Máquinas rotativas são sempre sujeitas à vibrações mecânicas, em menor ou maior grau, e para garantir um correto funcionamento destas máquinas, evitando falhas de operação, é necessário realizar o controle destas vibrações. Uma das frentes que vem se destacando nesta área é o controle ativo de vibrações. Neste tipo de abordagem as vibrações são controladas ativamente através de um sistema de atuação e de uma técnica de controle a ser empregada de forma satisfatória. Neste contexto, existem inúmeras abordagens da teoria de controle que podem ser aplicadas, e aqui é avaliada a aplicação da metodologia proposta por Udwadia e Kalaba para o controle de trajetória de sistemas não lineares, uma técnica de controle ainda não utilizada no controle ativo de vibrações em sistemas rotativos. Em um primeiro momento a avaliação do desempenho e potencial de aplicação desta metodologia é realizada em sistemas com quatro graus de liberdade através de comparação com controladores do tipo proporcional-integral-derivativo e regulador linear-quadrático. Os resultados obtidos pelo controlador avaliado são similares aos resultados obtidos pelo controlador proporcional-integral-derivativo com melhorias em termos de erro de posicionamento. A metodologia também é avaliada em um sistema rotativo com um maior número de graus de liberdade, no qual é possível compreender o comportamento do controlador em um sistema flexível. Por fim realiza-se um exemplo de aplicação da técnica em um sistema com um eixo rígido e mancal hidrodinâmico ativo de atuação eletromagnética. Os resultados de simulação obtidos mostram que a metodologia possui potencial de aplicação para sistemas que apresentam eixo rígido, no qual uma drástica redução na amplitude de vibração do sistema foi observada por toda faixa de operação avaliada, enquanto que a sua aplicação em sistemas com eixo flexível se tornou restrita aos dois primeiros modos de vibrar do sistema flexível utilizado, modelado através do método dos elementos finitos. / Rotating machinery are always subject to mechanical vibration to a lesser or greater degree, and to ensure proper operation of these machines, avoiding faulty operation, it is necessary to carry out the control of these vibrations. One of the fronts that stood out in this area is the active vibration control. In this type of approach, vibrations are actively managed through an actuation system and a control technique to be used satisfactorily. In this context, there are numerous approaches to control theory that can be applied, and here the application of the methodology proposed by Udwadia and Kalaba for trajectory control of nonlinear systems is evaluated, a control technique not yet used in active vibration control in rotating systems. At first the evaluation of the performance and potential application of this methodology is performed on systems with four degrees of freedom by comparison with controllers of the proportional-integral-derivative and linear-quadratic regulator type. The results of the evaluated controller are similar to results obtained by proportional-integral-derivative controller with improvements in positioning error. The methodology is also evaluated in a rotating system with a larger number of degrees of freedom, wherein we can understand the controllers behavior in a flexible system. Finally, an application example of the technique on a system with a rigid shaft and hydrodynamic bearing with electromagnetic actuators is presented. The obtained simulation results show that the method has application potential to systems having rigid shaft, in which a dramatic reduction in the amplitude of vibration of the system was observed at all the operating range evaluated, whereas their application in systems with flexible shaft became restricted to the first two vibration modes of the flexible system used, modeled by the finite element method.

A natureza vibratória, oriunda da transferência energética, manifesta-se em todos os sistemas e estruturas. Na engenharia, essa transferência energética se revela como um fenômeno vibratório indesejável ou desejável. Em sistemas mecânicos, o controle dinâmico para mitigação de vibrações indesejáveis se realiza através de diversas técnicas e configurações, entre os mais usuais, o Amortecedor de Massa Sintonizável (AMS). No entanto, sabe-se que seu desempenho é suscetível a alterações nas frequências de operação e na natureza das excitações. Em sistemas elétricos, as vibrações do ambiente podem ser desejáveis e convertidas em energia elétrica útil para a realimentação de rede de sensores sem fio e computação pervasiva. A fim de combinar estes fenômenos e reduzir custos de operação, é necessário projetar dispositivos sintonizáveis robustos capazes de operar eficientemente em uma banda larga de frequências. Portanto, este trabalho visa projetar e analisar experimentalmente um atenuador de vibrações eletromagnético sintonizável (semi-ativo) com captação energética (AEMSCE) através da introdução deliberada de não linearidades. O AEMSCE consiste em um sistema massa-mola-amortecedor não linear com um ímã oscilante central orientado sob forças repulsivas magnéticas e uma bobina instalada, sendo capaz de dissipar as vibrações da estrutura e convertê-las em energia elétrica útil. Os recursos e parâmetros do AEMSCE são apresentados e identificados. O fator de transdução eletromagnético que acopla o sistema mecânico ao elétrico é quantificado. Mostra-se que a variação da distância entre ímãs promove ao sistema ressonância ajustável e que a força de restauração magnética resultante apresenta uma faixa de operação linear. No trabalho, verifica-se que o campo de máxima captação energética está contido na faixa de operação linear confirmando a relevância deste campo linear. O comportamento do sistema é analisado considerando as influências da força restauradora magnética, das forças amortecidas e da força de atrito. A partir dessas análises e das aproximações realizadas, apresenta-se estratégias de controle passivas e técnicas de otimização para mitigação, cuja resultante é um campo de atenuação ótimo, assim como desenvolve-se métodos de otimalidade para maximizar a conversão energética do AEMSCE, cuja resultante é um amortecimento elétrico ótimo ou um amortecimento admissível ótimo (deslocamento máximo). Métodos analíticos e simulações numéricas são desenvolvidos em todo o trabalho com diferentes configurações para analisar a robustez e eficiência do dispositivo, através do comportamento dinâmico vibratório à resposta transiente e estacionária induzido por excitação de base harmônica. De maneira geral, os resultados mostram que os parâmetros de sintonia e amortecimento do AEMSCE podem ser combinados e ajustados para ampliar o controle de vibrações da estrutura e maximizar a captação energética, principalmente na ressonância. Verifica-se que existe uma relação de importância da tensão induzida e do amortecimento elétrico, através da variação da resistência de carga no resistor, com a atenuação e captação energética. Por fim, este trabalho buscou apresentar os melhores métodos e resultados de parâmetros de amortecimento a fim de obter informações como guia de projeto para otimizar os dispositivos futuros e para a proposição de incorporar um controle semiativo ao AEMSCE. Como forma de melhorar o desempenho em aplicações futuras, é possível combinar as propriedades ótimas resultantes e ajustá-las através de estratégias de controle semiativa, explorando a dinâmica linear e não linear do sistema. / Vibratory nature, derived from the energy transfer, manifests itself in all systems and structures. In engineering, this energy transfer is revealed as an undesirable or desirable vibrational phenomenon. In mechanical systems, the dynamic control to mitigate undesirable vibrations is achieved through several techniques and configurations, among the most usual, the Tunable Mass Damper (TMD). However, it is known that their performance is susceptible to changes in the operating frequencies and the nature of the excitations. In electrical systems, ambient vibrations may be desirable and converted into useful electrical energy for the feedback of wireless sensors network and pervasive computing. In order to combine these phenomena and reduce operating costs, it is necessary to design robust tunable devices capable of operating efficiently over a wide frequency band. Therefore, this work aims to design and experimentally analyze a tunable electromagnetic vibrations absorver (semi-active) with energy harvesting (TEMAEH) through the deliberated introduction of non-linearities. TEMAEH consists of a non-linear mass-spring-damper system with a central oscillating magnet oriented under magnetic repulsive forces and a coil installed, being able to dissipate vibrations of the structure and convert them into useful electrical energy. The TEMAEH features and parameters are presented and identified. Electromagnetic transduction factor that couples the mechanical to electrical system is quantified. It is shown that the variation of the distance between magnets provides adjustable resonance to the system and that the resulting magnetic restoring force has a linear operating range. In the work, it is verified that the field of maximum energy harvesting is contained in the linear operating range confirming the relevance of this linear field. The behavior of the system is analyzed considering the influences of magnetic restoring force, damped forces and frictional force. From these analyzes and the approximations performed, passive control strategies and optimization techniques for mitigation are presented, resulting in an optimum attenuation field, as well as optimization methods to maximize the energy conversion of the TEMAEH, resulting in an optimum electric damping or optimum permissible damping (maximum displacement). Analytical methods and numerical simulations are developed throughout the work with different configurations to analyze the robustness and efficiency of the device through the dynamic behavior of vibration to the transient and stationary response induced by harmonic based excitation. In general, the results show that the tuning and damping parameters of the TEMAEH can be combined and adjusted to increase the vibration control of the structure and to maximize energy harvesting, especially in resonance. It is verified that there is a relation of importance of the induced voltage and the electrical damping, through the variation of the load resistance in the resistor, with the attenuation and power generation. Finally, this work sought to present the best methods and results of damping parameters in order to obtain information as a project guide to optimize future devices and for the proposition to incorporate a semiative control to TEMAEH. As a way to improve performance in future applications, it is possible to combine the resulting optimal properties and adjust them through semiative control strategies, exploring the linear and non-linear dynamics of the system.

En conception de produits ou de systèmes, les approches d'optimisation déterministe sont de nos jours largement utilisées. Toutefois, ces approches ne tiennent pas compte des incertitudes inhérentes aux modèles utilises, ce qui peut parfois aboutir à des solutions non fiables. Il convient alors de s'intéresser aux approches d'optimisation stochastiques. Les approches de conception robuste à base d'optimisation stochastique (Reliablity Based Robust Design Optimization, RBRDO) tiennent compte des incertitudes lors de l'optimisation au travers d'une boucle supplémentaire d'analyse des incertitudes(Uncertainty Anlysis, UA). Pour la plupart des applications pratiques, l'UA est réalisée par une simulation de type Monte Carlo (Monte Carlo Simulation, MCS) combinée avec l’analyse structurale. L'inconvénient majeur de ce type d'approche réside dans le coût de calcul qui se révèle être prohibitif. Par conséquent, nous nous sommes intéressés dans nos travaux aux développements de méthodologies efficaces pour la mise en place de RBRDO s'appuyant sur une analyse MCS. Nous présentons une méthode d'UA s'appuyant sur une analyse MCS dans laquelle la réponse aléatoire est approximée sur une base du chaos polynomial (Polynomial Chaos Expansion, PCE). Ainsi, l'efficacité de l'UA est grandement améliorée en évitant une trop grande répétition des analyses structurales. Malheureusement, cette approche n'est pas pertinente dans le cadre de problèmes en grande dimension, par exemple pour des applications en dynamique. Nous proposons ainsi d'approximer la réponse dynamique en ne tenant compte que de la résolution aux valeurs propres aléatoires. De cette façon, seuls les paramètres structuraux aléatoires apparaissent dans le PCE. Pour traiter le problème du mélange des modes dans notre approche, nous nous sommes appuyés sur le facteur MAC qui permet de le quantifier. Nous avons développé une méthode univariable permettant de verifier quelle variable générait un mélange de modes de manière à le réduire ou le supprimer. Par la suite, nous présentons une approche de RBRDO séquentielle pour améliorer l'efficacité et éviter les problèmes de non-convergence présents dans les approches de RBRDO. Dans notre approche, nous avons étendu la stratégie séquentielle classique, visant principalement à découpler l'analyse de fiabilité de la procédure d'optimisation, en séparant l'évaluation des moments de la boucle d'optimisation. Nous avons utilisé une approximation exponentielle locale autour du point de conception courant pour construire des objectifs déterministes équivalents ainsi que des contraintes stochastiques. De manière à obtenir les différents coefficients pour notre approximation, nous avons développé une analyse de sensibilité de la robustesse basée sur une distribution auxiliaire ainsi qu'une analyse de sensibilité des moments basée sur l'approche PCE. Nous montrons la pertinence ainsi que l'efficacité des approches proposées au travers de différents exemples numériques. Nous appliquons ensuite notre approche de RBRDO pour la conception d'un amortisseur dans le domaine du contrôle passif vibratoire d'une structure présentant des grandeurs aléatoires. Les résultats obtenus par notre approche permettent non seulement de réduire la variabilité de la réponse, mais aussi de mieux contrôler l'amplitude de la réponse au travers d'un seuil choisi par avance. / Deterministic design optimization is widely used to design products or systems. However, due to the inherent uncertainties involved in different model parameters or operation processes, deterministic design optimization without considering uncertainties may result in unreliable designs. In this case, it is necessary to develop and implement optimization under uncertainties. One way to deal with this problem is reliability-based robust design optimization (RBRDO), in which additional uncertainty analysis (UA, including both of reliability analysis and moment evaluations) is required. For most practical applications however, UA is realized by Monte Carlo Simulation (MCS) combined with structural analyses that renders RBRDO computationally prohibitive. Therefore, this work focuses on development of efficient and robust methodologies for RBRDO in the context of MCS. We presented a polynomial chaos expansion (PCE) based MCS method for UA, in which the random response is approximated with the PCE. The efficiency is mainly improved by avoiding repeated structural analyses. Unfortunately, this method is not well suited for high dimensional problems, such as dynamic problems. To tackle this issue, we applied the convolution form to compute the dynamic response, in which the PCE is used to approximate the modal properties (i.e. to solve random eigenvalue problem) so that the dimension of uncertainties is reduced since only structural random parameters are considered in the PCE model. Moreover, to avoid the modal intermixing problem when using MCS to solve the random eigenvalue problem, we adopted the MAC factor to quantify the intermixing, and developed a univariable method to check which variable results in such a problem and thereafter to remove or reduce this issue. We proposed a sequential RBRDO to improve efficiency and to overcome the nonconvergence problem encountered in the framework of nested MCS based RBRDO. In this sequential RBRDO, we extended the conventional sequential strategy, which mainly aims to decouple the reliability analysis from the optimization procedure, to make the moment evaluations independent from the optimization procedure. Locally "first-torder" exponential approximation around the current design was utilized to construct the equivalently deterministic objective functions and probabilistic constraints. In order to efficiently calculate the coefficients, we developed the auxiliary distribution based reliability sensitivity analysis and the PCE based moment sensitivity analysis. We investigated and demonstrated the effectiveness of the proposed methods for UA as well as RBRDO by several numerical examples. At last, RBRDO was applied to design the tuned mass damper (TMD) in the context of passive vibration control, for both deterministic and uncertain structures. The associated optimal designs obtained by RBRDO cannot only reduce the variability of the response, but also control the amplitude by the prescribed threshold.

O objetivo deste trabalho é investigar o controle ativo de vibração em uma pá inteligente de helicóptero. O desenvolvimento de materiais inteligentes para trabalharem como sensores e atuadores apresentam uma nova alternativa no controle de vibração. A pá de helicóptero é modelada pelo método dos elementos finitos, considerando os movimentos de batimento, flexão no plano de rotação, estiramento axial e torção. O modelo da pá considera também ângulo de torção geométrica, não coincidência entre os eixos, elástico e do centro de gravidade das seções transversais e material isotrópico. O modelo matemático é desenvolvido, e nele é incorporado atuadores piezelétricos distribuídos ao longo da envergadura da pá. O controle ativo de vibração é baseado no controle individual da pá na condição de vôo pairado. As matrizes de elementos finitos são obtidas pelo método de energia e um procedimento de linearização é aplicado às equações resultantes. O carregamento aerodinâmico linearizado é calculado para a condição de vôo pairado e a representação no espaço de estados é usada para o projeto de um controlador. Usou-se a técnica de atribuição da autoestrutura por realimentação de saída no modelo de ordem reduzida, resultado da aplicação do método da expansão por frações parciais. As simulações do modelo em malha aberta e fechada, exibiu boas qualidades de resposta, o que mostra que o controle ativo é uma boa alternativa para a redução de vibrações em helicópteros. / The objective of this work is to investigate the performance of a smart helicopter blade. Developments on smart materials for both sensing and/or actuation have provided a novel alternative in vibration control. The helicopter blade is modeled by the finite element method, considering the motions of flapping, lead-lagging, axial stretching, and torsion. The blade model also considers a pretwist angle, offset between mass and elastic axes, and isotropic material. The helicopter blade mathematical model allows the incorporation of piezoelectric actuators distributed along the blade span. The active vibration control is based on the premise of individual blade control and the investigation is carried out for hovering flight condition the finite element matrices are obtained by energy methods and a linearization procedure is applied to the resulting expressions. The linearized aerodynamic loading is calculated for hover and the state-space approach is used to design the control law. The eigenstructure assignment by output feedback is used in the blade-reduced model resulting from the application of the expansion method by partial fractions. The simulations for open and closed-loop systems are presented, having exhibited good response qualities, which shows that output feedback is a good alternative for smart helicopter blade vibration attenuation.

"The recent years have seen the innovative system integration of a great many actuator technologies, such as point force actuators for space vehicle applications and the use of single fire actuators; such as pyrocharges to guide a free falling bomb to it’s target. The inherent limitations of these developments, such as nonlinear behavior under extreme environments and/or prolonged/repeated usage leading to a relaxation time component between firing of actuators and inherent system power limitations, have resulted in greater need for sophisticated control algorithms that allow for optimal switching between various actuators in any given embedded configuration so as to achieve the best possible performance of the system. The objective of this investigation is to offer a proof of concept experimental verification of a real time control algorithm, which switches between online piezoelectric actuators, employed for vibration control in an aluminum beam with fixed boundary conditions. In this investigation at a given interval of time, only one actuator is activated and the rest are kept dormant. The reason is to demonstrate the better vibration alleviation characteristics realized in switching between actuators depending on the state of the system, over the use of a single actuator that is always in fire mode. This effect is particularly pronounced in controlling systems affected by spatiotemporal disturbances. The algorithm can be easily adapted for various design configurations or system requirements. The optimality of switching is with respect to the minimal cost of an LQR performance index that corresponds to each actuator. Computer simulations with repeatable disturbance profiles, revealed that this algorithm offered better performance over the non-switched case. Performance measures employed were the time varying total energy norm of the dynamic system and position traces at any particular location on the beam. This algorithm was incorporated on a dSPACE rapid prototyping platform along with suitable hardware. Experimental and simulation results are discussed. "

Máquinas rotativas são sempre sujeitas à vibrações mecânicas, em menor ou maior grau, e para garantir um correto funcionamento destas máquinas, evitando falhas de operação, é necessário realizar o controle destas vibrações. Uma das frentes que vem se destacando nesta área é o controle ativo de vibrações. Neste tipo de abordagem as vibrações são controladas ativamente através de um sistema de atuação e de uma técnica de controle a ser empregada de forma satisfatória. Neste contexto, existem inúmeras abordagens da teoria de controle que podem ser aplicadas, e aqui é avaliada a aplicação da metodologia proposta por Udwadia e Kalaba para o controle de trajetória de sistemas não lineares, uma técnica de controle ainda não utilizada no controle ativo de vibrações em sistemas rotativos. Em um primeiro momento a avaliação do desempenho e potencial de aplicação desta metodologia é realizada em sistemas com quatro graus de liberdade através de comparação com controladores do tipo proporcional-integral-derivativo e regulador linear-quadrático. Os resultados obtidos pelo controlador avaliado são similares aos resultados obtidos pelo controlador proporcional-integral-derivativo com melhorias em termos de erro de posicionamento. A metodologia também é avaliada em um sistema rotativo com um maior número de graus de liberdade, no qual é possível compreender o comportamento do controlador em um sistema flexível. Por fim realiza-se um exemplo de aplicação da técnica em um sistema com um eixo rígido e mancal hidrodinâmico ativo de atuação eletromagnética. Os resultados de simulação obtidos mostram que a metodologia possui potencial de aplicação para sistemas que apresentam eixo rígido, no qual uma drástica redução na amplitude de vibração do sistema foi observada por toda faixa de operação avaliada, enquanto que a sua aplicação em sistemas com eixo flexível se tornou restrita aos dois primeiros modos de vibrar do sistema flexível utilizado, modelado através do método dos elementos finitos. / Rotating machinery are always subject to mechanical vibration to a lesser or greater degree, and to ensure proper operation of these machines, avoiding faulty operation, it is necessary to carry out the control of these vibrations. One of the fronts that stood out in this area is the active vibration control. In this type of approach, vibrations are actively managed through an actuation system and a control technique to be used satisfactorily. In this context, there are numerous approaches to control theory that can be applied, and here the application of the methodology proposed by Udwadia and Kalaba for trajectory control of nonlinear systems is evaluated, a control technique not yet used in active vibration control in rotating systems. At first the evaluation of the performance and potential application of this methodology is performed on systems with four degrees of freedom by comparison with controllers of the proportional-integral-derivative and linear-quadratic regulator type. The results of the evaluated controller are similar to results obtained by proportional-integral-derivative controller with improvements in positioning error. The methodology is also evaluated in a rotating system with a larger number of degrees of freedom, wherein we can understand the controllers behavior in a flexible system. Finally, an application example of the technique on a system with a rigid shaft and hydrodynamic bearing with electromagnetic actuators is presented. The obtained simulation results show that the method has application potential to systems having rigid shaft, in which a dramatic reduction in the amplitude of vibration of the system was observed at all the operating range evaluated, whereas their application in systems with flexible shaft became restricted to the first two vibration modes of the flexible system used, modeled by the finite element method.

Dans cette étude de thèse, le problème du co-design mécanique/contrôle d’attitude avec méthodesde la commande robuste structurée est considéré. Le problème est abordé en développant une techniquepour la modélisation de systèmes flexibles multi-corps, appelé modèle Two-Input Two-Output Port (TITOP).En utilisant des modèles d’éléments finis comme données d’entrée, ce cadre général permet de déterminer, souscertaines hypothèses, un modèle linéaire d’un système de corps flexibles enchaînés. De plus, cette modélisationTITOP permet de considérer des variations paramétriques dans le système, une caractéristique nécessaire pourréaliser des études de co-design contrôle/structure. La technique de modélisation TITOP est aussi étenduepour la prise en compte des actionneurs piézoélectriques et des joints pivots qui peuvent apparaître dans lessous-structures. Différentes stratégies de contrôle des modes rigides et flexibles sont étudiées avec les modèles obtenus afin de trouver la meilleure architecture de contrôle pour la réjection des perturbations basse fréquence etl’amortissement des vibrations. En exploitant les propriétés d’outils de synthèse H1 structurée, la mise enoeuvre d’un schéma de co-design est expliquée, en considérant les spécifications du système (bande passantedu système et amortissement des modes) sous forme de contraintes H1. L’étude d’un tel co-design contrôled’attitude/mécanique d’un satellite flexible est illustré en utilisant toutes les techniques développées, optimisantsimultanément une loi de contrôle optimisée et certains paramètres structuraux. / In this PhD thesis, the integrated control/structure design of a large flexible spacecraft isaddressed using structured H1 synthesis. The problem is endeavored by developing a modeling technique forflexible multibody systems, called the Two Input Two Output Port (TITOP) model. This general frameworkallows the assembly of a flexible multibody system in chain-like or star-like structure, using finite elementmodels as input data. Additionally, the TITOP modeling technique allows the consideration of parametricvariations inside the system, a necessary characteristic in order to perform integrated control/structure design. In contrast to another widely used method, the assumed modes method, the TITOP modelling technique is robust against changes in the boundary conditions which link the flexible bodies. Furthermore, the TITOP modeling technique can be used as an accurate approximation even when kinematic nonlinearities can be large. The TITOP modeling technique is extended to the modeling of piezoelectric actuators and sensors for the control of flexible structures and revolute joints. Different control strategies, either for controlling rigid body and flexible body motion, are tested with the developed models for obtaining the best controller’s architecture in terms of perturbation rejection and vibration damping. The implementation of the integrated control/structure design in the structured H1 scheme is developed considering the different system’s specifications, such as system’s bandwidth or modes damping, in the form of H1 weighting functions. The integrated attitude control/structure design of a flexiblesatellite is performed using all the developed techniques and the optimization of the control law and severalstructural parameters is achieved.

<p>Active vibration control to reduce vibrations and structure borne noise is considered using a powerful multi-disciplinary virtual design environment which enables control system design to be considered as an integral part of the overall vehicle design.</p><p>The main application studied is active automotive engine vibration isolation where, first, the potential of large frequency band multi-input multi-output H₂ feedback control is considered. Facilitated by the virtual environment, it is found necessary to take non-linear characteristics into account to achieve closed-loop stability.</p><p>A physical explanation to why receiver structure flexibility insignificantly affect the open and closed-loop characteristics in case of total force feedback in contrast to acceleration feedback is then given. In this context, the inherent differences between model order reduction by modal and by balanced truncation are being stressed.</p><p>Next, applying state-of-the-art algorithms for recursive parameter estimation, time-domain adaptive filtering is shown to lack sufficient tracking performance to deal with multiple spectral components of transient engine excitations corresponding to rapid car accelerations.</p><p>Finally, plant non-linearity as well as transient excitation are successfully handled using narrow band control based on feedback of disturbance states estimates. To deal with the non-linear characteristics, an approach to generate linear parameter varying descriptions of non-linear systems is proposed. Parameter dependent quadratic stability is assessed using a derived affine closed-loop system representation.</p><p>This thesis also considers actuator saturation induced limit cycles for observer-based state feedback control systems encountered when dealing with the active isolation application. It is stressed that the fundamental observer-based anti-windup technique could imply severely deteriorated closed-loop characteristics and even sustained oscillations. That is in the case when the observer is fed by the saturated control signal in contrast to the computed one. Based on piecewise affine system descriptions, analytical tools to conclude about limit cycles and exponential closed-loop stability are provided for the two observer implementations.</p>

Active vibration control to reduce vibrations and structure borne noise is considered using a powerful multi-disciplinary virtual design environment which enables control system design to be considered as an integral part of the overall vehicle design. The main application studied is active automotive engine vibration isolation where, first, the potential of large frequency band multi-input multi-output H2 feedback control is considered. Facilitated by the virtual environment, it is found necessary to take non-linear characteristics into account to achieve closed-loop stability. A physical explanation to why receiver structure flexibility insignificantly affect the open and closed-loop characteristics in case of total force feedback in contrast to acceleration feedback is then given. In this context, the inherent differences between model order reduction by modal and by balanced truncation are being stressed. Next, applying state-of-the-art algorithms for recursive parameter estimation, time-domain adaptive filtering is shown to lack sufficient tracking performance to deal with multiple spectral components of transient engine excitations corresponding to rapid car accelerations. Finally, plant non-linearity as well as transient excitation are successfully handled using narrow band control based on feedback of disturbance states estimates. To deal with the non-linear characteristics, an approach to generate linear parameter varying descriptions of non-linear systems is proposed. Parameter dependent quadratic stability is assessed using a derived affine closed-loop system representation. This thesis also considers actuator saturation induced limit cycles for observer-based state feedback control systems encountered when dealing with the active isolation application. It is stressed that the fundamental observer-based anti-windup technique could imply severely deteriorated closed-loop characteristics and even sustained oscillations. That is in the case when the observer is fed by the saturated control signal in contrast to the computed one. Based on piecewise affine system descriptions, analytical tools to conclude about limit cycles and exponential closed-loop stability are provided for the two observer implementations.

The presence of vibration is an important problem in many engineering applications. Various passive techniques have traditionally been used in order to reduce waves and vibrations, and their harmful effects. Passive techniques are, however, difficult to apply in the low frequency region. In addition, the use of passive techniques often involve adding mass to the system, which is undesirable in many applications. As an alternative, active techniques can be used to manipulate system dynamics and to control the propagation of waves and vibrations. This thesis deals with modeling, estimation and active control of systems that have resonant dynamics. The systems are exposed to stochastic disturbances. Some of them excite the system and generate vibrational responses and other corrupt measured signals. Feedback control of a beam with attached piezoelectrical elements is studied. A detailed modeling approach is described and system identification techniques are employed for model order reduction. Disturbance attenuation of a non-measured variable shows to be difficult. This issue is further analyzed and the problems are shown to depend on fundamental design limitations. Feedforward control of traveling waves is also considered. A device with properties analogous to those of an electrical diode is introduced. An `ideal´ feedforward controller based on the mechanical properties of the system is derived. It has, however, poor noise rejection properties and it therefore needs to be modified. A number of feedforward controllers that treat the measurement noise in a statistically sound way are derived. Separation of overlapping traveling waves is another topic under investigation. This operation also is sensitive to measurement noise. The problem is thoroughly analyzed and Kalman filtering techniques are employed to derive wave estimators with high statistical performance. Finally, a nonlinear regression problem with close connections to unbalance estimation of rotating machinery is treated. Different estimation techniques are derived and analyzed with respect to their statistical accuracy. The estimators are evaluated using the example of separator balancing.