Polynomial approximation of quasipolynomials based on digital filter design principles

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F70883521%3A28140%2F16%3A43874809" target="_blank" >RIV/70883521:28140/16:43874809 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1007/978-3-319-33389-2_3" target="_blank" >http://dx.doi.org/10.1007/978-3-319-33389-2_3</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/978-3-319-33389-2_3" target="_blank" >10.1007/978-3-319-33389-2_3</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Polynomial approximation of quasipolynomials based on digital filter design principles

Popis výsledku v původním jazyce

This contribution is aimed at a possible procedure approximating quasipolynomials by polynomials. Quasipolynomials appear in linear time-delay systems description as a natural consequence of the use of the Laplace transform. Due to their infinite root spectra, control system analysis and synthe-sis based on such quasipolynomial models are usually mathematically heavy. In the light of this fact, there is a natural research endeavor to design a sufficiently accurate yet simple engineeringly acceptable method that approximates them by polynomials preserving basic spectral information. In this paper, such a procedure is presented based on some ideas of discrete-time (digital) filters designing without excessive math. Namely, the particular quasipolynomial is subjected to iterative discretization by means of the bilinear transformation first; consequently, linear and quadratic interpolations are applied to obtain integer powers of the approximating polynomial. Since dominant roots play a decisive role in the spectrum, interpolations are made in their very neighborhood. A simulation example proofs the algorithm efficiency.

Název v anglickém jazyce

Polynomial approximation of quasipolynomials based on digital filter design principles

Popis výsledku anglicky

This contribution is aimed at a possible procedure approximating quasipolynomials by polynomials. Quasipolynomials appear in linear time-delay systems description as a natural consequence of the use of the Laplace transform. Due to their infinite root spectra, control system analysis and synthe-sis based on such quasipolynomial models are usually mathematically heavy. In the light of this fact, there is a natural research endeavor to design a sufficiently accurate yet simple engineeringly acceptable method that approximates them by polynomials preserving basic spectral information. In this paper, such a procedure is presented based on some ideas of discrete-time (digital) filters designing without excessive math. Namely, the particular quasipolynomial is subjected to iterative discretization by means of the bilinear transformation first; consequently, linear and quadratic interpolations are applied to obtain integer powers of the approximating polynomial. Since dominant roots play a decisive role in the spectrum, interpolations are made in their very neighborhood. A simulation example proofs the algorithm efficiency.

Druh

D - Stať ve sborníku

CEP obor

BC - Teorie a systémy řízení

OECD FORD obor

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Projekt

Výsledek vznikl pri realizaci vícero projektů. Více informací v záložce Projekty.

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2016

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název statě ve sborníku

Automation Control Theory Perspectives in Intelligent Systems: Proceedings of the 5th computer science on-line conference 2016. Vol. 3

ISBN

978-3-319-33387-8

ISSN

2194-5357

e-ISSN

—

Počet stran výsledku

10

Strana od-do

25-34

Název nakladatele

Springer-Verlag Berlin

Místo vydání

Heidelberg

Místo konání akce

on-line

Datum konání akce

27. 4. 2016

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

000385788100003