Оптимальне демпфування відхилень кутових швидкостей осесиметричного космічного літального апарата

Abstract

This paper considers the problem of optimal fuel consumption damping of sudden deviations of angular velocities of an axisymmetric spacecraft with a constant speed of rotation around the main axis of symmetry. This assumption has some practical significance and may be due to the creation of artificial gravity on the spacecraft. The idea of artificial gravity due to the rotation of an axisymmetric cylindrical spacecraft is based on the principle of equivalence of the force of gravity and the force of inertia. The urgency of the fuel consumption optimization problem is due to the presence of its limited stock onboard the spacecraft. The optimization problem is solved based on the maximum principle and the phase plane method. The authors of the article determine the structure of optimal fuel consumption processes with three levels of control, and the number of their switches depends on the initial conditions. Synthesized on the phase plane, the optimal switching curves divide the phase plane into eight curvilinear quadrants, which uniquely determine the values of the optimal control effects by the current values of the deviations of the angular velocities of the spacecraft. The problem of the possible presence of a delay in the control loop is proposed to be solved based on the Bess compensation method. To do this, the corresponding optimal curves of switching and disabling the controls are built as geometric locations of points remoted for the time of delay from the found curves of switching and the beginning of coordinates accordingly. It allows us to avoid the emergence of steady self-oscillations in a control contour and to provide a condition of keeping the spacecraft in a given final state after the completion of the stabilization process. Depending on the technical equipment of the spacecraft, two variants of the optimal damping algorithm are offered, namely: an autonomous device in the onboard control system of the spacecraft in the absence of a sufficiently powerful onboard computer, or the optimal damping algorithm, implemented entirely in the onboard computer of the spacecraft in case of its sufficient power.