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Dynamic analysis and bursting oscillation control of fractional-order permanent magnet synchronous motor system

Author

Listed:
  • Zhang, Shaohua
  • Wang, Cong
  • Zhang, Hongli
  • Ma, Ping
  • Li, Xinkai

Abstract

In fractional-order permanent magnet synchronous motor (FPMSM) systems, hidden bursting oscillation behaviors are found and a bursting oscillation suppression method is proposed for the first time. First, a FPMSM system model with the mismatched external load disturbance is established, and an auxiliary parameter is introduced to ensure that it have the correct time dimensionality. Second, when there is an order gap difference between the frequency of the external load disturbance and the natural frequency of the FPMSM system, it is found that the system undergo bursting oscillation behavior through bifurcation analysis and numerical simulations, and the evolution mechanism of the bursting oscillations is revealed by the fast-slow dynamics analysis method. Based on immersion and invariance (I&I) theory and fractional calculus theory, an adaptive backstepping super-twisting sliding mode control method with fractional I&I observer (I&I ABSSMC) is proposed to maintain the stable operation of the FPMSM system. The effectiveness of the I&I observer is verified by comparing with the adaptive method and disturbance observer under different forms of disturbances. Finally, comparisons of the I&I ABSSMC and other related methods show that the angular velocity tracking error accuracy and response speed of the I&I ABSSMC are superior. The proposed control method is easy to implement in practical applications.

Suggested Citation

  • Zhang, Shaohua & Wang, Cong & Zhang, Hongli & Ma, Ping & Li, Xinkai, 2022. "Dynamic analysis and bursting oscillation control of fractional-order permanent magnet synchronous motor system," Chaos, Solitons & Fractals, Elsevier, vol. 156(C).
    • Handle: RePEc:eee:chsofr:v:156:y:2022:i:c:s0960077922000200
    DOI: 10.1016/j.chaos.2022.111809
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    References listed on IDEAS

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    1. Jie Ran & Yuqin Li & Changchun Wang, 2018. "Chaos and Complexity Analysis of a Discrete Permanent-Magnet Synchronous Motor System," Complexity, Hindawi, vol. 2018, pages 1-8, December.
    2. Cong Wu, 2021. "Advances In Analysis Of Caputo Fractional-Order Nonautonomous Systems: From Stability To Global Uniform Asymptotic Stability," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 29(04), pages 1-17, June.
    3. Kim, Seong-S. & Choi, Han Ho, 2014. "Adaptive synchronization method for chaotic permanent magnet synchronous motor," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 101(C), pages 31-42.
    4. Du, Feifei & Lu, Jun-Guo, 2021. "New approach to finite-time stability for fractional-order BAM neural networks with discrete and distributed delays," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).
    5. Razvan, Mohammad Reza & Yasaman, Somaye, 2020. "Emergence of bursting in two coupled neurons of different types of excitability," Chaos, Solitons & Fractals, Elsevier, vol. 132(C).
    6. Lin, Y. & Liu, W.B. & Bao, H. & Shen, Q., 2020. "Bifurcation mechanism of periodic bursting in a simple three-element-based memristive circuit with fast-slow effect," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    7. Du, Feifei & Lu, Jun-Guo, 2020. "Finite-time stability of neutral fractional order time delay systems with Lipschitz nonlinearities," Applied Mathematics and Computation, Elsevier, vol. 375(C).
    8. Zijing Cheng & Guangyue Xue & Chong Wang & Qiang Chen, 2016. "Adaptive Chaos Synchronization Control of Nonlinear PMSM System Using Extended State Observer," Mathematical Problems in Engineering, Hindawi, vol. 2016, pages 1-10, December.
    9. Zhang, Shaohua & Zhang, Hongli & Wang, Cong & Ma, Ping, 2020. "Bursting oscillations and bifurcation mechanism in a permanent magnet synchronous motor system with external load perturbation," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
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    Cited by:

    1. Peng Gao & Liandi Fang & Huihui Pan, 2024. "Interdisciplinary Education Promotes Scientific Research Innovation: Take the Composite Control of the Permanent Magnet Synchronous Motor as an Example," Mathematics, MDPI, vol. 12(16), pages 1-18, August.
    2. Jiang, Y.D. & Zhang, W. & Zhang, Y.F. & Bi, Q.S., 2024. "Bursting oscillations in coupling Mathieu-van der Pol oscillator under parametric excitation," Chaos, Solitons & Fractals, Elsevier, vol. 178(C).
    3. Bai, Xiaoqin & Bai, Juan & Malomed, Boris A. & Yang, Rongcao, 2024. "Spectrum conversion and pattern preservation of Airy beams in fractional systems with a dynamical harmonic-oscillator potential," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).

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