Three-axis active magnetic attitude control asymptotical study

• Asymptotical methods are used to prove necessary three-axis attitude stability.
• Optimal in terms of time-response control parameters are found analytically.
• Floquet theory justifies and broadens analytical results.

Active magnetic attitude control system providing given inertial attitude is considered. Control algorithm is constructed on the basis of a planar motion model. It decreases attitude discrepancy. Alternative approach is based on the PD-controller design. System behavior is analyzed for specific motion cases and sometimes for specific inertia tensor (axisymmetrical satellite) using averaging technique. Overall satellite angular motion is covered. Necessary attitude is found to be accessible for some control parameters. Stability is proven and optimal algorithm parameters are obtained. Floquet-based analysis is performed to verify and broaden analytical results.