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 chi2 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