Engineering notes active formation flying along an elliptic orbit

An active formation flying for the Tschauner-Hempel equations (TH) is considered, in which the desired relative orbit of the follower is generated by an exosystem. This allows for flexibility of the shape and period of the reference orbit. The regulator differential equation is solved algebraically, exploiting the special structure of the Tschauner-Hempel equations. Hence, control implementation is straight forward. In the case of active formation, the total velocity change increases with penalty on the input. The settling time is independent of the frequency of the reference orbit. For the Tschauner-Hempel equations, the total velocity change for transition increases with frequency of the reference orbit, but the settling time remains almost constant, as in the circular case. For the eccentricity up to 0.3, the total velocity change for maintenance remains at the same level as in the circular case. Using these relations, feedback controls for active formation with given specifications and constraints can be designed effectively.