Removing singularity of orientation description for modeling and controlling an electrodynamic tether
Hao Wen, Dongping Jin and Haoyan Hu
Abstract: This Note presents a nonsingular formulation for modeling the attitude dynamics of the EDT system under the dumbbell assumption. Different from the conventional model in terms of two angular parameters, the governing equations of the attitude dynamics in this Note use a unit vector along the EDT for orientation definition. Consequently, the proposed formulation of the attitude dynamics inherently avoids the singularities arising from the conventional modeling method based on angular parameterization. In the absence of singularities, the proposed dynamic model makes it possible to globally reveal the dynamic behavior of the system over the complete configuration space of the EDT’s attitude. As an illustrative example, a feedback control law of the electric current is synthesized using the nonsingular formulation to stabilize the libration motions of the EDT system, with the consideration of the maximally allowable strength of the electric current. The stability characteristic of the controlled EDT system is clarified through the global Lyapunov analysis over the complete configuration space. Besides, it is further demonstrated by two numerical case studies that the libration motions of the EDT system can be effectively stabilized via the active regulation of the electric current within the prescribed bounds.
