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Minimum sliding mode error feedback control for inner-formation satellite system withJ2 and small eccentricity

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Abstract

With the recent flurry of the research on Inner-Formation satellite system, there has been apparent need for a set of linearized equations to describe the relative motion of satellites under the effect of theJ2 geopotential disturbance, which is the important perturbed-factor for low-orbit Inner-Formation system. Hence, on the assumption of small eccentricity, a new set of linearized equations of motion is proposed that accounts forJ2 perturbations in an elliptical orbit. To avoid the collision between the inner satellite and the outer satellite, the Minimum Sliding Mode Error Feedback Control (MSMEFC) is developed to perform a real-time control on the outer satellite with the uncertain perturbations from the space. The highlight of MSMEFC is to introduce the concept of equivalent control error, which is the key utilization of MSMEFC. It is shown that the proposed MSMEFC can compensate any kinds of uncertain perturbations. Besides, in this paper, the relationship between the equivalent control error and uncertain perturbations is discussed. The robustness and steady-state error of MSMEFC are also analyzed to show its theoretical advantages compared with traditional SMC. Numerical simulations are employed to check the fidelity of the linearized equations. In addition, the efficacy of MSMEFC is verified by the utilization of Inner-Formation system with high control precision.

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Authors and Affiliations

  1. The State Key Laboratory of Astronautic Dynamics, China Xi’an Satellite Control Center, Xi’an, 710073, China

    Lu Cao

  2. College of Aerospace Science and Engineering, National University of Defense Technology, Changsha, 410073, China

    Xiaoqian Chen

Authors
  1. Lu Cao

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  2. Xiaoqian Chen

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Correspondence toLu Cao.

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Cao, L., Chen, X. Minimum sliding mode error feedback control for inner-formation satellite system withJ2 and small eccentricity.Sci. China Inf. Sci.59, 072203 (2016). https://doi.org/10.1007/s11432-016-5573-1

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