Nesta dissertação, um tipo diferente de pêndulo invertido controlado por rodas de reação é apresentado. Sua principal diferença está em seu ponto de articulação, que é constituído por uma junta esférica que permite com que o pêndulo gire em torno de seus três eixos. Além disso, três rodas de reação são utilizadas para seu controle e estabilização. Primeiramente, um modelo do sistema é obtido a partir das equação de Euler-Lagrange, das leis de Newton e das leis de Kirchhoff. Em seguida, uma lei de controle que assegura a estabilização assintótica do sistema em um grande domínio é proposta. Por fim, simulações são realizadas para validar o controlador projetado. Esse sistema possui diversas características interessantes, tanto do ponto de vista teórico como do ponto de vista de pesquisa. Do ponto de vista teórico, o sistema é nãolinear e suas entradas são fortemente acopladas, o que torna particularmente adequado para o processo de projeto e implementação de diversas técnicas de estabilização. Do ponto de vista de pesquisa, são consideradas duas técnicas de controle não linear: linearização padrão e linearização exata. Para que o sistema seja robusto e não desperdice energia, essas duas leis de controle diferentes são comutadas para a obtencão de um número suficiente de domínio de estabilidade. / In this dissertation, a different kind of the reaction wheel pendulum is presented. The main difference is that its articulation point consists of a ball joint that allows the pendulum to rotate around its three axes. Furthermore, three reaction wheels are used for its control and stabilization. First, a model of the system is obtained from Euler-Lagrange equations, Newton laws and Kirchhoff laws. After that, a control law that assure asymptotic stabilization of the system in a large domain is proposed. Finally, simulations are performed to validate the designed controller. This system has several interesting features, both from a theoretical standpoint as from a research standpoint. From a theoretical standpoint, the system is nonlinear and its inputs are tightly coupled, making it particularly suitable for the design and implementation process of various stabilization techniques. From a research standpoint, two non-linear control techniques are considered: standard linearization and exact linearization. For the system to be robust and do not waste energy, these two different control laws are switched for obtaining a sufficiently large domain of stability.

Cette thèse traite de l’analyse et de la synthèse de multimodèles pour la simplification de modèles, l’estimation d’état et le diagnostic des systèmes non linéaires caractérisés par une ou plusieurs échelles de temps. Ces travaux visent, dans un premier temps, à développer une procédure systématique de transformation d’un système non-linéaire en le récrivant sous une forme multimodèle, en évitant quelques inconvénients majeurs : la transformation est réalisée sans perte d’information, le choix de différents points de fonctionnement n’est plus nécessaire, le choix de variables de prémisse est réalisé d’une façon systématique. De plus, la méthode offre le choix entre différents multimodèles. Ce degré de liberté sera utilisé pour faciliter les études de contrôlabilité, d’observabilité et d’analyse de stabilité. Dans un deuxième temps, l’obtention de la forme à perturbations singulières d’un système non linéaire est proposée, en éliminant quelques contraintes structurelles et en rendant l’identification et la séparation des échelles de temps indépendante de la structure du modèle. Dans un troisième temps, la synthèse de plusieurs observateurs robustes vis-à-vis des perturbations, des erreurs de modélisation et des entrées inconnues a été réalisée afin dereconstruire l’état et l’entrée inconnue du système. La difficulté de cette étude provient du fait que le multimodèle utilisé dépend de variables de prémisse non mesurables, situation qui n’est pas intensivement étudiée, alors qu’elle est naturellement issue de l’approche par transformation système non linéaire!multimodèle. Ensuite, le diagnostic de défauts de systèmes est réalisé au moyen de bancs d’observateur à entrées inconnues permettant la génération et la structuration de résidus indicateurs de défauts. Finalement, tous les travaux proposés sont appliqués au modèle d’une station d’´epuration, Activated Sludge Model No.1, qui est largement utilisé dans le domaine du traitement des eaux usées / This thesis deals with analysis and synthesis of multiple model structures for model simplification, state estimation and diagnosis of nonlinear systems represented by one or several time-scales. This work aims, at first, to develop a systematic procedure to transform a nonlinear system into a multiple model form, by avoiding some major drawbacks : the transformation causes no information loss, the choice of the different operating points is no more necessary, the choice of the premise variables is realized in a more systematic way. Furthermore, the method gives the possibility of choosing between different multiplemodel structures. This degree of freedom will be used to ease the controllability, observ-ability, stability analysis studies. Secondly, the derivation of a singularly perturbed form for a multiple time scale non linear system is proposed, by eliminating some structuralconstraints and by making the identification and the separation of the time-scales independent to the model structure. Thirdly, the robust observer synthesis with respect to perturbations, modeling errors and unknown inputs are presented for state and unknowninput estimation. The difficulty of these studies comes from the fact that the multiple model depends on unmeasurable premise variables, this case being not intensively studied, whereas it results naturally from the method of transformation nonlinear system - multiple model. Afterward, fault diagnosis is performed using banks of observer to generate andstructure residual signals. Finally, this works are applied to a model of wastewater treatment plant, Activated Sludge Model No.1 (ASM1) that is largely used in the concerned fiel

In recent years, response analysis of complex structures under impact loads has attracted a great deal of attention. For example, a collision or an accident that produces impact loads that exceed the design load can cause severe damage on the structural components. Although the AASHTO specification is used for impact-resistant bridge design, it has many limitations. The AASHTO specification does not incorporate complex and uncertain factors. Thus, a well-designed structure that can survive a collision under specific conditions in one region may be severely damaged if it were impacted by a different vessel, or if it were located elsewhere with different in-situ conditions. With these limitations in mind, we propose different solutions that use smart control technology to mitigate impact hazard on structures. However, it is challenging to develop an accurate mathematical model of the integrated structure-smart control systems. The reason is due to the complicated nonlinear behavior of the integrated nonlinear systems and uncertainties of high impact forces. In this context, novel algorithms are developed for identification, control and monitoring of nonlinear responses of smart structures under high impact forces. To evaluate the proposed approaches, a smart aluminum and two smart reinforced concrete beam structures were designed, manufactured, and tested in the High Impact Engineering Laboratory of Civil and Environmental Engineering at WPI. High-speed impact force and structural responses such as strain, deflection and acceleration were measured in the experimental tests. It has been demonstrated from the analytical and experimental study that: 1) the proposed system identification model predicts nonlinear behavior of smart structures under a variety of high impact forces, 2) the developed structural health monitoring algorithm is effective in identifying damage in time-varying nonlinear dynamic systems under ambient excitations, and 3) the proposed controller is effective in mitigating high impact responses of the smart structures.

Submitted by Cássia Santos (cassia.bcufg@gmail.com) on 2017-01-17T12:39:40Z No. of bitstreams: 3 Dissertação - Joaquim Orlando Parada (parte1) - 2013.pdf: 11591347 bytes, checksum: e970b2f0fffd5ccc2222bce05ea90d41 (MD5) Dissertação - Joaquim Orlando Parada (parte 2) - 2013.pdf: 18027973 bytes, checksum: 6bdbe04565ae04f1d810137fc59f37e2 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2017-01-18T10:31:58Z (GMT) No. of bitstreams: 3 Dissertação - Joaquim Orlando Parada (parte1) - 2013.pdf: 11591347 bytes, checksum: e970b2f0fffd5ccc2222bce05ea90d41 (MD5) Dissertação - Joaquim Orlando Parada (parte 2) - 2013.pdf: 18027973 bytes, checksum: 6bdbe04565ae04f1d810137fc59f37e2 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Made available in DSpace on 2017-01-18T10:31:58Z (GMT). No. of bitstreams: 3 Dissertação - Joaquim Orlando Parada (parte1) - 2013.pdf: 11591347 bytes, checksum: e970b2f0fffd5ccc2222bce05ea90d41 (MD5) Dissertação - Joaquim Orlando Parada (parte 2) - 2013.pdf: 18027973 bytes, checksum: 6bdbe04565ae04f1d810137fc59f37e2 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Previous issue date: 2013-06-21 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / In this work, the linear and nonlinear instability of pipes conveying static and pulsating fluid flow is analyzed. The dynamic equation of motion was derived for cantilevered and clamped-clamped pipes. For this purpose, the Euler Bernoulli beam theory and Hamilton’s principle were applied, resulting in a partial differential equation of second order in time. Thus, a model with four degrees of freedom, which satisfies the boundary condition, is used and, the Galekin method is applied to derive the set of coupled non linear ordinary equations of motion which are, in turn, solved by the fourth order Runge-Kutta method, and then some numerical results were obtained as Argand diagram, stability boudaries, time response, phase plane and, Poincaré section, through computational algorithms modeled in C++. These results revealed the importance of the nonlinear terms in the stability of the system, especially in the post-critical analysis, also revealed the existence of quasi-periodic motions, for the system subjected to a static flow and, chaotic motions for pulsating fluid flow / Nesta dissertação analisa-se a instabilidade linear e não linear de tubos com fluido interno em escoamento estático e pulsante. A equação de movimento dinâmico foi deduzida para tubos em balanço e biengastados. Para tanto, utilizou-se a teoria de vigas de Euler Bernoulli e o princípio variacional de Hamilton, resultado em uma equação diferencial parcial de segunda ordem no tempo. Tal equação foi discretizada, pelo método de Galerkin, em quatro equações diferenciais ordinárias, uma para cada grau de liberdade, em seguida transformadas em um conjunto de equações diferenciais de primeira ordem. Tais equações foram integradas pelo método de Runge-Kutta de quarta ordem e, posteriormente, foram obtidos alguns resultados numéricos como: diagrama de Argand, curvas de escape, diagrama de bifurcação, resposta no tempo, plano fase e, seção de Poincaré, através de algoritmos implementados computacionalmente na linguagem C++. Tais resultados revelaram a importância dos termos não lineares na estabilidade do sistema, especialmente na análise pós-crítica, revelaram também a existência de movimentos quase periódicos, para o sistema submetido a um fluxo estático e, caóticos para fluxo pulsante.

An Inverted double pendulum is a combination of two individual pendulums which represents an example of a nonlinear and unstable dynamic system and it is also a good example of a physical system which can exhibit chaotic behavior.This document contains a first analysis of the model and the control of this system. Also presented is the installation of the electrical materials needed to control the system contain instrumenting the motor, current measurement system, motor shaft angle sensor, vision systemand MYRIO which is an embedded hardware device created by National Instruments will be used for data acquisition and control the system

L'observateur est un outil essentiel pour accéder à l'information, non mesurable directement, d'un système dynamique. Dans le cas des systèmes non linéaires, il y a une grande carence concernant la synthèse d'observateur. Motivée par l'absence d'une solution générique, cette thèse élargit la classe des systèmes non linéaires pour lesquels on peut appliquer les observateurs connus. Dans l'approche adoptée, le système non linéaire est transformé à travers un changement de coordonnées sous forme normale d'observabilité qui a une structure adéquate à la synthèse d'observateurs. Les difficultés liées aux conditions d'existence d'un changement de coordonnées sont mises en évidence et des solutions sont proposées. Par conséquent, la classe des systèmes non linéaires qui peuvent se mettre sous une forme normale d'observabilité est élargie. Dans un premier temps, nous avons proposé une forme normale d'observabilité étendue dépendante de la sortie en augmentant l'espace d'état par des variables auxiliaires. Ainsi, nous avons établi les conditions nécessaires et suffisantes à l'existence d’un changement de coordonnées permettant d’obtenir une telle forme. En outre, nous avons proposé, pour certains modèles, des procédures heuristiques pour la mise sous forme normale d'observabilité étendue dépendante de la sortie. Dans un deuxième temps, nous avons traité la mise sous forme normale d'observabilité d'un système non linéaire partiellement observable. Enfin, nous avons abordé la transformation d'une classe spéciale de systèmes non linéaires sous la forme normale d'observabilité réduite. L'efficacité et l'intérêt des méthodes développées sont établis au travers de plusieurs applications. / Observer is an essential means to access to no-measurable information of a dynamical system. In the case of nonlinear systems, there is a great deficiency concerning the observer design theory. Motivated by the lack of a generic solution to observer design, this thesis enlarges the class of nonlinear systems which admit a standard observer. Using a geometrical approach, the considered nonlinear systems are transformed through a change of coordinates into observer form, which has an adequate structure to the observer design. The difficulties related to the conditions on the existence of such a change of coordinates are highlighted and solutions are proposed. Therefore, the class of nonlinear systems which can be transformed under an observer form is expanded. Firstly, we proposed an extended output depending observer form which does not preserve the size of the original state space and we established the sufficient conditions for the existence of a change of coordinates enabling to construct the proposed form. Moreover, we proposed a heuristic procedure to construct the extended output depending observer form of some models. Secondly, we dealt with the observer form for some partially observable nonlinear systems. Finally, we discussed the transformation into the reduced observer form for a class of nonlinear systems. The efficiency and interest of the developed methods is established through several applications.

Nesta dissertação, um tipo diferente de pêndulo invertido controlado por rodas de reação é apresentado. Sua principal diferença está em seu ponto de articulação, que é constituído por uma junta esférica que permite com que o pêndulo gire em torno de seus três eixos. Além disso, três rodas de reação são utilizadas para seu controle e estabilização. Primeiramente, um modelo do sistema é obtido a partir das equação de Euler-Lagrange, das leis de Newton e das leis de Kirchhoff. Em seguida, uma lei de controle que assegura a estabilização assintótica do sistema em um grande domínio é proposta. Por fim, simulações são realizadas para validar o controlador projetado. Esse sistema possui diversas características interessantes, tanto do ponto de vista teórico como do ponto de vista de pesquisa. Do ponto de vista teórico, o sistema é nãolinear e suas entradas são fortemente acopladas, o que torna particularmente adequado para o processo de projeto e implementação de diversas técnicas de estabilização. Do ponto de vista de pesquisa, são consideradas duas técnicas de controle não linear: linearização padrão e linearização exata. Para que o sistema seja robusto e não desperdice energia, essas duas leis de controle diferentes são comutadas para a obtencão de um número suficiente de domínio de estabilidade. / In this dissertation, a different kind of the reaction wheel pendulum is presented. The main difference is that its articulation point consists of a ball joint that allows the pendulum to rotate around its three axes. Furthermore, three reaction wheels are used for its control and stabilization. First, a model of the system is obtained from Euler-Lagrange equations, Newton laws and Kirchhoff laws. After that, a control law that assure asymptotic stabilization of the system in a large domain is proposed. Finally, simulations are performed to validate the designed controller. This system has several interesting features, both from a theoretical standpoint as from a research standpoint. From a theoretical standpoint, the system is nonlinear and its inputs are tightly coupled, making it particularly suitable for the design and implementation process of various stabilization techniques. From a research standpoint, two non-linear control techniques are considered: standard linearization and exact linearization. For the system to be robust and do not waste energy, these two different control laws are switched for obtaining a sufficiently large domain of stability.

Les systèmes de régulation des turbomoteurs actuels sont basés sur des architectures complexes que les constructeurs tendent à rendre plus modulaires avec des technologies plus économiques tout en garantissant un niveau de fiabilité supérieur ou égal. Dans ce contexte, la surveillance du circuit carburant, qui a pour but de déceler les dysfonctionnements des composants hydrauliques critiques, permet de réduire le coût de maintenance, d'améliorer le niveau de maintenabilité et d'assurer la disponibilité des turbomoteurs. La présente étude porte sur l'élaboration de méthodes de diagnostic performantes et robustes permettant la détection et la localisation des défauts impactant les fonctions hydrauliques primaires du circuit carburant. Des méthodes existantes de génération de résidus à base de modèles non linéaires sont présentées et appliquées au cas du circuit carburant. L'approche analytique pour le découplage, combinée avec des filtres de Kalman étendus, permet la structuration des résidus pour assurer la localisation des défauts. Une nouvelle approche basée sur la théorie de platitude différentielle est proposée pour le diagnostic de défauts des systèmes non linéaires avec une application au cas du circuit carburant. Les différentiateurs à modes glissants sont utilisés pour l'estimation des dérivées de signaux nécessaires à l'application de certaines méthodes de génération de résidus. Des simulations numériques illustrent la pertinence des résultats obtenus. Une application expérimentale est présentée en utilisant un jeu de données réelles issues d'un banc d'essais partiel et fournies par la société Turbomeca du groupe SAFRAN. / The current gas turbine regulation systems are based on complex architectures that manufacturers tend to make more modular with more cost effective technologies while ensuring a greater or equal level of reliability. In this context, the fuel system health monitoring, which aims to identify critical hydraulic components dysfunction, allows to reduce maintenance costs, to improve maintainability level and to ensure gas turbine availability. The present study focuses on the development of performant and robust diagnosis methods for the detection and isolation of faults affecting primary fuel system hydraulic functions. Existing nonlinear model based residual generation methods are presented and applied to the fuel system. The analytical approach for decoupling, combined with extended Kalman filters, helps fault isolation by generating residual structures. A new approach based on differential flatness theory is proposed for nonlinear systems fault diagnosis with an application to the fuel system. Sliding mode differentiators are used to estimate derived signals that are necessary for the application of some residual generation methods. Numerical simulations illustrate the efficiency of obtained results. An experimental application is presented using a real data set from a partial test bench provided by Turbomeca company of the SAFRAN group.

The present thesis employs fuzzy-polynomial control techniques in order to improve the stability analysis and control of nonlinear systems. Initially, it reviews the more extended techniques in the field of Takagi-Sugeno fuzzy systems, such as the more relevant results about polynomial and fuzzy polynomial systems. The basic framework uses fuzzy polynomial models by Taylor series and sum-of-squares techniques (semidefinite programming) in order to obtain stability guarantees. The contributions of the thesis are: ¿ Improved domain of attraction estimation of nonlinear systems for both continuous-time and discrete-time cases. An iterative methodology based on invariant-set results is presented for obtaining polynomial boundaries of such domain of attraction. ¿ Extension of the above problem to the case with bounded persistent disturbances acting. Different characterizations of inescapable sets with polynomial boundaries are determined. ¿ State estimation: extension of the previous results in literature to the case of fuzzy observers with polynomial gains, guaranteeing stability of the estimation error and inescapability in a subset of the zone where the model is valid. ¿ Proposal of a polynomial Lyapunov function with discrete delay in order to improve some polynomial control designs from literature. Preliminary extension to the fuzzy polynomial case. Last chapters present a preliminary experimental work in order to check and validate the theoretical results on real platforms in the future. / Pitarch Pérez, JL. (2013). Contributions to fuzzy polynomial techniques for stability analysis and control [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/34773 / TESIS

Cette thèse porte sur l’identification de systèmes non linéaires représentables en séries de Volterra, et son application à des systèmes sonores. Les séries de Volterra, qui permettent de représenter une large classe de systèmes non linéaires, correspondent à un développement en série organisé par ordre d'homogénéité par rapport à l’entrée: chaque terme homogène est caractérisé par un noyau convolutif dont l’ensemble fournit une "signature complète" du système représenté. Les travaux présentés reposent sur le développement d’une étape préalable de séparation des termes de la série pour améliorer l’identification des noyaux de Volterra. Par rapport aux méthodes déjà existantes de séparation en ordres homogènes, basées sur des relations d’amplitudes entre signaux tests, l'approche adoptée dans cette thèse consiste à exploiter les relations de phase entre signaux afin d'obtenir une méthode robuste. Cela est tout d’abord obtenu de manière abstraite pour le cas de signaux d’excitations complexes. De cette idée, plusieurs méthodes adaptées au cas des signaux réels sont développées. Ceci amène à définir de nouvelles catégories de signaux pour décrire la sortie d’une série de Volterra, regroupant les contributions selon leurs propriétés de phase. Les méthodes de séparation proposées sont testées et appliquées à une pédale d’effet de guitare. Ensuite, des méthodes d’identification spécifiques aux nouveaux types de signaux sont présentées. Enfin, une méthode d’estimation des paramètres d’une représentation d’état à non-linéarités polynomiales est développée. Celle-ci est appliquée à un haut-parleur électrodynamique, dont les caractéristiques non linéaires sont étudiées. / This thesis addresses the identification of nonlinear systems that can be represented with Volterra series, and its application to audio systems. Volterra series give an input-output representation, approximated to within a given error, of any time-invariant continuous nonlinear system with fading memory. Technically, they correspond to a series expansion sorted by homogeneity order with respect to the input: each homogeneous term is characterized by a convolutive kernel whose set provides a "complete signature" of the modelled system. The works presented are based on the development of a preliminary step that consists in separating the series' terms to improve Volterra kernels' identification. Compared to existing homogeneous order separation methods, which are based on amplitude relationships between test signals, the approach chosen in this thesis is to exploit phase relationships between signals to obtain a robust method. This is first obtained in the theoretical case of complex excitation signals. From this idea, several methods suited to the use of real signals are developed. This leads to define new signals categories that describes the output of a Volterra series, sorting nonlinear contributions according to their phase properties. The proposed separation methods are applied and tested on a guitar pedal effect. Then, specific identification methods for the new types of signals are presented Finally, a method for estimating the parameters of a polynomial nonlinear state-space representation is developed. This is applied to an electrodynamic loudspeaker whose nonlinear characteristics are studied.