Skip to main content
Log in

Nonlinear Sliding Mode Tracking Control of Underactuated Tower Cranes

  • Regular Papers
  • Robot and Applications
  • Published:
International Journal of Control, Automation and Systems Aims and scope Submit manuscript

Abstract

As representative underactuated systems, tower cranes exhibit high nonlinearity and strong state coupling, which makes their controller design (analysis) challenging and of great research values. In addition, since tower cranes are widely applied in outdoor environment with inevitable external disturbances, (the state variables tend to go far away from the equilibrium point), how to ensure the control performance in this case is particularly important; moreover, most existing control methods can only ensure closed loop stability, but cannot theoretically ensure the system states convergence time. Considering the above factors, this paper proposes a nonlinear sliding mode tracking controller, which can realize satisfactory tracking performance and effective swing suppression. To our knowledge, for tower cranes, this is the first tracking method designed based upon the nonlinear dynamics without any linearization, which can eliminate the tracking errors rapidly in finite time by introducing the elaborately constructed sliding mode surface and simultaneously suppress the swing. Furthermore, through rigorous analysis, the system closed loop stability is proven theoretically. Finally, hardware experiments imply that the proposed controller is effective and exhibits satisfactory robustness.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. C. Yang, Z. Li, R. Cui, and B. Xu, “Neural network-based motion control of an underactuated wheeled inverted pendulum model,” IEEE Transactions on Neural Networks and Learning Systems, vol. 25, no. 11, pp. 2004–2016, March 2014.

    Google Scholar 

  2. Y. Xin, Z. Qin, and J. Sun, “Robust experimental study of data-driven optimal control for an underactuated rotary flexible joint,” International Journal of Control, Automation, and Systems, vol. 18, no. 5, pp. 1202–1214, May 2020.

    Google Scholar 

  3. H. Chen and N. Sun, “Nonlinear control of underactuated systems subject to both actuated and unactuated state constraints with experimental verification,” IEEE Transactions on Industrial Electronics, vol. 67, no. 9, pp. 7702–7714, September 2020.

    MathSciNet  Google Scholar 

  4. W. Sun, S.-F. Su, J. Xia, and Y. Wu, “Adaptive tracking control of wheeled inverted pendulums with periodic disturbances,” IEEE Transactions on Cybernetics, vol. 50, no. 5, pp. 1867–1876, May 2020.

    Google Scholar 

  5. Y. Sun, J. Xu, H. Qiang, and G. Lin, “Adaptive neural-fuzzy robust position control scheme for maglev train systems with experimental verification,” IEEE Transactions on Industrial Electronics, vol. 66, no. 11, pp. 8589–8599, November 2019.

    Google Scholar 

  6. D. Qian, H. Ding, S. G. Lee, and H. Bae, “Suppression of chaotic behaviors in a complex biological system by disturbance observer-based derivative-integral terminal sliding mode,” IEEE/CAA Journal of Automatica Sinica, vol. 7, no. 1, pp. 126–135, January 2020.

    MathSciNet  Google Scholar 

  7. U. H. Shah, K.-S. Hong, and S.-H. Choi, “Open-loop vibration control of an underwater system: Application to refueling machine,” IEEE/ASME Transactions on Mechatronics, vol. 22, no. 4, pp. 1622–1632, August 2017.

    Google Scholar 

  8. H. Li, S. Zhao, W. He, and R. Lu, “Adaptive finite-time tracking control of full states constrained nonlinear systems with dead-zone,” Automatica, vol. 100, pp. 99–107, February 2019.

    MathSciNet  MATH  Google Scholar 

  9. Q. Zhou, S. Zhao, H. Li, R. Lu, and C. Wu, “Adaptive neural network tracking control for robotic manipulators with dead-zone,” IEEE Transactions on Neural Networks and Learning Systems, vol. 30, no. 12, pp. 3611–3620, December 2019.

    MathSciNet  Google Scholar 

  10. C. Yang, Y. Jiang, J. Na, Z. Li, L. Cheng, and C.-Y. Su, “Finite-time convergence adaptive fuzzy control for dualarm robot with unknown kinematics and dynamics,” IEEE Transactions on Fuzzy Systems, vol. 27, no. 3, pp. 574–588, March 2019.

    Google Scholar 

  11. Y. Li and Q. Xu, “Design and analysis of a totally decoupled flexure-based XY parallel micromanipulator,” IEEE Transactions on Robotics, vol. 25, no. 3, pp. 645–657, March 2009.

    Google Scholar 

  12. X. Lai, Y. Wang, M. Wu, and W. Cao, “Stable control strategy for planar three-link underactuated mechanical system,” IEEE/ASME Transactions on Mechatronics, vol. 21, no. 3, pp. 1345–1356, June 2016.

    Google Scholar 

  13. D. Liu, W. Guo, and J. Yi, “Dynamics and GA-based stable control for a class of underactuated mechanical systems,” International Journal of Control, Automation, and Systems, vol. 6, no. 1, pp. 35–43, February 2008.

    Google Scholar 

  14. K.-S. Hong and U. H. Shah, Dynamics and Control of Industrial Cranes, Springer, Singapore, 2019.

    Google Scholar 

  15. W. Blajer and K. Kolodziejczyk, “Motion planning and control of gantry cranes in cluttered work environment,” IET Control Theory and Applications, vol. 1, no. 5, pp. 1370–1379, September 2007.

    Google Scholar 

  16. Z. Wu and X. Xia, “Optimal motion planning for overhead cranes,” IET Control Theory and Applications, vol. 8, no. 17, pp. 1833–1842, November 2014.

    Google Scholar 

  17. H. H. Lee, “Motion planning for three-dimensional overhead cranes with high-speed load hoisting,” International Journal of Control, vol. 78, no. 12, pp. 875–886, August 2005.

    MathSciNet  MATH  Google Scholar 

  18. N. Uchiyama, H. Ouyang, and S. Sano, “Simple rotary crane dynamics modeling and open-loop control for residual load sway suppression by only horizontal boom motion,” Mechatronics, vol. 23, no. 8, pp. 1223–1236, December 2013.

    Google Scholar 

  19. M. Zhang, X. Ma, H. Chai, X. Rong, X. Tian, and Y. Li, “A novel online motion planning method for double-pendulum overhead cranes,” Nonlinear Dynamics, vol. 85, no. 2, pp. 1079–1090, July 2016.

    MATH  Google Scholar 

  20. H. I. Jaafar, Z. Mohamed, M. A. Shamsudin, N. A. Mohd Subhaa, L. Ramlia, and A. M. Abdullahic, “Model reference command shaping for vibration control of multimode flexible systems with application to a double-pendulum overhead crane,” Mechanical Systems and Signal Processing, vol. 115, pp. 677–695, January 2019.

    Google Scholar 

  21. Z. Masoud, K. Alhazza, E. Abu-Nada, and M. Majeed, “A hybrid command-shaper for double-pendulum overhead cranes,” Journal of Vibration and Control, vol. 20, no. 1, pp. 24–37, January 2014.

    Google Scholar 

  22. X. Zhao and J. Huang, “Distributed-mass payload dynamics and control of dual cranes undergoing planar motions,” Mechanical Systems and Signal Processing, vol. 126, no. 1, pp. 636–648, July 2019.

    Google Scholar 

  23. N. Sun, Y. Fang, H. Chen, Y. Fu, and Biao Lu, “Nonlinear stabilizing control for ship-mounted cranes with ship roll and heave movements: Design, analysis, and experiments,” IEEE Transactions on Systems, Man, and Cybernetics: Systems, vol. 48, no. 10, pp. 1781–1793, October 2018.

    Google Scholar 

  24. D. Chwa, “Sliding-mode-control-based robust finite-time antisway tracking control of 3-D overhead cranes,” IEEE Transactions on Industrial Electronics, vol. 64, no. 8, pp. 6775–6784, August 2017.

    Google Scholar 

  25. L. Ramli, Z. Mohamed, M. O. Efe, I. M. Lazim, and H. I. Jaafar, “Efficient swing control of an overhead crane with simultaneous payload hoisting and external disturbances,” Mechanical Systems and Signal Processing, vol. 135, pp. 106326, January 2020.

    Google Scholar 

  26. N. Sun, Y. Wu, Y. Fang, and H. Chen, “Nonlinear antiswing control for crane systems with double-pendulum swing effects and uncertain parameters: Design and experiments,” IEEE Transactions on Automation Science and Engineering, vol. 15, no. 3, pp. 1413–1422, July 2018.

    Google Scholar 

  27. K. A. Hekman and W. E. Singhose, “A feedback control system for suppressing crane oscillations with on-off motors,” International Journal of Control, Automation, and Systems, vol. 5, no. 3, pp. 223–233, June 2007.

    Google Scholar 

  28. N. Sun, Y. Fu, T. Yang, J. Zhang, Y. Fang, and X. Xin, “Nonlinear motion control of complicated dual rotary crane systems without velocity feedback: Design, analysis, and hardware experiments,” IEEE Transactions on Automation Science and Engineering, vol. 17, no. 2, pp. 1017–1029, April 2020.

    Google Scholar 

  29. W. He, S. Zhang, and S. S. Ge, “Adaptive control of a flexible crane system with the boundary output constraint,” IEEE Transactions on Industrial Electronics, vol. 61, no. 8, pp. 4126–4133, August 2013.

    Google Scholar 

  30. C. Y. Chang and H. W. Lie, “Real-time visual tracking and measurement to control fast dynamics of overhead cranes,” IEEE Transactions on Industrial Electronics, vol. 59, no. 3, pp. 1640–1649, March 2012.

    Google Scholar 

  31. M. Zhang, Y. Zhang, and X. Cheng, “An enhanced coupling PD with sliding mode control method for underactuated double-pendulum overhead crane systems,” International Journal of Control, Automation, and Systems, vol. 17, no. 6, pp. 1579–1588, June 2019.

    MathSciNet  Google Scholar 

  32. G. Bartolini, A. Pisano, and E. Usai, “Second-order sliding-mode control of container cranes,” Automatica, vol. 38, no. 10, pp. 1783–1790, October 2002.

    MathSciNet  MATH  Google Scholar 

  33. M. I. Solihin, Wahyudi, and A. Legowo, “Fuzzy-tuned PID anti-swing control of automatic gantry crane,” Journal of Vibration and Control, vol. 16, no. 1, pp. 127–145, January 2010.

    MATH  Google Scholar 

  34. K. Zavari, G. Pipeleers, and J. Swevers, “Gain-scheduled controller design: Illustration on an overhead crane,” IEEE Transactions on Industrial Electronics, vol. 61, no. 7, pp. 3713–3718, June 2013.

    Google Scholar 

  35. C. S. Kim and K.-S. Hong, “Boundary control of container cranes from the perspective of controlling an axially moving string system,” International Journal of Control, Automation, and Systems, vol. 7, no. 3, pp. 437–445, June 2009.

    Google Scholar 

  36. J. Huang, X. Xie, and Z. Liang, “Control of bridge cranes with distributed-mass payload dynamics,” IEEE/ASME Transactions on Mechatronics, vol. 20, no. 1, pp. 481–486, February 2015.

    Google Scholar 

  37. G. Boschetti, R. Caracciolo, D. Richiedei, and A. Trevisani, “A non-time based controller for load swing damping and path-tracking in robotic cranes,” Journal of Intelligent and Robotic Systems, vol. 76, no. 2, pp. 201–217, November 2014.

    Google Scholar 

  38. Y. Zhao and H. Gao, “Fuzzy-model-based control of an overhead crane with input delay and actuator saturation,” IEEE Transactions on Fuzzy Systems, vol. 20, no. 1, pp. 181–186, February 2012.

    Google Scholar 

  39. H. Ouyang, X. Xu, and G. Zhang, “Tracking and load sway reduction for double-pendulum rotary cranes using adaptive nonlinear control approach,” International Journal of Robust and Nonlinear Control, vol. 30, no. 5, pp. 1872–1885, 2020.

    MathSciNet  Google Scholar 

  40. S. Küchler, T. Mahl, J. Neupert, K. Schneider, and O. Sawodny, “Active control for an offshore crane using prediction of the vessel’s motion,” IEEE/ASME Transactions on Mechatronics, vol. 16, no. 2, pp. 297–309, April 2011.

    Google Scholar 

  41. A. Piazzi and A. Visioli, “Optimal dynamic-inversion-based control of an overhead crane,” IEE Proceedings-Control Theory and Applications, vol. 149, no. 5, pp. 405–411, Semptember 2002.

    Google Scholar 

  42. S. Frikha, M. Djemel, and N. Derbel, “A new adaptive neuro-sliding mode control for gantry crane,” International Journal of Control, Automation, and Systems, vol. 16, no. 2, pp. 559–565, April, 2018.

    Google Scholar 

  43. X. Wu and X. He, “Enhanced damping-based anti-swing control method for underactuated overhead cranes,” IET Control Theory and Applications, vol. 9, no. 12, pp. 1893–1900, August 2015.

    MathSciNet  Google Scholar 

  44. Q. H. Ngo, N. P. Nguyen, C. N. Nguyen, T. H. Tran, and K.-S. Hong, “Fuzzy sliding mode control of container cranes,” International Journal of Control, Automation, and Systems, vol. 13, no. 2, pp. 419–425, April 2015.

    Google Scholar 

  45. L. A. Tuan, “Neural observer and adaptive fractional-order back-stepping fast terminal sliding mode control of RTG cranes,” IEEE Transactions on Industrial Electronics, vol. 68, no. 1, pp. 432–442, January 2021.

    Google Scholar 

  46. L. A. Tuan, Q. Ha, and P. V. Trieu, “Observer-based nonlinear robust control of floating container cranes subject to output hysteresis,” Journal of Dynamic Systems, Measurement, and Control, vol. 141, no. 11, pp. 111002–1–11, November 2019.

    Google Scholar 

  47. H. M. Omar and A. H. Nayfeh, “Gain scheduling feedback control of tower cranes with friction compensation,” Modal Analysis, vol. 10, no. 2, pp. 269–289, February 2004.

    Google Scholar 

  48. D. Blackburn, J. Lawrence, J. Danielson, W. Singhose, T. Kamoib, and A. Taurab, “Radial-motion assisted command shapers for nonlinear tower crane rotational slewing,” Control Engineering Practice, vol. 18, no. 5, pp. 523–531, May 2010.

    Google Scholar 

  49. J. Lawrence and W. Singhose, “Command shaping slewing motions for tower cranes,” Journal of Vibration and Acoustics, vol. 132, pp. 011002–1–11, 2010.

    Google Scholar 

  50. J. Peng, J. Huang, and W. Singhose, “Payload twisting dynamics and oscillation suppression of tower cranes during slewing motions,” Nonlinear Dynamics, vol. 98, no. 2, pp. 1041–1048, September 2019.

    Google Scholar 

  51. F. Rauscher and O. Sawodny, “Modeling and control of tower cranes with elastic structure,” IEEE Transactions on Control Systems Technology, 2020. https://doi.org/10.1109/TCST.2019.2961639

  52. M. Böck and A. Kugi, “Real-time nonlinear model predictive path-following control of a laboratory tower crane,” IEEE Transactions on Control Systems Technology, vol. 22, no. 4, pp. 1461–1473, July 2014.

    Google Scholar 

  53. L. A. Tuan and S. G. Lee, “3D cooperative control of tower cranes using robust adaptive techniques,” Journal of the Franklin Institute, vol. 354, no. 18, pp. 8333–8357, December 2017.

    MathSciNet  MATH  Google Scholar 

  54. N. Sun, Y. Fang, H. Chen, B. Lu, and Y. Fu, “Slew/translation positioning and swing suppression for 4-DOF tower cranes with parametric uncertainties: Design and hardware experimentation,” IEEE Transactions on Industrial Electronics, vol. 63, no. 10, pp. 6407–6418, October 2016.

    Google Scholar 

  55. N. Sun, Y. Wu, H. Chen, and Y. Fang, “Antiswing cargo transportation of underactuated tower crane systems by a nonlinear controller embedded with an integral term,” IEEE Transactions on Automation Science and Engineering, vol. 16, no. 3, pp. 1387–1398, July 2019.

    Google Scholar 

  56. L. Ramli, I. M. Lazim, H. I. Jaafar, and Z. Mohamed, “Modelling and fuzzy logic control of an underactuated tower crane system,” Applications of Modelling and Sumulation, vol. 4, pp. 1–11, 2020.

    Google Scholar 

  57. S. C. Duong, E. Uezato, H. Kinjo, and T. Yamamoto, “A hybrid evolutionary algorithm for recurrent neural network control of a three-dimensional tower crane,” Automation in Construction, vol. 23, pp. 55–63, May 2012.

    Google Scholar 

  58. H. Hua and Y. Fang, “Neural network based adaptive feedback control for tower cranes,” Proceedings of IEEE Annual International Conference on CYBER Technology in Automation, Control, and Intelligent Systems, Tianjin, China, pp. 1–5, July 2018.

  59. J. Matuško, Š. Ileš, F. Kolonić, and V. Lešić, “Control of 3D tower crane based on tensor product model transformation with neural friction compensation,” Asian Journal of Control, vol. 17, no. 2, pp. 443–458, March 2015.

    MathSciNet  MATH  Google Scholar 

  60. T. S. Wu, M. Karkoub, W. S. Yu, C. T. Chena, M. G. Herc, and K. W. Wua, “Anti-sway tracking control of tower cranes with delayed uncertainty using a robust adaptive fuzzy control,” Fuzzy Sets and Systems, vol. 290, pp. 118–137, May 2016.

    MathSciNet  Google Scholar 

  61. R. C. Roman, R. E. Precup, E. M. Petriu, and F. Dragan, “Combination of data-driven active disturbance rejection and takagi-sugeno fuzzy control with experimental validation on tower crane systems,” Energies, vol. 12, no. 8, pp. 1548, April 2019.

    Google Scholar 

  62. H. M. Omar and A. H. Nayfeh, “Anti-swing control of gantry and tower cranes using fuzzy and time-delayed feedback with friction compensation,” Shock and Vibration, vol. 12, no. 2, pp. 73–89, 2005.

    Google Scholar 

  63. M. Ghasemi and S. G. Nersesov, “Finite-time coordination in multiagent systems using sliding mode control approach,” Automatica, vol. 50, no. 4, pp. 1209–1216, April 2014.

    MathSciNet  MATH  Google Scholar 

  64. L. Qiao and W. Zhang, “Adaptive second-order fast nonsingular terminal sliding mode tracking control for fully actuated autonomous underwater vehicles,” IEEE Journal of Oceanic Engineering, vol. 44, no. 2, pp. 363–385, April 2019.

    Google Scholar 

  65. M. Van, “Adaptive neural integral sliding-mode control for tracking control of fully actuated uncertain surface vessels,” International Journal of Robust and Nonlinear Control, vol. 29, no. 5, pp. 1537–1557, March 2019.

    MathSciNet  MATH  Google Scholar 

  66. X. Yu and Z. Man, “Model reference adaptive control systems with terminal sliding modes,” International Journal of Control, vol. 64, no. 6, pp. 1165–1176, 1996.

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Ning Sun.

Additional information

Publisher’s Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Recommended by Associate Editor Quoc Chi Nguyen under the direction of Editor-in-chief Keum-Shik Hong. This work is supported by the National Natural Science Foundation of China (61873134, U1706228), the Young Elite Scientists Sponsorship Program by Tianjin (TJSQNTJ-2017-02), and the program of JSPS (Japan Society for the Promotion of Science) International Research Fellow (18F18363). The authors gratefully acknowledge all the reviewers, the Associate Editor, and the Editor-in-Chief for their valuable comments and suggestions, which are very helpful to improve the quality of this paper.

Zhuoqing Liu received her B.S. degree in intelligent science and technology from Nankai University, Tianjin, China, in 2019. She is currently working towards an M.S. degree under the supervision of Prof. Ning Sun, with the Institute of Robotics and Automatic Information Systems, Nankai University, Tianjin, China. Her research interests include the nonlinear control of underactuated systems including tower cranes.

Ning Sun received his B.S. degree in measurement & control technology and instruments (with honors) from Wuhan University, Wuhan, China, in 2009, and a Ph.D. degree in control theory and control engineering (with honors) from Nankai University, Tianjin, China, in 2014. He is currently a Full Professor with the Institute of Robotics and Automatic Information Systems, Nankai University, Tianjin, China. He was awarded the Japan Society for the Promotion of Science (JSPS) Postdoctoral Fellowship for Research in Japan (Standard). His research interests include intelligent control for mechatronic/robotic systems with emphasis on (industrial) applications. Dr. Sun received the Wu Wenjun Artificial Intelligence Excellent Youth Award in 2019, the China 10 Scientific and Technological Developments in Intelligent Manufacturing (2nd achiever) in 2019, the First Class Prize of Wu Wenjun Artificial Intelligence Natural Science Award in 2017, the First Class Prize of Tianjin Natural Science Award in 2018, the Golden Patent Award of Tianjin in 2017, the IJCAS (International Journal of Control, Automation, and Systems) Academic Activity Award in 2018 and 2019, the Outstanding Ph.D. Dissertation Award from the Chinese Association of Automation (CAA) in 2016, etc. He is the Executive Editor for Measurement and Control and serves as an Associate Editor (editorial board member) for several journals, including IEEE Access, International Journal of Control, Automation, and Systems, Transactions of the Institute of Measurement and Control, International Journal of Precision Engineering and Manufacturing, etc. Dr. Sun has been an Associate Editor of the IEEE Control Systems Society (CSS) Conference Editorial Board since July 2019, and he is an Associate Editor for IEEE ICRA 2021 and IEEE/RSJ IROS 2020. He is a Senior Member of IEEE.

Yiming Wu received her B.S. degree in intelligent science and technology from Nankai University, Tianjin, China, in 2016. She is currently working towards a Ph.D. degree in control science and engineering, under the supervision of Prof. Ning Sun, with the Institute of Robotics and Automatic Information Systems, Nankai University, Tianjin, China. Her research interests include the control of underactuated systems.

Xin Xin received his B.S. degree in 1987 from the University of Science and Technology of China, Hefei, China, and a Ph.D. degree in 1993 from the Southeast University, Nanjing, China. From 1991 to 1993, he did his Ph.D. studies in Osaka University as a co-advised student of China and Japan with the Japanese Government Scholarship. He also received a Doctor degree in engineering in 2000 from Tokyo Institute of Technology. From 1993 to 1995, he was a postdoctoral researcher and then became an Associate Professor of Southeast University. From 1996 to 1997, he was with the New Energy and Industrial Technology Development, Japan as an advanced industrial technology researcher. From 1997 to 2000, he was a Research Associate of Tokyo Institute of Technology. From 2000, he has been with Okayama Prefectural University as an Associate Professor, where he is a Full Professor since 2008. He has over 190 publications in journals, international conferences and book chapters. He received the division paper award of SICE 3rd Annual Conference on Control Systems in 2004. His current research interests include robotics, dynamics and control of nonlinear and complex systems.

Yongchun Fang received his B.S. degree and an M.S. degree in control theory and applications from Zhejiang University, Hangzhou, China, in 1996 and 1999, respectively, and a Ph.D. degree in electrical engineering from Clemson University, Clemson, SC, in 2002. From 2002 to 2003, he was a Postdoctoral Fellow with the Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY. He is currently a Full Professor with the Institute of Robotics and Automatic Information Systems, Nankai University, Tianjin, China. His research interests include nonlinear control, visual servoing, control of underactuated systems, and AFM-based nano-systems. He was an Associate Editor for ASME Journal of Dynamic Systems, Measurement, and Control. Dr. Fang received the National Science Fund for Distinguished Young Scholars of China.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Liu, Z., Sun, N., Wu, Y. et al. Nonlinear Sliding Mode Tracking Control of Underactuated Tower Cranes. Int. J. Control Autom. Syst. 19, 1065–1077 (2021). https://doi.org/10.1007/s12555-020-0033-5

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12555-020-0033-5

Keywords

Navigation