Abstract
In this paper a comprehensive procedure for the analog modeling of Fractional-Order Elements (FOEs) is presented. Unlike most already proposed techniques, a standard approach from classical circuit theory is applied. It includes the realization of a system function by a mathematical approximation of the desired phase response, and the synthesis procedure for the realization of basic fractional-order (FO) one-port models as passive RC Cauer- and Foster-form canonical circuits. Based on the presented one-ports, simple realizations of two-port differentiator and integrator models are derived. Beside the description of the design procedure, illustrative examples, circuit diagrams, simulation results and practical realizations are presented.
Highlights
There are many processes in technology and science which can be efficiently interpreted and analyzed using fractionalorder (FO) derivatives and integrals
In order to verify the minimax approximation for Fractional-Order Elements (FOEs) design, it is compared to the most frequently referenced approximations obtained by analytical procedures and numerical optimization methods
We consider its application to fractional-order systems as a novelty because in spite of its excellent properties in many other applications, it was neglected in this field
Summary
There are many processes in technology and science which can be efficiently interpreted and analyzed using fractionalorder (FO) derivatives and integrals. We apply "maximally-flat" and "minimax" approximations to realize a rational function with a constant phase response of any value of i (− /2 i /2), e.g. of 90°, where −1<
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