• Zhijie LiuEmail author
  • Jinkun Liu
Part of the Springer Tracts in Mechanical Engineering book series (STME)


In recent decades, with the extensive application of flexible systems in the fields of biology, chemical engineering, medicine and aerospace and more and more challenges in theoretical research, dealing with vibration suppression of flexible systems has become an important research topic.


  1. 1.
    Balas MJ (1978) Active control of flexible systems. J Optim Theory Appl 25(3):415–436MathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    Bamieh B, Paganini F, Dahleh MA (2002) Distributed control of spatially invariant systems. IEEE Trans Autom Control 47(7):1091–1107MathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    Barbieri E, Ozguner U (1988) Unconstrained and constrained mode expansions for a flexible slewing link. J Dyn Syst Meas Control 110(4):416–421CrossRefGoogle Scholar
  4. 4.
    Cai G-P, Lim CW (2006) Active control of a flexible hub-beam system using optimal tracking control method. Int J Mech Sci 48(10):1150–1162zbMATHCrossRefGoogle Scholar
  5. 5.
    Cai G-P, Lim CW (2006) Optimal tracking control of a flexible hub-beam system with time delay. Multibody Syst Dyn 16(4):331–350zbMATHCrossRefGoogle Scholar
  6. 6.
    Canbolat H, Dawson D, Rahn C, Vedagarbha P (1998) Boundary control of a cantilevered flexible beam with point-mass dynamics at the free end. Mechatronics 8(2):163–186CrossRefGoogle Scholar
  7. 7.
    Caracciolo R, Richiedei D, Trevisani A, Zanotto V (2005) Robust mixed-norm position and vibration control of flexible link mechanisms. Mechatronics 15(7):767–791CrossRefGoogle Scholar
  8. 8.
    Chiu C-S, Lian K-Y, Tsu-Cheng W (2004) Robust adaptive motion/force tracking control design for uncertain constrained robot manipulators. Automatica 40(12):2111–2119MathSciNetzbMATHGoogle Scholar
  9. 9.
    Cho D, Vladimir N, Choi T (2015) Natural vibration analysis of stiffened panels with arbitrary edge constraints using the assumed mode method. Proc Inst Mech Eng Part M: J Eng Marit Environ 229(4):340–349Google Scholar
  10. 10.
    De Luca A, Lanari L (1995) Robots with elastic joints are linearizable via dynamic feedback. In Proceedings of the 34th IEEE Conference on Decision and Control, 1995, vol 4. IEEE, pp 3895–3897Google Scholar
  11. 11.
    De Queiroz MS, Rahn CD (2002) Boundary control of vibration and noise in distributed parameter systems: an overview. Mech Syst Signal Process 16(1):19–38CrossRefGoogle Scholar
  12. 12.
    Demetriou MA (2004) Natural second-order observers for second-order distributed parameter systems. Syst Control Lett 51(3):225–234MathSciNetzbMATHCrossRefGoogle Scholar
  13. 13.
    Do KD, Pan J (2008) Boundary control of transverse motion of marine risers with actuator dynamics. J Sound Vib 318(4):768–791CrossRefGoogle Scholar
  14. 14.
    Do KD, Pan J (2009) Boundary control of three-dimensional inextensible marine risers. J Sound Vib 327(3–5):299–321CrossRefGoogle Scholar
  15. 15.
    Dubljevic S, El-Farra NH, Mhaskar P, Christofides PD (2006) Predictive control of parabolic pdes with state and control constraints. Int J Robust Nonlinear Control: IFAC-Affil J 16(16):749–772MathSciNetzbMATHCrossRefGoogle Scholar
  16. 16.
    Endo T, Matsuno F (2004) Dynamics based force control of one-link flexible arm. In SICE 2004 Annual Conference, vol 3. IEEE, pp 2736–2741Google Scholar
  17. 17.
    Gamarra-Rosado VO, Yuhara EAO (1999) Dynamic modeling and simulation of a flexible robotic manipulator. Robotica 17(5):523–528CrossRefGoogle Scholar
  18. 18.
    Ge SS, Lee TH, Zhu G (1997) A nonlinear feedback controller for a single-link flexible manipulator based on a finite element model. J Robot Syst 14(3):165–178zbMATHCrossRefGoogle Scholar
  19. 19.
    Ge SS, Lee TH, Zhu G (1998) Improving regulation of a single-link flexible manipulator with strain feedback. IEEE Trans Robot Autom 14(1):179–185CrossRefGoogle Scholar
  20. 20.
    Ge SS, Zhang S, He W (2011) Vibration control of an euler-bernoulli beam under unknown spatiotemporally varying disturbance. Int J Control 84(5):947–960MathSciNetzbMATHCrossRefGoogle Scholar
  21. 21.
    Guo BZ, Guo W (2009) The strong stabilization of a one-dimensional wave equation by non-collocated dynamic boundary feedback control. Automatica 45(3):790–797MathSciNetzbMATHCrossRefGoogle Scholar
  22. 22.
    Guo BZ, Jin FF (2010) Arbitrary decay rate for two connected strings with joint anti-damping by boundary output feedback. Automatica 46(7):1203–1209MathSciNetzbMATHCrossRefGoogle Scholar
  23. 23.
    Guo BZ, Shao ZC (2009) Stabilization of an abstract second order system with application to wave equations under non-collocated control and observations. Syst Control Lett 58(5):334–341MathSciNetzbMATHCrossRefGoogle Scholar
  24. 24.
    Guo B-Z, Wang J-M (2005) The well-posedness and stability of a beam equation with conjugate variables assigned at the same boundary point. IEEE Trans Autom Control 50(12):2087–2093MathSciNetzbMATHCrossRefGoogle Scholar
  25. 25.
    Guo BZ, Xu CZ (2007) The stabilization of a one-dimensional wave equation by boundary feedback with noncollocated observation. IEEE Trans Autom Control 52(2):371–377MathSciNetzbMATHCrossRefGoogle Scholar
  26. 26.
    Gutierrez LB, Lewis FL, Lowe JA (1998) Implementation of a neural network tracking controller for a single flexible link: comparison with pd and pid controllers. IEEE Trans Ind Electron 45(2):307–318CrossRefGoogle Scholar
  27. 27.
    He W, Zhang S, Ge SS (2013) Boundary control of a flexible riser with the application to marine installation. IEEE Trans Ind Electron 60(12):5802–5810CrossRefGoogle Scholar
  28. 28.
    He W, Yan Z, Sun C, Chen Y (2017) Adaptive neural network control of a flapping wing micro aerial vehicle with disturbance observer. IEEE Trans Cybern 47(10):3452–3465CrossRefGoogle Scholar
  29. 29.
    He W, Ge SS (2012) Robust adaptive boundary control of a vibrating string under unknown time-varying disturbance. IEEE Trans Control Syst Technol 20(1):48–58Google Scholar
  30. 30.
    He W, Ge SS (2015) Vibration control of a flexible beam with output constraint. IEEE Trans Ind Electron 62(8):5023–5030CrossRefGoogle Scholar
  31. 31.
    He W, Ge SS (2016) Cooperative control of a nonuniform gantry crane with constrained tension. Automatica 66:146–154MathSciNetzbMATHCrossRefGoogle Scholar
  32. 32.
    He W, He X, Ge SS (2015) Boundary output feedback control of a flexible string system with input saturation. Nonlinear Dyn 80(1–2):871–888MathSciNetzbMATHCrossRefGoogle Scholar
  33. 33.
    He W, Qin H, Liu J-K (2015) Modelling and vibration control for a flexible string system in three-dimensional space. IET Control Theory Appl 9(16):2387–2394MathSciNetCrossRefGoogle Scholar
  34. 34.
    He W, Sun C, Ge SS (2014) Vibration control design for a flexible string with input saturation. In 2014 11th World Congress on Intelligent Control and Automation (WCICA). IEEE, pp 885–890Google Scholar
  35. 35.
    He W, Yang C, Zhu J, Liu J-K, He X (2017) Active vibration control of a nonlinear three-dimensional euler-bernoulli beam. J Vib Control 23(19):3196–3215MathSciNetzbMATHCrossRefGoogle Scholar
  36. 36.
    He W, Zhang S (2017) Control design for nonlinear flexible wings of a robotic aircraft. IEEE Trans Control Syst Technol 25(1):351–357CrossRefGoogle Scholar
  37. 37.
    He X, Wei H, Jing S, Sun C (2017) Boundary vibration control of variable length crane systems in two dimensional space with output constraints. IEEE/ASME Trans Mechatron 22(5):1952–1962CrossRefGoogle Scholar
  38. 38.
    Jnifene A, Andrews W (2005) Experimental study on active vibration control of a single-link flexible manipulator using tools of fuzzy logic and neural networks. IEEE Trans Instrum Meas 54(3):1200–1208CrossRefGoogle Scholar
  39. 39.
    Karayiannidis Y, Rovithakis G, Doulgeri Z (2007) Force/position tracking for a robotic manipulator in compliant contact with a surface using neuro-adaptive control. Automatica 43(7):1281–1288MathSciNetzbMATHCrossRefGoogle Scholar
  40. 40.
    Kelly R, Ortega R, Ailon A, Loria A (1994) Global regulation of flexible joint robots using approximate differentiation. IEEE Trans Autom Control 39(6):1222–1224zbMATHCrossRefGoogle Scholar
  41. 41.
    Kim E, Vadali SR (1995) Modeling issues related to retrieval of flexible tethered satellite systems. J Guid Control Dyn 18(5):1169–1176CrossRefGoogle Scholar
  42. 42.
    Korayem MH, Nikoobin A, Azimirad V (2009) Trajectory optimization of flexible link manipulators in point-to-point motion. Robotica 27(6):825–840CrossRefGoogle Scholar
  43. 43.
    Kostarigka AK, Doulgeri Z, Rovithakis GA (2013) Prescribed performance tracking for flexible joint robots with unknown dynamics and variable elasticity. Automatica 49(5):1137–1147MathSciNetzbMATHCrossRefGoogle Scholar
  44. 44.
    Krstic M, Siranosian AA, Balogh A, Guo BZ (2007) Control of strings and flexible beams by backstepping boundary control. In American Control Conference, 2007. ACC’07. IEEE, pp 882–887Google Scholar
  45. 45.
    Kyung-Jinn Y, Keum-Shik H, Fumitoshi M (2004) Robust adaptive boundary control of an axially moving string under a spatiotemporally varying tension. J Sound Vib 273(4):1007–1029MathSciNetzbMATHGoogle Scholar
  46. 46.
    Lahdhiri T, ElMaraghy HA (1998) ElMaraghy. Optimal nonlinear position tracking control of a two-link flexible-joint robot manipulator. In Experimental Robotics V, Experimental Robotics V. Springer, pp 502–514Google Scholar
  47. 47.
    Liu J, He W (2018) Distributed parameter modeling and boundary control of flexible manipulators. Springer Singapore, SingaporezbMATHCrossRefGoogle Scholar
  48. 48.
    Luo ZH (1993) Direct strain feedback control of flexible robot arms: new theoretical and experimental results. IEEE Trans Autom Control 38(11):1610–1622MathSciNetzbMATHCrossRefGoogle Scholar
  49. 49.
    Luo ZH, Guo BZ, Morgül Ö (2012) Stability and stabilization of infinite dimensional systems with applications. Springer Science & Business MediaGoogle Scholar
  50. 50.
    Luo ZH, Guo B (1995) Further theoretical results on direct strain feedback control of flexible robot arms. IEEE Trans Autom Control 40(4):747–751MathSciNetzbMATHCrossRefGoogle Scholar
  51. 51.
    Luo ZH, Kitamura N, Guo BZ (1995) Shear force feedback control of flexible robot arms. IEEE Trans Robot Autom 11(5):760–765CrossRefGoogle Scholar
  52. 52.
    Martins JM, Mohamed Z, Tokhi MO, Sa Da Costa J, Botto MA (2003) Approaches for dynamic modelling of flexible manipulator systems. IEE Proc-Control Theory Appl 150(4):401–411CrossRefGoogle Scholar
  53. 53.
    Martins J, Botto MA, Da Costa JS (2002) Modeling of flexible beams for robotic manipulators. Multibody Syst Dyn 7(1):79–100zbMATHCrossRefGoogle Scholar
  54. 54.
    Matsuno F, Asano T, Sakawa Y (1994) Modeling and quasi-static hybrid position/force control of constrained planar two-link flexible manipulators. IEEE Trans Robot Autom 10(3):287–297CrossRefGoogle Scholar
  55. 55.
    Matsuno F, Kasai S (1998) Modeling and robust force control of constrained one-link flexible arms. J Robot Syst 15(8):447–464zbMATHCrossRefGoogle Scholar
  56. 56.
    Harris McClamroch N, Wang D (1988) Feedback stabilization and tracking of constrained robots. IEEE Trans Autom Control 33(5):419–426MathSciNetzbMATHCrossRefGoogle Scholar
  57. 57.
    Meirovitch L, Baruh H (1983) On the problem of observation spillover in self-adjoint distributed-parameter systems. J Optim Theory Appl 39(2):269–291MathSciNetzbMATHCrossRefGoogle Scholar
  58. 58.
    Nguyen TL, Do KD, Pan J (2013) Boundary control of coupled nonlinear three dimensional marine risers. J Mar Sci Appl 12(1):72–88CrossRefGoogle Scholar
  59. 59.
    Zhihua Q (2001) Robust and adaptive boundary control of a stretched string on a moving transporter. IEEE Trans Autom Control 46(3):470–476MathSciNetzbMATHCrossRefGoogle Scholar
  60. 60.
    Rahn CD, Zhang F, Joshi S, Dawson DM (1999) Asymptotically stabilizing angle feedback for a flexible cable gantry crane. J Dyn Syst Meas Control 121(3):563–566CrossRefGoogle Scholar
  61. 61.
    Rakhsha F, Goldenberg A (1985) Dynamics modelling of a single-link flexible robot. In Robotics and Automation. Proceedings. 1985 IEEE International Conference on, vol 2.IEEE, pp 984–989Google Scholar
  62. 62.
    Ren B, Ge SS, Tee KP, Lee TH (2010) Adaptive neural control for output feedback nonlinear systems using a barrier lyapunov function. IEEE Trans Neural Netw 21(8):1339–1345CrossRefGoogle Scholar
  63. 63.
    Ro K, Kamman JW (2010) Modeling and simulation of hose-paradrogue aerial refueling systems. J Guid Control Dyn 33(1):53–63CrossRefGoogle Scholar
  64. 64.
    Ro K, Kuk T, Kamman J (2010) Active control of aerial refueling hose-drogue systems. In AIAA Guidance, Navigation, and Control Conference. p 8400Google Scholar
  65. 65.
    Ro K, Kuk T, Kamman J (2011) Design, test and evaluation of an actively stabilized drogue refueling system. In Infotech@ Aerospace 2011, Infotech@ Aerospace 2011, p 1423Google Scholar
  66. 66.
    Ro K, Kuk T, Kamman JW (2011) Dynamics and control of hose-drogue refueling systems during coupling. J Guid Control Dyn 34(6):1694–1708CrossRefGoogle Scholar
  67. 67.
    Sakawa Y, Luo ZH (2002) Dynamics and control of bending and torsional vibrations of flexible beams. IEEE Trans Autom Control 34(9):970–977zbMATHCrossRefGoogle Scholar
  68. 68.
    Singh TR (1991) Dynamics and control of flexible arm robots. Thesis Waterloo UniversityGoogle Scholar
  69. 69.
    Su L, Wang J-M, Krstic M (2018) Boundary feedback stabilization of a class of coupled hyperbolic equations with nonlocal terms. IEEE Trans Autom Control 63(8):2633–2640MathSciNetzbMATHCrossRefGoogle Scholar
  70. 70.
    Sun D, Liu YH (2001) Position and force tracking of a two-manipulator system manipulating a flexible beam. J Robot Syst 18(4):197–212zbMATHCrossRefGoogle Scholar
  71. 71.
    Sun D, Liu Y-H (2001) Position and force tracking of a two-manipulator system manipulating a flexible beam. J Robot Syst 18(4):197–212zbMATHCrossRefGoogle Scholar
  72. 72.
    Sun D, Mills JK, Liu Y (1998) Hybrid position and force control of two industrial robots manipulating a flexible sheet: Theory and experiment. In Proceedings. 1998 IEEE International Conference on Robotics and Automation, 1998, vol 2. IEEE, pp 1835–1840Google Scholar
  73. 73.
    Tang Y, Sun F, Sun Z (2006) Neural network control of flexible-link manipulators using sliding mode. Neurocomputing 70(1–3):288–295CrossRefGoogle Scholar
  74. 74.
    Tee KP, Ge SS, Tay EH (2009) Barrier lyapunov functions for the control of output-constrained nonlinear systems. Automat 45(4):918–927MathSciNetzbMATHCrossRefGoogle Scholar
  75. 75.
    Thomas PR, Bhandari U, Bullock S, Richardson TS, Du Bois JL (2014) Advances in air to air refuelling. Prog Aerosp Sci 71:14–35CrossRefGoogle Scholar
  76. 76.
    Tian Q, Zhang Y, Chen L, Yang JJ (2010) Simulation of planar flexible multibody systems with clearance and lubricated revolute joints. Nonlinear Dyn 60(4):489–511zbMATHCrossRefGoogle Scholar
  77. 77.
    Osman Tokhi M, Mohamed Z, Hasan Shaheed M (2001) Dynamic characterisation of a flexible manipulator system. Robotica 19(5):571–580CrossRefGoogle Scholar
  78. 78.
    Nguyen DT (2009) Boundary output feedback of second-order distributed parameter systems. Syst Control Lett 58(7):519–528MathSciNetzbMATHCrossRefGoogle Scholar
  79. 79.
    Williamson WR, Reed E, Glenn GJ, Stecko SM, Musgrave J, Takacs JM (2010) Controllable drogue for automated aerial refueling. J Aircr 47(2):515–527CrossRefGoogle Scholar
  80. 80.
    Wu F (2003) Distributed control for interconnected linear parameter-dependent systems. IEE Proc-Control Theory Appl 150(5):518–527CrossRefGoogle Scholar
  81. 81.
    Wu HN, Feng S (2017) Guaranteed-cost vinite-time fuzzy control for temperature-constrained nonlinear coupled beat-ode systems. IEEE Trans Syst Man Cybern Syst 47(8):1919–1930CrossRefGoogle Scholar
  82. 82.
    Wu HN, Wang HD (2017) Distributed consensus observers-vased \(h_{\infty } \) control of dissipative pde systems using sensor networks. IEEE Trans Control Netw Syst 2(2):112–121MathSciNetCrossRefGoogle Scholar
  83. 83.
    Wu HN, Wang J-W, Li H-X (2014) Fuzzy boundary control design for a class of nonlinear parabolic distributed parameter systems. IEEE Trans Fuzzy Syst 22(3):642–652CrossRefGoogle Scholar
  84. 84.
    Yang H, Liu J (2016) Distributed piezoelectric vibration control for a flexible-link manipulator based on an observer in the form of partial differential equations. J Sound Vib 363:77–96CrossRefGoogle Scholar
  85. 85.
    Yang HJ, Liu JK, He W (2018) Distributed disturbance-observer-based vibration control for a flexible-link manipulator with output constraints. Sci China Technol Sci 61(10):1528–1536CrossRefGoogle Scholar
  86. 86.
    Yang K-J, Hong K-S, Matsuno F (2005) Robust boundary control of an axially moving string by using a pr transfer function. IEEE Trans Autom Control 50(12):2053–2058MathSciNetzbMATHCrossRefGoogle Scholar
  87. 87.
    Zhang L, Liu J (2013) Adaptive boundary control for flexible two-link manipulator based on partial differential equation dynamic model. IET Control Theory Appl 7(1):43–51MathSciNetCrossRefGoogle Scholar
  88. 88.
    Zhang S, Dong Y, Ouyang Y, Yin Z, Peng K (2018) Adaptive neural control for robotic manipulators with output constraints and uncertainties. IEEE Trans Veural Vetworks Learn Syst 99:1–11Google Scholar
  89. 89.
    Zhang YL, Wang JM (2017) Exact controllability of a micro beam with boundary bending moment. Int J Control 1–9Google Scholar
  90. 90.
    Zhao Z, Liu Y, Luo F (2017) Output feedback boundary control of an axially moving system with input saturation constraint. ISA Trans 68:22–32CrossRefGoogle Scholar
  91. 91.
    Zhao Z, Liu Y, Fang G, Yun F (2017) Vibration control and boundary tension constraint of an axially moving string system. Nonlinear Dyn 89(1):1–10MathSciNetzbMATHCrossRefGoogle Scholar
  92. 92.
    Sabatini M, Palmerini GB, Leonangeli N, Gasbarri P (2014) Analysis and experiments for delay compensation in attitude control of flexible spacecraft. Acta Astronaut 104(1):276–292CrossRefGoogle Scholar
  93. 93.
    Meng D, Wang X, Wenfu X, Liang B (2017) Space robots with flexible appendages: dynamic modeling, coupling measurement, and vibration suppression. J Sound Vib 396:30–50CrossRefGoogle Scholar
  94. 94.
    Wenfu X, Meng D, Chen Y, Qian H, Yangsheng X (2014) Dynamics modeling and analysis of a flexible-base space robot for capturing large flexible spacecraft. Multibody Syst Dyn 32(3):357–401MathSciNetzbMATHCrossRefGoogle Scholar
  95. 95.
    Guan P, Liu X-J, Liu J-Z (2005) Adaptive fuzzy sliding mode control for flexible satellite. Eng Appl Artif Intell 18(4):451–459CrossRefGoogle Scholar
  96. 96.
    Qinglei H, Ma G (2005) Variable structure control and active vibration suppression of flexible spacecraft during attitude maneuver. Aerosp Sci Technol 9(4):307–317zbMATHCrossRefGoogle Scholar
  97. 97.
    Qinglei H, Ma G (2008) Adaptive variable structure controller for spacecraft vibration reduction. IEEE Trans Aerosp Electron Syst 44(3):861–876CrossRefGoogle Scholar
  98. 98.
    Cubillos XC, de Souza GLC (2009) Using of h-infinity control method in attitude control system of rigid-flexible satellite. Math Probl Eng 2009Google Scholar
  99. 99.
    Yang K-J, Hong K-S, Matsuno F (2005) Energy-based control of axially translating beams: varying tension, varying speed, and disturbance adaptation. IEEE Trans Control Syst Technol 13(6):1045–1054CrossRefGoogle Scholar

Copyright information

© Tsinghua University Press 2020

Authors and Affiliations

  1. 1.School of Automation and Electrical EngineeringUniversity of Science and Technology BeijingBeijingChina
  2. 2.School of Automation Science and Electrical EngineeringBeihang UniversityBeijingChina

Personalised recommendations