Journal of Power Electronics

The Korean Institute of Power Electronics (전력전자학회)
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Research on fractional-order PID control method for permanent magnetic levitation platform

  • Junjie Jin (School of Mechanical Engineering, Shenyang University of Technology) ;
  • Jiaqi Song (School of Mechanical Engineering, Shenyang University of Technology) ;
  • Chuan Zhao (School of Mechanical Engineering, Shenyang University of Technology) ;
  • Wenzhe Pei (School of Mechanical Engineering, Shenyang University of Technology) ;
  • Qiqiang Zhang (School of Mechanical Engineering, Shenyang University of Technology) ;
  • Fangchao Xu (School of Mechanical Engineering, Shenyang University of Technology) ;
  • Haining Zhao (School of Mechanical Engineering, Shenyang University of Technology) ;
  • Feng Sun (School of Mechanical Engineering, Shenyang University of Technology)
  • Received : 2024.12.23
  • Accepted : 2025.06.22
  • Published : 2026.04.20
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Abstract

To address the issues of prolonged adjustment time and significant overshoot associated with traditional integer-order PID control in its application to permanent magnet levitation platforms, a fractional-order PID controller is proposed in this paper. To reduce computational complexity, the Oustaloup filter within the controller is simplified. Given the large number of parameters in the fractional-order PID controller, the particle swarm optimization algorithm is employed for parameter tuning. The controller is subsequently simulated, debugged, and validated through suspension, step response, and sinusoidal tracking experiments. The experimental results demonstrate that, in comparison with the integer-order PID controller, the levitation time of the platform is reduced by 1.13 s and the overshoot is decreased by 6%. Furthermore, step response experiments indicate that the overshoot of the integer-order PID controller is 4.7 times greater than that of the fractional-order PID controller, while the response speed of the fractional-order PID controller is increased by 106%.

Keywords

Acknowledgement

This work was supported by the National Natural Science Foundation of China (Grant No. 52405284, No. 52375258), National Key R&D Plan of China (Grant No. 2024YFB3410002), China Postdoctoral Science Foundation (Grant No. 2024M762160), the Natural Science Foundation of Liaoning Province, China (Grant No. 2023-BS-127), Scientific Research Fund Project of Liaoning Provincial Department of Education (Grant No. LJ222410142008, JYTMS20231191, LJ212410142015).

References

  1. Sun, Y.G., Qiang, H.Y., Xu, J.Q., et al.: Internet of Things-based online condition monitor and improved adaptive fuzzy control for a Medium-low-speed Maglev train system. IEEE Trans. Ind. Inform. 16(4), 2629–2639 (2020) https://doi.org/10.1109/TII.9424
  2. Le, Y., Wang, D., Zheng, S.Q.: Design and optimization of a radial magnetic bearing considering unbalanced magnetic pull effects for magnetically suspended compressor. IEEE-ASME Trans. Mech. 27(6), 5760–5770 (2022) https://doi.org/10.1109/TMECH.2022.3189685
  3. Zhou, S.L., Li, G.L., Wang, Q.J., et al.: Geometrical equivalence principle based modeling and analysis for monolayer Halbach array spherical motor with cubic permanent magnets. IEEE Trans. Energy Conver. 36(4), 3241–3250 (2021) https://doi.org/10.1109/TEC.2021.3070207
  4. Hu, K., Qian, W.Q., Jiang, H., et al.: Study of controlled magnetic circuit permanent magnetic levitation belt conveyor support system. Adv. Eng. Sci. 55(06), 191–201 (2023)
  5. Wang, Z.X., Guo, Y.C., Hu, K.: Analysis on suspension force characteristics of the permanent magnet suspension belt conveyor of Halbach array. Mach. Des. Manuf. 07, 70–72 (2019)
  6. Zhao, C., Sun, F., Jin, J.J., et al.: Analysis of Quasi-zero power characteristic for a permanent magnetic levitation system with a variable flux path control mechanism. IEEE-ASME Trans. Mech. 26(1), 437–447 (2020) https://doi.org/10.1109/TMECH.3516
  7. Zhai, M.D., Zhang, B., Li, X.L., et al.: Design and implementation of magnetic suspension vibration isolation platform with quasi-zero stiffness based on fuzzy pid control. J. Southwest Jiaotong Univ. 58(04), 886–895 (2023)
  8. Bai, H.F., Bo, Y., Wu, O.Y., et al.: HF-based sensorless control of a FTPMM in ship shaftless rim-driven thruster system. IEEE Trans. Intell. Transp. 23(9), 16867–16877 (2022) https://doi.org/10.1109/TITS.2022.3143208
  9. Han, J.Q.: From PID technique to active disturbances rejection control technique. Inst. Syst. Sci. 9(03), 13–18 (2002)
  10. Qin, J.F., Du, J.L.: Robust adaptive asymptotic trajectory tracking control for underactuated surface vessels subject to unknown dynamics and input saturation. J. Marine Sci. Technol. 27, 307–319 (2022) https://doi.org/10.1007/s00773-021-00835-9
  11. Xue, D.Y., Zhao, C.N.: Fractional order PID controller design for fractional order system. Control Theory Appl. 24(05), 771–776 (2007)
  12. Xiao, M., Tao, B.B., Zheng, W.X., et al.: Fractional-order PID controller synthesis for bifurcation of fractional-order small-world networks. IEEE Trans. Syst. Man Cy. -S. 51(7), 4334–4346 (2021) https://doi.org/10.1109/TSMC.2019.2933570
  13. Rishika, T., Prabin, K.P.: Design of indirect fractional order IMC controller for fractional order processes. IEEE Trans. Circ. II 68(3), 968–972 (2021) https://doi.org/10.1109/TED.16
  14. Rafał, S., Marek, R., Li, Z.X.: A new Reduced-order implementation of discrete-time fractional-order PID controller. IEEE Access 10, 17417–17429d (2022) https://doi.org/10.1109/ACCESS.2022.3150883
  15. Mughees, A., Syed, A.M.: Design and control of magnetic levitation system by optimizing fractional order PID controller using ant colony optimization algorithm. IEEE Access 8, 116704–116723 (2020) https://doi.org/10.1109/Access.6287639
  16. Omar, W.A.: Design of a complex fractional order PID controller for a first order plus time delay system. ISA Trans. 99, 154–158 (2020) https://doi.org/10.1016/j.isatra.2019.10.010
  17. Yadav, S., Verma, S.K., Nagar, S.K.: Optimized PID controller for magnetic levitation system. Proc. IFAC Conf. Adv. Control. Optim. Dyn. Syst. 49(1), 778–782 (2016)
  18. Xue, D.Y.: Fractional calculus and fractional-order control, vol. 5. Science Press (2018)
  19. Liu, Y.Z., Li, J., Dai, G., et al.: Design of simplified fractional-order PID controller based on improved oustaloup filter. Inf. Control. 48(06), 723–728 (2019)
  20. Ziegler, J.G., Nichols, N.B.: Optimum settings for automatic controllers. Trans. Am. Soc. Mech. Eng. 64(8), 759–765 (1942)
  21. Cohen, G., Coon, G.A.: Theoretical consideration of retarded control. Trans. Am. Soc. Mech. Eng. 75(5), 827–834 (1953)