Bridge the gap between theory and practice with this accessible guide

Process control is an area of study which seeks to optimize industrial processes, applying different strategies and technologies as required to navigate the variety of processes and their many potential challenges. Though the body of chemical process control theory is robust, it is only in recent decades that it has been effectively integrated with industrial practice to form a flexible toolkit. The need for a guide to this integration of theory and practice has therefore never been more urgent.

Advanced Chemical Process Control meets this need, making advanced chemical process control accessible and useful to chemical engineers with little grounding in the theoretical principles of the subject. It provides a basic introduction to the background and mathematics of control theory, before turning to the implementation of control principles in industrial contexts. The result is a bridge between the insights of control theory and the needs of engineers in plants, factories, research facilities, and beyond.

Advanced Chemical Process Control readers will also find:

• Detailed overview of Control Performance Monitoring (CPM), Model Predictive Control (MPC), and more
• Discussion of the cost benefit analysis of improved control in particular jobs
• Authored by a leading international expert on chemical process control

Advanced Chemical Process Control is essential for chemical and process engineers looking to develop a working knowledge of process control, as well as for students and graduates entering the chemical process control field.

Preface xvii

Acknowledgments xxi

Acronyms xxiii

Introduction xxv

1 Mathematical and Control Theory Background 1

1.1 Introduction 1

1.2 Models for Dynamical Systems 1

1.2.1 Dynamical Systems in Continuous Time 1

1.2.2 Dynamical Systems in Discrete Time 2

1.2.3 Linear Models and Linearization 3

1.2.3.1 Linearization at a Given Point 3

1.2.3.2 Linearizing Around a Trajectory 6

1.2.4 Converting Between Continuous- and Discrete-Time Models 6

1.2.4.1 Time Delay in the Manipulated Variables 7

1.2.4.2 Time Delay in the Measurements 9

1.2.5 Laplace Transform 9

1.2.6 The z Transform 10

1.2.7 Similarity Transformations 11

1.2.8 Minimal Representation 11

1.2.9 Scaling 14

1.3 Analyzing Linear Dynamical Systems 15

1.3.1 Transfer Functions of Composite Systems 15

1.3.1.1 Series Interconnection 15

1.3.1.2 Parallel Systems 16

1.3.1.3 Feedback Connection 16

1.3.1.4 Commonly Used Closed-Loop Transfer Functions 17

1.3.1.5 The Push-Through Rule 17

1.4 Poles and Zeros of Transfer Functions 18

1.4.1 Poles of Multivariable Systems 19

1.4.2 Pole Directions 19

1.4.3 Zeros of Multivariable Systems 20

1.4.4 Zero Directions 22

1.5 Stability 23

1.5.1 Poles and Zeros of Discrete-Time Transfer Functions 23

1.5.2 Frequency Analysis 24

1.5.2.1 Steady-State Phase Adjustment 26

1.5.3 Bode Diagrams 27

1.5.3.1 Bode Diagram Asymptotes 27

1.5.3.2 Minimum Phase Systems 29

1.5.3.3 Frequency Analysis for Discrete-Time Systems 30

1.5.4 Assessing Closed-Loop Stability Using the Open-Loop Frequency Response 31

1.5.4.1 The Principle of the Argument and the Nyquist D-Contour 31

1.5.4.2 The Multivariable Nyquist Theorem 32

1.5.4.3 The Monovariable Nyquist Theorem 32

1.5.4.4 The Bode Stability Criterion 32

1.5.4.5 Some Remarks on Stability Analysis Using the Frequency Response 35

1.5.4.6 The Small Gain Theorem 36

1.5.5 Controllability 37

1.5.6 Observability 38

1.5.7 Some Comments on Controllability and Observability 39

1.5.8 Stabilizability 40

1.5.9 Detectability 40

1.5.10 Hidden Modes 41

1.5.11 Internal Stability 41

1.5.12 Coprime Factorizations 43

1.5.12.1 Inner-Outer Factorization 44

1.5.12.2 Normalized Coprime Factorization 44

1.5.13 Parametrization of All Stabilizing Controllers 44

1.5.13.1 Stable Plants 45

1.5.13.2 Unstable Plants 45

1.5.14 Hankel Norm and Hankel Singular Values 46

Problems 47

References 49

2 Control Configuration and Controller Tuning 51

2.1 Common Control Loop Structures for the Regulatory Control Layer 51

2.1.1 Simple Feedback Loop 51

2.1.2 Feedforward Control 51

2.1.3 Ratio Control 54

2.1.4 Cascade Control 54

2.1.5 Auctioneering Control 55

2.1.6 Split Range Control 56

2.1.7 Input Resetting Control 57

2.1.8 Selective Control 59

2.1.9 Combining Basic Single-Loop Control Structures 60

2.1.10 Decoupling 61

2.2 Input and Output Selection 62

2.2.1 Using Physical Insights 63

2.2.2 Gramian-Based Input and Output Selection 64

2.2.3 Input/Output Selection for Stabilization 65

2.3 Control Configuration 66

2.3.1 The Relative Gain Array 66

2.3.2 The RGA as a General Analysis Tool 68

2.3.2.1 The RGA and Zeros in the Right Half-Plane 68

2.3.2.2 The RGA and the Optimally Scaled Condition Number 68

2.3.2.3 The RGA and Individual Element Uncertainty 69

2.3.2.4 RGA and Diagonal Input Uncertainty 69

2.3.2.5 The RGA as an Interaction Measure 70

2.3.3 The RGA and Stability 70

2.3.3.1 The RGA and Pairing of Controlled and Manipulated Varia