Principles and Practice of Automatic Process Control Third Edition Carlos A. Smith, Ph.D., P.E. Department of Chemical Engineering University of South Florida Armando B. Corripio, Ph.D., P.E. Gordon A. and Mary Cain Department of Chemical Engineering Louisiana State University WILEY John Wiley & Sons, Inc.
1. Introduction 1 1-1 A Process Control System 1 1-2 Important Terms and Objective of Automatic Process Control 3 1-3 Regulatory and Servo Control 4 1-4 Transmission Signals, Control Systems, and Other Terms 5 1-5 Control Strategies 6 1-5.1 Feedback Control 6 1-5.2 Feedforward Control 7 1-6 Background Needed for Process Control 9 1-7 Summary 9 Problems 10 2. Mathematical Tools for Control Systems Analysis 11 2-1 The Laplace Transform 11 2-1.1 Definition of the Laplace Transform 11 2-1.2 Properties of the Laplace Transform 14 2-2 Solution of Differential Equations Using the Laplace Transform 19 2-2.1 Laplace Transform Solution Procedure 19 2-2.2 Inversion by Partial Fractions Expansion 20 2-2.3 Handling Time Delays 24 2-3 Characterization of Process Response 26 2-3.1 Deviation Variables 26 2-3.2 Output Response 27 2-3.3 Stability 33 2-4 Response of First-Order Systems 33 2-4.1 Step Response 35 2-4.2 Ramp Response 36 2-4.3 Sinusoidal Response 36 2-4.4 Response with Time Delay 38 2-4.5 Response of a Lead-Lag Unit 39 2-5 Response of Second-Order Systems 41 2-5.1 Overdamped Responses 42 2-5.2 Underdamped Responses 45 2-5.3 Higher-Order Responses 49 2-6 Linearization 50 2-6.1 Linearization of Functions of One Variable 51 2-6.2 Linearization of Functions of Two or More Variables 53 2-6.3 Linearization of Differential Equations 54 2-7 Summary 57 Problems 57
3. First-Order Dynamic Systems 61 3-1 Processes and Importance of Process Characteristics 61 3-2 Mathematical Process Modeling 63 3-3 Thermal Process Example 67 3-4 Dead Time 75 3-5 Transfer Functions and Block Diagrams 77 3-5.1 Transfer Functions 77 3-5.2 Block Diagrams 79 3-6 Gas Process Example 85 3-7 Chemical Reactors 90 3-7.1 Introductory Remarks 90 3-7.2 Chemical Reactor Example 91 3-8 Effects of Process Nonlinearities 94 3-9 Additional Comments 96 3-10 Summary 98 Problems 99 4. Higher-Order Dynamic Systems 107 4-1 Noninteracting Systems 107 4-1.1 Noninteracting Level Process 107 4-1.2 Thermal Tanks in Series 113 4-2 Interacting Systems 115 4-2.1 Interacting Level Process 115 4-2.2 Thermal Tanks with Recycle 120 4-2.3 Nonisothermal Chemical Reaction 122 4-3 Response of Higher-Order Systems 133 4-4 Other Types of Process Responses 135 4-4.1 Integrating Processes: Level Process 135 4-4.2 Open-Loop Unstable Process: Chemical Reactor 139 4-4.3 Inverse Response Processes: Chemical Reactor 145 4-5 Summary 147 4-6 Overview of Chapters 3 and 4 147 Problems 148 5. Basic Components of Control Systems 154 5-1 Sensors and Transmitters 154 5-2 Control Valves 156 5-2.1 The Control Valve Actuator 157 5-2.2 Control Valve Capacity and Sizing 159 5-2.3 Control Valve Characteristics 164 5-2.4 Control Valve Gain and Transfer Function 170 5-2.5 Control Valve Summary 173 5-3 Feedback Controllers 173 5-3.1 Actions of Controllers 174 5-3.2 Types of Feedback Controllers 175 5-3.3 Modifications to the PID Controller and Additional Comments 186
Contents XÜi 5-3.4 Reset Windup and Its Prevention 189 5-3.5 Feedback Controller Summary 191 5-4 Summary 191 Problems 192 6. Design of Single-Loop Process Control Systems 196 6-1 The Feedback Control Loop 196 6-1.1 Closed-Loop Transfer Function 199 6-1.2 Characteristic Equation of the Loop 204 6-1.3 Steady-State Closed-Loop Response 209 6-2 Stability of the Control Loop 212 6-2.1 Criterion of Stability 213 6-2.2 Direct Substitution Method 214 6-2.3 Effect of Loop Parameters on the Ultimate Gain and Period 217 6-2.4 Effect of Dead Time 218 6-2.5 Summary 220 6-3 Summary 220 Problems 220 7. Tuning of Feedback Controllers 229 7-1 Quarter Decay Ratio Response by Ultimate Gain 230 7-2 Open-Loop Process Characterization 234 7-2.1 Process Step Testing 236 7-2.2 Tuning for Quarter Decay Ratio Response 242 7-2.3 Tuning for Minimum Error Integral Criteria 245 7-2.4 Tuning Sampled-Data Controllers 250 7-2.5 Summary of Controller Tuning 251 7-3 Tuning Controllers for Integrating Processes 251 7-3.1 Model of Liquid Level Control System 252 7-3.2 Proportional Level Controller 254 7-3.3 Averaging Level Control 256 7-3.4 Summary of Tuning for Integrating Processes 258 7-4 Synthesis of Feedback Controllers 258 7-4.1 Development of the Controller Synthesis Formula 258 7-4.2 Specification of the Closed-Loop Response 259 7-4.3 Controller Modes and Tuning Parameters 260 7-4.4 Summary of Controller Synthesis Results 263 7-4.5 Tuning Rules by Internal Model Control (IMC) 265 7-5 Tips for Feedback Controller Tuning 267 7-5.1 Estimating the Reset and Rate Times 268 7-5.2 Adjusting the Proportional Gain 270 7-6 Summary 270 Problems 271 8. Root Locus and Frequency Response Techniques 279 8-1 Some Deflnitions 279 8-2 Analysis of Feedback Control Systems by Root Locus 280
8-3 Plotting Root Locus Diagrams 283 8-4 Analysis of Control Systems by Frequency Response 284 8-4.1 Bode Plots 291 8-4.2 Frequency Response Stability Criterion 298 8-5 Summary 306 Problems 307 9. Cascade Control 310 9-1 A Process Example 310 9-2 Stability Considerations 313 9-3 Implementation and Tuning of Controllers 315 9-3.1 Two-Level Cascade Systems 315 9-3.2 Three-Level Cascade Systems 317 9-4 Other Process Examples 318 9-5 Final Comments 320 9-6 Summary 322 Problems 322 10. Ratio, Override, and Selective Control 326 10-1 Signals, Software, and Computing Algorithms 326 10-1.1 Signals 326 10-1.2 Programming 327 10-1.3 Scaling Computing Algorithms 331 10-2 Ratio Control 333 10-3 Override, or Constraint, Control 340 10-4 Selective Control 344 10-5 Designing Control Systems 346 10-6 Summary 360 Problems 361 11. Feedforward Control 373 11-1 The Feedforward Concept 373 11-2 Block Diagram Design of Linear Feedforward Controllers 375 11-3 Lead-Lag Element 383 11-4 Back to the Previous Example 385 11-5 Design of Nonlinear Feedforward Controllers from Basic Process Principles 389 11-6 Some Closing Comments and Outline of Feedforward Controller Design 393 11-7 Three Other Examples 396 11-8 Summary 402 Problems 403 12. Multivariable Process Control 409 12-1 Loop Interaction 409 12-2 Pairing Controlled and Manipulated Variables 413 12-2.1 Calculating the Relative Gains for a 2 x 2 System 417 12-2.2 Calculating the Relative Gains for annxn System 422
Contents xv 12-3 Decoupling of Interacting Loops 424 12-3.1 Decoupler Design from Block Diagrams 425 12-3.2 Decoupler Design for n x n Systems 432 12-3.3 Decoupler Design from Basic Principles 434 12-4 Multivariable Control versus Optimization 436 12-5 Dynamic Analysis of Multivariable Systems 437 12-5.1 Dynamic Analysis of a 2 x 2 System 437 12-5.2 Controller Tuning for Interacting Systems 441 12-6 Design of Plantwide Control Systems 442 12-7 Summary 448 Problems 449 13. Dynamic Simulation of Control Systems 452 13-1 Uses and Tools of Dynamic Simulation 452 13-1.1 Uses of Dynamic Simulation 453 13-1.2 Tools for Dynamic Simulation 453 13-2 Simulation of Linear Transfer Functions 455 13-3 Process Simulation 457 13-4 Simulation of Control Instrumentation 464 13-4.1 Control Valve Simulation 465 13-4.2 Simulation of Feedback Controllers 467 13-4.3 Simulation of Sensors-Transmitters 471 13-4.4 Simulation of Lead-Lag Dynamic Compensation 472 13-5 Other Simulation Aspects 478 13-6 Summary 485 Problems 485 A. Instrumentation Symbols and Labels 491 B. Design Case Studies 498 Case 1. Methanol Synthesis Process 503 Case 2. Hydrocarbon Process 505 Case 3. Fatty Acid Process 506 Case 4. Control Systems in the Sugar-Refining Process 508 Case 5. Sulfuric Acid Process 509 Case 6. Ammonium Nitrate Prilling Plant Control System 511 Case 7. Natural Gas Dehydration Control System 512 C. Sensors, Transmitters, and Control Valves 514 C-l Pressure Sensors 514 C-2 Flow Sensors 514 C-3 Level Sensors 519 C-4 Temperature Sensors 520 C-5 Composition Sensors 523 C-6 Transmitters 523 C-6.1 Pneumatic Transmitters 523 C-6.2 Electronic Transmitters 524 C-7 Types of Control Valves 525
C-7.1 Reciprocating Stern 525 C-7.2 Rotating Stern 529 C-8 Control Valve Actuators 529 C-8.1 Pneumatically Operated Diaphragm Actuators 529 C-8.2 Piston Actuators 529 C-8.3 Electrohydraulic and Electromechanical Actuators 529 C-8.4 Manual-Handwheel Actuators 530 C-9 Control Valve Accessories 530 C-9.1 Positioners 530 C-9.2 Boosters 532 C-9.3 Limit Switches 532 C-10 Control Valves Additional Considerations 532 C-10.1 Viscosity Corrections 532 C-10.2 Flashing and Cavitation 533 C-ll Summary 536 D. Urning Case Studies 538 Process 1. Regenerator Feedback 538 Process 2. Regenerator Cascade 540 Process 3. Paper-Drying Process 541 Process 4. HCl Scrubber 543 Process 5. Mixing Process 544 Process 6. Reactor Process 547 Process 7. Distillation Process 547 E. Operating Case Studies 548 Index 559 Operating Case Study 1: HCl Scrubber 548 Operating Case Study 2: Water Treatment unit 550 Operating Case Study 3: Catalyst Regenerator 553 Operating Case Study 4: Baby Back Ribs 555 Operating Case Study 5: Paper Drying Unit 556