Understanding Process Dynamics and Control

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Cover Half-title page Series page Title page Copyright page Dedication Contents Preface 1 INTRODUCTION Study Objectives 1.1 What is Process Control? 1.2 Feedback Control System: Key Ideas, Concepts and Terminology 1.3 Process Control Notation and Control Loop Representation 1.4 Understanding Process Dynamics is a Prerequisite for Learning Process Control 1.5 Some Historical Notes Learning Summary Terms and Concepts Further Reading Problems 2 DYNAMIC MODELS FOR CHEMICAL PROCESS SYSTEMS Study Objectives 2.1 Introduction 2.2 Conservation Laws 2.3 Modeling Examples of Nonreacting Systems 2.4 Modeling of Reacting Systems 2.5 Modeling of Equilibrium Separation Systems 2.6 Modeling of Simple Electrical and Mechanical Systems 2.7 Software Tools Learning Summary Terms and Concepts Further Reading Problems 3 FIRST-ORDER SYSTEMS Study Objectives 3.1 Examples of First-Order Systems 3.2 Deviation Variables 3.3 Solution of Linear First-Order Differential Equations with Constant Coefficients 3.4 The Choice of Reference Steady State Affects the Mathematical Form of the Dynamics Problem 3.5 Unforced Response: Effect of Initial Condition under Zero Input 3.6 Forced Response: Effect of Nonzero Input under Zero Initial Condition 3.7 Standard Idealized Input Variations 3.8 Response of a First-Order System to a Step Input 3.9 Response of a First-Order System to a Pulse Input 3.10 Response of a First-Order System to a Ramp Input 3.11 Response of a First-Order System to a Sinusoidal Input 3.12 Response of a First-Order System to an Arbitrary Input – Time Discretization of the First-Order System 3.13 Another Example of a First-Order System: Liquid Storage Tank 3.14 Nonlinear First-Order Systems and their Linearization 3.15 Liquid Storage Tank with Input Bypass 3.16 General Form of a First-Order System 3.17 Software Tools Learning Summary Terms and Concepts Further Reading Problems 4 CONNECTIONS OF FIRST-ORDER SYSTEMS Study Objectives 4.1 First-Order Systems Connected in Series 4.2 First-Order Systems Connected in Parallel 4.3 Interacting First-Order Systems 4.4 Response of First-Order Systems Connected in Series or in Parallel 4.5 Software Tools Learning Summary Terms and Concepts Further Reading Problems 5 SECOND-ORDER SYSTEMS Study Objectives 5.1 A Classical Example of a Second-Order System 5.2 A Second-Order System can be Described by Either a Set of Two First-Order ODEs or a Single Second-Order ODE 5.3 Calculating the Response of a Second-Order System – Step Response of a Second-Order System 5.4 Qualitative and Quantitative Characteristics of the Step Response of a Second-Order System 5.5 Frequency Response and Bode Diagrams of Second-Order Systems with ζ > 0 5.6 The General Form of a Linear Second-Order System 5.7 Software Tools Learning Summary Terms and Concepts Further Reading Problems 6 LINEAR HIGHER-ORDER SYSTEMS Study Objectives 6.1 Representative Examples of Higher-Order Systems – Using Vectors and Matrices to Describe a Linear System 6.2 Steady State of a Linear System – Deviation Variables 6.3 Using the Laplace-Transform Method to Solve the Linear Vector Differential Equation and Calculate the Response – Transfer Function of a Linear System 6.4 The Matrix Exponential Function 6.5 Solution of the Linear Vector Differential Equation using the Matrix Exponential Function 6.6 Dynamic Response of a Linear System 6.7 Response to an Arbitrary Input – Time Discretization of a Linear System 6.8 Calculating the Response of a Second-Order System via the Matrix Exponential Function 6.9 Multi-Input–Multi-Output Linear Systems 6.10 Software Tools Learning Summary Terms and Concepts Further Reading Problems 7 EIGENVALUE ANALYSIS – ASYMPTOTIC STABILITY Study Objectives 7.1 Introduction 7.2 The Role of System Eigenvalues on the Characteristics of the Response of a Linear System 7.3 Asymptotic Stability of Linear Systems 7.4 Properties of the Forced Response of Asymptotically Stable Linear Systems 7.5 The Role of Eigenvalues in Time Discretization of Linear Systems – Stability Test on a Discretized Linear System 7.6 Nonlinear Systems and their Linearization 7.7 Software Tools Learning Summary Terms and Concepts Further Reading Problems 8 TRANSFER-FUNCTION ANALYSIS OF THE INPUT–OUTPUT BEHAVIOR Study Objectives 8.1 Introduction 8.2 A Transfer Function is a Higher-Order Differential Equation in Disguise 8.3 Proper and Improper Transfer Functions – Relative Order 8.4 Poles, Zeros and Static Gain of a Transfer Function 8.5 Calculating the Output Response to Common Inputs from the Transfer Function – the Role of Poles in the Response 8.6 Effect of Zeros on the Step Response 8.7 Bounded-Input–Bounded-Output (BIBO) Stability 8.8 Asymptotic Response of BIBO-Stable Linear Systems 8.9 Software Tools Learning Summary Terms and Concepts Further Reading Problems 9 FREQUENCY RESPONSE Study Objectives 9.1 Introduction 9.2 Frequency Response and Bode Diagrams 9.3 Straight-Line Approximation Method for Sketching Bode Diagrams 9.4 Low-Frequency and High-Frequency Response 9.5 Nyquist Plots 9.6 Software Tools Learning Summary Terms and Concepts Further Reading Problems 10 THE FEEDBACK CONTROL SYSTEM Study Objectives 10.1 Heating Tank Process Example 10.2 Common Sensors and Final Control Elements 10.3 Block-Diagram Representation of the Heating Tank Process Example 10.4 Further Examples of Process Control Loops 10.5 Commonly Used Control Laws Learning Summary Terms and Concepts Further Reading Problems 11 BLOCK-DIAGRAM REDUCTION AND TRANSIENT-RESPONSE CALCULATION IN A FEEDBACK CONTROL SYSTEM Study Objectives 11.1 Calculation of the Overall Closed-Loop Transfer Functions in a Standard Feedback Control Loop 11.2 Calculation of Overall Transfer Functions in a Multi-Loop Feedback Control System 11.3 Stirred Tank Heater under Negligible Sensor Dynamics: Closed-Loop Response Calculation under P or PI Control 11.4 Software Tools Learning Summary Terms and Concepts Further Reading Problems 12 STEADY-STATE AND STABILITY ANALYSIS OF THE CLOSED-LOOP SYSTEM Study Objectives 12.1 Steady-State Analysis of a Feedback Control System 12.2 Closed-Loop Stability, Characteristic Polynomial and Characteristic Equation 12.3 The Routh Criterion 12.4 Calculating Stability Limits via the Substitution s = iω 12.5 Some Remarks about the Role of Proportional, Integral and Derivative Actions 12.6 Software Tools Learning Summary Terms and Concepts Further Reading Problems 13 STATE-SPACE DESCRIPTION AND ANALYSIS OF THE CLOSED-LOOP SYSTEM Study Objectives 13.1 State-Space Description and Analysis of the Heating Tank 13.2 State-Space Analysis of Closed-Loop Systems 13.3 Time Discretization of the Closed-Loop System 13.4 State-Space Description of Nonlinear Closed-Loop Systems 13.5 Software Tools Learning Summary Further Reading Problems 14 SYSTEMS WITH DEAD TIME Study Objectives 14.1 Introduction 14.2 Approximation of Dead Time by Rational Transfer Functions 14.3 Parameter Estimation for FOPDT Systems 14.4 Feedback Control of Systems with Dead Time – Closed-Loop Stability Analysis 14.5 Calculation of Closed-Loop Response for Systems involving Dead Time 14.6 Software Tools Learning Summary Terms and Concepts Further Reading Problems 15 PARAMETRIC ANALYSIS OF CLOSED-LOOP DYNAMICS – ROOT-LOCUS DIAGRAMS Study Objectives 15.1 What is a Root-Locus Diagram? Some Examples 15.2 Basic Properties of the Root Locus – Basic Rules for Sketching Root-Locus Diagrams 15.3 Further Properties of the Root Locus – Additional Rules for Sketching Root-Locus Diagrams 15.4 Calculation of the Points of Intersection of the Root Locus with the Imaginary Axis 15.5 Root Locus with Respect to Other Controller Parameters 15.6 Software Tools Learning Summary Terms and Concepts Further Reading Problems 16 OPTIMAL SELECTION OF CONTROLLER PARAMETERS Study Objectives 16.1 Control Performance Criteria 16.2 Analytic Calculation of Quadratic Criteria for a Stable System and a Step Input 16.3 Calculation of Optimal Controller Parameters for Quadratic Criteria 16.4 Software Tools Learning Summary Terms and Concepts Further Reading Problems 17 BODE AND NYQUIST STABILITY CRITERIA – GAIN AND PHASE MARGINS Study Objectives 17.1 Introduction 17.2 The Bode Stability Criterion 17.3 The Nyquist Stability Criterion 17.4 Example Applications of the Nyquist Criterion 17.5 Software Tools Learning Summary Terms and Concepts Further Reading Problems 18 MULTI-INPUT–MULTI-OUTPUT SYSTEMS Study Objectives 18.1 Introduction 18.2 Dynamic Response of MIMO Linear Systems 18.3 Feedback Control of MIMO Systems: State-Space versus Transfer-Function Description of the Closed-Loop System 18.4 Interaction in MIMO Systems 18.5 Decoupling in MIMO Systems 18.6 Software Tools Learning Summary Terms and Concepts Further Reading Problems 19 SYNTHESIS OF MODEL-BASED FEEDBACK CONTROLLERS Study Objectives 19.1 Introduction 19.2 Nearly Optimal Model-Based Controller Synthesis 19.3 Controller Synthesis for Low-Order Models 19.4 The Smith Predictor for Processes with Large Dead Time 19.5 Effect of Modeling Error 19.6 State-Space Form of the Model-Based Controller 19.7 Model-Based Controller Synthesis for MIMO Systems Learning Summary Terms and Concepts Further Reading Problems 20 CASCADE, RATIO AND FEEDFORWARD CONTROL Study Objectives 20.1 Introduction 20.2 Cascade Control 20.3 Ratio Control 20.4 Feedforward Control 20.5. Model-Based Feedforward Control Learning Summary Terms and Concepts Further Reading Problems APPENDIX A LAPLACE TRANSFORM A.1 Definition of the Laplace Transform A.2 Laplace Transforms of Elementary Functions A.3 Properties of Laplace Transforms A.4 Inverse Laplace Transform A.5 Calculation of the Inverse Laplace Transform of Rational Functions via Partial Fraction Expansion A.6 Solution of Linear Ordinary Differential Equations using the Laplace Transform A.7 Software Tools Problems APPENDIX B BASIC MATRIX THEORY B.1 Basic Notations and Definitions B.2 Determinant of a Square Matrix B.3 Matrix Inversion B.4 Eigenvalues B.5 The Cayley–Hamilton Theorem and the Resolvent Identity B.6 Differentiation and Integration of Matrices B.7 Software Tools Index