Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 1980. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND AERO. / Includes bibliographical references. / by Edward Gregory Taylor. / Ph.D.

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A feedback design procedure known as extended linearization consists in replacing a mathematical model of a nonlinear dynamical system with its family of linearizations, parametrized by the operating point, and then combining feedback gains designed for representatives of the family into a single nonlinear feedback law. The principles of the procedure, applicable both to lumped-parameter and distributed-parameter systems, are discussed at the outset. The development shows limits on feedback laws that can be designed, as well as nonuniqueness of solutions, inherent in the method. / Ph. D.

The otolith organs are commonly modeled as a system consisting of three distinct elements, a viscous endolymph fluid in contact with a rigid otoconial layer that is attached to the skull by a viscoelastic gel layer. However, in this model the gel layer is considered as a bi-layered viscoelastic solid and is modeled as a simple Kelvin-Voigt material. The governing differential equations of motion are derived and nondimensionalized yielding - three non-dimensional parameters: nondimensional viscosity, nondimensional elasticity and nondimensional density. These non-dimensional parameters are derived from experimental research. The shear stresses acting at the interface of the viscoelastic bi-layered gel are nondimensionalized and equated. The governing differential equations are then solved using finite difference techniques on a digital computer for a step-change in velocity and a constant acceleration stimulus. The results indicate that the inclusion of a viscoleastic bi-layered gel is essential for the model to produce greater otoconial layer deflections that are consistent with physiologic displacements. Future mathematical modeling of the otolith organs should include the effects of a viscoelastic bi-layered gel, as this is a major contributor to system damping and response and increased otoconial layer deflections. / Master of Science

The design of controllers for structural systems, particularly those associated with large space structures, has received a considerable amount of attention in the past few years. The usual approach to designing these controllers is to apply modern control theory to a reduced linear system obtained from finite element analysis or from a truncated modal analysis. In most of these designs, the sensor signal must be processed to separate out the contributions from each mode so that it may be sent to the appropriate actuators. The analysis presented here, on the other hand, obtains exact solutions for a selected set of sensor and actuator positions for simple structural elements. Sensor signals are fed back directly to the actuators with appropriate gains. The method of analysis is that of classical control theory using Laplace transforms and the associated open and closed-loop transfer functions. Single-input-single-output feedback control is applied to various flexible cable and beam configurations. Root-loci for various values of gain are constructed and the system characteristics and the global system stability are determined. Although the procedure outlined above can be carried out for basic structural elements, more complex structures and control configurations are synthesized using the dynamic stiffness matrix method. With this method, the exact relationships of the basic elements can be combined to allow analysis of multi-input-multi-output control of more complex structures. Using this approach, examples for flexible cable and beam configurations are presented. It was found that exact solutions can be obtained using a finite number of sensors and actuators. It was also determined that a single co-located sensor-actuator at the boundary of a fixed-free cable or beam can control all the vibrational modes of the cable or beam. Also, pure signals from a perfect sensor can be used without any additional signal processing. The multi-input-multi-output investigation demonstrates that, even without cross-gain feedback, there is interaction between the sets of co-located sensor-actuator pairs. It appears that this interactive effect needs to be included in any multi-input-multi-output control design. By starting with fundamental elements of beams and cables, it was shown that reasonably sophisticated systems can be modeled. Finally, considerable insight is offered by analyzing the control of flexible structures using exact transfer function relationships. / Ph. D.

Ao empregar a teoria de controle para a dinâmica de uma estrutura, é possível projetar um observador potencialmente complexo que a partir da leitura de apenas um sensor estime o estado do sistema e determine os modos de vibração presentes. Este trabalho, no entanto, estuda o uso de filtros modais em controle de vibrações, com a motivação de que essa estratégia dependa de menos componentes eletrônicos. O objetivo é encontrar um filtro modal que possua alto desempenho em malha fechada mesmo com um número reduzido de sensores. Primeiramente foi desenvolvido o modelo dinâmico do sistema em malha aberta, com posterior otimização do filtro modal por meio do método do ponto interior. Depois, foi desenvolvido o modelo dinâmico do sistema em malha fechada. A seguir, um algoritmo genético otimizou o sistema de controle de vibrações seguindo duas metodologias. A primeira considera apenas as posições dos sensores como variáveis de otimização, enquanto a segunda leva em consideração não só as posições dos sensores como também os ganhos do filtro modal e o ganho de retroalimentação de velocidade. Os resultados do estudo do sistema em malha aberta mostram que se trata se um problema de otimização não-convexa, mas todas as tentativas levaram a crer que o mínimo global tenha sido encontrado para a função objetivo proposta, baseada no desvio quadrático da função de resposta em frequência do filtro modal com relação a uma referência pré-estabelecida. Os resultados do estudo do sistema em malha fechada mostram que considerar as posições e os ganhos como variáveis de otimização levam a um filtro modal mais conveniente do que o que é obtido levando-se em consideração apenas as posições. Finalmente, a partir da interpretação dos resultados, conclui-se que mesmo com um filtro modal composto por 5 sensores é possível ainda desenvolver um sistema de controle de vibrações que seja de fase mínima. Apesar de existir spillover de observação do ponto de vista de um filtro modal, nota-se que todos os modos estão em fase, o que acaba por ser até benéfico para o sistema de controle de vibrações. / The control systems theory may be applied to structural dynamics in order to design a potentially complex observer which is able to estimate the system\'s state from the readings of a sole sensor. This work, though, focused on the application of modal filters in vibration control based on the premise that this strategy will require a simpler hardware. The main target consists of finding a modal filter which can deliver high performance in vibration control despite being composed of a reduced number of sensors. In the first step, a dynamic model of a modal filter on a cantilever beam was developed, followed by an optimization carried on with the interior-point method. Then, the dynamic model of the closed-loop cantilever beam was developed aftwerwards. However, this time a genetic algorithm was used as the optimization method instead, with two methodologies being employed. While the first one considered only the placement of the sensors, the second one also takes into consideration the modal filter gains and the negative velocity feedback gain. The results yielded by the open-loop cantilever beam analysis showed that it is a non-convex optimization problem. However, all of the attempts support the belief that the global minimum has been found in the sense of the proposed objective function, which was based on the quadratic error between the frequency response function (FRF) of the modal filter and an idealized FRF used as reference. The results yielded by the closed-loop system optimization showed that it is more convenient to consider as optimization variables not only the placement of the sensors, but also their gains and the negative velocity feedback gain. Finally, after pondering over the obtained results, it has been concluded that the observation spillover resulting from a modal filter composed of a reduced number of sensors may be turned to the vibration control system\'s favour by means of optimization. The minimal-phase modal filter composed of 5 sensors found in this work stands out as the most notable example in this work, being able to guarantee stability for the first 12 modes since all of them are in-phase.

Thèse doctorat : Informatique : Villeurbanne, INSA : 2005. / Thèse rédigée en anglais. Résumé étendu en anglais. Titre provenant de l'écran-titre. Bibliogr. p. 214-226.

Viscoelastic materials can today be found in a wide range of practical applications. In order to make efficient use of these materials in construction, it is of importance to know how they behave when subjected to dynamic load. Characterization of viscoelastic materials is therefore an important topic, that has received a lot of attention over the years. This thesis treats different methods for identifying the complex modulus of an viscoelastic material. The complex modulus is a frequency dependent material function, that describes the deformation of the material when subjected to stress. With knowledge of this and other material functions, it is possible to simulate and predict how the material behaves under different kinds of dynamic load. The complex modulus is often identified through wave propagation testing, where the viscoelastic material is subjected to some kind of load and the response then measured. Models describing the wave propagation in the setups are then needed. In order for the identification to be accurate, it is important that these models can describe the wave propagation in an adequate way. A statistical test quantity is therefore derived and used to evaluate the wave propagation models in this thesis. Both nonparametric and parametric identification of the complex modulus is considered in this thesis.  An important aspect of the identification is the accuracy of the estimates.  Theoretical expressions for the variance of the estimates are therefore derived, both for the nonparametric and the parametric identification. In order for the identification to be as accurate as possible, it is also important that the experimental data contains as much valuable information as possible. Different experimental conditions, such as sensor locations and choice of excitation, can influence the amount of information in the data. The procedure of determining optimal values for such design parameters is known as optimal experiment design. In this thesis, both optimal sensor locations and optimal excitation are considered.

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