A linear solution for the artificial satellite's attitude optimal control

Abstract

A first order analytical model for a general problem of artificial satellite's attitude corrections maneuvers submitted to gravity gradient torque is presented in this paper. It is assumed that the satellite is a rigid body, with cylindrical or spherical symmetry and its orbit can be elliptical or circular. The problem of optimization is formulated as a Mayer problem and the control torques are provided by a power limited propulsion system. The state is defined by Andoyer's variables and the control by the components of non-conservative external torques in the artificial satellite's axes of inertia. The Pontryagin Maximum Principle is applied to the problem and the optimal torques are given explicitly in Andoyer's variables and their adjoints. The problem of optimal attitude corrections given by the linearized Hamiltonian around the reference attitude is also analyzed, considering the mean Hamiltonian related with the gravitygradient torque. The complete first-order analytical solutions for the problem with fixed duration are gotten by simple quadratures. A law of the optimal control is proposed and the required optimal consumption is presented.