Takagi-Sugeno fuzzy approach with compressed representation for overhead crane system
Main Article Content
Abstract
This paper proposes a Takagi-Sugeno (TS) fuzzy approach for 2-dimensional of freedom overhead crane. Since this system is underactuated with nonlinear mathematical dynamic model, the requirement of achieving accurate positioning while eliminating oscillation is a challenging issue. Besides, the number of TS fuzzy rules is exponential in the number of nonlinear elements in the system. Therefore, the reduced complexity method is introduced to minimize the scheduling variables in TS system. In addition, the uncertain system’s components are also taken into consideration to enhance the robust property of the system when working in practical environment. The controller is constructed based one parallel distributed compensation (PDC) approach while the linear matrix inequalities (LMIs) technique is employed to analyse the system’s stability. The effectiveness of the proposed method is demonstrated through numeral simulations.
Keywords
Overhead crane, Takagi-Sugeno fuzzy system, Parallel distributed compensation, Linear matrix inequalities
Article Details
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
References
[1] L. Ramli, Z. Mohamed, M. Efe, I. M. Lazim, H. Jaafar,
Efficient swing control of an overhead crane with
simultaneous payload hoisting and external
disturbances, Mechanical Systems and Signal
Processing, vol. 135, p. 106326, 2020.
https://doi.org/10.1016/j.ymssp.2019.106326
[2] M. J. Maghsoudi, Z. Mohamed, S. Sudin, S. Buyamin,
H. Jaafar, and S. Ahmad, An improved input shaping
design for an efficient sway control of a nonlinear 3D
overhead crane with friction, Mechanical Systems and
Signal Processing, vol. 92, pp. 364-378, 2017.
https://doi.org/10.1016/j.ymssp.2017.01.036
[3] D. Chwa, Sliding-mode-control-based robust finitetime antisway tracking control of 3-D overhead cranes,
IEEE Transactions on Industrial Electronics, vol. 64,
no. 8, pp. 6775-6784, 2017.
https://doi.org/10.1109/TIE.2017.2701760
[4] M. Zhang et al., Adaptive proportional-derivative
sliding mode control law with improved transient
performance for underactuated overhead crane
systems, IEEE/CAA Journal of Automatica Sinica,
vol. 5, no. 3, pp. 683-690, 2018.
https://doi.org/10.1109/JAS.2018.7511072
[5] T. Nguyen, M. Duong, and T. Do, A direct Lyapunovbackstepping approach for stabilizing gantry systems
with flexible cable, Proceedings of Engineering and
Technology Innovation, vol. 8, p. 15, 2018.
[6] G. Galuppini, L. Magni, and D. M. Raimondo, Model
predictive control of systems with deadzone and
saturation, Control Engineering Practice, vol. 78, pp.
56-64, 2018.
https://doi.org/10.1016/j.conengprac.2018.06.010
[7] H. M. Cuong, P. Van Trieu, L. C. Nho, and V. D.
Thuan, Adaptive neural network sliding mode control
of shipboard container cranes considering actuator
backlash, Mechanical Systems and Signal processing,
vol. 112, pp. 233-250, 2018.
https://doi.org/10.1016/j.ymssp.2018.04.030
[8] N. S. A. Shukor and M. A. Ahmad, Data-driven PID
tuning based on safe experimentation dynamics for
control of double-pendulum-type overhead crane, in
Intelligent Manufacturing & Mechatronics, Springer,
2018, pp. 295-303.
https://doi.org/10.1007/978-981-10-8788-2_27
[9] X. Sun and Z. Xie, Reinforcement Learning-Based
Backstepping Control for Container Cranes,
Mathematical Problems in Engineering, vol. 2020,
2020.
https://doi.org/10.1155/2020/2548319
[10] V.-A. Nguyen, A.-T. Nguyen, A. Dequidt, L.
Vermeiren, and M. Dambrine, LMI-based 2-DoF
control design of a manipulator via TS descriptor
approach, IFAC-PapersOnLine, vol. 51, no. 22, pp.
102-107, 2018.
https://doi.org/10.1016/j.ifacol.2018.11.525
[11] K. Akka and F. Khaber, Optimal fuzzy tracking control
with obstacles avoidance for a mobile robot based on
Takagi-Sugeno fuzzy model, Transactions of the
Institute of Measurement and Control, vol. 41, no. 10,
pp. 2772-2781, 2019.
https://doi.org/10.1177/0142331218811462
[12] M. H. Khooban, N. Vafamand, T. Niknam, T.
Dragicevic, and F. Blaabjerg, Model‐predictive
control based on Takagi‐Sugeno fuzzy model for
electrical vehicles delayed model, IET Electric Power
Applications, vol. 11, no. 5, pp. 918-934, 2017.
https://doi.org/10.1049/iet-epa.2016.0508
[13] A. Zemouche, R. Rajamani, B. Boulkroune, H.
Rafaralahy, and M. Zasadzinski, H∞ circle criterion
observer design for Lipschitz nonlinear systems with
enhanced LMI conditions, in 2016 American Control
Conference (ACC), 2016, pp. 131-136: IEEE.
https://doi.org/10.1109/ACC.2016.7524904
Efficient swing control of an overhead crane with
simultaneous payload hoisting and external
disturbances, Mechanical Systems and Signal
Processing, vol. 135, p. 106326, 2020.
https://doi.org/10.1016/j.ymssp.2019.106326
[2] M. J. Maghsoudi, Z. Mohamed, S. Sudin, S. Buyamin,
H. Jaafar, and S. Ahmad, An improved input shaping
design for an efficient sway control of a nonlinear 3D
overhead crane with friction, Mechanical Systems and
Signal Processing, vol. 92, pp. 364-378, 2017.
https://doi.org/10.1016/j.ymssp.2017.01.036
[3] D. Chwa, Sliding-mode-control-based robust finitetime antisway tracking control of 3-D overhead cranes,
IEEE Transactions on Industrial Electronics, vol. 64,
no. 8, pp. 6775-6784, 2017.
https://doi.org/10.1109/TIE.2017.2701760
[4] M. Zhang et al., Adaptive proportional-derivative
sliding mode control law with improved transient
performance for underactuated overhead crane
systems, IEEE/CAA Journal of Automatica Sinica,
vol. 5, no. 3, pp. 683-690, 2018.
https://doi.org/10.1109/JAS.2018.7511072
[5] T. Nguyen, M. Duong, and T. Do, A direct Lyapunovbackstepping approach for stabilizing gantry systems
with flexible cable, Proceedings of Engineering and
Technology Innovation, vol. 8, p. 15, 2018.
[6] G. Galuppini, L. Magni, and D. M. Raimondo, Model
predictive control of systems with deadzone and
saturation, Control Engineering Practice, vol. 78, pp.
56-64, 2018.
https://doi.org/10.1016/j.conengprac.2018.06.010
[7] H. M. Cuong, P. Van Trieu, L. C. Nho, and V. D.
Thuan, Adaptive neural network sliding mode control
of shipboard container cranes considering actuator
backlash, Mechanical Systems and Signal processing,
vol. 112, pp. 233-250, 2018.
https://doi.org/10.1016/j.ymssp.2018.04.030
[8] N. S. A. Shukor and M. A. Ahmad, Data-driven PID
tuning based on safe experimentation dynamics for
control of double-pendulum-type overhead crane, in
Intelligent Manufacturing & Mechatronics, Springer,
2018, pp. 295-303.
https://doi.org/10.1007/978-981-10-8788-2_27
[9] X. Sun and Z. Xie, Reinforcement Learning-Based
Backstepping Control for Container Cranes,
Mathematical Problems in Engineering, vol. 2020,
2020.
https://doi.org/10.1155/2020/2548319
[10] V.-A. Nguyen, A.-T. Nguyen, A. Dequidt, L.
Vermeiren, and M. Dambrine, LMI-based 2-DoF
control design of a manipulator via TS descriptor
approach, IFAC-PapersOnLine, vol. 51, no. 22, pp.
102-107, 2018.
https://doi.org/10.1016/j.ifacol.2018.11.525
[11] K. Akka and F. Khaber, Optimal fuzzy tracking control
with obstacles avoidance for a mobile robot based on
Takagi-Sugeno fuzzy model, Transactions of the
Institute of Measurement and Control, vol. 41, no. 10,
pp. 2772-2781, 2019.
https://doi.org/10.1177/0142331218811462
[12] M. H. Khooban, N. Vafamand, T. Niknam, T.
Dragicevic, and F. Blaabjerg, Model‐predictive
control based on Takagi‐Sugeno fuzzy model for
electrical vehicles delayed model, IET Electric Power
Applications, vol. 11, no. 5, pp. 918-934, 2017.
https://doi.org/10.1049/iet-epa.2016.0508
[13] A. Zemouche, R. Rajamani, B. Boulkroune, H.
Rafaralahy, and M. Zasadzinski, H∞ circle criterion
observer design for Lipschitz nonlinear systems with
enhanced LMI conditions, in 2016 American Control
Conference (ACC), 2016, pp. 131-136: IEEE.
https://doi.org/10.1109/ACC.2016.7524904