NDLI: Optimal continuous approximation of basic fractional elements: Theory and applications

Content Provider	IEEE Xplore Digital Library
Author	Cech, M. Schlegel, M.
Copyright Year	2011
Description	Author affiliation: Department of Cybernetics, University of West Bohemia in Pilsen, Czech Republic (Cech, M.; Schlegel, M.)
Abstract	In the last two decades, a boom of fractional calculus applications started in many technical areas including automation and process control. The generalization of integrals and derivatives to arbitrary real order (FO - Fractional Order) simplifies solution of many problems especially in frequency domain. Unfortunately, switching into time domain is always quite difficult due to the necessity to approximate fractional elements by integer-order ones. For this purpose, often a high order zero/pole transfer function is employed. This paper extends the authors' previous work and summarizes the results of numerical optimization of zero/pole positions for two important fractional elements: fractional integro-differential operator and fractional pole. The optimization is done on a limited frequency band up to four decades. The quadratic difference between the frequency response of ideal FO element and its zero/pole approximation was taken as an optimality criterion. It is shown, that the optimization decreases markedly the criterion value compared to traditional methods. The paper main results are provided in a form of analytical functions parametrizing the zero/pole positions dependent on element order. Additionally, prospective applications of presented fractional elements are discussed from both controller synthesis and process modeling point of view.
Starting Page	7051
Ending Page	7056
File Size	366606
Page Count	6
File Format	PDF
ISBN	9781612848006
ISSN	07431546
e-ISBN	9781612848013
e-ISBN	9781612847993
DOI	10.1109/CDC.2011.6160376
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2011-12-12
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Approximation methods Poles and zeros Optimization Frequency response Relays Process control
Content Type	Text
Resource Type	Article
Subject	Control and Optimization Control and Systems Engineering Modeling and Simulation

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