Using Sliding Mode Control to Set Up a Rotating Electrodynamic Space Tether System

Abstract

The paper considers the process of imparting rotation at a given angular velocity to an electrodynamic space tether system in a near-Earth orbit. The tether system is a linear cluster of three microsatellites connected by insulated conductive cables. Initially the system is gravitationally stabilised in the approximate vertical direction. Electromagnetic forces generated in the conductive cables by the geomagnetic field impart rotation to the system. We stated the equations of motion for the system in the Earth-fixed coordinate system, taking into account distributed load produced by gravitational and electromagnetic forces. The system is moving in a fairly high, almost circular orbit, so aerodynamic forces are not taken into account. Adjusting the current will reduce the strain in the tethers. The model under consideration represents those as a set of material points connected by unilateral elastic links. We propose a feedback current controller based on sliding mode control. The system variables lie on a single surface, moving across which ensures asymptotic stability of the control process. We used a simplified system motion model to synthesise the controller parameters. We analysed the angular motion of microsatellites with respect to the tether direction while rotation is imparted to the system. Numerical examples confirm the efficiency of our approach to setting up a rotating space tether system