This paper discusses the maintenance of an L1type artificial equilibrium point in the Sun-[Earth+Moon] circular restricted three-body problem by means of an Electric Solar Wind Sail. The reference configuration instability is compensated for with a feedback control law that adjusts the grid voltage as a function of the distance from the natural L1 point. Two different control strategies are analyzed assuming the solar wind fluctuations to be modelled through a statistical approach.Index Terms-Electric Solar Wind Sail, artificial Lagrangian equilibrium point, solar wind fluctuations, circular restricted three-body problem
I. IntroductionA N Electric Solar Wind Sail (E-sail) is an innovative propulsion system, invented in 2004 by Pekka Janhunen [1], which generates a propulsive acceleration by exploiting the solar wind dynamic pressure through the electrostatic interaction between a grid of charged tethers and the solar wind ions. After an on-ground experimental campaign [2], [3], the first in-flight testing of E-sail technology is being attempted in a geocentric environment by flying a variant of the E-sail working principle, the plasma brake [4], [5], [6]. The latter is a deorbiting system, consisting of a single charged tether that interacts with ions in the ionosphere to generate a drag. The first test was tried by the Estonian satellite EstCube [7], but a failure to the tether unreel mechanism occurred [8]. Currently, the Finnish Aalto-1 [9] satellite is equipped with a plasma brake tether that should enable an end-of-life deorbiting [10].The major advantage of an E-sail-based spacecraft over more conventional systems is in its capability of providing thrust without consuming any propellant mass [11], [12],[13], [14], in a similar way to a solar sail [15]. The latter however uses the interaction of the solar radiation pressure with a large and highly reflective surface. The peculiarity of propellantless propulsive systems allows exotic mission scenarios to be envisaged, such as the creation and maintenance of an artificial equilibrium point (AEP) in which the relative position of the spacecraft is constant with respect to the Sun and the [Earth+Moon]. Indeed, because an