Linear Time Varying Approach to Satellite Attitude Control Using only Electromagnetic Actuation

Recently small satellite missions have gained considerable interest due to low-cost launch opportunities and technological improvement of micro-electronics. Required pointing accuracy of small, inexpensive satellites is often relatively loose, within a couple of degrees. Application of cheap, lightweight, and power efficient actuators is therefore crucial and viable. This paper discusses linear attitude control strategies for a low earth orbit satellite actuated by a set of mutually perpendicular electromagnetic coils. The principle is to use the interaction between the Earth's magnetic field and the magnetic field generated by the coils. A key challenge is the fact that the mechanical torque can only be produced in a plane perpendicular to the local geomagnetic field vector, therefore the satellite is not controllable when considered at fixed time. Availability of design methods for time varying systems is limited, nevertheless, a solution of the Riccati equation gives an excellent frame for investigations provided in this paper. An observation that geomagnetic field changes approximately periodically when a satellite is on a near polar orbit is used throughout this paper. Three types of attitude controllers are proposed: an infinite horizon, a finite horizon, and a constant gain controller. Their performance is evaluated and compared in the simulation study of the realistic environment.