Power-Efficient Control of Plane Parameters of a Geostationary Spacecraft's Orbit Using an Adjustable Low-Thrust Rocket Engine

Abstract

A power-efficient algorithm is developed for discrete control of a geostationary spacecraft's orbital plane parameters using an adjustable low-thrust rocket engine. The algorithm is developed according to the approach described in [3] for a discrete feedback system. To reduce the onboard computer load, when the system operates during tens of days, the calculation interval is taken equal to 100 s. To use such a long interval, the author applied the approach described in [4], where the system state vector comprised the vector of coordinates of a geostationary spacecraft's centre of mass and the vector of its increments at one calculation step. A distinctive feature of the auxiliary system used for construction of the power-efficient control algorithm is the dependence of the current vector of the system state not from the previous one but from its initial state. That allowed using a transition matrix of the auxiliary system in the form of a diagonal matrix. The diagonal elements were taken in the form of hyperbolic first-order polynomials functions of the calculation step number. Besides, the weighting matrix in the control law was taken in the form of a constant matrix, since the elements of the weighting matrix in the control law quickly converge. To assess the efficiency of the algorithm proposed, the author compared results of its modeling to the results given in [2], where a three-step algorithm was proposed to control plane parameters of a geostationary spacecraft's orbit using a nonadjustable low-thrust rocket engine with the thrust applied in the transversal direction. The modeling was done with the same initial deviations of orbital parameters from the specified ones as those taken in [2]: for the revolution period the deviation was AT = 1,000 s, for the eccentricity it was Ae = 0,005 and for the longitude of the orbital position it was AX = 5 deg. The orbit correction time was also taken, according to [2], equal to 4,000 steps of 100 s each, that is about 5 days. As a result of modeling, it was determined that the characteristic velocity consumption for correction of an orbit, with the correction beginning at the orbit perigee, was 9.4 m/s, which is 20 % less than that in the case given for comparison (11.8 m/s). If, with the same initial deviations, the correction of the orbit begins at its apogee, the characteristic velocity required for correction increases up to 11.5 m/s.