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Dynamics and Control of a Multi-Tethered Aerostat Positioning System

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Dynamics and Control of a Multi-Tethered Aerostat Positioning System Dynamics and Control of a Multi-Tethered Aerostat Positioning System by Casey Lambert Department of Mechanical Engineering McGill University, Montreal Canada October 2006 A thesis submitted to McGill University in partial fulfillment of the requirements of the degree of Doctor of Philosophy © Casey Lambert, 2006 Library and Bibliothèque et 1+1 Archives Canada Archives Canada Published Heritage Direction du Branch Patrimoine de l'édition 395 Wellington Street 395, rue Wellington Ottawa ON K1A ON4 Ottawa ON K1A ON4 Canada Canada Your file Votre référence ISBN: 978-0-494-32203-1 Our file Notre référence ISBN: 978-0-494-32203-1 NOTICE: AVIS: The author has granted a non­ L'auteur a accordé une licence non exclusive exclusive license allowing Library permettant à la Bibliothèque et Archives and Archives Canada to reproduce, Canada de reproduire, publier, archiver, publish, archive, preserve, conserve, sauvegarder, conserver, transmettre au public communicate to the public by par télécommunication ou par l'Internet, prêter, telecommunication or on the Internet, distribuer et vendre des thèses partout dans loan, distribute and sell th es es le monde, à des fins commerciales ou autres, worldwide, for commercial or non­ sur support microforme, papier, électronique commercial purposes, in microform, et/ou autres formats. paper, electronic and/or any other formats. The author retains copyright L'auteur conserve la propriété du droit d'auteur ownership and moral rights in et des droits moraux qui protège cette thèse. this thesis. Neither the thesis Ni la thèse ni des extraits substantiels de nor substantial extracts from it celle-ci ne doivent être imprimés ou autrement may be printed or otherwise reproduits sans son autorisation. reproduced without the author's permission. ln compliance with the Canadian Conformément à la loi canadienne Privacy Act some supporting sur la protection de la vie privée, forms may have been removed quelques formulaires secondaires from this thesis. ont été enlevés de cette thèse. While these forms may be included Bien que ces formulaires in the document page count, aient inclus dans la pagination, their removal does not represent il n'y aura aucun contenu manquant. any loss of content from the thesis. ••• Canada Abstract The focus of this study is the dynamic behaviour of a novel aerial positioning system, which consists of a lighter-than-air aerostat attached to a series of actuated tethers in the form of a tripod. The objective of the positioning system is to achieve accurate station-keeping of a payload at heights up to 500 m. This work encompasses comprehensive dynamics modeling, experimental investigation, and advanced controller development and analysis of the tri-tethered aerostat system. The system's characteristics and positioning objectives are targeted to receiver placement during the operation of a large-scale radio telescope. The experimental test facility, built at one-third scale of the proposed radio telescope, was constructed for the dual purpose of measuring the precision of the positioning system and providing a basis for validating our computational model. The main components of the experimental apparatus are a 18-m helium aerostat, three synthetic braided tethers­ hundreds of meters in length, an instrumented payload, and three computer-controlled winches. The dynamics model of the tri-tethered aerostat system is achieved by discretiz­ ing it into a series of lumped-masses, and estimating the aerodynamic properties of each of its physical e1ements. The disturbance input to the model is provided by a wind model that includes stochastic turbulent gusts. A series of experimental fiight tests were conducted over a two-year period to study both the uncontrolled and controlled response of the system. This leads to an incremental model validation process where the passive elements of the model, such as the tethers and the aerostat are validated prior to the verification of the entire closed-Ioop system. The tether model shows excellent agreement with the measured response at a temporal level, while the validation of the aerostat model is conducted at a statistical level due to the uncertaintyassociated with recreating the actual test wind conditions. The controlled experiments were performed using basic proportional, integral, and derivative (PID) feedback gains applied to the position error of the payload. The closed­ loop system effectively reduces the standard deviation of the payload defiections to less than 10 cm over the range of operating conditions tested. A comparison of the predicted c1osed-Ioop behaviour of the dynamics shows favourable agreement to the experimental results, indicating that the tether actuation system is modeled appropriately. To improve on the PID controller tested in the field, various optimal control strategies are investigated that exploit the availability of our validated dynamics model. The optimal controllers, which are designed and simulated using linear time invariant versions of the dynamics model, result in approximately double the precision of the PID controller. The control system is improved further by incorporating a feedforward control input based on measurements of the primary disturbance force acting on the system. In general the advanced control techniques, tested in simulation, offer encouraging results that suggest the positioning system should exceed the requirements of the radio telescope application. 11 Résumé Cette thèse porte sur l'étude de la dynamique d'un nouveau système de positionnement aérien, composé d'un aérostat attaché à une série de câbles actionnés montés enforme de trépied. L'objectif du système de positionnement est de stabiliser une charge utile à une hauteur de 500 mètres. Cette étude présente la modélisation dynamique complète, une phase d'expérimentation, ainsi que le développement et une analyse avancée du système de positionnement aérien. Les caractéristiques et la position du système sont définies en fonction d'un récepteur d'un radiotélescope à grande échelle. Un prototype du système à l'échelle 1:3 a été développé dans le but d'évaluer la précision du système et de valider notre modèle mathématique. Les composantes prin­ cipales de l'appareil expérimental sont: un aérostat gonflé à l'hélium de 18 m; trois câbles tressés synthétiques de plusieurs centaines de mètres de longueur chacun; une charge utile avec des capteurs; et trois treuils commandés par ordinateur. Le modèle dynamique est obtenu en discrétisant le système en une série de masses ponctuelles et en estimant les car­ actéristiques aérodynamiques de chaque composant physique. La perturbation du modèle est définie par un modèle éolien qui tient compte de rafales turbulentes stochastiques. Une série d'essais expérimentaux de vol a été effectuée sur une période de deux ans pour étudier la réponse du système avec et sans commande. Ceci nous a mené à un procédé de validation incrémentaI, les éléments passifs étant validés avant la vérification du système complet. Le modèle des câbles montre un excellent accord avec la réponse mesurée à un niveau temporel. Par contre, la validation du modèle de l'aérostat est effectueé à un niveau statistique dû au fait de l'incertitude liée à la modélisation des conditions réelles du vent. La commande du système a été réalisée au moyen d'un asservissement de type PlO (Proportional-Integral-Oerivative) appliqué à l'erreur de position de la charge. Le système réduit considérablement l'écart-type des déplacements de la charge à moins de 10 cm pour nos conditions d'essai. Une comparaison du comportement prévu du modèle dynamique montre un accord favorable avec les résultats expérimentaux, indiquant que les câbles ac­ tionnés sont modélisés convenablement. iii Afin d'améliorer l'algorithme de commande primaire testé sur le terrain, plusieurs stratégies de commande optimale ont été étudiées, nécessitant entre autres un modèle dynamique validé de notre système. Les contrôleurs optimaux, qui sont développés et simulés en utilisant des versions linéaires du modèle dynamique, donnent une précision approximativement deux fois meilleure que notre contrôleur antérieur. Le système de commande est amélioré davantage en utilisant un asservissement de l'entrée basé sur des mesures de forces de perturbation primaires agissant sur le système. En général, les tech­ niques avancées de commande testées en simulations offrent des résultats encourageants qui suggèrent que le système de positionnement devrait dépasser du radiotélescope. IV Acknowledgements 1 am sincerely grateful for the assistance and guidance 1 have received from numerous sources, which have helped make my studies a pleasure instead of a chore. This was my second tour with my supervisor Meyer Nahon and 1 again would like to thank him for a job well done. He has a knack for supervising with a fortuitous balance of guidance and freedom, while also offering encouragement and criticism in appropriate doses. 1 am fortunate to have collaborated with the fine folks at DRAO in Penticton, B.C., and 1 would like to personally thank Dean Chalmers, Richard Hellyer and Peter Dewdney for their tireless dedication to the LAR project. 1 appreciate their efforts, often starting at 3:00 AM, to collect the ftight data 1 relied upon for my research. During my research it often felt like 1 was walking around with my head in the c1ouds, but 1 am grateful that 1 was not alone. 1 would like to acknowledge those who played with balloons alongside me inc1uding Alistair Howard, Philippe Coulombe-Pontbriand, Jonathan Miller, Francois Deschenes, Gabriel Meunier, Samuel Bouchard, Alexandre Boyer, Etienne Frenette, Dr. Hamid Taghirad, Dr. Wen Bo, Dr. Benoit Boulet and Dr. Clement Gosselin. Special thanks to Dr. Gabriele Gilardi who was always willing to help. 1 have only to look around my office to find several others who 1 would like to thank for their scholastic companionship. Thanks to Melita Hadzagic, Alessio Salerno, Shawn Arseneau, and Dany Dionne for inspiration, ideas, laughs and chocolate. 1 would like to thank my Mc Gill colleagues inc1uding Aki Sato, Aaron Saunders, Chad Abbey, Brian Wong, Philippe Cardou, James Smith, Jason Evans, Shivakumar Ran­ ganathan, Yuwen Li, Hiba Agha, and Lianzhen Luo.
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