An optimal finite-diemensional modeling in heat conduction and diffusion equations with partially known eigenstructure

Jun Imai, Yasuaki Ando, Masami Konishi

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Citations (Scopus)

Abstract

An optimal finite-dimensional modeling technique is presented for a standard class of distributed parameter systems for heat and diffusion equations. A finite-dimensional nominal model with minimum error bounds in frequency domain is established for spectral systems with partially known eigenvalues and eigenfunctions. The result is derived from a completely characterized geometric figure upon complex plane, of all the frequency responses of the systems that have (i) a finite number of given time constants Ti's and modal coefficients ki's, (ii) an upper bound ρ to the infinite sum of the absolute values of all the modal coefficients ki's, (iii) an upper bound T to the unknown Ti's, and (iv) a given dc gain G(0). Discussions are made on how each parameter mentioned above makes contribution to bounding error or uncertainty, and we stress that steady state analysis for dc input is used effectively in reduced order modeling and bounding errors. The feasibility of the presented scheme is demonstrated by a simple example of heat conduction in ideal copper rod.

Original languageEnglish
Title of host publicationProceedings of the IEEE Conference on Decision and Control
Pages330-335
Number of pages6
Volume1
Publication statusPublished - 2003
Event42nd IEEE Conference on Decision and Control - Maui, HI, United States
Duration: Dec 9 2003Dec 12 2003

Other

Other42nd IEEE Conference on Decision and Control
CountryUnited States
CityMaui, HI
Period12/9/0312/12/03

Fingerprint

Heat conduction
Eigenvalues and eigenfunctions
Frequency response
Copper

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Safety, Risk, Reliability and Quality
  • Chemical Health and Safety

Cite this

Imai, J., Ando, Y., & Konishi, M. (2003). An optimal finite-diemensional modeling in heat conduction and diffusion equations with partially known eigenstructure. In Proceedings of the IEEE Conference on Decision and Control (Vol. 1, pp. 330-335)

An optimal finite-diemensional modeling in heat conduction and diffusion equations with partially known eigenstructure. / Imai, Jun; Ando, Yasuaki; Konishi, Masami.

Proceedings of the IEEE Conference on Decision and Control. Vol. 1 2003. p. 330-335.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Imai, J, Ando, Y & Konishi, M 2003, An optimal finite-diemensional modeling in heat conduction and diffusion equations with partially known eigenstructure. in Proceedings of the IEEE Conference on Decision and Control. vol. 1, pp. 330-335, 42nd IEEE Conference on Decision and Control, Maui, HI, United States, 12/9/03.
Imai J, Ando Y, Konishi M. An optimal finite-diemensional modeling in heat conduction and diffusion equations with partially known eigenstructure. In Proceedings of the IEEE Conference on Decision and Control. Vol. 1. 2003. p. 330-335
Imai, Jun ; Ando, Yasuaki ; Konishi, Masami. / An optimal finite-diemensional modeling in heat conduction and diffusion equations with partially known eigenstructure. Proceedings of the IEEE Conference on Decision and Control. Vol. 1 2003. pp. 330-335
@inproceedings{ae33a2ebc0e6481bb797c89e5e924726,
title = "An optimal finite-diemensional modeling in heat conduction and diffusion equations with partially known eigenstructure",
abstract = "An optimal finite-dimensional modeling technique is presented for a standard class of distributed parameter systems for heat and diffusion equations. A finite-dimensional nominal model with minimum error bounds in frequency domain is established for spectral systems with partially known eigenvalues and eigenfunctions. The result is derived from a completely characterized geometric figure upon complex plane, of all the frequency responses of the systems that have (i) a finite number of given time constants Ti's and modal coefficients ki's, (ii) an upper bound ρ to the infinite sum of the absolute values of all the modal coefficients ki's, (iii) an upper bound T to the unknown Ti's, and (iv) a given dc gain G(0). Discussions are made on how each parameter mentioned above makes contribution to bounding error or uncertainty, and we stress that steady state analysis for dc input is used effectively in reduced order modeling and bounding errors. The feasibility of the presented scheme is demonstrated by a simple example of heat conduction in ideal copper rod.",
author = "Jun Imai and Yasuaki Ando and Masami Konishi",
year = "2003",
language = "English",
volume = "1",
pages = "330--335",
booktitle = "Proceedings of the IEEE Conference on Decision and Control",

}

TY - GEN

T1 - An optimal finite-diemensional modeling in heat conduction and diffusion equations with partially known eigenstructure

AU - Imai, Jun

AU - Ando, Yasuaki

AU - Konishi, Masami

PY - 2003

Y1 - 2003

N2 - An optimal finite-dimensional modeling technique is presented for a standard class of distributed parameter systems for heat and diffusion equations. A finite-dimensional nominal model with minimum error bounds in frequency domain is established for spectral systems with partially known eigenvalues and eigenfunctions. The result is derived from a completely characterized geometric figure upon complex plane, of all the frequency responses of the systems that have (i) a finite number of given time constants Ti's and modal coefficients ki's, (ii) an upper bound ρ to the infinite sum of the absolute values of all the modal coefficients ki's, (iii) an upper bound T to the unknown Ti's, and (iv) a given dc gain G(0). Discussions are made on how each parameter mentioned above makes contribution to bounding error or uncertainty, and we stress that steady state analysis for dc input is used effectively in reduced order modeling and bounding errors. The feasibility of the presented scheme is demonstrated by a simple example of heat conduction in ideal copper rod.

AB - An optimal finite-dimensional modeling technique is presented for a standard class of distributed parameter systems for heat and diffusion equations. A finite-dimensional nominal model with minimum error bounds in frequency domain is established for spectral systems with partially known eigenvalues and eigenfunctions. The result is derived from a completely characterized geometric figure upon complex plane, of all the frequency responses of the systems that have (i) a finite number of given time constants Ti's and modal coefficients ki's, (ii) an upper bound ρ to the infinite sum of the absolute values of all the modal coefficients ki's, (iii) an upper bound T to the unknown Ti's, and (iv) a given dc gain G(0). Discussions are made on how each parameter mentioned above makes contribution to bounding error or uncertainty, and we stress that steady state analysis for dc input is used effectively in reduced order modeling and bounding errors. The feasibility of the presented scheme is demonstrated by a simple example of heat conduction in ideal copper rod.

UR - http://www.scopus.com/inward/record.url?scp=1542269320&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=1542269320&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:1542269320

VL - 1

SP - 330

EP - 335

BT - Proceedings of the IEEE Conference on Decision and Control

ER -