Study on Stationkeeping for Halo Orbits at EL1: Dynamics Modeling and Controller Designing

Abstract

This paper deals with the stationkeeping control for halo orbits at EL₁ in the Sun-Earth/Moon system, and proposes an effective adaptive robust controller for the unknown spacecraft mass and perturbation boundaries. The controller has to deal with two divergence sources: one is the instability of the halo orbit, and the other is the perturbation imposed by the natural model onto the nominal model. The former source is displayed by the Floquet multiplier from the Poincaré mapping. However, the latter is revealed by the difference of Hamiltonian functions between the nominal reference model, the circular restricted three-body problem (CR3BP) and the natural simulation model, the spatial bicircular model (SBCM). Firstly, the algorithm of backstepping control theory is employed to generate the initial controller in the nominal reference model of CR3BP. Some improvements are then implemented for the estimations of the unknown parameters as the perturbation boundaries and the spacecraft mass, which may cause the failure of the initial unimproved controller in stationkeeping. The controller proves to be effective in terms of adaptive robust estimation and asymptotic stability from Lyapunov's stability theory. Furthermore, further improvements of the triggers for the on/off schedule are proposed to remedy the weakness in the capability of estimating for excessively long (infinite) time required to converge. Finally, the controller developed in this paper is implemented in the natural simulation model of SBCM to evaluate its performance. In the numerical simulation, the mass and perturbation boundaries will converge only after approximately three iterations. The deviation of the estimating mass is 1 kg from its true mass, but 55 kg for the unimproved controller. The total velocity increment over five years is only 126 m/s, which is equivalent to the fuel consumption of 3.8 kg for the Hall thrust engine carried by SMART-1.