Three-dimensional deployment of electro-dynamic tether via tension and current control with constraints

The concept of space tether has found a great deal of promising applications in space engineering. A prerequisite of any space tether mission is to deploy its tether to a commanded length. This paper aims to achieving the three-dimensional deployment of an electro-dynamic tether system in a propellant-free manner via the feedback control of the tension and electric current in the tether. The proposed controller is formulated in an analytical form with an extremely low level of computational load, and can explicitly account for the physical bounds of the tether tension and electric current by using a pair of strictly increasing saturation functions. In addition, the Lyapunov analysis is made to gain an insight into the stability characteristics of the proposed control strategy. To facilitate the theoretical analysis, the dynamic model of the system is developed under the widely used dumbbell assumption, along with the geomagnetic field modeled using a tilted dipole approximation. Finally, numerical case studies on a representative electro-dynamic tether system are conducted to evaluate the performance of the proposed controller and the influence of the actuating conditions and orbital inclinations.