Dynamical modelling of a flexible motorised momentum exchange tether and hybrid fuzzy sliding mode control for spin-up

A space tether is a long cable used to couple satellites, probes or spacecrafts to each other or to other masses, such as a spent booster rocket, space station, or an asteroid. Space tethers are usually made of thin strands of high-strength fibres or conducting wires, which range from a few hundred metres to several kilometres and have a relatively small diameter. Space tethers can provide a mechanical connection between two space objects that enables a transfer of energy and momentum from one object to the other, and as a result they can be used to provide space propulsion without consuming propellant. Additionally, conductive space tethers can interact with the Earth's magnetic field and ionospheric plasma to generate thrust or drag forces without expending propellant. The motorised momentum exchange tether (MMET) was first proposed by Cartmell in 1996 and published in 1998. The system comprises a specially designed tether connecting two payload modules, with a central launcher motor. For the purposes of fundamental dynamical modelling the launcher mass can be regarded as a two part assembly, where the rotor is attached to one end of each tether subspan, and the other side is the stator, which is attached to the rotor by means of suitable bearings. Both the launcher and the payload can be attached to the tether by means of suitable clamps or bearing assemblies, dependent on the requirements of the design. The further chapters in this thesis focus on a series of dynamical models of the symmetrical MMET syste, including the dumbbell MMET system, the solid massless MMET system, the flexible massless MMET system, the solid MMET system and the discretised flexible MMET system. The models in this context have shown that including axial, torsional and pendular elasticity, the MMET systems have a significant bearing on overall performance and that this effect should not be ignored in future, particularly for control studies. All subsequent analyses for control applications should henceforth include flexible compliance within the modelling procedure. Numerical simulations have been given for all types of MMET models, in which, accurate and stable periodic behaviours are observed, including the rigid body motions, the tether spin-up and the flexible motions, with proper parameter settings. The MMET system's spin-up control methods design and analysis will henceforth be referenced on the results. For the non-linear dynamics and complex control problem, it was decided to investigate fuzzy logic based controllers to maintain the desired length and length deployment rate of the tether. A standard two input and one output fuzzy logic control (FLC) is investigated with numerical simulations, in which the control effects on the MMET system's spin-up are observed. Furthermore, to make the necessary enhancement to the fuzzy sliding mode control, a specialised hybrid control law, named F$\alpha$SMC is proposed, which combines fuzzy logic control with a SkyhookSMC control law together, then it is applied for the control of motorised space tether spin-up coupled with an flexible oscillation phenomenon. It is easy to switch the control effects between the SkyhookSMC and the FLC modes when a proper value of $\alpha$ is selected $(0<\alpha<1)$ to balance the weight of the fuzzy logic control to that of the SkyhookSMC control, and the hybrid fuzzy sliding mode controller is thus generated. Next, the simulations with the given initial conditions have been devised in a connecting programme between the control code written in $MATLAB$ and the dynamics simulation code constructed within $MATHEMATICA$. Both the FLC and the hybrid fuzzy sliding mode control methods are designed for the control of spin-up of the discretised flexible MMET system with tether-tube subspans, and the results have shown the validated effects of both these control methods for the MMET system spin-up with included flexible oscillation. To summarise, the objectives of this thesis are, firstly, to propose a series of new dynamical models for the motorised momentum exchange tethers; secondly, to discuss two types of control methods for the spin-up behaviour of a flexible motorised momentum exchange tether, which include a fuzzy logic control and a hybrid fuzzy sliding mode control. By the weight factor $\alpha$, fuzzy logic control and SkyhookSMC controllers can be balanced from one to each other, and there is observed difference for each of the elastic behaviour in the MMET system involving these MMET systems with different controllers - FLC($\alpha = 1$), F$\alpha$SMC($\alpha = 0.5$) and SkyhookSMC($\alpha = 0.0$). The results state the control effects for FLC, F$\alpha$SMC and FLC, which lead to stable spin-up behaviour with flexible oscillations

Dynamics and control of tethered satellite formations in low-Earth orbits

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·limetric

Effects of Energy Dissipation on the Free Body Motions of Spacecraft

Modal model using deformation modes of slightly flexible, lightly damped structure to analyze effects of energy dissipation on free body motions of spacecraf

Satellite formation flying for an interferometry mission

The autonomous formation flying of multiple spacecraft to replace a single large satellite will be an enabling technology for many future missions. In this research, the current status of formation flying missions and technologies is determined, and the Darwin nulling interferometry mission, which aims to detect and characterise extrasolar planets, is selected as the research focus. Darwin requires high precision formation flying of multiple telescopes near the Sun-Earth L2 point. A comprehensive account of current research in astrobiology is presented which provides the motivation for a Darwin-type mission. Astrobiology is integral to the definition of formation manoeuvres and target identification. The system design issues associated with developing a higher resolution, Planet Imager mission are also explored through a preliminary mission design. Relative dynamics models for satellite formation flying control in Low Earth Orbit (LEO) and L2 are developed and methods of incorporating the Earth oblateness perturbation (J2) into the equations of relative motion to improve model fidelity are investigated. The linearised J2 effect is included in the Hill equations in time averaged and time varying form. The models are verified against the Satellite Tool Kit (STK) numerical orbit propagator, and applied to optimal control system design and evaluation for formation keeping tasks. The ‘reference orbit’ modelling approach applied in LEO is applied to the development of a new formation flying model at L2. In this case, linearised equations of motion of the mirror satellites relative to the hub are derived and performance evaluated for different initial conditions. These and other higher order models are compared to STK. The linearised model is applied to controller design for station keeping and formation manoeuvring tasks suitable for a Darwin-type mission, and the role of the model in developing controllers for a load levelling guidance system is explored.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

1999 Flight Mechanics Symposium

This conference publication includes papers and abstracts presented at the Flight Mechanics Symposium held on May 18-20, 1999. Sponsored by the Guidance, Navigation and Control Center of Goddard Space Flight Center, this symposium featured technical papers on a wide range of issues related to orbit-attitude prediction, determination, and control; attitude sensor calibration; attitude determination error analysis; attitude dynamics; and orbit decay and maneuver strategy. Government, industry, and the academic community participated in the preparation and presentation of these papers

Spacecraft nonlinear attitude control with bounded control input

The research in this thesis deals with nonlinear control of spacecraft attitude stabilization and tracking manoeuvres and addresses the issue of control toque saturation on a priori basis. The cascaded structure of spacecraft attitude kinematics and dynamics makes the method of integrator backstepping preferred scheme for the spacecraft nonlinear attitude control. However, the conventional backstepping control design method may result in excessive control torque beyond the saturation bound of the actuators. While remaining within the framework of conventional backstepping control design, the present work proposes the formulation of analytical bounds for the control torque components as functions of the initial attitude and angular velocity errors and the gains involved in the control design procedure. The said analytical bounds have been shown to be useful for tuning the gains in a way that the guaranteed maximum torque upper bound lies within the capability of the actuator and, hence, addressing the issue of control input saturation. Conditions have also been developed as well as the generalization of the said analytical bounds which allow for the tuning of the control gains to guarantee prescribed stability with the additional aim that the control action avoids reaching saturation while anticipating the presence of bounded external disturbance torque and uncertainties in the spacecraft moments of inertia. Moreover, the work has also been extended blending it with the artificial potential function method for achieving autonomous capability of avoiding pointing constraints for the case of spacecraft large angle slew manoeuvres. The idea of undergoing such manoeuvres using control moment gyros to track commanded angular momentum rather than a torque command has also been studied. In this context, a gimbal position command generation algorithm has been proposed for a pyramid-type cluster of four single gimbal control moment gyros. The proposed algorithm not only avoids the saturation of the angular momentum input from the control moment gyro cluster but also exploits its maximum value deliverable by the cluster along the direction of the commanded angular momentum for the major part of the manoeuvre. In this way, it results in rapid spacecraft slew manoeuvres. The ideas proposed in the thesis have also been validated using numerical simulations and compared with results already existing in the literature