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The feedback control of nonlinear differential and algebraic equation systems (DAEs) is a relatively new subject. 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 introduces readers to the inherent characteristics of nonlinear DAE systems and the methods used to address their control. It then discusses the significance of DAE systems to the modeling and control of chemical processes. Within a unified framework, the authors present recent results on the stabilization, output tracking, and disturbance elimination for a large class of nonlinear DAE systems.
List 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.
Summary
Introduces readers to the inherent characteristics of nonlinear DAE systems and the methods used to address their control. This work then discusses the significance of DAE systems to the modeling and control of chemical processes. It presents results on the stabilization and disturbance elimination for a large class of nonlinear DAE systems.
