Conditions Derivation of Implementability of Fractional-Order Functions by Passive Electrical Networks

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استخراج شرایط پیاده سازی توابع مرتبه کسری توسط شبکه های الکتریکی پسیو

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 46410 (05)
University: Sharif University of Technology
Department: Electrical Engineering
Advisor(s): Tavazoei, Mohammad Saleh
Abstract:
Today, the fractional-order systems are widely used in the system identification and design and implementation of control systems. By production of electrical elements with fractional-order relationship between voltage and current of their terminals, implementation of fractional-order functions with passive elements is possible. Fractional order capacitors are one of these elements. It was shown that necessary and sufficient condition for the implementation of an integer order function by passive elements is positive realness of such a function.
Like systems with integer-order, in this thesis the aim is to find corresponding conditions for implementation of fractional-order functions with passive elements.
For this purpose, first by attending to the theorems given in integer-order cases we find necessary conditions for implementation of fractional-order functions. Then using various methods we introduce implementable fractional-order functions. Finally we find necessary and sufficient condition for implementation of fractional-order impedances with a fractional-order capacitor and a network of passive integer-order elements
Keywords:
Fractional-Order Impedances ; Fractional-Order Copacitor ; Fractional-Order Electrical Element ; Passive Electrical Networks

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