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Recently there has been a resurgence of interest in missions to the moon and a major challenge of such missions is to provide a continuous communication between the Earth and the Moon's far side. Orbits around the $L_2$ Earth-Moon Lagrange point have been a topic of interest in this field due to their potential for constant communication with both the Earth and the Moon, however the Lagrange point orbits are innately unstable and so station-keeping control is required to maintain them. Station-keeping problems are highly nonlinear and a traditional approach to control design is first to linearize the nonlinear system. However, this first-order approximation introduces errors if there are large injection errors. This paper demonstrates how a simple Extended State Observer (ESO) can be used to improve the convergence time of spacecraft to the reference orbit given with large injection errors. Additionally, solar radiation pressure (SRP) a dominant disturbance in deep-space, can lead to inefficient station-keeping if it is not taken into account in the reference orbit design. New reference orbits can be designed that exploit the SRP perturbation but this assumes that it is known apriori. Here we show how an ESO could provide an in-orbit measurement of the SRP which could be used to modify the reference trajectory to a more fuel efficient one. Finally, it is shown how an ESO can be used to estimate, not only the disturbance, but simultaneously the velocity of the spacecraft meaning that only the position of the spacecraft is required.

Enhancing Station-Keeping Control With the Use of Extended State Observers