An analysis of vibration and wave-absorbing control of tether systems

Abstract

Tether Dynamics is a very complex phenomenon. To model tension gradients along the tether, its flexibility and transverse motions are described by a set of partial deferential equations. Wave-absorbing control is employed to suppress the vibration of the tether by using actuator on the mother satellite. In addition, traveling wave control is designed using the actuator, and it aims to damp the libration of present tether system of constant length. The numerical results show the behaviors of the transverse motions of the tether, and the satisfactory performance of these controllers damping the motions of present system, and the results are shown by Virtual Reality Modeling Language (VRML). INTRODUCTION The dynamics of a tether system in a station-keeping phase are mainly studied from the following three perspectives for a constant length of tether: libration or liberation of the tether system; string vibration or wave motion of flexible tether; and rigid body motion of a mother satellite or a sub-satellite. Taking the linear density of the tether into consideration, transverse motions of the tether can be treated similarly for the vibration of a string, which has a certain tension gradient along its length. [1][2]. The traveling wave approach is applied by Von Flotow, to the control problem of large space structures (LSS) [3] [4]. He has introduced the viewpoint that the elastic response of LSS may be aptly viewed in terms of the disturbance propagation characteristics of the structure. Wave absorbing control is studied in many fields of engineering and is mainly studied in order to suppress flexible vibration of LSS, such as in the Copyright © 2001 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved. *Professor, Department of Aerospace Engineering of TMIT. Associate Fellow AIAA. **Graduate Student, Department of Aerospace Engineering of TMIT. *** Associate Professor, Department of Aerospace Engineering of RMIT. experimental study of a flexible beam by Fujii et. Al [5] [6]. On the other hand, disturbances at the mother satellite side can produce transverse waves in the tether system and can also affect to the libration of the sub-satellite. Control law for libration has been studied for a small tethered satellite by utilizing the attitude motion of a mother satellite with a fixed arm [7]. In the present paper, two methods are described to control the tethered sub-satellite system by using the actuator on the mother satellite. The wave-absorbing controller of the tether system is designed to suppress the vibration of tether and a control input is applied to actuate the boundary condition of the tether at the end of mother satellite. Also, a traveling wave control method is designed to damp the libration of a sub-satellite by controlling the transverse motion propagating as waves. The motion of the system is described by the partial differential equations, and the Crank-Nicolson's implicit method is employed to analyze the behavior of the transverse vibration of the tether. Results of the numerical analysis show that the present controllers have satisfactory performance to suppress the disturbed motion of the tether system and to damp the libration of the tether system. Some of the results are shown using the Virtual Reality Modeling Language (VRML). VRML can display the simulation results by using 3D animations with brilliant interactive graphics and audio effects [8]. Some of the results from the present study described by VRML files can be downloaded [9].