Equilibrium Control of Electrodynamic Tethered Satellite Systems in Inclined Orbits

Abstract

S INCE the idea of the space tether system was suggested, much work has been done in this field. A main concern of tether research is control of the motion of the tether. Pasca [1] investigated the control of in-plane transversal vibrations of a tethered satellite system using a longitudinal thrust force. Two nonlinear control laws were developed to stabilize the station-keeping phase of the tether system. Brian and Jordi [2] developed a linear control system to control the unstable mode of an atmospheric tether system, with the tether modeled as a rigid rod, by using the attachment point motion and thrust as inputs. Yu [3] investigated a dynamic model for control of a mass-distributed and extensible tether system by considering the stationary configuration of the system. Tani and Qiu [4] proposed a two-dimensional motion control of the tethered satellite by using electrodynamic force generated through the interaction between the geomagnetic field and an applied electric current passing through the tether. Pelaez and Lorenzini [5] proposed two control schemes by using electrodynamic force to convert an unstable periodic orbit of the system into an asymptotically stable one. Williams et al. [6] developed a control method by using both tension and electromagnetic forces to regulate the librational motion of the tethered satellite system. Mankala and Agrawal [7] suggested a feedback control law for implementation of the in-plane tether maneuvers from one equilibrium configuration to another by means of electrodynamic force which is generated by the interaction between tether current and geomagnetic field. The stability control of equilibrium positions is an important technical problem. Steiner et al. [8] proposed a method to control the in-plane oscillation about the radial equilibrium positions by adjusting the tether tension with a tether modeled as a massless and rigid one. However, Steiner [8] only considered the in-plane motion of the tethered satellite system. In this paper, a more complete model of a tethered satellite system is considered, in which a main satellite and a subsatellite is connected by a conductive tether with mass distributed along it. To regulate both the in-plane and out-of-plane motions of the tether, the current and the rate of change in tether length are employed as two control parameters. A feedback control law is proposed to maintain the radial equilibrium position of the system. It is found that this control law is not applicable for the equatorial plane because no out-of-plane force is available there. For each inclined orbit, it is shown that there are two singularity points. To avoid these points, and by considering some other practical restrictions, the proposed control law is divided into four conditional parts. Numerical examples are provided in this Note and the results validate the applicability of the proposed control law.