CHARACTERISTIC ANALYSIS OF FRACTIONAL-ORDER RLC CIRCUIT BASED ON THE CAPUTO–FABRIZIO DEFINITION

Xiaozhong Liao, Donghui Yu, Da Lin, Manjie Ran and Jinhui Xia ()
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Xiaozhong Liao: Department of Automation, Beijing Institute of Technology, Beijing 100089, P. R. China
Donghui Yu: Department of Automation, Beijing Institute of Technology, Beijing 100089, P. R. China
Da Lin: Department of Automation, Beijing Institute of Technology, Beijing 100089, P. R. China
Manjie Ran: Department of Automation, Beijing Institute of Technology, Beijing 100089, P. R. China
Jinhui Xia: ��Department of Control Science and Engineering, Zhejiang University, Hangzhou 310058, P. R. China

FRACTALS (fractals), 2022, vol. 30, issue 04, 1-17

Abstract: The Caputo–Fabrizio (C–F) definition, which solves the singularity problem in the Caputo definition, has been preliminarily applied in the field of circuit system modeling. However, the complex characteristics of the C–F definition-based circuit systems are still understudied. Therefore, this paper proposes a C–F definition-based fractional-order RLC (CF-FORLC) circuit model and analyzes its basic characteristics. First, the effects of different component orders on the performance parameters including the impedance, quality factor, and bandwidth are analyzed, which gives insights into the design of CF-FORLC. Then, the analytical solutions and the frequency-domain characteristics of CF-FORLC with different capacitance and inductance orders under arbitrary input are derived. Finally, the data of actual circuits are fitted to obtain the parameters of the CF-FORLC model, and the orders of the C–F definition-based capacitors and inductors are estimated. The results of the comparative experiments show that the proposed modeling scheme can improve the consistency of the dynamic performance of the model with that of the actual circuit. In addition, the proposed CF-FORLC model shows higher accuracy and flexibility with more adjustable parameters.

Keywords: Fractional-order RLC Circuit; Caputo–Fabrizio Fractional Derivative; Impedance Analysis; System Analytical Solution (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1142/S0218348X22500785

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