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Chaos / Volume 9 / Issue 1 / FOCUS ISSUE: NONLINEAR SCIENCE IN CHEMICAL ENGINEERING

Chaos 9, 108 (1999); doi:10.1063/1.166398 (16 pages)

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

Carl Rhodes1, Manfred Morari2, and Stephen Wiggins3

1Chemical Engineering 210-41, California Institute of Technology, Pasadena, California 91125
2Institut für Automatik, ETH-Z/ETL, CH-8092 Zürich, Switzerland
3Control and Dynamical Systems 107-81, California Institute of Technology, Pasadena, California 91125

(Received 28 July 1998; accepted 30 December 1998)

The algorithm of 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 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. © 1999 American Institute of Physics.

© 1999 American Institute of Physics

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KEYWORDS and PACS

Keywords

singularly perturbed systems, nonlinear dynamical systems, chaos, nonlinear control systems, chemical variables control, identification, distillation

PACS

  • 05.45.Gg

    Control of chaos, applications of chaos

ARTICLE DATA

Permalink
http://link.aip.org/link/doi/10.1063/1.166398

PUBLICATION DATA

ISSN:

1054-1500 (print)  
1089-7682 (online)

Publisher:

$abstract.society.value is a Member of CrossRef American Institute of Physics

For access to fully linked references, you need to log in.
    Roussel, M. R. and Fraser, S. J. (1991). "On the geometry of transient relaxation," J. Chem. Phys. 94, 7106–7113JCPSA6000094000011007106000001.


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