Fractional-order Electric Spring Based on Fuzzy PIλDμ Adaptive Control
JOURNAL OF POWER ELECTRONICS（2025）
Hefei University of Technology
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.
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Key words
Fractional-order electric spring,Fractional-order calculus,Fractional-order modeling,Fractional-order control
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