Process Control

Preface x

About the Author xv

1. Introduction 1

2. Process Dynamics 3

2.1 Definition 3

2.2 Cascade Control 10

2.3 Model Identification 12

2.4 Integrating Processes 26

2.5 Other Types of Process 29

2.6 Robustness 31

3. PID Algorithm 35

3.1 Definitions 35

3.2 Proportional Action 36

3.3 Integral Action 41

3.4 Derivative Action 43

3.5 Versions of Control Algorithm 49

3.6 Interactive PID Controller 51

3.7 Proportional-on-PV Controller 56

3.8 Nonstandard Algorithms 64

3.9 Tuning 65

3.10 Ziegler-Nichols Tuning Method 66

3.11 Cohen-Coon Tuning Method 72

3.12 Tuning Based on Penalty Functions 73

3.13 Manipulated Variable Overshoot 77

3.14 Lambda Tuning Method 80

3.15 IMC Tuning Method 80

3.16 Choice of Tuning Method 83

3.17 Suggested Tuning Method for Self-Regulating Processes 84

3.18 Tuning for Load Changes 87

3.19 Tuning for SP Ramps 89

3.20 Tuning for Unconstrained MV Overshoot 91

3.21 PI Tuning Compared to PID Tuning 92

3.22 Tuning for Large Scan Interval 94

3.23 Suggested Tuning Method for Integrating Processes 97

3.24 Measure of Robustness 99

3.25 Implementation of Tuning 100

3.26 Tuning Cascades 101

3.27 Loop Gain 104

3.28 Adaptive Tuning 105

3.29 Initialisation 106

3.30 Anti-Reset Windup 108

3.31 On-Off Control 109

4. Level Control 112

4.1 Use of Cascade Control 112

4.2 Parameters Required for Tuning Calculations 113

4.3 Tight Level Control 120

4.4 Averaging Level Control 122

4.5 Error-Squared Controller 129

4.6 Gap Controller 132

4.7 Impact of Noise on Averaging Control 134

4.8 Potential Disadvantage of Averaging Level Control 136

4.9 General Approach to Tuning 137

4.10 Three-Element Level Control 139

5. Signal Conditioning 143

5.1 Instrument Linearisation 143

5.2 Process Linearisation 145

5.3 Control of pH 147

5.4 Constraint Conditioning 151

5.5 Pressure Compensation of Distillation Tray Temperature 153

5.6 Compensation of Gas Flow Measurement 153

5.7 Filtering 155

5.8 Exponential Filter 157

5.9 Nonlinear Exponential Filter 161

5.10 Moving Average Filter 161

5.11 Least Squares Filter 163

5.12 Tuning the Filter 169

5.13 Control Valve Characterisation 170

5.14 Equal Percentage Valve 172

5.15 Split-Range Valves 178

6. Feedforward Control 184

6.1 Ratio Algorithm 185

6.2 Bias Algorithm 188

6.3 Deadtime and Lead-Lag Algorithms 190

6.4 Tuning 194

6.5 Laplace Derivation of Dynamic Compensation 199

7. Deadtime Compensation 201

7.1 Smith Predictor 201

7.2 Internal Model Control 206

7.3 Dahlin Algorithm 206

8. Multivariable Control 210

8.1 Constraint Control 210

8.2 SISO Constraint Control 211

8.3 Signal Selectors 213

8.4 Relative Gain Analysis 217

8.5 Niederlinski Index 226

8.6 Condition Number 227

8.7 Steady State Decoupling 229

8.8 Dynamic Decoupling 231

8.9 MPC Principles 237

8.10 Parallel Coordinates 239

8.11 Enhanced Operator Displays 240

8.12 MPC Performance Monitoring 242

9. Inferentials and Analysers 248

9.1 Inferential Properties 248

9.2 Assessing Accuracy 256

9.3 Laboratory Update of Inferential 262

9.4 Analyser Update of Inferential 266

9.5 Monitoring On-Stream Analysers 268

10. Combustion Control 270

10.1 Fuel Gas Flow Correction 270

10.2 Measuring NHV 278

10.3 Dual Firing 280

10.4 Heater Inlet Temperature Feedforward 281

10.5 Fuel Pressure Control 284

10.6 Firebox Pressure 287

10.7 Combustion Air Control 288

10.8 Boiler Control 299

10.9 Fired Heater Pass Balancing 300

11. Compressor Control 306

11.1 Polytropic Head 306

11.2 Load Control (Turbo-Machines) 310

11.3 Load Control (Reciprocating Machines) 314

11.4 Anti-Surge Control 315

12. Distillation Control 322

12.1 Key Components 325

12.2 Relative Volatility 325

12.3 McCabe-Thiele Diagram 328

12.4 Cut and Separation 333

12.5 Effect of Process Design 345

12.6 Basic Controls 350

12.7 Pressure Control 350

12.8 Level Control 364

12.9 Tray Temperature Control 382

12.10 Pressure Compensated Temperature 393

12.11 Inferentials 402

12.12 First-Principle Inferentials 411

12.13 Feedforward on Feed Rate 413

12.14 Feed Composition Feedforward 416

12.15 Feed Enthalpy Feedforward 418

12.16 Decoupling 419

12.17 Multivariable Control 424

12.18 On-Stream Analysers 433

12.19 Towers with Sidestreams 433

12.20 Column Optimisation 435

12.21 Optimisation of Column Pressure 438

12.22 Energy/Yield Optimisation 441

13. APC Project Execution 444

13.1 Benefits Study 444

13.2 Benefit Estimation for Improved Regulatory Control 445

13.3 Benefits of Closed-Loop Real-Time Optimisation 455

13.4 Basic Controls 458

13.5 Basic Control Monitoring 459

13.6 Inferential Properties 464

13.7 Organisation 464

13.8 Vendor Selection 468

13.9 Safety in APC Design 471

13.10 Alarms 471

14. Statistical Methods 473

14.1 Central Limit Theorem 473

14.2 Generating a Normal Distribution 475

14.3 Quantile Plots 477

14.4 Calculating Standard Deviation 478

14.5 Skewness and Kurtosis 480

14.6 Correlation 480

14.7 Confidence Interval 481

14.8 Westinghouse Electric Company Rules 484

14.9 Gamma Function 485

14.10 Student t Distribution 486

14.11 ¿2 Distribution 489

14.12 F Distribution 492

14.13 Akaike Information Criterion 497

14.14 Adjusted R² 499

14.15 Levene's Test 500

14.16 Box-Wetz Ratio 501

14.17 Regression Analysis 502

14.18 Outliers 513

14.19 Model Identification 514

14.20 Autocorrelation and Autocovariance 518

14.21 Artificial Neural Networks 527

14.22 Repeatability 533

14.23 Reproducibility 533

14.24 Six-Sigma 535

14.25 Data Reconciliation 535

15. Mathematical Techniques 540

15.1 Fourier Transform 540

15.2 Recursive Filters 548

15.3 Lagrangian Interpolation 553

15.4 Padé Approximation 557

15.5 Laplace Transform Derivations 560

15.6 Laplace Transforms for Processes 563

15.7 Laplace Transforms for Controllers 569

15.8 I-PD versus PI-D Algorithm 572

15.9 Direct Synthesis 573

15.10 Predicting Filter Attenuation 578

15.11 Stability Limit for PID Control 579

15.12 Ziegler-Nichols Tuning from Process Dynamics 583

15.13 Partial Fractions 586

15.14 z-Transforms and Finite Difference Equations 588

References 594

Index 596