Multibody System Dynamics

, Volume 43, Issue 3, pp 279–295 | Cite as

Dynamics analysis and fuzzy anti-swing control design of overhead crane system based on Riccati discrete time transfer matrix method

  • Bao Rong
  • Xiaoting Rui
  • Ling TaoEmail author
  • Guoping Wang


This paper describes an efficient method called Riccati discrete time transfer matrix method of multibody system (MS-RDTTMM) for studying the dynamic modeling and anti-swing control design of a two-dimensional overhead crane system, which consists of a trolley, rope, load, and control subsystem. Regarding the rope as a series of rigid segments connected by hinges, a multibody model of the overhead crane system can be developed easily by using MS-RDTTMM. Then three separate fuzzy logic controllers are designed for positioning and anti-swing control. For improving the performance of the predesigned fuzzy control system, the genetic algorithm based on MS-RDTTMM is presented offline to tune the initial control parameters. Using the recursive transfer formula to describe the system dynamics, instead of the global dynamics equation in ordinary dynamics methods, the matrices involved in this method are always very small, and the computational cost of the dynamic analysis and control system optimization can be greatly reduced. The numerical verification is carried out to show the computational efficiency, numerical stability, and control performance of the proposed method.


Multibody system dynamics Discrete time transfer matrix method Fuzzy control Overhead crane Genetic algorithm 



The research was supported by the Natural Science Foundation of China (Grant Nos. 11702292, 11605234).


  1. 1.
    Chang, C.Y.: Adaptive fuzzy controller of the overhead cranes with nonlinear disturbance. IEEE Trans. Ind. Inform. 3(2), 164–172 (2007) CrossRefGoogle Scholar
  2. 2.
    Chang, C.Y., Chiang, K.H.: Fuzzy projection control law and its application to the overhead crane. Mechatronics 18, 607–615 (2008) CrossRefGoogle Scholar
  3. 3.
    Matsuo, T., Yoshino, R., Suemitsu, H., et al.: Nominal performance recovery by PID+Q controller and its application to antisway control of crane lifter with visual feedback. IEEE Trans. Control Syst. Technol. 12(1), 156–166 (2004) CrossRefGoogle Scholar
  4. 4.
    Park, M.S., Chwa, D., Hong, S.K.: Antisway tracking control of overhead cranes with system uncertainty and actuator nonlinearity using an adaptive fuzzy sliding-mode control. IEEE Trans. Ind. Electron. 55(11), 3972–3984 (2008) CrossRefGoogle Scholar
  5. 5.
    Lee, H.H., Cho, S.K.: A new fuzzy-logic anti-swing control for industrial three-dimensional overhead cranes. In: Proceedings of IEEE International Conference on Robotics & Automation, pp. 2956–2961 (2001) Google Scholar
  6. 6.
    Karkoub, M.A., Zribi, M.: Modeling and energy based nonlinear control of crane lifters. IEE Proc., Control Theory Appl. 149(3), 209–215 (2002) CrossRefGoogle Scholar
  7. 7.
    Fang, Y., Dixon, W.E., Dawson, D.M., Zergeroglu, E.: Nonlinear coupling control laws for an underactuated overhead crane systems. IEEE/ASME Trans. Mechatron. 8(3), 418–423 (2003) CrossRefGoogle Scholar
  8. 8.
    Liu, D.T., Yi, J.Q., Zhao, D.B.: Adaptive sliding mode fuzzy control for a two-dimensional overhead crane. Mechatronics 15, 505–522 (2005) CrossRefGoogle Scholar
  9. 9.
    Yu, W., Moreno-Armendariz, M.A., Rodriguez, F.O.: Stable adaptive compensation with fuzzy CMAC for an overhead crane. Inf. Sci. 181(21), 4895–4907 (2011) MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Tuan, L.A., Moon, S.C., Lee, W.G., et al.: Adaptive sliding mode control of overhead cranes with varying cable length. J. Mech. Sci. Technol. 27(3), 885–893 (2013) CrossRefGoogle Scholar
  11. 11.
    Pezeshki, S., Badamchizadeh, M.A., Ghiasi, A.R., et al.: Control of overhead crane system using adaptive model-free and adaptive fuzzy sliding mode controllers. J. Control Autom. Electr. Syst. 26(1), 1–15 (2015) CrossRefGoogle Scholar
  12. 12.
    Zhang, Z.C., Wu, Y.Q., Huang, J.M.: Differential-flatness-based finite-time anti-swing control of underactuated crane systems. Nonlinear Dyn. 87(3), 1749–1761 (2017) CrossRefzbMATHGoogle Scholar
  13. 13.
    Schiehlen, W.: Research trends in multibody system dynamics. Multibody Syst. Dyn. 18(1), 3–13 (2007) MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Wasfy, T.M., Noor, A.K.: Computational strategies for flexible multibody system. Appl. Mech. Rev. 56(6), 553–613 (2003) CrossRefGoogle Scholar
  15. 15.
    Shabana, A.A.: Dynamics of Multibody Systems. Cambridge University Press, New York (2005) CrossRefzbMATHGoogle Scholar
  16. 16.
    Ambrósio, J.A.C., Gonçalves, J.P.C.: Complex flexible multibody systems with application to vehicle dynamics. Multibody Syst. Dyn. 10(6), 168–182 (2001) MathSciNetzbMATHGoogle Scholar
  17. 17.
    Wittenburg, J.: Dynamics of Multibody Systems. Springer, Berlin (2008) zbMATHGoogle Scholar
  18. 18.
    Pestel, E.C., Leckie, F.A.: Matrix Method in Elastomechanics. McGraw-Hill, New York (1963) Google Scholar
  19. 19.
    Rui, X.T., He, B., Lu, Y.Q., et al.: Discrete time transfer matrix method for multibody system dynamics. Multibody Syst. Dyn. 14(3–4), 317–344 (2005) MathSciNetCrossRefzbMATHGoogle Scholar
  20. 20.
    Rong, B., Rui, X.T., Tao, L.: Dynamics and genetic fuzzy neural network vibration control design of a smart flexible four-bar linkage mechanism. Multibody Syst. Dyn. 28(4), 291–311 (2012) MathSciNetCrossRefGoogle Scholar
  21. 21.
    He, B., Rui, X.T., Wang, G.P.: Riccati discrete time transfer matrix method for elastic beam undergoing large overall motion. Multibody Syst. Dyn. 18(4), 579–598 (2007) MathSciNetCrossRefzbMATHGoogle Scholar
  22. 22.
    Wang, G.P., Rong, B., Tao, L., et al.: Riccati discrete time transfer matrix method for dynamic modeling and simulation of an underwater towed system. J. Appl. Mech. 79, 041014 (2012) CrossRefGoogle Scholar
  23. 23.
    Rong, B.: Efficient dynamics analysis of large-deformation flexible beams by using the absolute nodal coordinate transfer matrix method. Multibody Syst. Dyn. 32(4), 535–549 (2014) MathSciNetCrossRefzbMATHGoogle Scholar
  24. 24.
    Kamman, J.W., Huston, R.L.: Multibody dynamics modeling of variable length cable systems. Multibody Syst. Dyn. 5, 211–221 (2001) CrossRefzbMATHGoogle Scholar
  25. 25.
    Williams, P., Trivailo, P.: A study on the transitional dynamics of a towed-circular aerial cable system. In: AIAA Atmospheric Flight Mechanics Conference and Exhibit, 15–18 August 2005, San Francisco, California (2005) Google Scholar
  26. 26.
    Quisenberry, J.E., Arena, A.S.: Discrete cable modeling and dynamic analysis. In: 44th AIAA Aerospace Sciences Meeting and Exhibit, 9–12 January 2006, Reno, Nevada (2006) Google Scholar
  27. 27.
    Dokainish, M.A., Subbaraj, K.: A study of direct time-integration methods in computational structural dynamics-I. Explicit methods. Comput. Struct. 32(6), 1371–1386 (1989) CrossRefzbMATHGoogle Scholar
  28. 28.
    Zhou, Y.: Research and simulation on anti-swing of container crane using fuzzy intelligent control. Master’s Thesis, Wuhan University of Technology (2003) Google Scholar
  29. 29.
    Wang, Y.Y.: Research on fuzzy logic anti-swing control of overhead crane. Master’s Thesis, Dalian University of Technology (2008) Google Scholar
  30. 30.
    Murata, T., Ishibuchi, H., Tanaka, H.: Multi-objective genetic algorithm and its applications to flowshop scheduling. Comput. Ind. Eng. 30(4), 957–968 (1996) CrossRefGoogle Scholar
  31. 31.
    Li, Y., Liu, J.C., Wang, Y.: An improved adaptive weight approach GA for optimizing multi-objective rolling schedules in a tandem cold rolling. Control Theory Appl. 26(6), 687–693 (2009) Google Scholar
  32. 32.
    Poursamad, A., Montazeri, M.: Design of genetic-fuzzy control strategy for parallel hybrid electric vehicles. Control Eng. Pract. 16, 861–873 (2008) CrossRefGoogle Scholar
  33. 33.
    Horner, G.C.: The Riccati transfer matrix method. Ph.D. dissertation, University of Virginia, USA (1975) Google Scholar

Copyright information

© Springer Science+Business Media B.V., part of Springer Nature 2017

Authors and Affiliations

  • Bao Rong
    • 1
  • Xiaoting Rui
    • 2
  • Ling Tao
    • 1
    Email author
  • Guoping Wang
    • 2
  1. 1.Institute of Plasma PhysicsChinese Academy of Sciences (ASIPP)HefeiP.R. China
  2. 2.Institute of Launch DynamicsNanjing University of Science and TechnologyNanjingP.R. China

Personalised recommendations