Vibration control of a flexible satellite system with viscoelastic damping

Abstract

In this article, we are concerned with a viscoelastic flexible spacecraft subject to undesirable vibrations during attitude maneuvering. The system is composed of a centre body and two symmetric flexible appendages. The problem can be modelled by a set of partial differential equations taking into account therefore the dynamic boundary condition. Under a suitable control force applied at the center body of the spacecraft system, we shall attenuate these vibrations in a fast manner. Namely, we prove the arbitrary stabilisation of the system under appropriate assumptions imposed on the relaxation function. Finally, numerical examples illustrate the effectiveness of the proposed control scheme.