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Identification of low order manifolds: Validating the algorithm of Maas and Pope

Rhodes, Carl and Morari, Manfred and Wiggins, Stephen (1999) Identification of low order manifolds: Validating the algorithm of Maas and Pope. Chaos, 9 (1). pp. 108-123. ISSN 1054-1500. http://resolver.caltech.edu/CaltechAUTHORS:RHOchaos99

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Abstract

The algorithm of Maas and Pope (1992) is presented as a method for identification of invariant reduced-order manifolds for stable systems which exhibit dynamics with a time-scale separation. While this method has been published previously in the literature, theoretical justification for the algorithm was not presented in the original work. Here, it will be shown rigorously that the algorithm correctly identifies the slow manifold. Before the theoretical results are presented, a brief background on the behavior of singularly perturbed systems is presented. The algorithm of Maas and Pope (1992) is then introduced. This method will be applied to two different examples, a distillation column and a two-phase chemical reactor. For each of these examples, the resulting reduced-order description will be compared to other standard methods of producing reduced-order models. In addition, some preliminary thoughts on how this method can be used to form reduced-order models are presented.


Item Type:Article
Additional Information:Copyright © 1999 American Institute of Physics. Received 28 July 1998; accepted 30 December 1998.
Subject Keywords:singularly perturbed systems; nonlinear dynamical systems; chaos; nonlinear control systems; chemical variables control; identification; distillation
Record Number:CaltechAUTHORS:RHOchaos99
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:RHOchaos99
Alternative URL:http://dx.doi.org/10.1063/1.166398
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:1930
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:23 Feb 2006
Last Modified:26 Dec 2012 08:46

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