Control of Nonlinear Differential Algebraic Equation Systems with Applications to Chemical Processes: (Chapman & Hall/CRC Research Notes in Mathematics Series)

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.

Table of Contents:
Preface -- 1 DAEs: Background and Concepts -- 1. Introduction -- 1.2 Linear Systems -- 1.3 Nonlinear Systems -- 1.3.1 Descriptions -- 1.3.2 Solvability and Index -- 1.3.3 Comparison of high-index DAE and ODE systems -- 1.3.4 Regularity -- 2 Chemical Process Applications -- 2.1 Reactor with Fast Heat Transfer through Heating Jacket -- 2.2 Reactor with Fast and Slow Reactions -- 2.3 Two-Phase Reactor with Fast Mass Transfer -- 2.4 Cascade of Reactors with High Pressure Gaseous Flow -- 2.5 Reaction-Separation Process Network with Large Recycle -- 2.6 Reactor with High-Gain Pressure Controller -- 2.7 Flow of Incompressible Fluids -- 2.8 Conclusions -- 3 Feedback Control of Regular DAE systems -- 3.1 Introduction -- 3.2 Preliminaries -- 3.3 Derivation of State-Space Realizations -- 3.3.1 Algorithm for reconstruction of algebraic variables -- 3.3.2 State-space realizations of DAE system -- 3.4 State Feedback Controller Synthesis -- 3.4.1 Preliminaries -- 3.4.2 Problem formulation -- 3.4.3 Controller synthesis -- 3.5 Conclusions -- 4 Feedback Control of Nonregular DAE Systems -- 4.1 Introduction -- 4.2 Preliminaries -- 4.3 Algorithm for Derivation of Equivalent DAE System with Explicit Constraints in x Involving u -- 4.4 Dynamic State Feedback Regularization -- 4.5 State-Space Realizations and Controller Synthesis -- 4.6 Conclusions -- 5 Control of DAE Systems with Disturbance Inputs -- 5.1 Introduction -- 5.2 System Description and Preliminaries -- 5.3 Algorithm for Identification of Constraints -- 5.4 State-Space Realizations and Feedforward /State Feedback Control of Regular Systems -- 5.5 Feedforward /State Feedback Regularization and Control r• Nonregular Systems -- 5.6 Conclusions -- 6 DAEs and Singularly Perturbed Systems -- 6.1 Introduction -- 6.2 Standard vs. Nonstandard Singularly Perturbed Systems -- 6.3 Derivation of Standard Singularly Perturbed Representation of Rate-Based Models -- 6.4 Singularly Perturbed Models of Process Networks -- 7 Simulation Studies of Chemical Process Applications -- 7.1 A CSTR with heating jacket -- 7.2 A CSTR with multiple reactions -- 7.3 Two-Phase Reactor -- 7.3.1 State-space realization -- 7.3.2 Controller synthesis -- 7.3.3 Discussion of controller performance -- 7.4 Reactor-Condenser Network -- 7.4.1 Process description and modeling -- 7.4.2 Feedforward /feedback regularization and state-space realization -- 7.4.3 Feedforward /feedback controller synthesis and control performance -- Bibliography.

About the Author :
University of Minnesota. University of Minnesota.

Review :
"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