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

The paper is devoted to control algorithm development to nullify a relative secular drift due to the Earth oblateness in Formation Flight motion. It is assumed a chief satellite orbit to be circular and its orbit not to be controlled to maintain the formation. Deputy satellite is equipped with a passive magnetic attitude control system with permanent magnet alongwith the principal inertia axis and low-propulsion thruster alongwith the same direction. The investigation how to eliminate the relative secular drift by a limited control is carried out. The limitation consists in a constraint of direction and magnitude of feasible control. In the present work the control to eliminate the relative secular drift is analytically developed. Analytical results are approved by numerical simulation of the satellite motion like the first Russian nanosatellite TNS-0 № 1.