Vibration suppression of mine hoisting systems is essential for operational safety and efficiency in ultra-deep mining. In recent years, input shaping has been widely used for residual vibration suppression due to its efficient vibration suppression capability and ease of implementation. However, the natural frequency of the wire rope varies with the length of the rope and time during the hoisting process, posing a huge challenge to conventional input shaping methods. This paper proposes a novel control method employing Segmented Multi-Frequency Input Shapers (SMFIS) to suppress axial vibration by segmenting the lifting trajectory and incorporating multiple natural frequencies into the input shaper design. Based on SMFIS, a simpler velocity-based SMFIS (V-SMFIS) focusing on realizability and a more accurate acceleration-based SMFIS (A-SMFIS) focusing on control effectiveness are developed. Simulation results of various shapers in multiple working conditions verify the effectiveness and superiority of the method, providing a reference for the research of longitudinal vibration suppression method of time-varying mine winding hoister.
JiWYangjunPYumeiH, 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.
2.
HeWMengTHuangD, et al. Adaptive boundary iterative learning control for an Euler–Bernoulli beam system with input constraint. IEEE Trans Neural Netw Learn Syst2018; 29(5): 1539–1549.
3.
KumarKGoyalDBanwaitSS.Effect of key parameters on fretting behaviour of wire rope: a review. Arch Comput Methods Eng2020; 27(2): 549–561.
4.
ZhaoJHanJMaC, et al. Research on operation characteristics of hoisting conveyance under mining deformation action in mine vertical shaft. Nonlinear Dyn2024; 112(4): 2629–2659.
5.
DingXShenGTangY, et al. Axial vibration suppression of wire-ropes and container in double-rope mining hoists with adaptive robust boundary control. Mechatronics2022; 85: 102817.
6.
YuYGeSS.Adaptive boundary feedback control of a rigid–flexible system under unknown time-varying disturbance. J Franklin Inst Eng Appl Math2024; 361(18): 107256.
7.
ZhaoZLiuYHeW, et al. Adaptive boundary control of an axially moving belt system with high acceleration/deceleration. IET Control Theory Appl2016; 10(11): 1299–1306.
8.
WangZPZhaoFLWuHN, et al. Hfuzzy intermittent boundary control for nonlinear parabolic distributed parameter systems. J Franklin Inst Eng Appl Math2023; 360(12): 8008–8036.
9.
QuZ.An iterative learning algorithm for boundary control of a stretched moving string. Automatica2002; 38(5): 821–827.
10.
BiagiottiLMelchiorriCMorielloL.Optimal trajectories for vibration reduction based on exponential filters. IEEE Trans Automat Contr2016; 24(2): 609–622.
11.
WangNCaoG.Adaptive fuzzy backstepping control of underactuated multi-cable parallel suspension system with tension constraint. Trans Inst Meas Contr2021; 43(9): 1971–1984.
12.
WangJPiYHuY, et al. State-observer design of a pde-modeled mining cable elevator with time-varying sensor delays. IEEE Trans Control Syst Technol2020; 28(3): 1149–1157.
13.
KangCG.On the derivative constraints of input shaping control. J Mech Sci Technol2011; 25: 549–554.
14.
MaghsoudiMJMohamedZHusainAR, et al. Improved input shaping technique for a nonlinear system. In: 2014 IEEE International conference on control system computing and engineering, 2014, pp.261–266.
15.
KangCGLeeSG. Impulse vector: a basic mathematical tool to design and analyze flexible robots for removing residual vibrations. In: 2023 20th International conference on Ubiquitous Robots (UR), 2023, pp.6–12. IEEE.
16.
GlossiotisGAntoniadisI.Digital filter based motion command preconditioning of time varying suspended loads in boom cranes for sway suppression. J Vib Control2007; 13(5): 617–656.
17.
HeertjesMBruijnenD. Mimo fir feedforward design for zero error tracking control. In: 2014 American Control Conference (ACC), Proceedings of the American Control Conference, American Control Conference, Portland, OR, 4–6 December 2014.
18.
XieXHuangJLiangZ.Vibration reduction for flexible systems by command smoothing. Mech Syst Signal Process2013; 39(1-2): 461–470.
19.
HuangJLiangZZangQ.Dynamics and swing control of double-pendulum bridge cranes with distributed-mass beams. Mech Syst Signal Process2015; 54-55: 357–366.
20.
JaafarHIMohamedZShamsudinMA, et al. Model reference command shaping for vibration control of multimode flexible systems with application to a double-pendulum overhead crane. Mech Syst Signal Process2019; 115: 677–695.
21.
JaafarHIMohamedZAhmadMA, et al. Control of an underactuated double-pendulum overhead crane using improved model reference command shaping: design, simulation and experiment. Mech Syst Signal Process2021; 151: 107358.
22.
SinghoseW.Command shaping for flexible systems: a review of the first 50 years. Int J Precis Eng Manuf2009; 10: 153–168.
23.
WahrburgAJurvanenJNiemeläM, et al. Input shaping for non-zero initial conditions and arbitrary input signals with an application to overhead crane control. In: 2022 IEEE 17th International conference on advanced motion control (AMC), 2022, pp.36–41. IEEE.
24.
MaghsoudiMJMohamedZTokhiMO, et al. Control of a gantry crane using input-shaping schemes with distributed delay. Trans Inst Meas Contr2017; 39(3): 361–370.
25.
MaghsoudiMJNacerHTokhiM, et al. A novel approach in s-shaped input design for higher vibration reduction. Appl Model Simul2018; 2(2): 76–83.
26.
MaghsoudiMJRamliLSudinS, et al. Improved unity magnitude input shaping scheme for sway control of an underactuated 3D overhead crane with hoisting. Mech Syst Signal Process2019; 123: 466–482.
AlshayaAAlhazzaK.Smooth and robust multi-mode shaped commands. Mech Syst Signal Process2022; 168: 108658.
29.
FasihUrRehmanSMMohamedZHusainAR, et al. Input shaping with an adaptive scheme for swing control of an underactuated tower crane under payload hoisting and mass variations. Mech Syst Signal Process2022; 175: 109106.
30.
XuTTianzhuXJixiangY, et al. Vibration suppression of series elastic actuator used for robotic grinding based on reconstructed hybrid optimized input shaper. Mech Syst Signal Process2025; 223: 111817.
31.
PiYZhangJTangX, et al. Three-dimensional dynamic modeling and simulation of a multi-cable winding hoister system considering bidirectional coupling between cage and flexible guides. J Vib Control2023; 29(7–8): 1678–1699.
32.
ZhangJYangBPiY.Dynamical analysis of a time-varying length rope-driven system with boundary displacement excitation based on time-varying length finite element method. J Vib Control2024; 30: 3862–3878.
33.
ZhangLZuJWHouZ.Complex modal analysis of non-self-adjoint hybrid serpentine belt drive systems. J Vib Acoust2001; 123(2): 150–156.
34.
HangLJianZYachunC, et al. Finite element dynamic modeling and vibration analysis of a mine hoister system under complex boundary conditions. J Vib Control2025. DOI: 10.1177/10775463251341367
