### Abstract

A regulator problem for a heat conduction system, of which the eigenstructure is just partially known, is formulated to design a stabilizing controller that keeps a performance index less than a prescribed value. The index is made of the spatio integral of the squared deviation from reference temperature distribution. It is shown that through characterizing frequency response from input to temperature at each spatial point, a distributed parameter system with nominal model and additive uncertainty weight, both of which are real rational, is reconstructed using knowledge of the eigenstructure. A main result claims that the formulated problem is reduced to a standard mixed H_{2}/H_{∞} one for a linear finite dimensional time-invariant system. Numerical study demonstrates feasibility of the proposed design scheme.

Original language | English |
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Title of host publication | IFAC Proceedings Volumes (IFAC-PapersOnline) |

Pages | 119-124 |

Number of pages | 6 |

Volume | 16 |

Publication status | Published - 2005 |

Event | 16th Triennial World Congress of International Federation of Automatic Control, IFAC 2005 - Prague, Czech Republic Duration: Jul 3 2005 → Jul 8 2005 |

### Other

Other | 16th Triennial World Congress of International Federation of Automatic Control, IFAC 2005 |
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Country | Czech Republic |

City | Prague |

Period | 7/3/05 → 7/8/05 |

### Fingerprint

### Keywords

- Distributed-parameter systems
- Modeling errors
- Uncertainty

### ASJC Scopus subject areas

- Control and Systems Engineering

### Cite this

*IFAC Proceedings Volumes (IFAC-PapersOnline)*(Vol. 16, pp. 119-124)

**On regulator design for spatial temperature distribution using finite-dimensional modeling of heat equations.** / Imai, Jun; Ando, Yasuaki; Konishi, Masami; Nishi, Tatsushi.

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

*IFAC Proceedings Volumes (IFAC-PapersOnline).*vol. 16, pp. 119-124, 16th Triennial World Congress of International Federation of Automatic Control, IFAC 2005, Prague, Czech Republic, 7/3/05.

}

TY - GEN

T1 - On regulator design for spatial temperature distribution using finite-dimensional modeling of heat equations

AU - Imai, Jun

AU - Ando, Yasuaki

AU - Konishi, Masami

AU - Nishi, Tatsushi

PY - 2005

Y1 - 2005

N2 - A regulator problem for a heat conduction system, of which the eigenstructure is just partially known, is formulated to design a stabilizing controller that keeps a performance index less than a prescribed value. The index is made of the spatio integral of the squared deviation from reference temperature distribution. It is shown that through characterizing frequency response from input to temperature at each spatial point, a distributed parameter system with nominal model and additive uncertainty weight, both of which are real rational, is reconstructed using knowledge of the eigenstructure. A main result claims that the formulated problem is reduced to a standard mixed H2/H∞ one for a linear finite dimensional time-invariant system. Numerical study demonstrates feasibility of the proposed design scheme.

AB - A regulator problem for a heat conduction system, of which the eigenstructure is just partially known, is formulated to design a stabilizing controller that keeps a performance index less than a prescribed value. The index is made of the spatio integral of the squared deviation from reference temperature distribution. It is shown that through characterizing frequency response from input to temperature at each spatial point, a distributed parameter system with nominal model and additive uncertainty weight, both of which are real rational, is reconstructed using knowledge of the eigenstructure. A main result claims that the formulated problem is reduced to a standard mixed H2/H∞ one for a linear finite dimensional time-invariant system. Numerical study demonstrates feasibility of the proposed design scheme.

KW - Distributed-parameter systems

KW - Modeling errors

KW - Uncertainty

UR - http://www.scopus.com/inward/record.url?scp=79960731371&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79960731371&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:79960731371

SN - 008045108X

SN - 9780080451084

VL - 16

SP - 119

EP - 124

BT - IFAC Proceedings Volumes (IFAC-PapersOnline)

ER -