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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/sub i/'s and modal coefficients k/sub i/'s, (ii) an upper bound /spl rho/ to the infinite sum of the absolute values of all the modal coefficients k/sub i/'s, (iii) an upper bound T to the unknown T/sub 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.
distributed parameter systems
Digital Object Identifier: 10.1109/CDC.2003.1272582
Published with permission from the copyright holder. This is the institute's copy, as published in Decision and Control, 2003. Proceedings. 42nd IEEE Conference on, 9-12 Dec. 2003, Volume: 1 Pages 330-335.
Copyright © 2003 IEEE. All rights reserved.
Decision and Control