13. Attitude Regulation for Spacecraft with Magnetic Actuators: An LPV Approach

Magnetic torquers are an effective and reliable technology for the attitude control of small satellites in low Earth orbit. Such actuators operate by generating a magnetic dipole which interacts with the magnetic field of the Earth. The main difficulty in the design of attitude control laws based on magnetic torquers is that the torques they generate are instantaneously constrained to lie in the plane orthogonal to the local direction of the geomagnetic field vector, which varies according to the current orbital position of the spacecraft. This implies that the attitude regulation problem is formulated over a time-varyingmodel. In recent years, this control problem has been studied extensively, either using methods based on averaged models or via approaches which exploit the quasi-periodic variability of the geomagnetic field. With the exception of other approaches based on Model Predictive Control, none of the above actually exploits at the design stage the fact that the geomagnetic field can be reliably measured on board and, therefore, the above mentioned time-variability of the attitude dynamics can be represented in LPV form. Therefore, in this chapter an LPV approach to the problem of magnetic attitude control law design is proposed. To this purpose, an LPV model of the attitude dynamics is first derived, LPV control laws suitable for on board implementation are synthesized and eventually tested in simulation.