This article focuses on the boundary control for a lifting system during the loading process. A lifting system during the loading process is essentially a non-conservative system. The system dynamics are modelled based on the extended Hamilton’s principle. We consider the unmeasurable impact force caused by the uncertain materials falling velocity as a boundary disturbance and design a disturbance observer to eliminate its effect. The control system needs to guarantee the output constraints that the boundary vibration and dynamic tension fluctuation are both suppressed in a constrained scope of the desired value. Two appropriate boundary backstepping control schemes are proposed by actuators acting on different boundaries to realize the output constraints and to ensure the stability of the closed-loop system in theory. Numerical simulations are provided to illustrate the effectiveness of the proposed control laws in suppressing the cage vibration and rope dynamic tension fluctuation amplitude.
XingXLiuJ. Vibration and position control of overhead crane with three-dimensional variable length cable subject to input amplitude and rate constraints. IEEE Trans Syst Man Cybernet Syst2019; 51(7): 4127–4138.
2.
HeXHeWShiJ, et al. Boundary vibration control of variable length crane systems in two-dimensional space with output constraints. IEEE/ASME Trans Mech2017; 22(5): 1952–1962.
3.
GaikoNVvan HorssenWT. Resonances and vibrations in an elevator cable system due to boundary sway. J Sound Vib2018; 424: 272–292.
4.
ArrasateXKaczmarczykSAlmandozG, et al. The modelling, simulation and experimental testing of the dynamic responses of an elevator system. Mech Syst Signal Pr2014; 42(1-2): 258–282.
5.
KaczmarczykSOstachowiczW. Transient vibration phenomena in deep mine hoisting cables. Part 1: mathematical model. J Sound Vib2003; 262(2): 219–244.
6.
KaczmarczykSOstachowiczW. Transient vibration phenomena in deep mine hoisting cables. Part 2: numerical simulation of the dynamic response. J Sound Vib2003; 262(2): 245–289.
7.
WangJPiYKrsticM. Balancing and suppression of oscillations of tension and cage in dual-cable mining elevators. Automatica2018; 98: 223–238.
8.
WangJCaoGZhuZ, et al. Lateral response of cable-guided hoisting system with time-varying length: theoretical model and dynamics simulation verification. Proc IMechE, Part C: J Mechanical Engineering Science2015; 229(16): 2908–2920.
9.
CaoGWangJZhuZ. Coupled vibrations of rope-guided hoisting system with tension difference between two guiding ropes. Proc IMechE, Part C: J Mechanical Engineering Science2018; 232(2): 231–244.
10.
WangNCaoGYanL, et al. Modelling and passive control of flexible guiding hoisting system with time-varying length. Math Comput Model Dynam Syst2020; 26(1): 31–54.
11.
WangJPiYHuY, et al. Modeling and dynamic behavior analysis of a coupled multi-cable double drum winding hoister with flexible guides. Mech Mach Theory2017; 108: 191–208
12.
WangJKogaSPiY, et al. Axial vibration suppression in a partial differential equation model of ascending mining cable elevator. J Dynam Syst Meas Control2018; 140(11): 111003.
13.
WangJPiY. Output feedback vibration control of a string driven by a nonlinear actuator. Appl Math Model2019; 72: 403–419.
14.
WangJKrsticM. Adaptive event-triggered PDE control for load-moving cable systems. Automatica2021; 129: 109637.
15.
WangNCaoGWangL, et al. Modelling and control of flexible guided lifting system with output constraints and unknown input hysteresis. J Vib Control2020; 26(1-2): 112–128.
16.
OtsukiMYoshidaKNakagawaT, et al. Nonstationary robust control for vibration of elevator rope. J Syst Design Dynam2007; 1(2): 283–294.
17.
SorokinVSThomsenJJ. Vibration suppression for strings with distributed loading using spatial cross-section modulation. J Sound Vib2015; 335: 66–77.
18.
ChenLSunLNagarajaiahS. Cable with discrete negative stiffness device and viscous damper: passive realization and general characteristics. Smart Struct Syst2015; 15(3): 627–643.
19.
LiuYGuoFHeX, et al. Boundary control for an axially moving system with input restriction based on disturbance observers. IEEE Trans Syst Man Cybernet2018; 49(11): 2242–2253.
20.
ZhaoZHeXAhnCK. Boundary disturbance observer-based control of a vibrating single-link flexible manipulator. IEEE Trans Syst Man Cybernet2019; 51(4): 2382–2390.
21.
HeWZhangSGeSS. Adaptive control of a flexible crane system with the boundary output constraint. IEEE Trans Ind Electron2013; 61(8): 4126–4133.
22.
GuoFLuoFLiuY, et al. Adaptive output feedback boundary control for a class of axially moving system. IET Control Theory Appl2019; 13(2): 213–221.
23.
HeWYangCMengT, et al. Distributed control of a class of flexible mechanical systems with global constraint. Int J Control2016; 89(1): 128–139.
24.
ZhaoZLiuYLuoF. Boundary control for a vibrating string system with bounded input. Asian J Control2018; 20(1): 323–331.
25.
LiuZZhaoZAhnCK. Boundary constrained control of flexible string systems subject to disturbances. IEEE Trans Circuit Syst II Express Brief2019; 67(1): 112–116.
26.
HeWHeXZouM, et al. PDE model-based boundary control design for a flexible robotic manipulator with input backlash. IEEE Trans Control Syst Tech2018; 27(2): 790–797.
27.
WanMYinYLiuJ, et al. Active boundary control of vibrating marine riser with constrained input in three-dimensional space. Nonlin Dynam2021; 106(3): 2329–2345.
28.
HeWGeSSHuangD. Modeling and vibration control for a nonlinear moving string with output constraint. IEEE/ASME Trans Mech2014; 20(4): 1886–1897.
29.
GuoFLiuYLuoF, et al. Vibration suppression and output constraint of a variable length drilling riser system. J Franklin Inst2019; 356(3): 1177–1195.
30.
HeWSunCGeSS. Top tension control of a flexible marine riser by using integral-barrier lyapunov function. IEEE/ASME Trans Mech2014; 20(2): 497–505.
31.
ZhaoZLiuYGuoF, et al. Vibration control and boundary tension constraint of an axially moving string system. Nonlin Dynam2017; 89(4): 2431–2440.
32.
WangNCaoG. Adaptive fuzzy backstepping control of underactuated multi-cable parallel suspension system with tension constraint. Trans Inst Meas Control2021; 43(9): 1971–1984.
33.
CaoGHZhuZCPengWH, et al. Study on vibrant characteristic in skip’s loading. J China Coal Soc2007; 32(3): 327–330 (in Chinese).
34.
ZhuZCCaoGHPengWH, et al. Analysis of longitudinal vibration of wire rope in loading of skip. J China Univ Mining Tech2007; 36(3): 325–329 (in Chinese).
35.
HeMC. Research on deep shaft hoisting dynamics. Adv Mech2021; 51(3): 702–728 (in Chinese).
36.
IrschikHBelyaevAK. Dynamics of mechanical systems with variable mass. New York: Springer, 2014.
37.
De QueirozMSDawsonDMNagarkattiSP, et al. Lyapunov-based control of mechanical systems. New York: Springer, 2000.
38.
LeiGXuGZhangX, et al. Study on dynamic characteristics and compensation of wire rope tension based on oil pressure sensor. Adv Mech Eng2019; 11(3): 1–13.
