Nonlinear Control of Marine Surface Vessels

  • Swarup DasEmail author
  • S. E. Talole
Review Paper


In the present study, a robust yaw control law design derived from nonlinear extended state observer (NESO) based nonlinear state error feedback controller (NSEFC) in conjunction with nonlinear tracking differentiator (NTD) for marine surface vessels is presented. As marine vessel operates in an environment where significant uncertainties and disturbances are present, an NESO is used to estimate the effect of the uncertainties and disturbances along with the plant states leading to a robust design through disturbance estimation and compensation. Convergence of NESO and NTD is demonstrated. The notable feature of the formulation is that to achieve robustness, accurate plant model or any characterization of the uncertainties and disturbances is not needed. Efficacy of the design is illustrated by simulation. Further, performance of the proposed design is compared with some existing controllers to showcase the effectiveness of the proposed design.


Marine vessel Ship autopilot Nonlinear extended state observer Tracking differentiator Robust control 


  1. 1.
    K.J. Spyrou, Asymmetric surging of ships in following seas and its repercussions for safety. Nonlinear Dyn. 43, 149–172 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    K.J. Spyrou, V. Belenky, N. Themelis, K. Weems, Detection of surf-riding behavior of ships in irregular seas. Nonlinear Dyn. 78, 649–667 (2014)MathSciNetCrossRefGoogle Scholar
  3. 3.
    C.Y. Tzcng, An internal model control approach to the design of yaw-rate-control ship-steering autopilot. IEEE J. Ocean. Eng. 24, 507–514 (1999)CrossRefGoogle Scholar
  4. 4.
    T.A. Johansen, T.P. Fuglseth, P. Tondel, T.I. Fossen, Optimal constrained control allocation in marine surface. Control Eng. Pract. 16, 457–464 (2008)CrossRefGoogle Scholar
  5. 5.
    S.L. Dai, C. Wang, F. Luo, Identification and learning control of ocean surface ship using neural networks. IEEE Trans. Ind. Inform. 8, 801–810 (2012)CrossRefGoogle Scholar
  6. 6.
    S. Das, A. Bhatt, S.E. Talole, UDE based backstepping design for ship autopilot, in Proceedings of the International Conference on Industrial Instrumentation and Control (ICIC) (College of Engineering Pune, India, 2015), pp. 417–422Google Scholar
  7. 7.
    L. Yuan, H. Wu, Terminal sliding mode fuzzy control based on multiple sliding surfaces for nonlinear ship autopilot systems. J. Mar. Sci. Appl. 9, 425–430 (2010)CrossRefGoogle Scholar
  8. 8.
    M.R. Katebi, M.J. Grimble, Y. Zhang, \(\text{ H }_{\infty }\) robust control design for dynamic ship positioning. IEE Proc. Control Theory Appl. 144, 110–120 (1997)CrossRefzbMATHGoogle Scholar
  9. 9.
    N. Khaled, G. Nabil, G. Chalhoub, A self-tuning guidance and control system for marine surface vessels. Nonlinear Dyn. 73, 897–906 (2013)CrossRefGoogle Scholar
  10. 10.
    Y. Yang, J. Ren, Adaptive fuzzy robust tracking controller design via small gain approach and its application. IEEE Trans. Fuzzy Syst. 11, 783–795 (2003)CrossRefGoogle Scholar
  11. 11.
    G. Tao, Z. Jin, Generalized predictive control with constraints for ship autopilot, in Proceedings of the 24th Chinese Control and Decision Conference (CCDC) (2012), pp. 1648–1551Google Scholar
  12. 12.
    K.J. Astrom, Why use adaptive control for steering large tankers? Int. J. Control 32, 689–708 (1980)CrossRefGoogle Scholar
  13. 13.
    J.A. Profeta, W.G. Vogt, M.H. Mickle, Disturbance estimation and compensation in linear systems. IEEE Trans. Aerosp. Electron. Syst. 26, 225–231 (1990)CrossRefGoogle Scholar
  14. 14.
    T. Mita, M. Hirata, K. Murata, H. Zhang, \(\text{ H }_\infty\) control versus disturbance-observer-based control. IEEE Trans. Ind. Electron. 45(3), 488–495 (1998)CrossRefGoogle Scholar
  15. 15.
    S. Kwon, W.K. Chung, Robust performance of the multiloop perturbation compensator. IEEE/ASME Trans. Mechatron. 7(2), 190–200 (2002)CrossRefGoogle Scholar
  16. 16.
    R. Sreedhar, B. Fernandez, G.Y. Masada, Robust fault detection in nonlinear systems using sliding mode observers, in Proceedings of the IEEE International Conference on Control and Applications, 13–16 September 1993 (Vancouver, BC, Canada, 1993), pp. 715–721Google Scholar
  17. 17.
    Z. Gao, Active disturbance rejection control: a paradigm shift in feedback control system design, in Proceedings of the American Control Conference (ACC) (Minneapolis, MN, USA, 2006), pp. 2399–2405Google Scholar
  18. 18.
    W. Wang, Z. Gao, A comparison study of advanced state observer design techniques, in Proceedings of the American Control Conference (Colorado, USA, 2003), pp. 4754–4759Google Scholar
  19. 19.
    Q. Zheng, L. Dong, D.H. Lee, Z. Gao, Active disturbance rejection control for MEMS gyroscopes. IEEE Trans. Control Syst. Technol. 17, 1432–1438 (2009)CrossRefGoogle Scholar
  20. 20.
    C. Mingyue, L. Wei, L. Hongzhao, J. Hualong, W. Zhipeng, Extended state observer-based adaptive sliding mode control of differential-driving mobile robot with uncertainties. Nonlinear Dyn. 83, 667–683 (2016)MathSciNetCrossRefzbMATHGoogle Scholar
  21. 21.
    Y.X. Su, B.Y. Duan, C.H. Zheng, Y.F. Zhang, G.D. Chen, J.W. Mi, Disturbance-rejection high-precision motion control of a Stewart platform. IEEE Trans. Control Syst. Technol. 12, 364–374 (2004)CrossRefGoogle Scholar
  22. 22.
    S.E. Talole, S.B. Phadke, Extended state observer based control of flexible joint system, in Proceedings of the IEEE International Symposium on Industrial Electronics (ISIE08), 30 June–02 July 2008 (University of Cambridge, Cambridge, UK, 2008), pp. 2514–2519Google Scholar
  23. 23.
    A.A. Godbole, T.R. Libin, S.E. Talole, Extended state observer-based robust pitch autopilot design for tactical missiles. Proc. Inst. Mech. Eng. Part G J. Aerosp. Eng. 226, 1482–1501 (2011)CrossRefGoogle Scholar
  24. 24.
    B. Panchal, J.P. Kolhe, S.E. Talole, Robust predictive control of a class of nonlinear systems. J. Guid. Control Dyn. 37, 1437–1445 (2014)CrossRefGoogle Scholar
  25. 25.
    B. Panchal, N. Mate, S.E. Talole, Continuous time predictive control based integrated guidance and control. J. Guid. Control Dyn. 40, 1579–1595 (2017)CrossRefGoogle Scholar
  26. 26.
    S. Das, S.E. Talole, Robust steering autopilot design for marine vessels. IEEE J. Ocean. Eng. 41, 913–922 (2016)CrossRefGoogle Scholar
  27. 27.
    S. Das, S.E. Talole, GESO based robust output tracking controller for marine vessels. Ocean Eng. 121, 156–165 (2016)CrossRefGoogle Scholar
  28. 28.
    J.V. Amerongen, Adaptive steering of ships: a model reference approach. Automatica 20, 3–14 (1984)CrossRefzbMATHGoogle Scholar
  29. 29.
    T.I. Fossen, Guidance and Control of Ocean Vehicle (Wiley, New York, 1994)Google Scholar
  30. 30.
    C. Erazo, F. Angulo, G. Olivar, Stability analysis of the extended state observers by Popov criterion. Theor. Appl. Mech. Lett. 2(4), 043006-1-4 (2012)CrossRefGoogle Scholar
  31. 31.
    J.-J.E. Slotine, W. Li, Applied Nonlinear Control (Prentice-Hall, Englewood Cliffs, 1991)zbMATHGoogle Scholar
  32. 32.
    Y. Tang, Y. Wu, M. Wu, X. Hu, L. Shen, Nonlinear tracking-differentiator for velocity determination using carrier phase measurements. IEEE J. Sel. Top. Signal Process. 3, 716–725 (2009)CrossRefGoogle Scholar
  33. 33.
    B.-Z. Guoa, Z. Zhaoa, On convergence of tracking differentiator. Int. J. Control 84, 693–701 (2011)MathSciNetCrossRefGoogle Scholar
  34. 34.
    Y.X. Su, C.H. Zheng, D. Sun, B.Y. Duan, A simple nonlinear velocity estimator for high-performance motion control. IEEE Trans. Ind. Electron. 52, 1161–1169 (2005)CrossRefGoogle Scholar
  35. 35.
    Y.X. Su, C.H. Zheng, P.C. Mueller, B.Y. Duan, A simple improved velocity estimation for low-speed regions based on position measurements only. IEEE Trans. Control Syst. Technol. 14, 937–942 (2006)CrossRefGoogle Scholar
  36. 36.
    E. Zhu, J. Pang, N. Sun, Q. Sun, Z. Chen, Airship horizontal trajectory tracking control based on active disturbance rejection control (ADRC). Nonlinear Dyn. 75, 725–734 (2014)MathSciNetCrossRefGoogle Scholar
  37. 37.
    Q. Zheng, L. Dong, D.H. Lee, Z. Gao, Active disturbance rejection control for mems gyroscopes. IEEE Trans. Control Syst. Technol. 17, 1432–1438 (2009)CrossRefGoogle Scholar
  38. 38.
    C.L. Angel, L.J. Alberto, C. Isaac, Robust trajectory tracking of a delta robot through adaptive active disturbance rejection control. IEEE Trans. Control Syst. Technol. 23, 1387–1398 (2015)CrossRefGoogle Scholar
  39. 39.
    S. Guofa, R. Xuemei, D. Li, Neural active disturbance rejection output control of multimotor servomechanism. IEEE Trans. Control Syst. Technol. 23, 746–753 (2015)CrossRefGoogle Scholar
  40. 40.
    S.R. Hebertt, L.F. Jesus, G.R. Carlos, C.O.M. Antonio, On the control of the permanent magnet synchronous motor: an active disturbance rejection control approach. IEEE Trans. Control Syst. Technol. 22, 2056–2063 (2014)CrossRefGoogle Scholar
  41. 41.
    L. Fang, L. Yong, C. Yijia, S. Jinhua, M. Wu, A two-layer active disturbance rejection controller design for load frequency control of interconnected power system. IEEE Trans. Power Syst. 31(4), 1–2 (2015)Google Scholar
  42. 42.
    M. Pizzocaro, D. Calonico, C. Calosso, C. Costanzo, G.A. Levi, F. Mura, Active disturbance rejection control of temperature for ultrastable optical cavities. IEEE Trans. Ultrason. Ferroelectr. Freq. Control 60, 273–280 (2013)CrossRefGoogle Scholar
  43. 43.
    J. Tao, Q. Sun, P. Tan, Z. Chen, Y. He, Active disturbance rejection control (ADRC)-based autonomous homing control of powered parafoils. Nonlinear Dyn. 86, 1461–1476 (2016)CrossRefGoogle Scholar
  44. 44.
    V. Nicolau, On PID controller design by combining pole placement technique with symmetrical optimum criterion. Math. Probl. Eng. 2013, 1–8 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  45. 45.
    Z. Lei, C. Guo, Disturbance rejection control solution for ship steering system with uncertain time delay. Ocean Eng. 95, 78–83 (2015)CrossRefGoogle Scholar

Copyright information

© The Institution of Engineers (India) 2018

Authors and Affiliations

  1. 1.Department of Aerospace EngineeringDefence Institute of Advanced TechnologyGirinagar, PuneIndia

Personalised recommendations