Cette thèse de doctorat a été réalisée dans le cadre d’une convention CIFRE établie entre le laboratoire LAMIH UMR CNRS 8201 et l’équipementier automobile Valeo. Les problématiques de la thèse s’inscrivent dans un contexte proche de l’industrialisation à savoir l’estimation des couples embrayages lors des phases de changement de rapport dans une transmission à double embrayage et le contrôle de la vitesse de glissement de l’embrayage pour une transmission à simple ou à double embrayage. Afin de répondre à la problématique d’estimation de couple embrayage, un capteur virtuel de couple a été développé. Ce capteur virtuel est composé d’une estimation de la torsion des arbres de transmission basée sur une méthode d’ajout de dents virtuelles dans les capteurs incrémentaux d’une part, et d’un observateur Takagi-Sugeno discrétisé dans le domaine angulaire d’autre part. Ce procédé a permis l’estimation des couples embrayages d’une transmission à double embrayage sur une plateforme de simulation fournie par Valeo comportant un modèle complet de véhicule. Le procédé a également été testé sur des données réelles de débattement de double volant amortisseur, des estimations en ligne du couple moteur instantané acyclique et du couple embrayage ont alors été obtenues. Au cours de l’étude dédiée au glissement contrôlé de l’embrayage, une stratégie de contrôle robuste aux perturbations extérieurs induites par le conducteur et aux dispersions du système a été développée. Cette stratégie permet de répondre aux spécifications du cahier des charges en simulation. La stratégie de glissement contrôlé a également été validée sur véhicule lors d’essais sur piste et sur banc à rouleau. / This PhD has been done in an industrial framework with the so-called automotive equipment manufacturer Valeo and the laboratory of Automatic Control, Mechanics, Informatics and Human Sciences LAMIH UMR CNRS 8201 of Valenciennes, France. The issues of this PhD are closed to the industrialization context such as the clutch torque estimation during the gear shifting phases in a dual clutch transmission and the clutch slip speed control. In order to solve the inline clutch torque estimation issues, a virtual torque sensor has been developed. On one hand, this virtual sensor is composed of a shaft torsion angle estimation based on a method of virtual tooth adding into the encoder sensors. On another hand, discrete angular domain unknown input Takagi-Sugeno observer is used for the estimation of the dynamic part of transmitted torque. This methodology has permitted the estimation of the transmitted clutch torque of a dual clutch transmission in simulation. The simulation results have been obtained on a simulation platform provided by Valeo, including a complete vehicle model. The methodology has also been tested on real data of a dual mass flywheel angular deflection. Thus, online estimation of instantaneous acyclic engine torque and transmitted clutch torque has been obtained. Concerning the slip control, a robust control strategy against the external disturbances leaded to the driver and the system parameters incertitude has been developed. This strategy permits to ensure the required specifications in simulation. The strategy has been also validated on vehicle during track trials.

By exploiting the Projection Lemma, this thesis provides less conservative LMI-like conditions for mixed H2 and H_inf control of continuous-time systems than those appeared in the current literature. The same technique has been extended to problems with time-invariant polytopic uncertainties. Numerical examples are illustrated to show improvement of the proposed results. Finally, an attempt is made to apply the Projection Lemma to stability analysis and design of systems with time-varying polytopic uncertainties.

In this thesis, an LMI-based pole-clustering characterization for descriptor systems is investigated. A necessary and sufficient condition for checking simultaneously the regularity, impulse immunity, and finite eigenvalues locating in the generalized LMI regions is derived. Since uncertainty exists inevitably in control systems, we propose two sufficient conditions to guarantee the robust pole clustering in the generalized LMI regions for uncertain descriptor systems with two types of uncertainties, i.e. the norm bounded uncertainty and the convex polytopic uncertainty. The LMI-based state feedback controller design methods are developed as well. Finally, the validity and the feasibility of our theoretical results are verified by the numerical simulation results of several examples.

The paper investigates problems of designing controllers to linear time-invariant continuous descriptor systems subject to norm-bounded structured uncertainty so that the closed-loop systems are admissible or D-admissible with their transfer matrices having H-infinite norm bounded by a prescribed value. The constant state feedback and the dynamic output feedback designs are addressed. In both design methods, sufficient LMI conditions are derived to guarantee achievement of the desired specifications, such as robust H-infinite norm and pole-clustering constraints. Finally, two numerical examples are shown for the illustration.

In a context of heightened requirements for safety-critical embedded systems and ever-increasing costs of verification and validation, this research proposes to advance the state of formal analysis for control software. Formal methods are a field of computer science that uses mathematical techniques and formalisms to rigorously analyze the behavior of programs. This research develops a framework and tools to express and prove high level properties of control law implementations. One goal is to bridge the gap between control theory and computer science. An annotation language is extended with symbols and axioms to describe control-related concepts at the code level. Libraries of theorems, along with their proofs, are developed to enable an interactive proof assistant to verify control-related properties. Through integration in a prototype tool, the process of verification is made automatic, and applied to several example systems.In a context of heightened requirements for safety-critical embedded systems and ever-increasing costs of verification and validation, this research proposes to advance the state of formal analysis for control software. Formal methods are a field of computer science that uses mathematical techniques and formalisms to rigorously analyze the behavior of programs. This research develops a framework and tools to express and prove high level properties of control law implementations. One goal is to bridge the gap between control theory and computer science. An annotation language is extended with symbols and axioms to describe control-related concepts at the code level. Libraries of theorems, along with their proofs, are developed to enable an interactive proof assistant to verify control-related properties. Through integration in a prototype tool, the process of verification is made automatic, and applied to several example systems.

La pile à combustible (PàC) est un dispositif qui transforme l'énergie chimique en énergie électrique. Ce dispositif nécessite un certain nombre d’auxiliaires pour son fonctionnement. Afin d'assurer des performances en termes de sécurité, de fiabilité et de durée de vie de la PàC, des systèmes de diagnostic et de commande adéquats sont indispensables. Ainsi, cette thèse est une contribution au problème du diagnostic de défauts et à la commande de la PàC de type PEM. Le premier volet de ce travail est consacré au développement de méthodes de diagnostic appliquées à la PàC. Pour ce faire, deux approches ont été proposées. La première concerne la synthèse d’un filtre H-/H∞ permettant la détection de défauts capteurs et actionneurs tout en assurant un niveau de robustesse vis-à-vis d'éventuelles perturbations. En tenant compte des caractéristiques du système de la PàC, les conditions d'existence et de stabilité du filtre sont données sous la forme de LMI. La seconde approche traite le problème de la détection des défauts paramétriques. Pour cet objectif, un observateur adaptatif a été proposé, ce dernier permet d'estimer la valeur du paramètre susceptible de présenter une défaillance. Cette méthode donne la possibilité d'estimer simultanément les défauts paramétriques et les états non mesurés du système. Le deuxième volet de la thèse est dédié à la commande du système PàC. Le but est de synthétiser une loi de commande par rétroaction qui permet de répondre à la sollicitation de la charge tout en respectant une contrainte de fonctionnement nominal de la PàC. La synthèse de cette loi de commande a été réalisée en prenant compte tout le caractère non linéaire du système / The fuel cell is a device that transforms the chemical energy in electricity. This device requires some auxiliaries for its operation. In order to ensure the performances in terms of security, reliability and life cycle of the fuel cell, adequate diagnostic and control systems are indispensables. This thesis is a contribution to the problem of faults diagnosis and control of PEM Fuel Cell. The first part of this work is dedicated to the development of diagnostic methods applied to the fuel cell. To do this, two approaches are proposed. The first one concerns the synthesis of a H-/H∞ filter allowing the sensors and actuators faults detection while ensuring a level of robustness towards disturbances. Taking into account the fuel cell system characteristics, the conditions for existence and stability of the filter are given in the form of Linear Matrix Inequalities (LMI). The second approach deals with the problem of parametric faults detection. For this purpose, an adaptive observer has been proposed, which makes it possible to estimate the value of the parameter likely to exhibit a failure. This method gives the possibility of simultaneously estimating the parametric faults and the unmeasured states of the system. The second part of the thesis is dedicated to the control of the fuel cell system. The purpose is to synthesize a feedback control law that allows to answer the load request while respecting a nominal operating constraint of the fuel cell. Such a functioning allows to have a better efficiency while preserving the state of health of the fuel cell. The control law is obtained by using the original nonlinear model and without any kind of linearization

O objetivo do trabalho é apresentar dois algoritmos para a solução de problemas de controle ótimo quadrático robusto com restrições, dentro de um contexto de controladores preditivos (MPC do inglês Model Predictive Control). Inicialmente apresentamos uma breve introdução aos algoritmos MPC, com ênfase na abordagem do controlador linear quadrático. Em seguida são apresentados os dois algoritmos de interesse, que utilizam técnicas de otimização LMI. Dessa forma as restrições e as incertezas podem ser colocadas em formas computacionalmente tratáveis. Por fim são realizadas simulações e comparações entre esses algoritmos, bem como com técnicas de MPC encontradas na literatura atual. / The goal of the work is to present two algorithms for the solution of robust quadratic optimal control problems with restrictions, within a model predictive control (MPC) setup. Initially we present a brief introduction of the MPC algorithms, emphasizing the linear quadratic controller approach. Next the two algorithms of interest, using LMI optimization techniques, are presented. By using this technique the restrictions and uncertainties can be written in a computational way. Finally some simulations and comparisons between these algorithms, as well as with MPC techniques found in the current literature, are performed.

Cette thèse a pour objectif la modélisation et la commande d'un robot parallèle actionné pneumatiquement destiné à des applications de prise et dépose d'objets. Les actionneurs pneumatiques sont des actionneurs à bas coût et ayant des rapports poids/puissance plus importants que les actionneurs électriques. Ceci a pour avantage de réduire le coût de revient du robot en augmentant sa capacité de charge. Cependant, du fait des fortes non linéarités qui les caractérisent (compressibilité de l'air, caractéristique de la valve, frottement, hystérésis ...), le principal obstacle à leur utilisation en robotique est leur commande de façon précise et robuste. C'est pour cela que plusieurs stratégies de commande ont été proposées et implémentées expérimentalement sur un banc d'essai utilisant trois types d'actionneurs pneumatiques: deux vérins et des muscles artificiels travaillant en mode antagoniste. Ces stratégies sont des schémas en cascade qui –après une linéarisant exacte obtenue sur la base du système non linéaire- combinent un contrôleur externe de position et une boucle interne de force (équivalente à la différence de pression) dans le cas des vérins pneumatiques. Pour les muscles artificiels, le même principe est utilisé sauf que la boucle interne de force est remplacée par une boucle qui régule le couple en contrôlant les pressions de chacun des deux muscles. Un contrôleur prédictif généralisé (GPC) est synthétisé pour la boucle de position permettant ainsi de réduire sensiblement les temps de réponse. Pour la boucle interne de pression, un contrôleur robuste multi-objectif combinant des performances H infinie avec des contraintes de placement de pôle a été synthétisé. L'utilisation d'inégalités matricielles affines (LMI) a permis de combiner les objectifs du contrôleur de façon très intuitive. Le choix de ce contrôleur robuste est motivé par la nécessité de rejeter les fortes variations de charge qui caractérisent les applications de prise-et-dépose d'objets. Deux autres stratégies pour la commande prédictive en effort ont été synthétisées sur les vérins et les muscles et ont donné des résultats très encourageants. Les résultats expérimentaux obtenus ont montré l'apport de ces lois de commande en termes de performances (réduction des temps de réponse, erreurs de suivi faibles) et de robustesse (bon rejet des perturbations). Une étude comparative des trois actionneurs testés a conduit au choix du vérin à double effet standard car offrant le meilleur compromis entre performances, robustesse et coût de l'actionneur. En se basant sur ce choix, un nouveau prototype de robot parallèle à deux degrés de liberté utilisant les vérins standards a été conçu, modélisé et commandé en utilisant les différentes stratégies en cascade proposées. L'implémentation expérimentale des algorithmes de commande a conduit à des résultats encourageants en termes de qualité de suivi et de rejet de perturbations. / The thesis objective is the control of a parallel robot driven with pneumatic actuators for pick-and-place applications. The advantage of using pneumatic actuators rather than electrical ones is that they are cheaper and have a bigger power-to-weight ratio which can increase the payload abilities of the robot. However, due to their strong nonlinearities such as air compressibility, valve characteristic, friction, and hysteresis, they are still difficult to control precisely and in a robust way.That is why the main contribution of the thesis is in the control area where different control schemes have been proposed and experimentally implemented on a test bench that involves three types of pneumatic actuators: two cylinders and agonist/antagonist artificial muscles. After the modeling and identification of the nonlinear models, different strategies have been developed: for cylinders, a cascade scheme which uses an outer position control loop and an inner force (or pressure difference) loop is used. For muscles, the inner force loop is replaced by a torque loop controlled by acting on the pressures in each muscle. For position, a Generalized Predictive Controller (GPC) is synthesized reducing sensibly the time responses. For the inner pressure loop, an LMI based multi objective controller is synthesized combining H infinity performances and pole placement constraints. The choice of a robust controller is motivated by the necessity of rejecting load variation disturban ces that characterize pick-and-place applications. On the other hand, two predictive control strategies with feedback linearization were implemented showing very encouraging results.The different experimental results have shown the interest of such strategies in terms of performances (time response reduction, good dynamic tracking) and robustness (disturbance rejection). The comparison of the three tested actuators led to the choice of the standard double acting cylinder because it offers the best compromise in terms of performances and cost. This cylinder was then used to design a planar parallel robot and the implementation of the proposed cascade strategies. The experimental tests showed encouraging results in terms of disturbance rejection and ability of tracking dynamic references and performing pick-and-place cycles.

Universidade Federal do Cearà / A teoria de controle robusto evoluiu consideravelmente ao longo das Ãltimas dÃcadas, apresentando soluÃÃes para vÃrios tipos de problemas de anÃlise, desempenho e sÃntese de sistemas lineares incertos. As desigualdades matriciais lineares (LMIs) e suas tÃcnicas surgiram como poderosas ferramentas em diversas Ãreas de engenharia de controle para projetos estruturais. Uma propriedade importante das LMIs reside no fato de que o seu conjunto soluÃÃo à convexo. Esta propriedade à fundamental para que se possam formular problemas em controle robusto como sendo problemas de otimizaÃÃo convexa que minimizam uma funÃÃo objetivo. Diante destas afirmaÃÃes o presente trabalho utiliza um sistema de nÃvel de lÃquido com dois tanques interligados como planta onde a mesma foi modelada, e, em seguida, foi desenvolvido um controlador para garantir a sua estabilidade quadrÃtica, quando submetido a perturbaÃÃes externas incertas definidas em um politopo. Utilizou-se o regulador linear quadrÃtico com aÃÃo integral (LQI) como controlador, porÃm, o conceito Ãtimo do LQR nÃo leva em consideraÃÃo as incertezas paramÃtricas existentes nas plantas de projeto, com isso, foi apresentado um mÃtodo de resoluÃÃo do LQR utilizando otimizaÃÃo convexa. O LQR otimizado via LMIs permite a adiÃÃo de incertezas para a obtenÃÃo do ganho de realimentaÃÃo de estado. Os resultados obtidos comprovaram que a estratÃgia de controle LQI via resoluÃÃo LMI à eficaz como controle robusto, pois à capaz de incluir caracterÃsticas referentes à imprecisÃo do processo, alÃm disso, o controle LQI garante a otimalidade do controle. / The robust control theory has evolved considerably over the past decades, providing solutions for various problems of analysis, synthesis and performance of uncertain linear systems. The linear matrix inequalities (LMI) and its techniques have emerged as powerful tools in various areas of control engineering for structural projects. An important property of LMIs is the fact that its solution set is convex. This property is crucial in order to be able to make robust control problems as convex optimization problems that minimize an objective function. Given these statements the present work uses a liquid level system with two tanks connected to the plant where it was modeled, and then a controller is designed to ensure quadratic stability when subjected to external disturbances defined in an uncertain polytope. We used the linear quadratic regulator with integral action (LQI) as a controller, however, the concept of optimal LQR does not take into account the parametric uncertainties in the existing plant design, with it, was presented a method of solving the LQR using convex optimization. LQR optimized via LMI allows the addition of uncertainty to obtain the state feedback gain. The results obtained proved that the strategy of LQI control via LMI resolution is effective as robust control, because it can include features related to the imprecision of the process, moreover, the LQI control ensures the optimality of control.

O objetivo do trabalho é apresentar dois algoritmos para a solução de problemas de controle ótimo quadrático robusto com restrições, dentro de um contexto de controladores preditivos (MPC do inglês Model Predictive Control). Inicialmente apresentamos uma breve introdução aos algoritmos MPC, com ênfase na abordagem do controlador linear quadrático. Em seguida são apresentados os dois algoritmos de interesse, que utilizam técnicas de otimização LMI. Dessa forma as restrições e as incertezas podem ser colocadas em formas computacionalmente tratáveis. Por fim são realizadas simulações e comparações entre esses algoritmos, bem como com técnicas de MPC encontradas na literatura atual. / The goal of the work is to present two algorithms for the solution of robust quadratic optimal control problems with restrictions, within a model predictive control (MPC) setup. Initially we present a brief introduction of the MPC algorithms, emphasizing the linear quadratic controller approach. Next the two algorithms of interest, using LMI optimization techniques, are presented. By using this technique the restrictions and uncertainties can be written in a computational way. Finally some simulations and comparisons between these algorithms, as well as with MPC techniques found in the current literature, are performed.