Process Dynamics and Control (2007 Edition) (Hardbound) By K. T. Jadhav Size : B5, Pages: 428; Price : Rs. 390.00 Buy this book from : www.chinttanpublications.in

2. i
PROCESS
DYNAMICS
AND
CONTROL
Mr. K. T. Jadhav
B. Tech (Petrochemical Engineering ) Dr. B. A. Tech. University, Lonere.
M.E. (Chemical Engineering) M. S. University, Baroda.
Presently Head and Assistant Professor, Department of Chemical Engineering ,
D. Y. Patil College of Engineering and Technology, Kolhapur.
CHINTTAN PUBLICATIONS
4/8, Anandnagar, Paud Road, Kothrud, Pune-411038.

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First Indian Edition 2006
This Book contains information obtained from authentic and highly regarded resources. Reprinted Material is quoted with permission,
and resources are indicated. A wide variety of references are listed. Reasonable efforts have been made to publish reliable data and
information, but the author and the publisher cannot assume responsibility for the validity of all materials or for the consequences of
their use.
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The Indian Edition : Rs. 390.00
PROCESS DYNAMICS and CONTROL 1st Edition
By K. T. Jadhav
© 2006, Chinttan Publications
4/8, Anandnagar, Paud Road, Kothrud , Pune – 411038. Mobile: 8888101055,9226269333. E-mail: chinttanpublications@gmail.com
and Printed in Pune.

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PREFACE
This book has the aims of:
 To provide fundamentals of Process Dynamics and Process Control.
 This book is written in such a simple and easy way to understand the language,
so students will not only understand it completely but also they will enjoy its
reading.
 Each chapter contains simple theory, carefully selected examples and various
exercises to ensure that students clear understanding of the concept and its
applications.
 Reasonable Efforts have taken to make this book simple, clear and focused.
 This book covers entire syllabus of process dynamics and control.
 There is a thorough coverage of topics like dynamic behaviour of various
systems, transfer functions, basic mechanism of control system, control
aspects, controllers, control valves and stability analysis of given control
system by Routh test, Root locus method and Bode Diagram, etc.
Courses for which suitable
The book more than covers the Process control related part of the Diploma /
Bachelors / Masters Degree in Chemical, Engineering, Instrumentation Engineering
Petrochemical Engineering, Polymer Technology, Petroleum Engineering, Bio-
Technology and Instrument Technology. It is also seen as being of value to students of
MSc, BSc, Instrumentation and Technology Science.
Background knowledge assumed
A basic knowledge of science and mathematics has been assumed. The science
required is basic physical science. Key elements of science are developed in
appropriate chapters. The mathematics required is just the ability to handle the
numbers, integration, summation, interpret graphs and in a few instances handle
simple algebraic equation.
Mr. K. T. Jadhav

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ACKNOWLEGEMENT
I would like to give my deep sense of gratitude to the Chairman Hon’ble Sanjay D. Patil,
Principal Dr. A. N. Chapgaon, Director Bridg. U. D. Thorat and Director of Admin. Col. S. K.
Joshi for constant encouragement and support. I am also thankful to my colleagues and friends for
timely help and support which encourage me to write this book.
I give special thanks to my Publisher Mr. Chintan Dewalia, Mr.Vinod Kapse and his staff
of Centre: Technical Co-ordination for their countless efforts and support for bringing this book
with great care and innovative ideas.
Suggestion from readers will be highly appreciated.
K. T. Jadhav

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Dedicated to...
My Parents
and
My Wife

7. TABLE OF CONTENTS
vi
TABLE OF CONTENTS
CHAPTER 1 - BASIC PRINCIPLES OF PROCESS CONTROL 1-28
1.1 Historical background 1
1.2 Process control system 2
1.3 Languages of process control 3
1.4 Basic principles and objectives of process control 4
1.5 Laplace transform 5
1.6 Forcing functions 9
1.7 Initial and final value theorem 13
1.8 Process modeling and analysis 14
1.9 Formulating process models 15
1.10 State space model 16
1.11 Transfer functions model 17
Solved Problems – 1.1 to 1.7 19
Unsolved Problems 27
CHPATER 2 - FIRST ORDER SYSTEMS 29-62
2.1 Mercury in glass thermometer 29
2.2 Transfer function 32
2.3 Time constant 33
2.4 Transient response of first order system 34
Solved Problems – 2.1 to 2.6 46
Unsolved Problems 62

8. PROCESS DYNAMICS AND CONTROLS
vii
CHAPTER 3 - PHYSICAL EXAMPLES OF FIRST ORDER SYSTEMS 63-126
3.1 Single liquid level system 63
3.2 Single liquid level system with constant outlet 66
3.3 Resistance – capacitance system 67
3.4 Mixing process 70
3.5 Constant stirred tank heater 72
3.6 First order systems are in series 74
3.7 Generalization of non interacting systems in series 81
3.8 Linearization of non linear systems 83
3.9 Transportation lag or dead time 86
3.10 Comparison between non interacting and interacting system 88
Solved Problems – 3.1 to 3.11 89
Unsolved Problems 124
CHAPTER 4 - SECOND ORDER SYSTEM 127-156
4.1 U tube manometer 127
4.2 Damped vibrator 130
4.3 Damped coefficient 133
4.4 Transient response for second order system 134
4.5 Characteristics of under damped system for step change 140
4.6 Comparison of first order system and second order system 143
Solved Problems – 4.1 to 4.4 144
Unsolved Problem 154
CHAPTER 5 - MECHANISM OF CONTROL SYSTEM 157-178
5.1 Control system for continuous stirred tank heater 157

9. TABLE OF CONTENTS
viii
5.2 Block diagram of the control system 158
5.3 Feedback control systems 160
5.4 Servo & regulator control problems 161
5.5 Development of block diagram 163
Solved Problem – 5.1 to 5.2 168
CHAPTER 6 - FINAL CONTROL ELEMENT & CONTROLLERS 179-212
6.1 Pneumatic control valves 179
6.2 Valve characteristics 181
6.3 Valve sizing 182
6.4 Valve positioners 183
6.5 Transfer functions for the control valve 185
6.6 Control hardware for temperature of leaving stream through heat exchanger 188
6.7 Controllers 190
6.8 Comparison of the controllers 194
6.9 Applications of the controllers 196
6.10 Chemical reactor control system 197
Solved Problems – 6.1 to 6.5 201
Unsolved Problems 211
CHAPTER 7 - OVERALL TRANSFER FUNCTION 213-228
7.1 Open loop & closed loop transfer function 213
7.2 Overall transfer functions for change in set point 214
7.3 Overall transfer function for change in load variable 216
Solved Problems – 7.1 to 7.6 218
Unsolved Problems 227

10. PROCESS DYNAMICS AND CONTROLS
ix
CHAPTER 8 - TRANSIENT RESPONSE OF CONTROL SYSTEMS 229-258
8.1 Offset 229
8.2 Proportional controller for servo mechanism control problem 230
8.3 Proportional controller for regulator mechanism control problem 232
8.4 Proportional integral controller for servo mechanism control problem 234
8.5 Proportional integral controller for regulator mechanism control problem 236
8.6 Proportional derivative controller for servo mechanism control problem 238
8.7 Proportional derivative controller for regulator mechanism control problem 241
8.8 PID controller for servo mechanism control problem 243
8.9 PID controller for regulator mechanism control problem 245
Solved Problems – 8.1 to 8.3 248
Unsolved Problems 257
CHAPTER 9 – STABILITY CRITERION OF CONTROL SYSTEM 259-276
9.1 Stability of control system 259
9.2 Characteristics equation 259
9.3 Stability criterion 260
9.4 Routh - Hurwitz stability criterion 261
Solved Problems – 9.1 to 9.5 264
Unsolved Problems 276
CHAPTER 10 - ROOT LOCUS METHOD 277-300
10.1 Root locus method 277
10.2 Rules for plotting root locus diagram 277
10.3 Nature of root loci 280
Solved Problems – 10.1 to 10.3 281
Unsolved Problems 299

11. TABLE OF CONTENTS
x
CHAPTER 11 - INTRODUCTION TO FREQUENCY RESPONSE 301-340
11.1 Bode diagram 301
11.2 Bode diagram for first order system 301
11.3 Bode diagram for first order systems in series 304
11.4 Bode diagram for second order system 305
11.5 Bode diagram for transportation lag 306
11.6 Bode diagram for proportional controller 308
11.7 Bode diagram for proportional integral controller 309
11.8 Bode diagram for proportional derivative controller 311
11.9 Bode diagram for proportional integral derivative controller 313
11.10 Rules for plotting Bode diagram for the control system 317
11.11 Bode stability criterion 317
11.12 Gain and phase margin 318
11.13 Ziegler Nichols optimum controller settings 320
11.14 Cohen and Coon rules 322
11.15 Nyquist stability criterion 325
Solved Problems – 11.1 to 11.2 328
Unsolved Problems 339
CHAPTER 12 - ENHANCEMENT OF SINGLE LOOP PID FEEDBACK
CONTROLLERS 341-348
12.1 Cascade control 341
12.2 Feed forward control 343
12.3 Ratio control 344
12.4 Selective control 345
12.5 Split range control 346

12. PROCESS DYNAMICS AND CONTROLS
xi
CHAPTER 13 – INDUSTRIAL APPLICATIONS 349-356
13.1 Process control symbols 349
13.2 Stirred tank heater 351
13.3 Batch reactor 351
13.4 Distillation column 352
13.5 Compressor 352
13.6 Surge vessel level 353
13.7 Heat exchangers 353
13.8 Plug flow reactor 354
*13.9 Steam drum level 355
13.10 Plant wide control 355
13.11 Ph
control 356
CHAPTER 14 – PROCESS INSTRUMENTATION 357-378
14.1 Elements of instrument 357
14.2 Static characteristics of an instrument 358
14.3 Dynamic characteristics of an instrument 359
14.4 Functions of instruments 359
14.5 Temperature measuring instruments 360
14.6 Pressure measuring instruments 366
14.7 Level measuring instruments 371
14.8 Flow measuring instruments 374
IMPORTANT QUESTION OF GATE EXAM 379-416
REFERENCES 417
INDEX 419-421

13. INDEX
CENTRE : TECHNICAL CO-ORDINATION
419
INDEX
A
Amplitude ratio, 45,139,302,317
Asymptotes, 279
angles, 279
B
Batch reactor, 351
Bimetallic Thermometer, 360
Block diagram, 158-167
chemical reactor, 197-200
standard block diagram, 159
Bode diagram, 301-317
Controllers, 308-316
first order system, 301
rules for plotting bode plot, 317
second order system, 305
transportation lag, 306-307
C
Capacitance, 33,67-71
*Cascade control, 341-343
Characteristics equation, 259-264
roots of characteristics equation, 261-264
Chemical reactor control system, 196-200
Closed loop transfer function, 213-217
Comparator, 158-159
Cohen and Coons rules, 322-325
Compressor, 353
Constant stirred tank heater, 71-73, 57-59
Control hardware, 188-190
Control elements, 158
Controlled variables, 158-160
Controller, 166-167,190-196,308-316
Proportional, 166-167, 190-191, 308
proportional – integral, 191-192, 309-311
proportional – derivative, 192-193, 311-313
PID Controller, 193-194, 313-316
Control valve, 179-188
air to open, 179-180
air to close, 180-181
mechanism, 179-181
transfer function, 185-188
Corner frequency, 302-316
Critically damped system, 133, 136-137, 138
Cross over frequency, 319
Cyclic frequency, 142-143
D
Damped vibrator, 130-133
Damping coefficient, 133-134
Dead time, 85-87
Dead zone, 358-359
Decay ratio, 141-142
Derivates, 8-9
Laplace transform, 8-9
Distillation column, 352
Drift, 358
E
Elements, 157-159
of control systems, 158-159
of instruments, 357-358
F
Feedback control, 160-161
negative feedback, 160-161
positive feedback, 161
Feed forward control, 343-344
Final control element, 158-159,167
Final value theorem, 13
First order system, 29-45, 63-80, 301-304
impulse change, 36-38
in series, 73-80
interacting system, 77-80, 38
non interacting system, 73-77, 88
sinusoidal change, 41-45, 301-304
step change, 34-36
time constant, 33-34
transfer function, 32-33
Float and tape liquid level, 370-371
Forcing function, 9-13
Flow measuring instruments, 372-377
Impulse, 11
Ramp, 12
Sinusoidal, 12
Step, 10
Formulating process models, 15-16
Frequency response, 301-319
Bode diagram, 301
first order, 301-304
second order, 305-306
transportation lag, 306-308
Function of instruments, 359-360

14. PROCESS DYNAMICS AND CONTROL
CENTRE : TECHNICAL CO-ORDINATION
420
G
Gain margin, 320
Gain, 190-194, 321-322
of controller, 190-194
ultimate, 321-322
GATE exam questions, 379-415
Generalization of non interacting systems, 80-82
H
Heat exchangers, 354
Heaters, 71-73, 157-160
I
Impulse change, 36-38, 137-139
Impulse function, 11
Initial value theorem, 13
Integral action, 191-196
Interacting system, 77-80, 88
Interface level measuring unit, 372
Ionization of vacuum gage, 369-370
L
Lag
Transfer, 82
Phase, 139-140
Laplace transform, 5-9
Languages of process control, 3
Level measuring instruments 370-372
Linearization, 82-85
Liquid level system, 63-67
constant flow outlet, 66-67
Load variable, 158-167
M
Manometer, 127-130
Manipulated variable, 158-160
Measuring element, 165-166, 157-160
Mercury thermometer, 29-32
Mec leod vacuum gauge, 368-369
Mixing process, 70-71
Mechanism of control system, 179-181
Multi loop systems, 341-347
N
Natural frequency, 142-143
Natural period of oscillation, 143
Negative feed back system, 160-161
Non interaction system, 73-77
transfer function, 77
Non linear system, 82-85
Nyquist stability criterion, 325-328
O
Offset, 229-247
P controller, 230-234
PI controller, 234-238
PD controller, 238-243
PID controller, 243-247
Open loop transfer function, 213
Optical pyrometer, 364
Over damped system, 133, 137, 138
Overall transfer function, 213-217
Closed loop system, 213-217
Open loop system, 213
Overshoot, 140-141
P
Period of oscillation, 142-143
Phase angle, 45
Phase lag, 140
Phase margin, 320
Plant wide control, 355
Plug flow reactor, 354
Positive feedback, 161
Potentiometer, 365-366
Process instrumentation, 357-377
Process control symbols, 349-350
Pressure gauges, 366-367
Pressure measuring instruments, 366-370
Pressure spring thermometer, 362-363
Proportional controller, 166-167, 308-309, 230-234
transfer function, 190-191
Proportional integral controller, 191-192, 194-196,
234-238
transfer function, 191-192
Proportional derivative controller, 192-193, 194-
196, 238-243
transfer function, 192-193
Proportional integral derivative controller, 193-194,
195-196, 243-247
transfer function, 193-194
R
Radiation pyrometer, 363-364
Ramp change, 38-41
Ramp function, 10, 12
Ratio control, 344-345
R C circuit, 67-70

15. INDEX
CENTRE : TECHNICAL CO-ORDINATION
421
Regulator problems, 162-163, 232-247
Resistance, 63-70
Linear resistance, 63-67
Resistance thermometer, 364-365
Response time, 142
Rise time, 142
Root locus, 277-281
plotting of diagram, 281
rules for plotting, 277-281
Roots of characteristics equation, 261-264
Routh Hurwitz criterion, 261-264
routh array, 262-263
stability criterion, 261-262
S
Second order system, 127-143, 305-306
impulse change, 137-139
sinusoidal change, 139-140
step change, 134-136
transfer function, 127-133
Selective control, 345-346
Sensitivity, 190-194, 359
of controller, 190-194
of instruments, 359
Sinusoidal change, 41-45, 139-140
first order, 41-45
second order, 139-140
Servo mechanism control problems, 161-162
Split range control, 346-347
Stability, 259-264
Bode stability criterion, 317-318
Definition, 259
Routh test, 261-264
State space model, 16-17
Static characteristics, 358-359
Steam drum level, 355
Steady state gain, 190-194
Step function, 10
Stirred tank reactor, 71-73, 157-160, 351
block diagram, 158-159
transfer function, 164-165
Surge vessel level, 353
T
Taylor’s series of expansion, 83-84
Temperature measuring instruments, 360-366
Thermocouples, 33-34
Time constant, 361-362
Transfer function, 32
Transfer function model, 18-19
Transfer lag, 81-82
Transducer, 188-189
Transportation lag, 85-87, 306-308
transfer function, 87
Transform, 5-9
Laplace transform, 5-9
Translation, 13-14
of function, 14
of transform, 13
U
Under damped system, 133-143
Ultimate value, 140-142
Ultimate period, 321-322
U tube monometer, 127-130
V
Valve, 179-188
Characteristics, 181-182
Coefficient, 182-183
equal percentage, 182
hysteresis, 183-184
linear, 179
positioners, 183-184
sizing, 182-183
transfer function, 185-188
Z
Zeros, 278-281
Open loop, 278-281
Ziegler Nichols controller settings, 320-322