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Nonlinear Model Based Process Control pp 311–344Cite as

Control of Nonlinear Differential Algebraic Equation Systems : An Overview

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Part of the book series: NATO ASI Series ((NSSE,volume 353))

Abstract

Chemical processes are inherently nonlinear and their dynamics are naturally described by systems of coupled differential and algebraic equations (DAEs); the differential equations arise from the standard dynamic balances of mass, energy and momentum, while the algebraic equations typically include thermodynamic relations, empirical correlations, quasi-steady-state relations etc. In many cases, the algebraic equations in the DAE model can be readily eliminated to obtain an equivalent ordinary differential equation (ODE) model, which can be used as the basis for controller design. On the other hand, there is a broad class of chemical processes for which the algebraic equations in the DAE models are “singular” in nature, and thus, inhibit a direct reduction of the DAE model into an ODE system. Such DAE systems with singular algebraic equations are said to have a high “index” and they are fundamentally different from ODE systems.

Financial support for this work from the National Science Foundation, Grant CTS-9320402, is gratefully acknowledged.

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Authors and Affiliations

  1. Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, MN, 55455, USA

    Aditya Kumar & Prodromos Daoutidis

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  1. Aditya Kumar
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  2. Prodromos Daoutidis
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Editor information

Editors and Affiliations

  1. Department of Chemical Engineering, Ankara University, Tandoğan, Ankara, Turkey

    Ridvan Berber

  2. Department of Chemical Engineering, The University of Michigan, Ann Arbor, Michigan, USA

    Costas Kravaris

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© 1998 Springer Science+Business Media Dordrecht

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Kumar, A., Daoutidis, P. (1998). Control of Nonlinear Differential Algebraic Equation Systems : An Overview. In: Berber, R., Kravaris, C. (eds) Nonlinear Model Based Process Control. NATO ASI Series, vol 353. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-5094-1_11

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  • DOI: https://doi.org/10.1007/978-94-011-5094-1_11

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-6140-7

  • Online ISBN: 978-94-011-5094-1

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