Nonlinear control of ships minimizing the position tracking errors

“Nonlinear control of ships minimizing the position tracking errors”

Authors: Svein P. Berge, Kohei Ohtsu and Thor I. Fossen,
Affiliation: NTNU, Department of Engineering Cybernetics and Tokyo University of Mercantile Marine
Reference: 1999, Vol 20, No 3, pp. 177-187.

Keywords: Nonlinear control, Lyapunov stability, ship control, marine systems

Abstract: In this paper, a nonlinear tracking controller with integral action for ships is presented. The controller is based on state feedback linearization. Exponential convergence of the vessel-fixed position and velocity errors are proven by using Lyapunov stability theory. Since we only have two control devices, a rudder and a propeller, we choose to control the longship and the sideship position errors to zero while the heading is stabilized indirectly. A Virtual Reference Point (VRP) is defined at the bow or ahead of the ship. The VRP is used for tracking control. It is shown that the distance from the center of rotation to the VRP will influence on the stability of the zero dynamics. By selecting the VRP at the bow or even ahead of the bow, the damping in yaw can be increased and the zero dynamics is stabilized. Hence, the heading angle will be less sensitive to wind, currents and waves. The control law is simulated by using a nonlinear model of the Japanese training ship Shiojimaru with excellent results. Wind forces are added to demonstrate the robustness and performance of the integral controller.

PDF

PDF (1388 Kb) DOI: 10.4173/mic.1999.3.3

DOI forward links to this article:

[1] Shr-Shiung Hu, Pao-Hwa Yang, J. Y. Juang and B. C. Chang (2003), doi:10.1002/rnc.700

[2] Farshad Mahini, Leonard DiWilliams, Kevin Burke and Hashem Ashrafiuon (2013), doi:10.1017/S0263574712000720

[3] Mohamed Harmouche, Salah Laghrouche and Yacine Chitour (2014), doi:10.1080/00207179.2014.898188

[4] E. Lefeber, K.Y. Pettersen and H. Nijmeijer (2003), doi:10.1109/TCST.2002.806465

[5] F. Mazenc, K.Y. Pettersen and H. Nijmeijer (2002), doi:10.1109/CDC.2002.1184547

[6] Wenjie Dong and Yi Guo (2005), doi:10.1109/ACC.2005.1470664

[7] L. Consolini and M. Tosques (2012), doi:10.1109/TAC.2012.2199178

[8] Kilsoo Kim, Young-Ki Lee, Sehwan Oh, David Moroniti, Dimitri Mavris, George J. Vachtsevanos, Nikos Papamarkos and George Georgoulas (2013), doi:10.1109/MED.2013.6608750

[9] Jingbo Zhao and Jinmei Pang (2010), doi:10.1109/WCICA.2010.5555061

[10] Giovanni Indiveri and António Pascoal (2004), doi:10.1016/S1474-6670(17)31779-2

[11] Thor I. Fossen (2000), doi:10.1016/S1474-6670(17)37044-1

[12] Hongyun Huang and Yunsheng Fan (2018), doi:10.1109/CCDC.2018.8407687

[13] Li Chen, James F. Whidborne, Qi Dong, Dengping Duan and Jinguo Liu (2019), doi:10.1061/(ASCE)AS.1943-5525.0001005

[14] Shintaro MIYOSHI, Yohsuke HARA and Kohei OHTSU (2007), doi:10.9749/jin.117.183

[15] Olga Druzhinina and Natalya Sedova (2020), doi:10.1007/978-3-030-62867-3_6

[16] Min-Kyu Kim, Jong-Hwa Kim and Hyun Yang (2023), doi:10.3390/jmse11050970

[17] Loick Degorre, Thor I. Fossen, Olivier Chocron and Emmanuel Delaleau (2024), doi:10.1016/j.conengprac.2024.106068

References:
[1] FOSSEN, T.I. (1994). Guidance and Control of Ocean Vehicles, John Wiley and Sons Ltd.
[2] FOSSEN, T.I. STRAND, J.P. (1999). Passive nonlinear observer design for ships using Lyapunov methods: experimental results with a supply vessel, Automatica.
[3] FOSSEN, T.I., GODHAVN, J.-M., BERGE, S. P. LINDEGAARD, K.-P. (1998). Nonlinear control of underactuated ships with forward speed compensation, Proc. of the IFAC NOLCOS´98.
[4] GODHAVN, J.M. (1997). Topics in Nonlinear Motion Control: Nonholonomic, Underactuated and Hybrid Systems, PhD thesis. Dep. of Eng. Cybernetics, NTNU, Trondheim.
[5] GODHAVN, J.M., FOSSEN, T.I. BERGE., S.P. (1998). Nonlinear and adaptive backstepping designs for tracking control of ships, International Journal of Adaptive Control and Signal Processing.
[6] HOLZHÜTER, T. SCHULT7E, R. (1996). Operating experience with a high-precision track controller for commercial ships, Control Eng. Practice, CEP-4(3), 343-350 doi:10.1016/0967-0661(96)00011-1
[7] LINDEGAARD, K.-P. (1997). Nonlinear tracking control and station-keeping of underactuated ships, Master´s thesis. Dep. of Eng. Cybernetics, NTNU, Trondheim.
[8] MEGRETSKI, A. RANTZER, A. (1997). System analysis via integral quadratic constraints, IEEE Trans. on Control System Technology, TCST-4.6, 93-106.
[9] OHTSU, K., SHOJI, K. OKAZAKI, T. (1996). Minimum time maneuvering of a ship, with wind disturbances, Control Eng. Practice, CEP-4(3), 385-392 doi:10.1016/0967-0661(96)00016-0

BibTeX:
@article{MIC-1999-3-3,
  title={{Nonlinear control of ships minimizing the position tracking errors}},
  author={Berge, Svein P. and Ohtsu, Kohei and Fossen, Thor I.},
  journal={Modeling, Identification and Control},
  volume={20},
  number={3},
  pages={177--187},
  year={1999},
  doi={10.4173/mic.1999.3.3},
  publisher={Norwegian Society of Automatic Control}
};

Article

“Nonlinear control of ships minimizing the position tracking errors”