Sensitivity of Time Response to Characteristic Ratios

Youngchol KIM; Keunsik KIM; Shunji MANABE

doi:10.1093/ietfec/e89-a.2.520

Sensitivity of Time Response to Characteristic Ratios

Youngchol KIM, Keunsik KIM, Shunji MANABE

Full Text Views

0

Cite this

Summary :

In recent works [1],[4], it has been shown that the damping of a linear time invariant system relates to the so-called characteristic ratios (α_k, k=1,…, n-1) which are defined by coefficients of the denominator of the transfer function. However, the exact relations are not yet fully understood. For the purpose of exploring the issue, this paper presents the analysis of time response sensitivity to the characteristic ratio change. We begin with the sensitivity of output to the perturbations of coefficients of the system denominator and then the first order approximation of the α_k perturbation effect is computed by an explicit transfer function. The results are extended to all-pole systems in order to investigate which characteristic ratios act dominantly on step response. The same analysis is also performed to a special class of systems whose denominator is composed of so called K-polynomial. Finally, some illustrative examples are given.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E89-A No.2 pp.520-527

Publication Date: 2006/02/01

Publicized

Online ISSN: 1745-1337

DOI: 10.1093/ietfec/e89-a.2.520

Type of Manuscript: PAPER

Category: Systems and Control

Cite this

Copy

Youngchol KIM, Keunsik KIM, Shunji MANABE, "Sensitivity of Time Response to Characteristic Ratios" in IEICE TRANSACTIONS on Fundamentals, vol. E89-A, no. 2, pp. 520-527, February 2006, doi: 10.1093/ietfec/e89-a.2.520.
Abstract: In recent works [1],[4], it has been shown that the damping of a linear time invariant system relates to the so-called characteristic ratios (α_k, k=1,…, n-1) which are defined by coefficients of the denominator of the transfer function. However, the exact relations are not yet fully understood. For the purpose of exploring the issue, this paper presents the analysis of time response sensitivity to the characteristic ratio change. We begin with the sensitivity of output to the perturbations of coefficients of the system denominator and then the first order approximation of the α_k perturbation effect is computed by an explicit transfer function. The results are extended to all-pole systems in order to investigate which characteristic ratios act dominantly on step response. The same analysis is also performed to a special class of systems whose denominator is composed of so called K-polynomial. Finally, some illustrative examples are given.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1093/ietfec/e89-a.2.520/_p

Copy

@ARTICLE{e89-a_2_520,
author={Youngchol KIM, Keunsik KIM, Shunji MANABE, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Sensitivity of Time Response to Characteristic Ratios},
year={2006},
volume={E89-A},
number={2},
pages={520-527},
abstract={In recent works [1],[4], it has been shown that the damping of a linear time invariant system relates to the so-called characteristic ratios (α_k, k=1,…, n-1) which are defined by coefficients of the denominator of the transfer function. However, the exact relations are not yet fully understood. For the purpose of exploring the issue, this paper presents the analysis of time response sensitivity to the characteristic ratio change. We begin with the sensitivity of output to the perturbations of coefficients of the system denominator and then the first order approximation of the α_k perturbation effect is computed by an explicit transfer function. The results are extended to all-pole systems in order to investigate which characteristic ratios act dominantly on step response. The same analysis is also performed to a special class of systems whose denominator is composed of so called K-polynomial. Finally, some illustrative examples are given.},
keywords={},
doi={10.1093/ietfec/e89-a.2.520},
ISSN={1745-1337},
month={February},}

Copy

TY - JOUR
TI - Sensitivity of Time Response to Characteristic Ratios
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 520
EP - 527
AU - Youngchol KIM
AU - Keunsik KIM
AU - Shunji MANABE
PY - 2006
DO - 10.1093/ietfec/e89-a.2.520
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E89-A
IS - 2
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - February 2006
AB - In recent works [1],[4], it has been shown that the damping of a linear time invariant system relates to the so-called characteristic ratios (α_k, k=1,…, n-1) which are defined by coefficients of the denominator of the transfer function. However, the exact relations are not yet fully understood. For the purpose of exploring the issue, this paper presents the analysis of time response sensitivity to the characteristic ratio change. We begin with the sensitivity of output to the perturbations of coefficients of the system denominator and then the first order approximation of the α_k perturbation effect is computed by an explicit transfer function. The results are extended to all-pole systems in order to investigate which characteristic ratios act dominantly on step response. The same analysis is also performed to a special class of systems whose denominator is composed of so called K-polynomial. Finally, some illustrative examples are given.
ER -