工程科学学报.第43卷.第1期：150-160.2021年1月 Chinese Journal of Engineering,Vol.43,No.1:150-160,January 2021 https://doi.org/10.13374/j.issn2095-9389.2020.05.12.002;http://cje.ustb.edu.cn 空中加油机加油软管系统建模和控制研究进展 刘志杰12，宋丛丛”，梁金源”，李擎)四，贺威2 1)北京科技大学自动化学院.北京1000832)北京科技大学人工智能研究院，北京1000833)北京科技大学顺德研究生院.佛山528300 ☒通信作者，E-mail:liqing@ies.ustb.edu.cn 摘要空中加油软管系统作为空中加油过程最重要的组成部分，其建模和控制研究是一个重要研究方向，已经取得了很大 进展.首先在概述了空中加油的主要类型的基础上，分析了软管式空中加油的特点；然后分别介绍了基于常微分方程和基于 偏微分方程的两种软管系统的建模方法；进一步针对空中加油机加油全过程分析了加油软管系统的对接控制、软管的振动 抑制和可控锥套的研究：最后从加油软管系统的建模和控制方面展望了软管式空中加油未来的发展趋势 关键词自主空中加油：软管式加油：偏微分方程：对接控制：振动抑制 分类号TP273.3 Advances in modeling and control of probe-drogue aerial refueling LIU Zhi-jie SONG Cong-cong,LIANG Jin-yuan).LI Qing HE Wei2) 1)School of Automation and Electrical Engineering,University of Science and Technology Beijing,Beijing 100083,China 2)Institute of Artificial Intelligence,University of Science and Technology Beijing,Beijing 100083,China 3)Shunde Graduate School,University of Science and Technology Beijing,Foshan 528300,China Corresponding author,E-mail:liqing@ies.ustb.edu.cn ABSTRACT Spurred by the rapid integration of unmanned aerial vehicles (UAVs)in modern military missions,significant research has been performed in the field of autonomous aerial refueling with a focus on the detection,control,and guidance of the tanker and receiver.The concept of aerial refueling has been highly valued in the military since it was first proposed in 1917.Through aerial refueling.an aircraft can significantly expand its combat range,extend its flight time,and improve its carrying capacity;thus,its combat effectiveness can be greatly improved.Furthermore,aerial refueling is gradually showing its merits in the civil domain;for example,it can be used to increase the travel distance of postal aircraft.There are two main types of aerial refueling:flying boom refueling(FBR) and probe-drogue refueling (PDR).Compared with FBR,PDR meets the requirements of UAVs such as high flexibility,high safety,and simplicity.Thus,PDR is more suitable than FBR for unmanned aerial systems.Unique advantages of PDR have allowed it to become the most extensively used refueling method,and the study of PDR has attracted increasing attention.However,the most important and complicated part in such studies is the modeling and control design of a refueling hose system.This paper described the results of a study conducted on the modeling and control design of PDR.First,this paper summarized the main types of aerial refueling and analyzed the characteristics of PDR.Subsequently,two types of modeling of PDR were introduced:lumped parameter system and distributed parameter system.Next,based on the modeling of the aerial refueling hose system,the control design of docking control,vibration control,and controllable drogue was analyzed for the entire process of aerial refueling.Finally,avenues for future research on the modeling and control design of PDR such as the accuracy of the model,complexity of the control system,and details of the working environment at various altitudes were discussed 收稿日期：2020-05-12 基金项目：国家自然科学基金资助项目(62073030)：广东省基础与应用基础研究基金资助项目(2019A1515110728):北京科技大学顺德研 究生院科研经费资助项目(2020BH002):北京科技大学青年教师学科交叉研究项目资助项目(FRF-DRY-19-024)空中加油机加油软管系统建模和控制研究进展 刘志杰1,2,3)，宋丛丛1)，梁金源1)，李    擎1) 苣，贺    威1,2) 1) 北京科技大学自动化学院，北京 100083    2) 北京科技大学人工智能研究院，北京 100083    3) 北京科技大学顺德研究生院，佛山 528300 苣通信作者，E-mail：liqing@ies.ustb.edu.cn 摘    要    空中加油软管系统作为空中加油过程最重要的组成部分，其建模和控制研究是一个重要研究方向，已经取得了很大 进展. 首先在概述了空中加油的主要类型的基础上，分析了软管式空中加油的特点；然后分别介绍了基于常微分方程和基于 偏微分方程的两种软管系统的建模方法；进一步针对空中加油机加油全过程分析了加油软管系统的对接控制、软管的振动 抑制和可控锥套的研究；最后从加油软管系统的建模和控制方面展望了软管式空中加油未来的发展趋势. 关键词    自主空中加油；软管式加油；偏微分方程；对接控制；振动抑制 分类号    TP273.3 Advances in modeling and control of probe-drogue aerial refueling LIU Zhi-jie1,2,3) ，SONG Cong-cong1) ，LIANG Jin-yuan1) ，LI Qing1) 苣 ，HE Wei1,2) 1) School of Automation and Electrical Engineering, University of Science and Technology Beijing, Beijing 100083, China 2) Institute of Artificial Intelligence, University of Science and Technology Beijing, Beijing 100083, China 3) Shunde Graduate School, University of Science and Technology Beijing, Foshan 528300, China 苣 Corresponding author, E-mail: liqing@ies.ustb.edu.cn ABSTRACT    Spurred by the rapid integration of unmanned aerial vehicles (UAVs) in modern military missions, significant research has been performed in the field of autonomous aerial refueling with a focus on the detection, control, and guidance of the tanker and receiver.  The  concept  of  aerial  refueling  has  been  highly  valued  in  the  military  since  it  was  first  proposed  in  1917.  Through  aerial refueling, an aircraft can significantly expand its combat range, extend its flight time, and improve its carrying capacity; thus, its combat effectiveness can be greatly improved. Furthermore, aerial refueling is gradually showing its merits in the civil domain; for example, it can be used to increase the travel distance of postal aircraft. There are two main types of aerial refueling: flying boom refueling (FBR) and probe-drogue refueling (PDR). Compared with FBR, PDR meets the requirements of UAVs such as high flexibility, high safety, and simplicity. Thus, PDR is more suitable than FBR for unmanned aerial systems. Unique advantages of PDR have allowed it to become the most  extensively  used  refueling  method,  and  the  study  of  PDR  has  attracted  increasing  attention.  However,  the  most  important  and complicated part in such studies is the modeling and control design of a refueling hose system. This paper described the results of a study conducted on the modeling and control design of PDR. First, this paper summarized the main types of aerial refueling and analyzed the characteristics  of  PDR.  Subsequently,  two  types  of  modeling  of  PDR  were  introduced:  lumped  parameter  system  and  distributed parameter  system.  Next,  based  on  the  modeling  of  the  aerial  refueling  hose  system,  the  control  design  of  docking  control,  vibration control,  and  controllable  drogue  was  analyzed  for  the  entire  process  of  aerial  refueling.  Finally,  avenues  for  future  research  on  the modeling and control design of PDR such as the accuracy of the model, complexity of the control system, and details of the working environment at various altitudes were discussed. 收稿日期: 2020−05−12 基金项目: 国家自然科学基金资助项目（62073030）；广东省基础与应用基础研究基金资助项目（2019A1515110728）；北京科技大学顺德研 究生院科研经费资助项目（2020BH002）；北京科技大学青年教师学科交叉研究项目资助项目（FRF-IDRY-19-024） 工程科学学报，第 43 卷，第 1 期：150−160，2021 年 1 月 Chinese Journal of Engineering, Vol. 43, No. 1: 150−160, January 2021 https://doi.org/10.13374/j.issn2095-9389.2020.05.12.002; http://cje.ustb.edu.cn