基于Karhunen-Loève展开的分布式变体飞行器最优控制方法

doi:10.7527/S1000-6893.2017.21518

流体力学与飞行力学

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基于Karhunen-Loève展开的分布式变体飞行器最优控制方法

龚春林^1,2, 赤丰华^1,2, 谷良贤^1,2, 方海^1,2

1. 西北工业大学航天学院陕西省空天飞行器设计重点实验室, 西安 710072;
2. 西北工业大学航天飞行动力学技术重点实验室, 西安 710072

收稿日期:2017-06-15 修回日期:2017-10-24 出版日期:2018-02-15 发布日期:2017-10-24
通讯作者: 龚春林,E-mail:154552879@qq.com E-mail:leonwood@nwpu.edu.cn
基金资助:
国防基础科研项目（JCKY2016204B102）；中央高校基本科研业务费专项资金（G2016KY0302）

Optimal control method for distributed morphing aircraft based on Karhunen-Loève expansion

GONG Chunlin^1,2, CHI Fenghua^1,2, GU Liangxian^1,2, FANG Hai^1,2

1. Shaanxi Aerospace Flight Vehicle Design Key Laboratory, School of Astronautics, Northwestern Polytechnical University, Xi'an 710072, China;
2. National Key Laboratory of Aerospace Flight Dynamics, Northwestern Polytechnical University, Xi'an 710072, China

Received:2017-06-15 Revised:2017-10-24 Online:2018-02-15 Published:2017-10-24
Supported by:
Defense Industrial Technology Development Program (JCKY2016204B102); Fundamental Research Funds for the Cen-tral Universities(G2016KY0302)

摘要/Abstract

摘要： 针对分布式变体飞行器变形规律优化问题的特殊性和计算困难性，提出了一种有效的解决方法。该问题的变形变量在空间和时间上均具有无穷维度，求解难点体现在：现有最优控制方法无法直接求解无穷维控制量问题；变形引起的气动模型数据维度增加，计算量呈级数增长，制约了优化求解。针对这两个问题，基于Karhunen-Loève展开方法对分布变形域进行离散和降维，采用有限维变形控制参数和几何模态描述，将原优化问题转化为可求解的有限维最优控制问题；采用Kriging方法和拉丁超立方抽样（LHS）方法构造了与变形控制参数相关的气动代理模型，大幅降低求解该问题的严重计算负担；结合离散降维最优控制模型和气动代理模型，基于hp自适应伪谱方法，建立了变形规律优化求解过程。以翼型分布式变体问题为例，对给定的飞行任务要求，以燃料消耗最省为目标，实现了全弹道翼型变形过程和迎角、燃油消耗率等控制量的同时优化，获得了更省能量的变体飞行方案，验证了所提方法的可行性。本文所发展方法具有通用性，能扩展到机体/弹体等更为复杂的变体形式，可为未来变体飞行技术发展提供支持。

关键词: 分布式变体, 变体飞行器, Karhunen-Loève展开, 代理模型, 最优控制, hp自适应伪谱方法

Abstract: To solve the calculation difficulty in morphing rule optimization of the distributed morphing aircraft, an effective method is proposed. The morphing control parameters in the optimization have infinite dimensions in time and space, and the calculation difficulties are shown as follows:the present method cannot obtain the parameters for infinite dimension control; as morphing control parameters are added to the model, the aerodynamic calculation cost grows fastly to restrict the optimization process. To overcome the two difficulties, the Karhunen-Loève expansion is used to discrete the morphing area and reduce dimensions. The original optimization problem is then transformed into finite dimension optimal control problem based on parameters and geometry modalities of finite dimension morphing control. The surrogate model of aerodynamics relating to morphing control parameters is developed by Latin Hypercube Sampling (LHS) and Kriging method, reducing dramatically the high cost of computation based on CFD. The discrete finite dimension optimal control model and the surrogate model of aerodynamics are combined to build the optimization process of the morphing rule based on the hp-adaptive pseudospectral method. The optimization of the airfoil morphing progress and control parameters such as angle of attack and fuel mass flow rate in the whole trajectory is achieved in a given flight, obtaining the optimal fuel consumption morphing flight plan and demonstrating the effectiveness of the method proposed. The method can be expanded to more complex morphing objects such as airframe, and provides a support for future morphing flight technology.

Key words: distributed morphing, morphing aircraft, Karhunen-Loève expansion, surrogate model, optimal control, hp-adaptive pseudospectral method

中图分类号:

V212

龚春林, 赤丰华, 谷良贤, 方海. 基于Karhunen-Loève展开的分布式变体飞行器最优控制方法[J]. 航空学报, 2018, 39(2): 121518-121518.

GONG Chunlin, CHI Fenghua, GU Liangxian, FANG Hai. Optimal control method for distributed morphing aircraft based on Karhunen-Loève expansion[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2018, 39(2): 121518-121518.

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主管单位：中国科学技术协会主办单位：中国航空学会北京航空航天大学

基于Karhunen-Loève展开的分布式变体飞行器最优控制方法

Optimal control method for distributed morphing aircraft based on Karhunen-Loève expansion

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