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SYNTHESIS OF GEOSTATIONARY SATELLITE STABILIZATION CONTROL AT THE STANDING POINT

Methods and algorithms for ballistic support of the longitude stabilization control of the geostationary satellite (GSS) orbital position have been developed. The evolution of current GSS coordinates was modeled by differential equations of motion of a material point in the central gravitational field, taking into account limited structural-parametric perturbations of known intensity, caused by the general influence of the Sun, Moon, and the difference between the Earthʼs gravitational field and the central one. Specific mathematical modeling of these perturbations was not considered, only the properties of their general norm boundedness were used. For control synthesis, we applied an analogue of the method of decomposition of a general synthesis problem into kinematic and dynamic control problems. They were solved with the help of well-known generalizations of Lyapunovʼs direct method of studying the stability of solutions of differential equations to studying the stability of closed bounded sets (specifically, multidimensional ellipsoids) in their phase spaces. Along with the method for synthesis of stabilization control of the orbital position longitude, methods for ellipsoidal estimation of stabilization errors caused by the influence of the mentioned disturbances are proposed. The methods are based on the construction of external ellipsoidal estimates of reachability sets and limit sets in phase spaces of dynamical systems with limited structural perturbations. A method is also proposed for obtaining guaranteed interval estimates of steady-state stabilization errors for each of the coordinates. The effectiveness of the proposed control methods is illustrated by the results of computer simulation.