E-sail Attitude Control with Tether Voltage Modulation

The Electric Solar Wind Sail (E-sail) is a propellantless propulsion system that gains thrust from the interaction of solar wind particles with a grid of long charged tethers, which are deployed by spinning the spacecraft about a symmetry axis. In an ideal situation, the tethers are perfectly stretched and the E-sail takes the shape of a rigid disk. Actually, the solar wind dynamic pressure warps the tethers and, therefore, the expressions of the thrust and torque vectors are difficult to predict. Recent works have shown that the bending of the tethers induces a disturbance torque, which can be counterbalanced through a modulation of the tether electrical voltage. Under the assumption that the E-sail behaves like an axiallysymmetric rigid body, this paper proves that the modulation of the tether electrical voltage is a promising option for controlling and maintaining the spacecraft attitude. The proposed control law, which is analytically provided as a function of time and current sail attitude, is validated through numerical integration of the attitude dynamic equations.