In this thesis the synchronization of two different chaotic systems with matched and mismatched perturbations are developed by utilizing adaptive backstepping control technique. The adaptive mechanisms embeded in the proposed control scheme is used to adapt the unknown upper bounds of the perturbations. The resultant robust backstepping tracking controller with adaptive mechanisms can indeed drive the trajectories of the slave system to track those of the master system. Two numerical examples and simulations are given to illustrate the correctness of theoretical analyses.

Made available in DSpace on 2015-03-03T15:07:34Z (GMT). No. of bitstreams: 1 BrenoMMA_DISSERT.pdf: 2152939 bytes, checksum: 11e98e5a221057a9bd3545dd9b777bb5 (MD5) Previous issue date: 2012-04-12 / Coordena??o de Aperfei?oamento de Pessoal de N?vel Superior / This research aims at developing a variable structure adaptive backstepping controller (VS-ABC) by using state observers for SISO (Single Input Single Output), linear and time invariant systems with relative degree one. Therefore, the lters were replaced by a Luenberger Adaptive Observer and the control algorithm uses switching laws. The presented simulations compare the controller performance, considering when the state variables are estimated by an observer, with the case that the variables are available for measurement. Even with numerous performance advantages, adaptive backstepping controllers still have very complex algorithms, especially when the system state variables are not measured, since the use of lters on the plant input and output is not something trivial. As an attempt to make the controller design more intuitive, an adaptive observer as an alternative to commonly used K lters can be used. Furthermore, since the states variables are considered known, the controller has a reduction on the dependence of the unknown plant parameters on the design. Also, switching laws could be used in the controller instead of the traditional integral adaptive laws because they improve the system transient performance and increase the robustness against external disturbances in the plant input / Esta pesquisa objetiva desenvolver um controlador adaptativo backstepping a estrutura vari?vel (Variable Structure Adaptive Backstepping Controller, VS-ABC) utilizando observadores de estado para plantas monovari?veis, lineares e invariantes no tempo com grau relativo unit?rio. Para isso, os filtros K foram substitu?dos por um Observador Adaptativo de Luenberger e o algoritmo de controle utiliza leis chaveadas. As simula??es apresentadas comparam o desempenho do controlador quando as vari?veis de estado s?o estimadas por um observador, com o caso em que as vari?veis est?o dispon?veis para medic?o. Os controladores adaptativos backstepping mesmo com v?rias vantagens de desempenho, ainda possuem algoritmos muito complexos, principalmente quando n?o s?o medidas as vari?veis de estado do sistema, pois o uso de filtros nos sinais de entrada e sa?da da planta n?o ? algo trivial. Na inten??o de tornar o projeto do controlador mais intuitivo, pode-se utilizar um observador adaptativo em alternativa aos comumente utilizados filtros K. Al?m disso, o controlador tem uma menor depend?ncia dos par?metros desconhecidos da planta na fase de projeto, ja que as vari?veis de estado s?o consideradas conhecidas. E ainda, leis chaveadas podem ser utilizadas no controlador em vez das leis integrais tradicionais porque melhoram o desempenho transit?rio do sistema e aumentam a robustez perante dist?rbios externos na entrada da planta

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.

The omnicopter is a small unmanned aerial vehicle capable of executing decoupled translational and rotational motion (six degree of freedom, 6DOF, motion). The development of controllers for various 6DOF controllable multirotors has been much more limited than development for quadrotors, which makes selecting a controller for a 6DOF multirotor difficult. The omnicopter is subject to various uncertainties and disturbances from hardware changes, structural dynamics, and airflow, making adaptive controllers particularly interesting to investigate. The goal of this research is to design and evaluate the performance of various position and attitude controller combinations for the omnicopter, specifically focusing on adaptive controllers. Simulations are first used to compare combinations of three position controllers, PID, model reference adaptive control, augmented model reference adaptive control (aMRAC), and four attitude controllers, PI/feedback linearization (PIFL), augmented model reference adaptive control, backstepping, and adaptive backstepping (aBack). For the simulations, the omnicopter is commanded to point at and track a stationary aim point as it travels along a $C^0$ continuous trajectory and a trajectory that is $C^1$ continuous. The controllers are stressed by random disturbances and the addition of an unaccounted for suspended mass. The augmented model reference adaptive controller for position control paired with the adaptive backstepping controller for attitude control is shown to be the best controller combination for tracking various trajectories while subject to disturbances. Based on the simulation results, the PID/PIFL and aMRAC/aBack controllers are selected to be compared during three different flight tests. The first flight test is on a $C^1$ continuous trajectory while the omnicopter is commanded to point at and track a stationary aim point. The second flight test is a hover with an unmodeled added weight, and the third is a circular trajectory with a broken blade. As with the simulation results, the adaptive controller is shown to yield better performance than the nonadaptive controller for all scenarios, particularly for position tracking. With an added weight or a broken propeller, the adaptive attitude controller struggles to return to level flight, but is capable of maintaining steady flight when the nonadaptive controller tends to fail. Finally, while model reference adaptive controllers are shown to be effective, their nonlinearity can make them difficult to tune and certify via standard certification methods, such as gain and phase margin. A method for using time delay margin estimates, a potential certification metric, to tune the adaptive parameter tuning gain matrix is shown to be useful when applied to an augmented MRAC controller for a quadrotor. / Doctor of Philosophy / The omnicopter is a small unmanned aerial vehicle capable of executing decoupled translational and rotational motion. The development of controllers for these types of vehicles has been limited, making controller selection difficult. The omnicopter is subject to variations in hardware and airflow, making adaptive controllers particularly interesting to investigate. The goal of this research is to design and compare the performance of various position and attitude controller combinations for the omnicopter, specifically focusing on adaptive controllers. Simulations are first used to compare combinations of several position and attitude controllers on various trajectories and disturbances. Simulation results showed that a fully adaptive controller combination produced the best trajectory tracking while subject to disturbances. As with the simulation results, flight tests showed the adaptive controller yields better performance than the nonadaptive controller for all scenarios, particularly for position tracking. Finally, while the adaptive position controller was shown to be effective, it is difficult to tune and certify for widespread use. A method for using time delay margin estimates, a potential certification metric, to tune the adaptive controller is shown to be useful when applied to an adaptive controller for a quadrotor.