Abstract
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.
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References
Balas MJ (1978) Active control of flexible systems. J Optim Theory Appl 25(3):415–436
Bamieh B, Paganini F, Dahleh MA (2002) Distributed control of spatially invariant systems. IEEE Trans Autom Control 47(7):1091–1107
Barbieri E, Ozguner U (1988) Unconstrained and constrained mode expansions for a flexible slewing link. J Dyn Syst Meas Control 110(4):416–421
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):1150–1162
Cai G-P, Lim CW (2006) Optimal tracking control of a flexible hub-beam system with time delay. Multibody Syst Dyn 16(4):331–350
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):163–186
Caracciolo R, Richiedei D, Trevisani A, Zanotto V (2005) Robust mixed-norm position and vibration control of flexible link mechanisms. Mechatronics 15(7):767–791
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):2111–2119
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):340–349
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 3895–3897
De Queiroz MS, Rahn CD (2002) Boundary control of vibration and noise in distributed parameter systems: an overview. Mech Syst Signal Process 16(1):19–38
Demetriou MA (2004) Natural second-order observers for second-order distributed parameter systems. Syst Control Lett 51(3):225–234
Do KD, Pan J (2008) Boundary control of transverse motion of marine risers with actuator dynamics. J Sound Vib 318(4):768–791
Do KD, Pan J (2009) Boundary control of three-dimensional inextensible marine risers. J Sound Vib 327(3–5):299–321
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):749–772
Endo T, Matsuno F (2004) Dynamics based force control of one-link flexible arm. In SICE 2004 Annual Conference, vol 3. IEEE, pp 2736–2741
Gamarra-Rosado VO, Yuhara EAO (1999) Dynamic modeling and simulation of a flexible robotic manipulator. Robotica 17(5):523–528
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):165–178
Ge SS, Lee TH, Zhu G (1998) Improving regulation of a single-link flexible manipulator with strain feedback. IEEE Trans Robot Autom 14(1):179–185
Ge SS, Zhang S, He W (2011) Vibration control of an euler-bernoulli beam under unknown spatiotemporally varying disturbance. Int J Control 84(5):947–960
Guo BZ, Guo W (2009) The strong stabilization of a one-dimensional wave equation by non-collocated dynamic boundary feedback control. Automatica 45(3):790–797
Guo BZ, Jin FF (2010) Arbitrary decay rate for two connected strings with joint anti-damping by boundary output feedback. Automatica 46(7):1203–1209
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):334–341
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):2087–2093
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):371–377
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):307–318
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):5802–5810
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):3452–3465
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):48–58
He W, Ge SS (2015) Vibration control of a flexible beam with output constraint. IEEE Trans Ind Electron 62(8):5023–5030
He W, Ge SS (2016) Cooperative control of a nonuniform gantry crane with constrained tension. Automatica 66:146–154
He W, He X, Ge SS (2015) Boundary output feedback control of a flexible string system with input saturation. Nonlinear Dyn 80(1–2):871–888
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):2387–2394
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 885–890
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):3196–3215
He W, Zhang S (2017) Control design for nonlinear flexible wings of a robotic aircraft. IEEE Trans Control Syst Technol 25(1):351–357
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):1952–1962
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):1200–1208
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):1281–1288
Kelly R, Ortega R, Ailon A, Loria A (1994) Global regulation of flexible joint robots using approximate differentiation. IEEE Trans Autom Control 39(6):1222–1224
Kim E, Vadali SR (1995) Modeling issues related to retrieval of flexible tethered satellite systems. J Guid Control Dyn 18(5):1169–1176
Korayem MH, Nikoobin A, Azimirad V (2009) Trajectory optimization of flexible link manipulators in point-to-point motion. Robotica 27(6):825–840
Kostarigka AK, Doulgeri Z, Rovithakis GA (2013) Prescribed performance tracking for flexible joint robots with unknown dynamics and variable elasticity. Automatica 49(5):1137–1147
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 882–887
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):1007–1029
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 502–514
Liu J, He W (2018) Distributed parameter modeling and boundary control of flexible manipulators. Springer Singapore, Singapore
Luo ZH (1993) Direct strain feedback control of flexible robot arms: new theoretical and experimental results. IEEE Trans Autom Control 38(11):1610–1622
Luo ZH, Guo BZ, Morgül Ö (2012) Stability and stabilization of infinite dimensional systems with applications. Springer Science & Business Media
Luo ZH, Guo B (1995) Further theoretical results on direct strain feedback control of flexible robot arms. IEEE Trans Autom Control 40(4):747–751
Luo ZH, Kitamura N, Guo BZ (1995) Shear force feedback control of flexible robot arms. IEEE Trans Robot Autom 11(5):760–765
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):401–411
Martins J, Botto MA, Da Costa JS (2002) Modeling of flexible beams for robotic manipulators. Multibody Syst Dyn 7(1):79–100
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):287–297
Matsuno F, Kasai S (1998) Modeling and robust force control of constrained one-link flexible arms. J Robot Syst 15(8):447–464
Harris McClamroch N, Wang D (1988) Feedback stabilization and tracking of constrained robots. IEEE Trans Autom Control 33(5):419–426
Meirovitch L, Baruh H (1983) On the problem of observation spillover in self-adjoint distributed-parameter systems. J Optim Theory Appl 39(2):269–291
Nguyen TL, Do KD, Pan J (2013) Boundary control of coupled nonlinear three dimensional marine risers. J Mar Sci Appl 12(1):72–88
Zhihua Q (2001) Robust and adaptive boundary control of a stretched string on a moving transporter. IEEE Trans Autom Control 46(3):470–476
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):563–566
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 984–989
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):1339–1345
Ro K, Kamman JW (2010) Modeling and simulation of hose-paradrogue aerial refueling systems. J Guid Control Dyn 33(1):53–63
Ro K, Kuk T, Kamman J (2010) Active control of aerial refueling hose-drogue systems. In AIAA Guidance, Navigation, and Control Conference. p 8400
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 1423
Ro K, Kuk T, Kamman JW (2011) Dynamics and control of hose-drogue refueling systems during coupling. J Guid Control Dyn 34(6):1694–1708
Sakawa Y, Luo ZH (2002) Dynamics and control of bending and torsional vibrations of flexible beams. IEEE Trans Autom Control 34(9):970–977
Singh TR (1991) Dynamics and control of flexible arm robots. Thesis Waterloo University
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):2633–2640
Sun D, Liu YH (2001) Position and force tracking of a two-manipulator system manipulating a flexible beam. J Robot Syst 18(4):197–212
Sun D, Liu Y-H (2001) Position and force tracking of a two-manipulator system manipulating a flexible beam. J Robot Syst 18(4):197–212
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 1835–1840
Tang Y, Sun F, Sun Z (2006) Neural network control of flexible-link manipulators using sliding mode. Neurocomputing 70(1–3):288–295
Tee KP, Ge SS, Tay EH (2009) Barrier lyapunov functions for the control of output-constrained nonlinear systems. Automat 45(4):918–927
Thomas PR, Bhandari U, Bullock S, Richardson TS, Du Bois JL (2014) Advances in air to air refuelling. Prog Aerosp Sci 71:14–35
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):489–511
Osman Tokhi M, Mohamed Z, Hasan Shaheed M (2001) Dynamic characterisation of a flexible manipulator system. Robotica 19(5):571–580
Nguyen DT (2009) Boundary output feedback of second-order distributed parameter systems. Syst Control Lett 58(7):519–528
Williamson WR, Reed E, Glenn GJ, Stecko SM, Musgrave J, Takacs JM (2010) Controllable drogue for automated aerial refueling. J Aircr 47(2):515–527
Wu F (2003) Distributed control for interconnected linear parameter-dependent systems. IEE Proc-Control Theory Appl 150(5):518–527
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):1919–1930
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):112–121
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):642–652
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 363:77–96
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):1528–1536
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):2053–2058
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):43–51
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 99:1–11
Zhang YL, Wang JM (2017) Exact controllability of a micro beam with boundary bending moment. Int J Control 1–9
Zhao Z, Liu Y, Luo F (2017) Output feedback boundary control of an axially moving system with input saturation constraint. ISA Trans 68:22–32
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):1–10
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):276–292
Meng D, Wang X, Wenfu X, Liang B (2017) Space robots with flexible appendages: dynamic modeling, coupling measurement, and vibration suppression. J Sound Vib 396:30–50
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):357–401
Guan P, Liu X-J, Liu J-Z (2005) Adaptive fuzzy sliding mode control for flexible satellite. Eng Appl Artif Intell 18(4):451–459
Qinglei H, Ma G (2005) Variable structure control and active vibration suppression of flexible spacecraft during attitude maneuver. Aerosp Sci Technol 9(4):307–317
Qinglei H, Ma G (2008) Adaptive variable structure controller for spacecraft vibration reduction. IEEE Trans Aerosp Electron Syst 44(3):861–876
Cubillos XC, de Souza GLC (2009) Using of h-infinity control method in attitude control system of rigid-flexible satellite. Math Probl Eng 2009
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):1045–1054
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Liu, Z., Liu, J. (2020). Introduction. In: PDE Modeling and Boundary Control for Flexible Mechanical System. Springer Tracts in Mechanical Engineering. Springer, Singapore. https://doi.org/10.1007/978-981-15-2596-4_1
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DOI: https://doi.org/10.1007/978-981-15-2596-4_1
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