Choosing control parameters for three axis magnetic stabilization in orbital frame

Three-axis magnetic control in orbital reference frame is considered. Magnetorquers are the only actuators and gravitational torque is the only disturbance source. Full attitude knowledge is assumed. Control is constructed on the basis of PD-controller. Stability is analyzed using Floquet theory. Optimal in terms of degree of stability control parameters are found using this approach. These parameters may be further adjusted using numerical simulation. Results for three typical satellites are provided. Numerical example with Kalman filter implementation and additional disturbance sources is provided.