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

Jun Imai, Yasuaki Ando, Masami Konishi

Research output: Contribution to journalConference article

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
Pages (from-to)330-335
Number of pages6
JournalProceedings of the IEEE Conference on Decision and Control
Volume1
Publication statusPublished - Dec 1 2003
Event42nd IEEE Conference on Decision and Control - Maui, HI, United States
Duration: Dec 9 2003Dec 12 2003

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Modelling and Simulation
  • Control and Optimization

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