Satellite Attitude Control Using Only Electromagnetic Actuation

The primary purpose of this work was to develop control laws for three axis stabilization of a magnetic actuated satellite. This was achieved by a combination of linear and nonlinear system theory. In order to reach this goal new theoretical results were produced in both fields. The focus of the work was on the class of periodic systems reflecting orbital motion of the satellite. In addition to a theoretical treatment, the thesis contains a large portion of application considerations. The controllers developed were implemented for the Danish Ørsted satellite. The control concept considered was that interaction between the Earth's magnetic field and a magnetic field generated by a set of coils in the satellite can be used for actuation. Magnetic torquing was found attractive for generation of control torques on small satellites, since magnetic control systems are relatively lightweight, require low power and are inexpensive. However, this principle is inherently nonlinear and difficult to use, because control torques can only be generated perpendicular to the geomagnetic field vector. So far, this has prevented control in all three axes using magnetorquers only. A fact that the geomagnetic field changed periodically when a satellite is on a throughout this thesis. Confined computer capacity and a limit on electrical power supply were separate obstacles.They demanded computational simplicity and power optimality from the attitude control system. The design of quasi optimal controllers for a real-time implementation was a subject of considerations in the part on linear control methods for a satellite with a gravity gradient boom. Both time varying and constant gain controllers were developed and their performance was tested via simulation. The nonlinear controller for a satellite without appendages was given in the second part of the thesis. Its design was based on sliding mode control theory. The essence of the sliding control presented in the thesis was to split the controller design into two steps: a sliding manifold design and a sliding condition design. The emphasis was on the sliding condition design, which was stated as a continuous function of the state. A control law for magnetic actuated satellite was proposed. Complete comprehension of the nature of the satellite control problem required a new approach merging the nonlinear control theory with physics of the rigid body motion and an extension of earlier results in this field using the theory of periodic systems. The Lyapunov stability theory was employed based on the potential and kinetic energy of the rigid satellite. A velocity controller, that contributes to dissipation of both kinetic and potential energy, was proposed. The velocity control was shown to provide four stable equilibria, one of which was the desired orientation. It was explained how the equilibria depended on the ratio of the satellite's moments of inertia. It was further investigated how to control the attitude, such that the satellite was globally asymptotically stable in the desired orientation, avoiding the undesired equilibria. The main contribution of this work was to show that three axis control can be achieved with magnetorquers as sole actuators in a low Earth orbit. A rigorous stability analysis was presented, and detailed simulation results showed convincing performance over the entire envelope of operation of the Danish Ørsted satellite.