Advertisement

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

  • Fang Deng
  • Hua-Lin YangEmail author
  • Long-Jin Wang
  • Wei-Min Yang
Article
  • 12 Downloads

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.

Keywords

Dynamic positioning nonlinear model predictive control offset-free unscented Kalman filter 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Notes

References

  1. [1]
    A. J. Sørensen, “A survey of dynamic positioning control systems,” Annual Reviews in Control, vol. 35, no. 1, pp. 123–136, Apr. 2011.Google Scholar
  2. [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.CrossRefGoogle Scholar
  3. [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.CrossRefGoogle Scholar
  4. [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.CrossRefGoogle Scholar
  5. [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.CrossRefGoogle Scholar
  6. [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.Google Scholar
  7. [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.Google Scholar
  8. [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.MathSciNetzbMATHCrossRefGoogle Scholar
  9. [9]
    D. Q. Mayne, “Model predictive control: recent developments and future promise,” Automatica, vol. 50, no. 12, pp. 2967–2986, Dec. 2014.MathSciNetzbMATHCrossRefGoogle Scholar
  10. [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.CrossRefGoogle Scholar
  11. [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.CrossRefGoogle Scholar
  12. [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.CrossRefGoogle Scholar
  13. [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.CrossRefGoogle Scholar
  14. [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.CrossRefGoogle Scholar
  15. [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.CrossRefGoogle Scholar
  16. [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. [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.Google Scholar
  18. [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.Google Scholar
  19. [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. [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.CrossRefGoogle Scholar
  21. [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. [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.CrossRefGoogle Scholar
  23. [23]
    M. Ławryn´czuk, Computationally Efficient Model Predictive Control Algorithms: A Neural Network Approach, Springer, 2014.CrossRefGoogle Scholar
  24. [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.CrossRefGoogle Scholar
  25. [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.CrossRefGoogle Scholar
  26. [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.CrossRefGoogle Scholar
  27. [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.MathSciNetzbMATHCrossRefGoogle Scholar
  28. [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.MathSciNetCrossRefGoogle Scholar
  29. [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.CrossRefGoogle Scholar
  30. [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.CrossRefGoogle Scholar
  31. [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.CrossRefGoogle Scholar
  32. [32]
    U. Maeder, F. Borrelli, and M. Morari, “Linear offset-free model predictive control,” Automatica, vol. 45, no. 10, pp. 2214–2222, Oct. 2009.MathSciNetzbMATHCrossRefGoogle Scholar
  33. [33]
    U. Maeder and M. Morari, “Offset-free reference tracking with model predictive control,” Automatica, vol. 46, no. 9, pp. 1469–1476, Sep. 2010.MathSciNetzbMATHCrossRefGoogle Scholar
  34. [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.CrossRefGoogle Scholar
  35. [35]
    M. Morari and U. Maeder, “Nonlinear offset-free model predictive control,” Automatica, vol. 48, no. 9, pp. 2059–2067, Sep. 2012.MathSciNetzbMATHCrossRefGoogle Scholar
  36. [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.MathSciNetCrossRefGoogle Scholar
  37. [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.CrossRefGoogle Scholar
  38. [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.CrossRefGoogle Scholar
  39. [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.CrossRefGoogle Scholar
  40. [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.MathSciNetCrossRefGoogle Scholar
  41. [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.MathSciNetzbMATHCrossRefGoogle Scholar
  42. [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. [43]
    A. V. Fannemel, Dynamic Positioning by Nonlinear Model Predictive Control, Master of Science in Engineering Cybernetics, NTNU, 2008.Google Scholar
  44. [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.CrossRefGoogle Scholar
  45. [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.MathSciNetzbMATHCrossRefGoogle Scholar
  46. [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.CrossRefGoogle Scholar

Copyright information

© ICROS, KIEE and Springer 2019

Authors and Affiliations

  • Fang Deng
    • 1
  • Hua-Lin Yang
    • 1
    Email author
  • Long-Jin Wang
    • 1
  • Wei-Min Yang
    • 2
  1. 1.Mechanical and Electrical EngineeringQingdao University of Science and TechnologyQingdaoChina
  2. 2.College of Mechanical and Electrical EngineeringBeijing University of Chemical TechnologyBeijingChina

Personalised recommendations