Dissertations / Theses on the topic 'Tethered satellites'

Thesis (Ph.D.)--School of Mechanical Engineering, Georgia Institute of Technology, 2005.
Singhose, William, Committee Chair ; Banerjee, Arun, Committee Member ; Chen, Ye-Hwa, Committee Member ; Ebert-Uphoff, Imme, Committee Member ; Olds, John, Committee Member. Includes bibliographical references.

Command generation is a process by which input commands are constructed or modified such that the system's response adheres to a set of desired performance specifications. Previously, a variety of command generation techniques such as input shaping have been used to reduce residual vibration, limit transient deflection, conserve fuel or adhere to numerous other performance specifications or performance measures. This dissertation addresses key issues regarding the application of command generation techniques to tethered satellite systems. The three primary objectives of this research are as follows: 1) create analytically commands that will limit the deflection of flexible systems 2) combine command generation and feedback control to reduce the retrieval time of tethered satellites, and 3) develop command generation techniques for spinning tether systems. More specifically, the proposed research addresses six specific aspects of command generation for tethered satellites systems: 1) create command shapers that can limit the trajectory tracking for a mass under PD control to a pre-specified limit in real time 2) create commands analytically that can limit the transient deflection of a model with one rigid-body and one flexible mode during rest-to-rest maneuvers 3) command generation for a 2-D model of earth-pointing tethered satellites without tether flexibility, 4) command generation for a 2-D model of earth-pointing tethered satellites to reduce tether retrieval time and reduce swing angle, 5) command generation for a 3-D model of earth-pointing tethered satellites without tether flexibility, and 6) command generation for improved spin-up of spinning tethered satellite systems. The proposed research is anticipated to advance the state-of-the-art in the field of command generation for tethered satellite systems and will potentially yield improvements in a number of practical satellite and tether applications.

The space elevator has been proposed as an alternate method for launching cargo into space. However, the construction of such a structure requires a material much stronger than any currently in existence. Instead, a partial elevator is considered for satellite placement. In the first part of the thesis, the fundamentals of very long tethered systems are studied. From static analysis on a simple two-body system, it is demonstrated that an assumption made in the conventional analysis does not apply to very long tethered systems. For a uniform tether, the axial stress distribution is obtained. Following the Lagrangian approach, the equations of motion governing the planar librations of a multi-body tethered system are derived. From a linearization of these equations, the libration frequencies are found. Then, by solving the nonlinear equations numerically, the responses to various changes in the system parameters are determined. In the second part of the thesis, the use of a partial elevator in satellite placement is studied. In the case of single climber transit, residual librations occur, which alter the shape and size of the orbit of a satellite launched from the climber. An approach using two climbers is investigated in order to decrease the residual libration and thereby reduce orbit placement errors. Also, some energy calculations are done to determine whether the partial elevator offers significant advantages.

Thesis (MScEng)--Stellenbosch University, 2013.
ENGLISH ABSTRACT: The use of electrodynamic tethers on-board satellites is an exciting scientific prospect. These conductive tethers provide the means for satellites to generate power and to do propulsion by electrodynamic interaction with the geomagnetic field. Although well researched in theory, the concept has not enjoyed much success in practice. This study aims to utilise low-cost CubeSats as experimental tool to verify many of the theoretical principles that govern the behaviour of conductive tethers in orbit. The study provides a theoretical background of the concept by evaluating past tether missions and analysing existing theory. A feasible application of an electrodynamic tether within the size and weight limitations of a Nano-satellite is formulated. Existing theoretical work is adapted to model the dynamics and electrodynamics of specifically Nano-satellites. Using these mathematical models, control and estimation algorithms are designed which would provide stable deployment of a tethered CubeSat pair and stable control of the orientation of the tethered system. To be able to implement these algorithms on a satellite mission, a prototype of a sensor capable of measuring the angle of the tether using a CMOS camera is designed and built. A hardware platform is built to test the deployment of the tether using an electric motor. Electronics are designed to control the operation of the camera, to do motor control, and to run control and estimation algorithms. Using the results obtained from the practical tests done on the hardware, and using the theoretical models and control algorithms designed, a full orbital simulation of the deployment was done. This simulation includes the performance of the deployment system, the electrodynamic performance of the tether in earth‟s plasmasphere, and the estimation and control algorithms to control the system. Different deployment strategies are analysed and their performance are compared.
AFRIKAANSE OPSOMMING: Die gebruik van elektrodinamiese toue aanboord satelliete is 'n opwindende wetenskaplike vooruitsig. Hierdie geleidende toue verleen aan die satelliete die vermoë om krag op te kan wek en propulsie deur elektriese interaksie met die geomagnetiese veld te kan doen. Alhoewel dit goed nagevors is in teorie, het die konsep nog nie veel sukses in die praktyk geniet nie. Hierdie studie het dit ten doel om lae-koste CubeSats aan te wend as 'n eksperimentele instrument om baie van die teoretiese beginsels wat geld vir die gedrag van geleidende toue in wentelbane te verifieer. Die studie bied 'n teoretiese agtergrond van die konsep deur die evaluering van vorige tou-missies sowel as die analise van bestaande teorie. 'n Uitvoerbare toepassing van 'n elektrodinamiese tou binne die grootte- en gewigsbeperkinge van 'n Nano-satelliet is geformuleer. Bestaande teoretiese werk is aangepas om die dinamika en elektrodinamika spesifiek van toepassing op Nano-satelliete, te modelleer. Deur hierdie wiskundige modelle te gebruik, is beheer- en afskattingsalgoritmes ontwerp wat stabiele ontplooiing van 'n verbinde CubeSat-paar en stabiele beheer van die oriëntasie van die verbinde stelsel sal verseker. Om hierdie algoritmes te implementeer op 'n satelliet-sending, is 'n prototipe van 'n sensor wat in staat is om die hoek van die tou met behulp van 'n CMOS kamera te meet, ontwerp en gebou. 'n Hardeware platform is gebou om die ontplooiing van die tou met behulp van 'n elektriese motor te toets. Elektronika is ontwerp om die kamera te beheer, motor beheer te doen asook om beheer- en afskattingsalgoritmes uit te voer. Deur gebruik te maak van die resultate wat verkry is tydens die praktiese toetse wat gedoen is op die hardeware, en deur gebruik te maak van die teoretiese modelle en beheeralgoritmes wat ontwerp is, is 'n volle wentelbaan-simulasie van die ontplooiing gedoen. Hierdie simulasie sluit die gedrag van die ontplooiingstelsel, die elektriese gedrag van die geleidende tou in die aarde se plasmasfeer, en die afskatting- en beheeralgoritmes om die stelsel te beheer in. Verskillende ontplooiingstrategieë word ontleed en hul gedrag word vergelyk.

The increase of orbital debris and the consequent proliferation of smaller objects through fragmentation is driving the need for mitigation strategies that address this issue at its roots. The present guidelines for mitigation point out the need to deorbit new satellites injected into low Earth orbit (LEO) within a 25-year time. The issue is then how to deorbit the satellite with an efficient system that does not impair drastically the propellant budget of the satellite and, consequently, reduces its operating life. In this contest a passive system, which makes use of an electrodynamics tether to deorbit a satellite through Lorentz forces, has been investigated. The system collects electrons from the ionosphere at its anodic end (the conductive tether itself left bare) and emits electrons through a plasma contactor at the cathodic end. The current that circulates in the tether produces the Lorentz drag force through the interaction with the Earth’s magnetic field. Power can also be tapped from the tether for running the cathode and other ancillary on-board equipment. The deorbiting system will be carried by the satellite itself at launch and it will be deployed from the satellite at the end of its life. From that moment onward the system operates passively without requiring any intervention from the satellite itself. This thesis summarizes the results of the analysis carried out to show the deorbiting performance of the system starting from different orbital scenarios and for satellite configurations, and describing the tethered system by means of different mathematical models in order to include the lateral flexibility and increase the accuracy of the results, which can be easily scaled. Moreover high-fidelity and latest environmental routines has been used for magnetic field, ionospheric density, atmospheric density and a 4×4 gravity field model, since the environment is very important for describing appropriately each external interaction, in particular the electrodynamic one. The electric properties of the wire depends on its temperature, which is computed dynamically by a thermal model that considers all the major input fluxes and the heat emitted by the tether itself. At last the electric current along the rope is constantly evaluated during the reentry, since large variations happens passing from sunlight to shadow regions, and vice-versa. Without any control the system goes rapidly into instability, because the electrodynamic torque pumps continuously energy into the system enlarging the libration of the tether. So ad hoc strategies must be thought and included. In the past several techniques have been proposed, but with a lot of assumptions and limitations. In this work a new concept has been implemented, mounting in the satellite at the basis of the tether a damping mechanism for dissipating the energy associated with the lateral motion. At last the whole deployment of a tape tether has been analyzed. Several configurations have been studied, and the tradeoff analysis concluded that a non-motorized reeling deployer is well suited for a 1-3 cm wide tape like the tapes. Optimal reference profiles have been evaluated for two class of tether (3 and 5km), and are then used to regulate the brake mechanism mounted on the deployer itself to control the deployment. Different conditions have been analyzed to demonstrate the capabilities of the control law to provide a successful deployment in the presence of various errors
L'aumento dei detriti spaziali e la conseguente proliferazione dovuta alla frammentazione di piccoli oggetti, sta portando alla necessità di prevedere strategie di mitigazione. Le presenti linee guida per la mitigazione puntano alla necessità di far rientrare i nuovi satelliti in orbita terrestre bassa (LEO) in un lasso di tempo di 25 anni. Il problema è, dunque, come deorbitare il satellite con un sistema efficiente che non alteri drasticamente il budget di propellente del satellite e, di conseguenza, riduce la sua vita operativa. In questo contesto è stato studiato un sistema passivo, che utilizza fili elettrodinamici per deorbitare un satellite attraverso le forze di Lorentz. Il sistema raccoglie elettroni dalla ionosfera nell'estremità anodica e li riemette attraverso il catodo. La corrente che circola nel filo genera la forza elettrodinamica attraverso l'interazione con il campo magnetico terrestre. La potenza sviluppata può anche essere sfruttata per l'alimentazione del catodo e altri accessori di bordo. Il sistema per il deorbiting sarà montato nel satellite al lancio e verrà deploiato solo alla fine della sua vita operativa. Da quel momento in poi il sistema opererà passivamente senza richiedere alcun intervento da parte del satellite stesso. Questa tesi riassume i risultati delle analisi effettuate per mostrare le prestazioni del sistema a filo spaziando diversi scenari orbitali e configurazioni di satellite. Il sistema a filo è studiato mediante diversi modelli matematici per includere la flessibilità laterale e aumentare la precisione dei risultati, che possono essere facilmente scalati. Inoltre le più recenti routine ambientali sono stato adottate per il campo magnetico, la densità ionosferica e quella atmosferica, mentre un modello 4×4 è stato usato per il campo gravitazionale, in quanto l'ambiente è molto importante per descrivere adeguatamente ciascuna interazione esterna, in particolare quella elettrodinamica. Le proprietà elettriche del filo dipendono dalla sua temperatura, che è calcolato dinamicamente da un modello termico che considera tutti i principali flussi in ingresso e il calore emesso dalla stesso filo. Infine la corrente elettrica lungo il tether deve essere costantemente valutata durante la manovra di rientro, in quanto si possono notare grandi variazioni passando dalle zone illuminate dal sole a quelle in ombra, e vice-versa. Senza controllo il filo va rapidamente in instabilità, poiché la coppia elettrodinamica pompa continuamente energia nel sistema eccitando sempre più la librazione. Così strategie ad hoc devono essere pensate e studiate. In passato diverse tecniche sono state proposte, ma includendo molte ipotesi e limitazioni. In questo lavoro un nuovo concetto è stato implementato: un meccanismo di smorzamento per dissipare l'energia associata al movimento laterale è montato nel satellite alla base del tether. Infine il deployment di un tether a forma di nastro è stato analizzato. Diverse configurazioni sono state considerate, e l'analisi effettuata ha concluso che un deployment non motorizzato è adatto per un nastro largo 1-3 cm. Profili ottimali di riferimento sono stati valutati per due classe di tether (3 e 5 km), e sono stati quindi utilizzati per regolare il meccanismo di frenatura montato sul deployer, per controllare il dispiegamento. Condizioni differenti sono stati analizzate per dimostrare le capacità della legge di controllo nel fornire un dispiegamento corretto anche in presenza di errori diversi

Due to the unsustainable space debris environment in Low Earth Orbit, debris objects must be removed to ensure future safe satellite operations. One proposed concept for deorbiting larger space debris objects, such as decommissioned satellites or spent upper rocket stages, is to use a chaser spacecraft connected to the debris object by an elastic tether, but the required technology is immature and there is a lack of flight experience. The inoperable satellite, Envisat, has been chosen as a representative object for controlled re-entry by performing several high thrust burns. The aim of this paper is to develop a control system for the deorbit phase of such a mission. Models of the spacecraft dynamics, the tether, and sensors are developed to create a simulator. Two different tether models are considered: the massless model and the lumped mass model. A switched linear-quadratic-Gaussian (LQG) controller is designed to control the relative position of the debris object, and a switched proportional-integral-derivative (PID) controller is designed for attitude control. Feedforward compensation is used to counteract the couplings between relative position and attitude dynamics. An analysis of the system suggests that the tether should be designed in regard to the control system and it is found that the lumped mass model comes with higher cost than reward compared to the massless tether model in this case. Simulations show that the control system is able to control the system under the influence of modeling errors during a multi-burn deorbit strategy and even though more extensive models are suggested to enable assessment of the feasibility to perform this mission in reality, this study has resulted in extensive knowledge and valuable progress in the technical development.
En ökande mängd rymdskrot har lett till en ohållbar miljö i låga omloppsbanor och föremål måste nu tas bort för att säkerställa framtida satellitverksamhet. En föreslagen metod för att avlägsna större skrotföremål, såsom avvecklade satelliter och använda övre raketsteg, är att koppla en jagande rymdfarkost till föremålet med en elastisk lina. Dock är den teknik som behövs inte mogen och det finns en brist på praktisk erfarenhet. Den obrukbara satelliten Envisat har valts som representativt objekt för kontrollerat återinträde genom flera perigeumsänkande raketmanövrar. Syftet med detta arbete är att utveckla ett system för att kontrollera de två sammankopplade rymdfarkosterna under avlägsningsfasen under ett sådant uppdrag. Modeller för farkosternas dynamik, den sammankopplande linan och sensorer byggs för att utveckla en simulator. Två olika modeller för linan undersöks: den masslösa modellen och den klumpade nodmassmodellen. En omkopplande regulator designas genom minimering av kvadratiska kriterier för att kontrollera skrotföremålets relativa position till den jagande farkosten. Vidare designas en omkopplande proportionerlig-integrerande-deriverande (PID) regulator för att reglera pekningen hos den jagande farkosten. Kompensering genom framkoppling används för att motverka de korskopplingar som förekommer mellan translations- och rotationsdynamiken. En analys av systemet visar att linan bör designas med reglersystemet i åtanke och det framkommer att nackdelarna överväger fördelarna för den klumpade nodmassmodellen jämfört med den masslösa modellen. Simuleringar visar att reglersystemet klarar att kontrollera systemet under ett scenario med flera manövrar och under inverkan av modellfel. Även om mer omfattande modeller föreslås för att möjliggöra en fullständig bedömning av genomförbarheten för detta uppdrag så har denna studie resulterat i en omfattande kunskapsvinst och värdefulla framgångar i det tekniska utvecklingsarbetet.

Tethers have been used in space for quite some time. However, the concept of a multi-tethered system has received less attention. This thesis investigates the dynamics of certain configurations of multi-tethered satellite formations in Low Earth Orbits.
Certain simplifications have been made prior to the investigation of the problem; these include considering the satellites to be point-masses and the tethers to be massless and straight. Configurations termed hub-and-spoke and closed-hub-and-spoke are analyzed. The local motion is studied under two distinct specifications for the orbital motion of the system: first, prescribed motion of the system centre of mass and second, prescribed motion of the central body of the formation. Three-dimensional motion is studied for formations lying in the orbital plane and in the Earth-facing plane normal to the orbit, while given an initial spin rate in their nominal plane.
Later, two satellite formations deployed along the local vertical are examined: a closed-hub-and-spoke configuration with its spin axis along the long axis of symmetry, which is found to be unstable, and a double-pyramid configuration, which is found to be stable.

The equations of motion of a tethered satellite system are highly nonlinear and should possess many interesting related features; yet its nonlinear dynamics has never been thoroughly investigated in previous works. This thesis analyzes the nonlinear dynamics of two-body tethered satellite systems using numerical tools of analysis such as phase plane plots, power spectral densities (PSD's), Poincare sections and first Lyapunov exponents, as well as approximate analytical methods including the method of Melnikov. Motion in the stationkeeping phase wherein the tethered system is just a gravity gradient pendulum is studied, first considering pitch motion only, and then considering the coupled pitch and roll motions. The deployment/retrieval phases are studied next. For a circular orbit, pitch stability is examined for varying exponential length rates; for the unstable cases, it is compared to an equivalent uniform length rate scheme, which showed better stability behaviour. (Abstract shortened by UMI.)

Tethered satellite systems (TSS) can be utilized for a wide range of space-based applications, such as satellite formation control and propellantless orbital maneuvering by means of momentum transfer and electrodynamic thrusting. A TSS is a complicated physical system operating in a continuously varying physical environment, so most research on TSS dynamics and control makes use of simplified system models to make predictions about the behavior of the system. In spite of this fact, little effort is ever made to validate the predictions made by these simplified models. In an ideal situation, experimental data would be used to validate the predictions made by simplified TSS models. Unfortunately, adequate experimental data on TSS dynamics and control is not readily available at this time, so some other means of validation must be employed. In this work, we present a validation procedure based on the creation of a top-level computational model, the predictions of which are used in place of experimental data. The validity of all predictions made by lower-level computational models is assessed by comparing them to predictions made by the top-level computational model. In addition to the proposed validation procedure, a top-level TSS computational model is developed and rigorously verified. A lower-level TSS model is used to study the dynamics of the tether in a spinning TSS. Floquet theory is used to show that the lower-level model predicts that the pendular motion and transverse elastic vibrations of the tether are unstable for certain in-plane spin rates and system mass properties. Approximate solutions for the out-of-plane pendular motion are also derived for the case of high in-plane spin rates. The lower-level system model is also used to derive control laws for the pendular motion of the tether. Several different nonlinear control design techniques are used to derive the control laws, including methods that can account for the effects of dynamics not accounted for by the lower-level model. All of the results obtained using the lower-level system model are compared to predictions made by the top-level computational model to assess their validity and applicability to an actual TSS.
Ph. D.

In this thesis, dynamics and control of multi-body tethered satellite systems are investigated. First a dynamical model is developed that takes into account the three dimensional librational motion of the system as well as the nonlinear vibrations of the tethers, both in longitudinal and transverse directions. The assumed modes method is used to discretize the continuous tethers. Using Lagrange's equations, splitting the vector of generalized coordinates to a set of subvectors, where each subvector corresponds to a specific tether, a set of nonlinear ordinary differential equations governing the motion of the system is obtained in the explicit analytical form. A fourth order strain energy expression is used in the formulation to allow the possibility of moderately large deformation of the tethers. The equations are applicable whether the length of the tethers are constant (station-keeping phase) or changing with time (deployment and retrieval phases). They are transformed into vector form for simulation purposes.
Among the external forces, the aerodynamic forces and their effects on the dynamics and stability of the system are given more attention. The free molecular flow model is used to calculate the aerodynamic forces resulting from the material damping of the tethers are considered in this investigation. These forces, which are very difficult to model accurately, are modelled using a viscous damping model.
Equilibrium configurations of the system, as special solutions of the equations of motion, in the absence or presence of the aerodynamic forces, are studied in more detail. A closed form solution to the static equilibrium equations is obtained when there is no external force acting on the system other than the gravitational force. The set of nonlinear equations of motion is then linearized analytically about a particular equilibrium configuration for stability and eigenvalue analysis. The natural frequencies of some single-tether as well as multi-tether systems are calculated using these linearized equations.
Stability of a single-tether system in low orbit missions is investigated, ignoring the aerodynamic forces on the main-satellite as well as on the tether. Assuming a particular geometrical configuration for the subsatellite and using the linearized equations, the effect of the aerodynamic forces, particularly aerodynamic lift, on the stability of the system as well as the equilibrium configuration of the system is examined through the eigenvalue analysis. This analysis is then extended to multi-body systems.
Finally the problem of controlling the nonlinear system through the application of Lyapunov's stability theory is examined for multi-body tethered systems, ignoring the transverse oscillations of the tethers. Initially, based on the Hamiltonian of the system, a Lyapunov function is introduced for a system with massless and rigid tethers. It leads to a linear tension control law. When the mass of the tethers is taken into account the Lyapunov function is modified and a new tension control law is developed which is no longer linear. With the assumption that the longitudinal oscillations of the tethers are small compared to the length of the tethers, a Lyapunov functions is constructed for systems with elastic tethers. At the end, a hybrid control law is examined to improve the performance of the controlled system.

This thesis is focused on the study of dynamics and control of a multi-tethered satellite formation, where a multi-tethered formation is made up with several satellites (agents) connected by means of cables (tethers). The goal of the first part of the study is to evaluate the effect of tether mass on multi-tethered clusters. Due to the complexity of the formations analyzed, the stability of the formation is assessed through a numerical simulation. The behavior is evaluated in the ideal case of circular orbits, but also in non-ideal cases such as that of elliptical reference orbit or perturbed motion. For circular reference orbits, the dynamics of tethered satellite formation is studied, showing that tether mass affects formation dynamics for closed configurations featuring external tethers. This leads to significant instability effects affecting the position of deputies with respect to the parent body neglected by a more elementary modeling approach. When combined effect of orbit eccentricity and tether mass on tethered formations is analyzed, the most noticeable effect due to eccentricity is the increase in the variation of the local spin rate of the cluster between perigee and apogee passes of the reference elliptical orbit. This effect has consequences over the elongation of tethers, shape of tether oscillations and angular separation between adjacent tethers especially for open formations. When taking into account the J2 effect on massive tethered satellite formations, in the Earth¿facing scenario, the trajectory of the parent body presents oscillations of increasing amplitude in the direction perpendicular to the orbital plane. The second part of the study is focused on deriving a control law for position and attitude control of an Earth-facing double pyramid multi-tethered cluster. The control problem is decomposed in two levels: A first level to perform position and attitude coarse control of the formation as a whole, and a second level to achieve accurate position and control of each agent of the cluster. For the purpose of attitude control, and taking advantage again of the similarities between a tethered cluster and a rigid body, the virtual structure approach is chosen as the most suitable option. The formulation shown in this thesis augments the general virtual structure equations valid for a static formation by adding the kinematics of a spinning formation, since the original formulation is valid only to achieve a static final state. The controller is designed to modify the spin rate and the moment of inertia of the formation through a reeling mechanism, and therefore to be able to control the Likins-Pringle tilting angle of the cluster. For the derivation of the accurate positioning control law, the study initially discusses different alternatives based on the state of the art of the robotics control literature. After evaluating other alternatives, two control laws are chosen for this application: One based on a PID controller and one based on the sliding mode control technique. For the sliding mode based control, a proof of semi-global exponential stability is provided. Results of a representative simulation assess the viability of the control approach proposed leading to a submillimetric positioning accuracy.
La tesi es centra en l'estudi de la dinàmica i control de formacions de satèl·lits connectats per tethers. Aquestes formacions estan compostes per diversos satèl·lits (agents) connectats per cables (tethers). L'objectiu de la primera part de l'estudi, és l'avaluació de l'efecte de la massa a clústers connectats per múltiples tethers. Degut a la complexitat de les formacions analitzades, l'estabilitat de la formació s'analitza a través de simulacions. S'estudia el comportament pel cas ideal d'orbites circulars, així com en casos no ideals tals com orbites de referència el·liptiques, o moviment sota l'efecte de pertorbacions. La tesi analitza la dinàmica de les formacions per òrbites circulars, mostrant que l'efecte de la massa dels tethers afecta la dinàmica de formacions de geometria tancada (on el perímetre extern esta definit per tethers) amb un satèl·lit central. Aquest efecte dóna lloc a una clara inestabilitat que afecta la posició dels agents respecte a l'objecte central. Aquest efecte no és apreciable en models simplificats on s'ignora l'efecte de la massa al model. Quan es combina una òrbita de referència el·liptica amb un model que incorpora la massa dels tethers, l'efecte més notori és la variació de la velocitat de rotació local del clúster entre el pas per l'apogeu i perigeu de l'òrbita de referència. Aquest efecte té conseqüències sobre l'elongació dels tethers, la forma de les oscil·lacions, i la separació entre tethers adjacents (especialment en el cas de formacions obertes). Quan es té en compte l'efecte de la pertorbació J2, en el cas de formacions orientades envers la Terra, la trajectòria de l'objecte central presenta oscil·lacions d'amplitud creixent en la direcció perpendicular al pla orbital. La segona part de l'estudi es centra en la definició d'una llei de control per regular la posició i orientació d'un clúster amb geometria de doble piràmide orientat envers la Terra. El problema de control es descompon en dos nivells. Un primer nivell per un control primari de posició i orientació del cluster, i un segon nivell per un control de posició precís per a cada agent del cluster. Per tal d'aconseguir el primer nivell de control, i aprofitant les similituds entre un cluster connectat per tethers i un sòlid rígid, s'utilitza la tècnica d'estructura virtual. La formulació utilitzada en aquest estudi amplia el model general d'estructura virtual utilitzat per formacions estàtiques, tot afegint les equacions necessàries per a una formació que gira sobre un eix propi. El controlador esta dissenyat per permetre el canvi de la velocitat de gir i el moment d'inèrcia de la formació a través d'un sistema que permet modificar la longitud dels tethers. D'aquesta forma es permet controlar l'angle d'inclinació de Likins-Pringle del clúster. Per a la definició del control de precisió, l'estudi avalua inicialment diferents alternatives basades en l'estat de l'art de sistemes de control aplicats a robòtica. Després de descartar altres alternatives, es proposen dues lleis de control : Una primera basada en un controlador PID, i una basada en control lliscant. Per l'opció de control lliscant es presenta una demostració d'estabilitat exponencial semiglobal. Els resultats de simulacions confirmen la viabilitat de la solució de control que permet posicionament amb precisió submil·limetrica

In this thesis, an analytical investigation of the dynamics of three-body tethered satellite systems is presented. The analysis is performed for two cases: two-dimensional and three-dimensional motion. At first, the equations governing the motion of such systems are obtained assuming that the system center of mass moves in a circular orbit around the Earth. Then, the various equilibrium configurations are obtained. The equilibrium configurations are classified in eleven groups. Three of these groups are collinear configurations, and the others are triangular configurations. A stability analysis is performed for each equilibrium configuration. It is found that two of the collinear configurations are marginally stable. These are configurations with the three masses on the local vertical. The other collinear configurations are unstable. The triangular configurations are unstable except for some systems with a small middle mass. The results for two-dimensional motion are consistent with those for three-dimensional motion.

A relatively general mathematical model is proposed for studying the coupled attitude dynamics of space platform supported tethered subsatellite systems accounting for offset of the tether attachment point. The offset is treated as a function of time subject to constraints. General energy expressions allowing for flexibility of the tether as well as the platform are derived. The governing equations account for: (i) three-dimensional librational motion of the platform; (ii) inplane and out-of-plane libration of the tether of finite mass and connected to the platform with an offset; (iii) time dependent variations on the attachment point of the tether; (iv) generalized force contributions due to various active controllers; (v) orbits of arbitrary eccentricities; (vi) deployment and retrieval of the tether from the space platform. The second order coupled, nonlinear, nonautonomous, differential equations are linearized about a quasi-static equilibrium position. After nondimensionalizing with respect to the orbital rate and characteristic dimensions of the structure, they are collated into matrix form and integrated numerically. An extensive response analysis is carried out over a range of system parameters, operational maneuvers and orbit eccentricity to assess complex interactions involved and help evolve suitable control strategies. Two control schemes, tether tension modulation and thruster control, are extended to the case of an offset of the tether attachment point. It is shown that a linear control strategy is sufficient to control the tether inplane as well as out-of-plane librations in the presence of an out-of-plane offset. A new approach to control of platform based tethered satellite systems is proposed that utilizes motion of the offset to control the coupled system dynamics. The scheme involves specification of offset accelerations based on feedback of system states and feedforward of offset states. Controllability of the linearized equation is established numerically and relative merits of the three control strategies assessed. Results indicate that the controllers are effective even in the presence of severe disturbances during all three mission phases of deployment, stationkeeping and retrieval. During stationkeeping, the tension control procedure demands larger energy for shorter tethers. Damping characteristics of the thruster control are indeed superior but at the expense of the energy. The offset control has a tendency to dynamically isolate the tethered subsatellite from the space platform. From energy consideration, it proved to be the best, particularly at shorter tether lengths. However, due to offset constraint in a practical situation, its effectiveness diminishes with an increase in the tether length and becomes virtually ineffective for a tether length over 1 km. During retrieval, hybrid control strategies utilizing tension or thruster control at the onset of retrieval, with offset control at shorter tether lengths proved to be quite energy efficient. For space application, the thruster-offset hybrid control strategy appears to be quite promising both in terms of system dynamics and energy demand.
Applied Science, Faculty of
Mechanical Engineering, Department of
Graduate

The first analytical method that is used for the development of reel rate laws is the Liapunov's second method. In this work it is shown that the Hamiltonian can be used as a Liapunov function. A reel rate law is devised that stabilizes the in-plane and out-of-plane librations at the same time, for two-body systems. However, since the resulting motion has some deficiencies, this reel rate law is not extended to multi-body systems.
For overcoming these deficiencies, two new reel rate laws are proposed and their performances are examined through the energy dissipation approach together with the averaging method. The resulting motions with all the reel rate laws, including the one from Liapunov approach, are limit cycle oscillations. The reel rate laws obtained from the energy dissipation approach perform efficient retrievals with sufficiently small out-of-plane limit cycle amplitudes. These reel rate laws are extended to multi-body systems. For multi-body systems a station-keeping stage is added that brings the system to a final desired configuration. An analysis on the effects of different parameters and gains on the resulting motion has also been performed. (Abstract shortened by UMI.)

This paper examines the dynamics of a tether connected multi-spacecraft system, arranged in a wheel-spoke configuration, in the vicinity of the L 2 Lagrangian point of the Sun-Earth system. First, the equations of motion of a N-body system are obtained and equilibrium configurations of the system are determined and small motions about one of these configurations are analyzed. Then, a numerical analysis of the free tether libration is carried out for a three-mass case when the system is near L2 and the parent mass is assumed to be in a halo orbit of different sizes. Finally, a set of control goals are defined and a time domain state feedback control system is integrated into the numerical model. The performance of the control system is tested under different conditions.

Orbital debris poses a serious threat to ongoing operations in space.  Recognising this threat, the European Commission has funded the three-year Technology for Self Removal (TeSeR) project with the goal of developing a standard scalable Post Mission Disposal (PMD) module to remove satellites from orbit following the completion of their mission.  As the project coordinator and key member of the TeSeR Project, Airbus Defence and Space Germany will invest significant resources in achieving this goal over the course of the project. This thesis details the initial analysis of potential PMD module designs conducted by the author during an internship within the AOCS/GNC department of Airbus Defence and Space Friedrichshafen between 1 April 2016 and 31 August 2016.  Three main concepts, drag sails, drag balloons and Electrodynamic Tethers (EDTs), were evaluated during this time with an emphasis on determining the ability of each design to permit passive attitude stabilisation of the satellite during PMD.  Following the required modification of a pre-existing MATLAB/Simulink model, several key findings were made for each device concept.  It was found that no drag sail designs investigated permitted passive aerodynamic attitude stabilisation at orbit heights above 550 km.  When deorbiting from 800 km, however, the lack of the desired and stable attitude was not found to have a significant increase on the deorbit time or the area‑time product. Drag balloon designs were predicted to be comparatively unstable and less mass efficient for deorbiting purposes, with area‑time products up to approximately 50 per cent higher than the equivalent mass drag sail designs.  In spite of this, unstable drag balloons were found to provide shorter deorbit times than stable balloons due to the contribution of the satellite body and solar array to the total frontal area of the satellite.  This indicated that attitude stabilisation is not required for satellites equipped with drag balloon devices. Modelling of bare EDTs suggested that tethers with lengths of 1000 metres or more would not permit passive attitude stabilisation at an orbit height of 800 km.  Simulation of a 500 metre EDT, however, indicated that passive attitude stabilisation can be achieved with EDT devices and proved that EDTs can generate significantly higher drag forces than aerodynamic devices while possessing a significantly lower device mass.  Following the analysis of these results, a recommendation was made for future work to be aimed at improving the EDT model used in this investigation.

A mathematical model is developed for studying the inplane dynamics and control of tethered two-body systems in a Keplerian orbit. The formulation accounts for: • elastic deformation of the tether in both the longitudinal and inplane trans- verse directions; • inplane libration of the flexible tether as well as the rigid platform; • time dependent variation of the tether attachment point at the platform end; • deployment and retrieval of the point mass subsatellite; • generalized force contributions due to various control actuators (e.g. momentum gyros, thrusters and passive dampers); • structural damping of the tether; • shift in the center of mass of the system due to the tether deployment and retrieval. The governing nonlinear, nonautonomous and coupled equations of motion are obtained using the Lagrange procedure. They are integrated numerically to assess the system response as affected by the design parameters and operational disturbances. Attitude dynamics of the system is regulated by two different types of actuators, thruster and tether attachment point offset, which have advantages at longer and shorter tether lengths, respectively. The attitude controller is designed using the Feedback Linearization Technique (FLT). It has advantages over other control methods, such as gain scheduling and adaptive control, for the class of time varying systems under consideration. It is shown that an FLT controller based on the rigid system model, can successfully regulate attitude dynamics of the original flexible system. A hybrid scheme, using the thruster control at longer tether lengths and the offset control for a shorter tether, is quite attractive, particularly during retrieval, as its practical implementation for attitude control is significantly improved. Introduction of passive dampers makes the hybrid scheme effective even for vibration control during the retrieval. For the stationkeeping phase, the offset control strategy is also used to regulate both the longitudinal as well as inplane transverse vibrations of the tether. The LQG/LTR based vibration controller using the offset strategy is implemented in conjunction with the FLT type attitude regulator utilizing thrusters as before. This hybrid controller for simultaneous regulation of attitude and vibration dynamics is found to be quite promising. The performance of the vibration controller is further improved by introduction of passive dampers. The LQG based vibration controller is found to be robust against the unmodelled dynamics of the flexible system. Finally, effectiveness of the FLT and LQG based offset controllers is assessed through a simple ground based experiment. The controllers successfully regulated attitude dynamics of the tethered system during stationkeeping, deployment and retrieval phases.

博士
國立臺灣大學
應用力學研究所
86
This dissertation is concerned with the dynamics and the strategies for the Tethered-Satellite system (TSS). The TSS consists of a massive satellite (such as the space shuttle) and a subsatellite connected by a long tether. A typical mission can be mainly divided into three phases: deployment phase, station keeping phase, and the retrieval phase. For the deployment phase or the retrieval phase of TSS operation, the length of the tether is controlled to varied slowly, which may lead to a suitable application of the theory of adiabatic invariance. In this dissertation, an adiabatic invariance is computed for an approximate model of TSS during deployment/retrieval mode. It is observed that as the length of the tether becomes larger slowly (deployment mode), the amplitude of the oscillation becomes smaller. On the other hand, if the tether is shortened (retrieval mode), the oscillation becomes larger. Furthermore, for the deployment phase and the retrieval phase, a passive strategy, which is similar in spirit to that of the idea of Hohmann transfer, is developed here. Appropriate circular, elliptic, hyperbolic orbits are designed for the space shuttle and the subsatellite, respectively. Conditions on the designed transfer orbit can be derived from the orbital equations and Kepler''s equation. During the station-keeping phase, it is sometimes necessary to transport some device from space shuttle to the subsatellite. In order to deal with such transportation problem, a scheme similar to a woodpecker toy is proposed, in which the contact problem needs to be considered. We thus formulate the collision of two rigid bodies in a global setting. A new framework is obtained which can simultaneously handle conditions of rolling with or without sliding. The attitude of igid body is modeled as rotation matrix SO(3), which can avoid the singularity when using the local coordinates (such as Euler angles). With Gibbs-Appell''s equations and Coulomb friction law, the dynamical equations for two rigid bodies rolling with or without sliding are derived. Moreover, we adopt the principle of Least Constraint for impulses to model the impact between two rigid bodies. With these framework, the system of a small hollow cylinder connected with a payload by a torsional spring through a straight tether is studied. The motions of the cylinder relative to the tether includes: impact, contact with slip, losing contact,...,etc. The velocity of the transportation as it arrives at the designed height depends on the friction coefficient, the spring constant, the mass of the payload,...,etc. The developed contact formulations can be applied to the rolling problem of a bowling ball. Instead of a point contact case, we consider the surface contact model. The frictional force and the frictional torque acting on the bowling ball are derived through surface integral on a circular plate. It is observed that the frictional force and the frictional torque depend not only on the velocity of the center of the contact surface but also on the angular velocity of the ball. A computer program is implemented and the Helicopter style of bowling is studied. Numerical results agrees well with the qualitative

碩士
淡江大學
航空太空工程學系碩士班
101
The equation of motion of formation flight of satellite system is derived by using the HILL equation in this thesis. Comparing the thrusts required to keep the satellite systems in the formation flight between by the tethered or not is also discussed. By using the genetic algorithms, the configuration of satellite constellation for minimal thrust required is obtain. In the three satellite system, the mass of each is 10 kg, the initial position at the altitude 6978 km. The range of initial velocity is from 0.001 to 0.01 km/s, and the time is from 2000 to 3000 s. By using the genetic algorithms, in the range of the initial conditions, let the initial velocity in 0.005224 km/s and flying time in 2901 s, to arrive the position (19.29,-0.009881) km, then the minimal thrust becomes 0.005671 N.

Il lavoro affronta lo studio statico e dinamico di sistemi spaziali a filo, costituiti da due corpi rigidi collegati da un filo continuo elastico dotato di massa, orbitanti immersi in un mezzo viscoso. L'analisi è suddivisa in due campi in dipendenza del valore delle resistenze aerodinamiche. Per resistenze aerodinamiche trascurabili viene affrontato il problema della analisi dinamica intorno alla configurazione di equilibrio del sistema, preventivamente determinata. La distribuzione delle forze determina la presenza di tensione variabile lungo il cavo, la quale è studiata mediante l'introduzione di sviluppi perturbativi alla Linstedt-Poincaré. Le oscillazioni del sistema sono state studiate mediante analisi modale, proponendo una trattazione di tipo operazionale che consente la scrittura di relazioni caratteristiche dei sistemi giroscopici misti continuo-discreto. In presenza di atmosfera, l’analisi delle configurazioni di equilibrio viene effettuata mediante due modelli, il primo nell’ipotesi di filo rettilineo, il secondo che tiene conto in modo continuo delle caratteristiche geometriche e meccaniche del sistema e delle forze sul filo. Uno studio parametrico viene condotto in modo da ottimizzare la configurazione del sistema per il raggiungimento di quote basse dell’atmosfera. Il modello flessibile consente, ance in presenza di discontinuità, una più accurata determinazione della configurazione di equilibrio. Vengono infine determinati i campi di stabilità delle configurazioni di equilibrio del sistema.