Skip to main content
SpringerLink
Log in

UKF Based Nonlinear Offset-free Model Predictive Control for Ship Dynamic Positioning Under Stochastic Disturbances

  • Regular Papers
  • Published:
International Journal of Control, Automation and Systems Aims and scope Submit manuscript

Abstract

This paper presents the schemes of nonlinear offset-free model predictive control (MPC) for reference tracking of ship dynamic positioning (DP) systems, in the presence of slow-varying stochastic disturbances and input constraints. Two offset-free MPC strategies for nonlinear DP systems are proposed. The first approach, namely, the target calculation formulation, estimates the disturbance based on the augmented disturbance model, and employs a target calculator to address the MPC optimization problem. The second approach, namely, the delta input formulation, works with the augmented velocity model to lump the effects of disturbances into the input estimates. By successively on-line linearizing the state-space model at the current operating point, the future outputs are explicitly predicted, and then the nonlinear optimization problem becomes an easy quadratic optimization problem. The unscented Kalman filter is adopted for the state estimation. By implementing simulations for two scenarios of disturbances with parametric plant-model mismatch, the effectiveness of the two strategies is demonstrated. Results show that the closed-loop control performance of the delta input formulation method is superior, for its good robustness to the stochastic disturbance.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

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

  2. F. Wang, M. Lv, and F. Xu, “Design and implementation of a triple-redundant dynamic positioning control system for deepwater drilling rigs,” Applied Ocean Research, vol. 57, pp. 140–151, Apr. 2016.

    Article  Google Scholar 

  3. J. G. Balchen, N. A. Jenssen, M. Eldar, and S. Saelid, “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. Å. Grøvlen and T. I. Fossen, “Nonlinear control of dynamic positioned ships using only position feedback: an observer backstepping approach,” Proc. of the 35th IEEE Conference on Decision and Control, vol. 3, pp. 3388–3393, Jan. 1996.

    Article  Google Scholar 

  5. F. Deng, L. J. Wang, and D. M. Jiao, “Adaptive observer based backstepping controller design for dynamic ship positioning,” China Ocean Engineering, vol. 31, no. 5, pp. 639–645, Oct. 2017.

    Article  Google Scholar 

  6. E. A. Tannuri, A. C. Agostinho, H. M. Morishita, and L. M. Jr, “Dynamic positioning systems: an experimental analysis of sliding mode control,” Control Engineering Practice, vol. 18, no. 10, pp. 1121–1132, Oct. 2010.

  7. J. Du, Y. Yang, D. Wang, and C. Guo, “A robust adaptive neural networks controller for maritime dynamic positioning system,” Neurocomputing, vol. 110, no. 1, pp. 128–136, Jun. 2013.

  8. D. Q. Mayne, J. B. Rawlings, C. V. Rao, and P. O. M. Scokaert, “Constrained model predictive control: stability and optimality,” Automatica, vol. 36, no. 6, pp. 789–814, Jun. 2000.

    Article  MathSciNet  MATH  Google Scholar 

  9. D. Q. Mayne, “Model predictive control: recent developments and future promise,” Automatica, vol. 50, no. 12, pp. 2967–2986, Dec. 2014.

    Article  MathSciNet  MATH  Google Scholar 

  10. C. Sotelo, A. F. Contreras, F. B. Carbajal, G. D. Assad, P. R. Cañedo, and D. Sotelo, “A novel discrete-time nonlinear model predictive control based on state space model,” International Journal of Control, Automation and Systems, vol. 16, no. 6, pp. 2688–2696, Dec. 2018.

    Article  Google Scholar 

  11. T. Y. Kim, B. S. Kim, T. C. Park, and Y. K. Yeo, “Development of predictive model based control scheme for a molten carbonate fuel cell (MCFC) process.” International Journal of Control, Automation and Systems, vol. 16, no. 2, pp. 791–803, Apr. 2018.

    Article  Google Scholar 

  12. M. Yue, C. An, and J. Z. Sun, “An efficient model predictive control for trajectory tracking of wheeled inverted pendulum vehicles with various physical constraints.” International Journal of Control, Automation and Systems, vol. 16, no. 1, pp. 265–274, Feb. 2018.

    Article  Google Scholar 

  13. M. A. Mousavi, B. Moshiri, and Z. Heshmati, “A new predictive motion control of a planar vehicle under uncertainty via convex optimization.” International Journal of Control, Automation and Systems, vol. 15, no. 1, pp. 129–137, Feb. 2017.

    Article  Google Scholar 

  14. C. Shen, Y. Shi, and B. Buckham, “Trajectory tracking control of an autonomous underwater vehicle using Lyapunov-based model predictive control,” IEEE Transactions on Industrial Electronics, vol. 65, no. 7, pp. 5796–5805, Dec. 2018.

    Article  Google Scholar 

  15. S. Koo, S. Kim and J. Suk, Y. D. Kim and J. H. Shin, “Improvement of shipboard landing performance of fixed-wing UAV using model predictive control.” International Journal of Control, Automation and Systems, vol. 16, no. 6, pp. 2697–2708, Dec. 2017.

    Article  Google Scholar 

  16. Z. Sun, Y. Xia, L. Dai, K. Liu, D. Ma, Z. Sun, Y. Xia, L. Dai, K. Liu, and D. Ma, “Disturbance rejection MPC for tracking of wheeled mobile robot,” IEEE/ASME Transactions on Mechatronics, vol. PP, no. 99, pp. 1–10, Oct. 2017.

    Google Scholar 

  17. H. L. Chen, L. Wan, F. Wang, and G. C. Zhang, “Model predictive controller design for the dynamic positioning system of a semi-submersible platform,” Journal of Marine Science and Technology, vol. 11, no. 3, pp. 361–367, Sep. 2012.

  18. W. H. Li, Y. Q. Sun, H. Q. Chen, and G. Wang, “Model predictive controller design for ship dynamic positioning system based on state-space equations,” Journal of Marine Science and Technology, vol. 22, no. 3, pp. 426–431, Sep. 2017.

  19. X. B. Qian, Y. Yin, X. F. Zhang, X. F. Sun, and H. L. Shen, “Model predictive controller using Laguerre functions for dynamic positioning system,” Proc. of Chinese Control Conference, pp. 4436–4441, Jun. 2016.

    Google Scholar 

  20. H. R. Zheng, R. R. Negenborn, and G. Lodewijks, “Trajectory tracking of autonomous vessels using model predictive control,” IFAC Proceedings Volumes, vol. 47, no. 3, pp. 8812–8818, Jan. 2014.

    Article  Google Scholar 

  21. M. V. Sotnikova and E. I. Veremey, “Dynamic positioning based on nonlinear MPC,” Proc. of IFAC Conference on Control Applications in Marine Systems, pp. 37–42, Sep. 2013.

    Google Scholar 

  22. A. Veksler, T. A. Johansen, F. Borrelli, and B. Realfsen, “Dynamic positioning with model predictive control,” IEEE Transactions on Control Systems Technology, vol. 24, no. 4, pp. 1340–1353, Jan. 2016.

    Article  Google Scholar 

  23. M. Ławryn´czuk, Computationally Efficient Model Predictive Control Algorithms: A Neural Network Approach, Springer, 2014.

    Book  Google Scholar 

  24. R. Heydari and M. Farrokhi, “Robust model predictive control of biped robots with adaptive on-line gait generation.” International Journal of Control, Automation and Systems, vol. 15, no. 1, pp. 329–344, Feb. 2017.

    Article  Google Scholar 

  25. H. Z. Xiao and C. L. P. Chen, “Incremental updating multi-robot formation using nonlinear model predictive control method with general projection neural network,” IEEE Transactions on Industrial Electronics, vol. 66, no. 6, pp. 4502–4512, Jun. 2019.

    Article  Google Scholar 

  26. M. Ławryn´czuk, “Nonlinear predictive control of a boiler-turbine unit: A state-space approach with successive online model linearisation and quadratic optimisation,” ISA Transactions, vol. 67, no. 1, pp. 476–495, Jan. 2017.

    Article  Google Scholar 

  27. J. Köhler, M. A. Müller, and F. Allgöwer, “Nonlinear reference tracking: an economic model predictive control perspective,” IEEE Transactions on Automatic Control, vol. 64, no. 1, pp. 254–269, Jan. 2019.

    Article  MathSciNet  MATH  Google Scholar 

  28. M. Li and Y. Chen, “Robust time-varying H∞ control for networked control system with uncertainties and external disturbance,” International Journal of Control, Automation and Systems, vol. 16, no. 5, pp. 2125–2135, May 2019.

    Article  MathSciNet  Google Scholar 

  29. M. Zhao, C. C. Jiang, and M. H. She, “Robust contractive economic MPC for nonlinear systems with additive disturbance.” International Journal of Control, Automation and Systems, vol. 16, no. 5, pp. 2253–2263, Oct. 2018.

    Article  Google Scholar 

  30. N. C. Chi, “Adaptive feedback linearization control for twin rotor multiple-input multiple-output system.” International Journal of Control, Automation and Systems, vol. 15, no. 3, pp. 1267–1274, Jun. 2017.

    Article  Google Scholar 

  31. C. Liu, C. L. P. Chen, Z. J. Zou, and T. S. Li, “Adaptive NN-DSC control design for path following of underactu-ated surface vessels with input saturation,” Neurocomput-ing, vol. 267, no. 6, pp. 466–474, Dec. 2017.

    Article  Google Scholar 

  32. U. Maeder, F. Borrelli, and M. Morari, “Linear offset-free model predictive control,” Automatica, vol. 45, no. 10, pp. 2214–2222, Oct. 2009.

    Article  MathSciNet  MATH  Google Scholar 

  33. U. Maeder and M. Morari, “Offset-free reference tracking with model predictive control,” Automatica, vol. 46, no. 9, pp. 1469–1476, Sep. 2010.

    Article  MathSciNet  MATH  Google Scholar 

  34. F. A. Bender, S. Göltz, T. Bräunl, and O. Sawodny, “Modeling and offset-free model predictive control of a hydraulic mini excavator,” IEEE Transactions on Automation Science and Engineering, vol. 14, no. 4, pp. 1682–1694, Oct. 2017.

    Article  Google Scholar 

  35. M. Morari and U. Maeder, “Nonlinear offset-free model predictive control,” Automatica, vol. 48, no. 9, pp. 2059–2067, Sep. 2012.

    Article  MathSciNet  MATH  Google Scholar 

  36. P. Tatjewski, “Offset-free nonlinear model predictive control with state-space process models,” Archives of Control Sciences, vol. 27, no. LXIII, pp. 595–615, Dec. 2017.

    Article  MathSciNet  Google Scholar 

  37. A. González, E. Adam, and J. Marchetti, “Conditions for offset elimination in state space receding horizon controllers: a tutorial analysis,” Chemical Engineering and Processing, vol. 47, no. 12, pp. 2184–2194, Nov. 2008.

    Article  Google Scholar 

  38. J. G. Guo, Q. Peng, and J. Zhou, “Disturbance observer-based nonlinear model predictive control for air-breathing hypersonic vehicles,” Journal of Aerospace Engineering, vol. 32, no. 1, pp. 1–3, Jan. 2019.

    Article  Google Scholar 

  39. Y. Wen, L. Chen, Y. Wang, D. Sun, D. Duan and J. Liu, “Nonlinear DOB-based explicit NMPC for station-keeping of a multi-vectored propeller airship with thrust saturation,” The Aeronautical Journal, vol. 122, no. 1257, pp. 1753–1774, Nov. 2018.

    Article  Google Scholar 

  40. V. Stojanovic, N. Nedic, D. Prisc, and L. Dubonjic, “Optimal experiment design for identification of ARX models with constrained output in non-Gaussian noise,” Applied Mathematical Modelling, vol. 40, no. 13–14, pp. 6676–6689, Jul. 2016.

    Article  MathSciNet  Google Scholar 

  41. V. Stojanovic and N. Nedic, “Joint state and parameter robust estimation of stochastic nonlinear systems,” International Journal of Robust Nonlinear Control, vol. 26, no. 14, pp. 3058–3074, Sep. 2016.

    Article  MathSciNet  MATH  Google Scholar 

  42. S. J. Julier and J. K. Uhlmann, “New extension of the Kalman filter to nonlinear systems,” SPIE Proceedings of Signal Processing, Sensor Fusion, and Target Recognition VI, vol. 3068, pp. 1–12, Jul. 1997.

    Google Scholar 

  43. A. V. Fannemel, Dynamic Positioning by Nonlinear Model Predictive Control, Master of Science in Engineering Cybernetics, NTNU, 2008.

    Google Scholar 

  44. F. Deng, H. L. Yang, and L. J. Wang, “Adaptive unscented Kalman filter based estimation and filtering for dynamic positioning with model uncertainties,” International Journal of Control Automation and Systems, vol. 17, no. 3, pp. 667–678, Mar. 2019.

    Article  Google Scholar 

  45. J. Du, X. Hu, and Y. Sun, “Robust dynamic positioning of ships with disturbances under input saturation,” Automatica, vol. 73, no. SI, pp. 207–214, Nov. 2016.

    Article  MathSciNet  MATH  Google Scholar 

  46. M. R. Rajamani, J. B. Rawlings, and S. J. Qin, “Achieving state estimation equivalence for misassigned disturbances in offset-free model predictive control,” Aiche Journal, vol. 55, no. 2, pp. 396–407, Feb. 2009.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Mechanical and Electrical Engineering, Qingdao University of Science and Technology, Qingdao, 266061, China

    Fang Deng, Hua-Lin Yang & Long-Jin Wang

  2. College of Mechanical and Electrical Engineering, Beijing University of Chemical Technology, Beijing, 100029, China

    Wei-Min Yang

Authors
  1. Fang Deng
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hua-Lin Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Long-Jin Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Wei-Min Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hua-Lin Yang.

Additional information

Publisher’s Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Recommended by Associate Editor Muhammad Rehan under the direction of Editor Myo Taeg Lim. This research was supported by the Key Research and Development Program of ShanDong Province (Grant no. 2018GNC112007), the Project of Shandong Province Higher Educational Science and Technology Program (Grant no. J18KA015), and the Project of Shandong Provincial Natural Science Foundation (Grant no. ZR2019MEE102).

Fang Deng received her B.S. degree in Process Equipment and Control Engineering from SiChuan University, China, in 2003. She received an M.S. degree in chemical machinery from ZheJiang University in 2006. She is currently working toward a Ph.D. degree at Qingdao University of Science and Technology. Her current research interests include nonlinear control and estimation, adaptive control, and application in motion control of marine crafts.

Hua-Lin Yang received his B.S. degree in mechanical design and manufacturing from Shandong Institute of Light Industry in 1998. He received his M.S. degree in mechanical manufacturing and automation from Qingdao University of Science and Technology in 2003, and his Ph.D. degree in chemical machinery from ZheJiang University in 2006. His current research interests include intelligent manufacturing, mechanical design, control and automation.

Long-Jin Wang received his Ph.D. degree in Control Science and Engineering from Harbin Engineering University, Harbin, China, in 2009. From 2009 to 2013, he was an engineer at China Shipbuilding heavy Industry Corporation. Since 2013, he has been an associate professor in Control Science and Engineering at Qingdao University of Science and Technology. His current research interests include model identification and ship motion control.

Wei-Min Yang is a professor at the College of Mechanical and Electrical Engineering, Beijing University of Chemical Technology, China. His research interests include the principle and equipment of polymer molding processing in mechanical engineering and advanced manufacturing, and the design and construction of yachts.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Deng, F., Yang, HL., Wang, LJ. et al. UKF Based Nonlinear Offset-free Model Predictive Control for Ship Dynamic Positioning Under Stochastic Disturbances. Int. J. Control Autom. Syst. 17, 3079–3090 (2019). https://doi.org/10.1007/s12555-019-0036-2

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12555-019-0036-2

Keywords

Search

Navigation