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 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.

Small satellites are becoming increasingly important to the aerospace industry mainly due to their significantly reduced development and launch cost as well as shorter development time frames. In order to meet the requirements imposed by critically limited resources of very small satellites, e.g. picosatellites, innovative approaches have to be taken in the design of effective subsystem technologies. This thesis presents the design of an active attitude determination and control system for flight testing on-board the picosatellite 'Compass-1' of the University of Applied Sciences Aachen, Germany. The spacecraft of the CubeSat class with a net spacecraft mass of only 1kg uses magnetic coils as the only means of actuation in order to satisfy operational requirements imposed by its imagery payload placed on a circular and polar Low Earth Orbit. The control system is capable of autonomously dissipating the tumbling rates of the spacecraft after launch interface separ ation and aligning the boresight of the payload into the desired nadir direction within a pointing error of approximately 10°. This nadir-pointing control is achieved by a full-state feedback Linear Quadratic Regulator which drives the attitude quaternion and their respective rates of change into the desired reference. The state of the spacecraft is determined by a static statistical QUEST attitude estimator processing readings of a three-axis magnetometer and a set of five sun sensors. Linear Floquet theory is applied to quantify the stability of the controller and a non-linear dynamics simulation is used to confirm that the attitude asymptotically converges to the reference in the absence of environmental disturbances. In the presence of disturbances the system under control suffers from fundamental underactuaction typical for purely magnetic attitude control but maintains satisfactory alignment accuracies within operational boundaries.

In this dissertation the solutions of the dynamics and real-time optimal control of magnetic attitude control and formation flying systems are presented. In magnetic attitude control, magnetic actuators for the time-optimal rest-to-rest maneuver with a pseudospectral algorithm are examined. The time-optimal magnetic control is bang-bang and the optimal slew time is about 232.7 seconds. The start time occurs when the maneuver is symmetric about the maximum field strength. For real-time computations, all the tested samples converge to optimal solutions or feasible solutions. We find the average computation time is about 0.45 seconds with the warm start and 19 seconds with the cold start, which is a great potential for real-time computations. Three-axis magnetic attitude stabilization is achieved by using a pseudospectral control law via the receding horizon control for satellites in eccentric low Earth orbits. The solutions from the pseudospectral control law are in excellent agreement with those obtained from the Riccati equation, but the computation speed improves by one order of magnitude. Numerical solutions show state responses quickly tend to the region where the attitude motion is in the steady state. Approximate models are often used for the study of relative motion of formation flying satellites. A modeling error index is introduced for evaluating and comparing the accuracy of various theories of the relative motion of satellites in order to determine the effect of modeling errors on the various theories. The numerical results show the sequence of the index from high to low should be Hill's equation, non- J2, small eccentricity, Gim-Alfriend state transition matrix index, with the unit sphere approach and the Yan-Alfriend nonlinear method having the lowest index and equivalent performance. A higher order state transition matrix is developed using unit sphere approach in the mean elements space. Based on the state transition matrix analytical control laws for formation flying maintenance and reconfiguration are proposed using low-thrust and impulsive scheme. The control laws are easily derived with high accuracy. Numerical solutions show the control law works well in real-time computations.

The design of an attitude control system for a flexible spacecraft using magnetic actuation is considered. The nonlinear, linear, and modal equations of motion are developed for a general flexible body. Magnetic control is shown to be instantaneously underactuated, and is only controllable in the time-varying sense. A PD-like control scheme is proposed to address the attitude control problem for the linear system. Control gain limitations are shown to exist for the purely magnetic control. A hybrid control scheme is also proposed that relaxes these restrictions by adding a minimum control effort from an alternate three-axis actuation system. Floquet and passivity theory are used to obtain gain selection criteria that ensure a stable closed-loop system, which would aid in the design of a hybrid controller for a flexible spacecraft. The ability of the linearized system to predict the stability of the corresponding nonlinear system is also investigated.

The design of an attitude control system for a flexible spacecraft using magnetic actuation is considered. The nonlinear, linear, and modal equations of motion are developed for a general flexible body. Magnetic control is shown to be instantaneously underactuated, and is only controllable in the time-varying sense. A PD-like control scheme is proposed to address the attitude control problem for the linear system. Control gain limitations are shown to exist for the purely magnetic control. A hybrid control scheme is also proposed that relaxes these restrictions by adding a minimum control effort from an alternate three-axis actuation system. Floquet and passivity theory are used to obtain gain selection criteria that ensure a stable closed-loop system, which would aid in the design of a hybrid controller for a flexible spacecraft. The ability of the linearized system to predict the stability of the corresponding nonlinear system is also investigated.