论文:2012,Vol:30,Issue(2):196-200
引用本文:
王祥, 方群. 一种基于θ-D次优控制的三维末制导律设计[J]. 西北工业大学
Wang Xiang, Fang Qun. θ-D Approach-Based Design of 3-Dimensional Terminal Guidance Law[J]. Northwestern polytechnical university

一种基于θ-D次优控制的三维末制导律设计
王祥, 方群
西北工业大学 航天学院,陕西 西安 710072
摘要:
最优制导律在求解Hamilton-Jacobi-Bellman(HJB)方程时十分困难。θ-D方法是一种基于State Dependent Riccati Equation(SDRE)方法的新型次优控制方法,能够获得HJB偏微分方程的近似闭环解。针对最优制导律在求解HJB方程时十分困难的问题,文章在考虑导弹自动驾驶仪动态特性和末制导的三维真实拦截情况下,建立导弹和目标的三维相对运动方程,基于θ-D次优控制方法,经状态重定义后对模型方程的伪线性化处理,得到闭环形式的θ-D三维末制导律。为验证所提出制导律的制导性能,分别针对目标不机动和机动的拦截情况进行了数值仿真。仿真结果表明,相比自适应变结构制导律,文中设计的θ-D三维闭环末制导律能克服自动驾驶仪动态延迟对制导性能的影响;对于目标作大机动逃逸的情况,其制导性能更优。
关键词:    三维制导律    自动驾驶仪    θ-D方法    非线性次优控制   
θ-D Approach-Based Design of 3-Dimensional Terminal Guidance Law
Wang Xiang, Fang Qun
College of Astronautics,Northwestern Polytechnical University,Xi'an 710072,China
Abstract:
One of the terminal guidance problems based on optimal control is solving Hamilton-Jacobi-Bellman(HJB) partial differential equations. The θ-D method is a new suboptimal control method based on the State De-pendent Riccati Equation (SDRE) method, and has proven to be effective in solving the HJB equations approxi-mately. A suboptimal terminal guidance law is thus proposed for missiles intercepting maneuvering targets based onthe θ-D method. Sections 1, 2 and 3 of the full paper explain our proposed method, whose core consists of: " Thekinematical equations of the guidance problem is first formulated in the 3-dimentional space considering the autopi-lot lag; then, by redefining the state variables and transforming the nonlinear kinematics equations into a linear-likestructure, a closed form guidance law is then derived based on the θ-D method. "Finally, to verify the proposedguidance law, numerical simulations in section 4 respectively for intercepting the non-maneuvering and maneuveringtargets are made; the simulation results, presented in Figs. 2 through 4 and Table 1, and their analysis demonstratepreliminarily that, compared with the adaptive sliding mode guidance (ASMG) law, the proposed guidance law ismore effective in compensating for the bad influence of the autopilot lag on guidance accuracy.
Key words:    adaptive systems    approximation algorithms    design    efficiency    kinematics    maneuverability    mis-siles    nonlinear equations    optimal control systems    Riccati equations    sliding mode control    targets    three dimensional;autopilot    effects    nonlinear subopimal control    simulation    θ-D method    3-di-mensional guidance law   
收稿日期: 2011-05-12     修回日期:
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作者简介: 王祥(1988-),西北工业大学硕士研究生,主要从事导弹末制导律设计和飞行控制器设计研究。
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