Auswahl der wissenschaftlichen Literatur zum Thema „Contrôle par backstepping“

The slewing motion of a truss arm driven by a V-gimbaled control-moment gyro is studied. The V-gimbaled control-moment gyro consists of a pair of gyros that must precess synchronously. For open-loop slewing motion control, the controller design problem is simplified into finding a feedback controller to steer the two gyros to synchronously track a specific command. To improve the synchronization performance, the integral of synchronization error is introduced into the design as an additional state variable. Based on the second method of Lyapunov, an adaptive nonlinear feedback controller is designed. For more accurate but complicated closed-loop slewing motion control, the feedback linearization technique is utilized to partially linearize the nonlinear nominal model, where two specific output functions are chosen to satisfy the system tracking and synchronization requirements. The system tracking dynamics are bounded by properly determining system indices and command signals. For the partially linearized system, the backstepping tuning function design approach is employed to design an adaptive nonlinear controller. The dynamic order of the adaptive controller is reduced to its minimum. The performance of the proposed controllers is verified by simulation.

Les systèmes d'Equations aux Dérivées Partielles Hyperboliques Linéaires du Premier Ordre (EDPs HLPO) permettent de modéliser de nombreux systèmes de lois de conservation. Ils apparaissent, par exemple, lors de la modélisation de problèmes de trafic routier, d'échangeurs de chaleurs, ou de problèmes multiphasiques. Différentes approches ont été proposées pour stabiliser ou observer de tels systèmes. Parmi elles, la méthode de backstepping consiste à transformer le système originel en un système découplé pour lequel la synthèse de la loi de commande est plus simple. Les contrôleur obtenus par cette méthode sont explicites.Dans la première partie de cette thèse, nous présentons des résultats généraux de théorie des systèmes. Plus précisément, nous résolvons les problèmes de stabilisation en temps fini pour une classe générale d'EDPs HLPO. Le temps de convergence minimal atteignable dépend du nombre d'actionneurs disponibles. Les observateurs associés à ces contrôleurs (nécessaires pour envisager une utilisation industrielle de tels contrôleurs) sont obtenus via une approche duale. Un des avantages importants de l'approche considérée dans cette thèse est de montrer que l'espace généré par les solutions de l'EDPs HLPO considérée est isomorphe à l'espace généré par les solutions d'une système neutre à retards distribués.Dans la seconde partie de cette thèse, nous montrons la nécessité d'un changement de stratégie pour résoudre les problèmes de contrôle robuste. Ces questions surviennent nécessairement lorsque sont considérées des applications industrielles pour lesquelles les différents paramètres du système peuvent être mal connus, pour lesquelles des dynamiques peuvent avoir été négligées, de même que des retards agissant sur la commande ou sur la mesure, ou encore pour lesquels les mesures sont bruitées. Nous proposons ainsi quelques modifications sur les lois de commande précédemment développées en y incorporant plusieurs degrés de liberté permettant d'effectuer un compromis entre performance et robustesse. L'analyse de stabilité et de robustesse sous-jacente est rendue possible en utilisant l'isomorphisme précédemment introduit
Linear First-Order Hyperbolic Partial Differential Equations (LFOH PDEs) represent systems of conservation and balance law and are predominant in modeling of traffic flow, heat exchanger, open channel flow or multiphase flow. Different control approaches have been tackled for the stabilization or observation of such systems. Among them, the backstepping method consists to map the original system to a simpler system for which the control design is easier. The resulting controllers are explicit.In the first part of this thesis, we develop some general results in control theory. More precisely, we solve the problem of finite-time stabilization of a general class of LFOH PDEs using the backstepping methodology. The minimum stabilization time reachable may change depending on the number of available actuators. The corresponding boundary observers (crucial to envision industrial applications) are obtained through a dual approach. An important by-product of the proposed approach is to derive an explicit mapping from the space generated by the solutions of the considered LFOH PDEs to the space generated by the solutions of a general class of neutral systems with distributed delays. This mapping opens new prospects in terms of stability analysis for LFOH PDEs, extending the stability analysis methods developed for neutral systems.In the second part of the thesis, we prove the necessity of a change of strategy for robust control while considering industrial applications, for which the major limitation is known to be the robustness of the resulting control law to uncertainties in the parameters, delays in the loop, neglected dynamics or disturbances and noise acting on the system. In some situations, one may have to renounce to finite-time stabilization to ensure the existence of robustness margins. We propose some adjustments in the previously designed control laws by means of several degrees of freedom enabling trade-offs between performance and robustness. The robustness analysis is fulfilled using the explicit mapping between LFOH PDEs and neutral systems previously introduced

Abstract : Over the past three decades, various fields have witnessed a successful application of active magnetic bearing (AMB) systems. Their favorable features include supporting high-speed rotation, low power consumption, and rotor dynamics control. Although their losses are much lower than roller bearings, these losses could limit the operation in some applications such as flywheel energy storage systems and vacuum applications. Many researchers focused their efforts on boosting magnetic bearings energy efficiency via minimizing currents supplied to electromagnetic coils either by a software solution or a hardware solution. According to a previous study, we adopt the hardware solution in this thesis. More specifically, we investigate developing an efficient and yet simple control scheme for regulating a permanent magnet-biased active magnetic bearing system. The control objective here is to suppress the rotor vibrations and reduce the corresponding control currents as possible throughout a wide operating range. Although adopting the hardware approach could achieve an energy-efficient AMB, employing an advanced control scheme could achieve a further reduction in power consumption. Many advanced control techniques have been proposed in the literature to achieve a satisfactory performance. However, the complexity of the majority of control schemes and the potential requirement of powerful platform could discourage their application in practice. The motivation behind this work is to improve the closed-loop performance without the need to do model identification and following the conventional procedure for developing a model-based controller. Here, we propose applying the hybridization concept to exploit the classical PID control and some nonlinear control tools such as first- and second-order sliding mode control, high gain observer, backstepping, and adaptive techniques to develop efficient and practical control schemes. All developed control schemes in this thesis are digitally implemented and validated on the eZdsp F2812 control board. Therefore, the applicability of the proposed model-free techniques for practical application is demonstrated. Furthermore, some of the proposed control schemes successfully achieve a good compromise between the objectives of rotor vibration attenuation and control currents minimization over a wide operating range.
Résumé: Au cours des trois dernières décennies, divers domaines ont connu une application réussie des systèmes de paliers magnétiques actifs (PMA). Leurs caractéristiques favorables comprennent une capacité de rotation à grande vitesse, une faible consommation d'énergie, et le contrôle de la dynamique du rotor. Bien que leurs pertes soient beaucoup plus basses que les roulements à rouleaux, ces pertes pourraient limiter l'opération dans certaines applications telles que les systèmes de stockage d'énergie à volant d'inertie et les applications sous vide. De nombreux chercheurs ont concentré leurs efforts sur le renforcement de l'efficacité énergétique des paliers magnétiques par la minimisation des courants fournis aux bobines électromagnétiques soit par une solution logicielle, soit par une solution matérielle. Selon une étude précédente, nous adoptons la solution matérielle dans cette thèse. Plus précisément, nous étudions le développement d'un système de contrôle efficace et simple pour réguler un système de palier magnétique actif à aimant permanent polarisé. L'objectif de contrôle ici est de supprimer les vibrations du rotor et de réduire les courants de commande correspondants autant que possible tout au long d'une large plage de fonctionnement. Bien que l'adoption de l'approche matérielle pourrait atteindre un PMA économe en énergie, un système de contrôle avancé pourrait parvenir à une réduction supplémentaire de la consommation d'énergie. De nombreuses techniques de contrôle avancées ont été proposées dans la littérature pour obtenir une performance satisfaisante. Cependant, la complexité de la majorité des systèmes de contrôle et l'exigence potentielle d’une plate-forme puissante pourrait décourager leur application dans la pratique. La motivation derrière ce travail est d'améliorer les performances en boucle fermée, sans la nécessité de procéder à l'identification du modèle et en suivant la procédure classique pour développer un contrôleur basé sur un modèle. Ici, nous proposons l'application du concept d'hybridation pour exploiter le contrôle PID classique et certains outils de contrôle non linéaires tels que contrôle par mode glissement du premier et du second ordre, observateur à grand gain, backstepping et techniques adaptatives pour développer des systèmes de contrôle efficaces et pratiques. Tous les systèmes de contrôle développés dans cette thèse sont numériquement mis en oeuvre et évaluées sur la carte de contrôle eZdsp F2812. Par conséquent, l'applicabilité des techniques de modèle libre proposé pour l'application pratique est démontrée. En outre, certains des régimes de contrôle proposés ont réalisé avec succès un bon compromis entre les objectifs au rotor d’atténuation des vibrations et la minimisation des courants de commande sur une grande plage de fonctionnement.

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CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior
O presente trabalho tem como objetivo aplicar e comparar técnicas de controle lineares e não lineares no controle de estabilidade de um quadricóptero. Inicialmente, apresenta-se um modelo dinâmico da aeronave para a simulação e controle do sistema. Em seguida, descreve-se os princípios de funcionamento do veículo e algumas características importantes na construção do quadricóptero. Com base no modelo dinâmico, as técnicas de controle são utilizadas para projetar os controladores. Quatro diferentes controladores foram projetados: um controlador PID, um controlador LQR, um controlador com base na teoria de Lyapunov e um controlador utilizando a técnica de Backstepping. Eles são aplicados para controlar a atitude da aeronave, tendo como principal tarefa a estabilização do quadricóptero em voo. Por fim, os controladores são comparados, validados e os resultados das simulações e da implementação real no quadricóptero são apresentados. Os melhores resultados para o controle de estabilidade do quadricóptero são obtidos utilizando a técnica de controle não linear Backstepping.
This present work aims to apply and compare linear and nonlinear control techniques in attitude stabilization of a quadricopter. At first, is presented a aircraft dynamic model for simulation and control of the system. Then, will be described the principles of operation and some important characteristics about quadricopter’s assembling. Based on dynamic model, the control techniques are used to design the controllers. Four different controllers were designed: a PID controller, a LQR controller, a Lyapunov’s stability theory based controller, and a backstepping controller. They are applied to control the aircraft attitude, having as main task the inflight stabilization of quadricopter. At the end, the controllers are compared, validated and the simulation results and real implementation are presented. The best results of quadricopter attitude control are obtained using the nonlinear control technique of Backstepping.

Dissertação (mestrado) - Universidade Federal de Santa Catarina, Centro Tecnológico, Programa de Pós-Graduação em Engenharia de Automação e Sistemas, Florianópolis, 2010
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Estudamos, nesta dissertação, a aplicação de uma técnica de controle do tipo backstepping a sistemas de pós-tratamento de gases de escape em veículos diesel, operando com catalisadores SCR (selective catalytic reduction). Projetamos a lei de controle para um modelo reduzido do sistema SCR, adequado ao controle em malha fechada e também à implementação nas unidades de controle eletrônico de veículos comerciais. Avaliamos posteriormente o desempenho dessa lei de controle por meio de ciclos de testes estático e dinâmico, tanto para situações em que os parâmetros de entrada assumem valores nominais, quanto para aquelas em que esses parâmetros apresentam perturbações. A dissertação inicia com uma visão geral sobre os sistemas de controle dos veículos diesel e princípios de funcionamento de seus motores, passando pela formação de poluentes e pelas diferentes alternativas de redução das emissões nocivas de motores diesel, em especial de particulados e óxidos de nitrogênio. Em seguida, concentra-se na tecnologia SCR - utilizada para redução dos óxidos de nitrogênio - e sua modelagem matemática para, finalmente, aplicar a técnica de controle não-linear backstepping aos sistemas de pós-tratamento baseados em catalisadores SCR. Os resultados, obtidos por meio de simulações computacionais, mostram que o controle não-linear projetado oferece uma eficaz alternativa para melhorar a robustez dos sistemas de pós-tratamento analisados, quando esses estão sujeitos a variações paramétricas tipicamente encontradas nos motores diesel.

Esta tesis desarrolla un procedimiento para el diseño e implementación experimental de un sistema de control no lineal backstepping para controlar simultáneamente el nivel y la temperatura en el proceso tanque con agua. El sistema de control diseñado combina el modelo dinámico no lineal de Lagrange del proceso con un controlador backstepping multivariable. Los estudios de simulación y experimentación realizados demostraron el buen rendimiento de este controlador, el cual se comparó con el rendimiento de un controlador PID MIMO
This thesis develops a design and real-time implementation procedure of a nonlinear multivariable backstepping control system for controlling simultaneously level and temperature in a water tank process. The designed control system combines the nonlinear dynamic Lagrange model of the process with a multivariable backstepping controller. Intensive simulation studies and experimental results demonstrate the good performance of this controller. The performance of the backstepping controller was compared with those of a PID MIMO controller

Les problématiques de recherche abordées dans cette thèse concernent la conceptualisation, la modélisation et la commande générique des robots mobiles lors de leur évolution en milieux extérieurs et en présence de glissement pour des applications de suivi de précision. Ainsi, ce mémoire synthétise dans un premier temps les développements et résultats obtenus lors du suivi de trajectoire (localisation absolue), puis synthétise ensuite ceux obtenus lors de suivi de structure et de cible (localisation relative). Une dernière partie introduit un concept de plateforme robotique reconfigurable et sa commande associée pour adapter l’assiette et les dimensions du châssis en fonction de la topographie du terrain.Pour chaque application de suivi, ce mémoire présente un panel de lois de commande originales pour des robots différentiels, à un train et à deux trains directeurs. Chaque modalité de commande est présentée en quatre étapes : modélisation, estimation, commande et expérimentations. La première contribution majeure de la thèse concerne l’estimation du glissement. Cette dernière est adaptative et basée modèle. Elle intègre la modélisation cinématique étendue seule ou couplée à la modélisation dynamique du robot mobile pour assurer une estimation intègre quels que soient la vitesse, les phénomènes dynamiques rencontrés et la nature du sol. La seconde contribution majeure concerne le développement d’une stratégie de commande générique pour les robots mobiles. Cette stratégie est basée sur le principe de la commande en cascade (ou par backstepping) et est déclinée dans ce mémoire à travers un panel de lois de commande. Cette méthodologie de commande, lorsqu’elle est associée à l’observation du glissement précédent, permet d’obtenir des performances de suivi accrues quel que soit le contexte rencontré. L’ensemble des algorithmes ont été validés en simulation et/ou expérimentalement à l’aide de différentes plateformes robotiques en contextes réels
This work is focused on the conceptualization, the modeling and the genericcontrol of mobile robots when moving in off-road contexts and facing slipperyterrains, especially for very accurate tracking and following applications. Thisthesis summarizes the proposed methods and the obtained results to addressthis research issue, first for path following applications (absolute localization)and then for edge and target tracking applications (relative localization). A finalsection of this thesis introduces an adaptive robotic concept and its associatedcontroller allowing the adaptation of the pose (position and orientation) of thechassis with respect to the environment topography.For each application, this thesis introduces a panel of innovative control algorithmsfor controlling skid-steering, two-wheel steering and four-wheel steeringmobile robots. Each algorithm of the panel is described, in this thesis, infour steps : modeling, estimation, control and experiments.The first main contribution of this thesis deals with the slippage estimation.The latter is adaptive and model-based. It also includes the extended kinematicmodeling only or together with the dynamic modeling of the mobile robot toensure a robust estimation of the slippage whatever the speed of the robot, encountereddynamic phenomena or even ground characteristics.The second main contribution deals with the design of a generic control approachfor mobile robots when path following and target tracking. The proposedstrategy is mostly based on a backstepping method and is illustrated inthis thesis via a panel of control laws. When combining this proposed controlapproach with the slippage estimation described above, significant improvedtracking and following performances are obtained (in term of stability, repeatability,accuracy and robustness) whatever the encountered context.All algorithms have been tested and validated through simulations and/orfull-scale experiments, indoor and off-road, with different mobile robots

En aérospatial, les contraintes de masse ont conduit à utiliser des structures plus légères et par conséquent plus souples, induisant de nouveaux objectifs de commande, comme la réduction des efforts structuraux. Pour satisfaire ces objectifs, les modes de flexion doivent être considérés dès la synthèse de la loi de commande, ce qui entraîne certaines contraintes comme les non linéarités, le sous actionnement et l’altération des mesures par les modes souples. En considérant ces contraintes, cette thèse traite de la synthèse d’une méthode de commande non linéaire pour les systèmes aérospatiaux souples. Nous nous intéressons particulièrement au problème d’atténuation des oscillations provoquées par les modes souples. Pour cela, nous définissons une classe de système non linéaire, sous actionnée et à minimum de phase, représentative des systèmes aérospatiaux souples. Pour cette classe de système, nous proposons une loi de commande non linéaire synthétisée par retour d’état en utilisant des changements de variables et la technique du backstepping. La synthèse est effectuée de façon à améliorer le régime transitoire des modes souples. Les états souples n’étant pas mesurés, le problème du retour de sortie est également traité par l’intermédiaire d’observateurs adaptatifs (à temps fini et asymptotique). Des incertitudes sur la pulsation et l’amortissement des modes souples sont en particulier considérées. La méthode proposée est illustrée par des simulations numériques réalisées sur un lanceur et un avion hypersonique
Due to mass constraints aerospace systems tend to have lightweight and flexible structures leading to new control objectives such as structural load reduction. To fulfil these objectives, flexible modes must be considered from the design of the controller, requiring to consider some constraints such as nonlinearities, underactuation, or measurement corruption terms. Consider these constraints, this thesis treats the design of a nonlinear control method for flexible aerospace systems. We particularly focus on the problem of reducing oscillations caused by the bending modes. To do that, we define a class of nonlinear system which is both underactuated and minimum phase and that represents flexible aerospace systems. Consider this class, we propose a nonlinear full-state controller based on changes of coordinates and the backstepping technique. The control design is carried out to enhance the transient of the flexible modes. Flexiblestates being not measured, the output-feedback problem is also treated through adaptive observers (finite-time and asymptotic). Uncertainties of natural damping and frequency of the bending modes are particularly considered. The proposed method is illustrated by numerical simulations performed on a space launch vehicle and an hypersonic aircraft

De nos jours, l’exploitation des énergies renouvelables afin de générer de l’électricité est en croissance soutenue puisqu’elles sont à ressource illimitée, gratuites et ne provoquent pas de déchets ou d’émissions polluantes. Dans cette thèse, on se propose d’étudier l’un de ces types d’énergie à savoir l’énergie issue des courants marins. Il s’agit plus particulièrement de s’intéresser à la commande tolérante aux défauts des systèmes de récupération de l’énergie des courants marins. Le potentiel de la production d'électricité à partir des courants marins est estimé à une production de 100 GW dans le monde. Cependant, ces chaînes de conversion d’énergie sont exposées et soumises à des contraintes fonctionnelles et environnementales importantes et sévères. Ces contraintes favorisent inévitablement la dégradation des performances des différents blocs fonctionnels de ces systèmes et l’accélération de leur processus de vieillissement, conduisant ainsi à l’apparition des défauts d’origines mécaniques et/ou électriques. Ainsi, la mise en place des techniques de commande tolérantes aux défauts de ces systèmes permettra d’améliorer la fiabilité, les performances et réduire les coûts relatifs au fonctionnement en mode dégradé et aux opérations de maintenance. Le but des travaux de cette thèse est l’étude, la modélisation et la simulation d’une chaîne de conversion hydrolienne à vitesse variable dans le cas sain et le cas d’un défaut (soit au niveau de la machine synchrone à aimants permanents (défaut de la désaimantation) ou au niveau du convertisseur statique (défaut d’un circuit ouvert d’un interrupteur). Il s’agira donc d’étudier les différentes commandes tolérantes aux défauts utilisées en cas d’un défaut au niveau de la génératrice ou au niveau de l’électronique de puissance associée
Nowadays, the exploitation of renewable energies in order to generate electricity is growing steadily because they are unlimited resources, free and don’t cause waste or polluting emissions. In this context, it is proposed to study one of these types of energy, which is marine currents energy. In particular, we are interested in fault-tolerant control of tidal turbines. The potential for power generation from marine currents is estimated at 100GW in the world. However, tidal turbines are submitted to severe operational and environmental constraints. These constraints inevitably will lead to these systems performance degradation and the acceleration of their aging process, thus leading to the occurrence of mechanical and/or electrical faults. The implementation of fault-tolerant control techniques will improve the tidal turbines reliability, performance, and reduce costs relating to maintenance operations. The aim of this thesis is to study, model, and simulate a tidal turbine system in healthy and faulty conditions (either in the converter (switch open circuit) or in the permanent magnet synchronous generator (magnet failure). Various fault-tolerant control approaches are therefore evaluated and compared under these specific failure It will therefore be necessary to study the various fault-tolerant controls used in the event of a fault in the generator or in the associated power electronics

Orientador: Celso Pascoli Bottura
Tese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Eletrica e de Computação
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Resumo: Esta tese apresenta contribuições para o controle inteligente de sistemas não lineares com incertezas paramétricas e funcionais. São desenvolvidas duas abordagens. Em primeiro lugar, é proposta uma modificação ao backstepping adaptativo clássico, fundamentada em Extensão do Princípio de Invariância de La Salle que contempla o caso em que a derivada da função de Lyapunov ao longo das soluções do sistema é permitida ser definida positiva em regiões limitadas do espaço de estados, que favorece o pleno uso de técnicas de otimização baseadas em computação evolutiva com vistas à melhoria de desempenho da solução em termos de redução expressiva de esforço de controle e conformação da resposta transitória conforme critérios de tempo de estabilização, magnitude de sobre-sinal, etc. Em segundo lugar, é proposta uma metodologia de controle adaptativo neural, estruturada na técnica de backstepping, aplicável a sistemas não lineares com incertezas com múltiplas entradas e múltiplas saídas compostos de subsistemas interconectados cujas matrizes de entrada apresentam funções não lineares e cujas interconexões entre subsistemas também apresentam não linearidades. A estratégia apresentada propõe-se a sanar várias das dificuldades encontradas em metodologias análogas, eliminando a questão de singularidade nas leis de controle, evitando o uso de funções de Lyapunov com integrais e suprimindo a necessidade de introdução de derivadas dos controladores virtuais nas redes neurais, o que se traduz em projetos de controle menos complexos, com menor custo computacional e com melhor desempenho na solução em comparação aos métodos similares existentes
Abstract: This thesis presents contributions to the intelligent control of nonlinear systems with parametric and functional uncertainties. Two approaches are advanced. Firstly, it is proposed a modification to the traditional adaptive backstepping grounded on an Extension to the La Salle¿s Invariance Principle that allows the Lyapunov function derivative along the systems solutions to be positive definite in limited regions of the state space, which favours the deployment of optimisation techniques based on evolutionary computation aiming at the improvement of the solution performance in terms of an expressive reduction of control effort and transient conformation according to criteria such as settling time, overshoot magnitude, etc. Secondly, it is proposed a neural adaptive control methodology, structured on the backstepping technique, applicable to nonlinear systems with uncertainties with multiple inputs and multiple outputs constituted of interconnected subsystems whose input matrices feature nonlinear functions and whose subsystems interconnections also bear nonlinearities. The advanced strategy removes several difficulties found in analogous methodologies, namely eliminating control laws singularity issues, avoiding the use of Lyapunov functions with integrals, and suppressing the need for the introduction of virtual controllers¿ derivatives into the neural networks, which leads to less complex control designs, with decreased computational cost and with better response performance in comparison with similar existing methods
Doutorado
Automação
Doutor em Engenharia Elétrica

La chirurgie minimalement invasive est un domaine de recherche très actif puisqu’elle permet d’envisagerdes thérapies ciblées et des diagnostics in situ tout en minimisant traumatismes, effets secondaires et tempsde convalescence. En particulier, l’utilisation de systèmes miniaturisés actionnés à distance ouvre la voie àune navigation dans le système cardiovasculaire, permettant ainsi le ciblage et l’intervention sur zones dif-ficilement accessibles du corps humain. L’objectif de cette thèse est de proposer i) un état de l’art sur lamodélisation des forces s’exerçant sur un ou plusieurs microrobots naviguant dans des vaisseaux sanguins,ii) des représentations d’état exploitables à des fins de commande et d’observation, iii) différentes synthèsesde lois de commande pour stabiliser un ou plusieurs microrobots le long d’une trajectoire de référence, iv)des observateurs d’état pour reconstruire les états non mesurables du système. Un microrobot magnétiquenaviguant dans un vaisseau sanguin subit la force de traînée, les forces surfaciques, de contact, d’interactionmagnétique, et son poids apparent. Son actionnement est assuré par l’application de champs ou de gradientsde champ magnétiques, et sa localisation est assurée par un imageur médical. La dynamique du ou desmicrorobots (système réduit) est sous forme d’état non linéaire affine en la commande avec dérive, et dé-pend de plusieurs paramètres physiologiques incertains, en particulier de la vitesse du sang, qui est difficileà mesurer. La dynamique du flux sanguin (système fluidique) est alors modélisée sous forme d’une repré-sentation d’état autonome, combinée avec le système réduit pour aboutir au système étendu. L’objectif decommande est de stabiliser les états du système réduit le long d’une trajectoire de référence. Une commandestabilisante est synthétisée par backstepping, mais elle n’est pas utilisable en l’état. Des observateurs baséssur le théorème de la valeur moyenne et sur une immersion sont synthétisés respectivement dans le cas oùla pulsation cardiaque est connue ou non. La stabilité du retour de sortie est alors démontrée. La stabilitéet la robustesse aux bruits de mesure, aux incertitudes paramétriques, et aux erreurs de modélisation desapproches proposées sont alors illustrées par des simulations
Minimally invasive surgery is an active research area since such systems have the potential to perform complex surgical procedures such as targeted therapies or in situ diagnosis, while minimizing trauma, side effects and recovery time. Miniaturized systems magnetically propelled by remote actuation can achieve swimming through the blood vessels network in order to provide targeted therapy, even for hard-to-reach human organs. This PhD thesis aims at addressing i) a review on the modeling of microrobots immersed in blood vessels, ii) a classification of the state space forms of such systems, iii) the synthesis of state feedbacks ensuring the stabilization of the microrobots along a reference trajectory, iv) the synthesis of observers to rebuild the unmeasured state variables. Magnetic microrobots swimming in a blood vessel face the hydrodynamic drag, surfacic and contact forces, magnetic interactions, and their apparent weight. These untethered robots are actuated by magnetic fields or magnetic gradients generation, and their localization is ensured by a medical imager. The microrobots dynamics (the so-called reduced system) lead to a nonlinear affine control subsystem with drift, and exhibits many uncertain physiological parameters, such as the blood velocity which can hardly be measured. The blood flow dynamics (the so-called fluidic system) are then modeled as an autonomous subsystem. These two subsystems result in an extended system describing the whole (robot and fluid) dynamics. The control objective is to stabilize the state of the reduced system along a reference trajectory, which is performed by an adaptive backstepping synthesis. Yet the full state is not accessible. We then synthesize either MVT or immersion based observers for the extended system, when the blood pulsation is either known or not. The output feedback stability is then proved. The stability and robustness to output noise, parametric uncertainty, and modeling errors are then illustrated by simulations

Neste artigo, é proposta uma nova abordagem de aproximação adaptativa baseada na técnica de backstepping para o controle do ângulo de arfagem (modo de operação SISO) de um sistema eletromecânico conhecido como Twin-Rotor MIMO System -- TRMS. Aproximadores universais na lei de controle são usados para estimar a parte desconhecida da dinâmica, usando modelos nebulosos Takagi-Sugeno (TS). De modo a se reduzir a complexidade no projeto do controlador por backstepping, filtros de comando são utilizados para evitar o cálculo explícito das derivadas temporais das ações de controle virtuais. Uma modificação de zona morta, desligando a lei de adaptação na região em que não se pode garantir a convergência da função de Lyapunov, é utilizada de modo a evitar o problema de deriva dos parâmetros. A eficácia do projeto do controlador é investigada por meio de simulações numéricas, enfatizando-se a redução no número de parâmetros a serem estimados.

When developing a machine intended for interaction with humans such as rehabilitation equipment or powered prostheses, it is useful to test in simulation prior to hardware implementation, avoiding safety hazards. Few models of the human for such purposes are seen in the literature. This paper moves toward the realization of such a model by developing a simple muscle-actuated system and related controller. The backstepping control methodology is implemented such that the controller accounts for all of the levels of intricacy presented by the Hill muscle model as an actuator, including the activation dynamics. The neural inputs are used as the actual controls. To be able to derive the control law, a modified strict-feedback form of the model is also developed. Stable tracking performance is then achieved in simulation.

Neste artigo, a partir da apresentação de um esquema de busca extremal baseada no méetodo do gradiente para compensação da equação diferencial parcial (EDP) da onda, associada a um mapeamento estático a ser otimizado, estende-se a dinâmica de atuação para cascatas de EDPs, especicamente para: (a) uma EDP anti-estável da onda como uma interconexão de duas EDPs de transporte (atraso), e (b) uma EDP anti-estável da onda com entrada atrasada. As leis de controle dos sistemas em malha fechada são propostas a partir da aplicação de transformações do tipo backstepping e da formulação usando condições de Neumann e Dirichlet. Simulações numéricas ilustram os resultados teóricos.

Abstract A backstepping controller is designed for lateral guidance of the passenger car in automated highway systems. In this design, the vehicle lateral tracking error is viewed as the output regulated by the relative yaw angle of the car with respect to the road centerline, and the relative yaw angle is controlled by the vehicle’s front wheel steering angle. The closed loop performance of lateral and yaw dynamics can be specified and guaranteed simultaneously in this approach. A smooth road model is used in calculating the feedforward part of the steering command. Nonlinear position feedback, which acts as low gain control at small tracking errors and high gain control at larger tracking errors, is introduced to compromise between passenger ride comfort and tracking accuracy. Simulation results conducted on the complex vehicle model show the effectiveness of the backstepping design approach.

In this paper a nonlinear model-based controller is designed to globally asymptotically stabilize a single-degree-of-freedom shape memory alloy (SMA) actuated manipulator. A three part model was constructed based on the dynamics/kinematics of the arm, the thermomechanical behavior of SMA’s, and an assumed heat transfer model consisting of electrical heating and natural convection. The backstepping control is used to calculate the applied voltage to the SMA wire. Initially, the SMA’s wire stress is assumed to be the control input of the system. The stress is then chosen to asymptotically stabilize the desired position. The applied voltage to the SMA wire is the actual control input. This voltage is calculated based on the desired stress and the SMA’s thermomechanical and heat transfer models. It is shown that the calculated voltage can globally asymptotically stabilize the system. Numerical simulations are performed to investigate stabilizing performance as well as other issues such as robustness. The results demonstrate that the backstepping controller designs is highly accurate in stabilization.

Neste artigo, é proposto o projeto e análise do controlador extremal estocástico baseado no algoritmo do Gradiente na presença de atrasos de entrada e saída. Um novo preditor baseado na estimativa da Hessiana desconhecida será apresentado e incorporado à malha fechada. A estabilidade exponencial e convergência a uma pequena vizinhança do ponto de extremo são obtidas. Este resultado é rigorosamente alcançado utilizando a transformação backstepping e teoria da média em dimensões infinitas. Um exemplo numérico é apresentado para ilustrar a eficiência do controlador extremal estocástico baseado em preditor para compensação de atrasos.

Esse artigo apresenta o desenvolvimento e análise de um algoritmo backstepping aplicado ao controle de corrente de um conversor estático conectado à rede. A análise do sistema proposto é realizada com apresentação de uma metodologia de projeto de ganhos do controlador e vericação do impacto das variações paramétricas. Assim, o projeto do sistema é realizado de uma forma simples, em que a escolha de ganhos e associada a dinâmica requerida. Resultados de simulações são apresentados para validar o método proposto.

Abstract A desired compensation adaptive robust control (DCARC) approach is proposed for nonlinear systems having both parametric uncertainties and uncertain nonlinearities. DCARC of nonlinear systems transformable to a normal form is first solved. A DCARC backstepping design is then developed to overcome the design difficulties associated with unmatched model uncertainties. The proposed DCARC has the unique feature that the adaptive model compensation part depends on the reference trajectory and parameter estimates only. Such a structure has several implementation advantages. First, the regressor in the model compensation part can be calculated off-line and on-line computation time may be reduced. Second, the interaction between the parameter adaptation and the robust control law is minimized, which may facilitate the controller gain tuning process considerably. Third, the effect of measurement noise is minimized since the regressor does not depend on actual measurements. As a result, a fast adaptation rate may be chosen in implementation to speed up the transient response and to improve overall tracking performance. These claims have been verified in the comparative experimental studies for the control of robot manipulators.

Neste artigo, a otimalidade inversa é garantida em controle extremal escalar baseado no método de Newton sujeito a atrasos de entrada e saída. Diferente de trabalhos anteriores, um novo preditor com uma estimativa da inversa da Hessiana baseada em perturbações é incorporado à malha fechada tal que, a taxa de convergência do controlador em tempo real pode ser especificada pelo usuário, ao invés de ser dependente da Hessiana desconhecida do mapa estático não-linear a ser otimizado. A estabilidade exponencial e a convergência para uma pequena vizinhança do ponto extremo desconhecido são alcançadas utilizando a transformação backstepping e a teoria da média em dimensões infinitas. Aplica-se um filtro passa-baixa (com um polo suficientemente alto) na realimentação do preditor que permite aplicação da técnica do teorema da média de Hale e Lunel para equações diferenciais funcionais e também estabelece o resultado da otimalidade inversa para o sistema de malha fechada. A otimalidade inversa é pela primeira vez demonstrada em projetos de controle extremal baseado no método de Newton e justifica o uso heurístico de filtro passa-baixa entre o sinal de demodulação e o integrador, que tem sido historicamente utilizado em implementações de controle extremal sem atrasos.