Comparative Cost Functions Analysis in the Construction of a Reference Angular Motion Implemented by Magnetorquers

Abstract

This paper considers a construction procedure of a satellite reference angular motion in the vicinity of an unstable gravitational equilibrium position. The satellite is stabilized on the reference trajectory by the magnetic coils. The problem is solved in several stages. An optimization problem to be solved by the particle swarm optimization method is formulated at each stage. Cost functions are based on the linearized model analysis. The main stage is the construction of a special reference motion, which provides the minimum control torque projection on the geomagnetic induction vector. Optimal geomagnetic field dipole approximation for a given time interval is considered to reduce tracking errors. The paper compares combinations of different cost functions in terms of the terminal attitude accuracy in the presence of perturbations.