Advanced Process Dynamics and Control

Delhi-1100922015

Prabir Kumar SarkarFormer Reader

Chemical Engineering DepartmentJadavpur University

Kolkata

AdvAnced Process dynAmics And control (with cd-rom)Prabir Kumar Sarkar

© 2015 by PHI Learning Private Limited, Delhi. All rights reserved. No part of this book may be reproduced in any form, by mimeograph or any other means, without permission in writing from the publisher.

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isBn-978-81-203-4993-3

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Published by Asoke K. Ghosh, PHI Learning Private Limited, Rimjhim House, 111, Patparganj Industrial Estate, Delhi-110092 and Printed by Mohan Makhijani at Rekha Printers Private Limited, New Delhi-110020.

To

My Parents, Wife and

The students among whom I was able to raise an interest for this subject more than the others offered in chemical engineering course.

Contents

v

Preface xiiiAcknowledgements xxi

1. Introduction 1–81.1 Preliminary Roundup 11.2 PreliminaryDefinitions 2

1.2.1 The Block Diagram 41.2.2 Principal Entity 61.2.3 Dynamic Elements of a Process 61.2.4 Lumped and Distributed Parameter Process Models 71.2.5 Linearity of a Process 71.2.6 Stability 71.2.7 Degree of Freedom 71.2.8 Self Regulation 81.2.9 Order of a Process 8

2. Basic Modelling Principles (Time Domain Analysis) 9–492.1 Steady State Model 92.2 Dynamic Model 92.3 Different Descriptions of Process Model 14

2.3.1 State-Variable 142.3.2 The Transfer Function 15

2.4 Modelling for Continuous Systems 172.4.1 Lumped Parameter Single Stage Systems 182.4.2 Non-linear Process Characteristics—Linearisation 262.4.3 Method of Linearisation by Taylor’s Expansion 272.4.4 Lumped Parameter Multiple Stage Systems 302.4.5 Distributed Parameter Systems 332.4.6 Batch Process 40

Exercise Problems 47References 49

vi Contents

3. Review of Dynamics of Process Control System and Its Elements (Time Domain Solution from Complex Domain Analysis) 50–1053.1 First Order Systems 513.2 Definition andClassificationofSecondOrderSystems 54

3.2.1 Synthetic Type Second Order Systems 543.2.2 Second Order Systems of Natural or Inherent Variety 56

3.3 Ideal Input Functions 593.3.1 Step 593.3.2 Ramp 593.3.3 Impulse 603.3.4 Sinusoidal 60

3.4 Dynamic Response of the Processes 603.4.1 Response of First Order Systems 603.4.2 Response of Second Order Systems for Ideal Input Functions 653.4.3 Integrating Processes 733.4.4 Lead–Lag Element 743.4.5 Transfer Lag 763.4.6 Dead Time Element or Transportation Lag 77

3.5 Measuring Element 783.6 Final Control Element (FCE) 793.7 Electro–Pneumatic Converter (EPC) 793.8 The Automatic Controller 79

3.8.1 Output Bias 803.8.2 Action 803.8.3 Control Functions and Mode 803.8.4 Controller Mode 813.8.5 Comments on the Closed Loop Characteristics of Controller Modes 843.8.6 Certain Features of Commercial Controllers 85

3.9 Transfer Function of Closed Loop Systems and Their Response 893.9.1 Principle of Feedback Control 903.9.2 The Closed Loop Transfer Functions C(s)/L(s) and C(s)/R(s) 903.9.3 Closed Loop Response 93

References 105

4. Stability Analysis of Closed Loop Systems 106–1364.1 Concept and Measure of Stability 1064.2 Root–Locus Method 1124.3 Programme C10-1A.BAS (POLRT) 1164.4 Routh–Hurwitz Stability Criterion 121

4.4.1 Zero Elements in the First Column of Routh’s Array 1244.5 Method of Direct Substitution 1254.6 Stability Measure by Routh’s Array 132Exercise Problems 134References 136

5. Frequency Response Analysis 137–1925.1 Introduction 137

5.1.1 A Little Photographic Exposure 1375.1.2 Similar Frequency Domain Consideration about Sound Reproduction 139

Contents vii

5.2 Frequency Response of a Dynamic System 1405.2.1 The Fundamental Substitution Theorem 1405.2.2 Dynamics in Complex s-Plane 1415.2.3 Analytical Proof 1425.2.4 Different Descriptions of Frequency Response 1445.2.5 Frequency Response of Block Elements in Series 1505.2.6 Properties of Bode Plot of Individual Dynamic Blocks 158

5.3 Stability Analysis in Frequency Domain 1705.3.1 Bode Stability Criterion 1705.3.2 Measure of Stability 1725.3.3 Nyquist Stability Criterion 177

Exercise Problems 189References 192

6. Process Identification (Experimental Methods of Dynamic Model Development) 193–2366.1 On-Line Methods 1936.2 Off-Line Methods 1946.3 Open Loop Methods Based on Lumped Parameter Model

Structures 1946.4 Determination of FO Model Parameters 1966.5 Determination of FOPDT Model Parameters 1966.6 Determination of SO Model Parameters 2046.7 Determination of SOPDT Model Parameters 2136.8 Second Order Under-damped Plus Dead Time Model 2186.9 Approximation of SO Response by FOPDT Model 2206.10 Frequency Domain Methods 221

6.10.1 Direct Sine Wave Testing 2226.10.2 Pulse Testing 2236.10.3 Step Testing 231

Exercise Problems 233References 236

7. Controller Tuning and Controller Synthesis 237–2747.1 Controller Tuning 237

7.1.1 On Line Trial and Error Tuning Method 2387.1.2 Ziegler–Nichol’s Continuous Cycling Method 2397.1.3 Auto-tuning of Controllers by Forced Cycling 2417.1.4 Process Reaction Curve (PRC) 2427.1.5 Ziegler–Nichol’s Formulae Based on PRC 2437.1.6 Cohen and Coon Formulas Based on PRC 2447.1.7 Integral Error Criterions 254

7.2 Controller Synthesis Methods 2597.2.1 Direct Synthesis Algorithm 2607.2.2 Method of Internal Model Reference Control (IMRC or IMC) 265

7.3 Special Cases of IMC Application 2707.3.1 Unstable Processes 270

Exercise Problems 272References 274

viii Contents

8. Close Loop Response and Controller Synthesis in Frequency Domain 275–2958.1 Determination of Stability Limit, GM and PM on a Nichol’s

Plot 2758.2 Closed Loop Frequency Response from Open Loop Transfer

Function 2768.3 ControllerDesignSpecification inFrequencyDomain 283

8.3.1 DesignSpecificationBasedonOpenLoopData 2838.3.2 The Nichol’s Chart 2838.3.3 DesignSpecificationBasedonClosedLoopData 284

Exercise Problems 295References 295

9. Digital Simulation of Processes and Control Systems 296–4279.1 Historical 2979.2 Process Control System Analyzer (PCSA) 2979.3 Subroutine for One-dimensional Linear Interpolation

(LNNT1A), (LNNT1B), (LNNT1C) 2999.4 Scale Divisions and Captions on the Graphic Trace of a Variable 3059.5 Introducing the Branching Statement ON (NPS) GOTO A, B, C, …… 3079.6 Linear Interpolation in Two Dimensions 3119.7 Dead Time or Delay Element (SUBROUTINE DLAY1 and DLAY2) 314

9.7.1 DLAY1 3149.7.2 DLAY2 315

9.8 Integration Algorithms 3179.8.1 First and Second Order Dynamic Blocks (SUBROUTINE

FOTF, SOTFA) 3209.9 Modelling Nonlinear Systems 3259.10 Lead–Lag Element 3309.11 Implicit Convergence (SUBROUTINES INTHAV, NEWRAF

and DCSCRJ) 3319.11.1 INTHAV 3329.11.2 NEWRAF 3329.11.3 Decimal Section Rejection (DCSCRJ) 333

9.12 Modelling for Non-ideal Mixing 3389.13 Lumped Parameter Systems 344

9.13.1 Air–Water Vapour Equilibrium System—Psychometric Variables in Drying 344

9.13.2 Bio-chemical Process 3539.14 Systems Featuring Lumped Parameter Units in Series 355

9.14.1 CSTR Battery 3559.14.2 Plate Type Gas Absorber 358

9.15 Distributed Parameter Systems 3629.15.1 Co-current Double Pipe Heat Exchanger (Without Considering

Metal Wall Capacity) 3629.15.2 Sensible Heat Transfer in a Counter Current Exchanger 366

Contents ix

9.16 Subroutines for Control Hardware 3719.16.1 Measuring Element 3719.16.2 Comparator 3729.16.3 Controller 3729.16.4 Final Control Element 3739.16.5 Tuning of Controller 3779.16.6 Phase Diagram 3809.16.7 ON–OFF Controller 383

9.17 Systems with Multiple Control Loops 3879.18 Distillation Column Dynamics and Control 400

9.18.1 Vapour–Liquid Equilibrium 4019.18.2 The Dynamic Model 4019.18.3 LiquidHoldup andLiquidOverflow 4029.18.4 Vapour Velocity 4029.18.5 Liquid Flow from Condenser and Reboiler 4039.18.6 Control of Distillation Column 412

9.19 Control Valve 4149.20 Frequency Response Plotting 416

9.20.1 Program for Drawing of a Log–log Graph 4169.20.2 Program for Drawing of a Semi-log Graphs 4179.20.3 Drawing the Bode Plot on a Semi-log Graph 4189.20.4 Drawing of Nyquist Plot 4229.20.5 Drawing of Nichol’s Plot 424

References 426

10. Advanced Control Strategies 428–51010.1 DynamicSpecialtiesCausingControlDifficulties 42810.2 Feed Forward Control 429

10.2.1 Design of a Feed Forward Controller 43010.2.2 Combining Feedback with Feed Forward Action 43110.2.3 An Industrial Example of Feed Forward-Feedback Control Application 43210.2.4 Stability in Presence of Feed Forward Controller in a FF-FB Loop 43310.2.5 Tuning of a FF-FB Loop 43310.2.6 AnAlternativeConfigurationofFF+FBLoop 438

10.3 Ratio Control 44310.3.1 Air-Fuel Ratio Control of Combustion Systems 448

10.4 Cascade Control 45410.4.1 Example of Cascade Control Application 45510.4.2 Another Example of Cascade Control Application 45610.4.3 Analysis of Cascade Control System 45610.4.4 Tuning of Cascade Control System 461

10.5 Smith’s Predictor Algorithm 46610.5.1 Analysis of Smith’s Predictor Algorithm Block Diagram 468

10.6 Processes with Inverse Response 47210.6.1 Control System Design for Inverse Response Processes 475

10.7 Inferential Control 48010.8 Selective and Override Control 48510.9 Adaptive Control Schemes 486

10.9.1 Gain Scheduling Type Adaptation 48710.9.2 Reference Model Adaptive Control (RMAC) 493

Advanced Process Dynamics And Control

Publisher : PHI Learning ISBN : 9788120349933 Author : SARKAR, PRABIRKUMAR

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