Modelling of relative motion in multi-unit mechanical system with limited control

Abstract

The paper is devoted to the development of a control algorithm to nullify the relative secular drift due to the Earth’s oblateness for the motion of Formation Flying. The chief satellite’s orbit is assumed to be circular and not controlled to maintain the formation. A deputy satellite is equipped with a passive magnetic attitude control system with a permanent magnet and low-propulsion thruster, distributed along the principal inertia axis in the same direction. Research is conducted on the possibility of eliminating the relative secular drift through limited control. The limitation consists in the constraint in the direction and magnitude of feasible control. In the present work, the control to eliminate the relative secular drift is analytically developed. The analytical results are approved by numerical simulation of the satellite motion, such as, of the first Russian nanosatellite TNS-0 No. 1.