Nonlinear Mathematical Modeling and Vibration Suppression Control of a Flexible Tethered Satellite System in an Orbital Transfer Mission

Abstract

Due to the risks that the debris satellites pose to missions, one of the more recent study subjects in space is the removal of these debris masses from orbit. The usage of tethered satellites is one of the various approaches that are suggested for this objective and is taken into consideration in this research. That is, a tether from an operational satellite moves the debris satellite to a lower Earth orbit. This is done by extracting the mathematical model of the in-plane motion of a flexible tethered satellite system. The assumption of large deformations is also used for flexible appendages, which results in highly nonlinear governing equations. Four different types of controllers have been developed with the intention of suppressing the oscillations of flexible panels with an orbital transfer at a certain velocity decrease. Except for the basic PID controller, the other three are extensions of the classical form of sliding mode controller. In theory, every controller has unique qualities. Applying these features to the system in a computer simulation allows for their verification. The controllers' relative levels of efficacy are contrasted.