### 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 T_{i}'s and modal coefficients k_{i}'s, (ii) an upper bound ρ to the infinite sum of the absolute values of all the modal coefficients k_{i}'s, (iii) an upper bound T to the unknown T_{i}'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 |
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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 |
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Country | United States |

City | Maui, HI |

Period | 12/9/03 → 12/12/03 |

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### ASJC Scopus subject areas

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

### Cite this

*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.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*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.

}

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 -