Electric sail active control law for artificial Lagrangian point maintenance

This paper discusses the problem of maintaining an L1-type artificial equilibrium point in the Sun-[Earth+Moon] circular restricted three-body problem by means of an Electric Solar Wind Sail. The working principle of such a propulsion system enables a continuous thrust to be generated, thanks to the electrostatic interaction between a charged grid of tethers and the solar wind ions, without any propellant consumption. The intrinsic instability of the reference configuration is compensated for with a feedback control law that adjusts the grid voltage as a function of the spacecraft distance from the (artificial) equilibrium point. A purely proportional and a proportional-derivative control strategies are analyzed, and their performance are investigated, by first assuming constant environmental properties, and then introducing the fluctuations of the solar wind dynamic pressure, which are modelled with a statistical approach.