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Research Papers

Linearized J2 and Atmospheric Drag Model for Control of Inner-Formation Satellite System in Elliptical Orbits

[+] Author and Article Information
Lu Cao

The State Key Laboratory
of Astronautic Dynamics,
China Xi'an Satellite Control Center,
Xi'an 710043, China
e-mail: lu.cao2@mail.mcgill.ca

Hengnian Li

The State Key Laboratory
of Astronautic Dynamics,
China Xi'an Satellite Control Center,
Xi'an 710043, China
e-mail: Henry_xscc@aliyun.com

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received April 6, 2015; final manuscript received January 18, 2016; published online March 9, 2016. Assoc. Editor: Ming Xin.

J. Dyn. Sys., Meas., Control 138(5), 051004 (Mar 09, 2016) (15 pages) Paper No: DS-15-1158; doi: 10.1115/1.4032745 History: Received April 06, 2015; Revised January 18, 2016

A new set of linearized differential equations governing relative motion of inner-formation satellite system (IFSS) is derived with the effects of J2 as well as atmospheric drag. The IFSS consists of the “inner satellite” and the “outer satellite,” this special configuration formation endows its some advantages to map the gravity field of earth. For long-term IFSS in elliptical orbit, the high-fidelity set of linearized equations is more convenient than the nonlinear equations for designing formation control system or navigation algorithms. In addition, to avoid the collision between the inner satellite and the outer satellite, the minimum sliding mode error feedback control (MSMEFC) is adopted to perform a real-time control on the outer satellite in the presence of uncertain perturbations from the system and space. The robustness and steady-state error of MSMEFC are also discussed to show its theoretical advantages than traditional sliding mode control (SMC). Finally, numerical simulations are performed to check the fidelity of the proposed equations. Moreover, the efficacy of the MSMEFC is performed to control the IFSS with high precision.

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Figures

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Fig. 1

Illustration of inner–outer formation system

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Fig. 2

Relative motion J2 and atmospheric drag e = 0.01–10 orbits

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Fig. 3

Relative motion in three directions J2 and atmospheric drag e = 0.01–10 orbits

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Fig. 4

Relative motion J2 and atmospheric drag e = 0.01–10 orbits—different initial conditions

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Fig. 5

Relative motion errors J2 and atmospheric drag e = 0.01–2 orbits

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Fig. 6

Relative motion sliding mode and control force J2 and atmospheric drag e = 0.01–2 orbits

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Fig. 7

Equivalent control error and estimated perturbations J2 and atmospheric drag e = 0.01–2 orbits

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Fig. 8

Relative motion errors for serious case J2 and atmospheric drag e = 0.01–2 orbits

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Fig. 9

Relative motion sliding mode and control force for serious case J2 and atmospheric drag e = 0.01–2 orbits

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Fig. 10

Equivalent control error and estimated perturbations for serious case J2 and atmospheric drag e = 0.01–2 orbits

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