Control of in-plane orbit parameters of a geostationary low-thrust satellite

The article focuses on the development of algorithms for controlling the parameters of the orbit of a geostationary satellite with the help of a low- thrust engine. We consider only the control of two-dimensional parameters that define the position of the satellite in the orbital plane, namely, the orbit time, the eccentricity and the point longitude of satellite observation. A two-dimensional problem of geostationary spacecraft terminal control is formulated. It is assumed that the correction maneuver is carried out by creating low transversal acceleration with the help of low-thrust electric propulsion, and the control vector consists of a sequence of durations of powered and unpowered portions. In this regard, the two-dimensional terminal control problem is solved in a discrete setting. For this purpose, a discrete model of the motion of a geostationary spacecraft in the orbital plane under the influence of low transversal acceleration is developed. It is quite difficult to solve the problem posed by using the traditional method of dynamic programming based on the use of the Bellman equation since the resulting discrete model of the satellite motion is a non-linear system of equations. Therefore, an approximate pattern of solving the problem on the basis of a three-step algorithm of the terminal control of the orbit time, eccentricity and point longitude of satellite observation is proposed in the paper. As a result, the plane terminal control problem is solved in an analytical form. Analytical expressions for estimating the costs of characteristic velocity correction maneuver using a three-step algorithm of terminal control are obtained. In modeling the motion of a geostationary satellite under the influence of low transversal acceleration the algorithm showed sufficiently high accuracy.