Fuel and Time Optimize and Adaptive Control for Gravity Gradient Spacecraft

Abstract

This paper treats the time/fuel optimal control of gravity gradient spacecraft. The equations of motion of the spacecraft are simplified such that the maximum principle becomes applicable: the validity of this approximation is proven by comparison of the simulation results of the rigorous and the simplified system. Based upon the simplified equation, a time/fuel optimal law for space craft attitude control is developed. This law is based upon definition of a fuel savings angle, a new way of defining the trade-off between pure time optimality and pure fuel optimality. Chattering in the vicinity of zero angles and zero rates is limited by a simple adaptive modification