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 language | English |
|---|---|
| Title of host publication | Proceedings of the IEEE Conference on Decision and Control |
| Pages | 330-335 |
| Number of pages | 6 |
| Volume | 1 |
| Publication status | Published - 2003 |
| Event | 42nd IEEE Conference on Decision and Control - Maui, HI, United States Duration: Dec 9 2003 → Dec 12 2003 |
Other
| Other | 42nd IEEE Conference on Decision and Control |
|---|---|
| Country | United States |
| City | Maui, HI |
| Period | 12/9/03 → 12/12/03 |
Fingerprint
ASJC Scopus subject areas
- Control and Systems Engineering
- Safety, Risk, Reliability and Quality
- Chemical Health and Safety
Cite this
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 proceeding › Conference contribution
}
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 -