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Robust fuzzy controller design for dynamic positioning system of ships

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Abstract

This paper presents a robust fuzzy controller design approach for dynamic positioning (DP) system of ships using optimal H control techniques. The H control technique is used to exterminate the effects of environmental disturbances. Firstly, a Takagi-Sugeno (TS) fuzzy model is applied to approximate the nonlinear DP system. Next, linear matrix inequality (LMI) and general eigenvalue problem (GEVP) methods are employed to find a positive definite matrix and controller gains. The stability of the controller is proven by using Lyapunov stability theorems. A positive definite matrix is determined by solving LMI equations using robust control toolbox available in MATLAB. The obtained positive definite matrix proves that the designed fuzzy controller is stable. Finally, a uniformly ultimately bound (UUB) and control performance for the dynamic position system is guaranteed. Simulation is carried out, and results are presented to validate the effectiveness and performance of the proposed control system.

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References

  1. A. J. Sørensen, “A survey of dynamic positioning control systems,” Annual Reviews in Control, vol. 35, no. 1, pp. 123–136, 2011.

    Article  Google Scholar 

  2. A. Jensen, J. G. Balchen, and S. Sælid, “Dynamic positioning of floating vessels based on Kalman filtering and optimal control,” Proc. of the 19th IEEE Conf. on Decision and Control, New York, pp. 852–864, 1980.

    Google Scholar 

  3. A. Jensen, E. Mathisen, J. G. Balchen, and S. Sælid, “A dynamic positioning system based on Kalman filtering and optimal control,” Modeling, Identification and Control, vol. 1, no. 3, pp. 135–163, 1980.

    Article  Google Scholar 

  4. T. I. Fossen and J. P. Strand, “Passive nonlinear observer design for ships using Lyapunov methods: full-scale experiments with a supply vessel,” Automatica, vol. 35, no. 1, pp. 3–16, 1999.

    Article  MATH  MathSciNet  Google Scholar 

  5. A. Loria, T. I. Fossen, and E. Panteley, “A separation principle for dynamic positioning of ships: theoretical and experimental results,” IEEE Trans. on Control Systems Technology, vol. 8, no. 2, pp. 332–343, 2000.

    Article  Google Scholar 

  6. A. J. Smensenl, J. P. Strand, and H. Nybergl, “Dynamic positioning of ships and floaters in extreme seas,” Oceans MTS/IEEE, vol. 3, pp. 1849–1854, 2002.

    Google Scholar 

  7. J. G. Snijders and J. W. van der Woude, “Nonlinear observer design for dynamic positioning,” Proc. of Dynamic Positioning Conf., 2005.

    Google Scholar 

  8. K. D. Do, “Global robust and adaptive output feedback dynamic positioning of surface ships,” Proc. of IEEE International Conf. on Robotics and Automation, Roma, Italy, pp. 4271–4276, 2007.

    Google Scholar 

  9. H. Kaji and H. Katayama, “Digital control problems for dynamically positioned ships,” Proc. of 18th IEEE International Conf. on Control Applications, Part of IEEE Multi-conf. on Systems and Control, Saint Petersburg, Russia, pp. 1288–1293, 2009.

    Google Scholar 

  10. X. T. Chen and W. W. Tan, “A type-2 fuzzy logic controller for dynamic positioning systems,” Proc. of 8th IEEE International Conf. on Control and Automation, Xiamen, China, pp. 1013–101, 2010.

    Google Scholar 

  11. F. Benetazzo, G. Ippoliti, S. Longhi, P. Raspa, and A. J. Sørensen, “dynamic positioning of a marine vessel using DTVSC and robust control allocation,” Proc. of 20th Mediterranean Conf. on Control & Automation (MED), Barcelona, Spain, pp. 1211–1216, 2012.

    Google Scholar 

  12. A. Witkowska, “Dynamic positioning system with vectorial backstepping controller,” Proc. of 18th International Conf. on Methods and Models in Automation and Robotics (MMAR), IEEE Conf. Publications, pp. 842–847, 2013.

    Google Scholar 

  13. J. Du, Y. Yang, D. Wang, and C. Guo, “A robust adaptive neural networks controller for maritime dynamic positioning system,” Neurocomputing, vol. 110, pp. 128–136, 2013.

    Article  Google Scholar 

  14. W. E. Ngongi and J. Du, “A high-gain observerbased PD controller design for dynamic positioning of ships,” Applied Mechanics and Materials, vol. 803, pp. 490–491, 2014.

    Google Scholar 

  15. T. I. Fossen, Guidance and Control of Ocean Vehicles, Wiley, New York, 1994.

    Google Scholar 

  16. B. Chen, C. Tseng, and H. Uang, “Robustness design of nonlinear systems via fuzzy linear control,” IEEE Trans. on Fuzzy Systems, vol. 7, no. 5, pp. 571–585, 1999.

    Article  Google Scholar 

  17. K. Tanaka and H. O. Wang, Fuzzy Control Systems Design and Analysis: A Linear Matrix Inequality Approach, John Wiley and Sons, Inc., 2001.

    Book  Google Scholar 

  18. T. Takagi and M. Sugeno, “Fuzzy identification of systems and its applications to modelling and control,” IEEE Trans. on Man and Cybernetics, vol. 15, no. 1, pp. 116–132, 1985.

    Article  MATH  Google Scholar 

  19. H. O. Wang, K. Tanaka, and M. F. Griffin, “An approach to fuzzy control of nonlinear systems: stability and design issues,” IEEE Trans. on Fuzzy Systems, vol. 4, no. 1, pp. 14–23, 1996.

    Article  Google Scholar 

  20. G. Feng, S. G. Gao, N. W. Rees, and C. K. Chak, “Design of fuzzy control systems with guaranteed stability,” Fuzzy Sets Systems, vol. 85, no. 1, pp. 1–10, 1997.

    Article  MATH  Google Scholar 

  21. Z. Lendek, T. M. Guerra, R. Babuška, and B. De Schutter, “Stability analysis and nonlinear observer design using Takagi-Sugeno fuzzy models,” Studies in Fuzziness and Soft Computing, Springer, vol. 262, 2010.

  22. B. S. Chen, T. S. Lee, and J. H. Feng, “A nonlinear H control design in robotic systems under parameter perturbation and external disturbance,” International Journal of Control, vol. 59, no. 2, pp. 439–461, 1994.

    Article  MATH  MathSciNet  Google Scholar 

  23. S. Boyd, L. El Ghaoi, E. Feron, and V. Valakrishnan, Linear Matrix Inequalities in System and Control Theory, vol. 15, SIAM, Philadelphia, PA, 1994.

  24. K. Tanaka, T. Ikeda, and H. O. Wang, “Fuzzy control design via LMIs,” Proc. of the American Control Conf., Albuquerque, New Mexico, vol. 5, pp. 2873–2877, 1997.

    Google Scholar 

  25. W. Chang, G. Chen, and Y. Yeh, “Fuzzy control of dynamic positioning systems of ships,” International Journal of Marine Science and Technology, vol. 10, no. 1, pp. 47–53, 2002.

    Google Scholar 

  26. W. Ngongi, J. Du, and A. Mohamed, “Relaxed LMI stability conditions based fuzzy control design for dynamic positioning of ships,” Advanced Shipping and Ocean Engineering, vol. 2, no. 4, pp. 105–114, 2013.

    Google Scholar 

  27. W. Ho, S. Chen, and J. Chou, “Optimal control of Takagi-Sugeno fuzzy-model-based systems representing dynamic positioning systems,” Applied Soft Computing, vol. 13, no. 7, pp. 3197–3210, 2013.

    Article  Google Scholar 

  28. W. J. Chang, H. J. Liang, and C.-C. Ku, “Fuzzy controller design subject to actuator saturation for dynamic ship positioning systems with multiplicative noises,” Proc. of the Institution of Mechanical Engineers Part I, Journal of Systems and Control Engineering, vol. 1, no. 1, pp. 1–12, 2010.

    Article  Google Scholar 

  29. W. J. Chang, W. H. Huang, and C. C. Ku, “Robust fuzzy control for discrete perturbed time-delay affine Takagi-Sugeno fuzzy models,” International Journal of Control, Automation and Systems, vol. 9, no. 1, pp. 86–97, 2011.

    Article  Google Scholar 

  30. L. K. Wang and X. D. Liu, “Robust H fuzzy output feedback control for uncertain discrete-time nonlinear systems,” International Journal of Fuzzy Systems, vol. 12, no. 3, pp. 218–226, 2010.

    MathSciNet  Google Scholar 

  31. S. C. Tong, X. L. He, and H. G. Zhang, “A combined backstepping and small-gain approach to robust adaptive fuzzy output feedback control,” IEEE Trans. on Fuzzy Systems, vol. 17, no. 5, pp. 1059–1069, 2009.

    Article  Google Scholar 

  32. S. Tong and H. X. Li, “Fuzzy adaptive slidingmode control for MIMO nonlinear systems,” IEEE Trans. on Fuzzy Systems, vol. 11, no. 3, pp. 354–360, 2003.

    Article  Google Scholar 

  33. Y. J. Liu, S. C. Tong, and W. Wang, “Adaptive fuzzy output tracking for a class of uncertain nonlinear systems,” Fuzzy Sets and Systems, vol. 160, no. 19, pp. 2727–2754, 2009.

    Article  MATH  MathSciNet  Google Scholar 

  34. Y. J. Liu, S. Tong, and C. L. Philip Chen, “Adaptive Fuzzy control via observer design for uncertain nonlinear systems with unmodeled dynamics,” IEEE Trans. on Fuzzy Systems, vol. 21, no. 2, pp. 275–288, 2013.

    Article  Google Scholar 

  35. W. J. Chang and B. J. Huang, “Variance and passivity constrained fuzzy control for nonlinear ship steering systems with state multiplicative noises,” Mechanical Problems in Engineering, vol. 2013, 2013.

    Google Scholar 

  36. W. J. Chang, W. Chang, and H. H. Liu, “Modelbased fuzzy modeling and control for autonomous underwater vehicles in the horizontal plane,” Journal of Marine Science and Technology, vol. 11, no. 3, pp. 155–163, 2003.

    MathSciNet  Google Scholar 

  37. D. Gao, Z. Sun, and B. Xu, “Fuzzy adaptive control for pure-feedback system via time scale separation,” International Journal of Control, Automation and Systems, vol. 11, no. 1, pp. 147–158, 2013.

    Article  Google Scholar 

  38. Y. Q. Fan, Y. H. Wang, Y. Zhang, and Q. R. Wang, “Adaptive fuzzy control with compressors and limiters for a class of uncertain nonlinear systems,” International Journal of Control, Automation and Systems, vol. 11, no. 3, pp. 624–629, 2013.

    Article  Google Scholar 

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Correspondence to Werneld Egno Ngongi.

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Recommended by Associate Editor Do Wan Kim under the direction of Editor Euntai Kim.

This work was supported in part by the Natural Science Foundation of China (51079013), in part by Applied Basic Research Program of Ministry of Transport of P. R. China (2012- 329-225-070).

Werneld Egno Ngongi was born on April, 1976 in Tanzania. Received the M.Sc. degree in Electronics Engineering (2008) and the B.Sc. degree in Electrical Engineering (2002) at the University of Dar es Salaam, Tanzania. He is working as assistant lecturer at Dar es Salaam Maritime Institute, Tanzania. Presently, he is a Ph.D. candidate in Control Theory and Control Engineering at the School of Information Science and Technology, Dalian Maritime University, Dalian, China. His research interests include intelligent control design, nonlinear control design, ship position and motion control.

Jialu Du was born in Liaoning Province, P. R. China, in 1966. She received her Ph.D. degree from Dalian Maritime University, China, in 2005. She was a visiting scholar in Norwegian University of Science and Technology from 2006 to 2007 and in University of California, San Diego from 2012 to 2013, respectively. Currently she is a professor at the School of Information Science and Technology, Dalian Maritime University, China. Her current research interests include nonlinear control theory, intelligent control, and ship motion control.

Rui Wang was born in Shandong Province, P. R. China, in 1990. He received his B.Sc. degree from Shandong University of Technology, China in 2012. Now he is working as a master student at the Department of Information Science and Technology, Dalian Maritime University, China. His current research interests include model prediction control, ship motion control.

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Ngongi, W.E., Du, J. & Wang, R. Robust fuzzy controller design for dynamic positioning system of ships. Int. J. Control Autom. Syst. 13, 1294–1305 (2015). https://doi.org/10.1007/s12555-014-0239-5

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  • DOI: https://doi.org/10.1007/s12555-014-0239-5

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