Process Dynamics and Control

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.

ii

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: [email protected] and Printed in Pune.

http://www.chinttanpublications.in/

mailto:[email protected]

iii

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

iv

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

v

Dedicated to...

My Parents

and

My Wife

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



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



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


Unsolved Problem 154

CHAPTER 5 - MECHANISM OF CONTROL SYSTEM 157-178

5.1 Control system for continuous stirred tank heater 157

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



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




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



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



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



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



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


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

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


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

PROCESS DYNAMICS AND CONTROL


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


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


Proportional integral controller, 191-192, 194-196,

234-238


Proportional derivative controller, 192-193, 194-

196, 238-243


Proportional integral derivative controller, 193-194,

195-196, 243-247


R Radiation pyrometer, 363-364

Ramp change, 38-41

Ramp function, 10, 12

Ratio control, 344-345

R C circuit, 67-70

INDEX


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


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


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


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


Z Zeros, 278-281

Open loop, 278-281

Ziegler Nichols controller settings, 320-322

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