A. Kavruk1, A.S. Korotkov2

1,2 Peter the Great St. Petersburg Polytechnic University (St. Petersburg, Russia)

1 kavruk99@mail.ru; 2 korotkov@spbstu.ru

This paper addresses the problem of implementing frequency-selective prototype circuits with fractional-order transfer functions, which are widely used in modern control systems, including robotics and Fractional-Order PID (FOPID) controllers. The main challenge lies in the irrational nature of the fractional-order differentiation operator pα, which precludes its direct physical implementation. To solve this problem, the method of rational interpolation is proposed, enabling the transition from an irrational function to a rational fraction. The study analyzes the asymptotic behavior of the system of interpolation equation s, based on which a necessary con dition for physical realizabil ity is proved: the equality of the degr ees of the numerator and denomi nator of the approximating function (M N=). It is shown that the obtained solution satisfies the realizability conditions for RC circuits. Using a practical example for the case 0.5α =, an approximation of the operator pα is performed. A passive ladder prototype is synthesized, and b ased on it, an active ARC filter is designed using the operational simulation method. Simulation results confi rm the high accuracy of the proposed approach (the implementati on error does not exceed 0.003 dB). A comparative analysis of the rational interpolation method with approximations based on Tayl or series and continued fractions is carried out. It is establishe d that the proposed method provi des lower amplitude and phase r oot mean square errors for approximation orders higher than five.

Kavruk A., Korotkov A.S. The problem of implementing prototype circuits with fractional-order transfer functions based on rational interpolation. Radiotekhnika. 2026. V. 90. № 3. P. 158−167. DOI: https://doi.org/10.18127/j00338486-202603-14 (In Russian)

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