基于Radau伪谱法的制导炸弹最优滑翔弹道研究

doi:10.3969/j.issn.1000-1093.2014.08.007

兵工学报 ›› 2014, Vol. 35 ›› Issue (8): 1179-1186.doi: 10.3969/j.issn.1000-1093.2014.08.007

基于Radau伪谱法的制导炸弹最优滑翔弹道研究

袁宴波^1,2，张科¹，薛晓东²

(1.西北工业大学航天学院, 陕西西安 710072; 2.中国空空导弹研究院第12研究所, 河南洛阳 471009)

收稿日期:2013-09-10 修回日期:2013-09-10 上线日期:2014-11-03
通讯作者: 袁宴波 E-mail:runble@163.com
作者简介:袁宴波(1981—)男博士研究生

Optimization of Glide Trajectory of Guided Bombs Using a Radau Pseudo-spectral Method

YUAN Yan-bo^1,2， ZHANG Ke¹， XUE Xiao-dong²

(1.School of Astronautics, Northwestern Polytechnical University, Xi’an 710072, Shaanxi, China;2.No.12 Institute, China Airborne Missile Academy, Luoyang 471009, Henan, China)

Received:2013-09-10 Revised:2013-09-10 Online:2014-11-03
Contact: YUAN Yan-bo E-mail:runble@163.com

摘要/Abstract

摘要： 基于Radau伪谱法求解最优控制问题的原理，研究了滑翔型制导炸弹的最大射程优化问题。对制导炸弹动力学模型进行了无量纲化处理，结合极小值原理推导了最优控制轨迹的解析解和一阶必要性条件，采用Radau伪谱法将弹道优化问题转化为非线性规划问题，基于协态映射原理给出了数值解的最优性验证方法。仿真结果表明，Radau伪谱法能够提供具有工程应用价值的最优解，与常规的最大升阻比滑翔弹道相比，优化后的弹道射程增加10%以上。

关键词: 兵器科学与技术, 滑翔制导炸弹, 弹道优化, Radau伪谱法

Abstract: The problem of optimizing the maximum range of a glide guided bomb is studied based on the principle of solving optimal control problems using the Radau pseudo-spectral method. The dynamic model of the guided bomb is nondimensionalized. Combining with the Pontryagin minimum principle, the analytic solution of the optimal control and the first-order necessary condition are derived. The trajectory optimization problem is translated to a nonlinear programming via the Radau pseudo-spectral method. Based on covector mapping principle, an optimality verification method is presented for the numerical solution. Simulation results show that the Radau pseudo-spectral method can provide a highly valuable optimal solution for engineering application. Compared with the conventional maximum lift-to-drag ratio gliding trajectory, the trajectory after optimization can be extended by more than 10%.

Key words: ordnance science and technology, glide guided bomb, trajectory optimization, Radau pseudo-spectral method

中图分类号:

TJ765.5

袁宴波，张科，薛晓东. 基于Radau伪谱法的制导炸弹最优滑翔弹道研究[J]. 兵工学报, 2014, 35(8): 1179-1186.

YUAN Yan-bo， ZHANG Ke， XUE Xiao-dong. Optimization of Glide Trajectory of Guided Bombs Using a Radau Pseudo-spectral Method[J]. Acta Armamentarii, 2014, 35(8): 1179-1186.

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基于Radau伪谱法的制导炸弹最优滑翔弹道研究

Optimization of Glide Trajectory of Guided Bombs Using a Radau Pseudo-spectral Method

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