弹道可调的落角约束分数阶滑模制导律设计

doi:10.7527/S1000-6893.2022.27073

Abstract

Abstract:

A time-varying sliding mode guidance law based on fractional calculus is presented for the terminal guidance problem with corner constraint. The guidance trajectory can be adjusted in advance by setting parameters，and the introduction of fractional order increases the variability and diversity of the guidance trajectory. The stability of the guidance law is proved by using the Lyapunov stability theory. Through the fractional order integral mean value theorem，the fractional order differential equation is transformed into a first-order linear differential equation，which is used to solve the analytical formula of state error. Finally，the convergence of the guidance law is proved by using the Squeeze Theorem. The simulation results show that the guidance law can change the trajectory form in a large range while ensuring high guidance accuracy，which makes the guidance trajectory complex and difficult to predict.

Key words: guidance law, sliding mode control, fractional calculus, falling angle constraint, trajectory planning

CLC Number:

V448

Yongzhi SHENG, Jiahao GAN, Chengxin ZHANG. Fractional order sliding mode guidance law design with trajectory adjustable and terminal angular constraint[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2023, 44(7): 327073-327073.

Figures/Tables 9

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References 30

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参数	数值
导弹初始位置（x₀，y₀）/km	（0，30）
目标位置（x_f，y_f）/km	（80，0）
初始弹道倾角γ₀/（°）	-30
期望撞击角γ_f/（°）	-90
初始速度v₀/（m·s^-1）	2 000
切换项增益系数K	0.002
分数阶阶次λ	0.2
指数增益系数p，q	1，1
比例增益系数n，C₂	4，0.003

参数	均值	方差
脱靶量/m	2.68×10^-3	2.04×10^-6
落角误差/（°）	8.18×10^-2	3.52×10^-3

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Fractional order sliding mode guidance law design with trajectory adjustable and terminal angular constraint

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