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Robust path-following control of a container ship based on Serret–Frenet frame transformation

Journal of Marine Science and Technology volume 25, pages 69–80 (2020)Cite this article

Abstract

A novel disturbance observer-based backstepping controller (DOBBC) is developed and applied to the path-following system of a container ship. Our control objective is to enable the ships to follow a desired path despite the presence of environmental disturbances caused by current, wind, and wave actions. It is particularly challenging to achieve such an objective due to the underactuation and nonlinearity of container ships. To simplify controller design, a tracking error model is developed based on Serret–Frenet frame transformation. The proposed path-following control system is constructed on the model. In DOBBC, the disturbance observer estimates both constant and time-variant environmental disturbances. The backstepping controller compensates the nonlinearity and underactuation of the container ship. A feedback-dominance technique is utilized to design the controller parameters. The stability and robustness of the control system are successfully justified through Lyapunov approach. Simulation results demonstrate that the DOBBC effectively drives the ship to follow a desired trajectory in spite of the existence of time-varying environmental disturbances.

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References

  1. Pettersen Kristin Ytterstad, Fossen Thor I (2000) Underactuated dynamic positioning of a ship-experimental results. IEEE Trans Control Syst Technol 8(5):856–863

    Article  Google Scholar 

  2. Do Khac D, Jiang Zhong Ping, Pan Jie (2002) Underactuated ship global tracking under relaxed conditions. IEEE Trans Autom Control 47(9):1529–1536

    Article  MathSciNet  Google Scholar 

  3. Krstic Miroslav, Kanellakopoulos Ioannis, Kokotovic Petar (1995) Nonlinear and adaptive control design. Wiley, Hoboken

    MATH  Google Scholar 

  4. Zhou Jing, Wen Changyun (2008) Adaptive backstepping control of uncertain systems. Springer, Berlin

    MATH  Google Scholar 

  5. Wang Wei, Wen Changyun, Zhou Jing (2017) Adaptive backstepping control of uncertain systems with actuator failures, subsystem interactions, and nonsmooth nonlinearities. CRC Press, Boca Raton

    Book  Google Scholar 

  6. Skjetne R, Fossen TI (2001) Nonlinear maneuvering and control of ships. In: Proceedings of OCEANS 2001 MTS/IEEE conference, Honolulu, HI, USA, pp 1808–1815

  7. Fossen TI, Skjetne R, Breivik M (2003) Line-of-sight path following of underactuated marine craft. In: Proceedings of the 6th IFAC MCMC, Girona, Spain, pp 244–249

  8. Do KD, Pan J (2006) Underactuated ships follow smooth paths with integral actions and without velocity measurements for feedback: theory and experiments. IEEE Trans Control Syst Technol 14(2):308–322

    Article  Google Scholar 

  9. Li Zhen, Sun Jing, Soryeok Oh (2009) Design, analysis and experimental validation of a robust nonlinear path following controller for marine surface vessels. Automatica 45(7):1649–1658

    Article  MathSciNet  Google Scholar 

  10. Do KD, Jiang JP, Pan J (2004) Robust adaptive path following of underactuated ships. Automatica 31:929–944

    Article  MathSciNet  Google Scholar 

  11. Li T, Yang Y, Hong B, Ren J, Jiali D (2005) A robust adaptive nonlinear control approach to ship straight-path tracking design. In: Proceedings of American Control Conference, OR, USA, Portland, pp 4016–4021

  12. Do KD, Pan J (2006) Global robust adaptive path following of underactuated ships. Automatica 42(10):1713–1722

    Article  Google Scholar 

  13. Wang Xiaofei, Zou Zaojian, Li Tieshan, Luo Weilin (2010) Adaptive path following controller of underactuated ships using Serret–Ferenet frame. J Shanghai Jiaotong Univ (Sci) 15(3):334–339

    Article  Google Scholar 

  14. Dovgobrod GM (2012) Development of an adaptive algorithm for ship motion control on a nonlinear path. Gyrosc Navig 3(1):41–46

    Article  Google Scholar 

  15. Zhang Guoqing, Zhang Xianku (2014) Concise robust adaptive path-following control of underactuated ships using DSC and MLP. IEEE J Ocean Eng 39(4):685–694

    Article  MathSciNet  Google Scholar 

  16. Ren R, Zou Z (2015) \(L_1\) adaptive control used in ship control system when encountering slow varying disturbances. In: Proceedings of the Twenty-fifth international ocean and polar engineering conference, Kona, Hawaii, USA, pp 283–289

  17. Yi Bowen, Zhang Weidong (2016) A nonlinear updated gain observer for MIMO systems: design, analysis and application to marine surface vessels. ISA Trans 64:129–140

    Article  Google Scholar 

  18. Breivik M, Fossen TI (2004) Path following for marine surface vessels. In: Proceedings of IEEE techno-ocean’04 MTS, Kobe, Japan

  19. Zhang Xiaoguang, Li Zhengxi (2016) Sliding-mode observer-based mechanical parameter estimation for permanent magnet synchronous motor. IEEE Trans Power Electronics 31(8):5732–5745

    Article  Google Scholar 

  20. Slotine Jean, Li Weiping (1991) Appl Nonlinear Control. Prentice Hall, Upper Saddle River

    Google Scholar 

  21. Khalil HK (2002) Nonlinear systems, 3rd edn. Prentice Hall, Upper Saddle River

    MATH  Google Scholar 

  22. Perez T, Blanke M (1998) Mathematical ship modelling for control applications. Tech. Rep. The University of Newcastle, Callaghan, Australia

  23. Alarcin Faut (2007) Internal model control using neural network for ship roll stabilization. J Mar Sci Technol 15(2):141–147

    Google Scholar 

  24. Do Khac Duc (2010) Practical control of underactuated ships. Ocean Eng 37(13):1111–1119

    Article  Google Scholar 

  25. Bialystocki N, Konovessis D (2016) On the estimation of ship’s fuel consumption and speed curve: a statistical approach. J Ocean Eng Sci 1(3):157–166

    Article  Google Scholar 

Download references

Acknowledgements

The authors would like to thank Dr. Sally Shao, the mathematical professor at Cleveland State University, for her valuable inputs in proving the convergences of estimation errors of the disturbance observer.

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Authors and Affiliations

  1. Department of Electrical Engineering and Computer Science, Cleveland State University, Cleveland, OH, 44115, USA

    Yang Zhao & Lili Dong

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  1. Yang Zhao
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  2. Lili Dong
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Correspondence to Lili Dong.

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Zhao, Y., Dong, L. Robust path-following control of a container ship based on Serret–Frenet frame transformation. J Mar Sci Technol 25, 69–80 (2020). https://doi.org/10.1007/s00773-019-00631-6

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  • DOI: https://doi.org/10.1007/s00773-019-00631-6

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