Principles and Practice of Automatic Process Control

782 Pages·2002·17.98 MB·English

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PRACTICE OF A
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CARL& A. SMIT
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SELECTED TABLES AND FIGURES
TYPICAL RESPONSES
Common input s ignals 1 3
Stable and unstable responses 3 4
First-order step response 42
First-order ramp response 44
First-order sinusoidal response 4 5
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 699-706
labels
Control valve inherent characteristics 211
Control valve installed characteristics 217
Flow sensors and their characteristics 724-725
Temperature sensors and their 736-737
characteristics
Classification of filled-system thermometers 739
Thermocouple voltage versus temperature 740
Valve capacity (Cv) coefficients 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 � Chichester � Weinheim � Brisbane � Singapore � 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 1
l - l A Process Control System 1
1-2 Important Terms and the 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 S u m m a r y 9
P r o b l e m s 9
Chapter 2 Mathematical Tools for Control Systems Analysis 11
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 S tab i l i t y 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
vi i
viii Contents
2-8 S u m m a r y 7 4
Prob lems 74
Chapter 3 First-Order Dynamic Systems 80
3-1 Processes and the Importance of Process Characteristics 81
3-2 Thermal Process Example 82
3-3 Dead Time 92
3-4 Transfer Functions and Block Diagrams 95
3-4.1 Transfer Functions 95
3-4.2 Block Diagrams 96
3-5 Gas Process Example 104
3-6 Chemical Reactors 109
3-6.1 Introductory Remarks 109
3-6.2 Chemical Reactor Example 111
3-7 Effects of Process Nonlinearities 114
3-8 Additional Comments 117
3-9 Summary 119
Problems 120
Chapter 4 Higher-Order Dynamic Systems 1 3 5
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
Prob lems 183
Chapter 5 Basic Components of Control Systems 1 9 7
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
Contents ix
5-3.2 Types of Feedback Controllers 225
5-3.3 Modifications to the PID Controller and Additional Comments 238
5-3.4 Reset Windup and Its Prevention 241
5-3.5 Feedback Controller Summary 244
5-4 Summary 244
Prob lems 245
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
Prob lems 290
Chapter 7 Tuning of Feedback Controllers 303
7-1 Quarter Decay Ratio Response by Ultimate Gain 304
7-2 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
7-3 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
7-4 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
7-5 Tips for Feedback Controller Tuning 351
7-5.1 Estimating the Integral and Derivative Times 352
7-5.2 Adjusting the Proportional Gain 354
7-6 Summary 354
Problems 355
x Contents
Chapter 8 Root Locus 368
8-1 Some Definitions 368
8-2 Analysis of Feedback Control Systems by Root Locus 370
8-3 Rules for Plotting Root Locus Diagrams 375
8-4 Summary 385
Prob lems 386
Chapter 9 Frequency Response Techniques 389
9-1 Frequency Response 389
9- 1.1 Experimental Determination of Frequency Response 389
9-1 .2 Bode P lo t s 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
Prob lems 434
Chapter 10 Cascade Control 4 3 9
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
Prob lems 454
Chapter 11 Override and Selective Control 460
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
Prob lems 479
Chapter 12 Ratio and Feedforward Control 4 8 7
12-1 Ratio Control 487
12-2 Feedforward Control 494