Sliding mode control with linear quadratic hyperplane design : an application to an active magnetic bearing system

This paper deals with modeling and control of a nonlinear horizontal active magnetic bearing (AMB) system via current control scheme. The gyroscopic effect and mass imbalance inherited in the system are proportional to the rotor speed in which these nonlinearities cause high system instability as the rotational speed increases. In order to synthesize a robust controller that can stabilize the system under a wide range of rotational speed, the dynamic AMB model is transformed into a deterministic model to form a class of uncertain system. Then, based on Sliding Mode Control (SMC) theory and Lyapunov method, a new robust controller that stabilizes the system is proposed wherein the Linear Quadratic Regulator (LQR) is used to design the sliding surface. Under this control, the reaching condition is guaranteed and the closed loop system is stable. The performance of the controller applied to the AMB model is demonstrated through simulation works under various rotational speeds and system conditions

Investigation on the Applicability of Active Magnetic Bearings to High Speed Spindle Design

A novel concept applicable to the control of spindles at high speed is developed by using active magnetic bearings (AMBs) that are non-contact and of low vibration. Extensive literature reviews explicate that the broad applications of AMBs are severely hampered by the incomplete description of the underlying electro-magnetic-mechanical dynamics. The thesis considers the gyroscopic effect inherent of a flexible rotor and explores the geometry coupling of the electro-magnetic actuators to the formulation of a comprehensive nonlinear AMB-rotor model. The model provides the basis for the creation of a novel time-frequency control algorithm whose derivation requires no linearization or mathematical simplification of any kind, thus allowing the model system to retain its true fundamental characteristics. Unlike proportional-integral-derivative (PID) controllers that are dominant in most if not all AMB configurations, the controller developed for the research is inspired by the wavelet-based nonlinear time-frequency control methodology that incorporates the basic notions of online system identification and adaptive control. Wavelet filter banks and filtered-x least-mean-square (LMS) algorithm are two of the major salient physical features of the controller design, with the former providing concurrent temporal and spectral resolutions needed for identifying nonlinear states of motion and the latter ensuring the dynamic stability of the AMB-rotor system at all operating speeds subjected to the presence of external disturbances. It is shown in the thesis that the vibration of the rotor is unconditionally controlled by maintaining the mandatory 0.55 mm air gap at 150,000 and 187,500 rpm subject to a tight spatial constraint (tolerance) of the order of 0.1375mm. System responses with and without considering the gyroscopic motion and geometry coupling are studied to demonstrate the negative impact on misinterpreting the AMB-rotor dynamics when the two effects are neglected. The case of an impact of 5,000m/s2 in magnitude and 0.001 seconds in duration at 187,500rpm is also investigated to establish the robustness of the controller design. The time responses of all the cases considered are both temporally bounded and spectrally bandwidth-limited, thus demonstrating the effectiveness of the wavelet-based time-frequency controller design in mitigating the inherent instability of the AMB-rotor system at extreme speeds

Modelling and control of contact in magnetic bearing/flexible rotor systems

EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Commande par mode glissant de paliers magnétiques actifs économes en énergie : une approche sans modèle

Abstract : Over the past three decades, various fields have witnessed a successful application of active magnetic bearing (AMB) systems. Their favorable features include supporting high-speed rotation, low power consumption, and rotor dynamics control. Although their losses are much lower than roller bearings, these losses could limit the operation in some applications such as flywheel energy storage systems and vacuum applications. Many researchers focused their efforts on boosting magnetic bearings energy efficiency via minimizing currents supplied to electromagnetic coils either by a software solution or a hardware solution. According to a previous study, we adopt the hardware solution in this thesis. More specifically, we investigate developing an efficient and yet simple control scheme for regulating a permanent magnet-biased active magnetic bearing system. The control objective here is to suppress the rotor vibrations and reduce the corresponding control currents as possible throughout a wide operating range. Although adopting the hardware approach could achieve an energy-efficient AMB, employing an advanced control scheme could achieve a further reduction in power consumption. Many advanced control techniques have been proposed in the literature to achieve a satisfactory performance. However, the complexity of the majority of control schemes and the potential requirement of powerful platform could discourage their application in practice. The motivation behind this work is to improve the closed-loop performance without the need to do model identification and following the conventional procedure for developing a model-based controller. Here, we propose applying the hybridization concept to exploit the classical PID control and some nonlinear control tools such as first- and second-order sliding mode control, high gain observer, backstepping, and adaptive techniques to develop efficient and practical control schemes. All developed control schemes in this thesis are digitally implemented and validated on the eZdsp F2812 control board. Therefore, the applicability of the proposed model-free techniques for practical application is demonstrated. Furthermore, some of the proposed control schemes successfully achieve a good compromise between the objectives of rotor vibration attenuation and control currents minimization over a wide operating range.Résumé: Au cours des trois dernières décennies, divers domaines ont connu une application réussie des systèmes de paliers magnétiques actifs (PMA). Leurs caractéristiques favorables comprennent une capacité de rotation à grande vitesse, une faible consommation d'énergie, et le contrôle de la dynamique du rotor. Bien que leurs pertes soient beaucoup plus basses que les roulements à rouleaux, ces pertes pourraient limiter l'opération dans certaines applications telles que les systèmes de stockage d'énergie à volant d'inertie et les applications sous vide. De nombreux chercheurs ont concentré leurs efforts sur le renforcement de l'efficacité énergétique des paliers magnétiques par la minimisation des courants fournis aux bobines électromagnétiques soit par une solution logicielle, soit par une solution matérielle. Selon une étude précédente, nous adoptons la solution matérielle dans cette thèse. Plus précisément, nous étudions le développement d'un système de contrôle efficace et simple pour réguler un système de palier magnétique actif à aimant permanent polarisé. L'objectif de contrôle ici est de supprimer les vibrations du rotor et de réduire les courants de commande correspondants autant que possible tout au long d'une large plage de fonctionnement. Bien que l'adoption de l'approche matérielle pourrait atteindre un PMA économe en énergie, un système de contrôle avancé pourrait parvenir à une réduction supplémentaire de la consommation d'énergie. De nombreuses techniques de contrôle avancées ont été proposées dans la littérature pour obtenir une performance satisfaisante. Cependant, la complexité de la majorité des systèmes de contrôle et l'exigence potentielle d’une plate-forme puissante pourrait décourager leur application dans la pratique. La motivation derrière ce travail est d'améliorer les performances en boucle fermée, sans la nécessité de procéder à l'identification du modèle et en suivant la procédure classique pour développer un contrôleur basé sur un modèle. Ici, nous proposons l'application du concept d'hybridation pour exploiter le contrôle PID classique et certains outils de contrôle non linéaires tels que contrôle par mode glissement du premier et du second ordre, observateur à grand gain, backstepping et techniques adaptatives pour développer des systèmes de contrôle efficaces et pratiques. Tous les systèmes de contrôle développés dans cette thèse sont numériquement mis en oeuvre et évaluées sur la carte de contrôle eZdsp F2812. Par conséquent, l'applicabilité des techniques de modèle libre proposé pour l'application pratique est démontrée. En outre, certains des régimes de contrôle proposés ont réalisé avec succès un bon compromis entre les objectifs au rotor d’atténuation des vibrations et la minimisation des courants de commande sur une grande plage de fonctionnement