Este trabalho se insere no contexto de redução de vibrações de rotores via mancais ativos. Essas vibrações são causadas pelo desbalanço do próprio rotor e possuem frequência igual à frequência de rotação desse rotor. O desbalanço pode ser modelado como uma força de perturbação girante, sendo que uma técnica bastante conhecida para anular o efeito dessa perturbação é o balanceamento eletrônico, também chamado de compensação síncrona de desbalanço ou de regulação sincronizada. A presente dissertação traz duas contribuições para o tema. A primeira é a simplificação do compensador síncrono através de considerações de simetria do rotor e de isotropia dos mancais, e a segunda é a obtenção do modelo exato do sistema discreto resultante da aplicação da metodologia de compensação síncrona. Tais contribuições se valem da descrição do modelo em coordenadas complexas. À transformação de coordenadas reais para coordenadas complexas deu-se o nome de complexificação. Assim sendo, a complexificação do modelo permite dividir por dois a dimensão das variáveis do sistema (estados, entradas e saídas), além de dar sentido físico à separação entre os distúrbios diretos (caso do desbalanço) e os distúrbios retrógrados. Essa complexificação reduz o tempo de identificação da matriz de influência feita no balanceamento eletrônico, e o modelo complexificado obtido através das hipóteses de simetria e isotropia permite desacoplar completamente a compensação das perturbações diretas da compensação das perturbações retrógradas. / This work is inserted in the context of active attenuation of rotor vibrations. These vibrations are caused by the rotor\'s own unbalance and have a frequency equal to the rotor\'s rotation frequency. The unbalance can be modeled as a rotating disturbance force, and a well-known technique for cancelling the effect of such a disturbance is the so-called active balancing, also known as synchronous unbalance compensation or synchronized regulation. The present dissertation brings two contributions to the theme. The first one is the simplification of the synchronous compensator through considerations of rotor symmetry and bearing isotropy, and the second one is to obtain the exact model of the discrete system resulting from the application of the synchronous compensation methodology. These contributions make use of the model described in complex coordinates. The transformation from real coordinates to complex coordinates is defined as a complexification. Thus, the complexification of the model allows the division in half of the dimension of the system variables (states, inputs and outputs), as well as giving a physical sense to the separation between forward disturbances (case of the rotor unbalance) and backward disturbances. This complexification reduces the time of identification of the influence matrix made in active balancing, and the complexified model obtained through symmetry and isotropy hypotheses allows the completely uncouple of the forward disturbances compensation from the backward disturbances compensation.

Este trabalho se insere no contexto de redução de vibrações de rotores via mancais ativos. Essas vibrações são causadas pelo desbalanço do próprio rotor e possuem frequência igual à frequência de rotação desse rotor. O desbalanço pode ser modelado como uma força de perturbação girante, sendo que uma técnica bastante conhecida para anular o efeito dessa perturbação é o balanceamento eletrônico, também chamado de compensação síncrona de desbalanço ou de regulação sincronizada. A presente dissertação traz duas contribuições para o tema. A primeira é a simplificação do compensador síncrono através de considerações de simetria do rotor e de isotropia dos mancais, e a segunda é a obtenção do modelo exato do sistema discreto resultante da aplicação da metodologia de compensação síncrona. Tais contribuições se valem da descrição do modelo em coordenadas complexas. À transformação de coordenadas reais para coordenadas complexas deu-se o nome de complexificação. Assim sendo, a complexificação do modelo permite dividir por dois a dimensão das variáveis do sistema (estados, entradas e saídas), além de dar sentido físico à separação entre os distúrbios diretos (caso do desbalanço) e os distúrbios retrógrados. Essa complexificação reduz o tempo de identificação da matriz de influência feita no balanceamento eletrônico, e o modelo complexificado obtido através das hipóteses de simetria e isotropia permite desacoplar completamente a compensação das perturbações diretas da compensação das perturbações retrógradas. / This work is inserted in the context of active attenuation of rotor vibrations. These vibrations are caused by the rotor\'s own unbalance and have a frequency equal to the rotor\'s rotation frequency. The unbalance can be modeled as a rotating disturbance force, and a well-known technique for cancelling the effect of such a disturbance is the so-called active balancing, also known as synchronous unbalance compensation or synchronized regulation. The present dissertation brings two contributions to the theme. The first one is the simplification of the synchronous compensator through considerations of rotor symmetry and bearing isotropy, and the second one is to obtain the exact model of the discrete system resulting from the application of the synchronous compensation methodology. These contributions make use of the model described in complex coordinates. The transformation from real coordinates to complex coordinates is defined as a complexification. Thus, the complexification of the model allows the division in half of the dimension of the system variables (states, inputs and outputs), as well as giving a physical sense to the separation between forward disturbances (case of the rotor unbalance) and backward disturbances. This complexification reduces the time of identification of the influence matrix made in active balancing, and the complexified model obtained through symmetry and isotropy hypotheses allows the completely uncouple of the forward disturbances compensation from the backward disturbances compensation.

Le comportement dynamique des turbomachines industrielles doit respecter des critères émis par les normes internationales et les utilisateurs. Les rotors flexibles sont sensibles à la distribution de balourd, et sont soumis aux excitations aérodynamiques de leur environnement. Usuellement, les contrôleurs utilisés peinent à délivrer le niveau d’exigence demandé, par conséquent les propriétés mécaniques des paliers magnétiques sont fortement dépendantes de celles des rotors. L’objectif de ce mémoire est d’analyser le comportement dynamique des compresseurs centrifuges afin de proposer une stratégie de contrôle innovante. D’abord, chaque palier est considéré comme une entité a part entière en couplant ses deux axes d’action. Le comportement dynamique du rotor est exprimé dans le repère polaire. Par ailleurs, la logique floue, qui utilise un modèle de pensée proche du raisonnement humain, applique des actions correctives en fonction du comportement dynamique global du rotor. Ainsi, l’utilisation couplée de ces deux approches créé une synergie permettant d’agir sur le système de manière ciblée. Le contrôleur dissipe l’énergie cinétique du rotor lors du franchissement de vitesses critiques afin d’atténuer la réponse au balourd, ou augmente la raideur du palier lors de vibrations transitoires ou asynchrones afin de réduire la trajectoire du rotor. Le faible amortissement structurel du rotor le rend sensible au phénomène de « spillover » (l’énergie de contrôle affecte les modes de fréquence élevée). Or, la logique floue ne peut pas gérer ce phénomène. Ainsi, un contrôleur PID sous-jacent est utilisé pour maîtriser la stabilité des modes hautes fréquences. Au final, le contrôleur flou polaire permet d’obtenir des marges de performances entre les capacités de cet asservissement et le cahier des charges. Ces marges sont utilisées pour trois objectifs : le respect des spécifications, l’amélioration du comportement subsynchrone, et enfin la simplification et la standardisation du contrôleur sous-jacent nommé ici SPID. Ce contrôleur est tel que ses caractéristiques, dans la plage de fréquence utile, sont indépendantes du rotor pour une application donnée. Enfin, la stratégie développée est évaluée avec des simulations numériques et des essais expérimentaux. D’abord, le modèle numérique est validé, puis le contrôleur est appliqué à un banc d’essais académique. Le comportement est stable et robuste. Il présente des performances supérieures au PID augmenté fourni avec le banc, que ce soit pour la réponse au balourd, ou pour la réponse à des excitations subsynchrones. Finalement, la démarche est appliquée à un compresseur industriel. Les simulations montrent que le comportement est proche de celui exigé pour des machines sur paliers classiques. L’optimisation de l’approche et l’automatisation de la conception pourraient conduire à la standardisation des paliers magnétiques actifs. / The dynamic behaviour of large turbomachinery should satisfy stringent requirements dictated by international standards and final users. Their flexible rotor is sensitive to the unbalance distribution and subjected to particular excitations coming from the industrial process. Usually, the performance margins between the requirements and the classical controller capabilities are small. Consequently, the magnetic bearing characteristics depend on the rotor geometry. Designing such controllers is difficult and time consuming. The objective of this thesis is to investigate the dynamic behaviour of supercritical centrifugal compressors in order to propose a new control strategy. First, each bearing is considered as one entity by coupling its two axes of action. The introduction of polar quantities permits a better observation of the rotor dynamic behaviour. In addition, by using logic close to human being reasoning, the fuzzy logic modulates the action forces as a function of the global dynamic behaviour. The coupling of the two approaches is an efficient way to apply targeted corrective actions. This controller attenuates the unbalance vibration when crossing critical speeds by applying damping forces, or increases the stiffness during transient or asynchronous excitations in order to limit the maximum displacement reached. As their structural damping is low, flexible rotors are very sensitive to spillover effect, which cannot be managed by fuzzy controllers. Consequently, an underlying PID is necessary. This hand-synthesized controller has high frequency characteristics tuned in order to ensure stability and robustness for each rotor. Compared to a classical approach, the polar fuzzy controller enables to increase the performance margins. These margins are used to fulfil three objectives: the achievement of standards requirements, the improvement of the subsynchronous behaviour, and the simplification and the standardization of the PID controller that we called SPID. This SPID is designed for a given application, such that the bearing characteristics on the operating frequency range are always the same. The control strategy is assessed numerically and experimentally. First, the numerical model is validated with experimental tests. Then, the controller developed is applied to an academic test rig. The controller is stable and robust. It exhibits performance superior to the augmented PID supplied with the test rig for both unbalance response and response to subsynchronous excitations. Finally, the control of an industrial compressor is assessed numerically. The results obtained are close to the standards requirements used for classical bearings. The optimization of the approach and the utilization of an automatic tuning algorithm for high frequency characteristics could lead to the standardization of Active Magnetic Bearings.