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韩雅慧 , 杨春信 , 肖华军 , 等 . 翼伞精确空投系统关键技术和发展趋势 [J ] . 兵工自动化 , 2012 , 31 ( 7 ): 1 - 7 .

HAN Y H , YANG C X , XIAO H J , et al. Review on key technology and development of parafoil precise airdrop systems [J ] . Ordnance Industry Automation , 2012 , 31 ( 7 ): 1 - 7 . (in Chinese)

MORIVOSHI T , YAMADA K , NISHIDA H . The effect of rigging angle on longitudinal direction motion of parafoil-type vehicle:basic stability analysis and wind tunnel test [J/OL ] . International Journal of Aerospace Engineering , 2020 , 2020 : 8861714 [2021-07-12 ] . https://doi.org/10.1155/2020/8861714 https://doi.org/10.1155/2020/8861714 https://doi.org/10.1155/2020 /8861714.

STEIN J , MADSEN C , STRAHAN A . An overview of the guided parafoil system derived from X-38 experience [C ] //Proceedings of the 18th AIAA Aerodynamic Decelerator Systems Technology Conference and Seminar. Munich, Germany:AIAA , 2005 : 1652 .

SMITH J , BENNETT T , FOX R . Development of the NASA X-38 parafoil landing system [C ] //Proceedings of the 15th Aerodynamic Decelerator Systems Technology Conference. Toulouse, France:AIAA , 1999 : 1730 .

CARTER D , GEORGE S , HATTIS P , et al. Autonomous guidance, navigation and control of large parafoils [C ] //Proceedings of the 18th AIAA Aerodynamic Decelerator Systems Technology Conference and Seminar. Munich, Germany:AIAA , 2005 , 2005 - 1643 .

DEK C , OVERKAMP J L , TOETER A , et al. A recovery system for the key components of the first stage of a heavy launch vehicle [J ] . Aerospace Science and Technology , 2020 , 100 : 105778 . DOI: 10.1016/j.ast.2020.105778 http://doi.org/10.1016/j.ast.2020.105778 https://linkinghub.elsevier.com/retrieve/pii/S1270963819326458 https://linkinghub.elsevier.com/retrieve/pii/S1270963819326458

LÜ F K , HE W L , ZHAO L G . An improved nonlinear multibody dynamic model for a parafoil-UAV system [J ] . IEEE Access , 2019 , 7 : 139994 - 140009 . DOI: 10.1109/ACCESS.2019.2943496 http://doi.org/10.1109/ACCESS.2019.2943496 A recovery system for an unmanned aerial vehicle (UAV) using a steerable parafoil is an attractive concept. However, due to the complex interaction between the parafoil and the UAV, this parafoil system has not seen widespread use in the UAV recovery. Under the influence of the UAV, the suspension lines of the system are not always tight, so most of the existing models do not work. To analyze the parafoil and UAV interaction when the suspension lines are tight or slack, this study presents a method for improving a multibody dynamic model for a parafoil-UAV system. The parafoil and UAV are modeled as usual, while the suspension lines are modeled as a combination of several linear viscoelastic elements. All models are coupled, and the nonlinear equations of motion are then derived. To analyze the influence of the invalid suspension lines, this improved model has been compared with an 8-degrees of freedom model. The comparisons demonstrate that the simulation results of the improved model and the 8-DoF model are similar under a small control input. However, under a large control input, the results become significantly different. In an actual flight test, the accuracy of this improved model is found to be better than the 8-DoF model. Finally, an attitude optimal control system is designed for this improved model. The performance of this autonomous control is presented at the end of this paper.

ZHAO L G , HE W L , LÜ F K . Model-free adaptive control for parafoil systems based on the iterative feedback tuning method [J ] . IEEE Access , 2021 , 9 : 35900 - 35914 . DOI: 10.1109/Access.6287639 http://doi.org/10.1109/Access.6287639 https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6287639 https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6287639

NIE S , CAO Y H , WU Z L . Numerical simulation of parafoil inflation via a Robin-Neumann transmission-based approach [J ] . Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering , 2018 , 232 ( 4 ): 797 - 810 . DOI: 10.1177/0954410016688925 http://doi.org/10.1177/0954410016688925 http://journals.sagepub.com/doi/10.1177/0954410016688925 http://journals.sagepub.com/doi/10.1177/0954410016688925 In this paper, a partitioned coupled iterative approach based on the Robin–Neumann transmission condition is proposed for the fluid–structure interaction simulation of the inflation process of a parafoil. The Reynold-averaged Navier–Stokes equations and the versatile finite element method are employed to solve the fluid flow field and the structural deformation, respectively. The generalized-α time integration scheme for the structure and the second order back Euler scheme for the fluid are incorporated in the Robin-Neumann method. A modified spring-transfinite interpolation hybrid method is exploited to detect the deformation of the grid and regenerate the grid for the fluid architecture. Both a two-dimensional case and a three-dimensional case are studied to examine the feasibility of the present approach. The simulation results reveal the evolution of the flow regime during the inflation process when the air pours into the parafoil. The whole inflation process can be concluded as two stages: the span-wise deployment and the longitudinal expansion. The numerical aerodynamic performance agrees well with that obtained by wind-tunnel experiment, suggesting the effectiveness of this method in handling such a highly nonlinear fluid–structure interaction in parachute inflation.

ZHANG S Y , YU L , WU Z H , et al. Numerical investigation of ram-air parachutes inflation with fluid-structure interaction method in wind environments [J ] . Aerospace Science and Technology , 2021 , 109 : 106400 . DOI: 10.1016/j.ast.2020.106400 http://doi.org/10.1016/j.ast.2020.106400 https://linkinghub.elsevier.com/retrieve/pii/S1270963820310828 https://linkinghub.elsevier.com/retrieve/pii/S1270963820310828

LI B B , HE Y Q , HAN J D , et al. A new modeling scheme for powered parafoil unmanned aerial vehicle platforms: theory and experiments [J ] . Chinese Journal of Aeronautics , 2019 , 32 ( 11 ): 2466 - 2479 . DOI: 10.1016/j.cja.2019.04.001 http://doi.org/10.1016/j.cja.2019.04.001 https://linkinghub.elsevier.com/retrieve/pii/S1000936119301475 https://linkinghub.elsevier.com/retrieve/pii/S1000936119301475

YANG H , SONG L , CHEN W F . Research on parafoil stability using a rapid estimate model [J ] . Chinese Journal of Aeronautics , 2017 , 30 ( 5 ): 1670 - 1680 . DOI: 10.1016/j.cja.2017.06.003 http://doi.org/10.1016/j.cja.2017.06.003 https://linkinghub.elsevier.com/retrieve/pii/S1000936117301425 https://linkinghub.elsevier.com/retrieve/pii/S1000936117301425

TANAKA M , TANAKA K , WANG H O . Practical model construction and stable control of an unmanned aerial vehicle with a parafoil-type wing [J ] . IEEE Transactions on Systems, Man, and Cybernetics: Systems , 2017 , 49 ( 6 ): 1291 - 1297 . DOI: 10.1109/TSMC.6221021 http://doi.org/10.1109/TSMC.6221021 https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6221021 https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6221021

SLEGERS N , COSTELLO M . Model predictive control of a parafoil and payload system [J ] . Journal of Guidance, Control, and Dynamics , 2005 , 28 ( 4 ): 816 - 821 . DOI: 10.2514/1.12251 http://doi.org/10.2514/1.12251 https://arc.aiaa.org/doi/10.2514/1.12251 https://arc.aiaa.org/doi/10.2514/1.12251

ROGERS J , SLEGERS N . Robust parafoil terminal guidance using massively parallel processing [J ] . Journal of Guidance, Control, and Dynamics , 2013 , 36 ( 5 ): 1336 - 1345 . DOI: 10.2514/1.59782 http://doi.org/10.2514/1.59782 https://arc.aiaa.org/doi/10.2514/1.59782 https://arc.aiaa.org/doi/10.2514/1.59782

CHEN Q , SUN Y X , ZHAO M , et al. A virtual structure formation guidance strategy for multi-parafoil systems [J ] . IEEE Access , 2019 , 7 : 123592 - 123603 . DOI: 10.1109/Access.6287639 http://doi.org/10.1109/Access.6287639 https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6287639 https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6287639

高峰 , 郭锐 , 丰志伟 , 等 . 翼伞系统5段归航轨迹优化研究 [J ] . 兵工学报 , 2020 , 41 ( 5 ): 1025 - 1033 . DOI: 10.3969/j.issn.1000-1093.2020.05.022 http://doi.org/10.3969/j.issn.1000-1093.2020.05.022 为实现翼伞系统精确空投和方便归航过程下拉操控，需对翼伞归航轨迹分段处理并优化。建立翼伞系统高精度9自由度动力学模型，通过数值分析得到稳态滑翔比以及转弯角速率限值。以耗能最小为目标函数，耗时和转弯半径为输入变量，建立5段归航轨迹优化模型。将5段归航轨迹作为初始条件，利用伪谱法进行轨迹优化，给出归航最优参考路径，并对比分析了5段归航与直接归航过程能量损耗。仿真结果表明，所提出的5段归航轨迹优化策略，具有其控制量函数形式简单、便于应用的优点。

GAO F , GUO R , FENG Z W , et al. Optimization design of homing trajectory of parafoil system with five segments [J ] . Acta Armamentarii , 2020 , 41 ( 5 ): 1025 - 1033 . (in Chinese) DOI: 10.3969/j.issn.1000-1093.2020.05.022 http://doi.org/10.3969/j.issn.1000-1093.2020.05.022 The parafoil homing trajectory should be processed and optimized in segments in order to realize the accurate airdrop and easy drop-down control during homing. A high precision 9-degree-of-freedom dynamic model of parafoil system is established. A five-segment homing trajectory optimization model is established, in which the minimum energy consumption is taken as the objective function and the time consumption and turning radius are taken as the input variables. The optimal reference path of homing is given by using the five-segment homing trajectory as the initial condition and using the pseudo-spectral method to optimize the trajectory, and the energy losses in the five-segment homing and direct homing processes are compared and analyzed. The simulated results show that the five-segment homing trajectory optimization strategy proposed in this paper has the advantage of simple control function form and easy application. Key

GAO X L , ZHANG Q B , TANG Q G . Parachute dynamics and perturbation analysis of precision airdrop system [J ] . Chinese Journal of Aeronautics , 2016 , 29 ( 3 ): 596 - 607 . DOI: 10.1016/j.cja.2016.04.003 http://doi.org/10.1016/j.cja.2016.04.003 https://linkinghub.elsevier.com/retrieve/pii/S1000936116300218 https://linkinghub.elsevier.com/retrieve/pii/S1000936116300218

CANAN M R , COSTELLO M , WARD M , et al. Human-in-the-loop control of guided airdrop systems [J ] . Aerospace Science and Technology , 2019 , 84 : 1141 - 1149 . DOI: 10.1016/j.ast.2018.08.008 http://doi.org/10.1016/j.ast.2018.08.008 https://linkinghub.elsevier.com/retrieve/pii/S1270963818317723 https://linkinghub.elsevier.com/retrieve/pii/S1270963818317723

ZHU E L , SUN Q L , TAN P L , et al. Modeling of powered parafoil based on Kirchhoff motion equation [J ] . Nonlinear Dynamics , 2015 , 79 ( 1 ): 617 - 629 . DOI: 10.1007/s11071-014-1690-9 http://doi.org/10.1007/s11071-014-1690-9 http://link.springer.com/10.1007/s11071-014-1690-9 http://link.springer.com/10.1007/s11071-014-1690-9

HAN J . From PID to active disturbance rejection control [J ] . IEEE Transactions on Industrial Electronics , 2009 , 56 ( 3 ): 900 - 906 . DOI: 10.1109/TIE.2008.2011621 http://doi.org/10.1109/TIE.2008.2011621 http://ieeexplore.ieee.org/document/4796887/ http://ieeexplore.ieee.org/document/4796887/

SUN L , XUE W C , LI D H , et al. Quantitative tuning of active disturbance rejection controller for FOPDT model with application to power plant control [J ] . IEEE Transactions on Industrial Electronics , 2021 , 69 ( 1 ): 805 - 815 . DOI: 10.1109/TIE.2021.3050372 http://doi.org/10.1109/TIE.2021.3050372 https://ieeexplore.ieee.org/document/9325092/ https://ieeexplore.ieee.org/document/9325092/

LI B Y , GAO S , LI C , et al. Maritime buoyage inspection system based on an unmanned aerial vehicle and active disturbance rejection control [J ] . IEEE Access , 2021 , 9 : 22883 - 22893 . DOI: 10.1109/Access.6287639 http://doi.org/10.1109/Access.6287639 https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6287639 https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6287639