`
`
`Ex. PGS 1035
`
`
`
`EX. PGS 1035
`
`
`
`
`
`

`

`Computer-Controlled
`Systems
`
`Theory ancl Design
`
`THIRD EDITION
`
`Karl J. Astrom
`
`0
`
`Bjorn Wittenmark
`
`Prentice Hall, Upper Saddle River, New Jersey
`
`07458
`
`Ex. PGS 1035
`
`

`

`Library of Congress Cataloging-In-Publication Data
`
`Astr/im, Karl J. (Karl Johan)
`Computer-Controlled systems : theory and design I Karl J. Astr6m
`Bjl>m Wiucnmark. ·· 3rd cd.
`P· an.
`Includes bibliographical references and index.
`ISBN 0-13-314899-8
`I. Automatic control--Data processing. I. Wiuenmarlc, BjOrn.
`n. Title.
`TJ213.A78 1997
`629.8'9--dc20
`
`96-36745
`en>
`
`Publisher: Tom Robbins
`Associate editor: Alice Dworkin
`Editorial production supervision: Joseph Scordato
`Editor-in-chief: Marcia Horton
`Managing editor. Bayani Mendoza DeLeon
`Copyeditor: Peter J. Zurita
`Cover designer: Bruce Kenselaar
`Director of production and manufacturing: David W. Riccardi
`Manufacturing buyer: Donna Sullivan
`Editorial assistant: Nancy Garcia
`
`@1997 by Prentice·llaU, Inc.
`Simon & Schuster/A Viacom Company
`Upper Saddle River, NJ 07458
`
`All rights reserved. No part of this book may be
`reproduced, in any fom1 or by any means,
`without pem1ission in writing from the publisher.
`
`The author and publisher of this boolc have used their best cffons in preparing this book. lnese efforts
`include the development, research, and testing of the theories and programs to determine their effectivene.ss.
`The author and publisher make no warranty of any kind, expressed or implied, with regard to these programs
`or the documentation contained in this book. The author and pubtisher shaU not be liable in any event for
`incidental or consequential damages in connection with, or arising out of, the fumish.ing, performance, 9r use
`of these programs.
`
`·M.l.T. LIBHf\HiES
`
`MAY 0 2 1997
`
`Printed in the United States of America
`
`10 9 g 7 6 5 4 3 2
`
`ISBN 0-13-314899-8
`
`Prentice-Hall International (UK) Limited, London
`Prentice-Hall of Australia Pty. Limited, Sydney
`Prentice-HaU Canada Inc., Toronto
`Prentice-Hall Hispanoamericana, S.A., Mexico
`Prentice-Hall of India Private Limited, New Delhi
`Prentice-Hall of Japan. Inc., Tokyo
`Simon & Schuster Asia Pte. L•.d., Singapore
`Editora Prentice-Hall do Brasil, Ltda., Rio de Janeiro
`
`Ex. PGS 1035
`
`

`

`7
`
`Computer Control
`
`1.1 Introduction
`
`Practically all control systems that are implemented today are based on com(cid:173)
`puter control. It is therefore important to understand computer-controlled sys(cid:173)
`tems well. Such systems can be viewed as approximations of analog-control
`systems, but this is a poor approach because the full potential of computer con(cid:173)
`trol is not used. At best the results are only as good as those obtained with
`analog control. It is much better to master computer-controlled systems, so that
`the full potential of computer control can be used. 'rhere are also phenomena
`that occur in computer-controlled systems that have no correspondence in ana(cid:173)
`log systems. It is important for an engineer to understand this. The main goal
`of this book is to provide a solid background for understanding, analyzing, and
`designing computer-controlled systems.
`A computer-controlled system can be described schematically as in Fig. 1.1.
`The output from the process y(t) is a continuous-time signal. The output is
`converted into digital form by the analog-to-digital (A-D) converter. The A-D
`converter can be included in the computer or regarded as a separate unit, ac(cid:173)
`cording to one's preference. The conversion is done at the sampling times, tit.
`The computer interprets the converted signal, {y(tk)}, as a sequence of num(cid:173)
`bers, processes the measurements using an algorithm, and gives a new se(cid:173)
`quence of numbers, {u(tk)}. This sequence is converted to an analog signal by
`a digital-to-analog (D-A) converter. The events are synchronized by the real(cid:173)
`time clock in the computer. The digital computer operates sequentially in time
`and each operation takes some time. The D-A converter must, however, produce
`a continuous-time signal. This is normally done by keeping the control signal
`constant between the conversions. In this case the system runs open loop in
`the time interval between the sampling instants because the control signal is
`constant irrespective of the value of the output.
`The computer-controlled system contains both continuous-time signals and
`sampled, or discrete-time, signals. Such systems have traditionally been called
`
`Ex. PGS 1035
`
`

`

`2
`
`Computer Control
`r------------------ -- ------------,
`Computer
`:
`I
`I
`
`Chap. 1
`
`j
`I
`I
`L- -- -- ---- -------------------- --~
`
`Figure 1.1 Schematic diagram of a computer-controlled system.
`
`sampled-data systems, and this term will be used here as a synonym for com(cid:173)
`puler-controlled systems.
`The mixture of different types of signals sometimes causes difficulties. In
`most cases it is, however, sufficient to describe the behavior of the system at
`the sampling instants. The signals are then of interest only at discrete times.
`Such systems will be called discrete-time systems. Discrete-time systems deal
`with sequences of numbers, so a natural way to represent these systems is to
`use difference equations.
`The purpose of the book is to present the control theory tha t is relevant to
`the analysis and design of computer-controlled systems. This chapter provides
`some background. A brief overview of the development of computer-control tech(cid:173)
`nology is given in Sec. 1.2. The need for a suitable theory is discussed in Sec. 1.3.
`Examples are used to demonstrate that computer-eontrolled systems cannot be
`fully understood by the theory oflinear time-invariant continuous-time systems.
`An example shows not only that computer-controlled systems can be designed
`using continuous-time theory and approximations, but also that substantial im(cid:173)
`provements can be obtained by other techniques that use the full potential of
`computer control. Section 1.4 gives some examples of inherently sampled sys(cid:173)
`tems. The development of the theory of sampled-data systems is outlined in
`Sec. 1.5.
`
`1.2 Computer Technology
`
`The idea of using digital computers as components in control systems emerged
`around 1950. Applications in missile and aircraft control were investigated first.
`Studies showed that there was no potential for using the general-purpose digital
`computers that were available at that time. The computers were too big, they
`consumed too much power, and they were not sufficiently reliable. For this
`reason special-purpose computers-digital differential analyzers (DDAs)-were
`developed for the early aerospace applications.
`
`Ex. PGS 1035
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`

`

`Sec. 1.2
`
`Computer Technology
`
`3
`
`The idea of using d1gital computers for process control emerged in the
`mid-1950s. Serious work started in March 1956 when the aerospace company
`Thomson Ramo Woodridge (TRW) contacted Texaco to set up a feasibility study.
`After preliminary discussions it was decided to investigate a polymerization
`unit at the Port Arthur, Texas, refinery. A group of engineers from TRW and
`Texaco made a thorough feasibility study, which required about 30 people-years.
`A computer-controlled system for the polymerization unit was designed based
`on the RW-300 computer. The control system went on-line March 12, 1959. The
`system controlled 26 flows, 72 temperatures, 3 pressures, and 3 compositions.
`The essential functions were to minimize the reactor pressure, to determine
`an optimal distribution among the feeds of 5 reactors, to control the hot-water
`inflow based on measurement of catalyst activity, and to determine the optimal
`·
`recirculation.
`The pioneering work done by TRW was noticed by many computer manu(cid:173)
`facturers, who saw a large potential market for their products. Many different
`feasibility studies were initiated and vigorous development was started. To dis(cid:173)
`cuss the dramatic developm~nts, it is useful to introduce six periods:
`Pioneering period ~ 1955
`Direct-digital-control period ~ 1962
`Minicomputer period ~ 1967
`Microcomputer period ~ 1972
`General use of digital control ~ 1980
`Distributed control ~ 1990
`It is difficult to give precise dates, because the development was highly di(cid:173)
`versified. There was a wide difference between different application areas and
`different industries; there was also considerable overlap. The dates given refer
`to the emergence of new approaches.
`
`Pioneering Period
`
`The work done by TRW and Texaco evoked substantial interest in process in(cid:173)
`dustries, among computer manufacturers, and in research organizations. The
`industries saw a potential tool for increased automation, the computer indus(cid:173)
`tries saw new markets, and universities saw a new research field. Many feasi(cid:173)
`bility studies were initiated by the computer manufacturers because they were
`eager to learn the new technology and were very interested in knowing what a
`proper process-control computer should look like. Feasibility studies continued
`throughout the sixties.
`The computer systems that were used were slow, expensive, and unreliable.
`The earlier systems used vacuum tubes. Typical data for a computer atound
`1958 were an addition time of 1 ms, a multiplication time of 20 ms, and a mean
`time between failures (MTBF) for a central processing unit of 50-100 h. To make
`full use of the expensive computers, it was necessary to have them perform many
`
`Ex. PGS 1035
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`

`

`4
`
`Computer Control
`
`Chap. 1
`
`tasks. Because the computers were so unreliable, they controlled the process by
`printing instructions to the process operator or by changing the set points of
`analog regulators. These supervisory modes of operation were referred to as an
`operator guide and a set-point control.
`The major tasks of the computer were to find the optimal operating condi(cid:173)
`tions, to perform scheduling and production planning, and to give reports about
`production and raw-material consumption. The problem of finding the best op(cid:173)
`erating conditions was viewed as a static optimization problem. Mathematical
`models of the processes were necessary in order to perform the optimization.
`The models used-which were quite complicated-were derived from physical
`models and from regression analysis of process data. Attempts were also made
`to carry out on-line optimization.
`Progress was often hampered by lack of process knowledge. It also became
`clear that it was not sufficient to view the problems simply as static optimization
`problems; dynamic models were needed. A significant proportion of the effort
`in many of the feasibility studies was devoted to modeling, which was quite
`time-consuming because there was a lack of good modeling methodology. This
`stimulated research into system-identification methods.
`A lot of experience was gained during the feasibility studies. It became
`clear that process control puts special demands on computers. The need to re(cid:173)
`spond quickly to demands from the process led to development of the interrupt
`feature, which is a special hardware device that allows an external event to
`interrupt the computer in its current work so that it can respond to more ur(cid:173)
`gent process tasks. Many sensors that were needed were not available. There
`were also several difficulties in trying to introduce a new technology into old
`industries.
`The progress made was closely monitored at conferences and meetings
`and in journals. A series of articles describing the use of computers in process
`control was published in the journal Control Engineering. By March 1961, 37
`systems had been installed. A year later the number of systems had grown to
`159. The applications involved control of steel mills and chemical industries and
`generation of electric power. The development progressed at different rates in
`different industries. Feasibility studies continued through the 1960s and the
`1970s.
`
`Direct~Digltai-Control Period
`
`The early installations of control computers operated in a supervisory mode, ei(cid:173)
`ther as an operator guide or as a set-point control. The ordinary analog-control
`equipment was needed in both cases. A drastic departure from this approach
`was made by Imperial Chemical Industries (ICI) in England in 1962. A complete
`analog instrumentation for process control was replaced by one computer, a Fer(cid:173)
`ranti Argus. The computer measured 224 variables and controlled 129 valves
`directly. 'fhis was the beginning of a new era in process control: Analog technol(cid:173)
`ogy was simply replaced by digital technology; the function of the system was
`the same. The name direct digital control (DDC) was coined to emphasize that
`
`Ex. PGS 1035
`
`

`

`Sec. 1.2
`
`Computer Technology
`
`5
`
`the computer-controlled the process directly. In 1962 a typical process-control
`computer could add two numbers in 100 Jl.S and multiply them in 1 ms. The
`MTBF was around 1000 h.
`Cost was the major argument for changing the technology. The cost of an
`analog system increased linearly with the number of control loops; the initial
`cost of a digital system was large, but the cost of adding an additional loop
`was small. The digital system was thus cheaper for large installations. Another
`advantage was that operator communication could be changed drastically; an
`operator communication panel could replace a large wall of analog instruments.
`The panel used in the ICI system was very simpl&-a digital display and a few
`buttons.
`Flexibility was another advantage of the DDC systems. Analog systems
`were changed by rewiring; computer-controlled systems were changed by repro(cid:173)
`gramming. Digital technology also offered other advantages. It was easy to have
`interaction among several control loops. The parameters of a control loop could
`be made functions of operating conditions. The programming was simplified by
`introducing special DDC languages. A user of such a language did not need
`to know anything about programming, but simply introduced inputs, outputs,
`regulator types, scale factors, and regulator parameters into tables. To the user
`the systems thus looked like a connection of ordinary regulators. A drawback
`of the systems was that it was difficult to do unconventional control strategies.
`This certainly hampered development of control for many years.
`DDC was a major change of direction in the development of computer(cid:173)
`controlled systems. Interest was focused on the basic control functions instead
`of the supervisory functions of the earlier systems. Considerable progress was
`made in the years 1963-1965. Specifications for DDC systems were worked out
`jointly between users and vendors. Problems related to choice of sampling period
`and control algorithms, as well as the key problem of reliability, were discussed
`extensively. The DDC concept was quickly accepted although DDC systems often
`turned out to be more expensive than corresponding analog systems.
`
`Minicomputer Period
`
`There was substantial development of digital computer technology in the 1960s.
`The requirements on a process-control computer were neatly matched with
`progress in integrated-circuit technology. The computers became smaller, faster,
`more reliable, and cheaper. The term minicomputer was coined for the new com(cid:173)
`puters that emerged. It was possible to design efficient process-control systems
`by using minicomputers.
`The development of minicomputer technology combined with the increas(cid:173)
`ing knowledge gained about process control with computers during the pio(cid:173)
`neering and DDC periods caused a rapid increase in applications of computer
`control. Special process-control computers were announced by several manufac(cid:173)
`turers. A typical process computer of the period had a word length of 16 bits.
`The primary memory was 8-124 k words. A disk drive was commonly used as a
`secondary memory. The CDC 1700 was a typical computer of this period, with
`
`Ex. PGS 1035
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`

`

`6
`
`Computer Control
`
`Chap. 1
`
`a n addition time of 2 /J.S and a multiplication time of 7 !J.S. The MTBF for a
`central processing unit was about 20,000 h.
`An important factor in the rapid increase of computer control in this period
`was that digital computer control now came in a smaller "unit." It was thus
`possible to use computer control for smaller projects and for smaller problems.
`Because of minicomputers, the number of process computers grew from about
`5000 in 1970 to about 50,000 in 1975.
`
`Microcomputer Period and General Use of Computer Control
`
`The early use of computer control was restricted to large industrial systems
`because digital computing was only available in expensive,. large, slow, and
`unreliable machines. The minicomputer was still a fairly large system. Even
`as performance continued to increase and prices to decrease, the price of a
`minicomputer mainframe in 1975 was still about $10,000. This meant that a
`small system rarely cost less than $100,000. Computer control was still out
`of reach for a large number of control problems. But with the development of
`the microcomputer in 1972, the price of a card computer with the performance
`of a 1975 minicomputer dropped to $500 in 1980. Another consequence was
`that digital computing power in 1980 came in quanta as small as $50. The
`development of microelectronics has continued with advances in very large-scale
`integration (VLSI) technology; in the 1990s microprocessors became available
`for a few dollars. This has had a profound impact on the use of computer control.
`As a result practically all controllers are now computer-based. Mass markets
`such as automotive electronics has also led to the development of special-purpose
`computers, called microcontrollers, in which a standard computer chip has been
`augmented with A-D and D-A converters, registers, and other features that
`make it easy to interface with physical equipment.
`Practically all control systems developed today are based on computer
`control. Applications span all areas of control, generation, and distribution .
`of electricity; process control; manufacturing; transportation; and entertain(cid:173)
`ment . Mass-ma rket applications such as automotive electronics, CD players,
`and videos are particularly interesting because they have motivated computer
`manufacturers to make chips that can be used in a wide variety of applications.
`As an illustration Fig. 1.2 shows an example of a single-loop controller for
`process control. Such systems were traditionally implemented using pneumatic
`or electronic techniques, but they are now always computer-based. The con(cid:173)
`troller has the traditional proportional, integral, and derivative actions (PID),
`which are implemented in a microprocessor. With digital control it is also pos(cid:173)
`sible to obtain added functionality. In this particular case, the regulator is pro(cid:173)
`vided with automatic tuning, gain scheduling, and continuous adaptation of
`feedforward and feedback gains. These functions are difficult to implement with
`analog techniques. The system is a typical case that shows how the function(cid:173)
`ality of a traditional product can be improved substantially by use of computer
`control.
`
`Ex. PGS 1035
`
`

`

`Sec. 1.2
`
`Computer Technology
`
`7
`
`Figure 1.2 A standard single-loop controller for process l:ontrol. (By cour(cid:173)
`tesy of Alfa Laval Automation, Stockholm, Sweden.)
`
`Logic, Sequencing, and Control
`
`Industrial automation systems have traditionally had two components, con(cid:173)
`trollers and relay logic. Relays were used to sequen~e operations such as startup
`and shutdown and they were also used to ensure safety of the operations by pro(cid:173)
`viding interlocks. !Wlays and controllers were handled by different categories
`of personnel at the plant. Instrument engineers were responsible for the con(cid:173)
`trollers and electricians were responsible for the relay systems. We have already
`discussed how the controllers were influenced by microcomputers. The relay sys(cid:173)
`tems went through a similar change with the advent of microelectronics. The
`so-called programmable logic controller (PLC) emerged in the beginning of the
`1970s as replacements for relays. They could be programmed by electricians
`and in familiar notations, that is, as rungs of relay contact logic or as logic
`(AND/OR) statements. Americans were the first to bring this novelty to the
`market, relying primarily on relay contact logic, but the Europeans were hard
`op. their heels, preferring logic statements. The technology became a big success,
`primarily in the discrete parts manufacturing industry (for ol:>vious reasons).
`However, in time, it evolved ~o include regulatory control and data-handling
`capabilities as well, a development that has broadened the range of applica(cid:173)
`tions for it. The attraction was, and is, the ea.se with which controls, including
`intraloop dependencies, can be implemented and changed, without any impact
`on hardware.
`
`Ex. PGS 1035
`
`

`

`8
`
`Distributed Control
`
`Computer Control
`
`Chap. 1
`
`The microprocessor has also had a profound impact on the way computers were
`applied to control entire production plants. It became economically feasible to
`develop systems consisting of several interacting microcomputers sharing the
`overall workload. Such systems generally consist of process stations, controlling
`the process; operator stations, where process operators monitor activities; 'and
`various auxiliary stations, for example, for system configuration and program(cid:173)
`ming, data storage, and so on, all interacting by means of some kind of commu(cid:173)
`nications network. The allure was to boost performance by facilitating parallel
`multitasking, to improve overall availability by not putting "all the eggs in one
`basket," to further expandability and to reduce the amount of control cabling.
`The first system of this kind to see the light of day was Honeywell's TDC 2000
`(the year was 1975), but it was soon followed by others. The term "distributed
`control" was coined. The first systems were oriented toward regulatory control,
`but over the years distributed control systems have adopted more and ~ore of
`the capabilities of programmable (logic) controllers, making today's distributed
`control systems able to control all aspects of production and enabling operators
`to monitor and control activities from a single computer console.
`
`Plantwide Supervision and Control
`
`The next development phase in industrial process-control systems was facili(cid:173)
`tated by the emergence of common standards in computing, making it possible
`to integrate virtually all computers and computer systems in industrial plants
`into a monolithic whole to achieve real-time exchange of data across what used
`to be closed system borders. Such interaction enables
`
`• top managers to investigate all aspects of operations
`
`• production managers to plan and schedule production on the basis of cur(cid:173)
`rent information
`
`• order handlers and liaison officers to provide instant and current informa(cid:173)
`tion to inquiring customers
`
`• process operators to look up the cost accounts and the quality records of
`the previous production run to do better next time
`
`all from the computer screens in front of them, all in real time. An example of
`such a system is shown in Fig. 1.3. ABB's Advant OCS (open control system)
`seems to be a good exponent of this phase. It consists of process controllers with
`local and/or remote I/0, operator stations, information management stations,
`and engineering stations that are interconnected by high-speed communica(cid:173)
`tions buses at the field, process-sectional, and plantwide levels. By supporting
`industry standards in computing such as Unix, Windows, and SQL, it makes ·
`interfacing with the surrounding world of computers easy. The system features
`a real-time process database that is distributed among the process controllers
`of the system to avoid redundancy in data storage, data inconsistency, and to
`
`Ex. PGS 1035
`
`

`

`12
`
`Computer Control
`
`Chap. 1
`
`possible to use different sampling periods for different loops in a system. This
`is called multirate sampling.
`In this section we will give examples that illustrate the differences and the
`similarities of analog and computer-controlled systems. It will be shown that
`essential new phenomena that require theoretical attention do indeed occur.
`
`Time Dependence
`The presence of the the clock in Fig. 1.1 makes computer-controlled systems
`time-varying. Such systems can exhibit behavior that does not occur in linear
`time-invariant systems.
`
`Example 1.1 Time dependen ce in digit al filtering
`A digital filter is a simple example of a computer-controlled system. Suppose that
`we want to implement a compensator that is simply a first-order lag. Such a com(cid:173)
`pensator can be implemented using A-D conversion, a digital computer, and 0-A
`
`(a)
`
`Computer
`
`Y,
`
`Clock
`
`-
`
`-
`
`- --=-=-~-.....-.
`
`(b)
`
`1
`
`r -
`I
`I
`I
`o ~~--------------~
`10
`0
`
`1
`
`0~~----------------~
`10
`0
`
`1
`
`o._--~---------------
`0
`10
`
`0._+-~------------~
`10
`0
`
`Time
`
`Time
`
`(a) Block diagram of a digital filter. (b) Step responses (dots)
`F igure 1.4
`of a digital computer implementation of a first-order lag for different delays
`in the input step (dashed) compared with the first sampling instant. For
`comparison the response of the corresponding continuous-time system (solid)
`is also shown.
`
`Ex. PGS 1035
`
`

`

`28
`
`System Identification
`
`Computer Control
`
`Chap. 1
`
`All techniques for analysis and design of control systems are based on the ayail·
`ability of appropriate models for process dynamics. The success of classical con(cid:173)
`tr ol theory that almost exclusively builds on Laplace transforms was largely
`due to the fact that th e transfer function of a process can be determined ex·
`perimentally using frequency response. The development of digital control was
`accompanied by a similar development of system identification methods. These
`allow experimental determination of the pulse-transfer function or the differ(cid:173)
`ence equations that are the starting point of analysis and design of digital
`control systems. Good sources of information on these techniques are Astrom
`and Eykhoff (1971), Norton (1986), Ljung (1987), Soderstrom and Stoica (1989),
`and Johansson (1993).
`
`Adaptive Control
`
`When digital computers are used to implement a controller, it is possible to im(cid:173)
`plement more complicated control algorithms. A natural step is to include both
`par ameter estimation methods and control design algorithms. In this way it is
`possible to obtain adaptive control algorithms that determine· the mathematical
`models and perform control system design on-line. Research on adaptive control
`began in the mid-1950s. Significant progress was mad,e in the 1970s when feasi(cid:173)
`bility was demonstrated in industrial applications. The advent of the micropro·
`cessor made the algorithms cost-effective, and commercial adaptive regulators
`appeared in the early 1980s. This has stimulated vigorous research on theoret(cid:173)
`ical issues and significant product development. See, for instance, Astrom and
`Wittenmark (1973, 1980, 1995), Astrom (1983b, 1987), and Goodwin and Sin
`(1984).
`
`Automatic Tuning
`
`Controller parameters are often tuned manu ally. Experience has shown that it
`is difficult to adjust more than two parameters manually. From the user point of
`view it is therefore helpful to have tuning tools built into the controllers. Such
`systems are similar to adaptive controllers. They are, however, easier to design
`and use. With eomputer-based controllers it is easy to incorporate tunin~ tools.
`Such systems also started to appear industrially in the mid-1980s. See Astrom
`and Hagglund (1995).
`
`1.6 Notes and References
`
`To acquiro mature knowledge about a field it is useful to know its history and
`to read soma of the original papers. J w·y and Tsypkin (1971), and Jury (1980),
`written by two of the originators of sampled-data theory, give a useful per(cid:173)
`spective. Early work on sampled systems is found in MacColl (1945), Hurewicz
`
`Ex. PGS 1035
`
`