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Model predictive control for electrodynamic tether geometric profile in orbital maneuvering with finite element state estimator

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Abstract

This paper studies the control of the geometric profile of a librating electrodynamic tether by model predictive control using the induced electric current in tether only. First, a high-fidelity multiphysics model of an electrodynamic tether system is built based on the nodal position finite element method and the orbital-motion-limited theory. Second, a state estimator is proposed to estimate the geometric profile of a librating electrodynamic tether, where only the positions and velocities at the tether ends are measurable. The non-measurable geometric profile of the tether between two ends is estimated by the high-fidelity multiphysics model with the input of the measurement at tether ends in the spatial domain. The extended Kalman filter is applied to estimate the geometric profile of the tether while avoiding the singularity or ambiguity in the estimation. Third, the geometric profile control of a librating electrodynamic tether is converted into a trajectory tracking problem of the underactuated electrodynamic tether system. The induced electric current in the tether is the only control input. Its value is optimized by the model predictive control method subject to the output and input control constraints. The numerical simulation results show that the proposed approach can effectively control the shape of the librating electrodynamic tether to the reference trajectory.

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Availability of data and material

Data sharing not applicable to this article as no datasets were generated or analyzed during the current study.

Code availability (software application or custom code)

The custom codes in the current study are available from the corresponding author on reasonable request.

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Funding

This work is supported by the Discovery Grant (RGPIN-2018–05991) and Discovery Accelerator Supplements Grant (RGPAS-2018–522709) of Natural Sciences and Engineering Research Council of Canada.

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Authors and Affiliations

  1. Department of Mechanical Engineering, York University, 4700 Keele Street, Toronto, ON, M3J 1P3, Canada

    Gangqiang Li & Zheng H. Zhu

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  1. Gangqiang Li
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  2. Zheng H. Zhu
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Contributions

Dr. Gangqiang Li was the co-investigator of the project, conducted formal analysis and methodology development, coding, data analysis, and draft writing. Dr. Zheng H. Zhu was the principal investigator of the project, led the conceptualization and methodology development, formal analysis, acquired funding, project administration, and writing and editing of paper.

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Correspondence to Zheng H. Zhu.

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Li, G., Zhu, Z.H. Model predictive control for electrodynamic tether geometric profile in orbital maneuvering with finite element state estimator. Nonlinear Dyn 106, 473–489 (2021). https://doi.org/10.1007/s11071-021-06869-3

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