Robust sliding-mode control for a gantry crane system subject to external disturbance
This paper devotes to proposing a sliding-mode controller to reject external disturbance and stabilize the gantry crane system which formulated by the partial differential equations (PDEs). The control objectives are transporting trolley hanging with a payload to the specified place while eliminatin...
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| Published in | Nonlinear dynamics Vol. 112; no. 6; pp. 4599 - 4615 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Dordrecht
Springer Netherlands
01.03.2024
Springer Nature B.V |
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| Online Access | Get full text |
| ISSN | 0924-090X 1573-269X |
| DOI | 10.1007/s11071-024-09294-4 |
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| Abstract | This paper devotes to proposing a sliding-mode controller to reject external disturbance and stabilize the gantry crane system which formulated by the partial differential equations (PDEs). The control objectives are transporting trolley hanging with a payload to the specified place while eliminating the oscillation and rejecting the external disturbance in transportation. By applying the operator semigroup theory, it can be proved that proposed controller is well-posed to the gantry crane system. Furthermore, asymptotic stability has been proved through the application of the extended Krasovskii-LaSalles’ invariance principle. Ultimately, numerical simulations are given to illustrate the advance of proposed control scheme and an experiment is conducted to display the feasibility of proposed sliding-mode controller. |
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| AbstractList | This paper devotes to proposing a sliding-mode controller to reject external disturbance and stabilize the gantry crane system which formulated by the partial differential equations (PDEs). The control objectives are transporting trolley hanging with a payload to the specified place while eliminating the oscillation and rejecting the external disturbance in transportation. By applying the operator semigroup theory, it can be proved that proposed controller is well-posed to the gantry crane system. Furthermore, asymptotic stability has been proved through the application of the extended Krasovskii-LaSalles’ invariance principle. Ultimately, numerical simulations are given to illustrate the advance of proposed control scheme and an experiment is conducted to display the feasibility of proposed sliding-mode controller. |
| Author | Wu, Wei Huang, Xin Zhang, Jiayang |
| Author_xml | – sequence: 1 givenname: Jiayang surname: Zhang fullname: Zhang, Jiayang organization: Key Laboratory of Advanced Process Control for Light Industry (Ministry of Education), Jiangnan University – sequence: 2 givenname: Wei surname: Wu fullname: Wu, Wei email: weiwu@jiangnan.edu.cn organization: Key Laboratory of Advanced Process Control for Light Industry (Ministry of Education), Jiangnan University – sequence: 3 givenname: Xin surname: Huang fullname: Huang, Xin organization: Key Laboratory of Advanced Process Control for Light Industry (Ministry of Education), Jiangnan University |
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| Cites_doi | 10.1109/CCDC.2018.8407619 10.1109/TASE.2020.3015870 10.1177/1077546309105095 10.1080/00207179.2017.1335439 10.1109/ACC.1995.532365 10.1016/j.apm.2023.01.003 10.1016/j.neucom.2022.11.010 10.1007/978-1-0716-0590-5_3 10.1109/CAC53003.2021.9728393 10.1109/TIE.2021.3065835 10.1109/ChiCC.2014.6897064 10.1007/978-3-662-04641-8 10.1109/ACC.2000.876928 10.1016/j.automatica.2015.12.026 10.1016/S0005-1098(99)00182-X 10.1109/TIE.2013.2288200 10.1109/CAC53003.2021.9728710 10.1115/1.2364010 10.1016/j.ymssp.2017.03.015 10.1007/BF01211483 10.1109/TCYB.2022.3188494 10.1093/oso/9780198502777.001.0001 10.1007/s11071-022-07859-9 10.1201/b12209 10.1016/j.ymssp.2023.110368 10.1109/ComRob53312.2021.9628529 10.1016/j.ymssp.2018.11.005 10.1109/TSMC.2023.3257220 10.1524/auto.2005.53.8.400 10.1007/s11071-023-08420-y |
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| Keywords | Distributed parameters system Operator semigroup Sliding-mode controller Partial differential equations Gantry crane system |
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| References | AlbaltaMYalçınYModel reference input shaped neuro-adaptive sliding mode control of gantry craneProceed. Inst. Mech. Eng. Part I J. Syst. Control Eng.20232375824838 Wen, Y., Lou, X., Wu, W., Cui, B.: Backstepping boundary control for a class of gantry crane systems. IEEE Transactions on Cybernetics (2022) Banks, H.T.: A functional analysis framework for modeling, Estim. Control Sci. Eng. CRC Press (2012) WuXXuKLeiMHeXDisturbance-compensation-based continuous sliding mode control for overhead cranes with disturbancesIEEE Trans. Autom. Sci. Eng.20201742182218910.1109/TASE.2020.3015870 Joshi, S., Rahn, C.D.: Position control of a flexible cable gantry crane: theory and experiment. In: Proceedings of 1995 American Control Conference-ACC’95, vol. 4, pp. 2820–2824. IEEE (1995) HuangJWangWZhouJAdaptive control design for underactuated cranes with guaranteed transient performance: theoretical design and experimental verificationIEEE Trans. Industr. Electron.20216932822283210.1109/TIE.2021.3065835 LiMChenHLiZInput-limited optimal control for overhead cranes with payload hoisting/lowering and double pendulum effectsNonlinear Dyn.202311112111355110.1007/s11071-023-08420-y Wen, Y., Lou, X., Cui, B.: Boundary output feedback control for a class of gantry crane systems via backstepping approach. In: 2021 China Automation Congress (CAC), pp. 4030–4035. IEEE (2021) Adams, R.A., Fournier, J.J.: Sobolev Spaces. Elsevier (2003) AlmutairiNBZribiMSliding mode control of a three-dimensional overhead craneJ. Vib. Control2009151116791730258997610.1177/1077546309105095 MaLLouXJiaJNeural-network-based boundary control for a gantry crane system with unknown friction and output constraintNeurocomputing202351827128110.1016/j.neucom.2022.11.010 GuoQChaiLLiuHAnti-swing sliding mode control of three-dimensional double pendulum overhead cranes based on extended state observerNonlinear Dyn.2023111139141010.1007/s11071-022-07859-9 Aguilar, L.T.: State-feedback nonlinear H∞\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\text{H}_\infty $$\end{document} boundary control for a gantry crane with flexible cable. In: 2021 XXIII Robotics Mexican Congress (ComRob), pp. 7–12. IEEE (2021) WijnandMd’Andréa NovelBRosierLFinite-time stabilization of an overhead crane with a flexible cable submitted to an affine tensionESAIM Control Optimisat. Calc. Var.2021312194321231 He, W., He, X., Ge, S.S.: Adaptive control design for a nonuniform gantry crane with constrained tension. In: Proceedings of the 33rd Chinese Control Conference, pp. 2705–2710. IEEE (2014) ConradFMifdalAStrong stability of a model of an overhead craneControl. Cybern.19982733633741663955 ThullDWildDKugiAInfinit-dimensionale regelung eines brückenkranes mit schweren ketten infinite-dimensional control of a gantry crane with heavy chainsAutomatisierungstechnik20055384001010.1524/auto.2005.53.8.400 GolovinIPalisSRobust control for active damping of elastic gantry crane vibrationsMech. Syst. Signal Process.20191212642782019MSSP..121..264G10.1016/j.ymssp.2018.11.005 Cazenave, T., Haraux, A.: An Introduction to Semilinear Evolution Equations, vol. 13. Oxford University Press on Demand (1998) d’Andréa NovelBCoronJMExponential stabilization of an overhead crane with flexible cable via a back-stepping approachAutomatica2000364587593182890510.1016/S0005-1098(99)00182-X RamliLMohamedZAbdullahiAMJaafarHILazimIMControl strategies for crane systems: a comprehensive reviewMech. Syst. Signal Process.2017951232017MSSP...95....1R10.1016/j.ymssp.2017.03.015 Rahn Christopher D, C.: Mechatronic Control of Distributed Noise and Vibration. Springer (2001) d’Andréa NovelBBoustanyFConradFRaoBPFeedback stabilization of a hybrid Pde-ode system: application to an overhead craneMath. Control Signals Syst.19947122135901910.1007/BF01211483 Hagen, G., Mezic, I.: Control spillover in dissipative evolution equations. In: Proceedings of the 2000 American Control Conference. ACC (IEEE Cat. No. 00CH36334), vol. 6, pp. 3783–3787. IEEE (2000) HeWZhangSGeSSAdaptive control of a flexible crane system with the boundary output constraintIEEE Trans. Industr. Electron.20136184126413310.1109/TIE.2013.2288200 HuangXWuWYanWLouXNiHSliding-mode control of gantry crane system with recursive least square parameters identificationJ. Ambient Intell. Humaniz. Comput.202110111:CAS:528:DC%2BB3MXislymsrvI DongJChengWMRenYZWangYPResearch on the structural performance of large-tonnage gantry craneTrans. Tech. Publ.20131382324750 MaksakovAGolovinIShyshMPalisSData-driven modeling for damping and positioning control of gantry craneMech. Syst. Signal Process.202319710.1016/j.ymssp.2023.110368 Curtain, R., Zwart, H.: Introduction to Infinite-Dimensional Systems Theory: A State-Space Approach, vol. 71. Springer Nature (2020) Ma, L., Lou, X.: Adaptive boundary control of a gantry crane system with parametric uncertainty. In: 2021 China Automation Congress (CAC), pp. 4391–4395. IEEE (2021) Li, Y., Zhou, S., Zhu, H.: A Backstepping controller design for underactuated crane system. In: 2018 Chinese Control and Decision Conference (CCDC), pp. 2895–2899. IEEE (2018) CuongHM Robust control of rubber-tyred gantry cranes with structural elasticityAppl. Math. Modell.202311774161453759110.1016/j.apm.2023.01.003 StürzerDArnoldAKugiAClosed-loop stability analysis of a gantry crane with heavy chain and payloadInt. J. Control201891819311943383568010.1080/00207179.2017.1335439 HeWGeSSCooperative control of a nonuniform gantry crane with constrained tensionAutomatica201666146154345842310.1016/j.automatica.2015.12.026 LaxPThe initial value problem for nonlinear hyperbolic equations in two independent variablesContrib. Theory Partial Differ. Equ.19543321168093 Lee, H.H., Liang, Y., Segura, D.: A sliding-mode antiswing trajectory control for overhead cranes with high-speed load hoisting (2006) Ma, Y., Lou, X., Miller, T., Wu, W.: Fault-tolerant boundary control of an Euler–Bernoulli beam subject to output constraint. IEEE Transactions on Systems, Man, and Cybernetics: Systems (2023) W He (9294_CR16) 2016; 66 A Maksakov (9294_CR29) 2023; 197 M Li (9294_CR24) 2023; 111 F Conrad (9294_CR7) 1998; 27 J Dong (9294_CR10) 2013; 13 9294_CR21 9294_CR23 J Huang (9294_CR19) 2021; 69 9294_CR25 9294_CR26 M Albalta (9294_CR3) 2023; 237 P Lax (9294_CR22) 1954; 33 9294_CR17 M Wijnand (9294_CR36) 2021; 31 B d’Andréa Novel (9294_CR12) 2000; 36 HM Cuong (9294_CR8) 2023; 117 Q Guo (9294_CR14) 2023; 111 B d’Andréa Novel (9294_CR11) 1994; 7 X Wu (9294_CR37) 2020; 17 L Ramli (9294_CR31) 2017; 95 D Stürzer (9294_CR32) 2018; 91 NB Almutairi (9294_CR4) 2009; 15 9294_CR30 9294_CR34 X Huang (9294_CR20) 2021; 10 9294_CR35 9294_CR15 9294_CR1 9294_CR28 9294_CR9 I Golovin (9294_CR13) 2019; 121 L Ma (9294_CR27) 2023; 518 9294_CR6 W He (9294_CR18) 2013; 61 9294_CR5 D Thull (9294_CR33) 2005; 53 9294_CR2 |
| References_xml | – reference: CuongHM Robust control of rubber-tyred gantry cranes with structural elasticityAppl. Math. Modell.202311774161453759110.1016/j.apm.2023.01.003 – reference: HuangJWangWZhouJAdaptive control design for underactuated cranes with guaranteed transient performance: theoretical design and experimental verificationIEEE Trans. Industr. Electron.20216932822283210.1109/TIE.2021.3065835 – reference: ConradFMifdalAStrong stability of a model of an overhead craneControl. Cybern.19982733633741663955 – reference: MaksakovAGolovinIShyshMPalisSData-driven modeling for damping and positioning control of gantry craneMech. Syst. Signal Process.202319710.1016/j.ymssp.2023.110368 – reference: LaxPThe initial value problem for nonlinear hyperbolic equations in two independent variablesContrib. Theory Partial Differ. Equ.19543321168093 – reference: MaLLouXJiaJNeural-network-based boundary control for a gantry crane system with unknown friction and output constraintNeurocomputing202351827128110.1016/j.neucom.2022.11.010 – reference: GolovinIPalisSRobust control for active damping of elastic gantry crane vibrationsMech. Syst. Signal Process.20191212642782019MSSP..121..264G10.1016/j.ymssp.2018.11.005 – reference: He, W., He, X., Ge, S.S.: Adaptive control design for a nonuniform gantry crane with constrained tension. In: Proceedings of the 33rd Chinese Control Conference, pp. 2705–2710. IEEE (2014) – reference: LiMChenHLiZInput-limited optimal control for overhead cranes with payload hoisting/lowering and double pendulum effectsNonlinear Dyn.202311112111355110.1007/s11071-023-08420-y – reference: Joshi, S., Rahn, C.D.: Position control of a flexible cable gantry crane: theory and experiment. In: Proceedings of 1995 American Control Conference-ACC’95, vol. 4, pp. 2820–2824. IEEE (1995) – reference: Aguilar, L.T.: State-feedback nonlinear H∞\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\text{H}_\infty $$\end{document} boundary control for a gantry crane with flexible cable. In: 2021 XXIII Robotics Mexican Congress (ComRob), pp. 7–12. IEEE (2021) – reference: AlbaltaMYalçınYModel reference input shaped neuro-adaptive sliding mode control of gantry craneProceed. Inst. Mech. Eng. Part I J. Syst. Control Eng.20232375824838 – reference: HuangXWuWYanWLouXNiHSliding-mode control of gantry crane system with recursive least square parameters identificationJ. Ambient Intell. Humaniz. Comput.202110111:CAS:528:DC%2BB3MXislymsrvI – reference: Cazenave, T., Haraux, A.: An Introduction to Semilinear Evolution Equations, vol. 13. Oxford University Press on Demand (1998) – reference: WuXXuKLeiMHeXDisturbance-compensation-based continuous sliding mode control for overhead cranes with disturbancesIEEE Trans. Autom. Sci. Eng.20201742182218910.1109/TASE.2020.3015870 – reference: Ma, L., Lou, X.: Adaptive boundary control of a gantry crane system with parametric uncertainty. In: 2021 China Automation Congress (CAC), pp. 4391–4395. IEEE (2021) – reference: Wen, Y., Lou, X., Wu, W., Cui, B.: Backstepping boundary control for a class of gantry crane systems. IEEE Transactions on Cybernetics (2022) – reference: Banks, H.T.: A functional analysis framework for modeling, Estim. Control Sci. Eng. CRC Press (2012) – reference: HeWZhangSGeSSAdaptive control of a flexible crane system with the boundary output constraintIEEE Trans. Industr. Electron.20136184126413310.1109/TIE.2013.2288200 – reference: Li, Y., Zhou, S., Zhu, H.: A Backstepping controller design for underactuated crane system. In: 2018 Chinese Control and Decision Conference (CCDC), pp. 2895–2899. IEEE (2018) – reference: Rahn Christopher D, C.: Mechatronic Control of Distributed Noise and Vibration. Springer (2001) – reference: Adams, R.A., Fournier, J.J.: Sobolev Spaces. Elsevier (2003) – reference: Ma, Y., Lou, X., Miller, T., Wu, W.: Fault-tolerant boundary control of an Euler–Bernoulli beam subject to output constraint. IEEE Transactions on Systems, Man, and Cybernetics: Systems (2023) – reference: RamliLMohamedZAbdullahiAMJaafarHILazimIMControl strategies for crane systems: a comprehensive reviewMech. Syst. Signal Process.2017951232017MSSP...95....1R10.1016/j.ymssp.2017.03.015 – reference: AlmutairiNBZribiMSliding mode control of a three-dimensional overhead craneJ. Vib. Control2009151116791730258997610.1177/1077546309105095 – reference: Wen, Y., Lou, X., Cui, B.: Boundary output feedback control for a class of gantry crane systems via backstepping approach. 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| SubjectTerms | Automotive Engineering Classical Mechanics Closed loop systems Control Controllers Design Detainer Dynamical Systems Engineering Gantry cranes Hilbert space Mechanical Engineering Operators (mathematics) Original Paper Partial differential equations Process controls Robust control Sliding mode control Vibration |
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| Title | Robust sliding-mode control for a gantry crane system subject to external disturbance |
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