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 Variables 71 2.

3.4 Summary of RGA-Based Input-Output Pairing 72 2.3.5 Partial Relative Gains 72 2.3.6 The Niederlinski Index 73 2.3.7 The Rijnsdorp Interaction Measure 73 2.

3.8 Gramian-Based Input-Output Pairing 74 2.3.8.1 The Participation Matrix 75 2.3.8.2 The Hankel Interaction Index Array 75 2.

3.8.3 Accounting for the Closed-Loop Bandwidth 76 2.4 Tuning of Decentralized Controllers 76 2.4.1 Introduction 76 2.4.2 Loop Shaping Basics 77 2.

4.3 Tuning of Single-Loop Controllers 79 2.4.3.1 PID Controller Realizations and Common Modifications 79 2.4.3.2 Controller Tuning Using Frequency Analysis 81 2.

4.3.3 Ziegler-Nichols Closed-Loop Tuning Method 86 2.4.3.4 Simple Fitting of a Step Response Model 86 2.4.3.

5 Ziegler-Nichols Open-Loop Tuning 88 2.4.3.6 IMC-PID Tuning 88 2.4.3.7 Simple IMC Tuning 89 2.4.

3.8 The Setpoint Overshoot Method 91 2.4.3.9 Autotuning 95 2.4.3.10 When Should Derivative Action Be Used? 95 2.

4.3.11 Effects of Internal Controller Scaling 96 2.4.3.12 Reverse Acting Controllers 97 2.4.4 Gain Scheduling 97 2.

4.5 Surge Attenuating Controllers 98 2.4.6 Multiloop Controller Tuning 99 2.4.6.1 Independent Design 100 2.4.

6.2 Sequential Design 102 2.4.6.3 Simultaneous Design 103 2.4.7 Tools for Multivariable Loop-Shaping 103 2.4.

7.1 The Performance Relative Gain Array 103 2.4.7.2 The Closed-Loop Disturbance Gain 104 2.4.7.3 Illustrating the Use of CLDG''s for Controller Tuning 104 2.

4.7.4 Unachievable Loop Gain Requirements 107 Problems 108 References 112 3 Control Structure Selection and Plantwide Control 115 3.1 General Approach and Problem Decomposition 115 3.1.1 Top-Down Analysis 115 3.1.1.

1 Defining and Exploring Optimal Operation 115 3.1.1.2 Determining Where to Set the Throughput 116 3.1.2 Bottom-Up Design 116 3.2 Regulatory Control 117 3.2.

1 Example: Regulatory Control of Liquid Level in a Deaeration Tower 118 3.3 Determining Degrees of Freedom 121 3.4 Selection of Controlled Variables 122 3.4.1 Problem Formulation 123 3.4.2 Selecting Controlled Variables by Direct Evaluation of Loss 124 3.4.

3 Controlled Variable Selection Based on Local Analysis 125 3.4.3.1 The Minimum Singular Value Rule 127 3.4.3.2 Desirable Characteristics of the Controlled Variables 128 3.4.

4 An Exact Local Method for Controlled Variable Selection 128 3.4.5 Measurement Combinations as Controlled Variables 130 3.4.5.1 The Nullspace Method for Selecting Controlled Variables 130 3.4.5.

2 Extending the Nullspace Method to Account for Implementation Error 130 3.4.6 The Validity of the Local Analysis for Controlled Variable Selection 131 3.5 Selection of Manipulated Variables 132 3.5.1 Verifying that the Proposed Manipulated Variables Make Acceptable Control Possible 133 3.5.2 Reviewing the Characteristics of the Proposed Manipulated Variables 134 3.

6 Selection of Measurements 135 3.7 Mass Balance Control and Throughput Manipulation 136 3.7.1 Consistency of Inventory Control 138 Problems 140 References 141 4 Limitations on Achievable Performance 143 4.1 Performance Measures 143 4.1.1 Time-Domain Performance Measures 143 4.1.

2 Frequency-Domain Performance Measures 145 4.1.2.1 Bandwidth Frequency 145 4.1.2.2 Peaks of Closed-Loop Transfer Functions 146 4.1.

2.3 Bounds on Weighted System Norms 146 4.1.2.4 Gain and Phase Margin 147 4.2 Algebraic Limitations 148 4.2.1 S + T = I 148 4.

2.2 Interpolation Constraints 148 4.2.2.1 Monovariable Systems 148 4.2.2.2 Multivariable Systems 149 4.

3 Control Performance in Different Frequency Ranges 149 4.3.1 Sensitivity Integrals and Right Half-Plane Zeros 149 4.3.1.1 Multivariable Systems 150 4.3.2 Sensitivity Integrals and Right Half-Plane Poles 150 4.

3.3 Combined Effects of RHP Poles and Zeros 150 4.3.4 Implications of the Sensitivity Integral Results 150 4.4 Bounds on Closed-Loop Transfer Functions 151 4.4.1 The Maximum Modulus Principle 152 4.4.

1.1 The Maximum Modulus Principle 152 4.4.2 Minimum Phase and Stable Versions of the Plant 152 4.4.3 Bounds on S and T 153 4.4.3.

1 Monovariable Systems 153 4.4.3.2 Multivariable Systems 153 4.4.4 Bounds on KS and KSG d 154 4.5 ISE Optimal Control 156 4.6 Bandwidth and Crossover Frequency Limitations 156 4.

6.1 Bounds from ISE Optimal Control 156 4.6.2 Bandwidth Bounds from Weighted Sensitivity Minimization 157 4.6.3 Bound from Negative Phase 158 4.7 Bounds on the Step Response 158 4.8 Bounds for Disturbance Rejection 160 4.

8.1 Inputs for Perfect Control 161 4.8.2 Inputs for Acceptable Control 161 4.8.3 Disturbances and RHP Zeros 161 4.8.4 Disturbances and Stabilization 162 4.

9 Limitations from Plant Uncertainty 164 4.9.1 Describing Uncertainty 165 4.9.2 Feedforward Control and the Effects of Uncertainty 166 4.9.3 Feedback and the Effects of Uncertainty 167 4.9.

4 Bandwidth Limitations from Uncertainty 168 Problems 168 References 170 5 Model-Based Predictive Control 173 5.1 Introduction 173 5.2 Formulation of a QP Problem for MPC 175 5.2.1 Future States as Optimization Variables 179 5.2.2 Using the Model Equation to Substitute for the Plant States 180 5.2.

3 Optimizing Deviations from Linear State Feedback 181 5.2.4 Constraints Beyond the End of the Prediction Horizon 182 5.2.5 Finding the Terminal Constr.