Mikles J., Fikar M. Process Modelling, Identification, and Control

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Process Modelling, Identiﬁcation, and Control

Ján Mikleš · Miroslav Fikar

Process Modelling,

Identiﬁcation, and Control

With 187 Figures and 13 Tables

ABC

Ján Mikle

Department of Information Engineering

and Process Control

Slovak University of Technology in Bratislava

Radlinského 9

812 37 Bratislava 1

Slovak Republic

jan.mikles@stuba.sk

Miroslav Fikar

Department of Information Engineering

and Process Control

Slovak University of Technology in Bratislava

Radlinského 9

812 37 Bratislava 1

Slovak Republic

miroslav.ﬁkar@stuba.sk

Library of Congress Control Number: 2007928498

ISBN 978-3-540-71969-4 Springer Berlin Heidelberg New York

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To our wives, Eva and Zuzana, that showed so much

understanding during the preparation of the book

Preface

Control and automation in its broadest sense plays a fundamental role in

process industries. Control assures stability of technologies, disturbance at-

tenuation, safety of equipment and environment as well as optimal process

operation from economic point of view. This book intends to present modern

automatic control methods and their applications in process control in pro-

cess industries. The processes studied mainly involve mass and heat transfer

processes and chemical reactors.

It is assumed that the reader has already a basic knowledge about con-

trolled processes and about diﬀerential and integral calculus as well as about

matrix algebra. Automatic control problems involve mathematics more than it

is usual in other engineering disciplines. The book treats problems in a similar

way as it is in mathematics. The problem is formulated at ﬁrst, then the the-

orem is stated. Only necessary conditions are usually proved and suﬃciency

is left aside as it follows from the physical nature of the problem solved. This

helps to follow the engineering character of problems.

The intended audience of this book includes graduate students but can

also be of interest to practising engineers or applied scientists.

Organisation of the book follows the requirement of presentation of the

process control algorithms that take into account changes of static and dy-

namic properties of processes. There are several possibilities to capture these

changes. As the control objects in process industries are mainly nonlinear and

continuous-time, the ﬁrst possibility is to use nonlinear mathematical models

in the form of partial diﬀerential equations, or after some simpliﬁcations, non-

linear diﬀerential equations. Usage of these models in control is computation-

ally very demanding. Therefore, it is suitable to use robust control methods

based on linearised models with uncertainties. However, strong nonlineari-

ties can decrease performance of robust control methods and adaptive control

algorithms can possibly be used.

The book presents process control using self-tuning (ST) controllers based

on linear models. There are several reasons for their use. ST controllers can

take into account changes of operating regimes of nonlinear processes as well as

VIII Preface

changes in physical process parameters. These changes can be caused by ageing

or wearing of materials, etc. Finally, ST controllers can eliminate unmeasured

disturbances, process noise, and unmodelled dynamic properties of processes.

The last chapter of the book that discusses adaptive control makes use

of all previous parts. Here, discrete and continuous-time ST control of singl-

evariable and multivariable processes is investigated. For its implementation

it is necessary to have in disposition an algorithm of recursive identiﬁcation

that provides an up-to-date model of the controlled process. This model is

then used in feedback process control based on either explicit or implicit pole

placement methods.

A basic requirement for a successful control is to have a suitable model

for control. It is known that the process design in process industries involves

nonlinear models with states evolving in space and time. This corresponds to

models described by partial diﬀerential equations. Automatic control based

such models is very diﬃcult as it requires additional capacity of control com-

puters and can be used only in some special cases. Self-tuning control requires

linear models only described by ordinary diﬀerential equations of low order.

This is caused by the fact that higher order models can cause singularities in

calculation of the control law.

The ﬁrst chapter of the book explains basic concepts that can be encoun-

tered in process control.

The second chapter describes principles of process modelling. Some princi-

pal models as a packed absorption column, a distillation column, and a chem-

ical reactor are developed. Mathematical model of a plug-ﬂow reactor serves

for explanation of transport time delay that together with dynamic time delay

forms a basic phenomenon in continuous-time process models. Description of

speciﬁc process models is accompanied by assumptions when the models in

the form of ordinary diﬀerential equations can be valid. Finally, general pro-

cess models are explained together with the method of linearisation and the

notion of systems and processes.

The third chapter explains brieﬂy the use of the Laplace transform in

process modelling. State-space process models obtained in the previous chap-

ter are analysed. A concept of state is deﬁned and the Lyapunov stability

of continuous-time processes is investigated. The physical interpretation of

theoretical facts is explained on a model of a U-tube. Conditions of control-

lability and observability are applied to a continuously stirred tank reactor.

The state-space process models obtained from material and heat balances are

transformed into input-output models for the purposes of identiﬁcation and

control design.

The aim of the fourth chapter on dynamic behaviour of processes is to

show responses of processes to deterministic and stochastic inputs. Computer

simulations explain how Euler and Runge-Kutta methods for integration of

diﬀerential equations can be used. Examples include MATLAB/Simulink, C,

and BASIC implementations. Process examples in this chapter demonstrate

diﬀerences between original nonlinear and linearised models. The part dealing

Preface IX

with stochastic characteristics explains random variables and processes, the

deﬁnition of the white noise and others needed in state observation and in

stochastic control.

Direct digital process control that constitutes a part of discrete-time adap-

tive control needs discrete-time process models. Therefore, the ﬁfth chapter

deals with the Z-transform, conversion between continuous-time and sampled-

data processes. Also discussed are stability, controllability, observability, and

basic properties of discrete-time systems.

Both adaptive and non-adaptive control methods are usually based on a

mathematical model of a process. The sixth chapter is divided into two parts.

In the ﬁrst one identiﬁcation of process models is based on their response to

the step change on input. The second part deals in more detail with recursive

least-squares (RLS) methods. Although primarily developed for discrete-time

models, it is shown how to use it also for continuous-time models. The RLS

method described in the book has been in use for more than 20 years at the

authors place. Here we describe its implementation in MATLAB/Simulink

environment as a part of the IDTOOL Toolbox available for free in the Internet

(see the web page of the book). IDTOOL includes both discrete-time and

continuous-time process identiﬁcation.

The aim of the seventh chapter is to show the basic feedback control con-

ﬁguration, open and closed-loop issues, steady state behaviour and control

performance indices. The second part deals with the mostly used controllers

in practise - PID controllers. Several problems solved heuristically with PID

controllers are then more rigorously handled in next chapters dealing with

optimal and predictive control.

The most important part of the book covers design of feedback controllers

from the pole-placement point of view. Optimal control follows from the prin-

ciple of minimum and from dynamic programming. At ﬁrst, the problem of

pole-placement is investigated in a detail based on state-space process models.

The controller is then designed from a combination of a feedback and a state

observer. This controller can then also be interpreted from input-output point

of view and results in polynomial pole-placement controller design. The Youla-

Kuˇcera parametrisation is used to ﬁnd all stabilising controllers for a given pro-

cess. Also, its dual parametrisation is used to ﬁnd all processes stabilised by a

given controller. The Youla-Kuˇcera parametrisation makes it possible to unify

control design for both continuous-time and discrete-time systems using the

polynomial approach. This is the reason why mostly continuous-time systems

are studied. Dynamic programming is explained for both continuous-time and

discrete-time systems. The part devoted to the Youla-Kuˇcera parametrisation

treats also ﬁnite time control – dead-beat (DB) that describes a discrete-

time control of a continuous-time process that cannot be realised using a

continuous-time controller. State-space quadratically (Q) optimal control of

linear (L) process models, i.e. LQ control with observer and its polynomial

equivalent are interpreted as the pole-placement problem. Similarly, LQ con-

trol with the Kalman ﬁlter (LQG) or H2 control can also be interpreted as the

XPreface

pole-placement control problem. An attention is paid to integral properties of

controllers and it is shown that optimal controllers are often of the form of

modiﬁed PID controllers. The examples in the chapter make a heavy use of

the Polynomial Toolbox for MATLAB (http://www.polyx.com).

The chapter nine extends the optimal control design with predictive con-

trol approach. It is explained why this approach predetermines discrete-time

process control. At the beginning, the basic principles and ingredients of pre-

dictive control are explained. The derivation of the predictors and controllers

is then shown for both input-output and state-space process models. The

chapter also deals with incorporation of constraints on input variables and

discusses the issue of stability and stabilisability of predictive closed-loop sys-

tem. Finally, the chapter concludes with both singlevariable and multivariable

tuning and show examples of applications in process control.

The last chapter combines results of previous chapters in adaptive control.

We prefer to use the so-called explicit, or self-tuning approach to adaptive

control where process parameters are estimated on-line using recursive least-

squares methods. Then, at each sampling instant, the available model is used

in control design.

The book has an ambition to integrate interpretations of continuous-time

and discrete-time control, deterministic and stochastic control with incorpo-

ration of sets of all stabilising controllers. Notations used in separate parts of

the books have been adapted to this aim.

Some of the programs and ﬁgures of the examples in the book marked in

the margin are freely available at the web page of the book:

www

http://www.kirp.chtf.stuba.sk/~fikar/books/mic/.

The program sources are for MATLAB with toolboxes Simulink, Control

System Toolbox, Polynomial Toolbox (http://www.polyx.cz), Multipara-

metric Toolbox (MPT, http://control.ee.ethz.ch/~mpt) and, IDTOOL

(from the web site). The examples are veriﬁed in both simulation and real-

time test cases using Real-time MATLAB toolbox and the industrial system

SIMATIC STEP7.

Each chapter includes bibliographic references related to the text. Besides

the classical material on process dynamics or feedback control, there are some

parts of the book that follow from the journal publications of the authors.

Acknowledgements

The book has been in preparation in the form of study texts for almost 10

years and came into existence mainly at Department Information Engineering

and Process Control established at Faculty of Chemical and Food Technology,

Slovak University of Technology in 1960.

The authors wish to express their gratitude to all present and past employ-

ees of the department that helped to provide a creative environment and to all

students, PhD students that commented the manuscript. Namely we would

like to thank to our colleagues L’.

Cirka,

S. Koˇzka, F. Jelenˇciak, J. Dziv´ak, T.

Hirmajer, K. Cal´ık,L.Derm´ıˇsek, and to associated prof. M. Bakoˇsov´afrom

Slovak University of Technology for comments to the manuscript that helped

to ﬁnd some errors and problems.

Authors also thank for inspiration and ideas to all with whom they had

dialogues during numerous stays abroad at TU Darmstadt, Uni Birmingham,

TU Lyngby, Uni Dortmund, and ENSIC Nancy.

We are very thankful for the constructive remarks in identiﬁcation to

prof. Prokop from T. Bata University in Zl´ın, in modelling and dynamic simu-

lations of continuous-time processes to associated prof. Lavrin from Technical

University of Koˇsice and to prof. Alex´ık from University of

Zilina. We thank

for comments in parts of identiﬁcation and optimal control to prof. Dost´al

from T. Bata University in Zl´ın and to prof. Roh´al’ from Faculty of Mechani-

cal Engineering at Slovak University of Technology in Bratislava. The part on

predictive control has greatly been enhanced by suggestions of M. Kvasnica

and his work on MPT Toolbox and explicit predictive control during his stay

at ETH Z

urich.

We also thank to prof. Kuˇcera and prof.

Sebek from Czech Technical Uni-

versity in Prague for many inspiring ideas and long cooperation that has con-

tributed to the conception of the book. We have been involved in the project

EUROPOLY supported by European Union and have had the possibility to

use the most recent versions of the Polynomial Toolbox for MATLAB.

We are thankful to Dr. Hippe from University of N

urnberg-Erlangen for

comments to the manuscript.