# ATTITUDE CONTROL OF SATELLITE WITH PROPELLANT SLOSHING DYNAMICS

## Palavras-chave:

Attitude control, Sloshing, LQR, Equivalent mechanical model## Resumo

Space vehicles can carry large amounts of liquid propellant in their tanks, especially

when performing interplanetary missions. When these tanks are not completely filled, the move-

ment of the vehicle excites the propellant such that the free surface of the liquid describes an

oscillatory movement. This movement confined inside the tank is known as sloshing. Depend-

ing on the type of excitation and the geometry of the tank, the liquid sloshing may have an

infinite number of natural frequencies; these frequencies tend, in turn, to excite the movement

of the vehicle and, consequently, affect attitude control. This paper investigates the attitude

control of a satellite, modeled as a rigid body, whose motion is coupled with the slosh effect

of the liquid propellant in its interior, represented by an equivalent mechanical model, in this

case a simple pendulum. The equations of motion are obtained through Lagrangian formalism.

The excitation frequency is assumed to be remote from resonance. Only small amplitudes of

oscillation are allowed for the pendulum, so that the free surface remains planar without rota-

tion of its nodal diameter. Attitude control is investigated for different volumes of liquid in the

tank. The control technique used is the Linear Quadratic Regulator (LQR) and the results are

obtained numerically.