Exponentially convergent velocity observer for an electrodynamic tether in an elliptical orbit

TYPICAL electrodynamic tether (EDT) system consists of two end bodies connected by a conductive tether in space [1]. The technological interest of EDT systems arises mostly from their potential utilization for reboosting the spacecraft's orbit or deorbiting defunct satellites and space debris. The electric current flowing in an EDTwill interact with the magnetic field of the Earth to generate the Lorentz force, by which the orbital elements of the system can be altered without expending propellant. Over the past decades, various key aspects of the EDT technology have been demonstrated by missions in orbit [1]. However, the concept of the EDT has also faced challenging and interesting problems related to dynamics, control, and physical implementation. In particular, the stability of the attitude motion of an EDT system has called special attention because of the continuous pumping of energy from the Lorentz force into the tether attitude motion [2]. Thus, the attitude motion of an EDT system should be carefully controlled to prevent the tether from tumbling. It is also important to note that an EDT system with a fixed length tether is underactuated by nature if no thruster is available on the end bodies and the only controllable variable is the electric current. This fact results in a challenging problem of single input and multiple outputs.