This article describes an investigation of a boundary control for vibration suppression of an axially moving accelerated or decelerated belt system with input saturation. Firstly, after considering the effects of the high acceleration or deceleration and unknown distributed disturbance, an infinite-dimensional model of the belt system is described by a nonhomogeneous partial differential equation and a set of ordinary differential equations. Secondly, by synthesizing boundary control techniques and Lyapunov’s direct method, a boundary control is developed to suppress the belt’s vibration and to stabilize the belt system at its equilibrium position globally; an auxiliary system is proposed to compensate for the nonlinear input saturation characteristic; a disturbance adaptation law is employed to mitigate the effects of unknown boundary disturbance; and the S-curve acceleration/deceleration method is adopted to plan the belt’s axial speed. Thirdly, with the proposed boundary control, the wellposedness of the closed-loop belt system is mathematically demonstrated and uniformly bounded stability of the closed-loop system is achieved without any discretization of the system dynamic model. Finally, simulation results are presented to verify the validity and effectiveness of the proposed control scheme.
AdetolaVDeHaanDGuayM (2009) Adaptive model predictive control for constrained nonlinear systems. Systems & Control Letters58(5): 320–326.
2.
BalasMJ (1978) Active control of flexible systems. Journal of Optimization Theory and Applications25: 415–436.
3.
ChenMGeSSRenB (2011) Adaptive tracking control of uncertain MIMO nonlinear systems with input constraints. Automatica47(3): 452–465.
4.
ChenYDJiXDTaoYet al. (2013) Look-ahead algorithm with whole S-curve acceleration and deceleration. Advances in Mechanical Engineering2013: 1–9.
5.
De QueirozMS (2002) Boundary control of vibration and noise in distributed parameter systems: an overview. Mechanical Systems and Signal Processing16(1): 19–39.
6.
De QueirozMSDawsonDMAgarwalMet al. (1999) Adaptive nonlinear boundary control of a flexible link robot arm. IEEE Transactions on Robotics and Automation15(4): 779–787.
7.
De QueirozMSDawsonDMNagarkattiSPet al. (2000) Lyapunov Based Control of Mechanical Systems. Boston, MA: Birkhäuser.
8.
DoKPanJ (2008) Boundary control of transverse motion of marine risers with actuator dynamics. Journal of Sound and Vibration318: 768–791.
9.
EndoTMatsunoFKawasakiH (2009) Simple boundary cooperative control of two one-link flexible arms for grasping. IEEE Transactions on Automatic Control54(10): 2470–2476.
10.
FungRFChouJHKuoYL (2002a) Optimal boundary control of an axially moving material system. Journal of Dynamic Systems, Measurement, and Control-Transactions of the ASME124: 55–61.
11.
FungRFWuJWLuPY (2002b) Adaptive boundary control of an axially moving string system. Journal of Vibration and Acoustics124: 435–440.
GrimmGHatfieldJPostlethwaiteIet al. (2003) Antiwindup for stable linear systems with input saturation: an LMI-based synthesis. IEEE Transactions on Automatic Control48(9): 1509–1525.
14.
HardyGHLittlewoodJEPolyaG (1959) Inequalities. Cambridge, UK: Cambridge University Press.
15.
HeWGeSS (2015a) Vibration control of a nonuniform wind turbine tower via disturbance observer. IEEE/ASME Transactions on Mechatronics20(1): 237–244.
16.
HeWGeSS (2015b) Vibration control of a flexible beam with output constraint. IEEE Transactions on Industrial Electronics62(8): 5023–5030.
17.
HeWGeSS (2016) Cooperative control of a nonuniform gantry crane with constrained tension. Automatica66(4): 146–154.
18.
HeWGeSSHowBVet al. (2011) Robust adaptive boundary control of a flexible marine riser with vessel dynamics. Automatica47(4): 722–732.
19.
HeWGeSSHuangDQ (2015a) Modeling and vibration control for a nonlinear moving string with output constraint. IEEE/ASME Transactions on Mechatronics20(4): 1886–1897.
20.
HeWHeXYGeSS (2016) Vibration control of flexible marine riser systems with input saturation. IEEE/ASME Transactions on Mechatronics21(1): 254–265.
21.
HeWSunCGeSS (2015b) Top tension control of a flexible marine riser by using integral-barrier Lyapunov function. IEEE/ASME Transactions on Mechatronics20(2): 497–505.
22.
HeWZhangSGeSS (2014a) Adaptive control of a flexible crane system with the boundary output constraint. IEEE Transactions on Industrial Electronics61(8): 4126–4133.
23.
HeWZhangSGeSS (2014b) Robust adaptive control of a thruster assisted position mooring system. Automatica50(7): 1843–1851.
24.
KarasonSAnnaswamyA (1994) Adaptive control in the presence of input constraints. IEEE Transactions on Automatic Control39(11): 2325–2330.
25.
KimCWParkHHongKS (2005) Boundary control of axially moving continua: application to a zinc galvanizing line. International Journal of Control, Automation, and Systems3(4): 601–611.
26.
LaousyHXuCZSalletG (1996) Boundary feedback stabilization of a rotating body-beam system. IEEE Transactions on Automatic Control41(2): 241–244.
27.
LeeSYMoteCD (1996) Vibration control of an axially moving string by boundary control. Journal of Dynamic Systems, Measurement, and Control-Transactions of the ASME118: 66–74.
LiYGAronDRahnCD (2002) Adaptive vibration isolation for axially moving string: theory and experiment. Automatica38(3): 379–390.
30.
LinZSaberiA (1997) Low-and-high gain design technique for linear systems subject to input saturation – a direct method. International Journal of Robust and Nonlinear Control7(12): 1071–1101.
31.
LiuYXuBSWuYLet al. (2013) Boundary control of an axially moving belt. In: The 32nd Chinese control conference, Xi’an, China, 26–28 July 2013, pp. 1310–1315. Beijing, China: TCCT, CAA.
32.
MoustafaKAFGadEHEl-MoneerAMAet al. (2005) Modelling and control of overhead cranes with flexible variable-length cable by finite element method. Transactions of the Institute of Measurement and Control27: 1–20.
33.
NguyenQCHongKS (2012) Simultaneous control of longitudinal and transverse vibrations of an axially moving string with velocity tracking. Journal of Sound and Vibration331: 3006–3019.
34.
QuZH (2001) Robust and adaptive boundary control of a stretched string on a moving transporter. IEEE Transactions on Automatic Control46(3): 470–476.
35.
RahnCD (2001) Mechatronic Control of Distributed Noise and Vibration. New York, NY: Springer-Verlag.
36.
SmithGD (1978) Numerical Solution of Partial Differential Equations: Finite Difference Methods. Oxford, UK: Oxford University Press.
37.
SmyshlyaevAKrsticM (2010) Adaptive Control of Parabolic PDEs. Princeton, NJ: Princeton University Press.
38.
SuJYYangJLiSH (2014) Continuous finite-time anti-disturbance control for a class of uncertain nonlinear systems. Transactions of the Institute of Measurement and Control36(3): 300–311.
39.
XuCBaillieulJ (1993) Stabilizability and stabilization of a rotating body-beam system with torque control. IEEE Transactions on Automatic Control38(12): 1745–1765.
40.
YangJLiSHSuJY (2013) Continuous nonsingular terminal sliding mode control for systems with mismatched disturbances. Automatica49(7): 2287–2291.
41.
YangKJHongKSMatsunoF (2004) Robust adaptive boundary control of an axially moving string under a spatiotemporally varying tension. Journal of Sound and Vibration273: 1007–1029.
42.
YangKJHongKSMatsunoF (2005) Energy-based control of axially translating beams: varying tension, varying speed, and disturbance adaptation. IEEE Transactions on Control Systems Technology13(6): 1045–1054.
43.
ZhouJWenCY (2008) Adaptive Backstepping Control of Uncertain Systems: Nonsmooth Nonlinearities, Interactions or Time-Variations. Berlin, Germany: Springer.
