Abstract
This study employs the Caputo-Fabrizio fractional derivative to determine the model of fractional-order RC circuits with arbitrary voltage input which can be widely used in a variety of electrical systems. Analog circuit implementation of fractional-order RC circuits defined by Caputo-Fabrizio fractional derivative is presented and verified by comparing with the model proposed in this work. For the purpose of judging whether the fractional-order model defined by the Caputo-Fabrizio derivative is practical, the comparison experiments are carried out. By using Laplace transform, the analytical solutions of fractional-order RC circuits based on the Caputo-Fabrizio derivatives with constant and periodic voltage sources are deduced. Fractional-order model of RC circuits with arbitrary input are also calculated using the convolution formula. The correctness of the derivation of the model using the Caputo-Fabrizio derivative is verified. Through discussing the impedance model of capacitor in frequency domain, the analog realization of fractional capacitor based on the Caputo-Fabrizio derivative is derived. The fractional-orders of the RC circuits models defined by the Caputo and Caputo-Fabrizio fractional derivatives are fitted respectively through repeated charging and discharging experiment data. The fractional-order models based on the Caputo and Caputo-Fabrizio derivatives, and the integer-order model are all compared with the experiment data.
Original language | English |
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Article number | 9323030 |
Pages (from-to) | 1034-1044 |
Number of pages | 11 |
Journal | IEEE Transactions on Circuits and Systems I: Regular Papers |
Volume | 68 |
Issue number | 3 |
DOIs | |
Publication status | Published - Mar 2021 |
Keywords
- Caputo derivative
- Caputo-Fabrizio derivative
- Fractional-order RC circuits
- analog circuit implementation
- experimental study