Applied Process Control Essential Methods

by Michael Mulholland

Applied Process Control Essential Methods Focusing on the practical implementation of the methods of process modelling and control this book provides readers with rapid access to the methods described while including the theoretical background necessary Throughout the essential knowledge is built up from chapter to chapter starting with laying the foundations in plant instrumentation and control Modelling abilities are then developed by starting from simple time loop algorithms and passing on to discrete methods Laplace transform

Publisher : Wiley VCH

Author : Michael Mulholland

ISBN : 9783527341191

Year : 2016

Language: en

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Michael Mulholland
Applied Process Control

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Michael Mulholland

Applied Process Control
Essential Methods

Author
Professor Michael Mulholland

University of KwaZulu-Natal
Chemical Engineering
4041 Durban
South Africa

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V

Essential Methods Contents
Preface XI
Acknowledgements
Abbreviations XV
Frontispiece XIX

XIII

1

1

Introduction

1.1
1.2
1.3
1.4

The Idea of Control 1
Importance of Control in Chemical Processing 3
Organisation of This Book 5
Semantics 6
References 7

2

Instrumentation

2.1
2.2
2.3
2.4
2.4.1
2.4.1.1
2.4.1.2
2.4.2
2.4.2.1
2.4.2.2
2.4.3
2.4.4
2.4.4.1
2.4.4.2
2.4.4.3
2.4.5
2.5
2.6

Piping and Instrumentation Diagram Notation 9
Plant Signal Ranges and Conversions 11
A Special Note on Differential Pressure Cells 14
Measurement Instrumentation 16
Flow Measurement 17
Flow Measurement Devices Employing Differential Pressure 17
Other Flow Measurement Devices 22
Level Measurement 22
Level Measurement by Differential Pressure 22
Other Level Measurement Techniques 25
Pressure Measurement 25
Temperature Measurement 26
Thermocouple Temperature Measurement 26
Metal Resistance Temperature Measurement 28
Temperature Measurements Using Other Principles 28
Composition Measurement 29
Current-to-Pneumatic Transducer 31
Final Control Elements (Actuators) 31

9

VI

Essential Methods Contents

2.6.1
2.6.1.1
2.6.1.2
2.6.1.3
2.6.1.4
2.6.1.5
2.6.1.6
2.6.2
2.7
2.8
2.9

Valves 32
Pneumatically Operated Globe Control Valve 32
Valve Characteristics 35
Valve CV and KV 36
Specification of Valves for Installed Performance 37
Control Valve Hysteresis 39
Various Flow Control Devices 40
Some Other Types of Control Actuators 42
Controllers 42
Relays, Trips and Interlocks 44
Instrument Reliability 45
References 51

3

Modelling

3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.8
3.9
3.9.1
3.9.2
3.9.2.1
3.9.2.2
3.9.2.3
3.9.3
3.9.3.1
3.9.3.2
3.9.3.3
3.9.3.4
3.9.3.5
3.9.4
3.9.4.1
3.9.4.2
3.9.5
3.9.5.1
3.9.5.2
3.9.6
3.9.7
3.10
3.11

General Modelling Strategy 54
Modelling of Distributed Systems 59
Modelling Example for a Lumped System: Chlorination Reservoirs 61
Modelling Example for a Distributed System: Reactor Cooler 63
Ordinary Differential Equations and System Order 67
Linearity 69
Linearisation of the Equations Describing a System 73
Simple Linearisation ‘Δ’ Concept 75
Solutions for a System Response Using Simpler Equations 77
Mathematical Solutions for a System Response in the t-Domain 77
Mathematical Solutions for a System Response in the s-Domain 79
Review of Some Laplace Transform Results 79
Use of Laplace Transforms to Find the System Response 84
Open-Loop Stability in the s-Domain 95
Mathematical Solutions for System Response in the z-Domain 97
Review of Some z-Transform Results 98
Use of z-Transforms to Find the System Response 104
Evaluation of the Matrix Exponential Terms 109
Shortcut Methods to Obtain Discrete Difference Equations 110
Open-Loop Stability in the z-Domain 111
Numerical Solution for System Response 113
Numerical Solution Using Explicit Forms 114
Numerical Solution Using Implicit Forms 115
Black Box Modelling 117
Step Response Models 117
Regressed Dynamic Models 122
Modelling with Automata, Petri Nets and Their Hybrids 126
Models Based on Fuzzy Logic 132
Use of Random Variables in Modelling 136
Modelling of Closed Loops 141
References 142

53

Essential Methods Contents

143

4

Basic Elements Used in Plant Control Schemes

4.1
4.2
4.2.1
4.2.2
4.2.3
4.2.4
4.2.5
4.2.6
4.2.6.1
4.2.6.2
4.2.6.3
4.2.7
4.2.8
4.2.8.1
4.2.8.2
4.3
4.4
4.5
4.6
4.7
4.8

Signal Filtering/Conditioning 143
Basic SISO Controllers 147
Block Diagram Representation of Control Loops 147
Proportional Controller 150
Proportional–Integral Controller 151
Proportional–Integral–Derivative Controller 153
Integral Action Windup 155
Tuning of P, PI and PID Controllers 155
Step Response Controller Tuning 158
Frequency Response Controller Tuning 159
Closed-Loop Trial-and-Error Controller Tuning 160
Feedforward Control 160
Other Simple Controllers 162
On/Off Deadband Control 162
Simple Nonlinear and Adaptive Controllers 162
Cascade Arrangement of Controllers 163
Ratio Control 164
Split Range Control 165
Control of a Calculated Variable 165
Use of High Selector or Low Selector on Measurement Signals 168
Overrides: Use of High Selector or Low Selector on Control
Action Signals 168
Clipping, Interlocks, Trips and Latching 170
Valve Position Control 171
Advanced Level Control 172
Calculation of Closed-Loop Responses: Process Model with
Control Element 173
Closed-Loop Simulation by Numerical Techniques 174
Closed-Loop Simulation Using Laplace Transforms 176
References 177

4.9
4.10
4.11
4.12
4.12.1
4.12.2

179

5

Control Strategy Design for Processing Plants

5.1
5.2
5.2.1
5.2.2
5.2.3
5.2.4
5.3
5.3.1
5.3.1.1
5.3.2
5.3.3

General Guidelines to the Specification of an Overall Plant Control Scheme 180
Systematic Approaches to the Specification of an Overall Plant Control Scheme 180
Structural Synthesis of the Plant Control Scheme 181
Controllability and Observability 184
Morari Resiliency Index 188
Relative Gain Array (Bristol Array) 191
Control Schemes Involving More Complex Interconnections of Basic Elements 193
Boiler Drum-Level Control 193
Note on Boiler Drum-Level Inverse Response 194
Furnace Full Metering Control with Oxygen Trim Control 195
Furnace Cross-Limiting Control 196
References 198

VII

VIII

Essential Methods Contents

199

6

Estimation of Variables and Model Parameters from Plant Data

6.1
6.1.1
6.1.2
6.1.3
6.2

Estimation of Signal Properties 199
Calculation of Cross-Correlation and Autocorrelation 199
Calculation of Frequency Spectrum 202
Calculation of Principal Components 203
Real-Time Estimation of Variables for Which a Delayed Measurement Is
Available for Correction 205
Plant Data Reconciliation 208
Recursive State Estimation 211
Discrete Kalman Filter 213
Continuous Kalman–Bucy Filter 220
Extended Kalman Filter 222
Identification of the Parameters of a Process Model 225
Model Identification by Least-Squares Fitting to a Batch of
Measurements 227
Model Identification Using Recursive Least Squares on Measurements 229
Some Considerations in Model Identification 233
Type of Model 233
Forgetting Factor 239
Steady-State Offset 240
Extraction of Physical Parameters 241
Transport Lag (Dead Time) 243
Combined State and Parameter Observation Based on a System of Differential
and Algebraic Equations 243
Nonparametric Identification 246
Impulse Response Coefficients by Cross-Correlation 246
Direct RLS Identification of a Dynamic Matrix (Step Response) 247
References 250

6.3
6.4
6.4.1
6.4.2
6.4.3
6.5
6.5.1
6.5.2
6.5.3
6.5.3.1
6.5.3.2
6.5.3.3
6.5.3.4
6.5.3.5
6.6
6.7
6.7.1
6.7.2

251

7

Advanced Control Algorithms

7.1
7.1.1
7.1.2

Discrete z-Domain Minimal Prototype Controllers 251
Setpoint Tracking Discrete Minimal Prototype Controller 251
Setpoint Tracking and Load Disturbance Suppression with a Discrete
Minimal Prototype Controller (Two-Degree-of-Freedom Controller) 255
Continuous s-Domain MIMO Controller Decoupling Design by Inverse
Nyquist Array 256
Continuous s-Domain MIMO Controller Design Based on Characteristic Loci 259
Continuous s-Domain MIMO Controller Design Based on Largest Modulus 260
MIMO Controller Design Based on Pole Placement 261
Continuous s-Domain MIMO Controller Design Based on Pole Placement 261
Discrete z-Domain MIMO Controller Design Based on Pole Placement 264
State-Space MIMO Controller Design 266
Continuous State-Space MIMO Modal Control: Proportional Feedback 266
Discrete State-Space MIMO Modal Control: Proportional Feedback 267
Continuous State-Space MIMO Controller Design Based on ‘Controllable
System’ Pole Placement 267

7.2
7.3
7.4
7.5
7.5.1
7.5.2
7.6
7.6.1
7.6.2
7.6.3

Essential Methods Contents

7.6.4
7.6.5
7.6.6
7.7
7.7.1
7.8
7.8.1
7.8.1.1
7.8.1.2
7.8.2
7.8.2.1
7.8.2.2
7.8.2.3
7.8.2.4
7.8.2.5
7.8.3
7.8.3.1
7.8.3.2
7.8.3.3
7.8.3.4
7.8.3.5
7.8.3.6
7.9
7.9.1
7.9.2
7.10
7.11
7.11.1
7.11.2
7.12
7.12.1
7.12.2
7.13
7.14
7.14.1
7.14.2
7.14.3
7.15

Discrete State-Space MIMO Controller Design Based on ‘Controllable
System’ Pole Placement 270
Discrete State-Space MIMO Controller Design Using the Linear Quadratic
Regulator Approach 271
Continuous State-Space MIMO Controller Design Using the Linear
Quadratic Regulator Approach 277
Concept of Internal Model Control 279
A General MIMO Controller Design Approach Based on IMC 280
Predictive Control 282
Generalised Predictive Control for a Discrete z-Domain MIMO System 283
GPC for a Discrete MIMO System Represented by z-Domain Polynomials
(Input–Output Form) 284
Predictive Control for a Discrete MIMO System Represented in the
State Space 289
Dynamic Matrix Control 291
Linear Dynamic Matrix Control 296
Quadratic Dynamic Matrix Control in Industry 298
Recursive Representation of the Future Output 298
Dynamic Matrix Control of an Integrating System 300
Dynamic Matrix Control Based on a Finite Impulse Response 303
Approaches to the Optimisation of Control Action Trajectories 305
Some Concepts Used in Predictive Control Optimisation 306
Direct Multiple Shooting 309
Interior Point Method and Barrier Functions 311
Iterative Dynamic Programming 312
Forward Iterative Dynamic Programming 316
Iterative Dynamic Programming Based on a Discrete Input–Output
Model Instead of a State-Space Model 318
Control of Time-Delay Systems 320
MIMO Closed-Loop Control Using a Smith Predictor 321
Closed-Loop Control in the Presence of Variable Dead
Time 322
A Note on Adaptive Control and Gain Scheduling 323
Control Using Artificial Neural Networks 324
Back-propagation Training of an ANN 324
Process Control Arrangements Using ANNs 326
Control Based on Fuzzy Logic 328
Fuzzy Relational Model 330
Fuzzy Relational Model-Based Control 334
Predictive Control Using Evolutionary Strategies 337
Control of Hybrid Systems 341
Process Control Representation Using Hybrid Petri Nets 342
Process Control Representation Using Hybrid Automata 345
Mixed Logical Dynamical Framework in Predictive Control 350
Decentralised Control 358
References 364

IX

X

Essential Methods Contents

367

8

Stability and Quality of Control

8.1
8.2
8.2.1
8.2.1.1
8.2.1.2
8.2.1.3
8.2.1.4
8.2.1.5
8.3
8.4
8.5
8.6
8.6.1
8.6.2
8.6.3
8.6.4
8.6.5
8.7
8.8

Introduction 367
View of a Continuous SISO System in the s-Domain 369
Transfer Functions, the Characteristic Equation and Stability 369
Open-Loop Transfer Functions 369
Angles and Magnitutes of s and GO(s) 370
Open-Loop and Closed-Loop Stability 371
Open-Loop and Closed-Loop Steady-State Gain 373
Root Locus Analysis of Closed-Loop Stability 374
View of a Continuous MIMO System in the s-Domain 382
View of Continuous SISO and MIMO Systems in Linear State Space 383
View of Discrete Linear SISO and MIMO Systems 385
Frequency Response 386
Frequency Response from G(jω) 387
Closed-Loop Stability Criterion in the Frequency Domain 391
Bode Plot 393
Nyquist Plot 396
Magnitude versus Phase-Angle Plot and the Nichols Chart 401
Control Quality Criteria 403
Robust Control 404
References 408

9

Optimisation

9.1
9.2
9.3
9.4
9.5
9.5.1
9.5.2
9.5.3
9.5.3.1
9.5.3.2
9.6
9.6.1
9.7
9.8
9.8.1
9.8.2
9.9
9.9.1
9.9.2
9.9.3
9.10
9.11

Introduction 409
Aspects of Optimisation Problems 409
Linear Programming 412
Integer Programming and Mixed Integer Programming (MIP) 418
Gradient Searches 421
Newton Method for Finding a Minimum or a Maximum 421
Downhill Simplex Method 422
Methods Based on Chosen Search Directions 423
Steepest Descent Method 425
Conjugate Gradient Method 427
Nonlinear Programming and Global Optimisation 429
Global Optimisation by Branch and Bound 429
Combinatorial Optimisation by Simulated Annealing 432
Optimisation by Evolutionary Strategies 434
Reactor Design Example 435
Non-dominated Sorting Genetic Algorithm (NSGA) 437
Mixed Integer Nonlinear Programming 441
Branch and Bound Method 442
Outer Approximation Method (OA) 443
Comparison of Other Methods 444
The GAMS Modelling Environment 444
Real-Time Optimisation of Whole Plants 449
References 454
Index 457

409

XI

Preface
Material in this book is sequenced for the process engineer who needs ‘some’ background in process
control (Chapters 1–5) through to the process engineer who wishes to specialise in advanced pro­
cess control (Chapters 1–9). The theory needed to properly understand and implement the methods
is presented as succinctly as possible, with extensive recourse to linear algebra, allowing multi-input,
multi-output problems to be interpreted as simply as single-input, single-output problems.
Before moving on to the more advanced algorithms, an essential practical background is laid out
on plant instrumentation and control schemes (Chapters 2, 4 and 5). Chapter 3 builds modelling
abilities from the simplest time-loop algorithm through to discrete methods, transfer functions,
automata and fuzzy logic. By the end of Chapter 5, the engineer has the means to design simple
controllers on the basis of his or her models, and to use more detailed models to test these control­
lers. Moreover, ability has been developed in the use of the multi-element control schemes of
‘advanced process control’.
Chapter 6 focuses on observation. Whereas Chapter 3 reveals the tenuous chain of preparation of
plant signals, Chapter 6 aims to make sense of them. Important issues on the plant are signal con­
ditioning, data reconciliation, identification of model parameters and estimation of unmeasured
variables.
Chapter 7 addresses more advanced control algorithms, drawing on a wide range of successful
modern methods. To a large extent, continuous and discrete versions of an algorithm are presented
in parallel, usually in multi-input, multi-output formats – which simply devolve to the single-input,
single-output case if required. State–space, input–output, fuzzy, evolutionary, artificial neural
network and hybrid methods are presented. There is a strong emphasis on model predictive control
methods which have had major industrial benefits.
A review of the classical methods of stability analysis is delayed until Chapter 8. This has been
kept brief, in line with reduced application in the processing industries. One recognises that stability
criteria, such as pole locations, do underlie some of the design techniques of Chapter 7. Certainly,
frequency domain concepts are part of the language of control theory, and essential for advanced
investigation. But with the slower responses and inaccurate models of processing plants, controllers
are not predesigned to ‘push the limits’ and tend to be tuned up experimentally online.
A review of a range of optimisation techniques and concepts is given in Chapter 9. Although not a
deep analysis, this imparts a basic working knowledge, enabling the development of simple applica­
tions, which can then later be built upon. Topics covered include linear, integer, mixed, and non­
linear programming, search techniques, global optimisation, simulated annealing, genetic algorithms
and multi-objective optimisation. These methods, and dynamic programming, underlie the

XII

Preface

predictive control and optimal scheduling topics in Chapter 7, and are also important as static opti­
misers in such applications as supply chain, product blending/distribution and plant economic
optimisers.
This book tries to make the methods practically useful to the reader as quickly as possible. How­
ever, there is no shortcut to reliable results, without a basic knowledge of the theory. For example,
one cannot make proper use of a Kalman filter, without understanding its mechanism. Complex
multi-input, multi-output applications will require a good theoretical understanding in order to
trace a performance problem back to a poorly calibrated input measurement. Hence, an adequate
theoretical background is provided.
A few distinctions need to be clarified:
1) Modelling is a particular strength of the process engineer, and is a basis of all of the algorithms
– especially model predictive control. The reader needs to distinguish state-based models ver­
sus input–output models. The state-based models can predict forward in time knowing only
the initial state and future inputs. Some algorithms rely on this. In contrast, input–output
models will need additional information about past inputs and outputs, in order to predict
future outputs. To use state-based algorithms on these, a state observer algorithm (e.g. Kal­
man filter) will be required to estimate the states.
2) The forward shift operator z = eTs is used to relate discrete versions of systems to their transfer
function forms G(s) in the s (Laplace/frequency) domain. In a lot of what follows, this theoret­
ical connection is not significant, and the data sampling shift parameter q could be used, but
sometimes it is not in this text.
3) The text consistently uses bold characters to signify matrices [A], vectors [x] and matrix trans­
fer functions [G(s), G(z)]. Non-bold characters are used for scalars.
A number of examples are presented in this book in order to clarify the methods. In addition, the
separate accompanying book Applied Process Control: Efficient Problem Solving presents 226 solved
problems, using the methods of this text. These often make use of MATLAB code which is
arranged in obvious time loops, allowing easy translation to the real-time environment. There will,
however, be the challenge to provide additional routines such as matrix inversion.
A simple interactive simulator program has been made available at https://sourceforge.net/
projects/rtc-simulator/. It includes 20 different applications for such aspects as PID and DMC con­
troller tuning, advanced level control, Smith prediction, Kalman filtering and control strategies for a
furnace, a boiler and a hybrid system. No support is available for the simulator.
Although I have personally used a variety of methods on industrial and research applications, in
writing this book I have been fascinated to discover the brilliant ideas of many other workers in the
field. To all of those people who get excited about process control, I wish you an optimal trajectory.
University of KwaZulu-Natal
March, 2016

Michael Mulholland

XIII

Acknowledgements
Many of the problems in this book are dealt with using the MATLAB program, which is distrib­
uted by the MathWorks, Inc. They may be contacted at
The MathWorks, Inc.
3 Apple Hill Drive
Natick, MA 01760–2098, USA
Tel: 508-647-7000
Fax: 508-647-7001
E-mail: [email protected]
Web: mathworks.com
How to buy: http://www.mathworks.com/store
A few problems are dealt with in the GAMS optimisation environment, distributed by
GAMS Development Corporation
1217 Potomac Street, NW
Washington, DC 20007, USA
General Information and Sales: (+1) 202 342-0180
Fax: (+1) 202 342-0181
Contact: [email protected]
Some problems make use of the LPSOLVE mixed integer linear programming software which is
hosted on the SourceForge Web site at
http://sourceforge.net/projects/lpsolve/

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