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Ce travail étudie les stratégies de contrôle des limites pour l'analyse de stabilité et la stabilisation d'un système hyperbolique de premier ordre couplé à des conditions limites dynamiques non linéaires. La modélisation d'un écoulement à l'intérieur d'un tube (phénomène de transport de fluide) avec une stratégie de contrôle des limites appliquée dans une installation expérimentale physique est considérée comme une étude de cas pour évaluer les stratégies proposées. Dans le contexte des systèmes de dimension finie, des outils de contrôle classiques sont appliqués pour traiter des systèmes hyperboliques de premier ordre ayant des conditions limites données par le couplage d'un modèle dynamique de colonne de chauffage et d'un modèle statique de ventilateur. Le problème de suivi de cette dynamique complexe est abordé de manière simple en considérant des approximations linéaires, des schémas de différences finies et une action intégrale conduisant à un système linéaire à temps discret augmenté avec une dimension dépendant de la taille d'échelon de la discrétisation dans l'espace. Par conséquent, pour la contrepartie dimensionnelle infinie, deux stratégies sont proposées pour résoudre le problème de contrôle de frontière des systèmes hyperboliques de premier ordre couplé à des conditions de frontière dynamique non linéaires. Le premier se rapproche de la dynamique du système hyperbolique de premier ordre par un retard pur. La stabilité convexe et les conditions de stabilisation des systèmes quadratiques non linéaires retardés d'entrée incertaine sont proposées sur la base de la théorie de la stabilité de Lyapunov-Krasovskii (LK) qui sont formulées en termes de contraintes de l'inégalité matricielle linéaire (LMI) avec des variables supplémentaires lâches (introduites par le lemme de Finsler ). Ainsi, des fonctions strictement de Lyapunov sont utilisées pour dériver une approche basée sur LMI pour la stabilité de la frontière régionale robuste et la stabilisation des systèmes hyperboliques de premier ordre avec une condition de frontière définie au moyen d'un système dynamique non linéaire quadratique. Les conditions de stabilité et de stabilisation proposées pour LMI sont évaluées en tenant compte de plusieurs exemples universitaires et de l'écoulement à l'intérieur d'une étude de cas. / This work studies boundary control strategies for stability analysis and stabilization of first-order hyperbolic system coupled with nonlinear dynamic boundary conditions. The modeling of a flow inside a pipe (fluid transport phenomenon) with boundary control strategy applied in a physical experimental setup is considered as a case study to evaluate the proposed strategies. Firstly, in the context of finite dimension systems, classical control tools are applied to deal with first-order hyperbolic systems having boundary conditions given by the coupling of a heating column dynamical model and a ventilator static model. The tracking problem of this complex dynamics is addressed in a simple manner considering linear approximations, finite difference schemes and an integral action leading to an augmented discrete-time linear system with dimension depending on the step size of discretization in space. Hence, for the infinite dimensional counterpart, two strategies are proposed to address the boundary control problem of first-order hyperbolic systems coupled with nonlinear dynamic boundary conditions. The first one approximates the first-order hyperbolic system dynamics by a pure delay. Then, convex stability and stabilization conditions of uncertain input delayed nonlinear quadratic systems are proposed based on the Lyapunov-Krasovskii (L-K) stability theory which are formulated in terms of Linear Matrix Inequality (LMI) constraints with additional slack variables (introduced by the Finsler's lemma). Thus, strictly Lyapunov functions are used to derive an LMI based approach for the robust regional boundary stability and stabilization of first-order hyperbolic systems with a boundary condition defined by means of a nonlinear quadratic dynamic system. The proposed stability and stabilization LMI conditions are evaluated considering several academic examples and also the flow inside a pipe as case study.

[pt] O Aterro Metropolitano de Jardim Gramacho (AMG) é o local que recebe desde 1976 os resíduos sólidos gerados pelas atividades domésticas, além das comerciais e industriais da área metropolitana do Rio de Janeiro. Atualmente no AMG vem se desenvolvendo projetos de aterramento até o ano 2012, portanto, a estabilidade dos taludes do maciço cresce em importância e a presente dissertação está dirigida a compreender aspectos da análise de estabilidade do AMG. Nesse sentido, faz-se ênfase no comportamento da resistência dos materiais, fundamentalmente da fundação que é uma argila muito mole. Na área do AMG tem campanhas de ensaios do campo durante vários anos e em quantidade menor os ensaios laboratoriais. Neste trabalho são feitas atividades como a coleta e interpretação das sondagens desde 1992 até a campanha do ano 2009, esta informação é introduzida numa modelagem estratigráfica tridimensional, deles são gerados perfis bidimensionais para as análises de estabilidade, Outra atividade é interpretar informação do campo, ensaios de laboratório da campanha 2009 e realizar ensaios complementares na argila do local (compressão triaxial drenada e não drenada, cisalhamento direto e adensamento com medição do creep). A totalidade da informação é discutida obtendo correlações da resistência não drenada em base da teoria do estado critico. Os parâmetros geotécnicos do lixo são obtidos através das referências na literatura e retro-análises de taludes movimentados no local. Finalmente se avalia a estabilidade do AMG pelos métodos de equilíbrio limite e tensão deformação em termos de tensões totais e efetivas até chegar às geometrias finais projetadas. / [en] The Metropolitan Landfill Jardim Gramacho (AMG) is the site since 1976 that receives solid waste generated by domestic activities, also of commercial and industrial metropolitan area of Rio de Janeiro. Currently in AMG is developing projects ground to the year 2012, so the stability of slopes of the massive gains in importance and this dissertation is aimed at understanding aspects of the stability analysis of the AMG. Thus, it is an emphasis on the behavior of resistance of materials, primarily from a foundation that is very soft clay. In the area of AMG has field test in explorations for several years and fewer laboratory tests. This work made activities such as collection and interpretation of surveys from 1992 to the exploration of 2009, this information is entered into a three-dimensional stratigraphic modeling, their profiles are generated for the two-dimensional stability analysis, Another activity is to interpret information from field trials Campaign 2009 laboratory and perform additional tests on the clay site (triaxial drained and undrained, direct shear and consolidation with measurement of creep). The totality of the information obtained is discussed correlations of resistance undrained in the base of critical state theory. The geotechnical parameters of garbage are obtained through the references in the literature and analysis of retro-crowded slopes at the site. Finally it assesses the stability of the AMG methods of limit equilibrium and stress-strain curves in terms of total stresses and effective to reach the final designed geometry.

Il s’agit ici d’étudier un phénomène vibratoire ressenti par les utilisateurs d’un masque à oxygène au niveau de la fosse nasale. Le masque à oxygène intègre un régulateur qui envoie de l’oxygène en réponse à une demande de débit. Les vibrations prennent la forme de variations de pression à l’entrée du masque et leur origine est inconnue. Parmi les objectifs du travail de thèse, on essaiera de comprendre l’origine et de caractériser ce phénomène après une modélisation détaillée du régulateur, prenant en compte assez finement sa géométrie. Dans un deuxième temps, la stabilisation de la trajectoire dynamique de ce système sera étudiée par le biais de l’application du critère de Routh à un modèle linéarisé autour d’un point d’équilibre. Dans un troisième temps, quelques phénomènes dynamiques et physiques additionnels seront investis afin de pousser plus en avant la compréhension du fonctionnement du masque. Dans un quatrième temps et en guise d’ouverture, on prendra le temps d’évoquer des pistes supplémentaires pour l’étude de ce système. / The vibratory behavior of a regulated oxygen mask is studied here. The oxygen mask integrates a regulator which sends oxygen in response to a demand flow. The vibrations take the form of pressure variations in the mask volume, at the entry of the nasal ways, and their origin is unknown. Among the goals of this thesis work, we will try first to understand the origin and to characterize this phenomenon after a detailed modeling of the regulator, taking accurately into account its geometry. Second, the stabilization of the system’s dynamical trajectory will be studied by applying the Routh criterion to a linearized model around an equilibrium point. Third, some additional dynamical and physical phenomena will be investigated in order to push forward the understanding of the mask functionning. Fourth, and as an opening, time will be taken to mention supplementary tracks for the study of this system.

Philosophiae Doctor - PhD / Singularly perturbed problems have been studied extensively over the past few years from different perspectives. The recent research has focussed on the problems whose solutions possess interior layers. These interior layers appear in the interior of the domain, location of which is difficult to determine a-priori and hence making it difficult to investigate these problems analytically. This explains the need for approximation methods to gain some insight into the behaviour of the solution of such problems. Keeping this in mind, in this thesis we would like to explore a special class of numerical methods, namely, fitted finite difference methods to determine reliable solutions. As far as the fitted finite difference methods are concerned, they are grouped into two categories: fitted mesh finite difference methods (FMFDMs) and the fitted operator finite difference methods (FOFDMs). The aim of this thesis is to focus on the former. To this end, we note that FMFDMs have extensively been used for singularly perturbed two-point boundary value problems (TPBVPs) whose solutions possess boundary layers. However, they are not fully explored for problems whose solutions have interior layers. Hence, in this thesis, we intend firstly to design robust FMFDMs for singularly perturbed TPBVPs whose solutions possess interior layers and to improve accuracy of these approximation methods via methods like Richardson extrapolation. Then we extend these two ideas to solve such singularly perturbed TPBVPs with variable diffusion coefficients. The overall approach is further extended to parabolic singularly perturbed problems having constant as well as variable diffusion coefficients. / 2023-08-31

京都大学 / 新制・課程博士 / 博士(理学) / 甲第23017号 / 理博第4694号 / 新制||理||1673(附属図書館) / 京都大学大学院理学研究科地球惑星科学専攻 / (主査)准教授 成瀬 元, 准教授 堤 昭人, 教授 生形 貴男 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DGAM

This Master's thesis analyses business results of the entrepreneurial subject. The Master's thesis includes the fundamental analysis and the strategical analysis. On the basis of these analyses I propose the suggestions leading to the stability and perspective entrepreneurial activities.

Des systèmes avec des coefficients dépendant du retard ont été rencontrés dans diverses applications de la science et de l'ingénierie. Malgré la littérature abondante sur les systèmes de temporisation, il y a peu de résultats concernant l'analyse de stabilité des systèmes avec des coefficients dépendant du retard. Cette thèse est consacrée à l'analyse de stabilité de cette classe de systèmes.Les méthodes d'analyse de la stabilité sont développées à partir de l'équation caractéristique correspondante suivant une approche généralisée tau-décomposition. Étant donné un intervalle d'intérêt de retard, nous sommes capables d'identifier toutes les valeurs de retard critique contenues dans cet intervalle pour lesquelles l'équation caractéristique admet des racines sur l'axe imaginaire du plan complexe. Le critère de direction de croisement des racines sont proposées pour déterminer si ces racines caractéristique se déplacent vers le plan complexe demi-gauche ou demi-droite lorsque le paramètre de retard passe par ces valeurs de retard critique. Le nombre de racines caractéristiques instables pour un retard donné peut ainsi être déterminé. Notre analyse comprend les systèmes avec un seul retard ou des retards proportionnés sous certaines hypothèses. Le critère de direction de croisement des racines développés dans cette thèse peut être appliqués aux multiple racines caractéristiques, ou aux racines caractéristiques dont la position paramétrée par le retard est tangent à l'axe imaginaire. En tant qu'application, il est démontré que les systèmes avec des coefficients dépendant du retard peuvent provenir de schémas de contrôle qui utilisent une sortie retardée pour approcher ses dérivés pour la stabilisation. Les méthodes d'analyse de stabilité développées dans cette thèse sont adaptées et appliquées pour trouver les intervalles de retard qui atteignent un taux de convergence demandé du système en boucle fermée. / Systems with delay-dependent coefficients have been encountered in various applications of science and engineering. However, general and systematic stability analysis is rarely reported in the rich literature on time-delay systems. This thesis is committed to the stability analysis of such class of systems.Stability analysis methods are developed based on the corresponding characteristic equation following a generalized tau-decomposition approach. Given a delay interval of interest, we are able to identify all the critical delay values contained in this interval for which the characteristic equation admits roots on the imaginary axis of the complex plane. Various root crossing direction criteria are proposed to determine whether these characteristic roots move toward the left or the right half complex plane as the delay parameter sweeps through these critical delay values. The number of unstable characteristic roots for any given delay can thus be determined. Our analysis covers systems with a single delay or commensurate delays under certain assumptions. The root crossing direction criteria developed in this thesis can be applied to characteristic roots with multiplicity, or characteristic roots whose locus parametrized by the delay is tangent to the imaginary axis. As an application, it is demonstrated that systems with delay-dependent coefficients can arise from control schemes that use delayed output to approximate its derivatives for stabilization. The stability analysis methods developed in this thesis are tailored and applied to find the delay intervals that achieve a demanded convergence rate of the closed-loop system.

<div>This research consists of the development of a new educational tool for calculations of 2D slope stability problems, named PNW-SLOPE. Slope stability has been considered one of the most important topics in geotechnical engineering for many years, so this is a subject which students should build a good background in the university. This program was created in Microsoft Excel with the aid of VBA (Visual Basic for Applications). The use of VBA allowed the creation of a good user interface, therefore those who are using the program can easily follow the instructions to create, analyze the model and check the results. Even though there are many commercial programs with the same application, this research presents a new alternative, more focused on educational purposes. PNW-SLOPE is divided in several modules.The first consists of the geometry definition of the slope. The second module consists of a deterministic slope stability analysis considering limit equilibrium method and the method of slices. The third module consists of a probability analysis considering Monte Carlo simulation. With these two options, users can compare both analysis and understand how important is the consideration of probability analysis in Geotechnical Engineering. This is a pertinent topic nowadays, since reliability analysis is increasingly being incorporated in standards and design codes throughout the world. An additional module was created for rock slope stability problems in which the failure results from sliding on a single planar surface dipping into the excavation. Several examples are presented to demonstrate some of the features of PNW-SLOPE and results are verified with commercial programs such as Geostudio Slope/w and Rocscience Slide 2018.</div>

Rapid constructed embankments founded on soft deposits have a negative influence on the short term stability. Many engineering constructions such as road and railway embankments are often constructed on soft clay deposits. In stability analysis calculation of safety factor (SF), as the primary design criteria can be evaluated through different numerous methods such as limit equilibrium method (LEM) and finite element method (FEM). It is of particular interest to determine/estimate appropriate stability of the specified embankment which is highly dependent on the analysis method used. Therefore, it is a challenge for geotechnical engineers to judge which analysis method can simulate better the reality.  The aim of this thesis is to increase understanding applicability of the three applied programs; Plaxis2D, Plaxis3D and Slope/W in simulating and stability analysis/estimation of embankments founded on clay deposits.  The work has involved analysis and comparison of the stability through estimate of the SF and the critical failure surfaces obtained through 2D and 3D programs. Four case configurations were studied for the stability analysis. In each case variation in plastic parameters of clay (φ-c) or load geometry, was the scenario to make the comparison analysis. Moreover, application FEM3D offers an attractive alternative to traditional approaches to the problem (especially for LEM).  The main conclusions from this study are the following:  (1)   Concerning the three applied programs, FEM3D has the minimum SF sensitivity to change in plastic parameters of clay deposit. (2)   For embankments founded on clay deposit, the 3D failure surfaces are easily found via the FEM3D analysis program, which is closer to reality, while failure results of 2D analysis programs can never occur in reality. (3)   Using 2D analysis method instead of 3D, to investigate the stability of 3D embankment model tend to give higher SF results up to 14% for embankments  founded on undrained clay deposit. (4)   The failure surfaces in 3D analysis are likely to be shallower than in the corresponding 2D model. (5)   Results from the 3D analysis through hand calculation and program calculation do not correspond with each other for embankment founded on soft clay deposit. The first reason is rooted in limitation of the hand formula. The formula is suitable for embankment founded on one layer deposit (soil); however an embankment founded on 3 layers of deposit (soil) was analyzed in this study. The second reason is related to applied method of calculation. 3D hand calculation formula is based on method of slices however; analysis method in program calculation is based on FEM.