On the Numerical Determination of Stability Regions in the Delay Space via Dominant Pole Estimation

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F70883521%3A28140%2F19%3A63522747" target="_blank" >RIV/70883521:28140/19:63522747 - isvavai.cz</a>

Výsledek na webu

<a href="https://www.sciencedirect.com/science/article/pii/B9780128149287000019" target="_blank" >https://www.sciencedirect.com/science/article/pii/B9780128149287000019</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/B978-0-12-814928-7.00001-9" target="_blank" >10.1016/B978-0-12-814928-7.00001-9</a>

Jazyk výsledku

angličtina

Název v původním jazyce

On the Numerical Determination of Stability Regions in the Delay Space via Dominant Pole Estimation

Popis výsledku v původním jazyce

This contribution intends to provide the reader with the presentation of a numerical gridding iterative algorithm to determine all stability regions within the prescribed area of the delay space. In every single grid node, the iterative estimation of the rightmost pole is computed based on the polynomial approximation of the characteristic quasipolynomial, by utilizing the knowledge of the dominant pole estimation in the nearest grid node. The polynomial approximation is made via the Taylor series based expansion in the vicinity of the closest dominant poles estimation, and by using the bilinear transformation followed with pre-warping for a discrete-time approximation. Exponential terms are subjected to a quadratic extrapolation method to get commensurate delays. Two-step Newton’s iteration method with averaging is used to detect imaginary axis crossings. Neutral delay case is concisely discussed as well. Two numerical examples demonstrate the accuracy and efficiency of the algorithm. Possible future directions of this research and algorithm modifications are proposed and discussed in brief as well.

Název v anglickém jazyce

On the Numerical Determination of Stability Regions in the Delay Space via Dominant Pole Estimation

Popis výsledku anglicky

This contribution intends to provide the reader with the presentation of a numerical gridding iterative algorithm to determine all stability regions within the prescribed area of the delay space. In every single grid node, the iterative estimation of the rightmost pole is computed based on the polynomial approximation of the characteristic quasipolynomial, by utilizing the knowledge of the dominant pole estimation in the nearest grid node. The polynomial approximation is made via the Taylor series based expansion in the vicinity of the closest dominant poles estimation, and by using the bilinear transformation followed with pre-warping for a discrete-time approximation. Exponential terms are subjected to a quadratic extrapolation method to get commensurate delays. Two-step Newton’s iteration method with averaging is used to detect imaginary axis crossings. Neutral delay case is concisely discussed as well. Two numerical examples demonstrate the accuracy and efficiency of the algorithm. Possible future directions of this research and algorithm modifications are proposed and discussed in brief as well.

Druh

C - Kapitola v odborné knize

CEP obor

—

OECD FORD obor

20205 - Automation and control systems

Projekt

<a href="/cs/project/LO1303" target="_blank" >LO1303: Podpora udržitelnosti a rozvoje Centra bezpečnostních, informačních a pokročilých technologií (CEBIA-Tech)</a><br>

Návaznosti

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

Rok uplatnění

2019

Kód důvěrnosti údajů

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

Název knihy nebo sborníku

Stability, Control and Application of Time-Delay Systems

ISBN

978-0-12-814928-7

Počet stran výsledku

22

Strana od-do

1-22

Počet stran knihy

470

Název nakladatele

Elsevier

Místo vydání

Philadelphia

Kód UT WoS kapitoly

—