Feedback Control Law of Solar Sail with Variable Surface Reflectivity at Sun-Earth Collinear Equilibrium Points

A solar sail generates thrust without consuming any propellant, so it constitutes a promising option for mission scenarios requiring a continuous propulsive acceleration, such as the maintenance of a (collinear) L1-type artificial equilibrium point in the Sun-[Earth+Moon] circular restricted three-body problem. The usefulness of a spacecraft placed at such an artificial equilibrium point is in its capabilities of solar observation, as it guarantees a continuous monitoring of solar activity and is able to give an early warning in case of catastrophic solar flares. Because those vantage points are known to be intrinsically unstable, a suitable control system is necessary for station keeping purposes. This work discusses on how to stabilize an L1-type artificial equilibrium point with a solar sail by suitably adjusting its lightness number and thrust vector orientation. A full-state feedback control law is assumed, where the control gains are chosen with a linear-quadratic regulator approach. In particular, the numerical simulation results show that an L1-type artificial equilibrium point can be maintained with small required control torques, by using a set of reflectivity control devices.