Les actionneurs piézoélectriques font partie des outils les plus utilisés dans les applications à l'échelle micro/nano-métrique (micromanipulation, microassemblage, micropositionnement, etc…). Du point de vue fonctionnel, on distingue les actionneurs mono-axe (permettant d'obtenir la déflection suivant une direction) et les actionneurs multi-axes (pouvant fléchir suivant plusieurs directions). La notoriété des actionneurs piézoélectriques est due à un certain nombre de performances telles qu'une large bande passante (plus du kHz possible), une très bonne résolution (de l'ordre du nanomètre), une faible consommation en énergie électrique, une grande densité de force, une facilité d'alimentation et d'intégration, etc. Cependant, ces actionneurs sont caractérisés par des non-linéarités fortes (hystérésis et la dérive lente), des oscillations mal-amorties, et sont sensibles à la variation des conditions ambiantes (en particulier à la variation de la température). Pour les actionneurs multi-axes, il s'ajoute un problème des couplages entre les différents axes de l'actionneur. Cette thèse propose des stratégies innovantes de commande des actionneurs piézoélectriques multi-axes pour contrer les problèmes sus-mentionnés. Ces stratégies sont groupées en deux catégories. La première catégorie concerne les techniques de commande en boucle fermée. Ces techniques sont les plus adaptées pour garantir la robustesse et un niveau de précision élevé pour les actionneurs piézoélectriques. Cependant, à l'échelle micro/nano-métrique, ces techniques sont limitées par un manque d'espace suffisant pour installer des capteurs de position. La deuxième catégorie concerne la commande en boucle ouverte dont l'intérêt majeur est lié au fait qu'il n'y a pas besoin de capteurs pour la commande, ce qui constitue un avantage en terme de coût et facilité d'intégration. Dans cette thèse, nous proposons d'abord les techniques de modélisation et de commande en boucle ouverte multivariables. Ensuite, nous faisons une analyse des effets de la température sur les actionneurs piézoélectriques et nous proposons des techniques de commande en boucle ouverte et en boucle fermée de ces effets. Enfin, une stratégie de commande en boucle fermée par découplage, visant à obtenir des correcteurs d'ordre réduit pour les actionneurs multi-axes est proposée. Toutes ces techniques sont vérifiées et appliquées expérimentalement à un actionneur piézoélectrique de type tube. / Piezoelectric actuators are among the most used tools in many applications at micro/nano-scale (micromanipulation,microassembly, micropositioning, etc). From a functional perspective, there exist mono-axis actuators(which are made to bend in one direction) and multi-axis actuators (which provide deflections in different directions).The popularity of piezoelectric actuators is especially due to their high resolution (nanometric resolution),the large bandwidth (greater than 1kHz possible), the low electrical power consumption, the high force density,the ease of integration in positioning systems, etc. However, piezoelectric actuators are characterized by hysteresisand creep nonlinearities, badly damped vibrations and they are sensitive to the variation of ambient conditions(especially to the temperature variation). In addition, multi-axis actuators exhibit cross-couplings betweentheir axis. This thesis proposes novel strategies for modeling and control of multi-axis piezoelectric actuators,with the aim to counteract the aforementionned problems. These strategies are grouped into two categories.The first category concerns feedback control techniques. These techniques are the most suitable to ensurethe robustness and a high level of precision for piezoelectric actuators. However, at the micro/nanoscale, thesetechniques are limited by the lack of enough physical space to install feedback sensors. The second categoryconcerns the feedforward control techniques. The main advantage of these techniques is related to the factthat, in feedforward control schemes, feedback sensors are not needed for tracking. This allows to achieve ahigh degree of packageability and the cost reduction. In this thesis, we first propose multivariable modelingand feedforward control techniques. Then, we analyse the effects of temperature variation on piezoelectricactuators and we propose feedforward and feedback control techniques for these effects. Finally, a feedbackstrategy based on decoupling techniques with an aim to reduce the order of feedback controllers for multi-axispiezoelectric actuators, is proposed. All these modeling and control strategies are experimentally applied on apiezoelectric tube actuator.

In this thesis, a new method is followed to design an active control system which imparts viscoelastic phenomenological damping in an elastic structure. Properties of a hypothetical viscoelastic system are used to design an active feedback controller for an undamped structural system with distributed sensor, actuator and controller. The variational structure is projected on a solution space of a closed-loop system involving a weakly damped structure with distributed sensor and actuator with controller. These controller components assign the phenomenology based on internal strain rate damping parameter of a viscoelastic system to the undamped elastic structure. An elastic cantilever beam with proportional-derivative controller and displacement feedback is considered in all the design formulations. In the first part of the research, a closed-loop control system is designed using two time domain modern control system design methods, pole placement and optimal pole placement, which use viscoelastic damping parameter. Equation of motion of a viscoelastic system is employed to synthesize the desired closed-loop poles. Desired poles are then assigned to an elastic beam with an active controller. Time domain finite element formulation is used without considering actuator-sensor dynamics and the effect of transducer locations. Characteristics of closed-loop system gains are found as a function of desired damping parameter and realization of damping have been analyzed with closed loop system pole positions. The next part consists of a novel frequency domain active control system design to impart desired viscoelastic characteristics, which uses spectral method and the exact dynamic stiffness matrix of the system. In the first case, a sub-optimal local control system for a cantilever beam, with collocated actuator and sensor is designed. In the second case, a closed-loop local controller for an elastic system with non-collocated transducers is designed. Next, a global controller for non-collocated arrangement of sensor-actuator is designed by considering all the degrees-of freedom in the system, which leads to solving an eigenvalue problem. The reason for the failure of the collocated arrangement in global control is also explained. In this novel control system design method transducer dynamics and locations are considered in the formulation. In frequency domain design, the frequency responses of the system show satisfactory performance of the closed-loop elastic system. The closed-loop system is able to reproduce the desired viscoelastic characteristics as targeted in the design. Optimal and sub-optimal system gains are found as functions of transducer locations, transducer properties, excitation frequency and internal strain rate damping parameter of a hypothetical viscoelastic system. Performance of the closed loop system is established by comparing the specific damping capacity of the hypothetical viscoelastic system with that of the closed-loop elastic system. The novel frequency domain method is simple, accurate, efficient and can be extended to complex structures to achieve desired damping. The method can be a better way of designing structures with variable stiffness which has research potential in designing morphing airplanes/spacecrafts. The ultimate goal of this research is that, if this design method is applied to practical applications such as aircraft wings, where vibration is undesirable, one would be able to achieve strength and desired damping characters simultaneously.

This thesis contributes to the state of the art in integrated design of insect-scale piezoelectric actuated flapping wing vehicles through the development of novel theoretical models for flapping wing aerodynamics and piezoelectric actuator dynamics, and integration of these models into a closed form design process. A comprehensive literature review of available engineered designs of miniature rotary and flapping wing vehicles is provided. A novel taxonomy based on wing and actuator kinematics is proposed as an effective means of classifying the large variation of vehicle configurations currently under development. The most successful insect-scale vehicles developed to date have used piezoelectric actuation, system resonance for motion amplification, and passive wing pitching. A novel analytical treatment is proposed to quantify induced power losses in normal hover that accounts for the effects of non uniform downwash, wake periodicity and effective flapping disc area. Two different quasi-steady aerodynamic modelling approaches are undertaken, one based on blade element analysis and one based on lifting line theory. Both approaches are explicitly linked to the underlying flow physics and, unlike a number of competing approaches, do not require empirical data. Models have been successfully validated against experimental and numerical data from the literature. These models have allowed improved insight into the role of the wing leading-edge vortex in lift augmentation and quantification of the comparative contributions of induced and profile drag for insect-like wings in hover. Theoretical aerodynamic analysis has been used to identify a theoretical solution for the optimum planform for a flapping wing in terms of chord and twist as a function of span. It is shown that an untwisted elliptical planform minimises profile power, whereas a more highly tapered design such as that found on a hummingbird minimises induced power. Aero-optimum wing kinematics for hovering are also assessed. It is shown that for efficient flight the flapping velocity should be constant whereas for maximum effectiveness the flapping velocity should be sinusoidal. For both cases, the wing pitching at stroke reversal should be as rapid as possible. A dynamic electromechanical model of piezoelectric bending actuators has been developed and validated against data obtained from experiments undertaken as part of this thesis. An expression for the electromechanical coupling factor (EMCF) is extracted from the analytical model and is used to understand the influence of actuator design variables on actuator performance. It is found that the variation in EMCF with design variables is similar for both static and dynamic operation, however for light damping the dynamic EMCF will typically be an order of magnitude greater than for static operation. Theoretical contributions to aerodynamic and electromechanical modelling are integrated into a low order design method for propulsion system sizing. The method is unique in that aside from mass fraction estimation, the underlying models are fully physics based. The transparency of the design method provides the designer with clear insight into effects of changing core design variables such as the maximum flapping amplitude, wing mass, transmission ratio, piezoelectric characteristics on the overall design solution. Whilst the wing mass is only around 10% of the actuator mass, the effective wing mass is 16 times the effective actuator mass for a typical transmission ratio of 10 and hence the wing mass dominates the inertial contribution to the system dynamics. For optimum aerodynamic effectiveness and efficiency it is important to achieve high flapping amplitudes, however this is typically limited by the maximum allowable field strength of the piezoelectric material used in the actuator.

Bei der Fertigung von Siliziumwafern durch Zerteilen eines Siliziumblockes kommt das Drahttrennläppverfahren zur Anwendung. Es wird eine Erregereinheit entwickelt, die den Siliziumblock während des Schneidprozesses zu Schwingungen anregt. Die Verwendung von Piezoaktoren ermöglicht mehrachsige Schwingungen mit variabler Frequenz und Amplitude. Wesentliche Bestandteile der Arbeit sind experimentelle Untersuchungen an den Aktoren und der gesamten Erregereinheit sowie die Modellierung des Gesamtsystems mit Hilfe linearer Einzelmodelle. Es zeigt sich, dass die Aktoren bei dynamischen Anwendungen linear beschrieben werden können, während das Gesamtmodell besonders in den Resonanzbereichen aufgrund montagebedingter Einflüsse Schwächen aufweist. Abschließend wird der Einfluss der Schwingungsanregung beim Drahtsägen untersucht. Aus den Versuchen geht hervor, dass im getesteten Frequenz- und Amplitudenbereich sowohl hohe Erregerfrequenzen als auch –amplituden geringere Schnittkräfte zur Folge haben.

Bei der Fertigung von Siliziumwafern durch Zerteilen eines Siliziumblockes kommt das Drahttrennläppverfahren zur Anwendung. Es wird eine Erregereinheit entwickelt, die den Siliziumblock während des Schneidprozesses zu Schwingungen anregt. Die Verwendung von Piezoaktoren ermöglicht mehrachsige Schwingungen mit variabler Frequenz und Amplitude. Wesentliche Bestandteile der Arbeit sind experimentelle Untersuchungen an den Aktoren und der gesamten Erregereinheit sowie die Modellierung des Gesamtsystems mit Hilfe linearer Einzelmodelle. Es zeigt sich, dass die Aktoren bei dynamischen Anwendungen linear beschrieben werden können, während das Gesamtmodell besonders in den Resonanzbereichen aufgrund montagebedingter Einflüsse Schwächen aufweist. Abschließend wird der Einfluss der Schwingungsanregung beim Drahtsägen untersucht. Aus den Versuchen geht hervor, dass im getesteten Frequenz- und Amplitudenbereich sowohl hohe Erregerfrequenzen als auch –amplituden geringere Schnittkräfte zur Folge haben.