Scientific and Technical Journal

ELECTROTECHNIC AND COMPUTER SYSTEMS

ISSN Print 2221-3937
ISSN Online 2221-3805
APPROXIMATION OF TRANSITION FUNCTIONS BY FRACTIONAL ORDER POLYNOMIALS
Abstract:

We consider approximation of the standard transfer functions of binomial form and Butterworth form, as well as random parts of electromechanical systems, for which transition process is known, by fractional order polynomials, using an improved method of particlesswarmoptimization. It is concluded that the influence of parameters on the accuracy of the proposed method matches the transient and frequency characteristics. The analysis of the results shows that during approximation of the transition function of binominal form and Butterworth form above first ordered preference should be given to fractional unit of the second order, which ensures highly accurate matches for transition functions and sufficient ones in terms of frequency characteristics. The variation of particle swarm optimization method parameters, and the number of approximation points in particular, leads to a substantial increase in computing time and therefore it is recommended to choose their number at the rate of at least 100 points per 1 sec. of transition function. The increase in the initial transition process leads to the decrease in approximation error. The proposed method provides high accuracy approximation matches for transition functions and the sufficient ones in terms of frequency characteristics and can be used for the construction of self-tuning control electronic production mechanisms at the basis of modern fractional controllers in particular.

Authors:
Keywords
DOI
10.15276/etks.14.90.2014.05
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