Magnetic Torquer Attitude Control via Asymptotic Periodic Linear Quadratic Regulation

A method of using magnetic torque rods to do 3axis spacecraft attitude control has been developed. The goal of this system is to achieve a nadir pointing accuracy on the order of 0.1 to 1.0 deg without the need for thrusters or wheels. The open-loop system is under-actuated because magnetic torque rods cannot torque about the local magnetic field direction. This direction moves in space as the spacecraft moves along an inclined orbit, and the resulting system is roughly periodic. Periodic controllers are designed using an asymptotic linear quadratic regulator technique. The control laws include integral action and saturation logic. This system's performance has been studied via analysis and simulation. The resulting closed-loop systems are robust with respect to parametric modeling uncertainty. They converge from initial attitude errors of 30 deg per axis, and they achieve steady-state pointing errors on the order of 0.5 to 1.0 deg in the presence of drag torques and unmodeled residual dipole moments.