The Gravity Recovery and Climate Experiment (GRACE) mission is a breakthrough Earth science mission launched in the spring of 2002 that uses satellite-to-satellite tracking (SST) to map the Earth gravity field. In this framework, the non-uniform gravity distribution is inferred using the range change experienced between two satellites. The range change is measured using a microwave K-band ranging system, and non-gravitational forces are accounted for using accelerometer (ACC) data. The vector-offset between the satellite center of mass (CM) and the K-band phase center represents the correction between measured and modeled ranging data. In addition, the offset between the satellite CM and the ACC proof-mass multiplies the attitude angles, rates, and jitter which in turn add spurious signals to the ACC output. For both of these reasons, proper knowledge and control of attitude behavior is vital to successful mission performance. An examination of the GRACE attitude control system (ACS) is presented in this study. The GRACE ACS system is composed of a PD control law, star camera sensing as the knowledge source, cold-gas thrusters as primary actuators, and magnetic torque rods as supplementary actuators. The dependencies inherent in the ACS are inferred using a sensitivity analysis performed on a simulation model of the GRACE science mode ACS. The results from this sensitivity study are applicable to the general controller class of which the GRACE ACS system is an exemplar. In this study, the modeled attitude data quality is most sensitive to star camera measurement noise. It is hypothesized that this is because star cameras are used as the sole knowledge source in the ACS scheme. In contrast, the experimental results associated with magnetometer, thruster, and magnetic torque rod perturbations did not significantly affect attitude quality. However, these perturbations do cause thruster activity to significantly magnify. This results in higher attitude acceleration PSD for the frequency band in which time-variable gravity components are captured. A number of future experiments can be performed to improve both attitude quality performance and frequency-based magnifications. Examples include sensor fusion studies, reaction wheel versus thruster assessment, and gravity field estimation sensitivity in response to attitude quality degradation. / text

In this research study, several new in-orbit algorithms are proposed to improve the performance of Attitude Determination and Control System (ADCS) by estimating the inertia matrix and calibrating the cold gas thruster system of the UoSAT-12 spacecraft. Computer-based simulation models will be constructed using MATLAB and SIMULINK in order to evaluate the expected performance. The first focus is on the identification of the satellite inertia matrix. A new algorithm based on a Recursive Least Square (RLS) estimation technique is proposed for in-orbit use to estimate the inertia matrix (moments and products of inertia parameters) of a satellite. To facilitate this, one attitude axis is disturbed using a reaction wheel whilst the other two axes are controlled to keep their respective angular" rates small. Within a fraction of an orbit three components of the inertia matrix can be accurately determined. This procedure is then repeated for the other two axes to obtain all nine elements of the inertia matrix. The procedure is designed to prevent the build up of momentum in the reaction wheels, whilst keeping the attitude disturbance to the satellite within acceptable limits. It can also overcome potential errors introduced by unmodeled external disturbance torques and attitude sensor noise. The second focus is on a new algorithm for in-orbit use to calibrate thruster coefficients for thrust level and alignment, using three reaction wheel actuators. These algorithms will ensure robustness against modeling errors. The algorithms assume no prior knowledge of the thruster parameters and only an initial guess of the inertia matrix. It is proposed that this calibration can be used during normal mission conditions when the satellite is stabilised. The final goal of this research study was to apply the proposed algorithms in real-time. Firstly, the thruster calibration algorithm was tested on an air-bearing table. Finally, both thruster calibration and moment of inertia algorithms were tested using data generated by UoSAT-12 while in orbit. The practical estimation results proved the feasibility of proposed algorithms.

The thesis examines diverse methods of damping the librational motion of earth-orbiting satellites. Starting with passive stabilization, two classical mechanisms for energy dissipation are studied, for performance comparison, when executing librations in the orbital plane. The first model, consisting of a sliding mass restricted to relative translational motion with respect to the main satellite body, establishes the suitability of various approaches to the problem in circular orbit. In this case, numerical and analog methods do not readily yield information on the influence of parameters and approximate methods are found to be particularly helpful. Butenin's method based on averaging techniques predicts the response of the satellite with good accuracy for small damping constant while the exact solution to the linearized equations provides optimum damper characteristics for motion in the small. A comparison of the sliding mass damper model with a damper boom mechanism involving only relative rotational displacements, is then performed for equal equilibrium inertias of the damping devices. It indicates that, for optimum transient tuning, the damper boom would have a better time-index while the sliding mass would lead to smaller steady-state amplitudes for low eccentricity orbits. A numerical example using GEOS-A satellite data illustrates the outcome of the study when applied to physical situations. A stability analysis is also included which uses Routh and Lyapunov approaches to determine the domain of parameters leading to asymptotic stability, as well as numerical methods to define the bounds on stable initial disturbances: it is found that for most practical applications, the stability contour in circular orbit is close to that of the undamped case. How-ever, for eccentric trajectory, the amount of damping critically affects asymptotic stability. The next model, which involves active stabilization, uses solar radiation pressure to achieve planar librational control of a satellite orbiting in the plane of the ecliptic. This is obtained by adjusting the position of the center of pressure with respect to the center of mass through a controller depending on a linear combination of librational velocity and displacement. The motion in circular orbit is; first investigated through the W.K.B. method. Although the approximate equation involves an infinity of turning points, only a few of them are required to evaluate the damped behaviour of the system. A comparison of the analytical results with a numerical integration of the exact equation of motion shows good agreement only over a limited range of parameters and, therefore, the latter is used to complete the study for circular and elliptic cases. The concept leads to great versatility in positioning a satellite at any angle with respect to the local vertical. Also, high transient ; performance is observed about local vertical and horizontal and the dichotomous property of good transient associated with poor steady-state inherent to passive damping can be avoided by selecting appropriate controller parameters. An example is included which substantiates the feasibility of the configuration. Finally, the attention is directed towards the influence of gravity torques on the stability of damped axisymmetric dual-spin satellites. The nutation damper mounted on the slowly-spinning section is of the pendulum type. For this section rotating at orbital angular rate, application of the Kelvin-Tait-Chetaev theorem indicates that the asymptotic stability region reduces basically to the mainly positive stable spin region of the undamped case. However, some care is required depending upon the shape and natural frequency of the damper. If the damper section rotates at a much higher rate than the orbital one, torque-free motion need only be considered for short term pre-dictions. Stability charts corresponding to this case, given for comparison, emphasize the effect of gravity. / Applied Science, Faculty of / Mechanical Engineering, Department of / Graduate

The feasibility of utilizing the environmental forces for three-axis librational damping and attitude control of spinning satellites is investigated in detail. An appreciation of the environmental influence is first gained through a librational dynamics study of spinning, axisymmetric, cylindrical satellites in the solar radiation pressure field. The highly nonlinear, nonautonomous, coupled equations of motion are analyzed approximately using the method of variation of parameters. The closed form solution proves to be quite useful in locating periodic solutions and resonance characteristics of the system. A numerical parametric analysis, involving large amplitude motion, establishes the effect of the radiation pressure to be substantial and destabilizing. Next, a possibility of utilizing this adverse influence to advantage through judiciously located rotatable control surfaces is explored. A controller configuration for a dual-spin spacecraft is analyzed first. The governing equations, in the absence of a known exact solution, are solved numerically to evaluate the effect of system parameters on the performance of the control system. The available control moments are found to be sufficient to compensate for the rotor spin decay, thus dispensing with the necessity of energy sources maintaining the spin rate. The controller is able to damp extremely severe disturbances in a fraction of an orbit and is capable of imparting arbitrary orientations to a satellite, thus permitting it to undertake diverse missions. The development of an efficient yet structurally simple controller configuration is then considered. A logical approach for solar controller design is proposed which suggests a four-plate configuration. Its performance in conjunction with a bang-bang control law is studied in detail. The utilization of maximum available control moments leads to a substantial improvement of the damping characteristics. Attention is then focussed on using the earth's magnetic field interaction with onboard dipoles for attitude control. Magnetic torquing, however, is unable to provide first order pitch control in near equatorial orbital planes. The shortcoming is overcome by hybridizing the concepts of magnetic and solar control. Two magnetic controller models, employing a single rotatable dipole or two fixed dipoles, are proposed in conjunction with a solar pitch controller. The system performance is evaluated for a wide range of system parameters and initial conditions. Although high spin rates lend considerable gyroscopic stiffness to the spacecraft, the controllers continue to be quite effective even in the absence of any spin. Even with extremely severe disturbances, damping times of the order of a few orbital degrees are attainable. As before, the concept enables a satellite to change the desired attitude in orbit. The effectiveness of the controllers at high altitudes having been established, the next logical step was to extend the analysis to near-earth satellites in free molecular environment. A hybrid control system, using the solar pressure at high altitudes and the aerodynamic forces near perigee, is proposed. The influence of important system parameters on the bang-bang operation of the controller is analyzed. The concept appears to be quite effective in damping the satellite librations. Both the orbit normal and the local vertical orientations of the axis of symmetry of the satellite are attainable. However, for arbitrary pointing of the symmetry axis, small limit cycle oscillation about the desired final orientation results. Finally, the time-optimal control, through solar radiation pressure, of an unsymmetrical satellite executing planar pitch librations is examined analytically. The switching criterion, synthesized for the linear case, is found to be quite accurate even when the system is subjected to large disturbances. Throughout, the semi-passive character of the system promises an increased life-span for a satellite. / Applied Science, Faculty of / Mechanical Engineering, Department of / Graduate

Approved for public release; distribution is unlimited. / NPSAT1 is a gravity-gradient friendly, prolate body designed to fly at 600 Å 40 km inclined to 34.5 degrees. The satellite uses a magnetic 3-axis active attitude control system (ACS) using magnetic torque rods that interact with the Earth's magnetic field. This thesis accomplishes three goals. The first objective was to verify and to validate the magnetic attitude control system program and model developed by Leonard. The verification and validation process was completed in two steps. The first step accomplished an independent modeling of the Earth's magnetic field using MATLAB. The second step completed a verification via inspection of Leonard's ACS SIMULINK model. The verification confirmed that Leonard's modular sub-components of the disturbance torques, the quaternion vectors, the Euler angles, the spacecraft kinematics and dynamics, and the ACS control laws conformed to current ACS empirical theory. The second goal was to establish a laboratory used to demonstrate the ACS robustness and ability to perform as designed. The laboratory was created to house an air-bearing platform that simulates NPSAT1 characteristics. The third goal was to perform hardware-in-the-loop experiments with the NPSAT1 ACS software and model. Hardwarein- the-loop tests were performed to the magnetic torque rods, torque rod driver circuit board, micro-controller computer, and control interfaces. Specifically, solenoid current tests, magnetic field determination tests, and digital-to-analog conversion tests were completed. / Lieutenant Commander, United States Navy

Attitude control of spacecraft in low Earth orbits can be achieved by exploiting the torques generated by the geomagnetic field. Recent research has demonstrated that attitude stability of a spacecraft is possible using a linear combination of Euler parameters and angular velocity feedback. The research carried out in this thesis implements a hybrid scheme consisting of magnetic control using on-board dipole moments and a three-axis actuation scheme such as reaction wheels and thrusters. A stability analysis is formulated and analyzed using Floquet and Lyapunov stability theorems.

The problem of attitude control of a flexible satellite using magnetic attitude control is investigated. The work is motivated by JC2Sat - a joint CSA and JAXA mission whose main purpose is a proof of concept of two satellites performing differential drag formation flying. The impact of additional flexible drag panels (of various sizes) on the attitude control is assessed. JC2Sat's attitude control system consists of three perpendicular magnetorquers and one reaction/bias-momentum wheel. Four Linear Quadratic Regulator controllers are compared, ranging in complexity from being time-invariant and assuming a rigid satellite, to being periodic and actively suppressing panel vibrations. These include the first controllers which use magnetic attitude control to actively suppress vibrations, and where the periodic vibration suppression controller is able to guarantee asymptotic stability of the linearized system. It was found that for larger panels, the controllers which actively suppressed the vibrations outperformed those that did not.

Attitude control of spacecraft in low Earth orbits can be achieved by exploiting the torques generated by the geomagnetic field. Recent research has demonstrated that attitude stability of a spacecraft is possible using a linear combination of Euler parameters and angular velocity feedback. The research carried out in this thesis implements a hybrid scheme consisting of magnetic control using on-board dipole moments and a three-axis actuation scheme such as reaction wheels and thrusters. A stability analysis is formulated and analyzed using Floquet and Lyapunov stability theorems.

The problem of attitude control of a flexible satellite using magnetic attitude control is investigated. The work is motivated by JC2Sat - a joint CSA and JAXA mission whose main purpose is a proof of concept of two satellites performing differential drag formation flying. The impact of additional flexible drag panels (of various sizes) on the attitude control is assessed. JC2Sat's attitude control system consists of three perpendicular magnetorquers and one reaction/bias-momentum wheel. Four Linear Quadratic Regulator controllers are compared, ranging in complexity from being time-invariant and assuming a rigid satellite, to being periodic and actively suppressing panel vibrations. These include the first controllers which use magnetic attitude control to actively suppress vibrations, and where the periodic vibration suppression controller is able to guarantee asymptotic stability of the linearized system. It was found that for larger panels, the controllers which actively suppressed the vibrations outperformed those that did not.

The thesis identifies several limitations in the modelling and attitude stability analysis of two classes of spacecraft: rigid and flexible satellites. Attractive methods are proposed which promise to have far reaching consequences in spacecraft dynamics. These alternatives, developed based on techniques of differential equations, classical mechanics, and differential topology, are indicated below. (a) An Alternate Transition from the Lagrangian of a Satellite to Equations of Motion The classical procedure requires the Lagrangian to be expressed in terms of the corresponding generalized coordinates of the problem. This requirement significantly complicates the derivation of the equations of motion through an introduction of a set of librational generalized coordinates, which is strictly not a part of the dynamical system. Using the Lagrangian in the natural variables (angular velocity, direction cosines, and vibrational coordinates), one develops a procedure for derivation of equations of motion without an a priori choice of rotational generalized coordinates. For the case of a satellite with two flexible plate-type appendages, for example, the approach reduced the formulation time to one-third. (b) Synthesis and Depiction of Rotational Motion of Satellites and Robots The rotational coordinates in use for numerical prediction of orientation of a satellite are either singular or redundant. Furthermore, they lack a convenient visual interpretation. A new set of coordinates is proposed and an associated representation is developed which avoids these limitations. The procedure is applied to represent and integrate numerically the librational response of the flexible satellite mentioned in (a). (c) Resolution of Attitude Stability of Delp Satellites The development here tackles a long outstanding problem in the area of attitude stability of satellites. The resolution of this problem through normalization of the Hamiltonian leads to a better appreciation of stability associated with the class of gravity gradient structures such as the proposed Space Station. / Applied Science, Faculty of / Mechanical Engineering, Department of / Graduate