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Fuel efficient periodic gain control strategies for spacecraft relative motion in elliptic chief orbits

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Abstract

Periodic gain continuous control strategies are applied to the nonlinear time periodic equations of spacecraft relative motion when the chief orbit is elliptic. Specifically, control strategies based on time-varying linear quadratic regulator (LQR), Lyapunov–Floquet transformation (LFT) with time-invariant LQR, LFT with backstepping, and feedback linearization are implemented and shown to be much more fuel efficient than constant gain feedback control. Both natural and constrained leader-follower two-spacecraft formations are studied. Furthermore, a dead-band control is added for the constrained formation to reduce the amount of the fuel used. The closed-loop response and control effort required are investigated and compared for the same settling time envelopes for all control strategies.

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Acknowledgments

We are grateful for contribution of Dr. Afshin Mesbahi for the derivations of the control gain matrix for the constant gain feedback control [Eq. (43)].

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Authors and Affiliations

  1. Department of Aerospace and Mechanical Engineering, University of Arizona, Tucson AZ, 85721, USA

    Morad Nazari & Eric A. Butcher

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  1. Morad Nazari
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  2. Eric A. Butcher
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Correspondence to Morad Nazari.

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Nazari, M., Butcher, E.A. Fuel efficient periodic gain control strategies for spacecraft relative motion in elliptic chief orbits. Int. J. Dynam. Control 4, 104–122 (2016). https://doi.org/10.1007/s40435-014-0126-1

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  • DOI: https://doi.org/10.1007/s40435-014-0126-1

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