Process Control

B. Wayne Bequette is a Professor of Chemical and Biological Engineering and Technology Manager for the Smart Manufacturing Innovation Center (SMIC) at Rensselaer Polytechnic Institute, where his research efforts are focused on the modeling and control of chemical process, biomedical, biopharma, and food manufacturing systems. He serves as the Board Secretary for the American Automatic Control Council (AACC) and as a Trustee of the Computer Aids for Chemical Engineering (CACHE) Corporation. Dr. Bequette is a founding member of the editorial board of the Journal of Diabetes Science and Technology and serves on the editorial board of Industrial & Engineering Chemistry Research. He is a Fellow of IEEE, AIChE, and the American Institute of Medical and Biological Engineers (AIMBE), and was inducted into the Arkansas Academy of Chemical Engineers. He is the author of Process Control: Modeling, Design, and Simulation, Second Edition, and Process Dynamics: Modeling, Analysis, and Simulation (both from Pearson), and has published 17 book chapters and more than 125 refereed journal articles. While completing a BS in chemical engineering at the University of Arkansas, Dr. Bequette worked at Arkansas Eastman (handling utility and waste treatment problems) and Cosden Oil and Chemical. After his undergraduate studies, he was a process engineer at American Petrofina, where he had the chance to serve as a process operator during two work stoppages. This sparked his interest in process automation and control, enticing him to the University of Texas at Austin to earn a PhD with a focus on multivariable control-system analysis and design. He spent a year as a visiting lecturer at the University of California at Davis before becoming a professor at Rensselaer in 1988. While at Rensselaer, he has had the good fortune to serve as the advisor for 23 PhD students, in addition to teaching chemical process dynamics and control to at least 1500 undergraduate students. His outside interests include bicycling and pole-vaulting.

Preface to the Second Edition xxvii
About the Author xxxiii

Chapter 1: Introduction 1
1.1 Introduction 2
1.2 Instrumentation 14
1.3 Process Models and Dynamic Behavior 15
1.4 Redundancy and Operability 18
1.5 Industrial IoT and Smart Manufacturing 19
1.6 Control Textbooks 21
1.7 A Look Ahead 22
1.8 Summary 22
References 23
Student Exercises 24

Chapter 2: Fundamental Models 31
2.1 Background 32
2.2 Balance Equations 33
2.3 Material Balances 36
2.4 Constitutive Relationships 41
2.5 Material and Energy Balances 44
2.6 Form of Dynamic Models 48
2.7 Linear Models and Deviation Variables 50
2.8 Summary 55
Suggested Reading 57
Student Exercises 57

Chapter 3: Dynamic Behavior 69
3.1 Background 70
3.2 Linear State-Space Models 70
3.3 Laplace Transforms 75
3.4 Transfer Functions 87
3.5 First-Order Behavior 88
3.6 Integrating Behavior 94
3.7 Second-Order Behavior 100
3.8 Summary 107
References 107
Student Exercises 107

Chapter 4: Dynamic Behavior: Complex Systems 115
4.1 Introduction 116
4.2 Poles and Zeros 116
4.3 Lead-Lag Behavior 119
4.4 Processes with Deadtime 120
4.5 Padé Approximation for Deadtime 123
4.6 Converting State-Space Models to Transfer Functions 124
4.7 Converting Transfer Functions to State-Space Models 127
4.8 MATLAB and SIMULINK 128
4.9 Summary 130
Student Exercises 130

Chapter 5: Empirical and Discrete-Time Models 139
5.1 Introduction 140
5.2 First-Order + Deadtime 141
5.3 Integrator + Deadtime 144
5.4 Other Continuous Models 147
5.5 Discrete-Time Autoregressive Models 148
5.6 Parameter Estimation 152
5.7 Discrete Step and Impulse Response Models 156
5.8 Converting Continuous Models to Discrete 158
5.9 Digital Filtering 160
5.10 Summary 163
References 163
Student Exercises 164
Appendix 5.1: Discretization 170

Chapter 6: Introduction to Feedback Control 171
6.1 Motivation 172
6.2 Control Block Diagrams 176
6.3 Closed-Loop Analysis 179
6.4 PID Controller Algorithms 185
6.5 Routh Stability Criterion 192
6.6 Effect of Tuning Parameters 196
6.7 Open-Loop Unstable Systems 197
6.8 SIMULINK Block Diagrams 199
6.9 ODEs to Solve PID Problems 200
6.10 Summary 202
References 205
Student Exercises 205

Chapter 7: Model-Based Control 215
7.1 Introduction 216
7.2 Direct Synthesis 216
7.3 Internal Model Control 218
7.4 IMC-Based PID 223
7.5 IMC-Based PID for Time-Delay Processes 231
7.6 IMC-Based PID for Unstable Processes 237
7.7 Summary 240
References 242
Student Exercises 242
Appendix 7.1: SIMC-Based PID Design 252

Chapter 8: PID Controller Tuning 255
8.1 Introduction 256
8.2 Closed-Loop Oscillation-Based Tuning 257
8.3 Tuning Rules for First-Order + Deadtime Processes 261
8.4 Digital Control 263
8.5 Stability of Digital Control Systems 265
8.6 Performance of Digital Control Systems 267
8.7 Summary 268
References 268
Student Exercises 269

Chapter 9: Frequency-Response Analysis 275
9.1 Motivation 276
9.2 Bode and Nyquist Plots 279
9.3 Effect of Process Parameters on Bode and Nyquist Plots 284
9.4 Closed-Loop Stability 288
9.5 Bode and Nyquist Stability 290
9.6 Robustness 294
9.7 MATLAB Control Toolbox: Bode and Nyquist Functions 295
9.8 Summary 297
Reference 298
Student Exercises 298

Chapter 10: Cascade and Feedforward Control 305
10.1 Background 306
10.2 Introduction to Cascade Control 306
10.3 Cascade-Control Analysis 310
10.4 Cascade-Control Design 312
10.5 Feedforward Control 313
10.6 Feedforward Controller Design 315
10.7 Summary of Feedforward Control 320
10.8 Combined Feedforward and Cascade 321
10.9 Summary 321
References 321
Student Exercises 322

Chapter 11: PID Enhancements 333
11.1 Background 333
11.2 Antireset Windup 334
11.3 Autotuning Techniques 342
11.4 Nonlinear PID Control 347
11.5 Controller Parameter (Gain) Scheduling 348
11.6 Measurement/Actuator Selection 350
11.7 Implementing PID Enhancements in Simulink 351
11.8 Summary 353
References 354
Student Exercises 354

Chapter 12: Ratio, Selective, and Split-Range Control 357
12.1 Motivation 357
12.2 Ratio Control 358
12.3 Selective and Override Control 359
12.4 Split-Range Control 360
12.5 SIMULINK Functions 363
12.6 Summary 364
References 364
Student Exercises 365

Chapter 13: Control-Loop Interaction 371
13.1 Introduction 372
13.2 Motivation 372
13.3 The General Pairing Problem 375
13.4 The Relative Gain Array 382
13.5 Properties and Application of the RGA 385
13.6 Return to the Motivating Example 387
13.7 RGA and Sensitivity 389
13.8 Using the RGA to Determine Variable Pairings 392
13.9 MATLAB RGA Function File 396
13.10 Summary 397
References 398
Student Exercises 398
Appendix 13.1: Derivation of the Relative Gain for an n-Input-n-Output System 404
Appendix 13.2: m-File to Calculate the RGA 406

Chapter 14: Multivariable Control 407
14.1 Background 408
14.2 Zeros and Performance Limitations 408
14.3 Scaling Considerations 412
14.4 Directional Sensitivity and Operability 416
14.5 Block-Diagram Analysis 422
14.6 Decoupling 423
14.7 MATLAB tzero, svd 427
14.8 Summary 430
References 431
Student Exercises 431
Appendix 14.1 433

Chapter 15: Plantwide Control 435
15.1 Background 436
15.2 Steady-State and Dynamic Effects of Recycle 437
15.3 Unit Operations Not Previously Covered 444
15.4 The Control and Optimization Hierarchy 448
15.5 Further Plantwide Control Examples 451
15.6 Simulations 456
15.7 Startup, Safety, and the Human-in-the-Loop 458
15.8 Summary 459
References 460
Student Exercises 461
Appendix 15.1 463

Chapter 16: Model Predictive Control 467
16.1 Motivation 468
16.2 Optimization Problem 468
16.3 Dynamic Matrix Control 471
16.4 Constraints and Multivariable Systems 482
16.5 Other MPC Methods 485
16.6 MATLAB 487
16.7 Summary 487
References and Relevant Literature 488
Student Exercises 489
Appendix 16.1: Derivation of the Step Response Formulation 491
Appendix 16.2: Derivation of the Least-Squares Solution for Control Moves 492
Appendix 16.3: State Space Formulation for MPC 493

Chapter 17: Summary 497
17.1 Overview of Topics Covered in This Textbook 497
17.2 Process Engineering in Practice 502
17.3 Suggested Further Reading 504
Student Exercises 505

Module 1: Introduction to MATLAB 507
M1.1 Background 508
M1.2 Matrix Operations 509
M1.3 The MATLAB Workspace 513
M1.4 Complex Variables 514
M1.5 Plotting 514
M1.6 More Matrix Stuff 517
M1.7 for Loops 519
M1.8 m-Files 520
M1.9 Summary of Commonly Used Commands 523
M1.10 Frequently Used MATLAB Functions 524
Additional Exercises 524

Module 2: Introduction to SIMULINK 527
M2.1 Background 528
M2.2 Open-Loop Simulations 529
M2.3 Feedback-Control Simulations 530
M2.4 Summary 534
Additional Exercises 534

Module 3: Ordinary Differential Equations 537
M3.1 MATLAB ode--Basic 538
M3.2 MATLAB ode--Options 541
M3.3 SIMULINK sfun 541
M3.4 Summary 545
Additional Exercises 545

Module 4: MATLAB LTI Models 547
M4.1 Forming Continuous-Time Models 548
M4.2 Forming Discrete-Time Models 555
M4.3 Converting Continuous Models to Discrete 557
M4.4 Converting Discrete Models to Continuous 558
M4.5 Step and Impulse Responses 558
M4.6 Summary 560
Additional Exercises 561

Module 5: Isothermal Chemical Reactor 563
M5.1 Background 564
M5.2 Model 564
M5.3 Steady-State and Dynamic Behavior 565
M5.4 Closed-Loop Control 569
Reference 571
Additional Exercises 571

Module 6: Biochemical Reactors 573
M6.1 Background 573
M6.2 Steady-State and Dynamic Behavior 575
M6.3 Stable Steady-State Operating Point 577
M6.4 Unstable Steady-State Operating Point 578
M6.5 SIMULINK Model File 580
Reference 581
Additional Exercises 582

Module 7: CSTR 585
M7.1 Background 586
M7.2 Simplified Modeling Equations 586
M7.3 Example Chemical Process--Propylene Glycol Production 590
M7.4 Effect of Reactor Scale 591
M7.5 For Further Study: Detailed Model 594
M7.6 Other Considerations 598
M7.7 Summary 599
References 600
Additional Exercises 601
Appendix M7.1 602

Module 8: Steam Drum Level 605
M8.1 Background 605
M8.2 Process Model 606
M8.3 Feedback Controller Design 607
M8.4 Feedforward Controller Design 609
M8.5 Three-Mode Level Control 609
Appendix M8.1: SIMULINK Diagram for Feedforward/Feedback Control of Steam Drum Level 611
Appendix M8.2: SIMULINK Diagram for Three-Mode Control of Steam Drum Level 612

Module 9: Surge Vessel Level Control 613
M9.1 Background 613
M9.2 Process Model 614
M9.3 Controller Design 614
M9.4 Numerical Example 616
M9.5 Summary 619
Reference 620
Additional Exercises 620
Appendix M9.1: The SIMULINK Block Diagram 621

Module 10: Batch Reactor 623
M10.1 Background 624
M10.2 Batch Model 1: Jacket Temperature Manipulated 625
M10.3 Batch Model 2: Jacket Inlet Temperature Manipulated 629
M10.4 Batch Model 3: Cascade Control 632
M10.5 Summary 633
Reference 634
Additional Exercises 634

Module 11: Biomedical Systems 635
M11.1 Overview 635
M11.2 Pharmacokinetic Models 636
M11.3 Intravenous Delivery of Anesthetic Drugs 637
M11.4 Blood Glucose Control in ICU Patients 638
M11.5 Critical Care Patients 640
M11.6 Summary 641
References 641
Additional Exercises 642

Module 12: Automated Insulin Delivery 643
M12.1 Background: Physiology of Blood Glucose Regulation 644
M12.2 Type 1 Diabetes 644
M12.3 Closed-Loop Components and Diagram 646
M12.4 Simulation Model 648
M12.5 Open-Loop Responses to Meal and Insulin 649
M12.6 Closed-Loop Responses 652
M12.7 Summary 654
References 655
Suggested Further Study 655
Additional Exercises 656

Module 13: Distillation Control 657
M13.1 Description of Distillation Control 658
M13.2 Open-Loop Behavior 659
M13.3 SISO Control 661
M13.4 RGA Analysis 662
M13.5 Multiple SISO Controllers 663
M13.6 Singular Value Analysis 664
M13.7 Nonlinear Effects 667
M13.8 Other Issues in Distillation Column Control 667
M13.9 Summary 668
References 668
Additional Exercises 668

Module 14: Case Study Problems 671
M14.1 Background 671
M14.2 Reactive Ion Etcher 673
M14.3 Rotary Lime Kiln Temperature Control 674
M14.4 Fluidized Catalytic Cracking Unit 674
M14.5 Anaerobic Sludge Digester 675
M14.6 Suggested Case Study Schedule 676
M14.7 Summary 678
Additional Exercises 679

Module 15: Process Monitoring 681
M15.1 Concise Review of Probability 682
M15.2 Statistical Process Control 685
M15.3 Characteristic Process Noise 689
M15.4 Filtering and Smoothing 690
M15.5 Data Reconciliation 690
M15.6 Gross Error Detection 694
M15.7 Summary 696
References 696
Additional Exercises 696
Appendix M15.1 702

Module 16: Safety 705
M16.1 Overview 706
M16.2 Chemical Process Disasters 707
M16.3 Aircraft Disasters 708
M16.4 Fault Detection Algorithms and Safety Science 710
M16.5 Summary 710
References 711
Additional Exercises 713

Index 715