Magnetic attitude control design for small satellites via slowly-varying systems theory

This paper presents a three-axis attitude control algorithm for small satellites using only magnetic actuation. Such satellites are controllable only in two axes that are perpendicular to the local geomagnetic field vector at any point in time since the control torque can only be generated perpendicular to the geomagnetic field vector. We first model the attitude kinematics and dynamics in the geomagnetic frame in the form of an underactuated system. We then develop a three-axis magnetic attitude control algorithm using the theory of slowly-varying systems. The effectiveness of the proposed control law is illustrated through a computer simulation.