[pt] Neste trabalho descreve-se um procedimento para o desenvolvimento de modelos reduzidos de sistemas mecânicos lineares baseado na técnica dos Grafos de Ligação. A partir da análise da estrutura topológica dos principais modelos mecânicos descritos por esta técnica estabeleceu- se uma nova formulação que possibilita a obtenção de variadas formas de representação matemática e definiu-se um grafo genérico, formado por hipercampos armazenadores e dissipadores de energia, onde se encontram as matrizes que caracterizam a dinâmica do sistema. Sobre o grafo genérico, com algumas restrições, foi aplicada uma metodologia de normalização e desacoplamento dos campos armazenadores, com base nos seus modos locais, o que permitiu a criação de um grafo particionado, acoplado através do campo dissipador. A análise dos coeficientes do campo de acoplamento leva ao grafo de Ligação Reduzido do sistema. Comprova-se a validade do procedimento através de exemplos de fácil compreensão. / [en] It is described in this work a Bond Graph based procedure to the development of linear mechanical systems reduced order models. From the analysis of the topological structure of the main mechanical models represented by this technique it was established a new formulation that permits to obtain several mathematical representation forms and it was defined a generic graph, formed by energy storage and dissipative hiperfields, where the matrices that characterizes the system dynamics are included. On the generic graph, with some constraints, it was applied a methodology for the normalization and decoupling of the energy storage fields, based on its local modes, that permits to develop a partioned graph, couplec through the dissipative field. The analysis of the coupling field coefficients permits to define the system Reduced Bond Graph. The procedure was comproved by easy comprehensive examples.

[pt] O crescente uso de veículos aéreos não tripulados (VANTs) em diversos setores da sociedade é fruto de avanços da tecnologia. Por sua vez, a ampliação de aplicações de VANTs traz consigo a necessidade de aumento de robustez destes sistemas, especialmente em ambientes compartilhados com o ser humano. A presente dissertação aborda o desenvolvimento de uma plataforma para testes de veículos multicópteros, com o objetivo de contribuir para o processo de desenvolvimento e implementação de drones, permitindo sua movimentação em torno dos seus graus de liberdade de rotação e realizando medições de atitude e força geradas pelo sistema, sem colocar o veículo ou seu operador em risco. Todos os dados adquiridos pela plataforma são transmitidos para um computador, onde foi desenvolvida uma interface virtual para sua visualização em tempo real, além de permitir armazenamento para pós-processamento e análises futuras. Também apresenta-se e discute-se o desenvolvimento do simulador de trajetórias proposto, que mostra o deslocamento do veículo em função da sequência de comandos fornecida, com base nos dados adquiridos pela plataforma. No intuito de se propiciar um melhor entendimento do funcionamento do sistema aqui desenvolvido, é apresentado um estudo detalhado dos subsistemas que compõem um multicóptero, bem como do processo de modelagem dinâmica de um veículo quadricóptero, por meio da técnica de grafos de ligação. A modelagem do veículo é complementada com a identificação de parâmetros fundamentais para a implementação do modelo, sendo discutidos métodos para identificação de parâmetros inerciais do veículo e parâmetros dinâmicos do sistema motopropulsor. / [en] The growing use of unmanned aerial vehicles (UAVs) in various sectors of society is a result of advances in technology. In turn, the expansion of UAV applications brings with it the need to increase the robustness of these systems, especially in environments shared with humans. and comes together with the need for increased robustness due to its use in shared environments with humans. This dissertation approaches the development of a platform for testing multicopter vehicles aiming at assisting the process of developing and implementing drones, allowing movements around their rotational degrees of freedom and making measurements of attitude and forces generated by the system, without putting the vehicle or its operator at risk. All data acquired by the platform is transmitted to a computer, where a virtual interface was developed to provide real time visualization, in addition to allowing data storage for post-processing and future analysis. The development of the proposed trajectory simulator is also presented and discussed, that shows the displacement of the vehicle as a function of the sequence of commands provided, based on the acquired data. Aiming at allowing a better understanding of the functioning of the developed system, a detailed study of the subsystems that compose a multicopter is presented, as well as the process of dynamic modeling of a quadcopter vehicle, by using bond graph technique. The modeling of the vehicle is complemented with the identification of fundamental parameters for the model implementation, such as methods for the identification of inertial parameters of the vehicle and dynamics of the powertrain system.

A whole-stalk harvester was developed as part of a sweet sorghum-for-ethanol production system. Gathering chains grasped the stalks as they were cut at the base with a disk-cutter. These stalks were flipped onto a cross conveyor and deposited into an accumulator. Periodically the machine stopped and the accumulator was dumped. All the components on the harvester are powered hydraulically. Five pumps on the harvester supply flow to seven actuator circuits. Power is delivered to the pumps from the tractor PTO via a universal joint driveline. Each of the six existing circuits and one proposed circuit were modeled with bond graphs and implemented for computer analysis using TUTSIM. Model validation was done by comparing simulated and measured driveline torque, line pressure, and return line flow rate in each of the six existing circuits. Data collected on the gathering chains circuit was used to analyze the effect of driveline joint angles on transmitted torque and pump output. Torque measurements at three driveline angles showed a torsional vibration with a primary harmonic at driveline rpm and a secondary at twice driveline rpm. A combination of Cardan joint characteristics, mass unbalance, the secondary couple, and non-linear driveline and V-belt stiffness was used to model the driveline. Resulting simulated torque emulated the experimental very well. Measured pressure in the gathering chains circuit showed relatively low fluctuations at the highest amplitude torsional vibration (highest driveline joint angles). It was concluded that driveline vibration would not significantly affect the gathering chains circuit performance. The cross-conveyor motor circuit simulation showed close agreement to experimental results. Mean predicted flow, pressure, and torque were within 8.9, 7.3, and 7.7 percent of mean measured values. A simulation with a stalk load on the conveyor showed that power requirement increased only 8.0 percent. The accumulator dump circuit was analyzed to determine if the load on the motor would become over-running and cavitate the pump or motor as the stalks were being dumped. Simulation showed that a bundle up to 300 kg could be dumped without over-running the motor, and since this was a larger bundle than the bin could hold, a design modification was not necessary. The disk-cutter circuit was designed based on simulation results for several combinations of motor, pump, and sheave ratio. A 7.3 cm³/rad motor, 2.53 cm³/rad pump , and 2:1 sheave ratio produced the correct disk-cutter speed, and low torsional vibration when cutting the stalks, consequently this combination was selected for the design. / Ph. D.

[pt] O estudo de fenômenos transitórios em sistemas hidráulicos está presente em diversos ramos da engenharia, encontra-se na área de hidrelétricas e na indústria do petróleo. O presente trabalho apresenta uma análise comparativa deste fenômeno utilizando três abordagens de modelagem distintas: o clássico método das características, a técnica de grafos de ligação e o tratamento através do fluxo de potência. No caso do método das características emprega-se o procedimento proposto por Streeter. Na modelagem através de grafo de ligação adota-se a analogia generalizada entre os sistemas fluido, mecânico e elétrico. Na representação pelo fluxo de potência acopla-se módulos previamente desenvolvidos considerando as relações de causa e efeito entre os componentes de um sistema. Todos os métodos foram implementados em Matlab e foram testados e comparados a partir de simulações em dois sistemas simples compostos de um reservatório, linha fluida e válvula. Os resultados obtidos através da metodologia de fluxo de potência aproximam-se dos encontrados pelas abordagens tradicionais. / [en] The study of transitory phenomena in hydraulic systems is present in several branches of the engineering, in the hydroelectric power stations area and in the petroleum industry. The present work introduce a comparative analysis of this phenomenon using three approaches of distinct modeling: the classic characteristics method, the technique of bond graphs and the treatment through the power flow. In the case of characteristics method is used the procedure proposed by Streeter. In the modeling through bond graphs is adopted the generalized analogy among the fluid, mechanic and electric systems. In the representation by power flow modules previously developed are coupled considering the cause and effect relationships between components of one system. All methods were implemented in Matlab and were tested and compared from simulations in two simple systems composed of a reservoir, fluid lines and valve. The results obtained through the methodology of power flow are near of the discoveries by the traditional approaches.

L'objectif des travaux présentés dans ce mémoire concerne le développement d'un modèle global représentant le couplage de l'enveloppe du bâtiment avec les équipements énergétiques. Une approche systémique appelée les Bond Graphs, peu employée jusqu'ici dans la modélisation des systèmes thermiques, est utilisée. Le modèle global du bâtiment, regroupant sous le même environnement de simulation, les modèles de l'enveloppe du bâtiment, les apports solaires, les émetteurs de chauffage et de rafraîchissement et le système de ventilation, est développé pour reconstituer l'ensemble des articulations énergétiques entre l'enveloppe et les environnements intérieur et extérieur. A travers la modélisation d'un bâtiment multizone, le couplage systémique des modèles de l'enveloppe et des apports solaires est présenté. Par ailleurs, un système combinant un plancher chauffant et un plafond rafraîchissant est étudié à l'aide des modèles des émetteurs de chauffage et de rafraîchissement. Le renouvèlement d'air dans le bâtiment est également concerné par la modélisation Bond Graph. Enfin, des éléments de validation expérimentale sont présentés. Pour cela, la plateforme de tri-génération d'énergie ENERBAT est exploitée. L'objectif est d'étudier le couplage optimal enveloppe du bâtiment - équipements énergétiques pour lequel les modèles BG sont développés. Une étude paramétrique tenant compte des interactions entre les paramètres étudiés est menée sur un projet réel de rénovation. Finalement, une combinaison appropriée des paramètres étudiés a été retenue afin de réduire la consommation énergétique selon la réglementation thermique française (RT2012) / Our works focus on the setting of reliable tools able to analyze the interaction between the building envelope and HVAC systems. The developed approach is based on Bond Graphs methodology, a graphical modeling language which is particularly suitable for energy exchanges. A numerical model gathering, under the same simulation environment, sub-models representing the building envelope, the solar gains, the floor heating, the chilled ceiling and the ventilation system, is developed in order to predict the energy interactions between these sub-systems. The multi-zone building model is developed in order to simulate and analyze the overall building thermal behavior. Then, the solar gains model is also included to predict the solar radiation exchanges in a way close to reality. The model of the heating and cooling system, combining the floor heating and the chilled ceiling, is developed in order to improve the thermal comfort of the building. Afterwards, the ventilation system is modeled in order to represent the air exchange inside the building. The experimental validation is carried out on the tri-generation unit integrated with a thermal solar system (platform ENERBAT). Furthermore, the parametrical study was realized in order to gain a better understanding according to the impact of some factors in the energy performance of the single-family building located in Meurthe-et-Moselle region (France). Optimization of several measures, such as insulation of the building envelope, type of glazing, building orientation and ventilation system, is performed to respond to the requirements of the French thermal standard (RT2012)

Cette thèse a pour but l'étude de la propriété de platitude sur des modèles bond graphs (BGs) non linéaires et de contribuer à la résolution des problèmes rencontrés en pratique qui sont liés principalement à l'identification des sorties plates et le calcul de la paramétrisation différentielle. <br />Pour atteindre cet objectif, de nouveaux concepts et outils graphiques ont été introduits. En particulier, grâce à l'introduction de la notion de modèle BG tangent ou variationnel à l'aide de l'utilisation des différentielles de Kähler, il est possible de calculer les sorties plates d'un modèle BG non linéaire par intégration des bases du module qui lui est associé.<br />Par ailleurs, en définissant la notion d'anneau BG non commutatif, une nouvelle règle de gain connue sous le nom de "règle de Riegle" est introduite en BG. En montrant alors qu'un modèle BG variationnel est un cas particulier d'anneau BG non commutatif, l'obtention graphique de la paramétrisation différentielle en utilisant la règle de Riegle et la notion de bicausalité est rendue possible.<br />Enfin, pour aller plus loin dans l'introduction de l'outil d'algèbre et de modules différentiels aux BGs, le cas des modèles BGs non linéaires régis par des équations différentielles polynômiales a été abordé. Dans ce contexte, le BG permet de faire une analyse directe des propriétés principales du système telles que le choix des variables d'entrée, les dynamiques correspondant à un choix d'entrée, le calcul des degrés de transcendance (non différentiel) différentiel, etc. à partir de son modèle BG associé. Il est également montré que la règle graphique de Riegle peut être étendue à cette classe de modèles BGs.

Modelling and simulation are essential ingredients of the analysis and design process in power electronics. It helps a design engineer gain an increased understanding of circuit operation. Accordingly, for a set of specifications given, the designer will choose a particular topology, select component types and values, estimate circuit performance etc. Typically hierarchical modelling, analysis and simulation rather than full detailed simulation of the system provides a crucial insight and understanding. The combination of these insights with hardware prototyping and experiments constitutes a powerful and effective approach to design. Obtaining the mathematical model of the power electronic systems is a major task before any analysis or synthesis or simulation can be performed. There are circuit oriented simulators which uses inbuilt mathematical models for components. Simulation with equation solver needs mathematical models for simulation which are trimmed according to user requirement. There are various methods in the literature to obtain these mathematical models. However, the issues of multi-domain system modelling and causality of the energy variables are not sufficiently addressed. Further, specifically to power converter systems, the issue of switching power models with fixed causality is not addressed. Therefore, our research focuses on obtaining solutions to the above using relatively untouched bond graph method to obtain models for power electronic systems. The power electronic system chosen for the present work is Switched Mode Power Converters (SMPC’s) and in particular PWM DC-DC converters. Bond graph is a labelled and directed graphical representation of physical systems. The basis of bond graph modelling is energy/power flow in a system. As energy or power flow is the underlying principle for bond graph modelling, there is seamless integration across multiple domains. As a consequence, different domains (such as electrical, mechanical, thermal, fluid, magnetic etc.) can be represented in a unified way. The power or the energy flow is represented by a half arrow, which is called the power bond or the energy bond. The causality for each bond is a significant issue that is inherently addressed in bond graph modelling. As every bond involves two power variables, the decision of setting the cause variable and the effect variable is by natural laws. This has a significant bearing in the resulting state equations of the system. Proper assignment of power direction resolves the sign-placing problem when connecting sub-model structures. The causality will dictate whether a specific power variable is a cause or the effect. Using causal bars on either ends of the power bond, graphically indicate the causality for every bond. Once the causality gets assigned, bond graph displays the structure of state space equations explicitly. The first problem we have encountered in modelling power electronic systems with bond graph is power switching. The essential part of any switched power electronic system is a switch. Switching in the power electronic circuits causes change in the structure of the system. This results in change in dynamic equations of the circuit according to position of the switch. We have proposed the switched power junctions (SPJ) to represent switching phenomena in power electronic systems. The switched power junctions are a generalization of the already existing 0-junction and 1-junction concepts of the bond graph element set. The SPJ’s models ideal switching. These elements maintain causality invariance for the whole system for any operational mode of the system. This means that the state vector of the resulting state equation of the system does not change for any operating mode. As SPJs models ideal power switching, the problem of stiff systems and associated numerical stability problems while simulating the system is eliminated. Further, it maintains one to one correspondence with the physical system displaying all the feasible modes of operation at the same time on the same graph. Using these elements, the switched mode power converters (SMPC's) are modelled in bond graph. Bond graph of the converter is the large signal model of the converter. A graphical procedure is proposed that gives the averaged large signal, steady state and small signal ac models. The procedure is suitable for the converters operating in both Continuous Conduction Mode (CCM) and in Discontinuous Conduction Mode (DCM). For modelling in DCM, the concept of virtual switch is used to model the converter using bond graph. Using the proposed method, converters of any complexity can be modelled incorporating all the advantages of bond graph modelling. Magnetic components are essential part of the power electronic systems. Most common parts are the inductor, transformer and coupled inductors which contain both the electric and magnetic domains. Gyrator-Permeance approach is used to model the magnetic components. Gyrator acts as an interface between electric and magnetic domain and capacitor model the permeance of the magnetic circuits. Components like inductor, tapped inductor, transformer, and tapped transformer are modelled. Interleaved converters with coupled inductor, zero ripple phenomena in coupled inductor converters as well as integrated magnetic Cuk converter are also modelled. Modelling of integrated magnetic converters like integrated magnetic forward converter, integrated magnetic boost converter are also explored. To carry out all the simulations of proposed bond graph models, bond graph toolbox is developed using MATLAB/SIMULINK. The MATLAB/SIMULINK is chosen since it is general simulation platform widely available. Therefore all the analysis and simulation can be carried out using facilities available in MATLAB/SIMULINK. Symbolic equation extraction toolbox is also developed which extracts state equations from bond graph model in SIMULINK in symbolic form.

[pt] A sub-divisão de um veículo em módulos é muito útil quando se quer estudar o comportamento dinâmico de um determinado subsistema e sua influência nos demais componentes. Em alguns casos, devido ao tipo de tratamento empregado para descrever os elementos, não se consegue perceber de que modo as variáveis inerentes a um subsistema interagem com as demais, e, por conseguinte, os subsistemas entre si. A abordagem modular baseada no fluxo de potência permite uma melhor identificação das relações de causa e efeito entre subsistemas, uma vez que se pode definir, de forma clara e consistente, quem são as variáveis de entrada e de saída de cada componente ou módulo, e, conseqüentemente, seus acoplamentos. Neste tipo de tratamento, aplicado aos sistemas mecânicos, uma vez estabelecida a cinemática de um subsistema, podese obter as relações entre os esforços que seus componentes produzem uns sobre os outros, a partir da caracterização da potência transmitida através dos seus diversos elementos. Este trabalho apresenta um procedimento semi-analítico de equacionamento modular aplicado à modelagem e integração dos sistemas de suspensão e direção de veículos terrestres, no qual as variáveis de entrada e saída indicam o fluxo de potência entre os elementos de todo o sistema. Tal abordagem tem como base a técnica dos Grafos de Ligação, empregada em sistemas multidomínio em geral, e usa alguns conceitos da metodologia dos Transformadores Cinemáticos, normalmente aplicada aos sistemas multicorpos. A partir da definição da geometria dos mecanismos em questão, encontram-se as matrizes que representam os vínculos cinemáticos entre seus elementos, das quais o funcionamento dos sistemas integrados pode ser simulado e analisado, e informações necessárias aos seus projetos determinadas. As equações (malhas) algébricas que existem em mecanismos com estrutura cinemática fechada são analiticamente resolvidas, evitando deste modo modelos matemáticos com equações diferenciais e algébricas simultâneas. Das relações cinemáticas, o modelo dinâmico (matrizes de inércia, rigidez e amortecimento, etc) é obtido, e novamente informações essenciais à análise e síntese dos sistemas podem ser determinadas. O comportamento no tempo desses modelos pode ser encontrado por um método de integração de equações diferenciais qualquer. Adota-se o Simulink/MatLab® para representar o modelo assim desenvolvido em diagrama de blocos, e conseqüentemente simulá-lo. Através deste tratamento, cada bloco da implementaçao em Simulink/MatLab® contém o correspondente modelo analítico de um único módulo, cujo estabelecimento depende das características dinâmicas do sistema que se deseja analisar. A vantagem de adotar tal representação, baseada no fluxo de potência, consiste no fato de que um módulo pode ser substituído por outro, descritivo de um elemento ou subsistema com a mesma função, porém com configuração física distinta, e, conseqüentemente, modelo matemático específico, sem qualquer alteração nos demais componentes do sistema. Este procedimento está sendo adotado para modelagem dos diversos sistemas veiculares, como os de suspensão, direção, transmissão e freios, e também os pneus, inseridos em um chassi, incluindo os graus de liberdade desejados do veículo, todos descritos de forma modular semi- analítica através da mesma abordagem, empregando a técnica de modelagem mais apropriada para representá-los. / [en] The sub-division of a vehicle in modules is very useful when we want to study the dynamical behavior of a certain sub-system and its influence in other components. In some cases, due to the type of treatment employed to describe the dynamic behavior of the elements, we don`t get to notice the way that inherent variables in a sub-system interacts with the others, and, consequently, the subsystems amongst themselves. The modular approach based on the power flow allows a better identification of the causal relationships among sub-systems, once it can define, in clear and consistent way, what are the input and output variables of each component or module, and, consequently, their couplings. In this type of treatment applied to the mechanical systems, once established the kinematics of a sub-system, it can be obtained the relationships among the efforts that their components produce on the other ones, from the characterization of the power transmitted through their several elements. This paper presents a semi-analytical procedure of modular modeling applied to the suspension and steering systems of a ground vehicle, in which the input and output variables indicate the power flow among the elements of the whole system. Such approach has as base the Bond Graphs technique, used in multidomain systems in general, and uses some concepts of the Kinematic Transformers methodology, usually applied to the multibody systems. From the mechanisms geometry, the matrices that represent the kinematics links between its elements are found, the operation of the integrated systems can be simulated and analyzed, and information about its design can be obtained. The algebraic loops (equations) inherent to mechanisms with closed kinematic structure are solved analytically, and there is not a mathematical model with simultaneous algebraic and differential equations. From the kinematic relations, the dynamic model (inertial, stiffness and damping matrices) is obtained, and again essential information to the systems analysis and synthesis can be determined. The models time behavior can be found by any differential equations integration method. The Simulink/Matlab is adopted to represent the model developed by block diagrams, and consequently to simulate it. Through this treatment, each block in the Simulink/Matlab implementation contains the correspondent analytical model of a single module, whose establishment depends on the dynamic characteristics of the system to be analyzed. The advantage of adopting such representation, based on the power flow, consists in the fact that a module can be substituted for other, descriptive of an element or sub-system with the same function, however with different physical configuration, and, consequently, specific mathematical model, without any alteration in the other components of the system. This procedure is being adopted for modeling all vehicular systems, like the suspension, steering, transmission and brakes systems, and also the tires, inserted in the chassis, including the desired degrees of freedom of the vehicle, all described in a semi- analytical modular way by the same approach, using the most appropriate modeling technique to represent them.

[pt] Mecanismos são essencialmente (mas não exclusivamente) compostos por vários corpos rígidos que possuem movimento relativo entre si. Cada corpo rígido está ligado através de uma junta a um ou mais corpos, sendo a sequência de corpos conectados chamada de cadeia cinemática. Cadeias cinemáticas abertas (ou em série) não têm restrições sobre uma de suas extremidades, já cadeias fechadas (ou paralelas) têm restrições em ambas as extremidades. O foco neste trabalho será dado no estudo de mecanismos com cadeias cinemáticas fechadas ou mecanismos paralelos. Assim, este trabalho apresenta a determinação da solução analítica do modelo dinâmico de um mecanismo paralelo plano com três graus de liberdade através da caracterização do fluxo de potência entre os seus componentes. A partir das relações geométricas associadas ao deslocamento dos seus graus de liberdade, as relações cinemáticas associadas às suas velocidades são determinadas. Considerando o fluxo de potência entre os graus de liberdade, e também entre estes e os elementos de atuação (atuadores lineares elétricos), as relações de equilíbrio das forças e torques são obtidas. Levando em consideração os efeitos inerciais dos componentes do sistema, a rigidez e efeitos de amortecimento, as equações de movimento ou as equações de estado são analiticamente determinadas e representadas em qualquer sistema de referência, local ou global. Além disso, as relações entre a cinemática inversa e a dinâmica direta são apresentadas. Esta abordagem adota os mesmos fundamentos, conceitos e elementos da técnica dos grafos de ligação, com a sua notação simbólica e representação gráfica. A metodologia proposta é generalizada e aplicável em qualquer tipo de mecanismo (aberto ou fechado, plano ou espacial). O modelo cinemático inverso do mecanismo de cadeia fechada, que tem uma solução fácil quando comparado com o modelo direto, pode ser desenvolvido por qualquer metodologia conhecida. Neste trabalho, a técnica da cadeia vetorial é usada para determinar o modelo geométrico inverso, e com a sua derivação, as relações cinemáticas são obtidas, e, portanto, a matriz Jacobiana inversa. Desse modo, é construída a estrutura em grafos de ligação da cinemática inversa e, a partir das relações de causa e efeito, encontra-se o modelo dinâmico direto do mecanismo. Assim, esta metodologia (grafos de ligação ou fluxo de potência) é mais eficiente e segura para determinar os modelos dinâmicos analíticos (fechados) de mecanismos paralelos. Um conjunto de simulações foi realizado para validar esta abordagem, usando os dados reais (geometria, inércia, amortecimento, forças de atuação, etc.) a partir de um mecanismo plano projetado e construído especialmente para a finalidade de comparar os resultados simulados e experimentais. Uma estratégia de controle de malha fechada usando a cinemática inversa e os modelos dinâmicos diretos é proposta. Finalmente, testes experimentais validam esta estratégia. As equações analíticas levam a um processo de simulação e controle em tempo real mais eficientes destes sistemas. / [en] Mechanisms are essentially (but not exclusively) made up of multiple rigid bodies that have relative motion between themselves. Each rigid body is connected through a joint to one or more bodies, wherein the sequence of connected bodies is called kinematic chain. Open (or serial) kinematic chains have no restrictions on one of their ends, as closed (or parallel) chains have restrictions on both ends. The focus in this work will be given on the study of mechanisms with closed kinematic chains or parallel mechanisms. Thus, this work presents the analytical form determination of the dynamic model of a parallel planar mechanism with three degrees of freedom through the characterization of the power flow between its components. From the geometrical relations associated to the displacement of their degrees of freedom, the kinematic relations associated to their speeds are determined. Considering the power flow between the degrees of freedom, and also between these and the actuating elements (linear electric actuators) the equilibrium relations of the forces and torques are obtained. Accounting for inertial effects of system components, the stiffness and damping effects, the equations of motion or the state equations are analytically determined and represented in any reference frame, local or global. Besides, the relation between the inverse kinematics and the direct dynamics is presented. This approach adopts the same fundamentals, concepts and elements of the Bond Graph Technique, with its symbolic notation and graphical representation. The proposed methodology is generalized and applicable in any type of mechanism (open or closed, planar or spatial). The inverse kinematic model of the closed chain mechanism, which has easy solution when compared to the direct model, can be developed by any known methodology. In this work, the vector loop technique is used to determine the inverse geometric model, and with its derivation, the kinematic relations are obtained, and therefore the inverse Jacobian matrix. Thereby, the inverse kinematics bond graph is built and, from the cause and effect relations, the direct dynamic model of the mechanism is found. Thus, this methodology (bond graphs or power flow) is more efficient and secure to achieve the dynamic analytical (closed) models of parallel mechanisms. A set of simulations are performed to validate this approach, using the real data (geometry, inertia, damping, actuators forces, etc.) from a planar mechanism designed and built especially for the purpose to compare the simulated and experimental results. A closed-loop control strategy using the inverse kinematic and the direct dynamic models is proposed. Finally, experimental tests validate this strategy. The analytical equations lead to a more efficient simulation process and real-time control of these systems.

[pt] Modelagem e Controle Não Linear de um Veículo Terrestre sobre Suspensão descreve um estudo em dinâmica veicular no qual inicialmente apresenta-se um modelo analítico para representar a geração de forças longitudinais e laterais no contato do pneu com o solo. Em seguida é desenvolvido, para um automóvel de passeio terrestre sobre suspensão, um modelo não linear de 4 graus de liberdade (velocidades longitudinal, lateral, de guinada e de rolagem), e a sua linearização. Expande-se esse modelo para um de 8 graus de liberdade, no qual inclui-se o movimento de rotação axial de cada uma das quatro rodas, e consideram-se os movimentos do veículo somente no plano, sem efeitos de pitch ou bounce, mas apresentando alguma relação de distribuição de cargas devido ao roll. Descrevem-se ainda modelos em Grafos de Ligação para os três dinâmicas de um veículo terrestre (longitudinal, lateral e vertical) e seus acoplamentos, visando futuras análises mais detalhadas desse sistema. Todos os modelos em malha aberta são validados através simulações computacionais em diversas condições típicas de operação. Na segunda parte desse trabalho é apresentada a estratégia proposta para o tratamento do problema de controle direcional do veículo em uma manobra qualquer, empregando a metodologia da linearização por realimentação, tendo como base o modelo linear de 4 graus de liberdade. São analisados os resultados encontrados através de simulação computacional para a malha fechada com diferentes combinações de parâmetros, empregando os modelos não lineares de 4 e 8 graus de liberdade. Conclui-se discutindo a possibilidade de generalização deste procedimento para diferentes aplicações em Dinâmica Veicular. / [en] Modeling and Non Linear Control of a Ground Vehicle's Steering describles a study in vehicle dynamics, which presents an analytic model representing the generation of longitudinal and lateral forces at the contact patch between tire and ground. Next it is developed, for a typical passenger car, a non-linear model with four degrees of freedom (longitudinal, lateral, yaw and roll velocities), and its linearization. This model is then expanded to another one with eight degrees of freedom, which includes the axial rotation of each one of the four wheels, and considers the vehicle's movement only at a known plane, whithoud pitch and bounce effects, but including some load distribution among the wheels, due to roll. Computational simulation in varius typical operation condition validate all open loop models. The second part of this work presents the proposed strategy for directional control of a vehicle at any type of manoeuvre, using the feedback linearization methodology, directly applied to the linear four degrees of freedom model. Theresults obtained trhough computational simulation for a closed loop model with different parameters are analysed using both nonlinear four and eight degrees of freedom models. The possibility of generalizing this procedure to distinct applications in Vehicle Dynamics is, then, discussed.