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
DAEs: Background and Concepts
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