Control of Nonlinear Differential Algebraic Equation Systems with Applications to Chemical Processes: 1st Edition (Paperback) book cover

Control of Nonlinear Differential Algebraic Equation Systems with Applications to Chemical Processes

1st Edition

By Aditya Kumar, Prodromos Daoutidis

Chapman and Hall/CRC

174 pages

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Paperback: 9780849306099
pub: 1999-02-01
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pub: 2018-06-28
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The feedback control of nonlinear differential and algebraic equation systems (DAEs) is a relatively new subject. Developing steadily over the last few years, it has generated growing interest inspired by its engineering applications and by advances in the feedback control of nonlinear ordinary differential equations (ODEs). This book-the first of its kind-introduces the reader to the inherent characteristics of nonlinear DAE systems and the methods used to address their control, then discusses the significance of DAE systems to the modeling and control of chemical processes. Within a unified framework, Control of Nonlinear Differential Algebraic Equation Systems presents recent results on the stabilization, output tracking, and disturbance elimination for a large class of nonlinear DAE systems.

Written at a basic mathematical level-assuming some familiarity with analysis and control of nonlinear ODEs-the authors focus on continuous-time systems of differential and algebraic equations in semi-explicit form. Beginning with background material about DAE systems and their differences from ODE systems, the book discusses generic classes of chemical processes, feedback control of regular and non-regular DAE systems, control of systems with disturbance inputs, the connection of the DAE systems considered with singularly perturbed systems, and finally offers examples that illustrate the application of control methods and the advantages of using high-index DAE models as the basis for controller design.

Mathematicians and engineers will find that this book provides unique, timely results that also clearly documents the relevance of DAE systems to chemical processes.


"This valuable monograph presents in a unified framework, recent results on systems described by coupled nonlinear differential and algebraic equations …The book is an excellent reference for engineers and applied mathematicians interested in this relatively new subject, that has been developing steadily over the last few years."

-Dieter Franke in Mathematical Reviews

Table of Contents

DAEs: Background and Concepts


Linear Systems

Nonlinear Systems

Chemical Process Applications

Reactor with Fast Heat Transfer through Heating Jacket

Reactor with Fast and Slow Reactions

Two-Phase Reactor with Fast Mass Transfer

Cascade of Reactors with High Pressure Gaseous Flow

Reaction-Separation Process Network with Large Recycle

Reactor with High-Gain Pressure Controller

Flow of Incompressible Fluids


Feedback Control of Regular DAE Systems



Derivation of State-Space Realizations

Sate Feedback Controller Synthesis


Feedback Control of Non-Regular DAE Systems



Algorithm for Derivation of Equivalent DAE System

Dynamic State Feedback Regularization

State-Space Realizations and Controller Synthesis

Control of DAE Systems with Disturbance Inputs


System Description and Preliminaries

Algorithm for Identification of Constraints

State-Space Realizations and Feedforward/State Feedback Control of Regular Systems

Feedforward/State Feedback Regularization and Control of Non-Regular Systems


DAEs and Singularly Perturbed Systems


Standard vs. Non-Standard Singularly Perturbed Systems

Derivation of Standard Singularly Perturbed Representation of Rate-Based Models

Singularly Perturbed Models of Process Networks

Simulation Studies of Chemical Process Applications

A CSTR with Heating Jacket

A CSTR with Multiple Reactions

Two-Phase Reactor

Reactor-Condenser Network


About the Series

Chapman & Hall/CRC Research Notes in Mathematics Series

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Subject Categories

BISAC Subject Codes/Headings:
MATHEMATICS / Differential Equations