Cette thèse traite de la manière dont le musicien contrôle les régimes d'oscillation d'un instrument de la famille des cuivres. L'’association d’'un instrument et d'un musicien forme un système dynamique complexe. Le couplage non linéaire entre les lèvres et la colonne d’'air peut mener à un régime stationnaire, des auto-oscillations périodiques ou quasi-périodiques. De nombreux paramètres de contrôle permettent à un musicien de choisir le régime d’oscillation.Deux approches sont utilisées pour comprendre l’'émergence des régimes de l’'instrument et leur contrôle par le musicien. D'’une part, on étudie un modèle physique de cuivre, consistant en une valve à 1 degré de liberté couplée non linéairement à une expression modale de l’'impédance d’'entrée de l’'instrument. Les caractéristiques des régimes de ce modèle sont étudiés par analyse de stabilité linéaire, simulation numérique et équilibrage harmonique. L’'objectif est d'’estimer la capacité de ce modèle à reproduire le comportement de l’'instrument. Un outil expérimental est également développé pour mesurer simultanément des paramètres de contrôle employés par les musiciens et des variables de jeu.Les résultats améliorent la compréhension des régimes d’oscillation des cuivres. Les mesures expérimentales donnent les plages de variation des paramètres de jeu. Les résultats des méthodes d'’analyse se complètent, donnant une vision globale de l’'apparition des régimes oscillants du modèle et des informations détaillées sur certains points de fonctionnement. Certaines situations de jeu particulières sont étudiées: note pédale du trombone, ’influence de l’'utilisation d’'une sourdine et nature des sons multiphoniques. / This thesis focuses on how a musician controls and chooses the oscillation regimes of brass instruments.The association of an instrument and a musician is a complex dynamical system. The nonlinear coupling between the lips and the resonator can lead to a stationary regime, periodic or quasi-periodic self-sustained oscillations. Through several control parameters, a musician can select the desired regime.Two approaches are developed to understand the emergence of the instrument oscillation regimes and how a musician controls it. A physical model of brass instrument is studied. It consists in a one-degree-of-freedom lip valve nonlinearly coupled to a modal fit of the input impedance of the instrument. The features of several oscillation regimes of this model are studied through linear stability analysis, numerical simulation and harmonic balance. Goals are the assessment of the ability of this model to reproduce the behavior of the modelled instrument. An experimental setup is also developed to measure simultaneously playing parameters used by a musician and instrument variables.Results provide a better understanding of the behavior of brass instrument oscillation regimes. Measurements provide ranges of the control parameters. Results of the analysis methods of the model are complementary. A global vision of the occurrence of certain oscillation regimes is provided, along with more detailed information for some operating points. Some specific playing situations are examined in detail, such as the trombone pedal note, the influence of a passive or active mute on the latter, and the nature of multiphonic sounds.

Les réseaux de lois de bilan sont définis par l'interconnexion, via des conditions aux bords, de modules élémentaires individuellement caractérisés par la conservation de certaines quantités. Des applications industrielles se trouvent dans les réseaux de lignes de transmission électriques (réseaux HVDC), hydrauliques et pneumatiques (réseaux de distribution du gaz, de l'eau et du fuel). La thèse se concentre sur l'analyse modulaire et la commande au bord d'une ligne élémentaire représentée par un système de lois de bilan en dimension infinie, où la dynamique de la ligne est prise en considération au moyen d'équations aux dérivées partielles hyperboliques linéaires du premier ordre et couplées deux à deux. Cette dynamique permet de modéliser d'une manière rigoureuse les phénomènes de transport et les vitesses finies de propagation, aspects normalement négligés dans le régime transitoire. Les développements de ces travaux sont des outils d'analyse qui testent la stabilité du système, et de commande au bord pour la stabilisation autour d'un point d'équilibre. Dans la partie analyse, nous considérons un système de lois de bilan avec des couplages statiques aux bords et anti-diagonaux à l’intérieur du domaine. Nous proposons des conditions suffisantes de stabilité, tant explicites en termes des coefficients du système, que numériques par la construction d'un algorithme. La méthode se base sur la reformulation du problème en une analyse, dans le domaine fréquentiel, d'un système à retard obtenu en appliquant une transformation backstepping au système de départ. Dans le travail de stabilisation, un couplage avec des dynamiques décrites par des équations différentielles ordinaires (EDO) aux deux bords des EDP est considéré. Nous développons une transformation backstepping (bornée et inversible) et une loi de commande qui, à la fois stabilise les EDP à l'intérieur du domaine et la dynamique des EDO, et élimine les couplages qui peuvent potentiellement mener à l’instabilité. L'efficacité de la loi de commande est illustrée par une simulation numérique. / Networks of balance laws are defined by the interconnection, via boundary conditions, of elementary modules individually characterized by the conservation of physical quantities. Industrial applications of such networks can be found in electric (HVDC networks), hydraulic and pneumatic (gas, water and oil distribution) transmission lines. The thesis is focused on modular analysis and boundary control of an elementary line represented by a system of balance laws in infinite dimension, where the dynamics of the line is taken into consideration by means of first order two by two coupled linear hyperbolic partial differential equations. This representation allows to rigorously model the transport phenomena and finite propagation speed, aspects usually neglected in transient regime. The developments of this work are analysis tools that test the stability, as well as boundary control for the stabilization around an equilibrium point. In the analysis section, we consider a system of balance laws with static boundary conditions and anti-diagonal in-domain couplings. We propose sufficient stability conditions, explicit in terms of the system coefficients, and numerical by constructing an algorithm. The method is based on reformulating the analysis problem as an analysis of a delay system in the frequency domain, obtained by applying a backstepping transform to the original system. In the stabilization work, couplings with dynamic boundary conditions, described by ordinary differential equations (ODE), at both boundaries of the PDEs are considered. We develop a backstepping (bounded and invertible) transform and a control law that at the same time, stabilizes the PDEs inside the domain and the ODE dynamics, and eliminates the couplings that are a potential source of instability. The effectiveness of the control law is illustrated by a numerical simulation.

The main goal of this diploma thesis was to project a design of arch bridge‘s framework over the Svratka river. This single-span bridge has the span of 52,5m. The framework is constructed from a pair of beams, suspended from the pair of beams bent towards each other. The bridge deck is coupled with steel crosspieces. The construction design was executed in computing programme Dlubal RFEM 5.07. The individual components of the framework were assessed in Microsoft Excel. The calculation considered the load of wind and pedestrians’ movement and their effect on the dynamics of the construction. The phases of development were also considered. Assessments of coupled cross-section, main beams of steel construction, tension systems and selected construction joints were executed in a static calculation. Moreover, a design of a bearing and a bridge plug joint. Finally, a drawing documentation and a final report were prepared in regards with the requirements. The construction design and its assessment were executed according to valid standards.

The thesis describes the application of anchors in mining and tunneling and gives an up-to-date overview about anchor types, design principles and the interaction mechanisms between anchors and rockmass. A constitutive model was developed, implemented and tested for the 2- and 3-dimensional numerical codes FLAC and FLAC3D to simulate non-linear anchor behaviour including unloading and reloading. The interaction between rockbolts and rockmass was studied in detail via numerical simulations for 5 Vietnamese coal mines. An extended version of the so-called c-Φ reduction method and a new introduced reinforcement factor were applied to quantify the effect of bolting. Mine specific and generalised relations were deduced to quantify the influence of anchor length and distance between anchors on the effect of bolting.

Diese numerische Arbeit untersucht, wie sich die laminar-turbulente Transition in der Grenzschicht einer ebenen Platte mit elektromagnetischen Kräften verzögern lässt. Erzeugt von einer Elektroden-Magnet-Anordnung in der Platte wirken jene Kräfte im wandnahen Bereich der Strömung. Sie sind wandparallel sowie stromab gerichtet und besitzen zwei Parameter, die Amplitude und die Eindringtiefe. Zwei- und dreidimensionale Direkte Numerische Simulationen, Grenzschichtgleichungslöser sowie lineare Stabilitätsanalyse werden eingesetzt, um zwei Ansätze der Transitionsverzögerung zu verfolgen: Zum einen die aktive Wellenauslöschung, bei der ankommende Grenzschichtinstabilitäten von gegenphasig angeregten Wellen bis zu 97% ausgelöscht werden. Zum anderen können elektromagnetische Kräfte die Grenzschicht beschleunigen und so zu deutlich stabilieren Grenzschichtprofilen führen. Über evolutionäre Optimierung wurde eine räumliche Verteilung von Eindringtiefe und Kraftamplitude gefunden, die den Energieeinsatz minimiert und gleichzeitig laminare Strömung sicherstellt; dennoch bliebt die energetische Effizienz der Beeinflussung unter Eins. / This numerical work investigates how electromagnetic forces may delay laminar-turbulent transition of a flat plate boundary layer. Generated by an array of electrodes and magnets flush mounted in the wall, those forces act within the wall-near flow. They are oriented in wall-parallel, downstream direction and are characterized by two parameters, namely amplitude and penetration depth. Two- and three-dimensional Direct Numerical Simulations, numerical solutions of boundary layer equations and linear stability analysis are applied to study two possible ways of transition delay: first, the so-called active wave cancellation, where an anti-wave cancels incoming boundary layer instabilities by up to 97%. A second option is have electromagnetic forces accelerate the boundary layer, thereby modifying its mean velocity profile for greatly enhanced stability. Using evolutionary optimization, a spatial distribution of force amplitude and penetration depth was obtained that maintains laminar flow while minimizing electrical power consumption of the actuator. However, the energetic efficiency of actuation remains less than unity.

This work focusses on analysing the stability of the MSFR – a molten salt reactor with a fast neutron spectrum. The investigations are based on a model, which was published and studied by the Politecnico di Milano using a linear approach. Since linear methods can only provide stability information to a limited extent, this work continues the conducted investigations by applying nonlinear methods. In order to examine the specified reactor model, the system equations were implemented, adjusted and verified using MATLAB code. With the help of the computational tool MatCont, a so-called fixed-point solution was tracked and its stability monitored during the variation of selected control parameters. It was found that the considered fixed point does not change its stability state and remains stable. Coexisting fixed points or periodic solutions could not be detected. Therefore, the analysed MSFR model is considered to be a stable system, in which the solutions always tend towards a steady state.:1. Introduction 2. Molten Salt Reactor Technology 2.1. Introduction 2.2. Historical Development 2.3. Working Principle of Molten Salt Reactors 2.4. Molten Salt Coolants 2.5. Advantages and Drawbacks 2.6. Classification 2.7. Molten Salt Fast Reactor Design 3. Stability Characteristics of Dynamical Systems 3.1. Introduction 3.2. Dynamical Systems 3.3. Stability Concepts 3.3.1. Introduction 3.3.2. Lagrange Stability (Bounded Stability) 3.3.3. Lyapunov Stability 3.3.4. Poincaré Stability (Orbital Stability) 3.4. Fixed-Point Solutions 3.4.1. Stability Analysis of Fixed-Point Solutions 3.4.2. Bifurcations of Fixed-Point Solutions 3.5. Periodic Solutions 3.5.1. Stability Analysis of Periodic Solutions 3.5.2. Bifurcations of Periodic Solutions 4. Analysed Reactor System 4.1. Introduction 4.2. Specified Reactor Model 4.3. Implementation and Verification of the Linearised System of Equations 4.3.1. Linearised System of Delayed Differential Equations 4.3.2. Comparison with Reference Plots 4.3.3. Adaptation of Parameter Values 4.4. Implementation and Verification of the Nonlinear System of Equations 4.4.1. Nonlinear System of Delayed Differential Equations 4.4.2. Delayed Neutron Precursor Equation Adjustments 4.4.3. Salt Temperature Equation Adjustments 4.4.4. Nonlinear System of Ordinary Differential Equations 4.4.5. Verification of the Nonlinear System of Ordinary Differential Equations 5. Conducted Stability Analyses 5.1. Introduction 5.2. Nonlinear Stability Analysis 5.2.1. Implementation 5.2.2. Results 5.2.3. Interpretation 5.3. Linear Stability Analysis 5.3.1. Comparison Between the Linearised and Nonlinearised MSFR System of Equations 5.3.2. Stability Investigations Using a Linear Criterion 5.4. MatCont Reliability Test Using an MSBR Model 6. Conclusions and Recommendations for Future Studies / Im Fokus dieser Arbeit steht die Stabilitätsanalyse des MSFR – eines Flüssigsalzreaktors mit schnellem Neutronenspektrum. Als Grundlage wurde ein Modell verwendet, das am Politecnico di Milano erstellt und dort mittels linearer Methoden untersucht wurde. Da lineare Betrachtungen nur eingeschränkte Stabilitätsaussagen treffen können, erweitert diese Arbeit die Untersuchungen um die nichtlineare Stabilitätsanalyse. Zur Untersuchung des vorgegebenen Reaktormodells wurden die Systemgleichungen in MATLAB übertragen und verifiziert. Mithilfe der Rechensoftware MatCont wurde eine sogenannten Fixpunkt-Lösung des Modells unter der Variation ausgewählter Parameter verfolgt und deren Stabilität überprüft. Es hat sich gezeigt, dass der betrachtete Fixpunkt seinen Stabilitätszustand dabei nicht verändert und stabil bleibt. Koexistierende Fixpunkte oder periodische Lösungen konnten nicht nachgewiesen werden. Daher gilt das betrachtete MSFR-Modell als ein stabiles System, dessen Lösungen immer auf einen stationären Zustand zulaufen.:1. Introduction 2. Molten Salt Reactor Technology 2.1. Introduction 2.2. Historical Development 2.3. Working Principle of Molten Salt Reactors 2.4. Molten Salt Coolants 2.5. Advantages and Drawbacks 2.6. Classification 2.7. Molten Salt Fast Reactor Design 3. Stability Characteristics of Dynamical Systems 3.1. Introduction 3.2. Dynamical Systems 3.3. Stability Concepts 3.3.1. Introduction 3.3.2. Lagrange Stability (Bounded Stability) 3.3.3. Lyapunov Stability 3.3.4. Poincaré Stability (Orbital Stability) 3.4. Fixed-Point Solutions 3.4.1. Stability Analysis of Fixed-Point Solutions 3.4.2. Bifurcations of Fixed-Point Solutions 3.5. Periodic Solutions 3.5.1. Stability Analysis of Periodic Solutions 3.5.2. Bifurcations of Periodic Solutions 4. Analysed Reactor System 4.1. Introduction 4.2. Specified Reactor Model 4.3. Implementation and Verification of the Linearised System of Equations 4.3.1. Linearised System of Delayed Differential Equations 4.3.2. Comparison with Reference Plots 4.3.3. Adaptation of Parameter Values 4.4. Implementation and Verification of the Nonlinear System of Equations 4.4.1. Nonlinear System of Delayed Differential Equations 4.4.2. Delayed Neutron Precursor Equation Adjustments 4.4.3. Salt Temperature Equation Adjustments 4.4.4. Nonlinear System of Ordinary Differential Equations 4.4.5. Verification of the Nonlinear System of Ordinary Differential Equations 5. Conducted Stability Analyses 5.1. Introduction 5.2. Nonlinear Stability Analysis 5.2.1. Implementation 5.2.2. Results 5.2.3. Interpretation 5.3. Linear Stability Analysis 5.3.1. Comparison Between the Linearised and Nonlinearised MSFR System of Equations 5.3.2. Stability Investigations Using a Linear Criterion 5.4. MatCont Reliability Test Using an MSBR Model 6. Conclusions and Recommendations for Future Studies

Philosophiae Doctor - PhD / Fitted operator finite difference methods (FOFDMs) for singularly perturbed problems have been explored for the last three decades. The construction of these numerical schemes is based on introducing a fitting factor along with the diffusion coefficient or by using principles of the non-standard finite difference methods. The FOFDMs based on the latter idea, are easy to construct and they are extendible to solve partial differential equations (PDEs) and their systems. Noting this flexible feature of the FOFDMs, this thesis deals with extension of these methods to solve interior layer problems, something that was still outstanding. The idea is then extended to solve singularly perturbed time-dependent PDEs whose solutions possess interior layers. The second aspect of this work is to improve accuracy of these approximation methods via methods like Richardson extrapolation. Having met these three objectives, we then extended our approach to solve singularly perturbed two-point boundary value problems with variable diffusion coefficients and analogous time-dependent PDEs. Careful analyses followed by extensive numerical simulations supporting theoretical findings are presented where necessary.

Les sujets discutés dans cette thèses’inscrivent dans le cadre général des systèmesinterconnectés. Nous abordons les réseauxmulti-agent qui ont des tâches coopératives etnous proposons un nouveau protocole deconsensus qui comporte des retards et desagents anticipatifs. Nous étudions lesconditions pour lesquelles un réseau organiséconformément au protocole proposé atteint leconsensus. Nous dérivons également desrésultats théoriques valables pour une classeplus générale de systèmes. Ces résultatsconcernent le cas des racines multiples surl’axe des imaginaires, situation qui peutcorrespondre aux réseaux avec une topologiechangeante.Dans notre approche, nous discutonsséparément le cas des racines multiples àl’origine et racines multiples sur l’axe desimaginaires sauf l’origine. Un autre résultatimportant comporte un nouveau modèle pourun réseau génétique qui fonctionne comme unmultiplexeur. Ce circuit innovant utilise troisentrées pour commander deux signaux desortie. Nous effectuons une analyse destabilité pour le modèle proposé et nousdémontrons que son point d’équilibre estunique et stable. Pour valider ce réseaugénétique, nous étudions également le modèlestochastique dérivé du modèle déterministe. / This thesis discusses diverse types ofinterconnected systems through networks. Weaddress networks of agents with cooperativetasks and propose a new consensus protocolwith delays and anticipatory agents. We studythe consensus reaching conditions for networksorganized under the proposed model.Moreover, we derive some theoretical results,which can apply to a more general class ofsystems, concerning stability issues when theconsidered system has multiple imaginaryroots. In terms of networks, this situation cancorrespond to the case of switching topologynetworks, when the network can even bedisconnected at some point.We separately discuss the case of zerocharacteristic roots, and roots laying on theimaginary axis, except the origin. Finally, wepropose a gene network model with afunctionality similar to a multiplexer circuit.Thus, we control two outputs with three inputsignals, and we carry out a stability analysis.We prove the uniqueness and the stability ofthe network steady states, and validate thecontinuous and deterministic model with astochastic model.

The presented thesis deals with the utilization of TOF-LEIS analytical method in the area of nanostructure analysis. A new procedure for depth profiling of the elemental composition of the sample, based on the alternate measurement with the DSIMS method, was established. The TOF-LEIS method is able to detect the interface between the layers before its mixing by the ion beam of the DSIMS method. Furthermore, a procedure of TOF-LEIS spektra modification was established to obtain the actual concentration of elements in the sample by reduction of a multiple collision contribution. By comparison of TOF-LEIS spectra with the results received by the DSIMS method the ratio of molybdenum and silicon ion yields was obtained. In the next section advantages of the TOF-LEIS method in combination with XPS during analysis of thermal stability of gold nanoparticles are presented. The mutual complementarity of both methods is shown and final conclusions are supported by electron microscopy images. The final section deals with a newly assembled apparatus for the TOF-SARS analytical method and shows its possibilities regarding the detection of hydrogen on the graphene.

[pt] Nos últimos anos, os robôs móveis com pernas têm despertado o interesse da comunidade robótica, pois tais mecanismos apresentam maior versatilidade em relação aos robôs móveis de rodas e aéreos. Neste trabalho, o autor considera o problema de modelagem e projeto de controle robusto para uma classe de robôs móveis com pernas usando a abordagem de controle por modos deslizantes. Um estudo comparativo entre um algoritmo de planejamento baseado em técnicas de Fourier e controladores via modo deslizante é apresentado para o problema de estabilização de um robô móvel saltitante na fase de vôo. O autor também propõe a estabilização da postura de robôs móveis multipernas, como hexapod e robô bípede, utilizando duas abordagens de controle diferentes, o controle de regulação Cartesiana e o controle via modos deslizantes. A teoria de estabilidade de Lyapunov é usada para demonstrar as propriedades de estabilidade dos sistemas de controle em malha-fechada. Simulações numéricas em ambiente de simulação MATLAB e simulações computacionais em Gazebo, um simulador robótico 3D de código aberto, são incluídas para ilustrar o desempenho e a viabilidade da metodologia proposta. / [en] In the last years, legged mobile robots have increased the interest of the robotics community because such mechanisms have higher versatility compared to wheeled and aerial mobile robots. These characteristics make robot with legs a viable solution for rescue and monitoring operations in irregular terrains and difficult to access locations. Although singlelegged or multi-legged mechanisms can transverse any terrain, some of their disadvantages are higher complexity in modelling and control design and higher power consumption. In this work, the author considers the problem of modelling and robust control design for a class of legged mobile robots using the sliding mode control approach. A comparative study between a planning algorithm based on Fourier techniques and sliding mode controllers is presented for the stabilization problem of a hopping robot in flight phase. The author also proposes the stabilization of the posture of multilegged mobile robots such as, hexapod and biped robot, using two different control approaches, the Cartesian regulation control and the sliding mode control. The Lyapunov stability theory is used to demonstrate the stability properties of the closed-loop control systems. Numerical simulations in MATLAB simulation software and computer simulations in Gazebo, an open-source 3D robotic simulator, are included to illustrate the performance and feasibility of the propose methodology.