Nonlinear tracking control of a 3-D overhead crane with friction and payload compensations

Anh-Huy Vo, Quoc-Toan Truong, Ha-Quang-Thinh Ngo, Quoc-Chi Nguyen


In this paper, a nonlinear adaptive control of a 3D overhead crane is investigated. A dynamic model of the overhead crane was developed, where the crane system is assumed as a lumped mass model. Under the mutual effects of the sway motions of the payload and the hoisting motion, the nonlinear behavior of the crane system is considered. A nonlinear control model-based scheme was designed to achieve the three objectives: (i) drive the crane system to the desired positions, (ii) suppresses the vibrations of the payload, and (iii) velocity tracking of hoisting motion. The nonlinear control scheme employs adaptation laws that estimate unknown system parameters, friction forces and the mass of the payload. The estimated values were used to compute control forces applied to the trolley of the crane. The asymptotic stability of the crane system is investigated by using the Lyapunov method. The effectiveness of the proposed control scheme is verified by numerical simulation results.


3-D overhead crane; nonlinear adaptive control; Lyapunov method; Euler-Lagrange equation; sway control;

Full Text:



D. Liu, J. Yi, D. Zhao and W. Wang, “Adaptive sliding mode fuzzy control for a 2D overhead crane,” Mechatronics, vol. 15, no. 5, pp. 505–522, 2005.

H. H. Lee, Y. Liang and D. Segura, “A sliding mode anti-swing trajectory control for overhead cranes with high speed load hoisting,” Journal of Dynamic Systems, Measurement and Control, vol. 128, no. 4, pp. 842–845, 2006.

C. Y. Chang, “Adaptive fuzzy controller of the overhead cranes with nonlinear disturbance,” IEEE Transactions on Industrial Informatics, vol. 3, no. 2, pp. 164–172, 2007.

M. S. Park, D. Chaw and S. K. Hong, “Anti-sway tracking control of overhead cranes with system uncertainty and actuator nonlinearity using an adaptive fuzzy sliding mode control,” IEEE Transactions on Industrial Electronics, vol. 55, no. 11, pp. 3972–3984, 2008.

S. W. Su, H. T. Nguyen, R. Jarmon, J. Zhu, D. B. Lowe, P. B. McLean, S. Huang, N. Nguyen, R. S. Nicholson and K. Wing, “Model predictive control of gantry crane with input nonlinearity compensation,” in World Academy of Science, Engineering and Technology, 2009.

Y. Fang, B. Ma, P. Wang and X. Zhang, “A motion planning based adaptive control method for an under actuated crane system,” IEEE Transactions on Control Systems Technology, vol. 20, no. 1, pp. 241–248, 2011.

L. A. Tuan, S. C. Moon, W. G. Lee and S. G. Lee, “Adaptive sliding mode control of overhead cranes with varying cable length,” Journal of Mechanical Science and Technology, vol. 27, no. 3, pp. 885–893, 2013.

D. Qian and J. Yi, “Design of combining sliding mode controller for overhead crane systems,” International Journal of Control and Automation, vol. 6, no. 1, 2013.

H. Chen, B. GAO and X. Zhang, “Dynamical modeling and nonlinear control of a 3D crane,” in Proc. of the International Conference on Control and Automation, 2005, pp. 1085-1090.

J. H. Yang and K. S. Yang, “Adaptive control for 3-D overhead crane systems,” in Proc. Of the American Control Conference, 2006.

K. S. Lee and H. C. Cho, “Adaptive control and stability analysis of nonlinear crane systems with perturbation,” Journal of Mechanical Science and Technology, vol. 22, no. 6, pp. 1091–1098, 2008.

C. Y. Chang and K. H. Chiang, “Fuzzy projection control law and its application to the overhead crane,” Mechatronics, vol. 18, no. 10, pp. 607–615, 2008.

J.-H. Yang, Linear Adaptive control-Chapter 13: on the adaptive tracking control of 3-D overhead crane system, Intech, DOI: 10.5772/6511, 2009.

N. B. Almutairi and M. Zribi, “Sliding mode control of a three-dimensional overhead crane,” Journal of Vibration and Control, vol. 15, no. 11, pp. 1679–1730, 2009.

A. Pisano, S. Scodina and E. Usai, “Load swing suppression in the 3-dimensional overhead crane via second-order sliding-modes,” in Proc. Of the 2010 11th International Workshop on Variable Structure Systems (VSS), pp. 452-457, 2010.

J. H. Yang and S. H. Shen, “Novel approach for adaptive tracking control of a 3-D overhead crane system,” Journal of Intelligent & Robotic Systems, vol. 62, no. 1, pp. 59–80, 2010.

W. Yu, M. A. M. Armendariz and F. O. Rodriguez, “Stable adaptive compensation with fuzzy CMAC for an overhead crane,” Information Sciences, vol. 181, no. 21, pp. 4895–4907, 2011.

L. A. Tuan, S. G. Lee, V. H. Dang, S. Moon and B. S. Kim, “Partial feedback linearization control of a three-dimensional overhead crane,” International Journal of Control, Automation and Systems, vol. 11, no. 4, pp. 718–727, 2013.

R. M. T. R. Ismail, M. A. Ahmad, M. S. Ramli and F. R. M. Rashidi, “Nonlinear dynamic modeling and analysis of a 3-D overhead gantry crane system with payload variation,” in Proc. Of UKSim Third European Modeling Symposium on Computer Modeling and Simulation, pp. 350-354, 2009.

Q. H. Ngo and K. S. Hong, “Sliding-mode anti-sway control of an offshore container crane,” IEEE/ASME Transactions on Mechatronics, vol. 17, no. 2, pp. 662–668, 2012.

S-J. Ying, “Dynamics of mechanical systems,” in Plastics, Ed.Virginia: American Insitute of Areonautics Astronautics, 1997, pp. 55-56.

Article Metrics

Metrics Loading ...

Metrics powered by PLOS ALM


  • There are currently no refbacks.

Copyright (c) 2016 Journal of Mechatronics, Electrical Power, and Vehicular Technology

Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.



1. Equilibrium path and load trajectory deflections for polar cranes in nuclear power plant
Zhaohui Qi, Huitao Song, Shudong Guo
Advances in Mechanical Engineering  vol: 9  issue: 11  first page: 168781401774249  year: 2017  
doi: 10.1177/1687814017742496