Comparative Study of Riemann-Liouville and Caputo Derivative Definitions in Time-Domain Analysis of Fractional-Order Capacitor
Comparative Study of Riemann-Liouville and Caputo Derivative Definitions in Time-Domain Analysis of Fractional-Order Capacitor
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分数阶电容器时域分析中黎曼-刘维尔和卡普托导数定义的比较研究
DOI：
10.1109/tcsii.2019.2952693
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发表时间：
2020-10-01
影响因子：
4.4
通讯作者：
Zhang, Bo
中科院分区：
文献类型：
--
作者：
Jiang, Yanwei;Zhang, Bo
分数阶电容器由于具有高性能和灵活性等优点，在电力电子换流器、滤波器等电路中的应用已成为研究的热点。两种典型的分数阶导数定义：Riemann-Liouville(RL)和Caputo导数被广泛用于分析分数阶电容器的特性。然而，在分数阶电容器的时域分析中，何时以及哪种分数阶导数定义更合适，仍然是一个根本的挑战。在本文中，对采用这两种定义的分数阶电容器的暂态和稳态分析进行了对比研究。确定了不同之处在于对动态过程的描述。特别是，对于阶跃输入的情况，差异尤其明显。在此基础上，提出了用RL导数对分数阶电容进行时域建模和分析是一种更准确的选择。此外，RL导数也更适合于求解含有分数阶电容的分数阶电路。仿真和实验结果验证了这一结论。
The fractional-order capacitor applied in power electronic converters, filters or other circuits has become a hot spot due to benefits, such as high-performance and flexibility. Two typical kinds of fractional-order derivative definitions, Riemann-Liouville (RL) or Caputo derivatives are popularly used to analyze the characteristics of fractional-order capacitor. However, it remains a fundamental challenge to find that when and which fractional-order derivative definition is more suitable in the time-domain analysis of fractional-order capacitor. In this brief, comparative investigations about the transient and steady analysis of a fractional-order capacitor adopting these two definitions are performed. It is determined that difference comes from description of dynamic process. In particular, the difference is especially obvious for the cases of step-up input. Based on the analysis, this brief proposed that RL derivative is a more accurate choice for modeling and analyzing fractional-order capacitor in time domain. Moreover, RL derivative is also more suitable for solving fractional-order circuits with fractional-order capacitor. The results from simulations and experiments verify the conclusion.