Parametric Control of Plane Motions of a Barbell Shaped Satellite

Аuthors

Bezglasnyi S. P.^1*, Krasnov M. V.^2**, Mukhametzyanova A. A.^1***

1. Samara National Research University named after Academician S.P. Korolev, 34, Moskovskoye shosse, Samara, 443086, Russia
2. Space Rocket Centrе Progress, 18, Zemets str., Samara, 443009, Russia

*e-mail: bezglasnsp@rambler.ru
**e-mail: maxasgard@mail.ru
***e-mail: alain.20@mail.ru

Abstract

The paper considers the problem of a barbell shaped artificial satellite plane motions control. The satellite is modeled as a weighable rod with two point masses, fixed at its ends. The third mass point can move along the rod. The satellite motions in relation to its center of mass take place in Newtonian gravitational field. The barbell shaped satellite has two stable equilibrium positions in circular orbit.

The authors discuss the possibilities of a pendulum oscillation build-up and damping parametric control in the vicinity of low equilibrium position. Problems of the gravitational stabilization with reference to plane disturbances of diametrically opposite relative equilibrium positions of the satellite in a circular orbit are studied.

A continuous control law of a moving mass is formulated according to a swing-by concept. We implement the control law by continuous variation of the distance between the satellite center of mass and the moving mass. This control represents the function, depending on the phase state vector representative point of the barbell shaped satellite.

The goal of this paper is building new control laws with preset properties. These laws should realize the processes of the satellite oscillation build-up and damping in the vicinity of low equilibrium position. Moreover, they should provide the satellite re-orientation, while it moves from one equilibrium position to the other, diametrically opposite, as well as gravitational stabilization of the satellite two opposite equilibrium position in relation to the local vertical.

We solved the problem by the method of Lyapunov’s functions of the classical theory of stability.

In this paper control laws of oscillation build-up and damping, diametrical reorientation and gravitational stabilization in relation to the local vertical of the dumbbell shaped artificial satellite are built. The Lyapunov’s functions that prove the asymptotic stability and instability of the satellite two equilibrium positions in cases of its damping and oscillation build-up correspondingly are selected. It is shown that with controlled movements according to the first law the asymptotic damping of oscillation amplitude of satellite occurs under any initial conditions of the movements. When implementing control according to the second law the growth of the oscillations amplitude and transition from oscillatory to rotational motion takes place. Theoretical results are illustrated by graphical representation of the numerical results.

The results presented in the paper can be used for modeling and control of plane pendulum movements of various space mechanical systems.

Keywords:

barbell shaped satellite, moving mass, gravitational torque, Lyapunov's function, asymptotical stability

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