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Research on nonlinear coupled tracking controller for double pendulum gantry cranes with load hoisting/lowering

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A Correction to this article was published on 09 May 2022

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Abstract

Gantry cranes have attracted extensive attention that are mostly simplified as nonlinear single pendulum systems without load hoisting/lowering. However, due to the existence of the hook in practice, gantry cranes produce double pendulum effect. With an extra underactuated degree of freedom, the anti-swing control of double pendulum gantry cranes becomes more difficult than that of single pendulum gantry cranes. Moreover, double pendulum gantry cranes with load hoisting/lowering may cause large swings, which lead to inaccurate positioning and low transportation efficiency. In this paper, a novel nonlinear coupled tracking anti-swing controller is proposed to solve these problems. The proposed controller can ensure the stable startup and operation of the trolley by introducing a smooth expected trajectory. In addition, a composite signal is constructed to suppress and eliminate the swing angles of the gantry crane system. The system stability is analyzed by utilizing Lyapunov techniques and Barbalat’s lemma. Theoretical derivation, simulation and experimental results indicate that the proposed controller suppresses and eliminates the hook/load swing angle effectively. Furthermore, it can achieve superior control effects and strong robustness against the changes of the load mass, trolley target displacement, initial rope lengths, initial system swing angles and external disturbances.

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The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.

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References

  1. Shi, H., Li, G., Ma, X., Sun, J.: Research on nonlinear coupling anti-swing control method of double pendulum gantry crane based on improved energy. Symmetry 11(12), 1511 (2019)

    Article  Google Scholar 

  2. Sun, N., Zhang, J., Xin, X., Yang, T., Fang, Y.: Nonlinear output feedback control of flexible rope crane systems with state constraints. IEEE Access 7, 136193–136202 (2019)

    Article  Google Scholar 

  3. Shi, H., Li, G., Bai, X., Huang, J.: Research on nonlinear control method of underactuated gantry crane based on machine vision positioning. Symmetry 11(8), 987 (2019)

    Article  Google Scholar 

  4. Zhang, M., Ma, X., Rong, X., Sun, R., Tian, X.: Modeling and energy-based fuzzy controlling for underactuated overhead cranes with load transferring, lowering, and persistent external disturbances. Adv. Mech. Eng. 9(10), 1–13 (2017)

    Google Scholar 

  5. Lu, B., Fang, Y., Sun, N.: Enhanced-coupling adaptive control for double-pendulum overhead cranes with payload hoisting and lowering. Automatica 101, 241–251 (2017)

    Article  MathSciNet  Google Scholar 

  6. Xia, X., Wu, Z.: Optimal motion planning for overhead cranes. IET Control Theory Appl. 8(17), 1833–1842 (2014)

    Article  Google Scholar 

  7. Sun, N., Fang, Y., Chen, H.: A new anti-swing control method for underactuated cranes with unmodeled uncertainties: theoretical design and hardware experiments. IEEE Trans. Ind. Electron. 62(1), 453–465 (2015)

    Article  Google Scholar 

  8. Sun, N., Fang, Y., Chen, H., He, B.: Adaptive nonlinear crane control with load hoisting/lowering and unknown parameters: design and experiments. IEEE/ASME Trans. Mechatron. 20(5), 2107–2119 (2015)

    Article  Google Scholar 

  9. Vazquez, Z., Collado, J., Fridman, L.: Control of a parametrically excited crane: a vector Lyapunov approach. IEEE Trans. Control Syst. Technol. 21(6), 2332–2340 (2013)

    Article  Google Scholar 

  10. Boschetti, G., Caracciolo, R., Richiedei, D., Trevisani, A.: A non-time based controller for load swing damping and path-tracking in robotic cranes. Intell. Robot. Syst. 76(2), 201–217 (2014)

    Article  Google Scholar 

  11. Lee, L., Huang, C., Ku, S., Yang, Z., Chang, C.: Efficient visual feedback method to control a three-dimensional overhead crane. IEEE Trans. Ind. Electron. 61(8), 4073–4083 (2014)

    Article  Google Scholar 

  12. Masoud, Z., Alhazza, K., Abu-Nada, E., Majeed, M.: A hybrid command-shaper for double-pendulum overhead cranes. Vib. Control. 20(1), 24–37 (2014)

    Article  Google Scholar 

  13. Tuan, L., Lee, S.: Sliding mode controls of double-pendulum crane systems. Mech. Sci. Technol. 27(6), 1863–1873 (2013)

    Article  Google Scholar 

  14. Sun, N., Fang, Y., Chen, H., Fu, Y.: Super-twisting-based anti-swing control for underactuated double pendulum cranes. IEEE/ASME Int. Conf. Adv. Intell. Mechatron. 749–754 (2015)

  15. Qian, D., Tong, S., Yang, B., Lee, S.: Design of simultaneous input-shaping-based SIRMs fuzzy control for double-pendulum-type overhead cranes. Bull. Polish Acad. Sci. Tech. Sci. 63(4), 887–896 (2015)

    Google Scholar 

  16. Chen, H., Fang, Y., Sun, N.: A swing constrained time-optimal trajectory planning strategy for double pendulum crane systems. Nonlinear Dyn. 89(2), 1513–1524 (2017)

    Article  MathSciNet  Google Scholar 

  17. Sun, N., Wu, Y., Chen, H., Fang, Y.: An energy-optimal solution for transportation control of cranes with double pendulum dynamics: design and experiments. Mech. Syst. Signal Process. 102(MAR.1), 87–101 (2018)

  18. Zhang, M., Ma, X., Chai, H., Rong, X., Tian, X., Li, Y.: A novel online motion planning method for double-pendulum overhead cranes. Nonlinear Dyn. 85(2), 1079–1090 (2016)

    Article  Google Scholar 

  19. Sun, N., Fang, Y., Chen, H., Lu, B.: Amplitude-saturated nonlinear output feedback anti-swing control for underactuated cranes with double-pendulum cargo dynamics. IEEE Trans. Industr Inform. 64(3), 2135–2146 (2017)

    Article  Google Scholar 

  20. Zhang, M., Ma, X., Rong, X., Song, R., Tian, X., Li, Y.: A partially saturated adaptive learning controller for overhead cranes with payload hoisting/lowering and unknown parameters. Nonlinear Dyn. 89(2), 1779–1791 (2017)

  21. Sun, N., Fang, Y.: Nonlinear tracking control of underactuated cranes with load transferring and lowering: theory and experimentation. Automatica 50(9), 2350–2357 (2014)

  22. Huang, J., Liang, Z., Zang, Q.: Dynamics and swing control of double-pendulum bridge cranes with distributed-mass beams. Mech. Syst. Signal Process. 54–55, 357–366 (2015)

    Article  Google Scholar 

  23. Masoud, Z., Alhazza, K., Abu-Nada, E., Majeed, m.: A hybrid command-shaper for double- pendulum overhead cranes. J. Vib. Control. 20(1), 24–37 (2014)

  24. Manning, R., Clement, J., Kim, D., Singhose, W.: Dynamics and control of bridge cranes transporting distributed-mass payloads. J. Dyn. Syst. Meas. Control. 132(1), 1–8 (2010)

    Article  Google Scholar 

  25. Sun, N., Yang, T., Fang, Y.: Transportation control of double-pendulum cranes with a nonlinear quasi-PID scheme: design and experiments. IEEE Trans. Syst. Man Cybern. Syst. 49(7), 1408–1418 (2019)

    Article  Google Scholar 

  26. Sun, N., Wu, Y., Fang, Y.: Nonlinear anti-swing control for crane systems with double-pendulum swing eects and uncertain parameters: design and experiments. IEEE Trans. Autom. Sci. Eng. 15, 1413–1422 (2018)

    Article  Google Scholar 

  27. Zhang, M., Ma, X., Rong, X.: A novel energy-coupling-based control method for double-pendulum overhead cranes with initial control force constraint. Adv. Mech. Eng. 10(1), 168781401775221 (2018)

    Article  Google Scholar 

  28. Zhang, M., Zhang, Y., Cheng, X.: An enhanced coupling PD with sliding mode control method for underactuated double-pendulum overhead crane systems. Int. J. Control Autom. Syst. 17, 1579–1588 (2019)

    Article  Google Scholar 

  29. Tuan, L., Lee, S., Ko, D., Nho, L.: Combined control with sliding mode and partial feedback linearization for 3D overhead cranes. Int. J. Robust Nonlinear Control 24(18), 3372–3386 (2014)

    Article  MathSciNet  Google Scholar 

  30. Chwa, D.: Sliding-mode-control-based robust finite-time antisway tracking control of 3-D overhead cranes. IEEE Trans. Ind. Electron. 64(8), 6775–6784 (2017)

    Article  Google Scholar 

  31. Zhang, M., Zhang, Y., Ouyang, H., Ma, C., Cheng, X.: Adaptive integral sliding mode control with payload sway reduction for 4-DOF tower crane systems. Nonlinear Dyn. 99(7), 2727–2741 (2020)

    Article  Google Scholar 

  32. Zhang, M., Ma, X., Rong, X., Song, R., Tian, X., Li, B.: A partially saturated adaptive learning controller for overhead cranes with payload hoisting/lowering and unknown parameters. Nonlinear Dyn. 89(2), 1779–1791 (2017)

    Article  MathSciNet  Google Scholar 

  33. Khalil, H.: Nonlinear Systems, 3rd edn. Prentice-Hall, Englewood Cliffs (2002)

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Acknowledgements

This research has been supported in part by the National Natural Science Foundation of China (51905357, 52005352 and 52075348), in part by the Key Science and Technology Research Project of Shenyang (20-202-4-40) and in part by the Key Innovate R &D Program of Shenyang (Y19-1-004).

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Authors and Affiliations

  1. School of Mechanical Engineering, Shenyang Jianzhu University, Shenyang, 110168, China

    Huaitao Shi, Fuxing Yao, Zhe Yuan & Shenghao Tong

  2. Bourns College of Engineering, University of California Riverside, Los Angeles, CA, 90001, USA

    Yinghan Tang

  3. Shenyang Yadong Technology Co., Ltd, Shenyang, 110000, China

    Gang Han

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  1. Huaitao Shi
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  2. Fuxing Yao
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  3. Zhe Yuan
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  4. Shenghao Tong
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Correspondence to Zhe Yuan.

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Shi, H., Yao, F., Yuan, Z. et al. Research on nonlinear coupled tracking controller for double pendulum gantry cranes with load hoisting/lowering. Nonlinear Dyn 108, 223–238 (2022). https://doi.org/10.1007/s11071-021-07185-6

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  • DOI: https://doi.org/10.1007/s11071-021-07185-6

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