Fractional‑order electric spring based on fuzzy PIλDμ adaptive control

Xi Zhang; Xing Zhang; Ming Li; Xiangyu Deng; Lei Du

Fractional‑order electric spring based on fuzzy PIλDμ adaptive control

Vol. 25, No. 8, pp. 1561-1572, Aug. 2025

10.1007/s43236-024-00979-y

Fractional-order electric spring

Fractional-order calculus

Fractional-order modeling

Fractional-order control

Abstract

An electric spring (ES) is a power device with significant application potential, and accurate modeling of the ES is crucial for the research and analysis of practical systems. Current studies typically develop integer-order mathematical models of ESs based on integer-order inductors and capacitors, overlooking the fractional-order characteristics of actual inductors and capacitors. This omission leads to discrepancies between the modeling and analytical results and actual systems. To address this issue, this paper establishes a fractional-order ES circuit based on the fractional-order characteristics of inductors and capacitors. Then it develops a fractional-order small-signal model of the ES. Subsequently, the impact of the fractional orders α and β of the inductors and capacitors on the operational characteristics of the electric spring system is analyzed. Following this, a control strategy combining fuzzy adaptive control with fractional-order PIλDμ control is proposed to address the nonlinearity and parameter uncertainty of the fractional-order ES model. This strategy provides excellent dynamic performance and stability. In addition, it enables online parameter adjustment. Finally, the model and control strategy are validated through MATLAB/Simulink simulations and experiments. Results demonstrate that the fractional-order model significantly reduces the deviation from the actual system when compared to the integer-order model, offering a more accurate description of the system characteristics. Moreover, the introduction of fuzzy adaptive fractional-order PIλDμ control into the fractional-order ES model enhances control precision and adaptability.

Statistics

Show / Hide Statistics

Cumulative Counts from September 30th, 2019
Multiple requests among the same browser session are counted as one view. If you mouse over a chart, the values of data points will be shown.

Cite this article

[IEEE Style]

X. Zhang, X. Zhang, M. Li, X. Deng, L. Du, "Fractional‑order electric spring based on fuzzy PIλDμ adaptive control," Journal of Power Electronics, vol. 25, no. 8, pp. 1561-1572, 2025. DOI: 10.1007/s43236-024-00979-y.

[ACM Style]

Xi Zhang, Xing Zhang, Ming Li, Xiangyu Deng, and Lei Du. 2025. Fractional‑order electric spring based on fuzzy PIλDμ adaptive control. Journal of Power Electronics, 25, 8, (2025), 1561-1572. DOI: 10.1007/s43236-024-00979-y.