Gridding discretization-based multiple stability switching delay search algorithm: The movement of a human being on a controlled swaying bow

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F70883521%3A28140%2F17%3A63517006" target="_blank" >RIV/70883521:28140/17:63517006 - isvavai.cz</a>

Výsledek na webu

<a href="http://journals.plos.org/plosone/article?id=10.1371/journal.pone.0178950" target="_blank" >http://journals.plos.org/plosone/article?id=10.1371/journal.pone.0178950</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1371/journal.pone.0178950" target="_blank" >10.1371/journal.pone.0178950</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Gridding discretization-based multiple stability switching delay search algorithm: The movement of a human being on a controlled swaying bow

Popis výsledku v původním jazyce

Delay represents a significant phenomenon in the dynamics of many human-related systems - including biological ones. It has i.a. a decisive impact on system stability, and the study of this influence is often mathematically demanding. This paper presents a computationally simple numerical gridding algorithm for the determination of stability margin delay values in multiple-delay linear systems. The characteristic quasi-polynomial - the roots of which decide about stability, is subjected to iterative discretization by means of pre-warped bilinear transformation. Then, a linear and a quadratic interpolation are applied to obtain the associated characteristic polynomial with integer powers. The roots of the associated characteristic polynomial are closely related to the estimation of roots of the original characteristic quasi-polynomial which agrees with the system´s eigenvalues. Since the stability border is crossed by the leading one, the switching root locus is enhanced using the Regula Falsi interpolation method. Our methodology is implemented on - and verified by, a numerical bio-cybernetic example of the stabilization of a human-being´s movement on a controlled swaying bow. The advantage of the proposed novel algorithm lies in the possibility of the rapid computation of polynomial zeros by means of standard programs for technical computing; in the low level of mathematical knowledge required; and, in the sufficiently high precision of the roots loci estimation. The relationship to the direct search QuasiPolynomial (mapping) Rootfinder algorithm and computational complexity are discussed as well. This algorithm is also applicable for systems with non-commensurate delays.

Název v anglickém jazyce

Gridding discretization-based multiple stability switching delay search algorithm: The movement of a human being on a controlled swaying bow

Popis výsledku anglicky

Delay represents a significant phenomenon in the dynamics of many human-related systems - including biological ones. It has i.a. a decisive impact on system stability, and the study of this influence is often mathematically demanding. This paper presents a computationally simple numerical gridding algorithm for the determination of stability margin delay values in multiple-delay linear systems. The characteristic quasi-polynomial - the roots of which decide about stability, is subjected to iterative discretization by means of pre-warped bilinear transformation. Then, a linear and a quadratic interpolation are applied to obtain the associated characteristic polynomial with integer powers. The roots of the associated characteristic polynomial are closely related to the estimation of roots of the original characteristic quasi-polynomial which agrees with the system´s eigenvalues. Since the stability border is crossed by the leading one, the switching root locus is enhanced using the Regula Falsi interpolation method. Our methodology is implemented on - and verified by, a numerical bio-cybernetic example of the stabilization of a human-being´s movement on a controlled swaying bow. The advantage of the proposed novel algorithm lies in the possibility of the rapid computation of polynomial zeros by means of standard programs for technical computing; in the low level of mathematical knowledge required; and, in the sufficiently high precision of the roots loci estimation. The relationship to the direct search QuasiPolynomial (mapping) Rootfinder algorithm and computational complexity are discussed as well. This algorithm is also applicable for systems with non-commensurate delays.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

20205 - Automation and control systems

Projekt

<a href="/cs/project/ED2.1.00%2F19.0376" target="_blank" >ED2.1.00/19.0376: CEBIA - Tech Instrumentation</a><br>

Návaznosti

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

Rok uplatnění

2017

Kód důvěrnosti údajů

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

Název periodika

PLoS ONE

ISSN

1932-6203

e-ISSN

—

Svazek periodika

12

Číslo periodika v rámci svazku

6

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

23

Strana od-do

"nestrankovano"

Kód UT WoS článku

000402923200071

EID výsledku v databázi Scopus

2-s2.0-85020447208