1st Edition

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

By Aditya Kumar, Prodromos Daoutidis Copyright 1999
    174 Pages
    by Chapman & Hall

    174 Pages
    by Chapman & Hall

    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.

    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


    University of Minnesota. University of Minnesota.

    "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