A backstepping approach to ship course control

Anna Witkowska; Mirosław Tomera; Roman Smierzchalski

International Journal of Applied Mathematics and Computer Science (2007)

  • Volume: 17, Issue: 1, page 73-85
  • ISSN: 1641-876X

Abstract

top
As an object of course control, the ship is characterised by a nonlinear function describing static manoeuvring characteristics that reflect the steady-state relation between the rudder deflection and the rate of turn of the hull. One of the methods which can be used for designing a nonlinear ship course controller is the backstepping method. It is used here for designing two configurations of nonlinear controllers, which are then applied to ship course control. The parameters of the obtained nonlinear control structures are tuned to optimise the operation of the control system. The optimisation is performed using genetic algorithms. The quality of operation of the designed control algorithms is checked in simulation tests performed on the mathematical model of a tanker. In order to obtain reference results to be used for comparison with those recorded for nonlinear controllers designed using the backstepping method, a control system with the PD controller is examined as well.

How to cite

top

Witkowska, Anna, Tomera, Mirosław, and Smierzchalski, Roman. "A backstepping approach to ship course control." International Journal of Applied Mathematics and Computer Science 17.1 (2007): 73-85. <http://eudml.org/doc/207823>.

@article{Witkowska2007,
abstract = {As an object of course control, the ship is characterised by a nonlinear function describing static manoeuvring characteristics that reflect the steady-state relation between the rudder deflection and the rate of turn of the hull. One of the methods which can be used for designing a nonlinear ship course controller is the backstepping method. It is used here for designing two configurations of nonlinear controllers, which are then applied to ship course control. The parameters of the obtained nonlinear control structures are tuned to optimise the operation of the control system. The optimisation is performed using genetic algorithms. The quality of operation of the designed control algorithms is checked in simulation tests performed on the mathematical model of a tanker. In order to obtain reference results to be used for comparison with those recorded for nonlinear controllers designed using the backstepping method, a control system with the PD controller is examined as well.},
author = {Witkowska, Anna, Tomera, Mirosław, Smierzchalski, Roman},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {genetic algorithms; backstepping; ship control; nonlinear control; Lyapunov function},
language = {eng},
number = {1},
pages = {73-85},
title = {A backstepping approach to ship course control},
url = {http://eudml.org/doc/207823},
volume = {17},
year = {2007},
}

TY - JOUR
AU - Witkowska, Anna
AU - Tomera, Mirosław
AU - Smierzchalski, Roman
TI - A backstepping approach to ship course control
JO - International Journal of Applied Mathematics and Computer Science
PY - 2007
VL - 17
IS - 1
SP - 73
EP - 85
AB - As an object of course control, the ship is characterised by a nonlinear function describing static manoeuvring characteristics that reflect the steady-state relation between the rudder deflection and the rate of turn of the hull. One of the methods which can be used for designing a nonlinear ship course controller is the backstepping method. It is used here for designing two configurations of nonlinear controllers, which are then applied to ship course control. The parameters of the obtained nonlinear control structures are tuned to optimise the operation of the control system. The optimisation is performed using genetic algorithms. The quality of operation of the designed control algorithms is checked in simulation tests performed on the mathematical model of a tanker. In order to obtain reference results to be used for comparison with those recorded for nonlinear controllers designed using the backstepping method, a control system with the PD controller is examined as well.
LA - eng
KW - genetic algorithms; backstepping; ship control; nonlinear control; Lyapunov function
UR - http://eudml.org/doc/207823
ER -

References

top
  1. [Amerongen 1982] AmerongenJ. (1982): Adaptive steering of ship. A model reference approach to improved manoeuvering and economical course keeping. - Ph.D. thesis, Delft University of Technology, the Netherlands. 
  2. [Astrom 1989] Åström K.J. and Wittenmark B. (1989): Adaptive Control. - Reading, MA: Addison Weey. 
  3. [Do 2004] Do K.D., Jiang Z.P. and Pan J. (2004): Robust adaptive path following of underactuated ships. - Automatica, Vol.40, No.6, pp.929-944. Zbl1096.93021
  4. [Ezal 2000] Ezal K., Pan Z. and Kokotovic P. (2000): Locally optimal and robust backstepping design. - IEEE Trans. Automat. Contr., Vol.45, No.2, pp.260-271. Zbl0973.93008
  5. [Fang 2004] Fang Y., Zergeroglu E., Queiroz M.S. and Dawson D.M. (2004): Global output feedback control of dynamically positioned surface vessels: an adaptive control approach. - Mechatron. Vol.14, No.4, pp.341-356. 
  6. [Fleming 2002] Fleming P.J. and Purshouse R.C. (2002): Evolutionary algorithms in control systems engineering: A survey. - Contr. Engi. Pract., Vol.10, No.11, pp.1223-1241. 
  7. [Fossen 1998] Fossen T.I. and Strand J.P. (1998): Nonlinear ship control (Tutorial paper). - Proc. IFAC Conf. Control Application in Marine Systems CAMS'98. Fukuoka, Japan. pp.1-75. Available at http://www.itk.ntnu.no/ansatte/Fossen_Thor/book/tutorial98.pdf 
  8. [Fossen 1999] Fossen T.I. and Strand J.P. (1999): A tutorial on nonlinear backstepping: Applications to ship control. - Modell., Identif. Control, Vol.20, No.2, pp.83-135. 
  9. [Fossen 2002] Fossen T.I. (2002): Marine Control Systems. Guidance, Navigation, and Control of Ships, Rigs and Underwater Vehicles. - Trondheim, Norway: Marine Cybernetics. 
  10. [Goldberg 1989] Goldberg D.E. (1989): Genetic Algorithms in Searching, Optimisation and Machine Learning. - Reading, MA: Addison Weey. 
  11. [Harkegard 2003] Härkegard O. (2003): Backstepping and control allocation with applications to flight control. - Ph.D. thesis, Department of Electrical Engineering, Linkoping University, Sweden. 
  12. [He 1998] He S., Reif K. and Unbehauen R. (1998): A neural approach for control of nonlinear systems with feedback linearization. - IEEE Trans. Neural Netw., Vol.9, No.6, pp.1409-1421. 
  13. [Jiang 2002] Jiang Z.P. (2002): Global tracking control of underactuated ships by Lyapunov direct method. - Automat., Vol.38, No.2, pp.301-309. Zbl0991.93085
  14. [Kokotovic 2001] Kokotovic P. and Arcak M. (2001): Constructive nonlinear control: A historical perspective. - Automat., Vol.37, No.5, pp.637-662.newpage Zbl1153.93301
  15. [Krstic 1995] Krstić M., Kanellakopulos I. and Kokotovic P.V. (1995): Nonlinear and Adaptive Control Design. - New York: Wiley. 
  16. [Krstic 1998] Krstić M. and Deng H. (1998): Stabilization of Nonlinear Uncertain Systems.- Berlin: Springer. Zbl0906.93001
  17. [Krstic 1999] Krstić M. and Tsiotras P. (1999): Inverse optimal stabilization of a rigid spacecraft. - IEEE Trans. Automat. Contr., Vol.44, No.5, pp.1042-1049. Zbl1136.93424
  18. [Kuljaca 2001] Kuljaca O., Swamy N., Lewis F.L and Kwan C.M. (2001): Design and implementation of industrial neural network controller using backstepping. - Proc. 40th IEEE Conf. Decision and Control Orlando, FL, pp.2709-2714. 
  19. [Kwan 2000] Kwan C.M. and Lewis F.L. (2000): Robust backstepping control of nonlinear systems using neural networks. - IEEE Trans. Syst. Man Cybern.,Part A: Syst. Humans, Vol.30, No.6, pp.753-766. 
  20. [La_Salle 1966] La Salle J. and Lefschetz S. (1961): Stability by Liapunov's direct method with applications. - Academic Press, New York. Zbl0098.06102
  21. [Lim 1983] Lim C.C. and Forsythe W. (1983): Autopilot for ship control. - IEE Proc.Vol.130, No.6, pp.281-295. 
  22. [Michalewicz 1996] Michalewicz Z. (1996): Genetic Algorithms + Data Structures = Evolution Programs. - Berlin: Springer. Zbl0841.68047
  23. [Moradi 2001] Moradi M.H. and Katebi M.R. (2001): Predictive PID control for ship autopilot design. - Proc. Control Applications in Marine Systems 2001, CAMS'2001, Glasgow,UK, pp.375-380. 
  24. [Pettersen 2004] Pettersen K.Y. and Nijmeijer H. (2004): Global practical stabilization and tracking for an underactuated ship. A combined averaging and backstepping approach. - Modell. Identif. Contr., Vol.20, No.4, pp.189-199. 
  25. [Sepulchre 1997] Sepulchre R., Jankovic M. and Kokotovic P.V. (1997): Constructive Nonlinear Control. - Berlin: Springer. Zbl1067.93500
  26. [Skjetne 2005] Skjetne R., Fossen T.I. and Kokotovic P.V. (2005): Adaptive maneuvering, with experiments, for a model ship in a marine control laboratory. - Automat. Vol.41, No.2, pp.289-298. Zbl1096.93026
  27. [Zhang 2000] Zhang T., Ge S.S. and Hang C.C. (2000): Adaptive neural network control forstrict-feedback nonlinear systems using backstepping design. - Automat., Vol.36, No.12, pp.1835-1846. Zbl0976.93046
  28. [ZhangPeng 2000] Zhang Y., Peng P.Y. and Jiang Z.P. (2000): Stable neural controller design for unknown nonlinear systems using backstepping. - IEEE Trans. Neural Netw., Vol.11, No.6, pp.1347-1360 

Citations in EuDML Documents

top
  1. Anna Witkowska, Roman Śmierzchalski, Designing a ship course controller by applying the adaptive backstepping method
  2. Fei Yan, Mahjoub Dridi, Abdellah El Moudni, An autonomous vehicle sequencing problem at intersections: A genetic algorithm approach
  3. Shaoji Fang, Mogens Blanke, Fault monitoring and fault recovery control for position-moored vessels
  4. Stanisław Bańka, Paweł Dworak, Krzysztof Jaroszewski, Linear adaptive structure for control of a nonlinear MIMO dynamic plant
  5. Józef Lisowski, Sensitivity of computer support game algorithms of safe ship control
  6. Stanisław Bańka, Paweł Dworak, Krzysztof Jaroszewski, Design of a multivariable neural controller for control of a nonlinear MIMO plant

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.