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Xing, Xueyan; Liu, Jinkun

PDE modelling and vibration control of overhead crane bridge with unknown control directions and parametric uncertainties. (English) Zbl 07907040

IET Control Theory Appl. 14, No. 1, 116-126 (2020).
Summary: In this study, problems of the partial differential equation (PDE) modelling and vibration control design are first resolved for an overhead crane bridge system, which is regarded as a Timoshenko beam with an attached rigid body. With the established infinite-dimensional PDE model, a Nussbaum function-based adaptive control approach is developed in order to settle out parametric uncertainties of the system with unknown control directions. Under the proposed control method, states of the overhead crane bridge are globally bounded and finally converge to an adjustable region of zero. The stability of the closed-loop overhead crane bridge system is analysed by employing Lyapunov’s direct method. The effectiveness of the developed control strategy is verified through the simulation results.
© 2021 The Authors. IET Control Theory & Applications published by John Wiley & Sons, Ltd. on behalf of The Institution of Engineering and Technology

Cited in 3 Documents

MSC:

93C20 Control/observation systems governed by partial differential equations
93C95 Application models in control theory
93B52 Feedback control
70L05 Random vibrations in mechanics of particles and systems

Keywords:

cranes; partial differential equations; stability; feedback; Lyapunov methods; uncertain systems; nonlinear control systems; beams (structures); vibration control; control system synthesis; adaptive control; closed loop systems; unknown control directions; parametric uncertainties; vibration control design; attached rigid body; infinite-dimensional PDE model; Nussbaum function-based adaptive control approach; control method; closed-loop overhead crane bridge system; Lyapunov direct method; partial differential equation modelling; Timoshenko beam; stability
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References:

[1] HeW.OuyangY., and HongJ.: ‘Vibration control of a flexible robotic manipulator in the presence of input deadzone’, IEEE Trans. Ind. Inf., 2017, 13, (1), pp. 48-59
[2] YangC.LuoJ., and PanY.et al.: ‘Personalized variable gain control with tremor attenuation for robot teleoperation’, IEEE Trans. Syst. Man Cybern., Syst., 2018, 48, (10), pp. 1759-1770
[3] HeW.MengT., and HeX.et al.: ‘Unified iterative learning control for flexible structures with input constraints’, Automatica, 2018, 86, pp. 326-336 · Zbl 1406.93072
[4] LiuZ.LiuJ., and HeW.: ‘Robust adaptive fault tolerant control for a linear cascaded ODE‐beam systems’, Automatica, 2018, 98, pp. 42-50 · Zbl 1406.93094
[5] HamdyM.Abd‐ElhaleemS., and FkirinM.A.: ‘Adaptive fuzzy predictive controller for a class of networked nonlinear systems with time‐varying delay’, IEEE Trans. Fuzzy Syst., 2017, 26, (4), pp. 2135-2144
[6] HamdyM.Abd‐ElhaleemS., and FkirinM.A.: ‘Time‐varying delay compensation for a class of nonlinear control systems over network via adaptive fuzzy controller’, IEEE Trans. Syst. Man Cybern., Syst., 2016, 47, (8), pp. 2114-2124
[7] DoK.D.: ‘Boundary control of transverse motion of flexible marine risers under stochastic loads’, Ocean Eng., 2018, 155, pp. 156-172
[8] LiuZ.LiuJ., and HeW.: ‘Dynamic modeling and vibration control for a nonlinear three‐dimensional flexible manipulator’, Int. J. Robust Nonlinear Control, 2018, 28, (13), pp. 3927-3945 · Zbl 1397.93145
[9] KrsticM., and SmyshlyaevA.: ‘Backstepping boundary control for first‐order hyperbolic PDEs and application to systems with actuator and sensor delays’, Syst. Control Lett., 2008, 57, (9), pp. 750-758 · Zbl 1153.93022
[10] LiuY.GuoF., and HeX.et al.: ‘Boundary control for an axially moving system with input restriction based on disturbance observers’, IEEE Transactions on Systems, Man and Cybernetics: Systems, 2018, pp. 1-12, DOI: 10.1109/TSMC.2018.2843523
[11] ZhaoZ.AhnC.K, and LiH.‐X.: ‘Boundary antidisturbance control of a spatially nonlinear flexible string system’, IEEE Transactions on Industrial Electronics, 2019, pp. 1-1, in press, DOI: 10.1109/TIE.2019.2931230
[12] TuanL.A.CuongH.M., and LeeS.‐G.et al.: ‘Nonlinear feedback control of container crane mounted on elastic foundation with the flexibility of suspended cable’, J. Vib. Control, 2014, 22, (13), pp. 3067-3078
[13] TuanL.A.LeeS.‐G., and NhoL.C.et al.: ‘Robust controls for ship‐mounted container cranes with viscoelastic foundation and flexible hoisting cable’, Proc. Inst. Mech. Eng. I, J. Syst. Control Eng., 2015, 229, (7), pp. 662-674
[14] LeA.T., and LeeS.‐G.: ‘3D cooperative control of tower cranes using robust adaptive techniques’, J. Franklin Inst., 2017, 354, (18), pp. 8333-8357 · Zbl 1380.93146
[15] HamdyM.RaafatS., and MostafaS.: ‘A hybrid partial feedback linearization and deadbeat control scheme for a nonlinear gantry crane’, J. Franklin Inst., 2018, 355, (14), pp. 6286-6299 · Zbl 1398.93263
[16] SunN.FangY., and ChenH.et al.: ‘Adaptive nonlinear crane control with load hoisting/Lowering and unknown parameters: design and experiments’, IEEE/ASME Trans. Mechatronics, 2015, 20, (5), pp. 2107-2119
[17] MaB.FangY., and ZhangY.: ‘Switching‐based emergency braking control for an overhead crane system’, IET Control Theory Applic., 2010, 4, (9), pp. 1739-1747
[18] ChristophH.MartinB., and HeinerK.: ‘Modeling the beam deflection of a gantry crane under load’, J. Surv. Eng., 2014, 140, (1), pp. 52-59
[19] GerdemeliI.EsenI., and OzerD.: ‘Dynamic response of an overhead crane beam due to a moving mass using moving finite element approximation’, Key Eng. Mater., 2011, 450, pp. 99-102
[20] DuW.LuF., and LiuT.: ‘Folding‐boom lorry crane dynamic modeling and motion control’, Adv. Mater. Res., 2014, 945‐949, pp. 646-652
[21] OguamanamD.C.D.HansenJ.S., and HepplerG.R.: ‘Dynamic response of an overhead crane system’, J. Sound Vib., 1998, 213, (5), pp. 889-906
[22] OguamanamD.C.D.HansenJ.S., and HepplerG.R.: ‘Dynamics of a three‐dimensional overhead crane system’, J. Sound Vib., 2001, 242, (3), pp. 411-426
[23] QueirozM.S.DawsonD.M., and NagarkattiS.P.et al.: ‘Lyapunov based control of mechanical systems’ (Springer Press, USA, 2000) · Zbl 0956.70001
[24] MorgulO.: ‘Dynamic boundary control of the timoshenko beam’, Automatica, 1992, 28, (6), pp. 1255-1260 · Zbl 0775.93108
[25] XuG., and WangH.: ‘Stabilisation of Timoshenko beam system with delay in the boundary control’, Int. J. Control, 2013, 86, (6), pp. 1165-1178 · Zbl 1278.93221
[26] HeW.ZhangS., and GeS.S.et al.: ‘Adaptive boundary control for a class of inhomogeneous Timoshenko beam equations with constraints’, IET Control Theory Applic., 2014, 8, (14), pp. 1285-1292
[27] YildirimK., and KucukI.: ‘Active piezoelectric vibration control for a Timoshenko beam’, J. Franklin Inst., 2016, 353, (1), pp. 95-107 · Zbl 1395.93439
[28] GeS.S.YangC., and LeeT.H.: ‘Adaptive robust control of a class of nonlinear strict‐feedback discrete‐time systems with unknown control directions’, Syst. Control Lett., 2008, 57, (11), pp. 888-895 · Zbl 1149.93319
[29] YangC.GeS.S., and LeeT.H.: ‘Output feedback adaptive control of a class of nonlinear discrete‐time systems with unknown control directions’, Automatica, 2009, 45, (1), pp. 270-276 · Zbl 1154.93377
[30] SharmaV.K.MurthyS.S., and SinghB.: ‘Analysis of switched reluctance motor drive under fault conditions’. Conf. Record of 1998 IEEE Industry Applications Conf.. Thirty‐Third IAS Annual Meeting, St. Louis, MO, USA, 1998, pp. 553-562
[31] YeX.: ‘Asymptotic regulation of time‐varying uncertain nonlinear systems with unknown control directions’, Automatica, 1999, 35, (5), pp. 929-935 · Zbl 0945.93542
[32] ZhangJ.‐X., and YangG.‐H.: ‘Prescribed performance fault‐tolerant control of uncertain nonlinear systems with unknown control directions’, IEEE Trans. Autom. Control, 2017, 62, (12), pp. 6529-6535 · Zbl 1390.93381
[33] LiY.TongS., and LiT.: ‘Observer‐based adaptive fuzzy tracking control of MIMO stochastic nonlinear systems with unknown control directions and unknown dead‐zones’, IEEE Trans. Fuzzy Syst., 2015, 23, (4), pp. 1228-1241
[34] LabiodS., and GuerraT.M.: ‘Indirect adaptive fuzzy control for a class of nonaffine nonlinear systems with unknown control directions’, Int. J. Control Autom. Syst., 2010, 8, (4), pp. 903-907
[35] YeX., and JiangJ.: ‘Adaptive nonlinear design without a priori knowledge of control directions’, IEEE Trans. Autom. Control, 1998, 43, (11), pp. 1617-1621 · Zbl 0957.93048
[36] ParanjapeA.A.GuanJ., and ChungS.J.et al.: ‘PDE boundary control for flexible articulated wings on a robotic aircraft’, IEEE Trans. Robot., 2013, 29, (3), pp. 625-640
[37] HeW., and ZhangS.: ‘Control design for nonlinear flexible wings of a robotic aircraft’, IEEE Trans. Control Syst. Technol., 2017, 25, (1), pp. 351-357
[38] HeJ.‐H: ‘Hamilton’s principle for dynamical elasticity’, Appl. Math. Lett., 2017, 72, pp. 65-69 · Zbl 1462.74080
[39] RahnC.D.: ‘Mechatronic control of distributed noise and vibration: a Lyapunov approach’ (Springer Press, Germany, 2001) · Zbl 0978.70001
[40] HardyG.H.LittlewoodJ.E., and PolyaG.: ‘Inequalities’ (Cambridge University Press, Cambridge, 1959)
[41] HeW., and GeS.S.: ‘Cooperative control of a nonuniform gantry crane with constrained tension’, Automatica, 2016, 66, (4), pp. 146-154 · Zbl 1335.93012
[42] NussbaumR.D.: ‘Some remark on the conjecture in parameter adaptive control’, Syst. Control Lett., 1983, 3, (4), pp. 243-246 · Zbl 0524.93037
[43] WenC.ZhouJ., and LiuZ.et al.: ‘Robust adaptive control of uncertain nonlinear systems in the presence of input saturation and external disturbance’, IEEE Trans. Autom. Control, 2011, 56, (7), pp. 1672-1678 · Zbl 1368.93317
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