Chebyshev-series solutions for nonlinear systems with hypersonic gliding trajectory example

Jin Yang; Wenbin Yu; Wanchun ChenBo LiaoHengwei Zhu

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Chebyshev-series solutions for nonlinear systems with hypersonic gliding trajectory example

机译：Chebyshev-series solutions for nonlinear systems with hypersonic gliding trajectory example

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摘要

In order to design a drag-based predictor-corrector entry guidance in the future, new analytical formulae, expressed as finite-term Chebyshev series, are developed for fast predicting a three-dimensional (3D) Hypersonic Gliding Trajectory (HGT) by proposing a Newton-like method to solve a highly nonlinear entry dynamics model. Specifically, first, a new reduced-order dynamics model is developed by properly simplifying the original dynamics model such that the drag acceleration (A_D) and the ratio of the horizontal component of the lift to the drag (L_(Dz)), which are important for governing the 3D trajectory, emerge as key parameters of the dynamical equations. Then, A_D and L_(Dz) are planned as polynomials of speed. However, the simplified model is still not easy to solve due to its high nonlinearity. To deal with the difficulty, a Newton-like method is proposed to transform the simplified model into Linear Differential Recurrence Equations (LDREs). By evaluating the LDREs repeatedly, a sequence of approximations of the 3D HGT can be generated, the limit of which is the trajectory specified by that simplified model. In fact, due to the fast convergence speed of the Newton-like method, the LDREs need be solved only twice to achieve high accuracy. By using Chebyshev series to approximate some complex terms appearing in the LDREs, the LDREs become analytically solvable. As a result, the approximate analytical solutions to the 3D HGT are obtained. Simulation results show that the analytical solutions need to consume less than 1 ms of time on a laptop computer and have errors of less than 4 percentage. The computational efficiency is fundamental for onboard predictor-corrector guidance.

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来源
《Aerospace science and technology》 |2023年第9期|108424.1-108424.25|共25页
作者
Jin Yang; Wenbin Yu; Wanchun ChenBo LiaoHengwei Zhu;
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作者单位

School of Astronautics, Beihang University, Beijing 102206, China;

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收录信息美国《科学引文索引》(SCI);美国《工程索引》(EI);
原文格式 PDF
正文语种英语
中图分类航空;
关键词
Hypersonic gliding trajectory; Analytical trajectory solutions; Drag-acceleration profile; Newton-like method; Chebyshev series;

Chebyshev-series solutions for nonlinear systems with hypersonic gliding trajectory example

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