Computational control framework for tethered space systems using finite element method

Qi Zhang

doi:10.1016/j.actaastro.2024.12.013

2025-03-01

PRE

张

张崎 (Qi Zhang)

Zheng Zhu *

DOI：10.1016/j.actaastro.2024.12.013

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摘要

En 中文

This paper develops a computational feedback control framework for flexible tethered space systems by integrating dynamic models, state estimation, and optimal control with a moving horizon into a cohesive procedure using the finite element method. A high-fidelity dynamic model of the tethered space system is developed using the nodal position finite element method. The positions and velocities of the entire tether are estimated by a robust finite element Kalman state estimator. Then, optimal control in the finite element form is proposed to control the geometrical profile of flexible space tethers. The optimal control problem is recast into canonical equations by Hamilton's variational principle as a two-point boundary value problem with a moving terminal boundary condition. The control inputs are generated numerically from the canonical equations for closed-loop feedback control using a moving horizon. The effectiveness of the proposed computational optimal feedback control framework is verified through numerical simulations of an initially bent tethered space system. Analysis results show the proposed framework can be extended to other flexible elastic systems, indicating its potential for broader applications. The key advantages of the framework are algorithmic controller synthesis within a variational framework, preservation of high-fidelity of dynamic model in controller synthesis, and numerical algorithms in place of closed-form control commands for more adaptive and flexible control solutions.

Keyword:

Space tether

Dynamics

Optimal control

Computational control

Feedback

Hamilton principle

Canonical equations

Nodal position finite element method