A variable fractional‐order inductor design

Abstract

Recently, interest in fractional‐order inductors (FOIs) has increased since they allow for accurate and robust models of dynamical systems to be designed. However, practical implementation of these models has not been possible due to the lack of single FOI realizations. To address this challenge, in this work, we propose a simple‐to‐realize fractional‐order inductor design with variable constant phase angle (CPA). The design relies on characteristics of transverse electromagnetic (TEM) mode propagating on a coaxial structure filled with conductive material, more specifically NaCl‐water solution and flour‐based mixtures. The CPA of the resulting FOI can be tuned by changing the conductivity of the dough mixture. Analysis of the proposed FOI design show that the CPA can vary in a range from 0° to 90°. Two of these CPA values are verified against experiments in the frequency band changing from 1 to 10 MHz.

A unified modeling approach for characterization of fractional‐order memory elements

“…Also, these results are in agreement with the material-based CPE realizations in previous works. 19,21,42 To realize HðsÞ ¼ Ks β (FO differentiator), the network on the X and Z terminals of U a are reversed; likewise, reversing the X and Z terminals of U b produces an IO differentiator. The CPEs, IO differentiator, and IO integrator will be used in the next section to emulate the memelements, and their respective symbols are denoted in Figure 4A.…”

“…realizing the three classical elements. While Pu 14,15 mainly focuses on dimensional analysis of the CPEs, their dynamical properties are presented in works like Allagui et al, 16 Radwan and Elwakil, 17 and Fouda et al 18 and their equivalent circuit realizations and practical realizations in Zhang et al, 19 Caponetto et al, 20 and Hao and Wang. 21 The memristor definition in Table 1 corresponds to its known definition of v ¼ ∂φðqÞ ∂q h i i; thus, the function g½Á ¼ ∂φðqÞ ∂q h i is its memristance that defines its nonlinearity, same can be inferred of the memcapacitor and meminductor (their current-and voltage-controlled definitions listed therein).…”

“…While previous works [16][17][18][19][20][21] have presented several analytical and practical studies on CPEs, only recently did Fouda et al 32 looked into the energy relations of CPEs (supercapacitors and fractional-order coils). Also, memelements in integer an fractional orders have been analyzed in notable works, 5,22,25,26,31,[33][34][35][36] and previous studies 23,24,[27][28][29][30]37 even focused on designing different forms of memelement emulator circuits.…”

“…A combination makes makes and makes realizing the three classical elements. While Pu 14,15 mainly focuses on dimensional analysis of the CPEs, their dynamical properties are presented in works like Allagui et al, 16 Radwan and Elwakil, 17 and Fouda et al 18 and their equivalent circuit realizations and practical realizations in Zhang et al, 19 Caponetto et al, 20 and Hao and Wang 21 …”

Improved constant phase fractional order approximation method for induction motor FOPI speed controller

“…5 Some of the recently explored FO control system processes in the literature are conical water tank systems, 6 threephase voltage source PWM rectifier, 7 fractional-order buck-boost converter, 8 EEG recorder, 9 RL and RC circuits, 10 and PMSM speed servos. 11 A variable fractional-order inductor is designed by maintaining constant phase angle in Zhang et al 12 A generalized concept of the fractional-order mutual inductance in the frequency domain domain is studied in Soltan et al 13 The conventional IOPID controller performance can be improved using FO integrals and derivatives. FOPID controllers offer performance beyond those of IOPID controllers in designing a robust control system.…”