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Mathematical Problems in Engineering
Volume 2014, Article ID 410989, 14 pages
Research Article

Active Disturbance Rejection Station-Keeping Control of Unstable Orbits around Collinear Libration Points

1Department of Automation, University of Science and Technology of China, Hefei 230027, China
2Department of Engineering, Faculty of Engineering and Science, University of Agder, 4876 Grimstad, Norway
3School of Engineering and Information Technology, University of New South Wales at the Australian Defence Force Academy, Canberra, ACT 2600, Australia

Received 15 January 2014; Accepted 13 March 2014; Published 10 April 2014

Academic Editor: Shen Yin

Copyright © 2014 Min Zhu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


An active disturbance rejection station-keeping control scheme is derived and analyzed for station-keeping missions of spacecraft along a class of unstable periodic orbits near collinear libration points of the Sun-Earth system. It is an error driven, rather than model-based control law, essentially accounting for the independence of model accuracy and linearization. An extended state observer is designed to estimate the states in real time by setting an extended state, that is, the sum of unmodeled dynamic and external disturbance. This total disturbance is compensated by a nonlinear state error feedback controller based on the extended state observer. A nonlinear tracking differentiator is designed to obtain the velocity of the spacecraft since only position signals are available. In addition, the system contradiction between rapid response and overshoot can be effectively solved via arranging the transient process in tracking differentiator. Simulation results illustrate that the proposed method is adequate for station-keeping of unstable Halo orbits in the presence of system uncertainties, initial injection errors, solar radiation pressure, and perturbations of the eccentric nature of the Earth's orbit. It is also shown that the closed-loop control system performance is improved significantly using our method comparing with the general LQR method.