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Fractional system of the first kind: from concept to realization in the electrical domain

Abstract : This paper presents a fractional system of the first kind realized in the electrical domain. The main properties of this fractional system are firstly studied. Relationships between open-loop and closed-loop diagrams are used for dynamic behavior analysis such as stability, stability degree, robustness of stability degree, and characteristic frequencies. Moreover, integral causality leads to the use of a fractional integrator, so-called fractor. Then, from the analysis results, a design method in five steps is proposed in order to realize this fractional system in the electrical domain. Each step is presented in detail. Furthermore, practical realizations of these elementary fractional systems are presented in a limited frequency band, because in many fields of Physics and in many applications, fractional behavior is observed or synthesized only in a limited frequency band. As a consequence, a limited bandwidth fractor is designed. Finally, a numerical example is given to summarize and to illustrate this study, the simulation results being compared to the experiment ones.
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Contributor : Xavier Moreau <>
Submitted on : Thursday, May 1, 2014 - 9:58:08 AM
Last modification on : Wednesday, November 13, 2019 - 11:50:04 AM


  • HAL Id : hal-00986122, version 1


Xavier Moreau, Roy Abi Zeid Daou, Clovis Francis. Fractional system of the first kind: from concept to realization in the electrical domain. Theory of Operation, Behavior and Safety Regulations, Nova Science Publishers, pp.155-188, 2013, 978-1-62257-788-0. ⟨hal-00986122⟩



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