Control of geostationary spacecraft in orbital plane using a low thrust engine

Abstract

The control algorithm for the parameters of the geostationary spacecraft orbit was developed using low-thrust engine. We consider only flat parameters determining the geostationary spacecraft’s position in the orbit plane, namely, orbital period, eccentricity and longitude point of standing. The terminal control problem of geostationary spacecraft has been stated. It is assumed that the corrective maneuver is implemented by creating a small transversal acceleration using electric low-thruster. There is a developed discrete model of the geostationary spacecraft motion in the orbit plane under the influence of small transversal acceleration. The solution of this problem involving the use of the traditional dynamic programming method based on the use of Bellman equation is difficult to obtain, because the discrete model of geostationary spacecraft motion is a nonlinear system of equations. Therefore, the paper proposes approximate scheme for solving the problem based on the three-step algorithm of terminal control of the orbital period, eccentricity and longitude point of standing. The solution of the plane problem of the terminal control has been obtained in the analytical form. Analytical expressions for the cost estimate of characteristic speed of corrective maneuver have been obtained. When modeling the motion of a geostationary spacecraft under the influence of a small transversal acceleration the algorithm has showed high accuracy of solving the terminal control problem.