Dynamic Response of a Tethered System with Large Deformation and Large Displacement under Attitude Control

Abstract

In this paper, we discuss the dynamic response of a system consisting of a very flexible body and rigid bodies at its end under attitude control to the end body. A tethered subsatellite in space is known as an example of this system. Two mathematical models for a planer motion of a flexible body are considered using FEM and Absolute Nodal Coordinate Formulation. In A.N.C Formulation, it is easy to describe the motion of the flexible body with large deformation, rotation and translation displacement. We attempt to control the attitude of the end body using a reaction wheel. The control technique consists of an attitude control by the reaction wheel and a control by the reaction wheel with the joint torque control to cancel accumulation of angular momentum. First, eigenvalue analysis is carried out where control gain changes. Second, the motion under controlled system is discussed its free vibration, comparing the motions of FEM model and A.N.C one. It is pointed out that the axial stress in the tether plays an important role as constraint force at the joint between the tether and the rigid body. Furthermore we treat large deformation, large displacement problem, where the end of the flexible body moves horizontally. We confirm the interaction between flexible body with large deformation and rigid body under the attitude control and clarify its mechanism.