The goal of this paper is to study the LQG problem for a class of infinite dimensional systems. We investigate the convergence of compensator gains for such systems when standard finite element schemes are used to discretize the problem. We are particularly interested in the analysis of the uniformly exponential stability of the corresponding closed - loop systems resulting from the finite dimensional compensators. A specific multiple component flexible structure is used to focus the analysis and to test problem in numerical simulations. An abstract framework for analysis and approximation of the corresponding dynamics system is developed and used to design finite - dimensional compensators. Linear semigroup theory is used to establish that the systems are well posed and to prove the convergence of generic approximation schemes. Approximate solutions of the optimal regulator and optimal observer are constructed via Galerkin - type approximations. Convergence of the scheme is established and numerical results are presented to illustrate the method / Ph. D.

The interaction of an aircraft's structure and the flight dynamics can degrade the performance of a controller designed only considering the rigid body flight dynamics. These concerns are greater for the next generation adaptive controls. These interactions lead to an increase in the tracking error, instabilities in the control parameters, and significant structural excitations. To improve the understanding of these issues the interactions have been examined using simulation as well as flight testing of a subscale aircraft. The scaling required for such a subscale aircraft has also been examined. For the simulation a coordinate system where the non-linear flight dynamics are orthogonal to the linear structural dynamics was defined. The orthogonality allows the use of separates models for the aerodynamics. For the non-linear flight dynamics, preexisting table lookups with extended vortex lattice are used to determine the aerodynamic forces. Strip theory is then used to determine the smaller, but still important, unsteady aerodynamic forces due to the flexible motion. Because the orientation of the engines is dependent on the structural deformations, the propulsive force is modeled as a non-conservative follower force. The simulation of the integrated dynamics is then used to examine the effects of the aircraft flexibility and resultant ASE interactions on the performance of adaptive controls. For the scaling, the complete similitude of a flexible aircraft was examined. However, this complete similitude is unfeasible for an actual model, so partial similitude is investigated using two approaches. First, the classical approximations of the flight dynamic modes are used to reduce the order of the coupled model, and consequently the number of scaling parameters required to maintain the physics of the system. The second approach uses sensitivity of the response to errors in the aircraft's nondimensional parameters. Both methods give a consistent set of nondimensional parameters which do not have significant influence on the aeroservoelastic interaction. These parameters do not need to be scaled, thus leading to a viable scaled model. A subscale vehicle has been designed which shows significant coupling between the flight dynamics and structural dynamics. This vehicle was used to validate the results of the scaling theory. Output error system identification was used to identify a model from the flight test data. This identified model provides the frequency of the short-period mode, and the effects of the Froude number on the flexibility. / Ph. D.

Anti-roll bars aim to increase the vehicle\'s safety during curved trajectories. By reducing the roll angle, the bars minimize the risk of overturning during cornering in function of the increasing lateral acceleration, and also, as a consequence, improves the steering comfort. This work presents studies of vehicle\'s lateral dynamics in three dierent approaches: a vehicle without anti-roll system, a vehicle with passive roll bar and a vehicle with an active anti-roll bar. The active anti-roll bar is controlled by a torque-generating motor and comparisons between two robust controllers is presented. The bars are modeled by FEM (Finite Element Method) and controllers LQG/LTR (Linear Quadratic Gaussian/ Loop Transfer Recovery) and H? Loop-Shaping are designed to the active system in order to evaluated the best option. In addition, the vehicle\'s lateral dynamic is hybridized to the exible bar model in order to obtain an unique system. It reviews the vehicle\'s roll dynamic and describes in detail the FEM applied to dynamic modeling of exible structures. The influence of the active anti-roll system and the different controllers are illustrated through numerical simulation and a comparison between the passive system and the system without bar is performed. / As barras estabilizadoras têm como objetivo aumentar a segurança dos veículos durante trajetórias curvelíneas. Através da redução do ângulo de rolagem, as barras minimizam o risco de capotamento durante as curvas em função da aceleração lateral, e também, como consequência, melhoram o conforto de dirigibilidade. Este trabalho apresenta estudos da dinâmica lateral do veículo em três abordagens diferentes: um veículo sem sistema de anti-rolagem, um veículo com barra estabilizadora passiva e um veículo com barra estabilizadora ativa. A barra de anti-rolagem ativa é controlada por um motor gerador de torque e uma comparação entre dois controladores robustos é apresentada. As barras são modeladas pelo FEM (Método dos Elementos Finitos) e os controladores LQG/LTR (Gaussiano Quadrático Linear/Malha de Recuperação) e H? Loop-Shaping são projetados para o sistema ativo com o objetivo de avaliar a opção mais promissora. Além disso, à dinâmica lateral do veículo é adicionado o modelo flexível da barra de antirolagem para se obter um sistema único (modelo híbrido). O trabalho revisa a dinâmica lateral do veículo e descreve de forma detalhada o FEM aplicado à modelagem dinâmica de estruturas flexíveis. A influência do sistema ativo de anti-rolagem e dos diferentes controladores é ilustrada através de simulação comparando-a com o sistema passivo e o modelo dinâmico sem sistema de anti-rolagem.

[pt] Neste trabalho é formulado e analisado o equilíbrio estático e a dinâmica de uma viga elástica tridimensional. A teoria tridimensional empregada, que pode ser chamada de teoria de Cosserat para vigas, é exata geometricamente, ou seja, não está baseada em aproximações geométricas ou suposições mecânicas. Para a deformação da viga, assume-se a hipótese de Bernoulli e por simplicidade consideram-se relações constitutivas lineares para o material. A configuração deformada da viga é descrita através do vetor de deslocamento da curva de centróides, e uma base móvel, rigidamente unido à secção transversal da viga. A orientação da base móvel, relativo a um sistema inercial, é parametrizada usando três rotações elementares consecutivas. Na teoria de Cosserat para vigas, as equações do movimento são equações diferenciais parciais não-lineares em função do tempo e uma variável espacial. No entanto, para o equilíbrio estático, as equações tornam- se equações diferenciais ordinárias não-lineares com uma variável espacial que são resolvidas usando o método de perturbação. Da solução do equilíbrio estático, obtêm-se as funções de deslocamento da viga, em função dos deslocamentos e rotações nodais, as quais são usadas para a análise dinâmica. Para obter a dinâmica da viga usa-se a equação de Lagrange, que é formada pelas expressões da energia cinética e da energia potencial de deformação. Além disso, usa-se o método de Newmark para resolver as equações do movimento. Como aplicação, estuda-se numérica e experimentalmente, a dinâmica de uma viga rotativa curva contida numa cavidade uniforme. Quando se usa a teoria de Cosserat para vigas, que leva em conta as não linearidades geométricas, a alta precisão da resposta dinâmica é obtida dividindo o sistema em poucos elementos, as quais são bem menores que o tradicional MEF, essa é a principal vantagem da teoria desenvolvida. / [en] In this work, it is formulated and analyzed the static equilibrium and the dynamics for three dimensional deformation of elastic rods. The intrinsically one-dimensional theory that is employed, which may be called the special Cosserat theory of rods, is geometrically exact, namely, it is not based upon geometrical approximations or mechanical assumptions. For the rod deformation, it is adopted the Bernoulli hypotheses and for simplicity, the linear constitutive relations are employed. The deformed configuration of the rod is described by the displacement vector of the deformed centroid curve and an orthonormal moving frame, rigidly attached to the cross-section of the rod. The orientation of the moving frame, relative to the inertial one, is related by the rotation matrix, parameterized by three elemental rotations. In the sense of Cosserat theory, the equations of motion are nonlinear partial dfferential equations, which are functions of time and one space variable. For the static equilibrium, however, the equations become nonlinear ordinary differential equations with one space variable, which can be solved approximately using standard techniques like the perturbation method. After the static equilibrium equation are solved, the displacement functions are obtained. These nonlinear displacement functions, which are functions of generic nodal displacements and rotations, are used for dynamical analysis. To obtain the dynamics of the Cosserat rod, it is used the Lagrangian approach, formed from the kinetic and strain energy expressions. Furthermore, the equations of motion, which are nonlinear ordinary dfferential equations, are solved numerically using the Newmark method. As an application, a curved rod, constrained to rotate inside a hole, is investigated numerically and experimentally. When using the Cosserat rod approach, that take into account all the geometric nonlinearities in the rod, the higher accuracy of the dynamic responses is achieved by dividing the system into a few elements, which is much less than in the traditional FEM

Orientador : João Mauricio Rosario / Tese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Mecanica / Made available in DSpace on 2018-08-03T08:57:26Z (GMT). No. of bitstreams: 1 David_SergioAdriani_D.pdf: 6908391 bytes, checksum: 3f7717f958c96997fd34af75cca160e5 (MD5) Previous issue date: 2003 / Resumo: Neste trabalho desenvolveu-se a modelagem dinâmica de estruturas flexíveis, a investigação de seu comportamento não linear por meio de simulações numéricas e a validação experimental através da montagem de um protótipo. Ressalta-se que em se tratando de sistemas não lineares, embora existam métodos de procedimento, não existe uma teoria única que possa atender às diferentes aplicações e necessidadesde análise não linear. Dessa maneira, abordou-se formas específicas de se tratar duas aplicações distintas, uma envolvendo manipuladores robóticos flexíveis e a outra um oscilador mecânico flexível. Desenvolveu-se ferramentas de modelagem, simulação, análise e implementação. A aplicação envolvendo o oscilador mecânico flexível teve âmbitos experimentais e os resultados de alguns ensaios sugerem uma boa concordância com o modelo teórico. Os resultados obtidos desse trabalho e o aparato experimental montado, ambos, permitem que diversas investigações futuras ainda possam ser realizados definidas e podem agregar conhecimento sobretudo aos interessados em temas relacionados à estruturas flexíveis e análise não linear / Abstract: This work deserihes the dynamic modeling of flexible structures. the investigation about its nonlinear behaviour through numerical simulations and the construction of an experimental appararus in order to validate the model. I outline the fact that to deal with nonlinear systems, although there are conduct method, there isn't a unique theory that could to attend to different applications and necessities of nonlinear analysis. For this reason, specific approach had been presented to deal with two applications, flexible robot manipulators and flexible mechanical oscillator. Dynamic modeling, numerical simulation, analysis and implement are performed. The application which involves the flexible mechanical oscillator have experimental scope and the results have showed a good agreement with the theoretical model. The results obtained and the experimental apparatus COnstructed. both, allow sundry future investigations and can add knowledge specially to the interested in flexible structures and nonlinear analysis / Doutorado / Mecanica dos Sólidos e Projeto Mecanico / Doutor em Engenharia Mecânica

[pt] Neste trabalho é abordado o problema do controle durante o período de transição de contato em manipuladores robóticos. Tipicamente é o controlador de força que deve atuar durante o período transiente, no entanto esse controlador não está preparado para lidar com o fenômeno altamente não-linear que representam os impactos e as perdas de contato. No trabalho, inicialmente é feita uma análise do desempenho e estabilidade dos controladores de força convencionais durante a transição de contato. Essa análise é baseada em modelos simplificados: um de manipulador rígido e outro de flexível. É mostrado que os impactos não originam instabilidade dinâmica mas podem deteriorar severamente o desempenho do sistema. Posteriormente, com a finalidade de obter modelos mais realistas que validassem a efetividade de novos controladores, é desenvolvido um modelo para um manipulador rígido-flexível de dois elos em que se colocam pastilhas piezoelétricas coladas ao longo do braço flexível. Também são estudados modelos de contato. Finalmente, são apresentados três novos controladores que são projetados especificamente para lidar com os impactos e perdas de contato que aparecem na transição de contato. A idéia do primeiro controlador é detectar o primeiro impacto e a partir dele reformular a trajetória que a extremidade do manipulador deverá seguir para atingir a superfície do meio com velocidade mínima, evitando assim outros impactos. O projeto deste controlador é feito usando a teoria de controle ótimo. O segundo controlador baseia-se na linearização do movimento de um manipulador flexível em torno do movimento do manipulador considerado rígido. A equação resultante é usada para projetar um controlador de posição de alta precisão que permite evitar, ou diminuir, a severidade do impacto inicial. A idéia do terceiro controlador é amortecer ativamente a parte flexível do manipulador através das pastilhas piezoelétricas que funcionam como atuadores e sensores colocados de maneira a garantir estabilidade em presença de dinâmica residual. O projeto do controlador é formulado como um problema de otimização que é resolvido através de técnicas de programação não-linear. / [en] In this work it is considered the problem of control during the contact transition period in robotic manipulators. Typically it is the force controller that acts during the transient period, however that controller is not prepared to deal effectively with impacts and losses of contact. In this work, it is initially performed an analysis of the stability and performance of conventional force controllers working during the contact transition. The analysis is based on simplified models for rigid and flexible manipulators. It is proved that the impacts do not cause dynamic instability, but they can severely degrade the system performance. Later, with the purpose of getting more realistic models to validate the effectiveness of new controllers, a model of a two-link rigid-flexible manipulator is developed considering glued piezoelectric sheets along the flexible arm. Contact models are also studied. Finally, three new controllers are presented which are designed to specifically deal with impacts and losses of contact during the contact transition period. The main idea of the first controller is to identify the first and unavoidable impact and then to reformulate the trajectory that the endeffector will follow to approach the collision surface with a minimum velocity, thus preventing new impacts. The controller is designed by using the theory of optimal control. The second controller is based on the equation of the motion of a flexible manipulator linearized around the motion of the manipulator when all the links are considered rigid. The obtained equation is used to design a high precision position controller to prevent or lessen the severity of the initial impact. The idea of the third controller is to actively damp the flexible part of the manipulator through the piezoelectric sheets that act as collocated actuators and sensors, this way the stability in presence of residual dynamics is guaranteed. The controller design is formulated as an optimization problem that is solved through nonlinear programming techniques.

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Future solar sail and solar power satellite missions require deployment of large and lightweight flexible structures in space. One option is to spin the assembly and use the centrifugal force for deployment, stiffening and stabilization. Some of the main advantages with spin deployment are that the significant forces are in the plane of rotation, a relatively simple control can be used and the tension in the membrane or web can be adjusted by the spin rate to meet the mission requirements. However, a successful deployment requires careful development of new control schemes. The deployment rate can be controlled by a torque, applied either to a satellite in the center or by thrusters in the corners, or by deployment rate control, obtained by tether, spool braking or folding properties. Analytical models with only three degrees of freedom were here used to model the deployment of webs and membranes for various folding patterns and control schemes, with focus on space webs folded in star-like arms coiled around a center hub. The model was used to investigate control requirements and folding patterns and to obtain optimal control laws for centrifugal deployment. New control laws were derived from the optimal control results and previously presented control strategies. Analytical and finite element simulations indicate that the here developed control laws yield less oscillations, and most likely more robustness, than existing controls. Rotation-free (RF) shell elements can be used to model inflation or centrifugal deployment of flexible memebrane structures by the finite element method. RF elements approximate the rotational degrees of freedom from the out-of-plane displacements of a patch of elements, and thus avoid common singularity problems for very thin shells. The performance of RF shell elements on unstructured grids is investigated in the last article of this thesis, and it is shown that a combination of existing RF elements performs well even for unstructured grids. / QC 20100729

published_or_final_version / Architecture / Master / Master of Architecture