<p>Dynamic systems and robotic manipulators designed for time-optimal point-to-point motion are adversely affected by residual vibrations introduced due to the joint flexibility inherent in the system. Over the years, multiple techniques have been employed to improve the efficiency of such systems. While some techniques focus on increasing the system damping to efficiently dissipate the residual energy at the end of the move, several techniques achieve rapid repositioning by developing cleverly shaped input profiles that aim to reduce energy around the natural frequency to avoid exciting the resonant modes altogether. In this work, a numerical framework for constructing shaped inputs using a Versine basis function with peak acceleration constraint has been developed and improvements for the existing numerical framework for the Ramped Sinusoid basis function have been made to extend the range of values of the weighting function and improve the computational time. Performance metrics to evaluate the effectiveness of the numerical framework in minimizing residual vibrations have been developed. The effects of peak input acceleration and weighting function on the residual vibration in the system have been studied. The effectiveness of the method has been tested under multiple conditions in simulations and the results were validated by performing experiments on a two-link flexible joint robotic arm. The simulation and experimental results conclusively show that the inputs developed using the constrained numerical approach result in better residual vibration performance as compared to that of an unshaped input. </p>

Chatter é uma vibração auto-excitada que ocorre durante usinagens e limita a produtividade do processo. Esta instabilidade causa qualidade superficial inaceitável, diminuição da vida da ferramenta e ruído. Estratégias para definição de modelos e controle desta vibração são importantes, devendo ser avaliadas e implementadas. Neste trabalho foram realizados experimentos e características como frequências naturais, respostas em frequência e respostas temporais foram obtidas. Analisando tais resultados é possível a visualização do acoplamento existente nas duas direções de vibração. Uma estratégia de redução de chatter foi implementada, através do uso de shunts passivos conectados ao sistema mecânico por meio de material piezoelétrico, e sua viabilidade foi verificada. A estratégia foi adaptada para ser utilizada nas duas direções de vibração e o resultado da redução da vibração se provou mais eficiente após esta adaptação. Diagramas de fase, respostas temporais e espectros foram obtidos durante a usinagem e um comportamento não-linear se mostrou presente. Após a validação do uso de material piezoelétrico para o controle de chatter, existe a necessidade de modelos numéricos para a descrição do fenômeno, para que controles ativos e mais efetivos possam ser desenvolvidos. Devido ao acoplamento entre as duas direções de vibração e ao comportamento não linear do fenômeno, modelos que contenham tais características foram estudados, modificados e adaptados. Os resultados numéricos obtidos pelos modelos estudados foram então comparados aos resultados experimentais e conclusões sobre similaridades foram apresentadas. Considerando os resultados obtidos, acredita-se que o modelo que melhor representa o sistema real pode ser utilizado para o desenvolvimento de controles ativos, que garantam uma redução mais efetiva do chatter. / Chatter is a self-excited vibration that leads to instability during ongoing machining, which affects productivity. Chatter instability causes poor surface quality, diminishes the tool\'s life and may cause clatter. Therefore, strategies to control chatter and chatter models are highly necessary, and must be evaluated and implemented. In an experimental campaign done during this work, characteristics such as natural frequencies, frequency responses and temporal responses were obtained. Trough these analysis, it was observed that the system presents a coupling in its two normal directions of vibration. One strategy for chatter reduction was then implemented, in which a passive shunt using piezoelectric material was used. The feasibility of this chatter reduction strategy for one direction could be verified. In addition, the strategy was adapted in order to be utilized in both main vibration directions and the results confirmed that this approach grants better results for the reduction of chatter. Phase-planes, temporal responses and spectras could also be derived from the turning experiments and a nonlinear behavior could be seen present. Being verified the possibility of using a piezoelectric material in chatter control, numerical models that describe the phenomena should be pursued, so that more effective active control could be developed. Because the experiments show the mode coupling between two directions and a nonlinear behavior, models that represent such characteristics were studied, modified and adapted. The numerical results from this models were then compared to the experiments and conclusions were drawn. Considering the obtained results, it is believed that the most similar model should be used in the development of active control that could guarantee a better chatter reduction.

Absorvedores de vibração são comumente usados em aplicações com intuito de reduzir indesejadas amplitudes de vibração de estruturas e maquinas vibrantes. O conceito de um absorvedor de vibração linear consiste na ideia de projetar um subsistema com frequência de ressonância coincidente com uma dada frequência de interesse, tal que a amplitude de vibração do sistema primário e significativamente reduzida quando comparada a situação original, sem o absorvedor de vibração. Porem, uma deficiência dos absorvedores de vibração lineares típicos e sua estreita faixa de frequência de operação. Para superar essa deficiência, muitas tentativas de solução usando subsistemas não lineares tem sido propostas na literatura, ja que se apropriadamente projetados, eles podem aumentar a faixa de frequência de absorção de vibração e/ou melhorar a redução das amplitudes de vibração do sistema primário. Contudo, a síntese e o projeto de tais absorvedores não lineares não e tão simples e direta como no caso linear. Baseado na geometria de uma topologia proposta e encontrada na literatura, que compreende a inclusão de uma montagem do tipo snap through truss no lugar da mola linear do absorvedor de vibração, este trabalho tem intenção de apresentar um estudo sobre o projeto e otimização de um absorvedor dinâmico de vibrações não linear. Portanto, o efeito dos parâmetros do absorvedor e analisado quanto as perspectivas de redução das amplitudes de vibração do sistema principal como também de aumento da faixa de frequência de operação. A analise paramétrica do absorvedor foi promovida para responder questões sobre as variáveis de projeto, tanto físicas como geométricas. Realizou-se otimização do absorvedor com objetivo de sintoniza-lo a frequência de trabalho desejada, através de busca extensiva e algoritmos genéticos. Os resultados mostram que o absorvedor não linear proposto pode ser mais efetivo que seu correspondente linear em ambos os aspectos, na redução da máxima amplitude de vibração e no aumento da faixa de frequência de absorção. Portanto, apesar da dificuldade inicial de projeto, esse tipo de absorvedor representa uma alternativa interessante na atenuação das amplitudes de vibração ao longo de uma extensa faixa de frequência. / Dynamic vibration absorbers are commonly used in several applications in order to reduce undesired vibration amplitudes of vibrating machinery and structures. The concept of a linear vibration absorber is based on the idea of designing a subsystem with a resonance frequency coincident with a given frequency of interest such that the vibration amplitude of the primary system is significantly reduced when compared to the original situation (without the vibration absorber). But one of the known handicaps of typical linear vibration absorbers is their narrow frequency range of operation. To overcome this handicap, a number of tentative solutions have been proposed in the literature using nonlinear subsystems. If properly designed, they could enlarge the frequency range of vibration absorption and/or improve vibration reduction of the primary system. However, the synthesis and design of such nonlinear absorbers are not as straightforward as for their linear counterpart. A proposed design found in the open literature consists of replacing the linear spring of the vibration absorber by a nonlinear snap-through truss. This work aims to present a study on the design and optimization of a nonlinear dynamic vibration absorber based on snap-through absorber geometry. The effect of the absorber parameters was analyzed on both, the primary system vibration amplitude reduction and the frequency range of operation. Parametric analyses of the absorber were carried out to answer questions about the physical and geometric design variables. The absorber optimization was performed in two different ways, by extensive search and genetic algorithms, in order to tune it in the desired working frequency. The results show that the proposed nonlinear vibration absorber may be more effective than its linear counterpart both in terms of maximum vibration amplitude reduction and absorption frequency-range. Therefore, despite the increased design complexities such an absorber is an interesting alterna- tive in attenuating vibration amplitudes over a wide frequency range.

[pt] Dentro do campo dos controladores passivos, um dos dispositivos usados pelas suas propriedades de amortecimento são os Apoios Elásticos, que constituem uma solução econômica e efetiva na supressão ou atenuação das vibrações em sistemas dinâmicos com problemas de ressonância ou instabilidade, freqüentemente pela falta de amortecimento suficiente. Este trabalho envolve o estudo de um rotor horizontal com apoios elásticos (silicone), adaptado a partir de um rotor existente, o estudo de diversos efeitos sobre a sua operação, a medição de seu movimento, a identificação dos parâmetros do problema, a medição e validação a partir de resultados simulados em um modelo numérico. Os fenômenos incluídos no estudo são o efeito giroscópio (rotor descentrado com respeito do vão), desbalanceamento do rotor e empenamento do eixo. Neste trabalho os parâmetros do sistema foram determinados usando técnicas de identificação, análise modal e otimização não linear devido à anisotropia do sistema. / [en] Viscoelastic Passive Controllers are an important field of technological research due to the development of new materials and design techniques. Damping properties allow an easy retrofit of existing machines with excessive vibration problems, developing Elastomeric Bearing Supports. They are an economic and effective solution in the suppression or attenuation of vibrations in dynamic systems suffering from instability or resonance problems, which often lack of sufficient damping. This work involves the study of an horizontal rotor with elastomeric bearing supports, adapted of another one, the study of several effects on his operation, the measurement of his motion, the identification of the problems parameters, the measurement and validation from the simulated results in a numeric model. Phenomena included in the study are the gyroscopic effect (rotor out of the middle), rotor unbalance and shaft bow. In this work the systems parameters were determined using identification, modal analysis and nonlinear optimization techniques due to the anisotropy of the system.

Orientador: Vicente Lopes Júnior / Banca: Luiz de Paula do Nascimento / Banca: Marcus Antonio Viana Duarte / Resumo: Este trabalho apresenta o desenvolvimento analítico da modelagem de estruturas flexíveis do tipo treliça com o objetivo de atenuação de vibrações através do uso de técnicas de controle ativo. Atuadores de pilha piezelétricos são usados para exercer as forças de controle na estrutura, os quais substituem barras inteiras ou somente uma parte delas. Estes tipos de atuadores, também, satisfazem a necessidade de obtenção de estruturas leves. O posicionamento ótimo desses atuadores e de sensores é encontrado através da norma Hx, que é usada como função objetivo. Como técnica de controle é aplicado o Controle no Espaço Modal Independente (IMSC), no qual os estados são estimados por um estimador modal e são realimentados de acordo com a teoria de controle ótimo, o Regulador Linear Quadrático (LQR). O IMSC é eficiente computacionalmente mesmo aplicado a sistemas de alta ordem e também reduz os efeitos de spillover. Uma melhoria do IMSC, o Controle Modal Eficiente (EMC) também é apresentado com o propósito de reduzir as amplitudes das forças de controle. O modelo matemático da estrutura inteligente é obtido a partir do Método dos Elementos Finitos (MEF) considerando o acoplamento eletromecânico entre os atuadores de pilhas piezelétricos e a estrutura base. O projeto de uma treliça espacial, o posicionamento ótimo dos atuadores e sensores e o controle ativo de vibração são apresentados em simulações numéricas. Os resultados mostram que ambos os controladores aumentam o amortecimento da estrutura e, ainda, o EMC reduz as amplitudes das forças de controle. / Abstract: This work presents the analytic development of the modeling of flexible truss structures with the aim to suppress the mechanical vibration using active control techniques. Piezoelectric stack actuators are used to produce control force in the structure, which can replace an entire bar or can be coupled to structural members. They also satisfy the necessity to obtain lighter structures. The optimal placement of actuators and sensors is found through the Hã norm as objective function. As control technique is presented the Independent Modal Space Control (IMSC), in which a modal estimator is used and the Linear Quadratic Regulator (LQR) feedback the estimated states according the optimal control theory. IMSC is computationally efficient also applied in high order system and reduces the negative effects of the control and observer spillover. An improvement in the IMSC is the Efficient Modal Control (EMC) that is proposed to reduce the amplitudes of control forces. The mathematical model of the intelligent structure is obtained from Finite Elements Method (FEM) considering the electromechanical coupling between the piezoelectric stack actuators and the base structure. The design of a space truss structure, the optimal placement of active members and the active damping vibration control is numerically implemented. Two control techniques are tested and compared: IMSC and EMC. Results show that the controllers increase the damping of the structure noticeably. The EMC controller provides better performance, reducing the amplitudes of control forces. / Mestre

Resumo: Este trabalho tem como propósito utilizar técnicas de controle robusto para atenuação ativa de vibração mecânica em estruturas acopladas a atuadores e sensores piezelétricos. Os controladores são projetados segundo o enfoque de otimização convexa, com os requisitos envolvendo desigualdades matriciais lineares (LMIs). A proposta é ilustrar duas sínteses diferentes de realimentação via LMIs. A primeira é o projeto de controladores por realimentação de estados, estimados por um observador, considerando incertezas paramétricas do tipo politópicas. A segunda metodologia é baseada no controle H8 via realimentação do sinal de saída, considerando incertezas dinâmicas limitadas por norma. Os sensores/atuadores são posicionados em pontos ótimos utilizando-se a norma H8 como índice de desempenho. Os modelos matemáticos utilizados na síntese dos controladores foram obtidos a partir do método dos elementos finitos considerando o acoplamento eletromecânico entre os atuadores/sensores e a estrutura base ou a partir de métodos de identificação. Neste contexto, este trabalho também discute e exemplifica o algoritmo de realização de autosistemas (ERA). Três exemplos são solucionados para exemplificar a metodologia implementada: uma estrutura tipo placa, uma viga engastada-livre e a supressão ativa de flutter em um aerofólio 2-D, problema de grande interesse na indústria aeronáutica. Os resultados mostraram uma significante atenuação da vibração estrutural na faixa de freqüência de interesse e o atendimento dos requisitos impostos na fase de projeto. / Abstract: The proposal of this work is to use robust control techniques in order to suppress mechanical vibration in structures with pieozoelectric sensors and actuators coupled. The controllers are designed by convex optimization and the constraints are dealt through linear matrix inequalities (LMIs) frameworks. Two different methodologies to feedback the system by using LMIs are explained. The first one is the observer-based state-feedback considering polytopic uncertainties. The second one is the H output feedback control considering norm-bound uncertainties. The sensors/actuators are located in optimal placements by using H norm as performance index. The mathematical models used in the controller design were obtained by finite element methods considering eletromechanical effects between the host structure and piezoelectric sensors/actuators patches or by using identification methods. In this sense, it is also discussed the eigensystem realization algorithm (ERA). Three different applications are proposed and solved in order to illustrate the applicability of the methodology: a cantilever plate; a cantilever beam; and an active flutter suppression in a 2-D airfoil, a problem of considered interest in the aeronautic industry. The results showed the vibration suppression in the bandwidth of interest when submited to the requirements imposed by practical situations. / Orientador: Vicente Lopes Junior / Coorientador: Edvaldo Assunção / Banca: Vicente Lopes Junior / Banca: Marcelo Carvalho Minhoto Teixeira / Banca: Edilson Hiroshi Tamai / Mestre

This thesis presents the practical and novel work in the area of optimal placement of actuators and sensors for sound-structure interaction systems. The work has been done by the author during his PhD candidature. The research is concentrated in systems with non-ideal boundary conditions as in the case in practical engineering applications. An experimental acoustic cavity with five walls of timber and a thin aluminium sheet fixed tightly on the cavity mouth is chosen in this thesis as a good representation of general sound-structure interaction systems. The sheet is intentionally so fixed that it does not satisfy ideal boundary conditions. The existing methods for obtaining optimal sensor-actuator location using analytic models with ideal boundary conditions are of limited use for such problem with non-ideal boundary conditions. The method presented in this thesis for optimal placement of actuators and sensors is motivated by energy based approach and model uncertainty inclusion. The optimal placement of actuator and sensor for the experimental acoustic cavity is used to construct a robust feedback controller based on minimax LQG control design method. The controller is aimed to reduce acoustic potential energy in the cavity. This energy is due to the structure-borne sound inside the sound-structure interaction system. Practical aspects of the method for optimal placement of actuator and sensors are highlighted by experimental vibration and acoustic noise attenuation for arbitrary disturbance using feedback controllers with optimal placement of actuator and sensor. The disturbance is experimentally set to enter the system via a spatial location different from the controller input as would be in any practical applications of standard feedback disturbance rejections. Experimental demonstration of the novel methods presented in this thesis attenuate structural vibration up to 13 dB and acoustic noise up to 5 dB for broadband frequency range of interest. This attenuation is achieved without the explicit knowledge of the model of the disturbance.

<p>Achieving better NVH (noise, vibration, and harshness) comfort necessitates the use of active technologies when product targets are beyond the scope of traditional passive insulators, absorbers, and dampers. Therefore, a lot of effort is now being put in order to develop various active solutions for vibration control, where the development of actuators is one part. </p><p>Active hydraulic engine mounts have shown to be a promising actuator for vibration isolation with the benefits of the commonly used passive hydraulic engine mount in addition to the active ones. In this thesis, a benchmark of actuators for active vibration control has been carried out. Piezoelectric actuators and electromagnetic actuators are studied further and two methods to estimate parameters for electromagnetic actuators have been developed. A parameterized model of an active hydraulic engine mount valid for frequencies from zero to about 300 Hz, has also been developed. Good agreement with experimental data has been achieved.</p>

Achieving better NVH (noise, vibration, and harshness) comfort necessitates the use of active technologies when product targets are beyond the scope of traditional passive insulators, absorbers, and dampers. Therefore, a lot of effort is now being put in order to develop various active solutions for vibration control, where the development of actuators is one part. Active hydraulic engine mounts have shown to be a promising actuator for vibration isolation with the benefits of the commonly used passive hydraulic engine mount in addition to the active ones. In this thesis, a benchmark of actuators for active vibration control has been carried out. Piezoelectric actuators and electromagnetic actuators are studied further and two methods to estimate parameters for electromagnetic actuators have been developed. A parameterized model of an active hydraulic engine mount valid for frequencies from zero to about 300 Hz, has also been developed. Good agreement with experimental data has been achieved.

Command shaping creates reference commands that reduce residual vibrations in a flexible system. This thesis examines the use of command shaping for flexible system control in three industrial applications: cam-follower systems, sloshing liquids, and cherrypickers. One common type of command shaping is command smoothing which creates a smooth transition between setpoints. A specific type of command smoothing used in cam-follower systems is the polynomial profile. An alternative technique to reduce vibration in flexible systems is input shaping. In this thesis, input-shaped commands are compared to polynomial profiles for applications requiring both vibration suppression and fast motion. Simulation and experimental results show that input shaping is faster than polynomial profiles and provides a simple approach to suppressing residual vibration. Secondly, significant experimental contributions have been made in the area of slosh control. The oscillation of liquids in a container can cause liquid spillage or can cause stability issues, especially in space vehicles. In the past, a number of control techniques have been proposed, but only a few recommend the use of input shaping. This thesis describes the use of command shaping to limit slosh. Results are supported by numerical and experimental testing. Input-shaped commands reduce residual slosh amplitude compared to unshaped commands and polynomial profiles. Input-shaped commands can also accommodate uncertainties and changes in the sloshing frequencies. Lastly, a small-scale cherrypicker was constructed to study the use of input-shaping control on these types of aerial lifts. Cherrypickers have flexible dynamic effects that can cause dangerous and life-threatening situations. To study this class of machines and to provide future students an experimental testbed, several design criteria were established before construction began. The resulting machine achieved most design objectives, including a simple-to-use graphical user interface and accurate state measurements. Robust input-shaping controllers were implemented to limit endpoint vibration. The design of the cherrypicker is discussed and experimental results are reported.