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Equivalent diagrams of fractional order elements

Różowicz Sebastian, Włodarczyk Maciej, Zawadzki Andrzej

Archives of Control Sciences

2023

Vol. 33, No. 4

801--827

This paper presents equivalent impedance and operator admittance systems for fractional order elements. Presented models of fractional order elements of the type: sαLα and 1/sαCα, (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.

Voltage modelling in ignition coil using magnetic coupling of fractional order

Różowicz Sebastian

Archives of Electrical Engineering

2019

Vol. 68, nr 2

227--235

The paper discusses the modelling of magnetic coupling in ignition coils by fractional differential equations. The use of fractional-order coupling allows us to consider the losses caused by the non-linearity of the ferromagnetic core of the ignition coil and obtain the waveform of the ignition coil’s secondary voltage closest to the values obtained experimentally.