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Advanced Chemical Process Control
Bridge the gap between theory and practice with this accessible guide
Process control is an area of study which seeks to optimize industrial processes, applying different strategies and technologies as required to navigate the variety of processes and their many potential challenges. Though the body of chemical process control theory is robust, it is only in recent decades that it has been effectively integrated with industrial practice to form a flexible toolkit. The need for a guide to this integration of theory and practice has therefore never been more urgent.
Advanced Chemical Process Control meets this need, making advanced chemical process control accessible and useful to chemical engineers with little grounding in the theoretical principles of the subject. It provides a basic introduction to the background and mathematics of control theory, before turning to the implementation of control principles in industrial contexts. The result is a bridge between the insights of control theory and the needs of engineers in plants, factories, research facilities, and beyond.
Advanced Chemical Process Control readers will also find:
- Detailed overview of Control Performance Monitoring (CPM), Model Predictive Control (MPC), and more
- Discussion of the cost benefit analysis of improved control in particular jobs
- Authored by a leading international expert on chemical process control
Advanced Chemical Process Control is essential for chemical and process engineers looking to develop a working knowledge of process control, as well as for students and graduates entering the chemical process control field.
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Veröffentlichungsjahr: 2023
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Table of Contents
Cover
Title Page
Copyright
Dedication
Preface
References
Notes
Acknowledgments
Acronyms
Introduction
I.1 Why Is Chemical Process Control Needed?
I.2 What Knowledge Does a chemical Process Control Engineer need?
I.3 What Makes Chemical Process Control Unique?
I.4 The Structure of Control Systems in the Chemical Process Industries
I.5 Notation
Notes
1 Mathematical and Control Theory Background
1.1 Introduction
1.2 Models for Dynamical Systems
1.3 Analyzing Linear Dynamical Systems
1.4 Poles and Zeros of Transfer Functions
1.5 Stability
Problems
References
Notes
2 Control Configuration and Controller Tuning
2.1 Common Control Loop Structures for the Regulatory Control Layer
2.2 Input and Output Selection
2.3 Control Configuration
2.4 Tuning of Decentralized Controllers
Problems
References
Notes
3 Control Structure Selection and Plantwide Control
3.1 General Approach and Problem Decomposition
3.2 Regulatory Control
3.3 Determining Degrees of Freedom
3.4 Selection of Controlled Variables
3.5 Selection of Manipulated Variables
3.6 Selection of Measurements
3.7 Mass Balance Control and Throughput Manipulation
Problems
References
Notes
4 Limitations on Achievable Performance
4.1 Performance Measures
4.2 Algebraic Limitations
4.3 Control Performance in Different Frequency Ranges
4.4 Bounds on Closed‐Loop Transfer Functions
4.5 ISE Optimal Control
4.6 Bandwidth and Crossover Frequency Limitations
4.7 Bounds on the Step Response
4.8 Bounds for Disturbance Rejection
4.9 Limitations from Plant Uncertainty
Problems
References
Notes
5 Model‐Based Predictive Control
5.1 Introduction
5.2 Formulation of a QP Problem for MPC
5.3 Step‐Response Models
5.4 Updating the Process Model
5.5 Disturbance Handling and Offset‐Free Control
5.6 Feasibility and Constraint Handling
5.7 Closed‐Loop Stability with MPC Controllers
5.8 Target Calculation
5.9 Speeding up MPC Calculations
5.10 Robustness of MPC Controllers
5.11 Using Rigorous Process Models in MPC
5.12 Misconceptions, Clarifications, and Challenges
Problems
References
Notes
6 Some Practical Issues in Controller Implementation
6.1 Discrete‐Time Implementation
6.2 Pure Integrators in Parallel
6.3 Anti‐Windup
6.4 Bumpless Transfer
Problems
References
7 Controller Performance Monitoring and Diagnosis
7.1 Introduction
7.2 Detection of Oscillating Control Loops
7.3 Oscillation Diagnosis
7.4 Plantwide Oscillations
7.5 Control Loop Performance Monitoring
7.6 Multivariable Control Performance Monitoring
7.7 Some Issues in the Implementation of Control Performance Monitoring
7.8 Discussion
Problems
References
Notes
8 Economic Control Benefit Assessment
8.1 Optimal Operation and Operational Constraints
8.2 Economic Performance Functions
8.3 Expected Economic Benefit
8.4 Estimating Achievable Variance Reduction
8.5 Worst‐Case Backoff Calculation
References
Note
A Fourier–Motzkin Elimination
B Removal of Redundant Constraints
Reference
C The Singular Value Decomposition
D Factorization of Transfer Functions into Minimum Phase Stable and All‐Pass Parts
D.1 Input Factorization of RHP Zeros
D.2 Output Factorization of RHP Zeros
D.3 Output Factorization of RHP Poles
D.4 Input Factorization of RHP Poles
D.5 SISO Systems
D.6 Factoring Out Both RHP Poles and RHP Zeros
Reference
E Models Used in Examples
E.1 Binary Distillation Column Model
E.2 Fluid Catalytic Cracker Model
References
Note
Index
End User License Agreement
List of Tables
Chapter 2
Table 2.1 Tuning parameters for the closed‐loop Ziegler–Nichols method.
Table 2.2 Tuning parameters for the open‐loop Ziegler–Nichols method.
Chapter 7
Table 7.1 Analysis of variance table.
List of Illustrations
Introduction
Figure I.1 Typical structure of the control system for a large plant in the ...
Chapter 1
Figure 1.1 A simple feedback loop with a one‐degree‐of‐freedom controller an...
Figure 1.2 A simple feedback loop with a two‐degree‐of‐freedom controller an...
Figure 1.3 Simple level control problem.
Figure 1.4 Series interconnection of two transfer function matrices.
Figure 1.5 Two transfer function matrices in parallel.
Figure 1.6 Feedback interconnection of systems.
Figure 1.7 Basic feedback loop excited by disturbances , reference changes
Figure 1.8 The phase and gain of a simple term for .
Figure 1.9 The Bode diagram for the simple system .
Figure 1.10 A simple feedback loop.
Figure 1.11 Bode diagram for the system .
Figure 1.12 The monovariable Nyquist theorem applied to the system . The cu...
Figure 1.13 Feedback loop with uncertainty converted to structure for smal...
Figure 1.14 A simple feedback loop with input and output disturbances.
Figure 1.15 Representation of all stabilizing controllers.
Figure 1.16 Bode diagram for a system – as given by Matlab.
Chapter 2
Figure 2.1 Simple feedback control loop.
Figure 2.2 Feedforward control from measured disturbances combined with ordi...
Figure 2.3 Ratio control for mixing two streams to obtain some specific prop...
Figure 2.4 Cascaded control loops. Controller C1 controls the output of proc...
Figure 2.5 A chemical reactor with auctioneering temperature control.
Figure 2.6 A buffer tank with split range control of tank level.
Figure 2.7 Three different ways of implementing input resetting control.
Figure 2.8 Selective control of pressure of both side of a control valve. No...
Figure 2.9 The basic idea behind decoupling: A precompensator () is used to...
Figure 2.10 System without independent propagation paths for effects of actu...
Figure 2.11 The structure of the PID controller. (a) Ideal PID, (b) cascaded...
Figure 2.12 PID controllers with setpoint weighting. (a) Ideal PID, (b) casc...
Figure 2.13 Gain of plant, controller, and open‐loop gain with the original ...
Figure 2.14 Phase of plant, controller, and open‐loop gain with the original...
Figure 2.15 Response to a unit step in the reference at time , with the ori...
Figure 2.16 Response to a unit sinusoidal disturbance with frequency , with...
Figure 2.17 Disturbance gain and open‐loop gains with original and new tunin...
Figure 2.18 Open‐loop phase with the new tuning.
Figure 2.19 Response to sinusoidal disturbance with new controller tuning.
Figure 2.20 Estimating model parameters from the process step response.
Figure 2.21 An internal model controller.
Figure 2.22 The setpoint overshoot method.
Figure 2.23 (a) Open‐loop step response. (b) Closed‐loop response to step in...
Figure 2.24 (a) Open‐loop step response. (b) Closed‐loop response to a step ...
Figure 2.25 Block diagram showing controller with relay‐based autotuner.
Figure 2.26 Illustrating the internal scaling in controller implementations....
Figure 2.27 Block diagram of proposed surge attenuating control scheme.
Figure 2.28 CLDG's and loop gain for loop 1.
Figure 2.29 CLDG's and loop gain for loop 2.
Figure 2.30 Response to a step in disturbance 1 of unit magnitude.
Figure 2.31 Response to a step in disturbance 2 of unit magnitude.
Figure 2.32 The ‐element of the RGA matrix of a system.
Figure 2.33 Response in liquid level in subproblem a.
Figure 2.34 Response in flowrate in subproblem a.
Figure 2.35 Response in liquid level in subproblem b.
Figure 2.36 Response in flowrate in subproblem b.
Chapter 3
Figure 3.1 Deaerator tower with rudimentary regulatory control.
Figure 3.2 Deaerator tower with improved regulatory control.
Figure 3.3 Final stage separator and coalescer with proposed (inconsistent) ...
Figure 3.4 Throughput manipulator located internally in the plant – and the ...
Figure 3.5 Throughput manipulator used to control cooling capacity to a safe...
Figure 3.6 Illustrations of inventory control systems for recycle loops. Top...
Figure 3.7 Inventory control which adheres to Aske's self‐consistency rule, ...
Chapter 4
Figure 4.1 Illustration of the closed‐loop response to a unit step in the re...
Figure 4.2 Block diagram corresponding to minimization of weighted sensitivi...
Figure 4.3 Illustration of the rise time definition used in this section....
Figure 4.4 Output response with feedback controller only – with and without ...
Figure 4.5 Control loop with input constraint, output disturbance, and feedf...
Figure 4.6 Output response with feedback only and with two different feedfor...
Figure 4.7 Illustrating input and output multiplicative uncertainty. (a) Mul...
Figure 4.8 Magnitude plots for plant and disturbance transfer functions.
Chapter 5
Figure 5.1 Structure of an MPC controller.
Figure 5.2 Measured and estimated outputs in Case 1.
Figure 5.3 Estimated output disturbances in Case 1.
Figure 5.4 Measured and estimated outputs in Case 2.
Figure 5.5 Estimated output disturbances in Case 2.
Figure 5.6 MPC for FCC model: resulting temperatures.
Figure 5.7 MPC for FCC model: input usage.
Figure 5.8 Effect of integrator resetting on measured output.
Figure 5.9 Input usage with and without integrator resetting.
Chapter 6
Figure 6.1 High‐frequency being mistaken for a low‐frequency signal due to t...
Figure 6.2 Multiple integrating controllers with a single measurement.
Figure 6.3 Simple anti‐windup scheme for a PI controller.
Figure 6.4 Illustration of a general anti‐windup scheme.
Figure 6.5 Illustration of anti‐windup with the controller implemented in ...
Figure 6.6 Illustration of anti‐windup for controllers based on static state...
Figure 6.7 State estimator and static state feedback augmented with integral...
Figure 6.8 Implementation of anti‐windup for state estimator and static stat...
Figure 6.9 Implementation of anti‐windup for state estimator and static stat...
Figure 6.10 Implementation of decoupler in order to reduce the effect of inp...
Figure 6.11 Pipeline with control valve and two flow controllers.
Figure 6.12 Response to an increased reference for PID1.
Chapter 7
Figure 7.1 Calculation of the Miao–Seborg oscillation index from the autocor...
Figure 7.2 The oscillation detection method of Forsman and Stattin.
Figure 7.3 Hägglund's method for manual oscillation diagnosis.
Figure 7.4 Stiction detection by twice differentiating the process output.
Figure 7.5 Histograms for detecting valve stiction in integrating processes....
Figure 7.6 Histograms for detecting valve stiction in integrating processes,...
Figure 7.7 Use of OP–PV plot to detect stiction. The blue curve shows a syst...
Figure 7.8 Use of OP–PV plot to detect stiction. Left: regular OP–PV plot. R...
Figure 7.9 Illustration of backlash with deadband of width .
Figure 7.10 Illustration of two‐parameter model for behavior of a pneumatica...
Figure 7.11 High‐density plot of industrial data.
Figure 7.12 Power spectral correlation map for industrial data.
Chapter 8
Figure 8.1 Probability density functions for the controlled variable under o...
Figure 8.2 Three commonly used economic performance functions: (a) linear wi...
A
Figure A.1 Feasible region for for Example A.1.
E
Figure E.1 Simplified schematic of a binary distillation process.
Figure E.2 Schematic diagram of the FCC process.
Guide
Cover
Table of Contents
Title Page
Copyright
Dedication
Preface
Acknowledgments
Acronyms
Introduction
Begin Reading
A Fourier–Motzkin Elimination
B Removal of Redundant Constraints
C The Singular Value Decomposition
D Factorization of Transfer Functions into Minimum Phase Stable and All‐Pass Parts
E Models Used in Examples
Index
End User License Agreement
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Advanced Chemical Process Control
Putting Theory into Practice
Morten Hovd
Author
Prof. Morten HovdNorwegian University of Science and Technology7491 TrondheimNorway
Cover Image: © Voranee/Shutterstock
All books published by WILEY‐VCH are carefully produced. Nevertheless, authors, editors, and publisher do not warrant the information contained in these books, including this book, to be free of errors. Readers are advised to keep in mind that statements, data, illustrations, procedural details or other items may inadvertently be inaccurate.
Library of Congress Card No.: applied for
British Library Cataloguing‐in‐Publication DataA catalogue record for this book is available from the British Library.
Bibliographic information published by the Deutsche NationalbibliothekThe Deutsche Nationalbibliothek lists this publication in the Deutsche Nationalbibliografie; detailed bibliographic data are available on the Internet at <http://dnb.d-nb.de>.
© 2023 WILEY‐VCH GmbH, Boschstr. 12, 69469 Weinheim, Germany
All rights reserved (including those of translation into other languages). No part of this book may be reproduced in any form – by photoprinting, microfilm, or any other means – nor transmitted or translated into a machine language without written permission from the publishers. Registered names, trademarks, etc. used in this book, even when not specifically marked as such, are not to be considered unprotected by law.
Print ISBN: 978‐3‐527‐35223‐4ePDF ISBN: 978‐3‐527‐84247‐6ePub ISBN: 978‐3‐527‐84248‐3oBook ISBN: 978‐3‐527‐84249‐0
To Ellen
Preface
Half a century ago, Alan Foss [1] wrote his influential paper about the gap between chemical process control theory and industrial application. Foss clearly put the responsibility on the chemical process control theorists to close this gap. Since then, several advances in control theory, some originating within academia, while others originated in industry and was later adopted and further developed by academia, have contributed to addressing the shortcomings of chemical process control theory, as addressed by Foss:
The extension of the
relative gain array
(
RGA
) to nonzero frequencies and Graminan‐based control structure selection tools have extended the toolkit for designing control structures.
1
Self‐optimal control
[4]
provides a systematic approach to identifying controlled variables for a chemical plant.
Model predictive control
(
MPC
) has great industrial success
[3]
.
Robustness to model error received significant research focus from the 1980s onward.
Control Performance Monitoring has, since the seminal paper by Harris
[2]
, resulted in tools both for monitoring and diagnosing the performance of individual loops as well as for identifying the cause of plantwide disturbances.
The aforementioned list notwithstanding, many would agree to the claim that there is still a wide gap between control theory and common industrial practice in the chemical process industries. This book is the author's attempt to contributing to the reduction of that gap. This book has two ambitious objectives:
To make more advanced control accessible to chemical engineers, many of whom will only have background from a single course in control. While this book is unlikely to effortlessly turn a plant engineer into a control expert, it does contain tools that many plant engineers should find useful. It is also hoped that it will give the plant engineer more weight when discussing with control consultants – either from within the company or external consultants.
To increase the understanding among control engineers (students or graduates moving into the chemical process control area) of how to apply their theoretical knowledge to practical problems in chemical processes.
The third approach to reducing the gap, i.e. to develop and present tools to simplify the application of control, is not a focus of this book – although some colleagues would surely claim that this is what proportional integral derivative (PI(D)) tuning rules are doing.
The reader should note that this book does not start “from scratch,” and some prior knowledge of control is expected. The introduction to the Laplace transform is rudimentary at best, and much more detail could be included in the presentation of frequency analysis. Some knowledge of finite‐dimensional linear algebra is expected. Readers who have never seen a linear state‐space model will face a hurdle. Still, the book should be accessible to readers with background from a course in process control.
Readers with a more extensive knowledge of control theory may find the book lacks rigor. Frequently, results are presented and discussed, without presenting formal proofs. Readers interested in mathematical proofs will have to consult the references. This is in line with this author's intent to keep the focus on issues of importance for industrial applications (without claiming to “know it all”).
The structure of the Book
This book has grown out of more than three decades of learning, teaching, and discussing the control of chemical processes. What has become clear is that process control engineers are faced with a wide variety of tasks and problems. The chapters of this book therefore address a range of different topics – most of which have been the subject of entire books. The selection of material to include is therefore not trivial nor obvious.
Chapter 1
presents some mathematical and control theory background. Readers with some knowledge of control may choose to skip this chapter and only return to it to look up unfamiliar (or forgotten) concepts that appear in the rest of the book. This chapter definitely has a more theoretical and less practical flavor that much of the rest of the book.
Chapter 2
addresses controller tuning for PI(D) controllers, as well as control configuration. The term control configuration here covers both the control functionality often encountered in the regulatory control layer (feedback, feedforward, ratio control,...) and determining which input should be used to control which output in a multi‐loop control system.
Chapter 3
focuses on determining what variables to use for control. Typically, there are more variables that can be measured than can be manipulated, so the most focus is given to the choice of variables to control.
Chapter 4
presents limitations to achievable control performance. Clearly, if it is not possible to achieve acceptable performance, it makes little sense trying to design a controller. Understanding the limitations of achievable performance is also very useful when designing controllers using loop shaping, as presented in
Chapter 2
.
Chapter 5
is about MPC, which is the most popular advanced control type in the chemical process industries.
2
In addition to presenting MPC problem formulations
per se
, important issues such as model updating, offset‐free control, and target calculation are also discussed.
Chapter 6
presents some practical issues in controller implementation. This list is far from complete, some of the issues included are well known and may be considered trivial – but all are important.
Chapter 7
addresses
control performance monitoring
(
CPM
). The number of controllers in even a modestly sized chemical process is too large for plant personnel to frequently monitor each of them, and automated tools are therefore needed for the maintenance of the control. The chapter also includes some tools for finding the root cause of distributed oscillations – oscillations originating at one location in the plant will tend to propagate and disturb other parts of the plant, and hence it is often nontrivial to find where the oscillation originates and what remedial action to take.
Chapter 8
addresses control benefit analysis, i.e. tools to
a priori
assess the economic benefit that can be obtained from improved control. This author admits that the chapter is disappointingly short. Developing generic tools to estimate such economic benefit is indeed difficult. On the other hand, the inability to estimate economic benefit with some certainty is also one of the major obstacles to more pervasive application of advanced control in the chemical process industries.
What's Not in the Book
Selecting what to cover in a textbook invariably requires leaving out interesting topics. Some topics that are relevant in a more general setting, but which this book does not make any attempt to cover, include
Nonlinear control
. Real‐life systems are nonlinear. Nevertheless, this book almost exclusively addresses linear control – with the main exception being the handling of constraints in MPC.
3
Linearization and linear control design suffices for most control problems in the chemical process industries, and in other cases static nonlinear transforms of inputs or outputs can make more strongly nonlinear systems closer to linear. The book also describes briefly approaches to nonlinear MPC (with nonlinearity in the model, not only from constraints). Such complications are needed mainly for control of batch processes (where continuous changes in the operating point are unavoidable), or for processes frequently switching between different operating regimes (such as wastewater treatment plants with anaerobic and aerobic stages). Although linear control often suffices, it is clearly prudent to verify a control design with nonlinear simulation and/or investigate the control at different linearization points (if a nonlinear model is available).
Modeling and system identification
. The availability of good system models are of great importance to control design and verification. This book only briefly describes how to fit a particularly simple monovariable model – more complete coverage of these topics is beyond the scope of this book.
Adaptive and learning control
. While classical adaptive control seems to have been out of favor in the chemical process industries for several decades, there is currently a lot of research on integrating machine learning with advanced control such as MPC. This author definitely accepts the relevance of research on learning control but is of the opinion that at this stage a research monograph would be more appropriate than a textbook for covering these developments.
In leaving out many of the more theoretically complex areas of control theory, readers from a control engineering background may find the book title somewhat puzzling – especially the word Advanced. Although some of the topics covered by this book are relatively standard also within the domain of chemical process control, this author would claim that much of the book covers topics that are indeed advanced compared to common application practice in the chemical process industries. The Introduction will hopefully enlighten readers from outside chemical process control about the unique challenges faced by this application domain and contribute to explaining the prevalence of linear control techniques.
August, 2022
M. HovdTrondheim, Norway
References
1
Foss, A.S. (1973). Critique of chemical process control theory.
AIChE Journal
19: 209–214.
2
Harris, T.J. (1989). Assessment of control loop performance.
The Canadian Journal of Chemical Engineering
67: 856–861.
3
Qin, S.J. and Badgwell, T.A. (2003). A survey of industrial model predictive control technology.
Control Engineering Practice
11 (7): 733–764.
4
Skogestad, S. (2000). Plantwide control: the search for the self‐optimizing control structure.
Journal of Process Control
10: 487–507.
Notes
1
This author is aware that many colleagues in academia are of the opinion that the frequency‐dependent RGA is not “rigorous.” This book will instead take the stance that the dynamic RGA has proved useful and therefore should be disseminated. It is also noted that the “counterexamples” where the steady‐state RGA is claimed to propose a wrong control structure are themselves flawed.
2
And, indeed, the chemical process industries is where MPC was first developed.
3
Constraints represent a strong nonlinearity.
Acknowledgments
It is noted in the preface that this book is a result of more than three decades of learning, teaching, discussing, and practicing chemical process control. Therefore, a large number of people have directly or indirectly influenced the contents of this book, and it is impossible to mention them all. The person with the strongest such influence is Professor Sigurd Skogestad at NTNU, whom I had the fortune to have as my PhD supervisor. At that time, I had an extended research stay in the group of Professor Manfred Morari (then at Caltech). Discussions these outstanding professors as well as with my contemporaries as a PhD student, both in Skogestad's group and in Morari's group, greatly enhanced my understanding of process control. I would particularly like to mention Elling W. Jacobsen, Petter Lundström, John Morud, Richard D. Braatz, Jay H. Lee, and Frank Doyle.
In later years, I have benefited from discussions with a number of people, including Kjetil Havre, Vinay Kariwala, Ivar Halvorsen, Krister Forsman, Alf Isaksson, Tor A. Johansen, Lars Imsland, and Bjarne A. Foss. My own PhD candidates and Postdocs have also enriched my understanding of the area, in particular, Kristin Hestetun, Francesco Scibilia, Giancarlo Marafioti, Florin Stoican, Selvanathan Sivalingam, Muhammad Faisal Aftab, and Jonatan Klemets.
Special thanks are due to my hosts during sabbaticals, when I have learned a lot: Bob Bitmead (UCSD), Jan Maciejowski (University of Cambridge), Sorin Olaru (CentraleSupelec), and Andreas Kugi (TU Vienna).
M. H.
Acronyms
AKF
augmented Kalman filter
AR
auto‐regressive (model)
BLT
biggest log modulus (tuning rule)
CCM
convergent cross mapping
CLDG
closed-loop disturbance gain
CPM
control performance monitoring
DNL
degree of nonlinearity
EKF
extended Kalman filter
EnKF
ensemble Kalman filter
FCC
fluid catalytic cracking
FOPDT
first-order plus deadtime (model)
GM
gain margin
IAE
integral (of) absolute error
IEKF
iterated extended Kalman filter
IMC
internal model control
ISE
integral (of) squared error
KISS
keep it simple, stupid
LHP
left half-plane (of the complex plane)
LP
linear programming
LQ
linear quadratic
LQG
linear quadratic Gaussian
MHE
moving horizon estimation
MIMO
multiple input multiple output
MPC
model predictive control
MV
manipulated variable
MVC
minimum variance controller
MWB
moving window blocking
NGI
non-Gaussianity index
NLI
nonlinearity index
OCI
oscillation contribution index
OP
controller output
PCA
principal component analysis
PID
proportional integral derivative
PSCI
power spectral correlation index
P&ID
piping and instrument diagram
PM
phase margin
PRGA
performance relative gain array
PV
process variable
QP
quadratic programming
RGA
relative gain array
RHE
receding horizon estimation
RHP
right half-plane (of the complex plane)
RHPZ
right half-plane zero
RSS
residual sum of squares
RTO
real time optimization
SIMC
simple (or Skogestad) internal model control (tuning rules)
SISO
single input single output
SP
setpoint (reference value)
SOPDT
second-order plus deadtime (model)
SVD
singular value decomposition
UKF
unscented Kalman filter
Introduction
I.1 Why Is Chemical Process Control Needed?
Many texts on control implicitly assume that it is obvious when and why control is needed. It seems obvious that even a moderately complex process plant will be very difficult to operate without the aid of process control. Nevertheless, it can be worthwhile to spend a few minutes thought on why control is needed. In the following, a short and probably incomplete list of reasons for the need of control is provided, but the list should illustrate the importance of control in a chemical process plant.
Stabilizing the process
. Many processes have integrating or unstable modes. These have to be stabilized by feedback control, otherwise the plant will (sooner or later) drift into unacceptable operating conditions. In the vast majority of cases, this stabilization is provided by automatic feedback control.
1
Note that in practice, “feedback stabilization” of some process variable may be necessary even though the variable in question is asymptotically stable according to the control engineering definition of stability. This happens whenever disturbances have sufficiently large effect on a process variable to cause unacceptably large variations in the process variable value. Plant operators therefore often use the term “stability” in a much less exact way than how the term is defined in control engineering. A control engineer may very well be told that, e.g. “this temperature is not sufficiently stable,” even though the temperature in question is asymptotically stable.
Regularity
. Even if a process is stable, control is needed to avoid shutdowns due to unacceptable operating conditions. Such shutdowns may be initiated automatically by a shutdown system but may also be caused by outright equipment failure.
Minimizing effects on the environment
. In addition to maintaining safe and stable production, the control system should also ensure that any harmful effects on the environment are minimized. This is done by optimizing the conversion of raw materials,
2
and by maintaining conditions which minimize the production of any harmful byproducts.
Obtaining the right product quality
. Control is often needed both for achieving the right product quality and for reducing quality variations.
Achieving the right production rate
. Control is used for achieving the right production rate in a plant. Ideally, it should be possible to adjust the production rate at one point in the process, and the control system should automatically adjust the throughput of up‐ or downstream units accordingly.
Optimize process operation
. When a process achieves safe and stable operation, with little downtime and produces the right quality of product at the desired production rate, the next task is to optimize the production. The objective of the optimization is normally to achieve the most cost‐effective production. This involves identifying, tracking, and maintaining the optimal operating conditions in the face of disturbances in production rate, raw material composition, and ambient conditions(e.g. atmospheric temperature). Process optimization often involves close coordination of several process units and operation close to process constraints.
The list aforementioned should illustrate that process control is vital for the operation of chemical process plants. Even plants of quite moderate complexity would be virtually impossible to operate without control. Even where totally manual operation is physically feasible, it is unlikely to be economically feasible due to product quality variations and high personnel costs, since a high number of operators will be required to perform the many (often tedious) tasks that the process control system normally handles.
Usually many more variables are controlled than what is directly implied by the list above, and there are often control loops for variables which have no specification associated with them. There are often good reasons for such control loops – two possible reasons are:
To stop disturbances from propagating downstream
. Even when there are no direct specification on a process variable, variations in the process variable may cause variations in more important variables downstream. In such cases, it makes sense to remove the disturbance at its source.
Local removal of uncertainty
. By measuring and controlling a process variable, it may be possible to reduce the effect of uncertainty with respect to equipment behavior or disturbances. Examples of such control loops are valve positioners used to minimize the uncertainty in the valve opening, or local flow control loops which may be used to counteract the effects of pressure disturbances up‐ or downstream of a valve, changes in fluid properties, or inaccuracies in the valve characteristics.
I.2 What Knowledge Does a chemical Process Control Engineer need?
The aforementioned list of reasons for why process control is needed also indicates what kind of knowledge is required for a process control engineer. The process control engineer needs to have a thorough understanding of the process. Most stabilizing control loops involve only one process unit (e.g. a tank or a reactor), and most equipment limitations are also determined by the individual units. Process understanding on the scale of the individual units is therefore required. Understanding what phenomena affect product quality also require an understanding of the individual process units. On the other hand, ensuring that the specified production rate propagates throughout the plant, understanding how the effects of disturbances propagate, and optimizing the process operation require an understanding of how the different process units interact, i.e. an understanding of the process on a larger scale.
Most basic control functions are performed by single loops, i.e. control loops with one controlled variable and one manipulated variable. Thus, when it is understood why a particular process variable needs to be controlled, and what manipulated variable should be used to control it, 3 the controller design itself can be performed using traditional single‐loop control theory (if any theoretical considerations are made at all). Often a standard type of controller, such as a proportional integral derivative (PID) controller, is tuned online, and there is little need for a process model. Other control tasks are multivariable in nature, either because it is necessary to resolve interactions between different control loops or because the control task requires coordination between different process units. Process models are often very useful for these types of control problem. The models may either be linear models obtained from experiments on the plant or possibly nonlinear models derived from physical and chemical principles. Some understanding of mathematical modeling and system identification techniques are then required. Nonlinear system identification from plant experiments are not in standard use in the process industries.
Optimizing process operation requires some understanding of plant economics, involving the costs of raw materials and utilities, the effect of product quality on product price, the cost of reprocessing off‐spec product, etc. Although it is rare that economics is optimized by feedback controllers, 4 an understanding of plant economics will help understanding where efforts to improve control should be focused and will help when discussing the need for improved control with plant management.
A process control engineer must thus have knowledge of both process and control engineering. However, it is not reasonable to expect the same level of expertise in either of these disciplines from the process control engineer as for “specialist” process or control engineers. There appears to be a “cultural gap” between process and control engineers, and the process control engineer should attempt to bridge this gap. This means that the process control engineer should be able to communicate meaningfully with both process and control engineers and thereby also be able to obtain any missing knowledge by discussing with the “specialists.” However, at a production plant, there will seldom be specialists in control theory, but there will always be process engineers. At best, large companies may have control theory specialists at some central research or engineering division. This indicates that a process control engineer should have a fairly comprehensive background in control engineering, while the process engineering background should at least be sufficient to communicate effectively with the process engineers.
In the same way as for other branches of engineering, success at work will not come from technological competence alone. A successful engineer will need the ability to work effectively in multidisciplinary project teams, as well as skills in communicating with management and operators. Such nontechnical issues will not be discussed further here.
I.3 What Makes Chemical Process Control Unique?
Control engineering provides an extensive toolbox that can be applied to a very wide range of application domains. Still, process control is characterized by a few features, the combination of which make process control uniquely challenging:
Physical scale
. Although small‐scale industrial plants do exist, more common are large‐scale industrial production plants, with hundreds of meters or even kilometers from one end to the other, and the need for some degree of coordination between different sections of the plant.
One‐of‐a‐kind plants
. Most plants are unique. Although many of the individual components may be standard issue, their assembly into the overall plant is typically unique to the plant in question. Even in the rather rare cases when plants are built to be nominally identical, differences in external disturbances, raw materials, and operating and maintenance practices will mean that differences accumulate over time. The sheer scale of industrial plants also mean that the number of ways in which plant behavior may differ is very large. This differs from, say, automobiles or airplanes, where the aim is to produce a large number of identical units. From a control perspective, the main consequence for chemical process control is that the
cost of modeling and model maintenance
must be borne by each individual plant. Model‐based control design or plant operation will therefore often have to be based on rather simple and inaccurate models.
Plant experimentation
. Another aspect of the point above is that in order to learn plant behavior or verify control designs, experiments often have to be performed on the plant itself. Experiments disrupt plant operation and can also involve the risk of damage or accident. Again this differs from control applications in mass produced items, where damage to a few items during testing is often expected.
Lots of data, little information
. In many chemical process plants, fast and reliable measurement of key variables are not available. In some processes, measurements of temperatures, pressures, and flows are readily available, while composition measurements require either costly online analyzers with long time delays or require manual sampling and laboratory analysis. In other cases, harsh process conditions means that not even pressures and temperatures can be measured, and control must be based on measurements obtained externally to the process itself (such as currents and voltages in electrochemical plants). Again, this is in contrast to other application areas of control, such as motion control where positions and velocities often can be measured fairly accurately.
I.4 The Structure of Control Systems in the Chemical Process Industries
When studying control systems in the chemical process industries, one may observe that they often share a common structure. This structure is illustrated in Figure I.1.
The lower level in the control system is the regulatory control layer. The structure of the individual controllers in the regulatory control layer is normally very simple. Standard single‐loop controllers, typically of proportional integral (PI)/PID type, are the most common, but other simple control functions like feedforward control, ratio control, or cascaded control loops may also be found. Truly multivariable controllers are rare at this level. The regulatory control system typically controls basic process variables such as temperatures, pressures, flowrates, speeds, or concentrations, but in some cases the controlled variable may be calculated based on several measurements, e.g. a component flowrate based on measurements of both concentration and overall flowrate or a ratio of two flowrates. Usually, a controller in the regulatory control layer manipulates a process variable directly (e.g. a valve opening), but in some cases the manipulated variable may be a setpoint of a cascaded control loop. Most control functions that are essential to the stability and integrity of the process are executed in this layer, such as stabilizing the process and maintaining acceptable equipment operating conditions.
The supervisory control layer coordinates the control of a process unit or a few closely connected process units. It coordinates the action of several control loops and tries to maintain the process conditions close to the optimal while ensuring that operating constraints are not violated. The variables that are controlled by supervisory controllers may be process measurements, variables calculated or estimated from process measurements, or the output from a regulatory controller. The manipulated variables are often setpoints to regulatory controllers, but process variables may also be manipulated directly. Whereas regulatory controllers are often designed and implemented without ever formulating any process model explicitly, supervisory controllers usually contain an explicitly formulated process model. The model is dynamic and often linear and obtained from experiments on the plant. Typically, supervisory controllers use some variant of model predictive control (MPC).
The optimal conditions that the supervisory controllers try to maintain may be calculated by a RTO control layer. The RTO layer identifies the optimal conditions by solving an optimization problem involving models of the production cost, value of product (possibly dependent on quality), and the process itself. The process model is often nonlinear and derived from fundamental physical and chemical relationships, but they are usually static.
Figure I.1 Typical structure of the control system for a large plant in the process industries.
The higher control layer shown in Figure I.1 is the production planning and scheduling layer. This layer determines what products should be produced and when they should be produced. This layer requires information from the sales department about the quantities of the different products that should be produced, the deadlines for delivery, and possibly product prices. From the purchasing department, information about the availability and price of raw materials are obtained. Information from the plant describes what products can be made in the different operating modes and what production rates can be achieved.
In addition to the layers in Figure I.1, there should also be a separate safety system that will shut the process down in a safe and controlled manner when potentially dangerous conditions occur. There are also higher levels of decision‐making which are not shown, such as sales and purchasing, and construction of new plants. These levels are considered to be of little relevance to process control and will not be discussed further.
Note that there is a difference in timescale of execution for the different layers. The regulatory control system typically have sampling intervals on the scale of 1 second (or faster for some types of equipment), supervisory controllers usually operate on the timescale of minutes, the RTO layer on a scale of hours, and the planning/scheduling layer on a scale of days (or weeks). The control bandwidths achieved by the different layers differ in the same way as sampling intervals differ. This difference in control bandwidths can simplify the required modeling in the higher levels; if a variable is controlled by the regulatory control layer, and the bandwidth for the control loop is well beyond what is achieved in the supervisory control layer, a static model for this variable (usually the model would simply be variable value = setpoint) will often suffice for the supervisory control.
It is not meaningful to say that one layer is more important than another, since they are interdependent. The objective of the lower layers are not well defined without information from the higher layers (e.g. the regulatory control layer needs to know the setpoints that are determined by the supervisory control layer), whereas the higher layers need the lower layers to implement the control actions. However, in many plants, human operators perform the tasks of some the layers as shown in Figure I.1, and it is only the regulatory control layer that is present (and highly automated) in virtually all industrial plants.
Why has this multilayered structure for industrial control systems evolved? It is clear that this structure imposes limitations in achievable control performance compared to a hypothetical optimal centralized controller which perfectly coordinates all available manipulated variables in order to achieve the control objectives. In the past, the lack of computing power would have made such a centralized controller virtually impossible to implement, but the continued increase in available computing power could make such a controller feasible in the not too distant future. Is this the direction industrial control systems are heading? This appears not to be the case. In the last two decades, development has instead moved in the opposite direction, as increased availability of computing power has made the supervisory control and RTO layers much more common. Some reasons for using such a multilayered structure are:
Economics
. Optimal control performance – defined in normal control engineering terms (using, e.g. the ‐ or norm) – does not necessarily imply optimal economic performance. To be more specific, an optimal controller synthesis problem does not take into account the cost of developing and maintaining the required process (or possibly plant economic) models. An optimal centralized controller would require a dynamic model of most aspects of the process behavior. The required model would therefore be quite complex and difficult to develop and maintain. In contrast, the higher layers in a structured control system can take advantage of the model simplifications made possible by the presence of the lower layers. The regulatory control level needs little model information to operate, since it derives most process information from feedback from process measurements.
5
Redesign and retuning
. The behavior of a process plant changes with time, for a number of reasons such as equipment wear, changes in raw materials, changes in operating conditions in order to change product qualities or what products are produced, and plant modifications. Due to the sheer complexity of a centralized controller, it would be difficult and time‐consuming to update the controller to account for all such changes. With a structured control system, it is easier to see what modifications need to be made, and the modifications themselves will normally be less involved.
Start‐up and shutdown
. Common operating practice during start‐up is that many of the controls are put in manual. Parts of the regulatory control layer may be in automatic, but rarely will any higher layer controls be in operation. The loops of the regulatory control layer that are initially in manual are put in automatic when the equipment that they control are approaching normal operating conditions. When the regulatory control layer for a process section is in service, the supervisory control system may be put in operation, and so on. Shutdown is performed in the reverse sequence. Thus, there may be scope for significant improvement of the start‐up and shutdown procedures of a plant, as quicker start‐up and shutdown can reduce plant downtime. However, a model, which in addition to normal operating conditions, is able to describe start‐up and shutdown and is necessarily much more complex than a model which covers only the range of conditions that are encountered in normal operation. Building such a model would be difficult and costly. Start‐up and shutdown of a plant with an optimal centralized control system which does not cover start‐up and shutdown may well be more difficult than with a traditional control system, because it may not be difficult to put an optimal control system gradually into or out of service.
Operator acceptance and understanding
. Control systems that are not accepted by the operators are likely to be taken out of service. An optimal centralized control system will often be complex and difficult to understand. Operator understanding obviously makes acceptance easier, and a traditional control system, being easier to understand, often has an advantage in this respect. Plant shutdowns may be caused by operators with insufficient understanding of the control system. Such shutdowns should actually be blamed on the control system (or the people who designed and installed the control system), since operators are an integral part of the plant operation, and their understanding of the control system must therefore be ensured.
Failure of computer hardware and software
. In traditional control systems, the operators retain the help of the regulatory control system in keeping the process in operation if a hardware or software failure occurs in higher levels of the control system. A hardware backup for the regulatory control system is much cheaper than for the higher levels in the control system, as the regulatory control system can be decomposed into simple control tasks (mainly single loops). In contrast, an optimal centralized controller would require a powerful computer, and it is therefore more costly to provide a backup system. However, with the continued decrease in computer cost, this argument may weaken.
Robustness
.The complexity of an optimal centralized control system will make it difficult to analyze whether the system is robust with respect to model uncertainty and numerical inaccuracies. Analyzing robustness need not be trivial even for traditional control systems. The ultimate test of robustness will be in the operation of the plant. A traditional control system may be applied gradually, first the regulatory control system, then section by section of the supervisory control system, etc. When problem arise, it will therefore be easier to analyze the cause of the problem with a traditional control system than with a centralized control system.
Local removal of uncertainty
. It has been noted earlier that one effect of the lower layer control functions is to remove model uncertainty as seen from the higher layers. Thus, the existence of the lower layers allow for simpler models in the higher layers and make the models more accurate. The more complex computations in the higher layers are therefore performed by simpler, yet more accurate models. A centralized control system will not have this advantage.
Existing traditional control systems
. Where existing control systems perform reasonably well, it makes sense to put effort into improving the existing system rather than to take the risky decision to design a new control system. This argument applies also to many new plants, as many chemical processes are not well understood. For such processes, it will therefore be necessary to carry out model identification and validation on the actual process. During this period, some minimum amount of control will be needed. The regulatory control layer of a traditional control system requires little information about the process and can therefore be in operation in this period.
It should be clear from the above that this author believes that control systems in the future will continue to have a number of distinct layers. Two prerequisites appear to be necessary for a traditional control system to be replaced with a centralized one:
The traditional control system must give unacceptable performance.
The process must be sufficiently well understood to be able to develop a process model which describes all relevant process behavior.
Since it is quite rare that a traditional control system is unable to control a chemical process for which detailed process understanding is available (provided sufficient effort and expertise have been put into the design of the control system), it should follow that majority of control systems will continue to be of the traditional structured type.
In short, the layered control system is consistent with the common approach of breaking down big problems into smaller, more manageable parts, and as such agrees with the keep it simple, stupid (KISS) principle.
I.5 Notation
Vector of system
states
.
The time derivative of the state vector (for continuous‐time systems).
The vector of manipulated variables (the variables manipulated by the control system to control the plant), sometimes also referred to as
inputs
. In some literature, the vector is also called the
control variables
.
The
controlled variables
(the variables that the control system attempts to control). Often, the vector is also identical to the vector of
measured variables
.
The vector of
disturbance variables
.
The vector at timestep (for discrete‐time systems).
Elements and of the vector .
Capital letters are used for matrices.
Element of the matrix .
For the linear(ized) system in continuous time:
are matrices of appropriate dimension, and
are the corresponding plant and disturbance transfer function matrices, respectively. An alternative notation which is often used for complex state‐space expressions, is
That is, matrices in square brackets with a vertical and a horizontal line contain expressions for the state‐space representation of some transfer function matrix.
Matrices are used also to define dynamical linear(ized) models in discrete time:
where the subscript ( or ) defines the discrete sampling instant in question. For simplicity of notation, the same notation is used often for continuous‐ and discrete‐time models, and it should be clear from context whether continuous or discrete time is used. Note, however, that the model matrices will be different for discrete and continuous time, i.e. converting from continuous to discrete time (or vice versa) will change the matrices .6
Notes
1
However, some industries still use very large buffer tanks between different sections in the process. For such tanks, it may be sufficient with infrequent operator intervention to stop the buffer tank from overfilling or emptying.
2
Optimizing the conversion of raw materials usually means maximizing the conversion, unless this causes unacceptably high production of undesired byproducts or requires large energy inputs.
3
Determining what variables are to be controlled, what manipulated variables should be used for control, and the structure of interconnections between manipulated and controlled variables are quite critical tasks in the design of a process control system. This part of the controller design is often not described in textbooks on “pure” control engineering but will be covered in some detail in later sections.
4
It is more common that economic criteria are used in the problem formulation for so‐called
real time optimization
(
RTO
) problems, or for plant production planning and scheduling, as shown in
Figure I.1
.
5
A good process model may be of good use when
designing control structures
for regulatory control. However, after the regulatory controllers are implemented, they normally do not make any explicit use of a process model.
6
Whereas the matrices describe instantaneous effects (not affected by the passing of time) and will be the same for continuous‐ and discrete‐time models.
1Mathematical and Control Theory Background
1.1 Introduction
This chapter will review some mathematical and control theory background, some of which is actually assumed covered by previous control courses. Both the coverage of topics and their presentation will therefore lack some detail, as the presentation is aiming
to provide sufficient background knowledge for readers with little exposure to control theory,
to correct what is this author's impression of what are the most common misconceptions
to establish some basic concepts and introduce some notation.
1.2 Models for Dynamical Systems
Many different model representations are used for dynamical systems, and a few of the more common ones will be introduced here.
1.2.1 Dynamical Systems in Continuous Time
A rather general way of representing a dynamical system in continuous time is via a set of ordinary differential equations:
where the variables are termed as the system states and is the time derivative of the state. The variables and are both external variables that affect the system. In the context of control, it is common to distinguish between the manipulated variables or (control) inputs that can be manipulated by a controller, and the disturbances that are external variables that affect the system but which cannot be set by the controller.
The system states are generally only a set of variables that are used to describe the system's behavior over time. Whether the individual components of the state vector can be assigned any particular physical interpretation will depend on how the model is derived. For models derived from fundamental physical and chemical relationships (often termed as “rigorous models”), the states will often be quantities like temperatures, concentrations, and velocities. If, in contrast, the model is an empirical model identified from observed data, it will often not be possible to assign any particular interpretation to the states.
Along with the state equation (1.1), one typically also needs a measurement equation such as:
where the vector is a vector of system outputs, which often correspond to available physical measurements from the systems. Control design is usually at its most simple when all states can be measured, i.e. when .
Disturbances need not be included in all control problems. If no disturbances are included in the problem formulation, Eqs. (1.1) and (1.2) trivially simplify to and , respectively.
Since we are dealing with dynamical systems, it is hopefully obvious that the variables may all vary with time . In this section, time is considered as a continuous variable, in accordance with our usual notion of time.
Together, Eqs. (1.1) and (1.2) define a system model in continuous time. This type of model is rather general and can deal with any system where it suffices to consider system properties at specific points in space, or where it is acceptable to average/lump system properties over space. Such models where properties are averaged over space are often called lumped models.
For some applications, it may be necessary to consider also spatial distribution of properties. Rigorous modeling of such systems typically result with a set of partial differential equations (instead of the ordinary differential equations of (1.1)). In addition to derivatives with respect to time, such models also contain derivatives with respect to one or more spatial dimensions. Models described by partial differential equations will not be considered any further here. Although control design based on partial differential equations is an active research area, the more common industrial practice is to convert the set of partial differential equations to a (larger) set of ordinary differential equations through some sort of spatial discretization.
