Title: Optimal trajectory design of a deorbiting electrodynamic tether system

Authors: Rui Zhong; Zheng H. Zhu

Addresses: Department of Earth and Space Science and Engineering, York University, 4700 Keele Street, Toronto, Ontario M3J 1P3, Canada ' Department of Earth and Space Science and Engineering, York University, 4700 Keele Street, Toronto, Ontario M3J 1P3, Canada

Abstract: This paper studies the optimal control problem of a nano-satellite deorbiting by a short electrodynamic tether. The optimal control theory is introduced by forming the control problem as a cost index minimisation subjected to several constraints. A direct method based on Hermite-Simpson discretisation is adopted to solve the constraint cost minimisation problem, resulting in an optimal trajectory including the time history of the states and control input, which achieves best deorbiting efficiency and libration stability simultaneously under the given mission requirements. In order to reduce the computation efforts, the continuous deorbiting process of an electrodynamic tether is discretised into a sequential time intervals, where during each interval the slowly varying orbital parameters of the electrodynamic tether are assumed constant. Thus, the whole optimal trajectory is obtained by combining the solutions to the optimal control problems in the intervals. Numerical simulations are performed to test the performance of the optimal trajectory by applying the control input profile to an electrodynamic tether under complex environment perturbations.

Keywords: electrodynamic tethers; EDTs; attitude control; optimal control; direct method; Hermite-Simpson discretisation; space science; optimal design; trajectory design; deorbiting tether systems; nanosatellites; numerical simulation.

DOI: 10.1504/IJSPACESE.2013.054459

International Journal of Space Science and Engineering, 2013 Vol.1 No.2, pp.128 - 141

Received: 16 Feb 2013
Accepted: 05 Mar 2013
Published online: 30 Apr 2014 *

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