INCIp PRACTICE OF A PR PROCESSCONT CARL& A. SMIT / ARMAND~ B. Co SELECTED TABLES AND FIGURES TYPICAL RESPONSES Common input signals 13 Stable and unstable responses 34 First-order step response 42 First-order ramp response 44 First-order sinusoidal response 45 Lead-lag step response 41 Lead-lag ramp response 48 Second-order step response 55,56 TRANSFORMS Laplace transforms 15 z-transforms and modified z-transforms 607 TUNING FORMULAS On-line quarter decay ratio 306 Open-loop quarter decay ratio 320 Minimum error integral for disturbance 324 Minimum error integral for set point 325 Controller synthesis (IMC) rules 345 Computer PID control algorithms 666 Dead time compensation algorithms 675 INSTRUMENTATION ISA standard instrumentation symbols and labels Control valve inherent characteristics Control valve installed characteristics Flow sensors and their characteristics Temperature sensors and their characteristics Classification of filled-system thermometers Thermocouple voltage versus temperature Valve capacity (Cv) coefficients 699-706 211 217 724-725 736-737 739 740 754-755 BLOCK DIAGRAMS Rules 98 Feedback loop 254 Unity feedback loop 257 Temperature control loop 261 Flow control loop 268 Pressure control loop 281 Level control loop 333 Multivariable (2 X 2) control loop 565 Decoupled multivariable (2 X 2) system 566 Sampled data control loop 630 Smith predictor 679 Internal Model Control (IMC) 680 Dynamic Matrix Control (DMC) 689 Principles and Practice of Automatic Process Control Second Edition Carlos A. Smith, Ph.D., P.E. University of South Florida Armando B. Corripio, Ph.D., P.E. Louisiana State University John Wiley & Sons, Inc. New York l Chichester l Weinheim l Brisbane l Singapore l Toronto This work is dedicated with all our love to The Lord our God, for all his daily blessings made this book possible The Smiths: Cristina, Carlos A. Jr., Tim, Cristina M., and Sophia C. Livingston, and Mrs. Rene M. Smith, my four grandsons: Nicholas, Robert, Garrett and David and to our dearest homeland, Cuba Preface This edition is a major revision and expansion to the first edition. Several new subjects have been added, notably the z-transform analysis and discrete controllers, and several other subjects have been reorganized and expanded. The objective of the book, however, remains the same as in the first edition, “to present the practice of automatic process control along with the fundamental principles of control theory.” A significant number of applications resulting from our practice as part-time consultants have also been added to this edition. Twelve years have passed since the first edition was published, and even though the principles are still very much the same, the “tools” to implement the controls strategies have certainly advanced. The use of computer-based instrumentation and control sys- tems is the norm. Chapters 1 and 2 present the definitions of terms and mathematical tools used in process control. In this edition Chapter 2 stresses the determination of the quantitative characteristics of the dynamic response, settling time, frequency of oscillation, and damping ratio, and de-emphasizes the exact determination of the analytical response. In this way the students can analyze the response of a dynamic system without having to carry out the time-consuming evaluation of the coefficients in the partial fraction expansion. Typical responses of first-, second-, and higher-order systems are now pre- sented in Chapter 2. The derivation of process dynamic models from basic principles is the subject of Chapters 3 and 4. As compared to the first edition, the discussion of process modelling has been expanded. The discussion, meaning, and significance of process nonlinearities has been expanded as well. Several numerical examples are presented to aid in the understanding of this important process characteristic. Chapter 4 concludes with a pre- sentation of integrating, inverse-response, and open-loop unstable processes. Chapter 5 presents the design and characteristics of the basic components of a control system: sensors and transmitters, control valves, and feedback controllers. The presen- tation of control valves and feedback controllers has been expanded. Chapter 5 should be studied together with Appendix C where practical operating principles of some common sensors, transmitters, and control valves are presented. The design and tuning of feedback controllers are the subjects of Chapters 6 and 7. Chapter 6 presents the analysis of the stability of feedback control loops. In this edition we stress the direct substitution method for determining both the ultimate gain and period of the loop. Routh’s test is deemphasized, but still presented in a separate section. In keeping with the spirit of Chapter 2, the examples and problems deal with the de- termination of the characteristics of the response of the closed loop, not with the exact analytical response of the loop. Chapter 7 keeps the same tried-and-true tuning methods from the first edition. A new section on tuning controllers for integrating processes, and a discussion of the Internal Model Control (IMC) tuning rules, have been added. Chapter 8 presents the root locus technique, and Chapter 9 presents the frequency response techniques. These techniques are principally used to study the stability of control systems. V vi Preface The additional control techniques that supplement and enhance feedback control have been distributed among Chapters 10 through 13 to facilitate the selection of their cov- erage in university courses. Cascade control is presented first, in Chapter 10, because it is so commonly a part of the other schemes. Several examples are presented to help understanding of this important and common control technique. Chapter 11 presents different computing algorithms sometimes used to implement control schemes. A method to scale these algorithms, when necessary, is presented. The chapter also presents the techniques of override, or constraint, control, and selective control. Examples are used to explain the meaning and justification of them. Chapter 12 presents and discusses in detail the techniques of ratio and feedforward control. Industrial examples are also presented. A significant number of new problems have been added. Multivariable control and loop interaction are the subjects of Chapter 13. The cal- culation and interpretation of the relative gain matrix (RGM) and the design of de- couplers, are kept from the first edition. Several examples have been added, and the material has been reorganized to keep all the dynamic topics in one section. Finally Chapters 14 and 15 present the tools for the design and analysis of sampled- data (computer) control systems. Chapter 14 presents the z-transform and its use to analyze sampled-data control systems, while Chapter 15 presents the design of basic algorithms for computer control and the tuning of sampled-data feedback controllers. The chapter includes sections on the design and tuning of dead-time compensation algorithms and model-reference control algorithms. Two examples of Dynamic Matrix Control (DMC) are also included. As in the first edition, Appendix A presents some symbols, labels, and other notations commonly used in instrumentation and control diagrams. We have adopted throughout the book the ISA symbols for conceptual diagrams which eliminate the need to differ- entiate between pneumatic, electronic, or computer implementation of the various con- trol schemes. In keeping with this spirit, we express all instrument signals in percent of range rather than in mA or psig. Appendix B presents several processes to provide the student/reader an opportunity to design control systems from scratch. During this edition we have been very fortunate to have received the help and en- couragement of several wonderful individuals. The encouragement of our students, especially Daniel Palomares, Denise Farmer, Carl Thomas, Gene Daniel, Samuel Pee- bles, Dan Logue, and Steve Hunter, will never be forgotten. Thanks are also due to Dr. Russell Rhinehart of Texas Tech University who read several chapters when they were in the initial stages. His comments were very helpful and resulted in a better book. Professors Ray Wagonner, of Missouri Rolla, and G. David Shilling, of Rhode Island, gave us invaluable suggestions on how to improve the first edition. To both of them we are grateful. We are also grateful to Michael R. Benning of Exxon Chemical Amer- icas who volunteered to review the manuscript and offered many useful suggestions from his industrial background. In the preface to the first edition we said that “To serve as agents in the training and development of young minds is certainly a most rewarding profession.” This is still our conviction and we feel blessed to be able to do so. It is with this desire that we have written this edition. CARLOSA.SMITH Tampa, Florida, 1997 ARMANDOB.CORRIPIO Baton Rouge, Louisiana, 1997 Contents Chapter 1 Introduction l-l 1-2 1-3 1-4 1-5 1-6 1-7 A Process Control System 1 Important Terms and the Objective of Automatic Process Control Regulatory and Servo Control 4 Transmission Signals, Control Systems, and Other Terms 5 Control Strategies 6 1-5.1 Feedback Control 6 1-5.2 Feedforward Control 7 Background Needed for Process Control 9 Summary 9 Problems 9 3 1 Chapter 2 Mathematical Tools for Control Systems Analysis 2-1 The Laplace Transform 11 2- 1.1 Definition of the Laplace Transform 12 2-1.2 Properties of the Laplace Transform 14 2-2 Solution of Differential Equations Using the Laplace Transform 21 2-2.1 Laplace Transform Solution Procedure 21 2-2.2 Inversion by Partial Fractions Expansion 23 2-2.3 Handling Time Delays 27 2-3 Characterization of Process Response 30 2-3.1 Deviation Variables 3 1 2-3.2 Output Response 32 2-3.3 Stability 39 2-4 Response of First-Order Systems 39 2-4.1 Step Response 41 2-4.2 Ramp Response 43 2-4.3 Sinusoidal Response 43 2-4.4 Response with Time Delay 45 2-4.5 Response of a Lead-Lag Unit 46 2-5 Response of Second-Order Systems 48 2-5.1 Overdamped Responses 50 2-5.2 Underdamped Responses 53 2-5.3 Higher-Order Responses 57 2-6 Linearization 59 2-6.1 Linearization of Functions of One Variable 60 2-6.2 Linearization of Functions of Two or More Variables 62 2-6.3 Linearization of Differential Equations 65 2-7 Review of Complex-Number Algebra 68 2-7.1 Complex Numbers 68 2-7.2 Operations with Complex Numbers 70 11 vii viii Contents 2-8 Summary 74 Problems 74 Chapter 3 First-Order Dynamic Systems 80 3-1 3-2 3-3 3-4 3-5 3-6 3-7 3-8 3-9 Processes and the Importance of Process Characteristics Thermal Process Example 82 Dead Time 92 Transfer Functions and Block Diagrams 95 3-4.1 Transfer Functions 95 3-4.2 Block Diagrams 96 Gas Process Example 104 Chemical Reactors 109 3-6.1 Introductory Remarks 109 3-6.2 Chemical Reactor Example 111 Effects of Process Nonlinearities 114 Additional Comments 117 Summary 119 Problems 120 81 Chapter 4 Higher-Order Dynamic Systems 4-1 Noninteracting Systems 135 4- 1.1 Noninteracting Level Process 135 4- 1.2 Thermal Tanks in Series 142 4-2 Interacting Systems 145 4-2.1 Interacting Level Process 145 4-2.2 Thermal Tanks with Recycle 151 4-2.3 Nonisothermal Chemical Reactor 154 4-3 Response of Higher-Order Systems 164 4-4 Other Types of Process Responses 167 4-4.1 Integrating Processes: Level Process 168 4-4.2 Open-Loop Unstable Process: Chemical Reactor 172 4-4.3 Inverse Response Processes: Chemical Reactor 179 4-5 Summary 181 4-6 Overview of Chapters 3 and 4 182 Problems 183 Chapter 5 Basic Components of Control Systems 5-1 Sensors and Transmitters 197 5-2 Control Valves 200 5-2.1 The Control Valve Actuator 200 5-2.2 Control Valve Capacity and Sizing 202 5-2.3 Control Valve Characteristics 210 5-2.4 Control Valve Gain and Transfer Function 216 5-2.5 Control Valve Summary 222 5-3 Feedback Controllers 222 5-3.1 Actions of Controllers 223 135 197 Contents ix 5-4 5-3.2 Types of Feedback Controllers 225 5-3.3 Modifications to the PID Controller and Additional Comments 5-3.4 Reset Windup and Its Prevention 241 5-3.5 Feedback Controller Summary 244 Summary 244 Problems 245 238 Chapter 6 Design of Single-Loop Feedback Control Systems 252 6-1 The Feedback Control Loop 252 6- 1.1 Closed-Loop Transfer Function 255 6-1.2 Characteristic Equation of the Loop 263 6-1.3 Steady-State Closed-Loop Gains 270 6-2 Stability of the Control Loop 274 6-2.1 Criterion of Stability 274 6-2.2 Direct Substitution Method 275 6-2.3 Effect of Loop Parameters on the Ultimate Gain and Period 283 6-2.4 Effect of Dead Time 285 6-2.5 Routh’s Test 287 6-3 Summary 290 Problems 290 Chapter 7 Tuning of Feedback Controllers 303 7-1 7-2 7-3 7-4 7-5 7-6 Quarter Decay Ratio Response by Ultimate Gain 304 Open-Loop Process Characterization 308 7-2.1 Process Step Testing 310 7-2.2 Tuning for Quarter Decay Ratio Response 319 7-2.3 Tuning for Minimum Error Integral Criteria 321 7-2.4 Tuning Sampled-Data Controllers 329 7-2.5 Summary of Controller Tuning 330 Tuning Controllers for Integrating Processes 331 7-3.1 Model of Liquid Level Control System 331 7-3.2 Proportional Level Controller 334 7-3.3 Averaging Level Control 336 7-3.4 Summary 337 Synthesis of Feedback Controllers 337 7-4.1 Development of the Controller Synthesis Formula 337 7-4.2 Specification of the Closed-Loop Response 338 7-4.3 Controller Modes and Tuning Parameters 339 7-4.4 Summary of Controller Synthesis Results 344 7-4.5 Tuning Rules by Internal Model Control (IMC) 350 Tips for Feedback Controller Tuning 351 7-5.1 Estimating the Integral and Derivative Times 352 7-5.2 Adjusting the Proportional Gain 354 Summary 354 Problems 355 x Contents Chapter 8 Root Locus 368 8-1 8-2 8-3 8-4 Some Definitions 368 Analysis of Feedback Control Systems by Root Locus Rules for Plotting Root Locus Diagrams 375 Summary 385 Problems 386 370 Chapter 9 Frequency Response Techniques 9-1 Frequency Response 389 9- 1.1 Experimental Determination of Frequency Response 389 9-1.2 Bode Plots 398 9-2 Frequency Response Stability Criterion 407 9-3 Polar Plots 419 9-4 Nichols Plots 427 9-5 Pulse Testing 427 9-5.1 Performing the Pulse Test 428 9-5.2 Derivation of the Working Equation 429 9-5.3 Numerical Evaluation of the Fourier Transform Integral 431 9-6 Summary 434 Problems 434 Chapter 10 Cascade Control 10-1 A Process Example 439 10-2 Stability Considerations 442 10-3 Implementation and Tuning of Controllers 445 10-3.1 Two-Level Cascade Systems 446 10-3.2 Three-Level Cascade Systems 449 10-4 Other Process Examples 450 10-5 Further Comments 452 10-6 Summary 453 Problems 454 Chapter 11 Override and Selective Control 11-1 Computing Algorithms 460 1 1 - 1.1 Scaling Computing Algorithms 464 1 l-l.2 Physical Significance of Signals 469 11-2 Override, or Constraint, Control 470 11-3 Selective Control 475 11-4 Summary 479 Problems 479 Chapter 12 Ratio and Feedforward Control 12-1 Ratio Control 487 12-2 Feedforward Control 494 389 439 460 487 [...]... the successful practice of automatic process control The book is full of actual cases drawn from our years of industrial experience as full-time practitioners or part-time consultants We sincerely hope that you get excited about studying automatic process control It is a very dynamic, challenging, and rewarding area of process engineering l-l A PROCESS CONTROL SYSTEM To illustrate process control, let... of the basic principles mentioned in the previous paragraph and of mathematics through differential equations Laplace transforms are used heavily in process control This greatly simplifies the solution of differential equations and the dynamic analysis of processes and their control systems Chapter 2 of this book is devoted to the development and use of the Laplace transforms, along with a review of. .. principles of process engineering Therefore, this book assumes that the reader is familiar with the basic principles of thermodynamics, fluid flow, heat transfer, separation processes, reaction processes, and the like For the study of process control, it is also fundamental to understand how processes behave dynamically Thus it is necessary to develop the set of equations that describes different processes... sensor/ transmitter, controller, and final control element The most common types of signalspneumatic, electrical, and digital-were introduced, along with the purpose of transducers Two control strategies were presented: feedback and feedforward control The advantages and disadvantages of both strategies were briefly discussed Chapters 6 and 7 present the design and analysis of feedback control loops PROBLEMS... Chapters 3 and 4 offer an introduction to the modeling of some processes 1-7 SUMMARY In this chapter, we discussed the need for automatic process control Industrial processes are not static but rather very dynamic; they are continuously changing as a result of many types of disturbances It is principally because of this dynamic nature that control systems are needed to continuously and automatically... the variables that must be controlled The working principles of a control system can be summarized with the three letters M, D, and A M refers to the measurement of process variables D refers to the decision made on the basis of the measurement of those process variables Finally, A refers to the action taken on the basis of that decision The fundamental components of a process control system were also... fact, most controllers are microprocessor-based Chapter 5 presents different types of controllers and defines some terms related to controllers and control systems I/P Figure 1-4.1 I/P transducer /, I/ // I, // /I ) 6 Chapter 1 Introduction 1-5 CONTROL STRATEGIES 1-5.1 Feedback Control The control scheme shown in Fig l-l.2 is referred to as feedback control and is also called afeedback control. .. meant by automatic process control To achieve automatic process control, a control system must be designed and implemented A possible control system for our heat exchanger is shown in Fig 1-1.2 (Ap- Steam return Figure l-l.2 Heat exchanger control system 1-2 Important Terms and the Objective of Automatic Process Control 3 pendix A presents the symbols and identifications for different devices.) The... of the process to be controlled Once these characteristics are known, the control system can be designed and the controller tuned Process characteristics are explained in Chapters 3 and 4, Chapter 5 presents the meaning of the three terms in the controllers, and Chapter 7 explains how to tune them 14.2 Feedforward Control Feedback control is the most common control strategy in the process industries... popularity In some processes, however, feedback control may not provide the required control performance For these processes, other types of control strategies may have to be designed Chapters 10, 11, 12, 13, and 15 present additional control strategies that have proved profitable One such strategy is feedforward control The objective of feedforward control is to measure disturbances and compensate for