Fractional-Order Sliding Mode Control of Overhead Cranes
Main Article Content
Abstract
We constitute a control system for overhead crane with simultaneous motion of trolley and payload hoist to destinations and suppression of payload swing. Controller core made by sliding mode control (SMC) assures the robustness. This control structure is inflexible since using fixed gains. For overcoming this weakness, we integrate variable fractional-order derivative into SMC that leads to an adaptive system with adjustable parameters. We use Mittag–Leffler stability, an enhanced version of Lyapunov theory, to analyze the convergence of closed-loop system. Applying the controller to a practical crane shows the efficiency of proposed control approach. The controller works well and keeps the output responses consistent despite the large variation of crane parameters.
Keywords
Fractional-order control, overhead cranes, sliding mode control
Article Details
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References
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[21] Y. Li, Y.Q. Chen, I. Podlubny, Mittag–Leffler stability of fractional order nonlinear dynamic systems. Automatica 45 (2009) 1965-1969. https://doi.org/10.1016/j.automatica.2009.04.001
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[2] L.A. Tuan, S.-G. Lee, V.-H. Dang, S. Moon, B.S. Kim, Partial feedback linearization control of a three-dimensional overhead crane, International Journal of Control, Automation and Systems 11 (2013) 718-727. https://doi.org/10.1007/s12555-012-9305-z
[3] A.C. Lecours, S. Foucault, T. Laliberté, B. Mayer-StOnge, C. Gosselin, A cable-suspended intelligent crane assist device for the intuitive manipulation of large payloads, IEEE/ASME Transactions on Mechatronics 21 (2016) 2073-2084. https://doi.org/10.1109/TMECH.2016.2531626
[4] A.Z. Al-Garni, K.A.F. Moustafa, and S.S.A.K. Javeed Nizami, Optimal control of overhead cranes, Control Engineering Practice 3 (1995) 1277-1284. https://doi.org/10.1016/0967-0661(95)00126-F
[5] X. Wu, X. He, Nonlinear energy-based regulation control of three-dimensional overhead cranes, IEEE Transactions on Automation Science and Engineering 14 (2017) 1297-1038. https://doi.org/10.1109/TASE.2016.2542105
[6] H. Chen, Y. Fang, N. Sun, A swing constraint guaranteed mpc algorithm for underactuated overhead cranes, IEEE/ASME Transactions on Mechatronics 21 (2016) 2543-2555. https://doi.org/10.1109/TMECH.2016.2558202
[7] Y.J. Hua, Y.K. Shine, Adaptive coupling control for overhead crane systems, Mechatronics 17 (2007) 143-152. https://doi.org/10.1016/j.mechatronics.2006.08.004
[8] L.A. Tuan, S.-G. Lee, L.C. Nho, D.-H. Kim, Model reference adaptive sliding mode control for three dimensional overhead cranes, International Journal of Precision Engineering and Manufacturing 14 (2013) 1329-1338. https://doi.org/10.1007/s12541-013-0180-1
[9] G Bartolini, A. Levant, A. Pisano, E. Usai, Adaptive second-order sliding mode control with uncertainty compensation, International Journal of Control 89 (2016) 1747-1758. https://doi.org/10.1080/00207179.2016.1142616
[10] D. Chwa, Sliding-mode-control-based robust finite-time antisway tracking control of 3-D overhead cranes, IEEE Transactions on Industrial Electronics 64 (2017) 6775-6784. https://doi.org/10.1109/TIE.2017.2701760
[11] X. Li, W. Yu, Anti-swing control for an overhead crane with fuzzy compensation, Intelligent Automation & Soft Computing 18 (2012) 1-11. https://doi.org/10.1080/10798587.2012.10643223
[12] L.-H. Lee, P.-H. Huang, Y.-C. Shih, T.-C. Chiang, C.-Y. Chang, Parallel neural network combined with sliding mode control in overhead crane control system, Journal of Vibration and Control 20 (2014) 749-760. https://doi.org/10.1177/1077546312464681
[13] N.B. Almutairi, M. Zribi. Sliding mode control of a three-dimensional overhead crane, Journal of Vibration and Control 15 (2009) 1679-1730. https://doi.org/10.1177/1077546309105095
[14] Z. Zhang, Y. Wu, Disturbance-observer-based antiswing control of underactuated crane systems via terminal sliding mode, IET Control Theory & Applications 12 (2018) 2588-2594. https://doi.org/10.1049/iet-cta.2018.5344
[15] D.P. Nam, N.D. Phuoc, N.T.V Huong, Adaptive robust ability of high order sliding mode control for a 3-D overhead crane system, Advances in Information and Communication Technology, Springer, (2017). https://doi.org/10.1007/978-3-319-49073-1_14
[16] Q.H. Ngo, N.P. Nguyen, C.N. Nguyen, T.H. Tran, Q.P Ha, Fuzzy sliding mode control of an offshore container crane, Ocean Eng. 140 (2017) 125-134. https://doi.org/10.1016/j.oceaneng.2017.05.019
[17] S. Frikha, M. Djemel, N. Derbel, A new adaptive neuro-sliding mode control for gantry crane, Int. J. Control Autom. Syst. 16 (2018) 559-565. https://doi.org/10.1007/s12555-017-0070-x
[18] G. Kim, K. Hong, Adaptive sliding-mode control of an offshore container crane with unknown disturbances, IEEE-ASME Trans. Mechatron. 24 (2019) 2850-2861. https://doi.org/10.1109/TMECH.2019.2946083
[19] I. Petráš (Ed.), Handbook of Fractional Calculus with Applications, vol. 6: Applications in Control, De Gruyter, (2019). https://doi.org/10.1515/9783110571745
[20] M.A. Duarte-Mermoud, N. Aguila-Camacho, J.A. Gallegos, R. Castro-Linares, Using general quadratic Lyapunov functions to prove Lyapunov uniform stability for fractional order systems, Commun. Nonlinear Sci. Numer. Simul. 22 (2015) 650-659. https://doi.org/10.1016/j.cnsns.2014.10.008
[21] Y. Li, Y.Q. Chen, I. Podlubny, Mittag–Leffler stability of fractional order nonlinear dynamic systems. Automatica 45 (2009) 1965-1969. https://doi.org/10.1016/j.automatica.2009.04.001
[22] D. Matignon, Stability properties for generalized fractional differential systems, Proc. of Fractional Differential Systems: Models, Methods and App. 5 (1998) 145-158. https://doi.org/10.1051/proc:1998004