Lumped Mass Models of Gantry Cranes

  • Keum-Shik HongEmail author
  • Umer Hameed Shah
Part of the Advances in Industrial Control book series (AIC)


This chapter discusses the mathematical modeling of gantry crane systems, considering the subsystems of a crane to be rigid bodies. Such a formulation does not reflect the deflections within the individual parts of the crane but only considers their rigid body movements and results in a lumped mass model (LMM). Both the overhead and container cranes, shown in Figs.  1.1 and  1.3, respectively, lie within the category of gantry cranes. In developing the LMMs of gantry cranes, three different approaches for modeling the hoisting mechanism are usually followed: (i) single-rope hoisting mechanism, (ii) multi-rope hoisting mechanism, and (iii) double-pendulum system. The first approach, which considers a single-rope hoisting mechanism, represents the dynamics of a simple overhead crane considering the hook and the payload as a single-lumped mass.


  1. Al-Garni AZ, Moustafa KAF, Nizami S (1995) Optimal control of overhead cranes. Control Eng Practice 3(9):1277–1284CrossRefGoogle Scholar
  2. Cartmell MP, Morrish L, Taylor AJ (1998) Dynamics of spreader motion in a gantry crane. Proc Inst Mech Eng Part C-J Mech Eng Sci 212(2):85–105CrossRefGoogle Scholar
  3. Daqaq MF, Masoud ZN (2006) Nonlinear input-shaping controller for quay-side container cranes. Nonlinear Dyn 45(1–2):149–170MathSciNetzbMATHCrossRefGoogle Scholar
  4. Ebeid AM, Moustafa KAF, Emarashabaik HE (1992) Electromechanical modeling of overhead cranes. Int J Syst Sci 23(12):2155–2169CrossRefGoogle Scholar
  5. Hong K-S, Sohn S-C, Lee M-H (1997) Sway control of a container crane (Part I): modeling, control strategy, error feedback control via reference velocity profiles. J Control Autom Syst 3(1):23–31Google Scholar
  6. Karihaloo BL, Parbery RD (1982) Optimal control of a dynamical system representing a gantry crane. J Optim Theory Appl 36(3):409–417MathSciNetzbMATHCrossRefGoogle Scholar
  7. Karkoub MA, Zribi M (2002a) Modelling and energy based nonlinear control of crane lifters. IEE Proc-Control Theory Appl 149(3):209–216CrossRefGoogle Scholar
  8. Karkoub MA, Zribi M (2002b) Modelling and non-linear discontinuous feedback control of crane lifter systems. Proc Inst Mech Eng Part I-J Syst Control Eng 216(I2):157–167CrossRefGoogle Scholar
  9. Kim DH, Singhose W (2010) Performance studies of human operators driving double-pendulum bridge cranes. Control Eng Practice 18(6):567–576CrossRefGoogle Scholar
  10. Kim DH, Lee JW, Park KT et al (2003) Closed-form kinematic solution of a non-parallel cable reeving crane system. Proc Inst Mech Eng Part C-J Mech Eng Sci 217(2):257–269CrossRefGoogle Scholar
  11. Kim YS, Hong K-S, Sul SK (2004) Anti-sway control of container cranes: Inclinometer, observer, and state feedback. Int J Control Autom Syst 2(4):435–449Google Scholar
  12. Lee HH (1998) Modeling and control of a three-dimensional overhead crane. J Dyn Syst Meas Control-Trans ASME 120(4):471–476CrossRefGoogle Scholar
  13. Maleki E, Singhose W (2012) Swing dynamics and input-shaping control of human-operated double-pendulum boom cranes. J Comput Nonlinear Dyn 7(3):031006CrossRefGoogle Scholar
  14. Manson GA (1982) Time–optimal control of an overhead crane model. Optim Control Appl Methods 3(2):115–120zbMATHCrossRefGoogle Scholar
  15. Masoud ZN (2009) Effect of hoisting cable elasticity on anti-sway controllers of quay-side container cranes. Nonlinear Dyn 58(1–2):129–140zbMATHCrossRefGoogle Scholar
  16. Masoud ZN, Alhazza K (2014) Frequency-modulation input shaping control of double-pendulum overhead cranes. J Dyn Syst Meas Control-Trans ASME 136(2):021005CrossRefGoogle Scholar
  17. Masoud ZN, Alhazza K, Abu-Nada E et al (2014) A hybrid command-shaper for double-pendulum overhead cranes. J Vib Control 20(1):24–37CrossRefGoogle Scholar
  18. Masoud ZN, Daqaq MF (2006) A graphical approach to input-shaping control design for container cranes with hoist. IEEE Trans Control Syst Technol 14(6):1070–1077CrossRefGoogle Scholar
  19. Masoud ZN, Nayfeh AH (2003) Sway reduction on container cranes using delayed feedback controller. Nonlinear Dyn 34(3–4):347–358zbMATHCrossRefGoogle Scholar
  20. Masoud ZN, Nayfeeh AH, Nayfeh NA (2005) Sway reduction on quay-side container cranes using delayed feedback controller: simulations and experiments. J Vib Control 11(8):1103–1122zbMATHGoogle Scholar
  21. Morrish L, Cartmell MP, Taylor AJ (1996) Cable stretch asymmetries in multi-cable spreader suspension systems undergoing combined translations and rotations. Proc Inst Mech Eng Part C-J Mech Eng Sci 210(3):225–237CrossRefGoogle Scholar
  22. Morrish L, Cartmell MP, Taylor AJ (1997) Geometry and kinematics of multicable spreader lifting gear. Proc Inst Mech Eng Part C-J Mech Eng Sci 211(3):185–194CrossRefGoogle Scholar
  23. Moustafa KAF, Abou-El-Yazid TG (1996) Load sway control of overhead cranes with load hoisting via stability analysis. JSME Int J Ser C-Dynam Control Robot Des Manuf 39(1):34–40Google Scholar
  24. Moustafa KAF, Ebeid AM (1988) Nonlinear modeling and control of overhead crane load sway. J Dyn Syst Meas Control-Trans ASME 110(3):266–271CrossRefGoogle Scholar
  25. O’Connor W, Habibi H (2013) Gantry crane control of a double-pendulum, distributed-mass load, using mechanical wave concepts. Mech Sci 4(2):251–261CrossRefGoogle Scholar
  26. Ramli L, Mohamed Z, Abdullahi AM et al (2017) Control strategies for crane systems: a comprehensive review. Mech Syst Signal Proc 95:1–23CrossRefGoogle Scholar
  27. Sakawa Y, Sano H (1997) Nonlinear model and linear robust control of overhead traveling cranes. Nonlinear Anal-Theory Methods Appl 30(4):2197–2207zbMATHCrossRefGoogle Scholar
  28. Shah UH, Hong K-S (2014) Input shaping control of a nuclear power plant’s fuel transport system. Nonlinear Dyn 77(4):1737–1748CrossRefGoogle Scholar
  29. Sun N, Fang YC, Chen H et al (2017) Amplitude-saturated nonlinear output feedback antis wing control for under actuated cranes with double-pendulum cargo dynamics. IEEE Trans Ind Electron 64(3):2135–2146CrossRefGoogle Scholar
  30. Tuan LA, Lee SG (2013) Sliding mode controls of double-pendulum crane systems. J Mech Sci Technol 27(6):1863–1873CrossRefGoogle Scholar
  31. Vaughan J, Kim D, Singhose W (2010) Control of tower cranes with double-pendulum payload dynamics. IEEE Trans Control Syst Technol 18(6):1345–1358Google Scholar
  32. Zhang MH, Ma X, Rong XW et al (2016) Adaptive tracking control for double-pendulum overhead cranes subject to tracking error limitation, parametric uncertainties and external disturbances. Mech Syst Signal Proc 76–77:15–32CrossRefGoogle Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  1. 1.School of Mechanical EngineeringPusan National UniversityBusanKorea (Republic of)

Personalised recommendations