刘志杰等：空中加油机加油软管系统建模和控制研究进展 159· 55:92 trajectory tracking controller for the tanker with strict posture [29]Liu Z J,Liu J K,He W.Modeling and vibration control of a constraints under unknown flow perturbations.Merospace Sci flexible aerial refueling hose with variable lengths and input Technol.2016.56:34 constraint.Automatica,2017,77:302 [45]Vassberg J,Yeh D,Blair A,et al.Numerical simulations of KC-10 [30]Valasek J,Gunnam K,Kimmett J,et al.Vision-based sensor and wing-mount aerial refueling hose-drogue dynamics with a reel navigation system for autonomous air refueling.J Guid Control take-up system//21st Applied Aerodynamics Conference.Orlando, Dm,2005,28(5:979 2003:23 [31]Tandale M D,Bowers R,Valasek J.Trajectory tracking controller [46]Alden R E,Vennero GG.Aerial Refueling System:US Patent, for vision-based probe and drogue autonomous aerial refueling. 5141178.1992-8-25 Guid Control Dyn,2006,29(4):846 [47]Wang H T,Dong X M,Xue J P,et al.Dynamic modeling of a [32]Wang J,Patel VV,Cao C Y,et al.Novel LI adaptive control hose-drogue aerial refueling system and integral sliding mode methodology for aerial refueling with guaranteed transient backstepping control for the hose whipping phenomenon.Chin performance.J Guid Control Dyn,2008,31(1):182 4erom,2014,27(4):930 [33]Su Z K,Wang H L,Shao X L,et al.Autonomous aerial refueling [48]Su Z K,Xie M Y,Li C T.RISE based active vibration control for precise docking based on active disturbance rejection control// the flexible refueling hose.Merospace Sci Technol,2019,92:387 IECON 2015-41st Annual Conference of the IEEE Industrial [49]Liu Z J,Liu J K,He W.Adaptive boundary control of a flexible Electronics Society.Yokohama,2015:4574 manipulator with input saturation.Int J Control,2016,89(6): [34]Su Z K,Wang H L,Li N.Anti-disturbance rapid vibration 1191 suppression of the flexible aerial refueling hose.Mech Syst Signal [50]Nguyen T L,Do K D,Pan J.Boundary control of two-dimensional Process,.2018.104:87 marine risers with bending couplings./Sound Vib,2013,332(16): [35]Su Z K,Wang H L.Probe motion compound control for 3605 autonomous aerial refueling docking.Aerospace Sci Technol, [51]He W,Zhang S,Ge S S.Robust adaptive control of a thruster 2018,72:1 assisted position mooring system.Auomarica,2014,50(7):1843 [36]Yu Z Q.Zhang Y M,Qu Y H.Fault-tolerant control for [52]Kang W,Fridman E.Distributed stabilization of Korteweg de autonomous aerial refueling against actuator fault in receiver Vries Burgers equation in the presence of input delay.Automarica, UAV.IFAC PapersOnLine,2018.51(24):274 2019,100:260 [37]Ren JR.Dai X H,Quan Q,et al.Reliable docking control scheme [53]Orlov Y,Pisano A,Usai E.Exponential stabilization of the for probe-drogue refueling.J Guid Control Dyn,2019,42(11): uncertain wave equation via distributed dynamic input extension 2511 IEEE Trans Autom Control,2011,56(1):212 [38]Philip N K,Ananthasayanam M R.Relative position and attitude [54]Conrad F.Stabilization of beams by pointwise feedback control estimation and control schemes for the final phase of an SIAMJ Control Optim,1990,28(2):423 autonomous docking mission of spacecraft.Acta Astron,2003, [55]Ammari K,Tucsnak M.Stabilization of Bernoulli-Euler beams by 52(7):511 means of a pointwise feedback force.SIAMJ Control Oprim,2000, [39]Sinopoli B,Micheli M,Donato G,et al.Vision based navigation 39(4):1160 for an unmanned aerial vehicle//Proceedings of the 2001 IEEE [56]Xu G Q,Wang H X.Stabilisation of Timoshenko beam system International Conference on Robotics and Automation.Seoul, with delay in the boundary control.Int Control,2013,86(6): 2001:1757 1165 [40]Fravolini M L,Ficola A,Napolitano M R,et al.Development of [57]Liu Z J,Liu J K,He W.Deadzone compensation based boundary modelling and control tools for aerial refueling for UAVs//A/44 control of a flexible aerial refueling hose with output constraint. Guidance,Navigation,and Control Conference and Exhibit. IFAC PapersOnline,2017,50(1):645 Austin,2003:AIAA2003-5798 [58]Chang L,Jia Y M.Adaptive control of a hose and drogue system [41]Fravolini M L,Ficola A,Campa G,et al.Modeling and control with input nonlinearities and partial state constraints.Int/Control issues for autonomous aerial refueling for UAVs using a probe- 4tomS1,2019,17(10):2508 drogue refueling system.Aerospace Sci Technol,2004,8(7):611 [59]Ro K,Kuk T,Kamman J W.Active control of aerial refueling [42]Wang L X,Yin H P.Guo Y G.et al.Closed-loop motion hose-drogue systems/lAIAA Guidance,Navigation,and Control characteristic requirements of receiver aircraft for probe and Conference.Toronto,2010:AIAA 2010-8400 drogue aerial refueling.Aerospace Sci Technol,2019,93:105293 [60]Ro K,Basaran E.Aerodynamic investigations of Paradrogue [43]Thomas P R,Bullock S,Richardson T S,et al.Collaborative assembly in aerial refueling system//44th AlAA Aerospace control in a flying-boom aerial refueling simulation.J Guid Sciences Meeting and Exhibit.Reno,2006:AlAA 2006-855 Control Dyn,2015,38(7):1274 [61]Michael S F.Controllable Drogue:US Patent,8186623 B2.2012- [44]Su Z K,Wang HL,Shao X L,et al.A robust back-stepping based 0555: 92 Liu  Z  J,  Liu  J  K,  He  W.  Modeling  and  vibration  control  of  a flexible  aerial  refueling  hose  with  variable  lengths  and  input constraint. Automatica, 2017, 77: 302 [29] Valasek J, Gunnam K, Kimmett J, et al. Vision-based sensor and navigation  system  for  autonomous  air  refueling. J Guid Control Dyn, 2005, 28（5）: 979 [30] Tandale M D, Bowers R, Valasek J. Trajectory tracking controller for vision-based probe and drogue autonomous aerial refueling. J Guid Control Dyn, 2006, 29（4）: 846 [31] Wang  J,  Patel  V  V,  Cao  C  Y,  et  al.  Novel  L1  adaptive  control methodology  for  aerial  refueling  with  guaranteed  transient performance. J Guid Control Dyn, 2008, 31（1）: 182 [32] Su Z K, Wang H L, Shao X L, et al. Autonomous aerial refueling precise  docking  based  on  active  disturbance  rejection  control// IECON 2015  -  41st Annual Conference of the IEEE Industrial Electronics Society. Yokohama, 2015: 4574 [33] Su  Z  K,  Wang  H  L,  Li  N.  Anti-disturbance  rapid  vibration suppression of the flexible aerial refueling hose. Mech Syst Signal Process, 2018, 104: 87 [34] Su  Z  K,  Wang  H  L.  Probe  motion  compound  control  for autonomous  aerial  refueling  docking. Aerospace Sci Technol, 2018, 72: 1 [35] Yu  Z  Q,  Zhang  Y  M,  Qu  Y  H.  Fault-tolerant  control  for autonomous  aerial  refueling  against  actuator  fault  in  receiver UAV. IFAC PapersOnLine, 2018, 51（24）: 274 [36] Ren J R, Dai X H, Quan Q, et al. Reliable docking control scheme for  probe-drogue  refueling. J Guid Control Dyn,  2019,  42（11）: 2511 [37] Philip N K, Ananthasayanam M R. Relative position and attitude estimation  and  control  schemes  for  the  final  phase  of  an autonomous  docking  mission  of  spacecraft. Acta Astron,  2003, 52（7）: 511 [38] Sinopoli B, Micheli M, Donato G, et al. Vision based navigation for  an  unmanned  aerial  vehicle//Proceedings of the 2001 IEEE International Conference on Robotics and Automation.  Seoul, 2001: 1757 [39] Fravolini M L, Ficola A, Napolitano M R, et al. Development of modelling  and  control  tools  for  aerial  refueling  for  UAVs//AIAA Guidance, Navigation, and Control Conference and Exhibit. Austin, 2003: AIAA 2003-5798 [40] Fravolini  M  L,  Ficola  A,  Campa  G,  et  al.  Modeling  and  control issues  for  autonomous  aerial  refueling  for  UAVs  using  a  probe￾drogue refueling system. Aerospace Sci Technol, 2004, 8（7）: 611 [41] Wang  L  X,  Yin  H  P,  Guo  Y  G,  et  al.  Closed-loop  motion characteristic  requirements  of  receiver  aircraft  for  probe  and drogue aerial refueling. Aerospace Sci Technol, 2019, 93: 105293 [42] Thomas  P  R,  Bullock  S,  Richardson  T  S,  et  al.  Collaborative control  in  a  flying-boom  aerial  refueling  simulation. J Guid Control Dyn, 2015, 38（7）: 1274 [43] [44] Su Z K, Wang H L, Shao X L, et al. A robust back-stepping based trajectory  tracking  controller  for  the  tanker  with  strict  posture constraints  under  unknown  flow  perturbations. Aerospace Sci Technol, 2016, 56: 34 Vassberg J, Yeh D, Blair A, et al. Numerical simulations of KC-10 wing-mount  aerial  refueling  hose-drogue  dynamics  with  a  reel take-up system//21st Applied Aerodynamics Conference. Orlando, 2003: 23 [45] Alden  R  E,  Vennero  G  G. Aerial Refueling System:  US  Patent, 5141178. 1992-8-25 [46] Wang  H  T,  Dong  X  M,  Xue  J  P,  et  al.  Dynamic  modeling  of  a hose-drogue  aerial  refueling  system  and  integral  sliding  mode backstepping  control  for  the  hose  whipping  phenomenon. Chin J Aeron, 2014, 27（4）: 930 [47] Su Z K, Xie M Y, Li C T. RISE based active vibration control for the flexible refueling hose. Aerospace Sci Technol, 2019, 92: 387 [48] Liu Z J, Liu J K, He W. Adaptive boundary control of a flexible manipulator  with  input  saturation. Int J Control,  2016,  89（6）: 1191 [49] Nguyen T L, Do K D, Pan J. Boundary control of two-dimensional marine risers with bending couplings. J Sound Vib, 2013, 332（16）: 3605 [50] He  W,  Zhang  S,  Ge  S  S.  Robust  adaptive  control  of  a  thruster assisted position mooring system. Automatica, 2014, 50（7）: 1843 [51] Kang  W,  Fridman  E.  Distributed  stabilization  of  Korteweg  de Vries Burgers equation in the presence of input delay. Automatica, 2019, 100: 260 [52] Orlov  Y,  Pisano  A,  Usai  E.  Exponential  stabilization  of  the uncertain wave equation via distributed dynamic input extension. IEEE Trans Autom Control, 2011, 56（1）: 212 [53] Conrad  F.  Stabilization  of  beams  by  pointwise  feedback  control. SIAM J Control Optim, 1990, 28（2）: 423 [54] Ammari K, Tucsnak M. Stabilization of Bernoulli-Euler beams by means of a pointwise feedback force. SIAM J Control Optim, 2000, 39（4）: 1160 [55] Xu  G  Q,  Wang  H  X.  Stabilisation  of  Timoshenko  beam  system with  delay  in  the  boundary  control. Int J Control,  2013,  86（6）: 1165 [56] Liu Z J, Liu J K, He W. Deadzone compensation based boundary control  of  a  flexible  aerial  refueling  hose  with  output  constraint. IFAC PapersOnline, 2017, 50（1）: 645 [57] Chang L, Jia Y M. Adaptive control of a hose and drogue system with input nonlinearities and partial state constraints. Int J Control Autom Syst, 2019, 17（10）: 2508 [58] Ro  K,  Kuk  T,  Kamman  J  W.  Active  control  of  aerial  refueling hose-drogue  systems//AIAA Guidance, Navigation, and Control Conference. Toronto, 2010: AIAA 2010-8400 [59] Ro  K,  Basaran  E.  Aerodynamic  investigations  of  Paradrogue assembly  in  aerial  refueling  system//44th AIAA Aerospace Sciences Meeting and Exhibit. Reno, 2006: AIAA 2006-855 [60] Michael S F. Controllable Drogue: US Patent, 8186623 B2. 2012- 05 [61] 刘志杰等： 空中加油机加油软管系统建模和控制研究进展 · 159 ·