dynamiques non modelées. La première technique de contrôle non linéaire robuste proposée est appliquée au projet d’un autopilote pour un missile air-air et au développement d’une loi de commande d’attitude pour un satellite avec appendices flexibles. L’efficacité du «recursive Lyapunov redesign» est mis en évidence dans le deux cas d’étude considérés. En parallèle, on propose une méthode systématique de calcul des termes incertains basée sur un modèle déterministe d’incertitude. La partie finale du travail de thèse est relative à la stabilisation des systèmes sous échantillonnage. En particulier, on reformule, dans le contexte digital, la technique d’Immersion et Invariance. En premier lieu, on propose des solutions constructives en temps continu dans le cas d’une classe spéciale des systèmes en forme triangulaire «feedback form», au moyen de «backstepping» et d’arguments de domination non linéaire. L’implantation numérique est basée sur une loi multi-échelles, dont l’existence est garantie pour la classe des systèmes considérée. Le contrôleur digital assure la propriété d’attractivité et des trajectoires bornées. La loi de commande, calculée par approximation finie d’un développement asymptotique, est validée en simulation de deux exemples académiques et deux systèmes physiques, le pendule inversé sur un chariot et le satellite rigide. / The dissertation deals with the problems of stabilization and control of nonlinear systems with deterministic model uncertainties. First, in the context of uncertain systems analysis, we introduce and explain the basic concepts of robust stability and stabilizability. Then, we propose a method of stabilization via state-feedback in presence of unmatched uncertainties in the dynamics. The recursive backstepping approach allows to compensate the uncertain terms acting outside the control span and to construct a robust control Lyapunov function, which is exploited in the subsequent design of a compensator for the matched uncertainties. The obtained controller is called recursive Lyapunov redesign. Next, we introduce the stabilization technique through Immersion \& Invariance (I\&I) as a tool to improve the robustness of a given nonlinear controller with respect to unmodeled dynamics. The recursive Lyapunov redesign is then applied to the attitude stabilization of a spacecraft with flexible appendages and to the autopilot design of an asymmetric air-to-air missile. Contextually, we develop a systematic method to rapidly evaluate the aerodynamic perturbation terms exploiting the deterministic model of the uncertainty. The effectiveness of the proposed controller is highlighted through several simulations in the second case-study considered. In the final part of the work, the technique of I\& I is reformulated in the digital setting in the case of a special class of systems in feedback form, for which constructive continuous-time solutions exist, by means of backstepping and nonlinear domination arguments. The sampled-data implementation is based on a multi-rate control solution, whose existence is guaranteed for the class of systems considered. The digital controller guarantees, under sampling, the properties of manifold attractivity and trajectory boundedness. The control law, computed by finite approximation of a series expansion, is finally validated through numerical simulations in two academic examples and in two case-studies, namely the cart-pendulum system and the rigid spacecraft.

Ce mémoire est consacré à l'étude du phénomène d'instabilité pouvant apparaître sur les bus continus des réseaux DC. En effet, l'interaction entre les différents sous-systèmes électriques (source, charge, filtre) composant le réseau DC peut conduire, sous certaines conditions, à l'instabilité du système. A partir de la modélisation des charges sous forme de "Charge à Puissance Constante" (notée CPL), des méthodes d'études permettant l'analyse de la stabilité "petit-signal" et "grand-signal" des systèmes électriques sont présentées. Celles-ci permettent de mettre en évidence le fait qu'un réseau DC ne peut pas fournir n'importe quelle puissance à ses charges sans devenir instable. Ces puissances limites dépendent à la fois de la structure du réseau et des valeurs de ses éléments passifs et de sa tension de bus. Afin de pouvoir augmenter l'amortissement/les marges de stabilité du système, des méthodes de stabilisation sont présentées dans ce mémoire. Elles proposent d'adapter les commandes des charges de manière à assurer sa stabilité. Ceci se fait grâce à l'addition d'un signal stabilisant sur la référence de chaque charge. Ce signal n'est visible que durant les régimes transitoires de la charge afin de ne pas modifier le point de fonctionnement demandé. Néanmoins, plus on voudra stabiliser une charge et plus son signal stabilisant sera important. Un bon compromis doit donc être trouvé afin d'assurer la stabilité du système sans altérer les performances dynamiques des charges. Deux approches différentes sont proposées afin de générer ces commandes stabilisantes. La première se base sur la mise en place d'un stabilisateur centralisé. Deux méthodes centralisées sont alors proposées : la première s'appuie sur la théorie des multimodèles de Takagi-Sugeno alors que la seconde s'appuie sur la théorie de Lyapunov. Cette dernière permettra d'orienter les efforts de stabilisation sur les charges souhaitées pour par exemple, les diriger principalement vers les organes de récupération d'énergie. La seconde approche se base sur la mise en place d'un système de stabilisation multi-agent. Celui-ci présente une structure décentralisée où chaque agent correspond à un bloc de stabilisation. Ceux-ci vont compenser localement les impacts déstabilisants de leur charge respective et leurs actions combinées permettront d'assurer la stabilité du système. De plus, on propose d'utiliser un algorithme d'optimisation sous contraintes qui permettra de donner un dimensionnement du système minimisant les efforts de stabilisation tout en considérant des cas de défaut tels que la perte de l'un des agents ou la reconfiguration du réseau / This thesis is devoted to the analysis of the instability phenomenon that may appear on the DC bus of DC microgrids. Indeed, interaction between the different electrical subsystems of the grid (source, load, filters) can lead, under certain conditions, to the system instability. From the "Constant Power Load" (CPL) hypothesis for the loads, this thesis presents studying methods for "small-signal" and "large-signal" stability analysis of electrical systems. This highlights that a DC microgrid cannot power the loads more than a maximum limit without becoming unstable. This power limitation depends on the structure of the grid, the value of its passive components, and its bus voltage. In order to improve the microgrid stability, stabilization methods are presented in this thesis. They propose to adapt the loads control to ensure the system stability. This is achieved by the addition of a stabilizing signal to the reference of each load. This signal is only visible during the load power transient mode to not change the requested operating point. However, a good trade-off must be found to ensure system stability without affecting the dynamic performance of its loads. Two approaches are investigated to generate the stabilizing commands. The first one is based on the establishment of a centralized stabilization block. Two centralized methods have been developed: the first one is based on the Takagi-Sugeno theory while the second is based on the Lyapunov theory. This latest permits to guide the stabilizing effort on the desired loads. For example, stabilizing effort can be oriented on the energy storage device. The second approach is based on the establishment of a multi-agent stabilizing system. It consists of a decentralized structure in which each agent corresponds to a stabilization block. These will locally compensate the destabilizing impact of their respective load on the microgrid, and their combined actions ensure the system stability. To design the system, the use of a constrained optimization algorithm is proposed. This permits to minimize stabilization efforts while considering faulty events such as the failure of one of the agents or a reconfiguration of the microgrid

Made available in DSpace on 2016-08-10T10:47:02Z (GMT). No. of bitstreams: 1 FABIANA PEREIRA BARBALHO.pdf: 1767202 bytes, checksum: 32aeda02c693ba5c109ce2b3edd24f2a (MD5) Previous issue date: 2014-03-12 / The objective of this work is to analyze the United Nations Mission for the Stabilization of Haiti (MINUSTAH) in the foreign policy of the Luiz Inacio Lula da Silva government. The intention is to present some considerations regarding Brazilian foreign policy and the effects of the performance of the Midwest region contingent. This will be done by presenting the Haitian historical setting and by examining the motivations that led Brazil to accept the MINUSTAH command. Haiti, the second colony in the American continent to obtain independence, has gone through decades of dictatorships and political struggles and, therefore, several foreign interventions were carried out in the country. However, over the years, the deficient state structure intensified, and, along with serious socio-economic crisis, natural disasters and disease outbreaks, suffering among the population also increased. In 2004, with the resignation of President Jean-Bertrand, a widespread chaos broke out and caught the attention of the international community. MINUSTAH (approved by Resolution 1542 of UNSC on April 30, 2004) arrived in Haiti on June 1st of the same year under the leadership of Maj. Gen. Augusto Heleno Ribeiro Pereira. The mission aims were: to support the constitutional and political process of the country; to seek to guarantee a safe and stable environment to all the citizens; to aid the transitional government in monitoring and reforming the Haitian National Police; to assist in conducting municipal, parliamentary and presidential elections; and to promote and protect human rights. MINUSTAH had their mandates renewed several times through UNSC resolutions, which established the conduct guidelines of the troops and redefined the strategies, adapting these to political, socioeconomic and security transformations that the country presented. The Midwest region contingent, our main research object, arrived in Port au Prince in the first half of December 2006 together with Peacekeeping Operations Group (DOPaz). This group, originally from the Special Operations Brigade based in Goiânia (Brazil), found an environment of immense insecurity. A series of extremely violent kidnappings and several killings were broadcasted in newspapers around the world. The contingent conducted several enforcement operations, which achieved short-term decrease in the levels of violence in the Haitian capital, Port au Prince, and in neighborhoods like Cité Militaire and Cité Soleil. The research was developed with a dialectical approach, with a historical analysis procedure and through literature and document analysis. Various sources of information were used, such as articles from specialized and non-specialized journals, theses, Brazilian Government and the UN official documents, and multiple books that deal with the topic. / Esse trabalho tem por objetivo analisar a Missão das Nações Unidas para a Estabilização do Haiti (MINUSTAH) na política externa do Governo Luiz Inácio Lula da Silva. Pretende-se, por meio da exposição de um cenário histórico do Haiti e do exame das motivações que levaram o Brasil a aceitar o comando da MINUSTAH, apresentar algumas considerações a respeito da política externa brasileira e dos reflexos da atuação do contingente região Centro Oeste na missão. O Haiti, a segunda colônia nas Américas a conquistar sua independência, passou por décadas de ditaduras e lutas políticas, com isso, várias intervenções estrangeiras foram realizadas no país com a finalidade de minimizar os efeitos da ineficiência estatal. No entanto, com o passar dos anos, a estrutura estatal deficitária foi se intensificando, ademais, graves crises socioeconômicas, catástrofes naturais e surtos de doenças aumentaram o sofrimento da população. Em 2004, com a renúncia do presidente Jean-Bertrand Aristide eclodiu um caos generalizado que despertou a atenção da comunidade internacional. A MINUSTAH (aprovada pela Resolução 1542 do CSNU, em 30 de abril de 2004) chegou ao Haiti no dia 1º de junho do mesmo ano sob chefia do General de Divisão Augusto Heleno Ribeiro Pereira. A missão tinha como objetivo dar apoio ao processo constitucional e político do país; buscar assegurar a todos os cidadãos um ambiente seguro e estável; apoiar o governo de transição no monitoramento e reforma da Polícia Nacional Haitiana; auxiliar na realização de eleições municipais, parlamentares e presidenciais; e promover e proteger os direitos humanos. A MINUSTAH teve seus mandatos renovados diversas vezes por meio de resoluções do CSNU que estabeleciam as diretrizes de conduta das tropas e a redefinição de estratégias, adaptando-as transformações políticas, socioeconômicas e de segurança que o país apresentava. O contingente região Centro Oeste, nosso principal objeto de pesquisa, chegou em Porto Príncipe na primeira quinzena de dezembro de 2006 juntamente com o Destacamento de Operações de Paz (DOPaz). Esse grupo, oriundo da Brigada de Operações Especiais, sediado em Goiânia, encontrou um ambiente de grande insegurança, uma sequência de sequestros extremamente violentos e várias mortes sendo noticiadas em jornais de todo o mundo. O contingente realizou várias operações coercitivas, conseguindo em curto prazo diminuir os índices de violência na capital do Haiti, Porto Príncipe, e em bairros como Cité Militaire e Cité Soleil. A pesquisa foi desenvolvida sob uma abordagem dialética, utilizando como procedimento uma análise histórica, através de pesquisas bibliográficas e documentais, sendo usada várias fontes de informações como artigos de periódicos especializados e não especializados, teses, documentos oficiais do Governo Brasileiro e da ONU, e múltiplos livros que versam sobre o tema.

Le problème principalement étudié dans ce manuscrit est la stabilisation d’orbites périodiques de systèmes dynamiques non linéaires à l’aide d’une commande de rétroaction (feedback). Le but des méthodes de contrôle proposées ici est d’obtenir une oscillation périodique stable. Ces méthodes de contrôle sont appliquées à des systèmes présentant des orbites périodiques instables dans l’espace d’état, et ces dernières sont les orbites destinées à être stabilisées.Les méthodes proposées ici sont telles que l’oscillation stable qui en résulte est obtenue avec un effort de contrôle faible, et que la valeur de la commande tend vers zéro lorsque la trajectoire tend vers l’orbite stabilisée. La stabilité locale des orbites périodiques est analysée par l’étude de la stabilité des systèmes linéaires périodiques à l’aide de la théorie de Floquet. Ces systèmes linéaires sont obtenus par linéarisation des trajectoires au voisinage de l’orbite périodique.Les méthodes de contrôle utilisées ici pour la stabilisation des orbites périodiques sont une loi de commande proportionnelle, une loi de commande de rétroaction retardée et une loi de commande de rétroaction basée sur une prédiction. Ces méthodes sont appliquées aux systèmes en temps discret et aux systèmes en temps continu avec les modifications nécessaires. Les contributions principales de cette thèse sont associées à ces méthodes, proposant une méthode alternative de design de gain, une nouvelle loi de commande et des résultats associés. / The main problem evaluated in this manuscript is the stabilization of periodic orbits of non-linear dynamical systems by use of feedback control. The goal of the control methods proposed in this work is to achieve a stable periodic oscillation. These control methods are applied to systems that present unstable periodic orbits in the state space, and the latter are the orbits to be stabilized.The methods proposed here are such that the resulting stable oscillation is obtained with low control effort, and the control signal is designed to converge to zero when the trajectory tends to the stabilized orbit. Local stability of the periodic orbits is analyzed by studying the stability of some linear time-periodic systems, using the Floquet stability theory. These linear systems are obtained by linearizing the trajectories in the vicinity of the periodic orbits.The control methods used for stabilization of periodic orbits here are the proportional feedback control, the delayed feedback control and the prediction-based feedback control. These methods are applied to discrete and continuous-time systems with the necessary modifications. The main contributions of the thesis are related to these methods, proposing an alternative control gain design, a new control law and related results. / O principal problema avaliado neste manuscrito é a estabilização de órbitas periódicas em sistemas dinâmicos não-lineares utilizando controle por realimentação. O objetivo dos métodos de controle propostos neste trabalho é obter uma oscilação periódica estável. Estes métodos de controle são aplicados a sistemas que apresentam órbitas periódicas instáveis no espaço de estados, estas são as órbitas a serem estabilizadas.Os métodos propostos aqui são tais que a oscilação periódica estável resultante é obtida utilizando um baixo esforço de controle, e o sinal de controle é projetado de forma a convergir para zero quanto a trajetória tende à órbita estabilizada. A estabilidade local de órbitas periódicas é analisada através do estudo da estabilidade de alguns sistemas lineares periódicos no tempo, utilizando a teoria de estabilidade de Floquet. Estes sistemas lineares são obtidos por linearização das trajetórias na vizinhança da órbita periódica.Os métodos de controle utilizados aqui para estabilização de órbitas periódicas são o proportional feedback control, o delayed feedback control e o prediction-based feedback control (controle por realimentação baseado em predição). Estes métodos são aplicados a sistemas de tempo discreto e de tempo contínuo, com as modificações necessárias. As principais contribuições da tese são relacionadas a esses métodos, propondo um projeto de ganho de controle alternativo, uma nova lei de controle e resultados relacionados.

Made available in DSpace on 2016-03-15T19:33:59Z (GMT). No. of bitstreams: 1 Jaime Goncalves Filho.pdf: 863240 bytes, checksum: e960a09eb78ee2841ff94326cf87aa72 (MD5) Previous issue date: 2012-08-13 / This dissertation has for object of study the Provisional Measure 168/90 which served as the political and economic instrument for a specific context, namely, the Collor administration. It will analyze, therefore, the legal limits existing at the time of the mentioned Provisional Measure, weighing the economic needs and the legal system in force, and will account for the decisions of the courts that evaluated the constitutionality and legality of the seizure of assets. The Provisional Measure 168/90, put in place to serve economic and political interests during the Collor administration, with the goal of comparing such measures with the existing legal limits in order to come to a conclusion on the illegality of these facts. / A presente dissertação tem por objeto de estudo analisar a Medida Provisória 168/90 que serviu de instrumento político-econômico para um contexto específico, qual seja, o governo Collor. Analisar-se-á, portanto, os limites jurídicos existentes à época da mencionada Medida Provisória, sopesando as necessidades econômicas e a ordem jurídica vigente, fazendo, inclusive, menção às decisões dos Tribunais que apreciaram a constitucionalidade e legalidade do bloqueio de haveres. A Medida Provisória 168/90 foi manejada em razão de interesses econômicos e políticos durante o governo Collor, de modo a cotejar tais medidas com os limites jurídicos existentes, a fim de concluir sobre a ilicitude desses fatos.

Cette thèse aborde le problème de la calibration d’un ensemble de capteurscomposé d’une centrale inertielle, d’un magnétomètre et d’une caméra, avecpour objectif leur intégration sur un système très compact : un mini-drone.Cette étude expose tout d’abord les contraintes imposées par l’application surle choix des capteurs et les solutions envisagées notamment pour résoudre leproblème de la synchronisation des mesures. Après avoir étudié les techniquesde calibration existantes, une méthode permettant la calibration de l’ensembledes capteurs (accéléromètre, gyromètre, magnétomètre et caméra) est présentée.La solution proposée permet également d’estimer les changements de repèresentre les différents capteurs. Elle a la particularité de ne nécessiter l’emploid’aucun matériel particulier. D’autre part, l’intégration de ces capteurs dans unsystème aussi compact soulève de nouvelles difficultés. Dans ces conditions, leschamps magnétiques créés par les actionneurs du drone perturbent les mesuresdu magnétomètre se trouvant à proximité. Une nouvelle méthode est proposéeafin d’estimer et de compenser dynamiquement ces perturbations magnétiquesen fonction de l’état des actionneurs du drone. Enfin, deux applications dusystème comprenant une centrale inertielle et une caméra sont présentées :la construction de mosaïques d’images géo-référencées et la stabilisation devidéos. Ces deux applications exploitent les mesures des capteurs inertiels afind’effectuer un traitement en temps réel pour un coût calculatoire très faible. / This thesis deal with the issue of the calibration of a group of sensor composedof an inertial unit, a magnetometer and a camera. It aims at integratingthem into a very compact system : a mini-drone. First of all, this study outlinesthe constraints imposed by the application on the choice of the sensors andthe solutions considered to solve the measures synchronization issue. Afterstudying existing calibration techniques, a method for the calibration of allthe sensors (accelerometer, gyroscope, magnetometer and camera) is presented.The proposed solution allows to estimate the frame transformation between thedifferent sensors. It has the advantage of not requiring the use of any specialequipment. Furthermore, the integration of these sensors into a compact systemraises new difficulties. Under these conditions, the magnetic fields created bythe drone actuators disrupt magnetometer measurements. A new method isproposed to estimate and compensate for these magnetic disturbances. Thecompensation is dynamically adapted based on the state of the drone actuators.Finally, two applications of the system including an inertial unit and a cameraare presented : the construction of geo-referenced images mosaic and videostabilization. Both applications use measurements of inertial sensors and precisecalibration to perform a real-time processing for a very low computational cost.

<p>A time-discrete formulation of the variational principle of mechanics is used to provide a consistent theoretical framework for the construction and analysis of low order integration methods. These are applied to mechanical systems subject to mixed constraints and dry frictional contacts and impacts---machines. The framework includes physics motivated constraint regularization and stabilization schemes. This is done by adding potential energy and Rayleigh dissipation terms in the Lagrangian formulation used throughout. These terms explicitly depend on the value of the Lagrange multipliers enforcing constraints. Having finite energy, the multipliers are thus massless ghost particles. The main numerical stepping method produced with the framework is called SPOOK.</p><p>Variational integrators preserve physical invariants globally, exactly in some cases, approximately but within fixed global bounds for others. This allows to product realistic physical trajectories even with the low order methods. These are needed in the solution of nonsmooth problems such as dry frictional contacts and in addition, they are computationally inexpensive. The combination of strong stability, low order, and the global preservation of invariants allows for large integration time steps, but without loosing accuracy on the important and visible physical quantities. SPOOK is thus well-suited for interactive simulations, such as those commonly used in virtual environment applications, because it is fast, stable, and faithful to the physics.</p><p>New results include a stable discretization of highly oscillatory terms of constraint regularization; a linearly stable constraint stabilization scheme based on ghost potential and Rayleigh dissipation terms; a single-step, strictly dissipative, approximate impact model; a quasi-linear complementarity formulation of dry friction that is isotropic and solvable for any nonnegative value of friction coefficients; an analysis of a splitting scheme to solve frictional contact complementarity problems; a stable, quaternion-based rigid body stepping scheme and a stable linear approximation thereof. SPOOK includes all these elements. It is linearly implicit and linearly stable, it requires the solution of either one linear system of equations of one mixed linear complementarity problem per regular time step, and two of the same when an impact condition is detected. The changes in energy caused by constraints, impacts, and dry friction, are all shown to be strictly dissipative in comparison with the free system. Since all regularization and stabilization parameters are introduced in the physics, they map directly onto physical properties and thus allow modeling of a variety of phenomena, such as constraint compliance, for instance.</p><p>Tutorial material is included for continuous and discrete-time analytic mechanics, quaternion algebra, complementarity problems, rigid body dynamics, constraint kinematics, and special topics in numerical linear algebra needed in the solution of the stepping equations of SPOOK.</p><p>The qualitative and quantitative aspects of SPOOK are demonstrated by comparison with a variety of standard techniques on well known test cases which are analyzed in details. SPOOK compares favorably for all these examples. In particular, it handles ill-posed and degenerate problems seamlessly and systematically. An implementation suitable for large scale performance and accuracy testing is left for future work.</p>

A time-discrete formulation of the variational principle of mechanics is used to provide a consistent theoretical framework for the construction and analysis of low order integration methods. These are applied to mechanical systems subject to mixed constraints and dry frictional contacts and impacts---machines. The framework includes physics motivated constraint regularization and stabilization schemes. This is done by adding potential energy and Rayleigh dissipation terms in the Lagrangian formulation used throughout. These terms explicitly depend on the value of the Lagrange multipliers enforcing constraints. Having finite energy, the multipliers are thus massless ghost particles. The main numerical stepping method produced with the framework is called SPOOK. Variational integrators preserve physical invariants globally, exactly in some cases, approximately but within fixed global bounds for others. This allows to product realistic physical trajectories even with the low order methods. These are needed in the solution of nonsmooth problems such as dry frictional contacts and in addition, they are computationally inexpensive. The combination of strong stability, low order, and the global preservation of invariants allows for large integration time steps, but without loosing accuracy on the important and visible physical quantities. SPOOK is thus well-suited for interactive simulations, such as those commonly used in virtual environment applications, because it is fast, stable, and faithful to the physics. New results include a stable discretization of highly oscillatory terms of constraint regularization; a linearly stable constraint stabilization scheme based on ghost potential and Rayleigh dissipation terms; a single-step, strictly dissipative, approximate impact model; a quasi-linear complementarity formulation of dry friction that is isotropic and solvable for any nonnegative value of friction coefficients; an analysis of a splitting scheme to solve frictional contact complementarity problems; a stable, quaternion-based rigid body stepping scheme and a stable linear approximation thereof. SPOOK includes all these elements. It is linearly implicit and linearly stable, it requires the solution of either one linear system of equations of one mixed linear complementarity problem per regular time step, and two of the same when an impact condition is detected. The changes in energy caused by constraints, impacts, and dry friction, are all shown to be strictly dissipative in comparison with the free system. Since all regularization and stabilization parameters are introduced in the physics, they map directly onto physical properties and thus allow modeling of a variety of phenomena, such as constraint compliance, for instance. Tutorial material is included for continuous and discrete-time analytic mechanics, quaternion algebra, complementarity problems, rigid body dynamics, constraint kinematics, and special topics in numerical linear algebra needed in the solution of the stepping equations of SPOOK. The qualitative and quantitative aspects of SPOOK are demonstrated by comparison with a variety of standard techniques on well known test cases which are analyzed in details. SPOOK compares favorably for all these examples. In particular, it handles ill-posed and degenerate problems seamlessly and systematically. An implementation suitable for large scale performance and accuracy testing is left for future work.

Die Filtration unter aggressiven Einsatzbedingungen, z.B. Einsatz in korrosiven Medien, Abgasfiltration, stellt besondere Anforderungen an das Filtermaterial. Sogenanntes &amp;quot;Liquid Phase Sintered Silicon Carbide&amp;quot; (LPS-SiC) erfüllt die Anforderungen sehr gut. Deshalb bestand das Ziel der Arbeit besteht darin, erstmals aus LPS-SiC asymmetrische keramische Membranen (grobporöses Substrat mit dünner, feinporiger Membran) herzustellen. Als Additivsystem fanden Yttriumoxid und Aluminiumoxid Verwendung. Es wurde Siliciumcarbid der Körnung F1200 auf Substrat der Körnung F500 abgeschieden. Dem Herstellungsverfahren kommt für die Qualität der Membran eine große Bedeutung zu. Daher wurden in dieser Arbeit folgende Beschichtungsmethoden untersucht, um die optimale Methode zu identifizieren: Tauchbeschichtung, elektrophoretische Abscheidung, Druckfiltration und Einsatz von Transfertapes (Transfertapes: Mischung aus Polyacrylatkleber und Pulver). Im Mittelpunkt stand dabei die Druckfiltration. Hierfür wurde eine neue Apparatur konzipiert und aufgebaut. Für die schlickerbasierten Methoden wurde ein wässriges System entwickelt, bei dem auf den Einsatz von organischen Hilfsstoffen verzichtet werden konnte. Die elektrostatische Stabilisierung konnte durch gezieltes Anlösen von Yttriumoxid, Ausfällen von feinskaligem Yttriumhydroxid und Belegung des Siliciumcarbids mit dem Yttriumhydroxid erreicht werden. Die Elektrophorese führte zu keinen befriedigenden Ergebnissen aufgrund des undefinierten spezifischen Widerstandes des Substrats (siehe Dissertation Jan Ihle, Bergakademie Freiberg 2004). Die Druckfiltration erwies sich als das geeignetste Verfahren. Mit ihr konnten ohne Einschränkungen hochwertige Membranen erzeugt werden. Druck und Zeit sind bei gegebenen Feststoffgehalt frei wählbar. Der Druck wurde zwischen 2*10E4 und 1*10E5 Pa variiert. Höherer Druck führte zu feineren Porengrößen (mittlere und maximale Porengröße). Mit der Druckfiltration konnten Membranen ohne makroskopische Defekte erzeugt werden. Sie führte im Vergleich aller Verfahren zu der geringsten Rauhtiefe der Membranen. Die Tauchbeschichtung ließ sich in diesem System nur über den Feststoffgehalt steuern. Membranen aus der Tauchbeschichtung wiesen makroskopische Fehler (große oberflächliche Poren) auf. Die Methode führte hinsichtlich Porengrößen und Rauhtiefe zu den schlechtesten Werten. Die Transfertape-Methode als neuartiger Ansatz erwies sich für das LPS-SiC System als noch nicht ausgereift. Das direkte Bekleben der Substrate war möglich. Hinsichtlich der Membrandicke sind aber Grenzen bei ca. 50 µm gesetzt. Darüber hinaus reißen die Membranen. Es wurden Schwankungen in der Entbinder- und Sinterschwindung verzeichnet. Weiterhin werden große Hohlräume im Substrat nicht von den Transfertapes abgeformt. Beide Effekte erhöhen die Spannungen beim Sintern, so dass bei geringeren Schichtdicken Risse entstehen. / Silicon Carbide (SiC) fulfills many requirements, e.g. a high robustness in terms of corrosion, which makes it a suitable Material for ceramic membranes. The aim of this work was to produce ceramic membranes out of porous liquid phase sintered Silicon Carbide (LPS-SiC). As additives Alumina and Yttria were used. The SiC based on commercial abrasive powders F1200 (Membrane) and F500 (Substrate). Different techniques of membrane formation were applied in order to find the optimum processing procedure: Dip Coating, Electrophoretic Deposition (EPD), Pressure Filtration and the usage of so called Transfer Tapes, a blend of Polyacrylate and ceramic powders). For the slip based methods a water based system was developed without the need of organic additives. A pure electrostatic stabilization was facilitated by solving Yttria with Hydrochloride Acid and precipitation, resulting in the coverage of the SiC particles with finely dispersed Yttria. The EPD was not successful due to a undefined specific resistance of the substrate. The pressure filtration turned out to be the best, most versatile method, leading to defect free membranes with the lowest measured surface roughness. The pressure ranged between 2*10E4 and 1*10E5 Pa. Higher pressure lead to finer pores. The Dip Coating was controlled only by the solids content. Membranes by Dip Coating showed macroscopic defects. As a new concept for ceramic membrane fabrication the Transfer Tapes needed further investigation. The direct gluing on the substrate was possible. The thickness of the membrane was limited to 50 microns in order to keep free of cracks. The Transfer Tapes exhibited pronounced fluctuations in the debinding and sintering shrinkage, leading to increased tension during sintering. Furthermore cavities, (e.g. big pores) were bridged. Both effects lead to increased tension during sintering.