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.

Keywords:

• Vibration control
• flexible spacecraft system
• viscoelastic damping
• PDEs
• dynamic boundary condition
• Euler–Bernoulli beam

AMS CLASSIFICATIONS:

• 35L20
• 93D15
• 93D20

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by the Directorate General for Scientific Research and Technological Development [grant number C00L03UN440120220001].