Holding geostationary satellite at given standing point, taking into account additional phase restrictions

The active lifetime of orbital facilities in the geostationary orbit (GSO), which include stationary artificial earth satellites (SAES) for various purposes, can be more than 15 years. At the same time, in modern conditions of orbital grouping increment, the number of space debris, including those on the GSO, also increases: SAES, which have finished its active lifetime and were not transferred to disposal orbit for some reasons, shards of SAES appeared from collision with meteors or accidents. This leads to the increase of probability of collisions with active SAESs. The listed factors determine the need of considering not only the problem of keeping SAESs in vicinities of position, but also the task of avoiding collisions with space debris objects (SDO), while the costs of the working fluid should not increase.
A great attention is being paid to rational power units placing during the projection of new space shuttles, especially those with long useful lifetime. In this article, it is assumed that SESs are equipped with several correction motors, which make it possible to create control accelerations in only several directions, without changing the orientation of the SES itself. In other words, in this task it is assumed that the corrections of the parameters of the AES orbit do not affect the orientation of the SAES itself. This condition is a severe limitation in the synthesis of the SES’s control system.
In the considered methodological approach, the costs of the working fluid are set as a functionality from control, which are necessary to perform the next correction, after which the SAES will not have dangerous distances and approaching in projection horizon’s interval. This makes it possible to avoid situations when the decision on control is being made after the SES leaves the vicinity of the station point, and first of all, the approach to the SDO at a distance less than a liminal one. This article provides the results of modeling, which indicate the effectiveness of the proposed solutions.
An important advantage compared with the existing methods is the consideration of the movement of the SAES relatively not only to the stationary point, but also to several other objects located in its vicinity, both controlled and uncontrolled. Moreover, there can be any given number of objects.