Equivalent diagrams of fractional order elements

• Autorzy: Różowicz Sebastian , Włodarczyk Maciej , Zawadzki Andrzej

Identyfikatory

DOI

10.24425/acs.2023.148882

• Języki publikacji: EN

Abstrakty

EN

This paper presents equivalent impedance and operator admittance systems for fractional order elements. Presented models of fractional order elements of the type: s^αL_α and 1/s^αC_α, (0 α 1) were obtained using the Laplace transform based on the expansion of the factor sign to an infinite fraction with varying degrees of accuracy - the continued fraction expansion method (CFE). Then circuit synthesis methods were applied. As a result, equivalent circuit diagrams of fractional order elements were obtained. The obtained equivalent schemes consist both of classical RLC elements, as well as active elements built based on operational amplifiers. Numerical experiments were conducted for the constructed models, presenting responses to selected input signals.

Słowa kluczowe

EN

fractional order derivative; Laplace transform for fractional order systems; CFE method; circuit synthesis; numerical experiments

• Wydawca: Polish Academy of Sciences, Committee of Automatic Control and Robotics
• Czasopismo: Archives of Control Sciences
• Rocznik: 2023
• Tom: Vol. 33, No. 4
• Strony: 801--827
• Opis fizyczny: Bibliogr. 37 poz., rys., wzory

Twórcy

autor

Różowicz Sebastian

• Kielce University of Technology, Department of Industrial Electrical Engineering and Automatic Control, Tysiąclecia Państwa Polskiego 7, 25-314 Kielce, Poland

• https://orcid.org/0000-0002-3614-9654

autor

Włodarczyk Maciej

• Kielce University of Technology, Department of Industrial Electrical Engineering and Automatic Control, Tysiąclecia Państwa Polskiego 7, 25-314 Kielce, Poland

• https://orcid.org/0000-0002-8628-0773

autor

Zawadzki Andrzej

• Kielce University of Technology, Department of Industrial Electrical Engineering and Automatic Control, Tysiąclecia Państwa Polskiego 7, 25-314 Kielce, Poland

• https://orcid.org/0000-0002-0039-8499

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Uwagi

The article was realized within the framework of the internship of Sebastian Różowicz, Ph.D., realized at the Rzeszow University of Technology from 1 March 2021, to 30 June 2021, Internship topic: Application of mathematical methods to systems analysis in electrical engineering.