ATTITUDE CONTROL ON SO(3) WITH PIECEWISE SINUSOIDS

This dissertation addresses rigid body attitude control with piecewise sinusoidal signals. We consider rigid-body attitude kinematics on SO(3) with a class of sinusoidal inputs. We present a new closed-form solution of the rotation matrix kinematics. The solution is analyzed and used to prove controllability. We then present kinematic-level orientation-feedback controllers for setpoint tracking and command following. Next, we extend the sinusoidal kinematic-level control to the dynamic level. As a representative dynamic system, we consider a CubeSat with vibrating momentum actuators that are driven by small $\epsilon$-amplitude piecewise sinusoidal internal torques. The CubeSat kinetics are derived using Newton-Euler\u27s equations of motion. We assume there is no external forcing and the system conserves zero angular momentum. A second-order approximation of the CubeSat rotational motion on SO(3) is derived and used to derive a setpoint tracking controller that yields order O(ε2) closed-loop error. Numerical simulations are presented to demonstrate the performance of the controls. We also examine the effect of the external damping on the CubeSat kinetics. In addition, we investigate the feasibility of the piecewise sinusoidal control techniques using an experimental CubeSat system. We present the design of the CubeSat mechanical system, the control system hardware, and the attitude control software. Then, we present and discuss the experiment results of yaw motion control. Furthermore, we experimentally validate the analysis of the external damping effect on the CubeSat kinetics

Gerilim kararlılığı iyileştiricilerinin akıllı algoritma tabanlı kayan kipli kontrolü

06.03.2018 tarihli ve 30352 sayılı Resmi Gazetede yayımlanan “Yükseköğretim Kanunu İle Bazı Kanun Ve Kanun Hükmünde Kararnamelerde Değişiklik Yapılması Hakkında Kanun” ile 18.06.2018 tarihli “Lisansüstü Tezlerin Elektronik Ortamda Toplanması, Düzenlenmesi ve Erişime Açılmasına İlişkin Yönerge” gereğince tam metin erişime açılmıştır.Gerilim kararlılığı iyileştiricileri, iletim hatlarındaki gerilim düşümlerinde gerilimi nominal değerlere taşımada yaygın olarak kullanılmaktadır. Bu nedenle gerilim kararlılığı iyileştiricilerin sisteme hızlı ve etkin müdahalesi için etkili kontrolü öne çıkmaktadır. Gerilim kararlılığı iyileştiricilerinin en önemlilerinden biri SVC dir. SVC nin kontrolü için, lineerleştirme, bulanık mantık, yapay sinir ağları gibi çeşitli tekniklerle kullanılmıştır. SVC’nin yapısında tristörler bulunmaktadır. Tristörlerin iletime geçirilerek SVC kontrol edilmektedir. Bu nedenle SVC nin anahtarlı kontrolü kaçınılmaz olarak önem arz etmektedir. Bu tez çalışmasında öncelikle non-lineer SVC sistem Taylor Serisi açılımı ile çeşitli noktalarda lineerleştirilerek durum uzay modeli elde edilmiş ve PID ile kapalı döngü denetimi gerçekleştirilmiştir. Daha sonra, referans bir nokta seçilerek, Acermann kutup yerleştirme yöntemi için geliştirilen algoritmayla test sisteminin on-line denetimi sağlanmıştır. On-line denetimin, algoritma hesaplamalarını daha hızlı yapabilmesi için YSA modelleme yapılarak, sistemin denetimi gerçekleştirilmiştir. öncelikle iki baralı test sisteminin SMC ile kontrolü için, sistemin SMC matematiksel modeli elde edilmiştir. Bu modelden yararlanarak, Matlab-Simulink ortamında SMC başarımları elde edilip gösterilmiştir. SMC başarımlarının daha iyi performans göstermesi için, SMC katsayıları GA algoritmasıyla elde edilmiştir. Bu katsayılardan yararlanarak GASMC başarımları elde edilerek, SMC ve PI kontrolörlerin başarımlarıyla karşılaştırılmıştır. Ayrıca N-Baralı sistemin GASMC matematiksel modeli elde edilerek, başarım simulasyon sonuçları verilmiştir.Voltage stability improver is commonly used to carry the voltage to nominal values in case of a voltage drop. For this reason, the effective control of the voltage stability improvers becomes prominent for a rapid and effective intervention in the system. SVC is one of the important voltage stability improvers. Various techniques such as linearisation, fuzzy logic, artificial neural networks are used to control the SVC. SVC has thyristors within its structure. SVC is controlled by taking the thyristors into transmission. Because of that, SVC control with switches bears an inevitable significance. In this thesis study, state space model is first obtained by linearising the non-linear SVC system by Taylor Series expansion in various points and closed loop control is carried out with PID. Later, by choosing a reference point, an on-line control is realised for the testing system with the algorithm developed for the Acermann pole arrangement method. The control of the system is realised by ANN modeling for the on-line control to perform the algorithmic calculations faster. First, an SMC mathematical model is achieved for the control of the 2-bus testing system with SMC. With the usage of this model, SMC achievements are shown in MatlabSimulink. SMC coefficients are obtained by the GA algorithm for the SMC achievements to perform more efficiently. GASMC achievements are obtained by using these coefficients and compared to the achievements of SMC and PI controllers. Also, the achievement simulation outcomes are given by getting the GASMC mathematical model of an N-bus system

Conception d'un mécanisme déployable à grand ratio d'expansion et de son système d'actionnement par roues d'inertie pour applications spatiales

Cette thèse propose de développer des mécanismes déployables pour applications spatiales ainsi que des modes d’actionnement permettant leur déploiement et le contrôle de l’orientation en orbite de l’engin spatial les supportant. L’objectif étant de permettre le déploiement de surfaces larges pour des panneaux solaires, coupoles de télécommunication ou sections de station spatiale, une géométrie plane simple en triangle est retenue afin de pouvoir être assemblée en différents types de surfaces. Les configurations à membrures rigides proposées dans la littérature pour le déploiement de solides symétriques sont optimisées et adaptées à l’expansion d’une géométrie ouverte, telle une coupole. L’optimisation permet d’atteindre un ratio d’expansion plan pour une seule unité de plus de 5, mais présente des instabilités lors de l’actionnement d’un prototype. Le principe de transmission du mouvement d’un étage à l’autre du mécanisme est revu afin de diminuer la sensibilité des performances du mécanisme à la géométrie de ses membrures internes. Le nouveau modèle, basé sur des courroies crantées, permet d’atteindre des ratios d’expansion plans supérieurs à 20 dans certaines configurations. L’effet des principaux facteurs géométriques de conception est étudié afin d’obtenir une relation simple d’optimisation du mécanisme plan pour adapter ce dernier à différents contextes d’applications. La géométrie identique des faces triangulaires de chaque surface déployée permet aussi l’empilement de ces faces pour augmenter la compacité du mécanisme. Une articulation spécialisée est conçue afin de permettre le dépliage des faces puis leur déploiement successivement. Le déploiement de grandes surfaces ne se fait pas sans influencer lourdement l’orientation et potentiellement la trajectoire de l’engin spatial, aussi, différentes stratégies de contrôle de l’orientation novatrices sont proposées. Afin de tirer profit d’une grande surface, l’actionnement par masses ponctuelles en périphérie du mécanisme est présentée, ses équations dynamiques sont dérivées et simulées pour en observer les performances. Celles-ci démontrent le potentiel de cette stratégie de réorientation, sans obstruction de l’espace central du satellite de base, mais les performances restent en deçà de l’effet d’une roue d’inertie de masse équivalente. Une stratégie d’actionnement redondant par roue d’inertie est alors présentée pour différents niveaux de complexité de mécanismes dont toutes les articulations sont passives, c’est-à-dire non actionnées. Un mécanisme à quatre barres plan est simulé en boucle fermée avec un contrôleur simple pour valider le contrôle d’un mécanisme ciseau commun. Ces résultats sont étendus à la dérivation des équations dynamiques d’un mécanisme sphérique à quatre barres, qui démontre le potentiel de l’actionnement par roue d’inertie pour le contrôle de la configuration et de l’orientation spatiale d’un tel mécanisme. Un prototype à deux corps ayant chacun une roue d’inertie et une seule articulation passive les reliant est réalisé et contrôlé grâce à un suivi par caméra des modules. Le banc d’essai est détaillé, ainsi que les défis que l’élimination des forces externes ont représenté dans sa conception. Les résultats montrent que le système est contrôlable en orientation et en configuration. La thèse se termine par une étude de cas pour l’application des principaux systèmes développés dans cette recherche. La collecte de débris orbitaux de petite et moyenne taille est présentée comme un problème n’ayant pas encore eu de solution adéquate et posant un réel danger aux missions spatiales à venir. L’unité déployable triangulaire entraînée par courroies est dupliquée de manière à former une coupole de plusieurs centaines de mètres de diamètre et est proposée comme solution pour capturer et ralentir ces catégories de débris. Les paramètres d’une mission à cette fin sont détaillés, ainsi que le potentiel de réorientation que les roues d’inertie permettent en plus du contrôle de son déploiement. Près de 2000 débris pourraient être retirés en moins d’un an en orbite basse à 819 km d’altitude.This thesis presents the design of deployable mechanisms for space applications and means of actuation for the control of their deployment and the attitude control of their satellite base. For this purpose, the triangular geometry is selected as a planar deployable basic unit to tessellate any surface. Each such module needs to achieve a high expansion ratio. From the literature, planar mechanisms based only on rigid links and developed for deployable Platonic solids are optimized and adapted for open geometries such as a cupola. The resulting expansion ratio is above 5, but the corresponding prototype shows instability of the deployment movement close to the retracted position. The paradigm of power transmission is revised to reduce the sensitivity of the mechanism to its internal transmission angles. The novel solution, based on timing belts, can achieve expansion ratios above 20 in particular configurations. The influence of the principal geometric parameters of design on the expansion ratio is discussed to allow the derivation of a simple optimization relation. The optimization can be performed to adapt this mechanism to different contexts of application. In order to further improve the compactness of the mechanism for transport purposes, a novel joint is presented, allowing two successive phases of rotation on non parallel axes. This way the triangular units can be piled before being deployed. The deployment of a large surface in orbit is prone to impact the spacecraft attitude and maybe its course. Hence, control strategies are proposed to manage these effects. Since the deployment targets a large surface, its edges are far from the centre of mass and are advantageous to induce torque from the linear motion of point masses. The dynamic equations are derived based on the conservation of the angular momentum and the resulting matrix form of the equation set is used to simulate the system and assess its performances. The results validate the strategy for orientation control without obstruction of the spacecraft central space, but a flywheel of equivalent mass still outperforms this design. Redundant actuation by flywheel on each link of a multibody mechanism composed only of passive revolute joints is presented. The dynamic equations are derived for a two-body architecture and a four-bar planar mechanism. The closed-loop control of the four-bar mechanism is using a PD controller to achieve the control of a scissor mechanism unit. The results are then extended to a four-bar spherical mechanism and its simulation demonstrates the potential of this strategy for the control of both the configuration and the orientation of a spatial mechanism. A two-body prototype, linked by a passive revolute joint, is manufactured and controlled with visual tracking feedback. The results confirm that the system is controllable in orientation and configuration. This thesis ends with a case study for the application of the main components developed in this research. The capture of small to medium sized orbital debris is introduced. The triangular deployable unit based on timing belts is replicated in order to create a cupola of hundreds of metres to catch and slow down the debris. The parameters of such a mission are detailed as well as the flywheel potential to control the spacecraft attitude on top of the mechanism deployment. It is estimated that almost 2000 pieces of debris can be removed from the orbit at 819 km altitude in a one year mission