This work presents an alternative method for 3D bipedal gait design using independent controllers for the plane of motion frontal and sagittal. The use of virtual constraints to design a stable gait for the frontal system is fully developed and studied in this work and the resulting gait simulated. The results, although not definitive, are promising. / Esta tese apresenta um método alternativo de síntese de marcha bípede 3D usando controladores independentes projetados para os planos de movimento frontal e sagital. O uso de restrições virtuais no projeto de uma marcha estável para o plano frontal é completamente desenvolvido e estudado neste trabalho. A marcha resultante é simulada e os resultados, apesar de ainda não definitivos, são promissores.

<p>Periodic signal modeling plays an important role in different fields. The unifying theme of this thesis is using nonlinear techniques to model periodic signals. The suggested techniques utilize the user pre-knowledge about the signal waveform. This gives these techniques an advantage as compared to others that do not consider such priors.</p><p>The technique of Part I relies on the fact that a sine wave that is passed through a static nonlinear function produces a harmonic spectrum of overtones. Consequently, the estimated signal model can be parameterized as a known periodic function (with unknown frequency) in cascade with an unknown static nonlinearity. The unknown frequency and the parameters of the static nonlinearity are estimated simultaneously using the recursive prediction error method (RPEM). A treatment of the local convergence properties of the RPEM is provided. Also, an adaptive grid point algorithm is introduced to estimate the unknown frequency and the parameters of the static nonlinearity in a number of adaptively estimated grid points. This gives the RPEM more freedom to select the grid points and hence reduces modeling errors.</p><p>Limit cycle oscillations problem are encountered in many applications. Therefore, mathematical modeling of limit cycles becomes an essential topic that helps to better understand and/or to avoid limit cycle oscillations in different fields. In Part II, a second-order nonlinear ODE is used to model the periodic signal as a limit cycle oscillation. The right hand side of the ODE model is parameterized using a polynomial function in the states, and then discretized to allow for the implementation of different identification algorithms. Hence, it is possible to obtain highly accurate models by only estimating a few parameters.</p><p>In Part III, different user aspects for the two nonlinear approaches of the thesis are discussed. Finally, topics for future research are presented. </p>

Switched electronic systems are used in a huge number of everyday domestic and industrial utilities: liquid crystal displays, home appliances, lighting, personal computers, power plants, transportation vehicles and so on. Efficient operations of all such applications depend on the essential "hidden work" done by switched electronic systems, whose behavior is determined by a suitable interconnection and control of analog and digital devices. As a motivation of this work, we consider the DC-DC power converters. This thesis contributes to provide hybrid and nonlinear control problem solutions to several types of power converters. In the first part we are interested in the problem of voltage regulation of power converters operating in discontinuous conducting mode. Two power converters are considered: the boost converter and the buck-boost converter. The system does not admit a (continuous--time) average model approximation, hence is a hybrid system where the control objective is the generation of a periodic orbit and the actuator commands are switching times. Our main contribution is a simple robust algorithm that gives explicit formulas for the switching times without approximations. Simulation and experimental results that illustrate the robustness of the scheme to parameter uncertainty, as well as performance comparisons with current practice, are presented. In the second part a class of power converters that can be globally stabilized with an output-feedback PI controller has been identified. Moreover, we will prove that the I&I observer can be combined with the PI controller preserving the GAS properties of the closed-loop. The class is characterized by a simple linear matrix inequality. The new controller is illustrated with the widely-popular, and difficult to control, single-ended primary inductor converter, for which simulation and experimental results are presented.

Periodic signal modeling plays an important role in different fields. The unifying theme of this thesis is using nonlinear techniques to model periodic signals. The suggested techniques utilize the user pre-knowledge about the signal waveform. This gives these techniques an advantage as compared to others that do not consider such priors. The technique of Part I relies on the fact that a sine wave that is passed through a static nonlinear function produces a harmonic spectrum of overtones. Consequently, the estimated signal model can be parameterized as a known periodic function (with unknown frequency) in cascade with an unknown static nonlinearity. The unknown frequency and the parameters of the static nonlinearity are estimated simultaneously using the recursive prediction error method (RPEM). A treatment of the local convergence properties of the RPEM is provided. Also, an adaptive grid point algorithm is introduced to estimate the unknown frequency and the parameters of the static nonlinearity in a number of adaptively estimated grid points. This gives the RPEM more freedom to select the grid points and hence reduces modeling errors. Limit cycle oscillations problem are encountered in many applications. Therefore, mathematical modeling of limit cycles becomes an essential topic that helps to better understand and/or to avoid limit cycle oscillations in different fields. In Part II, a second-order nonlinear ODE is used to model the periodic signal as a limit cycle oscillation. The right hand side of the ODE model is parameterized using a polynomial function in the states, and then discretized to allow for the implementation of different identification algorithms. Hence, it is possible to obtain highly accurate models by only estimating a few parameters. In Part III, different user aspects for the two nonlinear approaches of the thesis are discussed. Finally, topics for future research are presented.

Flutter analyses and tests are the major items in flight certification efforts required when a new air vehicle is developed or when a new external store is developed for an existing aircraft. The flight envelope of a new aircraft as well as the influence of aircraft modifications on an existing flight envelope can be safely determined only by flutter tests. In such tests, the aircraft is instrumented by accelerometers and exciters. Vibrations of the aircraft at specific dynamic pressures are measured and transmitted to a ground station via telemetry systems during flutter tests. These vibration data are analyzed online by using a flutter test software with various methods implemented in order to predict the safety margin with respect to flutter. Tests are performed at incrementally increasing dynamic pressures and safety regions of the flight envelope are determined step by step. Since flutter is a very destructive instability, tests are performed without getting too close to the flutter speed and estimations are performed by extrapolation. In this study, pretest analyses and flutter prediction methods that can be used in various flight conditions are investigated. Existing methods are improved and their applications are demonstrated with experiments. A novel method to predict limit cycle oscillations that are encountered in some modern fighter aircraft is developed. The prediction method developed in this study can effectively be used in cases where the nonlinearities in aircraft dynamics and air flow reduce the applicability of the classical prediction methods. Some further methods to reduce the adverse effects of these nonlinearities on the predictions are also developed.

Os dispositivos robóticos bípedes tem um grande potencial de aplicações tanto comerciais como para pesquisa. Dentre as presentes lacunas existentes que limitam a sua aplicabilidade prática tem um destaque especial a incapacidade de realizar uma marcha estável, robusta, versátil e eficiente no ponto de vista energético. No presente estado da arte, existem três principais estratégias de abordagem para o problema e algumas de suas implementações obtiveram sucesso em satisfazer pelo menos um dos requisitos listados, porém nunca todos eles de forma simultânea. Dentro deste cenário, este trabalho se propôs desenvolver um novo critério de estabilidade para marcha bípede que possibilite marchas versáteis, robustas e eficientes. Inicialmente foi realizada uma avaliação de diversos simuladores de código aberto e o Simbody foi definido como o mais apropriado para ser utilizado no desenvolvimento das simulações dinâmicas realizadas nesta Tese. Uma toolbox de MATLAB para auxiliar nos cálculos cinemáticos e dinâmicos foi desenvolvida em conjunto com um módulo de Inter Process Communication para realizar a comunicação entre o MATLAB e o simulador. Foi realizado um estudo da marcha bípede, implementando e avaliando as estratégias do Zero Moment Point e do Limit CycleWalking. Este estudo resultou numa proposta de controlador não linear comutado para robôs em Ciclo Limite. Na procura de um novo critério de estabilidade foi abordado o estudo da marcha humana. Um procedimento para identificar os mecanismos que controlam a estabilidade da marcha humana é analisar a mesma sob perturbações, como tropeços, ou na ultrapassagem de obstáculos. Na literatura existiam bastantes referências sobre este tema, porém, faltou uma comparação da marcha humana sob diferentes condições de visão com a marcha de robôs que utilizam o ZMP. Foi descoberto que os seres humanos privados de visão têm uma estratégia de ultrapassagem de obstáculos semelhante a um robô com ZMP. A partir do conhecimento adquirido deste estudo é proposto e formulado um novo critério de estabilidade, o Step Viability, inspirado na marcha humana e no conceito de N-Step Capturability. O Step Viability baseia-se na definição de restrições que garantem a viabilidade de realizar passos futuros que garantam a convergência para um ponto fixo em tempo finito. O critério foi implementado utilizando-se uma otimização de trajetória multi-fase. Múltiplos testes foram realizados utilizando-se o modelo Compass Gait com diferentes parâmetros (distribuição de massa, torque máximo disponível), com diferentes inclinações e com vários padrões de marcha desejados (periódico, aumento uniforme e até aleatório não periódico). Adicionalmente o critério foi testado em um modelo de 5 segmentos, sintetizando uma marcha com variação tanto linear quanto aleatória. O critério foi bem-sucedido na geração de uma marcha estável em todos os testes e os resultados foram consistentes. A marcha pode ser sintetizada completamente desacoplada do critério de estabilidade, e o modelo renunciou automaticamente do padrão desenhado em favor da estabilidade. / Bipedal robots present a great potential for both commercial and research applications. However, there are some drawbacks that limit their applicability in the real world. The most prominent is the inability to perform a stable, robust, versatile and efficient gait. There are three main state of the art strategies to approach this problem. However, none of them has been successful in satisfying all the listed requirements simultaneously. In this context, this work conducted a study of bipedal gait, both in humans and robots, in order to implement and evaluate existing stability strategies. As a first step, an evaluation of several open source simulators was performed and Simbody was chosen as the most adequate for the dynamic simulations carried out in this Thesis. A MATLAB toolbox to help in the kinematic and dynamic calculations was developed in conjunction with a module of an Inter Process Communication to perform the communication between MATLAB and the simulator. A bipedal gait study was carried out, implementing and evaluating Zero Moment Point and Limit Cycle Walking strategies. This study resulted in a proposed nonlinear switched controller for Limit Cycle robots. In the search for a new stability criterion, human gait was analyzed. A procedure to identify the mechanisms controlling human gait stability is to analyze gait under disturbances such as stumbling or overcoming obstacles. In the literature, there were many references on this subject, however, there was a lack of comparison of the human gait under different vision conditions with the gait of robots that use the ZMP. It was found that vision-deprived humans have an obstacle crossing strategy similar to robots with ZMP. From the knowledge acquired from this study, it is proposed a novel stability criterion, the Step Viability, inspired on human gait and the N-Step Capturability concept. The Step Viability is based on the definition of constraints that ensure the viability of performing future steps that guarantee convergence to a fixed point in finite time. The criterion was implemented using a multi-phase trajectory optimization. Multiple tests were performed using the Compass Gait model with different parameters (mass distribution, maximum available torque), with different slopes and with several desired gait patterns (periodic, uniform increase and even random non-periodic). Additionally, the criterion was tested in a 5-links model, synthesizing a gait with both linear and random velocity variation. The criterion was successful on generating a stable gait in all the tests and the results presented consistent data. The gait could be designed completely uncoupled from the stability criterion, yet the model automatically renounced to follow the desired pattern in favor of maintaining stability.

A conversão de vibração em energia elétrica tem sido investigada por diversos grupos de pesquisa na última década. A principal motivação é a prospecção de fontes alternativas de energia elétrica para sistemas eletroeletrônicos remotamente operados e com fontes limitadas de energia. Diferentes mecanismos de transdução são investigados na literatura para a coleta de energia, entretanto, o piezelétrico tem se destacado devido à densidade de energia que proporciona e também facilidade de uso. Uma alternativa promissora que começa a ser estudada por alguns grupos de pesquisas é a conversão de energia de oscilações aeroelásticas em energia elétrica. Apesar da natureza destrutiva da maioria dos fenômenos aeroelásticos, eles apresentam um grande potencial para o estudo de novos mecanismos e sistemas para coleta de energia. A conversão piezelétrica de energia a partir de oscilações aeroelásticas lineares tem sido investigada. Entretanto, a geração piezoaeroelástica de energia pode se tornar mais atrativa e prática se realizada a partir sistemas aeroelásticos não lineares. A conversão se daria a partir de oscilações persistentes e com amplitude limitada (oscilações em ciclo limite &#8211; LCO) ocorrendo em um amplo intervalo de velocidades de escoamento. Define-se o objetivo deste projeto como a investigação numérica da conversão piezelétrica de energia a partir de oscilações aeroelásticas não lineares. Um modelo por elementos finitos para placa plana com piezocerâmicas é desenvolvido, respeitando-se as hipóteses de uma placa de von Kàrmàn. O carregamento aerodinâmico não estacionário é determinado a partir do método de malha de dipolos e uma aproximação do domínio do tempo obtida a partir da formulação apresentada por Roger. Os resultados eletroaeroelásticos são apresentados para asas com diferentes razões de aspecto investigadas em uma ampla faixa de velocidades e considerando-se diversos valores de resistores no domínio elétrico. / The converting of vibration into usable electrical energy has been investigated by several researches groups in the last decade. The main motivation is the possibility of obtaining alternatives electrical energy sources to power electronic system remotely operated and with limited energy sources. Different transduction mechanism has been presented in the energy harvesting literature. However the piezoelectric has been gained more attention because not only of its power density but also its ease of use. A promissory alternative that is becoming studied is the converting of aeroelastic oscillation into electrical energy. Despite of the destructive nature of unstable aeroelastic phenomena (such as, flutter), they present a great potential to the study of innovative mechanism to harvest energy. Although the piezoelectric energy conversion using linear aeroelastic has been investigated in the literature, the use of non linear aeroelastic system can be more practical and attractive. The non linear aeorelastic harvesting occurs by persistent oscillation and with limited amplitudes (Limited Cycle Oscillation &#8211; LCO) and can be performed by considerable velocity interval greater than the linear flutter speed. The objective of this work is to investigate the energy harvesting by non linear aeroelastic oscillation. A finite element model of a thin plate (with piezoceramics) is developed), using the non linear hypothesis of von Karman. The unstable aerodynamic loading is obtained by a doublet-lattice method (DLM) and with its time domain conversion using the Roger approximation. The eletroaeroelastic results are presented for several wings with different aspect ratios, and with different resistance values in the electrical domain. The eletroaeroelastic results of the generator wing are investigated for several airspeed greater than its linear flutter speed.

Submitted by Marlene Santos (marlene.bc.ufg@gmail.com) on 2016-06-02T21:00:54Z No. of bitstreams: 2 Dissertação - Jeidy Johana Jimenez Ruiz - 2016.pdf: 946402 bytes, checksum: 0a36384eddfdcc5620d74725a24dd86a (MD5) license_rdf: 19874 bytes, checksum: 38cb62ef53e6f513db2fb7e337df6485 (MD5) / Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2016-06-03T11:43:02Z (GMT) No. of bitstreams: 2 Dissertação - Jeidy Johana Jimenez Ruiz - 2016.pdf: 946402 bytes, checksum: 0a36384eddfdcc5620d74725a24dd86a (MD5) license_rdf: 19874 bytes, checksum: 38cb62ef53e6f513db2fb7e337df6485 (MD5) / Made available in DSpace on 2016-06-03T11:43:02Z (GMT). No. of bitstreams: 2 Dissertação - Jeidy Johana Jimenez Ruiz - 2016.pdf: 946402 bytes, checksum: 0a36384eddfdcc5620d74725a24dd86a (MD5) license_rdf: 19874 bytes, checksum: 38cb62ef53e6f513db2fb7e337df6485 (MD5) Previous issue date: 2016-03-04 / Conselho Nacional de Pesquisa e Desenvolvimento Científico e Tecnológico - CNPq / The study under existence and uniqueness of limit cycles of equations systems differential is a very active research topic in the qualitative theory of dynamical systems. In this theme we study this topic in discontinuous dynamic systems. Let’s make this in Liénard differentials equation systems, allowing a line of discontinuity. Furthermore, we present the known method of Averaging firstly in your classic version, that is, for class fields at least C2, we study also to generalized version, to piecewise- smooth dynamical systems. As a result, we use this tool to determine the number of limit cycles that can bifurcate of a planar center, inside the equation Liénard differentials equation class. / O estudo sobre existência e unicidade de ciclos limites de sistemas de equações diferenciais é um tópico de grande interesse na teoria qualitativa de sistemas dinâmicos. Nesta dissertação, estudamos este tópico em sistemas dinâmicos descontínuos. Vamos fazer esta análise em sistemas de equações diferenciais de Liénard, permitindo uma linha de descontinuidade. Além disso, vamos apresentar o conhecido método Averaging de primeira ordem, em primeiro lugar na sua versão clássica, isto é, para campos de classe pelo menos C2, depois apresentaremos também a versão generalizada, para sistemas diferenciais definidos por partes. Como resultado, fazemos uso desta ferramenta para determinar o número de ciclos limites que podem bifurcar de um centro planar, dentro da classe de equações diferenciais de Liénard.

Nesta tese estudamos um dos principais problemas na teoria qualitativa das equações diferenciais planares: o problema de determinar a bacia de atração de um ponto de equilíbrio. Damos uma prova rigorosa de que para sistemas lineares por partes de costura com duas zonas no plano, definidas por matrizes Hurwitz o único ponto de equilíbrio na reta de separação é globalmente assintoticamente estável. Por outro lado, provamos que nesta classe de sistemas, podemos ter um ponto de equilíbrio instável na origem quando uma curva poligonal separa as zonas, levando a um resultado contra-intuitivo do comportamento dinâmico de sistemas lineares por partes no plano. Além disso, estudamos os ciclos limites em perturbações suaves por partes de centros Hamiltonianos. Neste cenário, é comum adaptar resultados clássicos de sistemas suaves, como funções de Melnikov, para sistemas não-suaves. No entanto, existe pouca justificativa para este procedimento na literatura. Ao utilizar o método de regularização damos uma prova que suporta o uso de funções de Melnikov diretamente do problema não-suave original. / In this thesis we study one of the main problems in the qualitative theory of planar differential equations: the problem of determining the basin of attraction of an equilibrium point. We give a rigorous proof that for planar sewing piecewise linear systems with two zones, defined by Hurwitz matrices the unique equilibrium point in the separation straight line is globally asymptotically stable. On the other hand, we prove that sewing piecewise linear systems with two zones in the plane, defined by Hurwitz matrices can have one unstable equilibrium point at the origin allowing a broken line to separate the zones, leading to counterintuitive dynamical behaviors of simple piecewise linear systems in the plane. Furthermore, we study limit cycles in piecewise smooth perturbations of Hamiltonians centers. In this setting it is common to adapt classical results for smooth systems, like Melnikov functions, to non-smooth ones. However, there is little justification for this procedure in the literature. By using the regularization method we give a proof that supports the use of Melnikov functions directly from the original non-smooth problem.

The skin panels used in high-speed flights are exposed to various types of loads, such as inertial, elastic, and aerodynamic loads. In addition, oblique shock impingement can cause flow separation and unsteady aerodynamic loading, which can reduce vehicle performance and result in acoustic noise and viscous heating. These loads, when combined, can result in a complex dynamic response, such as flutter. Flutter is characterized by sustained unsteadiness or structural vibrations. Although flutter might not be immediately harmful, it can lead to fatigue failure of the structural components. A vast amount of literature already exists on the panel flutter induced by two and three-dimensional supersonic flows with oblique shock impingement. The majority of the studies are focused on predicting the onset of flutter and understanding the influence of non-dimensional parameters on the amplitude and frequency of the oscillations. Recently, numerous experimental campaigns were conducted to understand the influence of thermal loading on panel flutter and provide validation datasets to develop fluid-structure-thermal interaction solvers. The focus of this dissertation is divided into three tasks. The first task focuses on how shock impingement can affect the coupling between fluid and structural interactions and the onset of chaotic flutter. The second task focuses on controlling chaotic flutter using a passive micro vortex generator. The third task focuses on the development and validation of the fluid-structure-thermal interaction solver for 3D FSI problems. The results indicate that sufficiently strong shocks can induce flow separation and boundary layer instabilities that interact nonlinearly with the structural instabilities, resulting in chaotic oscillations. Micro vortex generators can delay the onset of the chaotic flutter by lowering the fluid frequency, thereby synchronizing fluid and structural unsteadiness. A thermoelastic solver has been developed, and the role of thermal stresses on panel flutter characteristics is considered a future task.