Digital Control Systems: Volume 2: Stochastic Control, Multivariable Control, Adaptive Control, Applications

340 Pages·1991·9.57 MB·English

by  Professor Dr.-Ing. Rolf Isermann (auth.)

Rolf Isermann
Digital
Control Systems
Volume 2:
Stochastic Control, Multivariable Control,
Adaptive Control, Applications
Second, revised edition
With 120 Figures
Springer-Verlag
Berlin Heidelberg NewY ork
London Paris Tokyo
Hong Kong Barcelona Budapest
Professor Dr.-Ing. Rolf Isermann
Institut fUr Regelungstechnik
Technische Hochschule Darmstadt
SchloBgraben 1
D-6100 Darmstadt, West Germany
ISBN-13: 978-3-642-86422-3 e-ISBN-13: 978-3-642-86420-9
DOl: 10.1007/978-3-642-86420-9
Library of Congress Cataloging-in-Publication Data
Isermann, Rolf.
Digital control systems.
Rev. and eni. translation of: Digitale Regelsysteme.
Includes bibliographical references (v. 1, p. [321]-
327) and index.
Contents: v. /. Fundamentals, deterministic
control-v. 2. Stochastic control, multi variable
control, adaptive control, applications.
/. Digital control systems. I. Title.
TJ213.164713 1989 629.8'312 88-38730
ISBN 0-387-50266-1 (U.S.: v. 1: alk. paper)
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© Springer-Verlag Berlin Heidelberg 1991
Softcover reprint of the hardcover 2nd edition 1991
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Preface
The great advances made in large-scale integration of semiconductors and the
resulting cost-effective digital processors and data storage devices determine the
present development of automation.
The application of digital techniques to process automation started in about
1960, when the first process computer was installed. From about 1970 process
computers with cathodic ray tube display have become standard equipment for
larger automation systems. Until about 1980 the annual increase of process
computers was about 20 to 30%. The cost of hardware has already then shown a
tendency to decrease, whereas the relative cost of user software has tended to
increase. Because of the high total cost the first phase of digital process automation
is characterized by the centralization of many functions in a single (though
sometimes in several) process computer. Application was mainly restricted to
medium and large processes. Because of the far-reaching consequences of a
breakdown in the central computer parallel standby computers or parallel back-up
systems had to be provided. This meant a substantial increase in cost. The tendency
to overload the capacity and software problems caused further difficulties.
In 1971 the first microprocessors were marketed which, together with large-scale
integrated semiconductor memory units and input/output modules, can be assem
bled into cost-effective microcomputers. These microcomputers differ from process
computers in fewer but higher integrated modules and in the adaptability of their
hardware and software to specialized, less comprehensive tasks. Originally, micro
processors had a shorter word length, slower operating speed and smaller opera
tional software systems with fewer instructions. From the beginning, however, they
could be used in a manifold way resulting in larger piecenumbers and leading to
lower hardware costs, thus permitting the operation with small-scale processes.
By means of these process-microcomputers which exceed the efficiency of former
process computers decentralized automatic systems can be applied. To do so, the
tasks up to now been centrally processed in a process computer are delegated to
various process microcomputers. Together with digital buses and possibly placed
over computers many different hierarchically organized automatization structures
can be build up. They can be adapted to the corresponding process. Doing so the
high computer load of a central computer is avoided, as well as a comprehensive
and complex user-software and a lower reliability. In addition decentralized
systems can be easier commissioned, can be provided with mutual redundancy
VI Preface
(lower susceptibility to malfunctions) and can lead to savings in wiring. The second
phase of process automation is thus characterized by decentralization.
Besides their use as substations in decentralized automation systems process
computers have found increasing application in individual elements of automation
systems. Digital controllers and user-programmable sequence control systems,
based on microprocessors, have been on the market since 1975.
Digital controllers can replace several analog controllers. They usually require an
analog-digital converter at the input because of the wide use of analog sensors,
transducers and signal transmission, and a digital-analog converter at the output
to drive actuators designed for analog techniques. It is to be expected that, in the
long run, digitalization will extend to sensors and actuators. This would not only
save a-d and d-a converters, but would also circumvent certain noise problems,
permit the use of sensors with digital output and the reprocession of signals in
digital measuring transducers (for example choice of measurement range, correc
tion of nonlinear characteristics, computation of characteristics not measurable in
a direct way, automatic failure detection, etc.). Actuators with digital control will be
developed as well. Digital controllers not only are able to replace one or several
analog controllers they also succeed in performing additional functions, previously
exercised by other devices or new functions. These additional functions are such as
programmed sequence control of setpoints, automatic switching to various con
trolled and manipulated variables, feedforward adjusted controller parameters as
functions of the operating point, additional monitoring of limit values, etc.
Examples of new functions are: communication with other digital controllers,
mutual redundancy, automatic failure detection and failure diagnosis, various
additional functions, the possibility of choice between different control algorithms
and, in particular, selft uning or adaptive control algorithms. Entire control systems
such as cascade-control systems, multi variable control systems with coupling
controllers, control systems with feedforward control which can be easily changed
by configuration of the software at commissioning time or later, can be realized by
use of one digital controller. Finally, very large ranges of the controller parameters
and the sample time can be realized. It is because of these many advantages that,
presently various digital devices of process automation are being developed, either
completing or replacing the process analog control technique.
As compared to analog control systems, here are some of the characteristics of
digital control systems using process computers or process microcomputers:
- Feedforward and feedback control are realized in the form of software.
- Discrete-time signals are generated.
- The signals are quantized in amplitude through the finite word length in a-d
converters, the central processor unit, and d-a converters.
- The computer can automatically perform the analysis of the process and the
synthesis of the control.
Because of the great flexibility of control algorithms stored in software, one is not
limited, as with analog control systems, to standardized modules with P-, 1-and D
behaviour, but one can further use more sophisticated algorithms based on
Preface vii
mathematical process models. Many further functions can be added. It is especially
significant that on-line digital process computers permit the use of process
identification-, controller design-, and simulation methods, thus providing the
engineer with new tools.
Since 1958 several books have been published dealing with the theoretical
treatment and synthesis of linear sampled-data control, based on difference
equations, vector difference equations and the z-transform. Up to 1977, when the
first German edition of this book appeared, books were not available in which the
various methods of designing sampled-data control have been surveyed, compared
and presented so that they can be used immediately to design control algorithms
for various types of processes. Among other things one must consider the form and
accuracy of mathematical process models obtainable in practice, the computa
tional effort in the design and the properties of the resulting control algorithms,
such as the relationship between control performance and the manipulation effort,
the behaviour for various processes and various disturbance signals, and the
sensitivity to changes in process behaviour. Finally, the changes being effected in
control behaviour through sampling and amplitude quantization as compared
with analog control had also be studied.
Apart from deterministic control systems the first edition of this book dealt also
with stochastic control, multi variable control and the first results of digital
adaptive control. In 1983 this book was translated into Chinese. In 1981 the
enlarged English version entitled "Digital Control Systems" was edited, followed
by the Russian translation in 1984, and, again a Chinese translation in 1986. In
1987 the 2nd edition appeared in German, now existing in two volumes. This book
is now the 2nd English edition.
As expected, the field of digital control has been further developed. While new
results have been worked out in research projects, the increased application
provided a richer experience, thus allowing a more profound evaluation of the
various possibilities. Further stimulation of how to didactically treat the material
has been provided by several years of teaching experience and delivering courses in
industry. This makes the second edition a complete revision of the first book,
containing many supplements, especially in chapters 1,3,5,6, 10,20,21,23,26,30,
31. Since, compared with the first edition, the size of the material has been
significantly increased, it was necessary to divide the book in two volumes.
Both volumes are directed to students and engineers in industry desiring to be
introduced to theory and application of digital control systems. Required is only a
basic familiarity of continuous-time (analog) control theory and control technique
characterized by keywords such as: differential equation, Laplace-Transform,
transfer function, frequency response, poles, zeroes, stability criterions, and basic
matrix calculations. The first volume deals with the theoretical basics of linear
sampled-data control and with deterministic control. Compared with the first
edition the introduction to the basics of sampled-data control (part A) has been
considerably extended. Offering various examples and exercises the introduction
concentrates on the basic relationships required by the up-coming chapters and
necessary for the engineer. This is realized by using the input/output-, as well as the
VIII Preface
state-design. Part B considers control algorithms designed for deterministic noise
signals. Parameter-optimized algorithms, especially with PID-behaviour are in
vestigated in detail being still the ones most frequently used in industry. The sequel
presents general linear controllers (higher order), cancellation controllers, and
deadbeat controllers characteristic for sampled-data control. Also state controllers
including observers due to different design principles and the required supplements
are considered. Finally, various control methods for deadbeat processes, insensitive
and robust controllers are described and different control algorithms are compared
by simulation methods. Part C of the second volume is dedicated to the control
design for stochastic noise signals such as minimum variance controllers. The
design of interconnected control systems (cascade control, feedforward control) are
described in Part D while part E treats different multi variable control systems
including multi variable state estimation. Digital adaptive control systems which
have made remarkable progress during the last ten years are thoroughly investig
ated in Part F. Following a general survey, on-line identification methods,
including closed loop and various parameter-adaptive control methods are pre
sented. Part G considers more practical aspects, such as the influence of amplitude
quantization, analog and digital noise filtering and actuator control. Finally the
computer-aided design of control with special program systems is described,
including various applications and examples of adaptive and selftuning control
methods for different technical processes. The last chapters show, that the control
systems and corresponding design methods, in combination with process modeling
methods described in the two volumes were compiled in program systems. Most of
them were tried out on our own pilot processes and in industry. Further specifica
tion of the contents is given in chapter 1.
A course "Digital Control Systems" treats the following chapters: 1,2, 3.1-3.5,
3.7,4,5,6, 7, 3.6, 8, 9, 11. The weekly three hours lecture and one hour exercises is
given at the Technische Hochschule Darmstadt for students starting the sixth
semester. For a more rapid apprehension of the essentials for applications the
following succession is recommended: 2, 3.1 to 3.5 (perhaps excluding 3.2.4, 3.5.3,
3.5.4) 4,5.1,5.2.1,5.6,5.7,6.2, 7.1, 11.2, 11.3 with the corresponding exercises.
Many of the described methods, development and results have been worked out
in a research project funded by the Bundesminister fur Forschung und Technologie
(DV 5.505) within the project "ProzeBlenkung mit DV-Anlagen (PDV)" from
1973-1981 and in research projects funded by the Deutsche Forschungsgemein
schaft in the Federal Republic of Germany. The author is very grateful for this
support.
His thanks also go to his coworkers,-who had a significant share in the
generation of the results through several years of joint effort-for developing
methods, calculating examples, assembling program packages, performing simu
lations on digital and on-line computers, doing practical trials with various
processes and, finally, for proofreading.
The book was translated by my wife, Helge Isermann.
Darmstadt, June 1991 Rolf Isermann
Contents
C Control Systems for Stochastic Disturbances
12 Stochastic Control Systems (Introduction) ....... . 3
12.1 Preliminary Remarks . . . . . . . . . . . . . . . . 3
12.2 Mathematical Models of Stochastic Signal Processes 3
12.2.1 Basic Terms. . . . . . . . . . . . . . . . . 4
12.2.2 Markov Signal Processes ........ . 6
12.2.3 Scalar Stochastic Difference Equations. 8
13 Parameter-optimized Controllers for Stochastic Disturbances . . . . . .. 10
14 Minimum Variance Controllers for Stochastic Disturbances ... 13
14.1 Generalized Minimum Variance Controllers for Processes
without Deadtime . . . . . . . . . . . . . . . . . . . . . . . . 13
14.2 Generalized Minimum Variance Controllers for Processes
with Deadtime . . . . . . . . . . . . . . . . . . . . . . 21
14.3 Minimum Variance Controllers for Processes with
Pure Deadtime ................... . 25
14.4 Minimum Variance Controllers without Offset. 27
14.4.1 Additional Integral Acting Term .... . 27
14.4.2 Minimization of the Control Error .. . 28
14.5 Simulation Results with Minimum Variance Controllers 28
14.6 Comparison of Various Deterministic and
Stochastic Controllers ................... . 32
15 State Controllers for Stochastic Disturbances. . . . . . . . . . . . . . . .. 36
15.1 Optimal State Controllers for White Noise. . . . . . . . . . . . .. 36
15.2 Optimal State Controllers with State Estimation for White Noise. 38
15.3 Optimal State Controllers with State Estimation for External
Disturbances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 40
x Contents
D Interconnected Control Systems
16 Cascade Control Systems . . 49
17 Feedforward Control. . . . . 56
17.1 Cancellation Feedforward Control ....... . 56
17.2 Parameter-optimized Feedforward Control . . . 60
17.2.1 Parameter-optimized Feedforward Control without a
Prescribed Initial Manipulated Variable ......... . 60
17.2.2 Parameter-optimized Feedforward Control with Prescribed
Initial Manipulated Variable. . . . . . . . . . . . . . . . . 61
17.2.3 Cooperation of Feedforward and Feedback Control. . . 64
17.3 State Variable Feedforward Control . . . . . .. 65
17.4 Minimum Variance Feedforward Control .. 66
E Multivariable Control Systems
18 Structures of Multivariable Processes . . . . 71
18.1 Structural Properties of Transfer Function Representations. 71
18.1.1 Canonical Structures . . . . . . . . . . . . . . . . . . . . 71
18.1.2 The Characteristic Equation and Coupling Factor. . . .. 75
18.1.3 The Influence of External Signals. . . . . . . . . . . . 78
18.1.4 Mutual Action of the Main Controllers. . 79
18.1.5 The Matrix Polynomial Representation. . 82
18.2 Structural Properties of the State Representation. 82
19 Parameter-optimized Multivariable Control Systems . . . . . . . . . . .. 89
19.1 Parameter Optimization of Main Controllers without
Coupling Controllers . . . . . . . . . . . . . . . . . . . . . . . . . 89
19.1.1 Stability Regions. . . . . . . . . . . . . . . . . . . . . . . . 92
19.1.2 Optimization of the Controller Parameters and Tuning
Rules for Twovariable Controllers . . . . . . . . . . . . . 96
19.2 Decoupling by Coupling Controllers (Non-interaction) . . . . . 99
19.3 Parameter Optimization of the Main and Coupling Controller 103
20 Multivariable Matrix Polynomial Control Systems . . . . . . . . . . . . . 105
20.1 The General Matrix Polynomial Controller. . . . . . . . . . .. 105
20.2 The Matrix Polynomial Deadbeat Controller. . . . . . 105
20.3 Matrix Polynomial Minimum Variance Controllers ......... 107
21 Multivariable State Control Systems .............. . . . 109
21.1 Multivariable State Control Systems. . . . . . . . . . . . . 109
21.2 Multivariable Matrix Riccati State Controllers ............ 112
Contents Xl
21.3 Multivariable Decoupling State Controllers. . . . . . 113
21.4 Multivariable Minimum Variance State Controllers. 113
22 State Estimation . . . . . . . . . . . . . . . . . . . . 116
22.1 Vector Signal Processes and Assumptions. . 117
22.2 Weighted Averaging of Two Measurements. 119
22.3 Recursive Estimation of Vector States (Kalman Filter) 121
F Adaptive Control Systems
23 Adaptive Control Systems (A Short Review) 127
23.1 Model Reference Adaptive Systems (MRAS). 129
23.1.1 Local Parameter Optimization 130
23.1.2 Ljapunov Design. . . . . . . . . . . . . 132
23.1.3 Hyperstability Design. . . . . . . . . . 133
23.2 Adaptive Controllers with Identification Model (MIAS). 138
24 On-line Identification of Dynamical Processes and
Stochastic Signals. . . . . . . . . . . . . . . . . . . . 141
24.1 Process and Signal Models. . . . . . . . . . . 141
24.2 The Recursive Least Squares Method (RLS). 143
24.2.1 Dynamical Processes . . . . . . . . . . 143
24.2.2 Stochastic Signals . . . . . . . . . . . . 148
24.3 The Recursive Extended Least Squares Method (RELS). 149
24.4 The Recursive Instrumental Variables Method (RIV) . . 150
24.5 A Unified Recursive Parameter Estimation Algorithm. . 152
24.6 Modifications to Recursive Parameter Estimation Algorithms. 154
25 On-line Identification in Closed Loop . . . . . . . 158
25.1 Parameter Estimation with Perturbations. 159
25.1.1 Indirect Process Identification. . . . 160
25.1.2 Direct Process Identification. . . . . 164
25.2 Parameter Estimation with Perturbations. 167
25.3 Methods for Closed Loop Parameter Estimation. 168
25.3.1 Indirect Process Identification without Perturbation 169
25.3.2 Direct Process Identification without Perturbation 169
25.3.3 Direct Process Identification with Perturbation 169
26 Parameter-adaptive Controllers. . . 170
26.1 Design Principles. . . . . . . 170
26.2 Suitable Control Algorithms 175
26.2.1 Deadbeat Control Algorithms 175
26.2.2 Minimum Variance Controllers 176