Conformal airborne antennas have several advantages compared to externally mounted antennas, and they will play an important role in future aircrafts. However, they are subjected to vibration induced deformations which degrade their electromagnetic performances. With the motivation of suppressing such vibrations, use of active vibration control techniques with piezoelectric actuators is investigated in this study. At first, it is aimed to control the first three bending modes of a cantilever beam. In this scope, four different modal controllers / positive position feedback (PPF), resonant control (RC), integral resonant control (IRC) and positive position feedback with feed-through (PPFFT) are designed based on both reduced order finite element model and the system identification model. PPFFT, is a modified version of PPF which is proposed as a new controller in this study. Results of real- time control experiments show that PPFFT presents superior performance compared to its predecessor, PPF, and other two methods. In the second part of the study, it is focused on controlling the first three modes of a rectangular plate with four clamped edges. Best location alternatives for three piezoelectric actuators are determined with modal strain energy method. Based on the reduced order finite element model, three PPFFT controllers are designed for three collocated transfer functions. Disturbance rejection performances show the convenience of PPFFT in multi-input multi-output control systems. Performance of the control system is also verified by discrete-time simulations for a random disturbance representing the in-flight aircraft vibration characteristics.

A novel combined piezoelectric-composite actuator configuration is proposed and analytically modeled in this work. The actuator is a low complexity, active compliant mechanism obtained by coupling a modified star cross sectional configuration composite beam with a helicoidal bimorph piezoelectric actuator coiled around it. This novel actuator is a good candidate as a hinge tension-torsion bar actuator for a helicopter rotor blade flap or blade tip and mirror rotational positioning. In the wing tip case, the tip deflection angle is different only according to the aerodynamic moment depending on the hinge position of the actuator along the chord and applied voltage because there is no centrifugal force. For an active blade tip subject to incompressible flow and 2D quasi steady airloads, its twist angle is related not only to aerodynamic moment and applied voltage but also to coupling terms, such as the trapeze effect and the tennis racquet effect. Results show the benefit of hinge position aft of the aerodynamic center, such that the blade tip response is amplified by airloads. Contrary to this effect, results also show that the centrifugal effects and inertial effect cause an amplitude reduction in the response. Summation of these effects determines the overall blade tip response. The results for a certain hinge position of Xh=1.5% chord aft of the quarter chord point proves that the tip deflection target design range[-2,+2] can be achieved for all pitch angle configurations chosen.

No description available.

Flexible structures are increasingly used in various applications such as aerospace, automotive and so on. Since they are lightly damped and susceptible to vibrations, active vibration control is desirable. In practice, in addition to achieving effective vibration reduction, we have also to consider the required control energy to avoid the energy insufficiency, the control input to avoid control saturation and reduce the effects of measurement noises. On the other hand, as flexible structures have infinite number of resonant modes and only the first few can be employed in the system modeling and the controller design, there always exist neglected high-frequency dynamics, which can induce the spillover instability. Furthermore, the parametric uncertainties on modal parameters can degrade the control performances and even destabilize the closed-loop system. In this context, a quantitative robust control methodology for active vibration control of flexible structure is proposed in this thesis. Phase and gain control polices are first proposed to enforce frequency-dependent phase and gain requirements on the controller, which can be realized by the output feedback H1 control design. The phase and gain control polices based H1 control can make a trade-off among the complete set of control objectives and offer a qualitative robust controller. Especially, the LPV H1 control is used to reduce the required control energy for LPV systems. The generalized polynomial chaos (gPC) framework with finite element analysis is employed for uncertainty quantification. It allows us to investigate the effects of structural property uncertainties on natural frequencies and achieve their probabilistic information. Then, in the presence of parametric and dynamic uncertainties, µ / v analysis and the random algorithm using Monte Carlo Method are used to quantitatively ensure the closed-loop stability and performance robustness properties both in deterministic and probabilistic senses. The proposed quantitative robust control methodology is thus developed by employing various techniques from automatic control and mechanical engineering, thus reducing the gap between them for robust vibration control of flexible structures. Its effectiveness are verified by numerical simulations and experimental validation on LTI and LPV non-collocated piezoelectric cantilever beams.

Orientador: Prof. Dr. Andre Fenili / Dissertação (mestrado) - Universidade Federal do ABC, Programa de Pós-Graduação em Engenharia Mecânica, 2016. / Uma viga em rotação é equipada com sensores e atuadores piezoelétricos em conjunto com um controlador proporcional-derivativo (PD) ou um controlador do tipo regulador linear quadrático (LQR) para comparação. O objetivo dos controladores é a minimização da deflexão na extremidade livre da estrutura devido ao seu movimento em torno do eixo de rotação. Utilizando o efeito piezoelétrico ¿ a geração de uma voltagem quando a estrutura está sujeita a uma tensão mecânica ¿ e, inversamente, a geração de uma deformação quando sujeito a uma voltagem, a estrutura do tipo viga é considerada como um sistema inteligente, tendo a capacidade de detectar e corrigir deflexões ao longo de seu comprimento. Usando as equações de Lagrange, a equação governante do movimento é obtida para a viga. A força (momento) e a rigidez da cerâmica piezoelétrica são subsequentemente adicionadas à equação governante da viga. A função de Heaviside é usada para a localização do atuador piezoelétrico ao longo da viga. A posição do atuador piezoelétrico varia a partir da extremidade engastada até a extremidade livre da viga ocupando três diferentes posições. O comprimento do atuador piezoelétrico é de um terço do comprimento da viga. O melhor posicionamento do piezoelétrico dentre os investigados é determinado para os três primeiros modos de vibração. Duas técnicas de controle linear são investigadas com o objetivo de eliminar a vibração na estrutura flexível: PD e LQR. O grau de liberdade associado ao movimento de rotação da viga (e suas derivadas) é prescrito por meio de um perfil pré-definido. / A rotating beam is fitted with piezoelectric sensors and actuators in conjunction with a proportional-derivative (PD) controller and a linear quadratic regulator (LQR) controller in order to minimize the deflection of the tip due to the rotational motion of the structure. Utilizing the piezo effects, the generation of a voltage, when subjected to a strain, and conversely the generation of a strain when subjected to a voltage, the system is considered as smart, having the ability to sense and correct deflections of the tip of the beam. Using the equations of Lagrange, the governing equation of motion is derived for the beam. The force (moment) and the stiffness of the piezo ceramic are subsequently added to the governing equation of the beam. In a model of the system, a Heaviside function is used to manipulate the position of the piezo. The position of the piezo will be varied from the root of the beam (the clamped end) to the free end of the beam, occupying three different positions; the length of the piezo is a third of the beam¿s length. The best position of the piezo is determined for three modes of vibration. Two linear control techniques are investigated in order to eliminate vibration in the flexible structure. The degree of freedom associated with the rotational motion is obtained by a predefined profile.

Les travaux de thèse présentés dans ce manuscrit portent sur l’alimentation d’actionneurs de type piézo-électrique qui seront placés sur la partie tournante d’une perceuse. Ces actionneurs possèdent un comportement capacitif et sont habituellement alimentés par des systèmes linéaires. Une étude de dimensionnement et de conception a été menée sur différents amplificateurs à découpage qui peuvent fournir, dans un repère fixe, un signal de puissance sinusoïdal à fréquence variable dans les meilleures conditions possibles (rendement et THD). Ensuite, un système pouvant transférer l’énergie sans contact à l’actionneur piézo-électrique placé sur un repère tournant a été analysé. Cela a été possible grâce à l’utilisation des systèmes à induction, c’est-à-dire, par couplage magnétique à travers un transformateur tournant présentant un entrefer. Trois types de systèmes de transfert d’énergie sans contact ont été étudiés : l’un qui travaille à la fréquence de l’actionneur [50-500 Hz] et deux autres basés sur des stratégies de résonance permettant ainsi de diminuer les dimensions du coupleur magnétique. Pour cela, la modélisation tant magnétique qu’électrique a été effectuée dans les trois systèmes.Un prototype d’onduleur en pont complet fournissant jusqu’à 680 VAR a été réalisé. Ce dernier est placé en amont d’un coupleur magnétique basse fréquence transférant 1,75 kVAR à l’actionneur piézo-électrique en rotation. Les résultats obtenus en pratique ont montré la pertinence du travail de dimensionnement et conception. / Placed on the rotating part of a drilling system. These actuators have a capacitive behavior and are usually supplied by linear systems. In this case, the design and the sizing of different switching amplifiers that provide, in a fixed frame, a sinusoidal power signal with modular frequency in the best possible conditions (efficiency and THD) have been made. Then, a contactless power system for piezoelectric actuators placed in a rotating frame was analyzed. This was possible thanks to the use of induction systems through a rotating transformer with an air gap. Three types of contactless systems were studied. The first one works at modular low frequencies [50-500 Hz] and the other two use resonant strategies in order to reduce transformer’s size. For this, both magnetic and electrical modeling was performed in the three cases.A full-bridge inverter prototype that can deliver up to 680 VAR and a low frequency contactless energy transfer system of 1.75 kVAR that supplies the piezoelectric actuator at rotating frame have been made. Experimental results showed satisfactory results and proved the system feasibility.

As estruturas aeronáuticas estão sujeitas a uma variedade de fenômenos aeroelásticos que podem comprometer o desempenho das aeronaves. Com o desenvolvimento de novos materiais, essas estruturas têm se tornado mais leves e flexíveis, e portanto mais sujeitas a problemas aeroelásticos, tais como flutter e buffeting. Pesquisadores têm trabalhado em soluções alternativas para resolver esses problemas aeroelásticos indesejáveis. Uma dessas soluções envolve o conceito de estruturas inteligentes, que são aquelas que apresentam atuadores e sensores incorporados, integrado com sistema de controle e processamento de sinal, possibilitando a adaptação do sistema estrutural a mudanças nas condições operacionais. Modelos matemáticos que incorporam elementos atuadores e sensores são de grande importância nas fases preliminares de análise de estruturas aeronáuticas inteligentes. Neste contexto, métodos de modelagem são necessários para capturar a ação da dinâmica estrutural e de carga aerodinâmica. O presente trabalho apresenta o estudo de um controlador difuso ativo para resposta aeroelástica de uma asa inteligente com atuadores piezelétricos incorporados. Características não-lineares da resposta aeroelástica são analisadas para condições críticas de flutter. É utilizado o método de elementos finitos para o modelo estrutural não-linear e o método de malha de vórtices para o modelo aerodinâmico não-estacionário. / Aeronautical structures are submitted to a variety of aeroelastic phenomena that may compromise its performance. With this development of new materials, aeronautical structures have become lighter, more flexible, and more subjected to aeroelastic problems, such as flutter and buffeting. Researchers have been working on alternatives to solve these undesired aeroelastic problems, as the recent concept of smart or intelligent structures. Smart structures are those that present embedded sensors and actuators, integrated with control systems and signal processing, to enable the adaptation of the structural system to changes in the operational conditions. Mathematical models that incorporate actuator elements or sensors are of great importance in preliminary phases of analysis of smart aeronautical structures. In this context, modeling methods are necessary to capture dynamic-structural behavior and unsteady aerodynamic loading. The present work is the study of an active fuzzy controller for aeroelastic response of a smart wing with embedded piezoelectric actuators. Nonlinear characteristics of aeroelastic responses are analyzed for critical flutter conditions. The finite elements method for the nonlinear structural model and vortex-lattice method for the unsteady aerodynamic model has been used.

Il a été montré dans différentes études que l'application de vibrations ultrasonores durant le forgeage permettaient entre autre de réduire les efforts et d'améliorer la qualité du produit. Plus récemment, des effets similaires ont été obtenu à basse fréquence, pour des formes d'ondes plus complexes, mais nécessitant moins de puissance. En raison de leur rigidité, et compte tenu des amplitudes et des fréquences mises en jeu, les actionneurs piézoélectriques sont bien adaptés à la génération des vibrations nécessaires mais leurs efforts restent limités et l'effet de vibrations est bénéficié selon une seule direction verticale. L'objectif de cette étude est de proposer un système multi-actionneurs piézoélectriques afin d'obtenir une plus grande force totale et des vibrations complexes combinant des rotations autour des axes du plan de la matrice et des translation selon son axe vertical. Un système mécanique à trois degrés de liberté est conçu à cet effet en utilisant des guidages élastiques en raison des faibles déplacements des actionneurs qui excluent la présence de jeux. Pour uniformiser les étapes de conception, modélisation et commande du système, une approche systémique énergétique est abordée en utilisant l'outil de Représentation Énergétique Macroscopique (REM). A l'aide de règles d'inversion de la REM, une structure de commande et une stratégie de gestion d'énergie dans le système sont développées et validées expérimentalement. / The superimposition of vibration during forging is known to reduce force and improve the mechanical properties of the workpiece. Until now, ultrasonic frequencies were used, but more recent results have shown that more complex vibrations at low frequencies had similar effects, with less power. Although piezoelectric actuator can generate high forces and have large rigidity, they are still limited with regards to the necessary forces during forging.Therefore, this work addresses the design of a worktool combining several actuators to generate complex vibration waveforms consisting in rotations in the plane of the die and displacement along the vertical direction. It relies on the use of flexible hinges due to the small displacement generated by the actuators. The design and control of the system is realized using a systemic approach based on the Energetic Macroscopic Representation. Thank to this tool, the control is systematically deduced by inversion. The design and its control strategy is validated experimentally on a mock-up specially realized during this work.

Les structures flexibles sont de plus en plus utilisées dans des domaines variés comme l'aérospatiale, l'automobile, etc. Les avantages du contrôle actif des vibrations sont son faible amortissement et sa sensibilité aux vibrations. Dans la réalité, en plus des exigences de réduction effective des vibrations, il faut également prendre en compte la quantité d'énergie nécessaire pour le contrôle, les entrées du contrôle pour éviter la saturation de commande, ainsi que la réduction des effets des bruits de mesure. D'autre part, comme les structures flexibles ont une infinité de modes de résonance et que seuls les premiers modes peuvent être utilisés dans la modélisation du système et dans la conception de contrôleur, les dynamiques négligées en hautes fréquences peuvent induire une instabilité dite "spill over". De plus, les incertitudes sur les paramètres modaux peuvent dégrader les performances de contrôle et même déstabiliser le système en boucle fermée. Dans ce contexte, on propose dans cette thèse une méthodologie quantitative de contrôle actif et robuste des vibrations des structures flexibles. Des stratégies de contrôle de la phase et du gain sont d'abord proposées pour assurer des spécifications dépendant de la fréquence sur la phase et le gain du contrôleur. Ces spécifications peuvent être réalisées par la conception du contrôleur par la méthode Hoo . Le contrôle H00 basé sur ces stratégies permet d'obtenir un compromis entre l'ensemble des objectifs de contrôle et d'offrir un contrôleur robuste qualitatif. En particulier, nous avons utilisé le contrôle LPV Hoo pour réduire l'énergie nécessaire au contrôle du système LPV. Le cadre généralisé du chaos polynomial (gPC) avec analyse par éléments finis, qui permet l'étude des effets des incertitudes de propriétés structurelles sur les fréquences naturelles et qui permet d'obtenir leurs informations probabilistes, est employé pour la quantification des incertitudes. Ensuite, en présence des incertitudes paramétriques et dynamiques, nous avons utilisé l'analyse 11/v et l'algorithme aléatoire en utilisant la méthode de Monte-Carlo pour assurer en même temps la stabilité en boucle fermée et les propriétés de robustesse de la performance à la fois dans le sens déterministe et le sens .probabiliste. La méthodologie de contrôle robuste quantitatif proposée est donc développée en employant des techniques diverses du contrôle automatique et du génie mécanique, et ainsi permet de réduire l'écart entre eux pour le contrôle robuste de la vibration pour des structures flexibles. Son efficacité est vérifiée par des simulations numériques et la validation expérimentale sur des poutres équipées de piézoélectriques non-colocalisés, LTI et LPV. / Flexible structures are increasingly used in various applications such as aerospace, automotive and so on. Since they are lightly damped and susceptible to vibrations, active vibration control is desirable. In practice, in addition to achieving effective vibration reduction, we have also to consider the required control energy to avoid the energy insufficiency, the control input to avoid control saturation and reduce the effects of measurement noises. On the other hand, as flexible structures have infinite number of resonant modes and only the first few can be employed in the system modeling and the controller design, there always exist neglected high-frequency dynamics, which can induce the spillover instability. Furthermore, the parametric uncertainties on modal parameters can degrade the control performances and even destabilize the closed-loop system. In this context, a quantitative robust control methodology for active vibration control of flexible structure is proposed in this thesis. Phase and gain control polices are first proposed to enforce frequency-dependent phase and gain requirements on the controller, which can be realized by the output feedback H1 control design. The phase and gain control polices based H1 control can make a trade-off among the complete set of control objectives and offer a qualitative robust controller. Especially, the LPV H1 control is used to reduce the required control energy for LPV systems. The generalized polynomial chaos (gPC) framework with finite element analysis is employed for uncertainty quantification. It allows us to investigate the effects of structural property uncertainties on natural frequencies and achieve their probabilistic information. Then, in the presence of parametric and dynamic uncertainties, µ / v analysis and the random algorithm using Monte Carlo Method are used to quantitatively ensure the closed-loop stability and performance robustness properties both in deterministic and probabilistic senses. The proposed quantitative robust control methodology is thus developed by employing various techniques from automatic control and mechanical engineering, thus reducing the gap between them for robust vibration control of flexible structures. Its effectiveness are verified by numerical simulations and experimental validation on LTI and LPV non-collocated piezoelectric cantilever beams.

La prochaine génération de télescopes spatiaux devra repousser les limites des technologies actuelles afin d’accroitre les performances techniques et opérationnelles. Dans le cas d’observations difficiles, l'utilisation de plus grandes ouvertures des miroirs primaires est essentielle pour obtenir la résolution optique et la sensibilité requises. Toutefois, les grandes ouvertures primaires induisent un certain nombre de défis techniques tels que la masse, le volume et la raideur du miroir. La masse et le volume doivent rester acceptables par rapport au lanceur et la raideur du miroir, qui diminue avec l’augmentation du diamètre du miroir, doit être suffisante afin que les performances ne soient pas altérées par les déformations statiques et dynamiques. Pour surmonter ces limitations, des configurations de miroirs déformables comportant des éléments de contrôle actifs sont étudiées pour les futurs télescopes spatiaux. Les actionneurs piézoélectriques, qui répondent aux exigences de puissance massique et de bande passante, peuvent être utilisés comme éléments de contrôle actifs intégrés dans la structure de miroir. Toutefois, ces actionneurs montrent en fonctionnement en boucle ouverte des comportements non linéaires indésirables, comme le fluage et l'hystérésis, qui peuvent conduire à des inexactitudes indésirables et limiter les performances des systèmes. Par conséquent, pour les miroirs déformables activés par des actionneurs piézoélectriques, la compensation des non linéarités dans les actionneurs piézoélectriques est indispensable.La conception d’un miroir léger, compact et déformable à raideur adéquate est un défi très important pour les télescopes spatiaux mais n'est pas abordée dans cette thèse. Cette thèse porte sur le contrôle de surfaces de miroirs déformables actionnés par des actionneurs piézoélectriques et en particulier sur la compensation du fluage et de l'hystérésis dans les actionneurs piézoélectriques. La technologie de miroir actif étudié (avec des pieds activés, type miroir fakir) requiert un grand nombre d’actionneurs afin de tenir les exigences en termes de planéité de surface et ne permet pas un contrôle en boucle fermée de chaque actionneur (ce type de contrôle est trop exigeant en nombre de capteurs). La compensation du fluage et de l’hystérésis est donc réalisée en boucle ouverte et s’appuie sur des modèles précis des non linéarités à compenser et sur l’implémentation de modèles inverses. Un support d’étude expérimental a été élaboré au cours de la thèse afin de valider les études théoriques par des résultats expérimentaux. Il représente une partie d’un miroir de grande taille et consiste en une plaque de verre circulaire de diamètre 300mm dont la surface peut être actionnée par 7 actionneurs piézoélectriques annulaires.Les premières chapitres de la thèse concernent l’étude de la compensation en boucle ouverte du fluage et de l’hystérésis dans un seul actionneur qui est alors considéré comme un système SISO (single input – single output). Dans le dernier chapitre de la thèse, le fluage et de l’hystérésis sont compensés dans 3 actionneurs simultanément, ceux-ci formant un système MIMO (multi input – multi output). Les apports de la thèse concernent le développement de nouveaux modèles directs et inverses de fluage et d’hystérésis qui ont été validés par des expérimentations réalisées dans un contexte difficile de par la faible étendue des amplitudes de déplacement ( de l’ordre du micromètre). / The next generation of space-based observation systems will make use of larger primary mirrors to achieve higher image resolution. Large primary mirrors lead to the increase of structural flexibility and are more susceptible to distortions. Thus maintaining optical tolerances across the mirror surface becomes increasingly difficult. The techniques of active shape control may be required for spatial mirror surfaces in future space observation systems. Piezoelectric actuators are often studied as embedded elements for the active control of mirror structures due to their excellent properties. However, unwanted nonlinear effects in piezoelectric actuators, i.e., hysteresis and creep, severely limit the service performance. This thesis aims at developing openloopcontrol laws to compensate hysteresis and creep effects in piezoelectric actuators. The studies led during this thesis are applied to the shape control of spatial mirror surfaces. An experimental setup with a small-scale mirror test structure involving multiple piezoelectric actuators is first developed and is used as support for all the measurements conducted during this thesis. Then the open-loop control methodologies of creep compensation, hysteresis compensation, and simultaneous compensation of both the nonlinear effects in a single piezoelectric actuator are respectively developed. To compensate creep, a nonlinear viscoelastic model is used to portray creep, and a new inverse model of creep based on the concept of “voltage relaxation” is proposedRegarding the hysteresis compensation, the classical Preisach model is modified by adding a derivative term in parallel to describe hysteresis more accurately with relatively few measurements, and the new inverse model is constructed in the similar way. For the simultaneous compensation of the two nonlinear effects, the hysteresis is first compensated and then, the creepof the hysteresis-compensated piezoelectric actuator is attenuated by open-loop control. The methodology is first developed for a single actuator. Finally, the shape control of a mirror surface with several piezoelectric actuators is achieved by actuating the points on the mirror surface in such a way as to reach the required displacements. The mirror test structure involving multiplepiezoelectric actuators compensated in hysteresis and creep is considered as a linear system on which the superposition principle can be applied. The influence coefficients characterizing the coupling effect between the piezoelectric actuators are determined by measurements. The influence coefficient matrix is first constructed using the superposition principle, and is then inverted. By insertion of the inverse matrix in cascade with multiple piezoelectric actuators with hysteresis and creep compensation, a feed-forward control approach to actuate the multiple interesting points of the mirror surface is developed. A number of experimental results demonstrate that the developed control methodologies are effective and feasible in practice.