К вопросу о выборе алгоритма синтеза элементов с фрактальным импедансом на основе резистивно-емкостных элементов с распределенными параметрами со структурой слоев вида C-R-NC

I V Knyazev; P A Ushakov

doi:10.22213/2410-9304-2021-2-62-71

Authors

I. V. Knyazev Kalashnikov ISTU
P. A. Ushakov Kalashnikov ISTU

DOI:

https://doi.org/10.22213/2410-9304-2021-2-62-71

Keywords:

fractal impedance elements, synthesis of elements with fractal impedance, C-R-NC-line, RC- element with distributed parameters

Abstract

Elements with a fractal impedance (FOE) having a fractional-power dependence of impedance on frequency can be used to integrate differential equations of arbitrary fractional order, which most often describe real processes in nature and technology. In a particular case, when replacing integrators and differentiators in PID controllers of control systems with fractional integrators and differentiators, it can greatly increase the basic parameters of control systems. However, to date, commercial FOEs that could be produced on an industrial scale have not been developed yet. The greatest potential in this sense is possessed by FOEs built on the basis of multilayer resistive-capacitive elements with distributed parameters (RC-EDP). One of the constructive variants of this type of FOE with a layer structure of the R-C-NR type was made as sample prototypes. But during its manufacture and testing, shortcomings were revealed that could impede its use in designed products. In this work, it is proposed to create the FOE with a layer structure of the C-R-NC type, in which it is possible to avoid the disadvantages of the FOE with a layer structure of the R-C-NR type. However, to solve this problem, it is necessary to choose a synthesis algorithm that will make it possible to create the FOE with similar or better parameters than that of the existing FOE with a layer structure of the R-C-NR type. For this purpose, three synthesis programs have been developed and tested, forming FOE models from a combination of two R-C-NR lines used as mathematical models of RC-EDP: synthesis based on a simple enumeration (SE) algorithm with options that provide the required FOE characteristics, particle swarm optimization (PSO), and genetic algorithm (GA) synthesis. The results of the study showed that the SE algorithm for the synthesis of FOE based on a combination of three or more R-C-NR elements is inexpedient due to the huge number of enumeration objects (about 107), and the PSO is not effective for optimizing a discrete objective function. GA meets the parameters of the synthesized object better than others, since it has no restrictions on the form of the objective function and has already been used to solve optimization problems in a similar subject area with a high-dimensional space.

Author Biographies

I. V. Knyazev, Kalashnikov ISTU

Student

P. A. Ushakov, Kalashnikov ISTU

DSc in Engineering, Professor

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