APPLICATION OF THE PID CONTROL SYSTEM TO THE ROTATIONAL MOTION OF THE ARTIFICIAL SUBSATELLITE OF THE SPACE TETHER SYSTEM
DOI:
https://doi.org/10.69609/1516-2893.2025.v31.n1.a4006Keywords:
Palavras-chave: PID; STS; Satélite Artificial; Quatérnions; Sistemas de ControleAbstract
The present work aims to analyze and apply a PID control system in the rotational movement of a subsatellite S2 and its movement around the main satellite S1 of a Space Tether System, composed of two satellites connected by a cable in space. This study will be carried out through the numerical integrations of the equations of motion, starting from known initial conditions. The translational movement of the subsatellite around the main satellite is described in spherical coordinates (l, α, β), defined by the distance and angles that position the position vector between the two satellites. The results of the numerical propagation show that S2 moves around S1 in the orbital plane of S1 around the Earth and oscillates vertically to that plane. Rotational motion is described by Euler's equations and by kinematic equations, described by quaternions, because in certain situations the kinematic equations described by Euler's angles can present singularities, making it difficult to solve the problem. The adopted methodology aims to eliminate these singularities through quaternions, since the kinematic equations in terms of quaternions do not depend on trigonometric functions. As the adopted geometry is a parallelepiped for the subsatellite S2, its behavior regarding rotation is very similar along its x and z axes. The results of the numerical integration of the equations of rotational motion with quaternions highlight the proper behavior of the quaternions and the components of the rotational velocity of the subsatellite S2. The angular velocities stabilized close to 0 rad/s, even concluding that the control was not ideal, it presented good results for the problem analyzed at that moment.
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Copyright (c) 2025 Ramon Oliveira Borges dos Santos, Regina Elaine Santos Cabette, Leandro Baroni, Maria Cecília França de Paula Santos Zanardi, Giulliano Assis Sodero Boaventura
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