Optimization of spatial turns of «AIST-2» small spacecraft on the basis of the principle of minimum control

Abstract

The efficiency of using the principle of minimum control in solving the task of synthesizing the system of controlling a spacecraft spatial turn by arbitrarily set angles up to 180 degrees is analyzed, with the Aist-2 small spacecraft taken as an example. The tensor of inertia has the form of a diagonal matrix. Flywheels the rotors of which are parallel to the principal central axes of the spacecraft inertia are used as actuating devices of the system that controls motion round the center of masses. The control moment developed by each flywheel, is proportional to the angular acceleration of its rotor. The energy spent on the control, proportional to the sum of modules of angular accelerations of flywheel rotors is accepted as an index of the optimality of the spacecraft spatial turn. Euler dynamic equations are reduced to finite-difference recurrent relations to model unperturbed spacecraft motion around the center of masses. An auxiliary dynamic system is introduced the parameters of which are chosen on the basis of the solution of the task posed to use the principle of minimum control that ensures minimum costs of control. The results of mathematical modeling confirmed the efficiency of the proposed principle. In comparison with the traditional method of control (acceleration, motion at a constant angular velocity, braking) two-fold economy of electrical power is achieved.