historic control textbooks (ifac symposia series) (ifac symposia series)

HISTORIC CONTROL

TEXTBOOKS

This Page Intentionally Left Blank

IFAC

1 6

HISTORIC CONTROL

T E XTBOOKS

Edited by

Janos Gertler

INTERNATIONAL FEDERATION OF AUTOMATIC CONTROL

Cover design by Balint D. S6s

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First edition 2006

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EDITOR'S FOREWORD

The mathematical foundations of control go back to the classical mechanics of the eighteenth and nineteenth centuries, marked by such names as Lagrange, Hamilton and Jacobi, and to mathematical results on stability obtained in the last third of the nineteenth century by Maxwell, Routh, Lyapunov and Hurwitz. Following the celebrated steam engine regulator of James Watt in 1784, controllers were designed for various engineering systems, most notably in power systems, in the late eighteen and early nineteen hundreds. Automatic control as a separate engineering discipline was born during World War II, when fundamental development took pace, in parallel, in the UK and USA, in Germany and Japan, and in Russia.

The objective of this collection is to present the earliest textbooks that grew out of the original development of automatic control, and the many others that followed very soon, in various countries (now all members of IFAC), and in various languages. We set out to collect information on one to four books from each country (nine from the USA), including a brief description of the background, history and contents of the book, a picture of the front page, and copies of one to a few "typical" pages. With the latter, we intended to show pages that contain an equation or figure, easily recognizable to anyone familiar with control, embedded in the text written in one of the many languages and, in some cases, in various scripts.

The present collection contains 62 entries from 21 countries.

Rather than going through the official channels of the National Member Organizations of IFAC, most of the material was collected via a network of personal friends. As many as thirty nine people have contributed to this work, to whom the Editor is greatly indebted. The selection of the books from each country was left to the person invited to contribute. Strict selection rules were not enforced; the number of books does not necessarily reflect the perceived significance of the particular subculture. Also, some of the early entries were lecture notes rather than typeset hardcover books. Finally, the number of pages shown is in no way representative of the perceived importance of the book; while books known only locally may be there with several pages, some of the classics recognized world-wide are present with only a single page.

The Editor wishes to express his special thanks to Stephen Kahne who initiated this project and, as coordinator of the entire I FAC 50 effort, has supported it all the way to its completion.

May examining this volume bring the Reader as much joy as its creation has given the Editor.

February 2006. Janos Gertler

CONTRIBUTORS

Javier ARACIL

Karl Johan ASTROM

Jens BALCHEN

Liu BAO

Ruth BARS

Stuart BENNETT

Sergio BITTANTI

Mogens BLANKE

Claudio BONIVENTO

Celso BOTTURA

Plinio CASTRUCCI

Huitang CHEN

Talha DINIBOTON

Peter DORATO

Wladislaw FINDEISEN

Katsuhisa FURUTA

Jose GEROMEL

Ryszard GESSING

Adolf GLATTFELDER

Alberto ISIDORI

Michel KINNAERT

Heikki KOIVO

Oh-Kyu KWON

Giovanni MARRO

Istvan NAGY

Antti NIEMI

Boris POLYAK

Patrice REMAUD

Walter SCHAUFFELBERGER

Marcel STAROSWlECKI

Vladimir STREJC

Manfred THOMA

Jean-Claude TRIGEASSOU

Paul VAN den HOF

Baiwu WAN

Zhongtuo WANG

Deyun XlAO

Raimo YLINEN

Dazhong ZHENG

PRESIDENT'S FOREWORD

In 1956, a declaration to create an international organization of automatic control was signed in Heidelberg and, in 1957, the Constitution and By-Laws of I FAC were adopted in Paris. For the past 50 years IFAC has fulfilled its original purpose to promote the science and technology of control in the broadest sense in all systems. I FAC has served all those concerned with the theory and application of automatic control systems engineering and has grown into a truly world-wide organization, now encompassing more than 50 National Member Organizations.

An I FAC 50 Task Force was created to commemorate the 50 th anniversary of I FAC. A team of IFAC Advisors has undertaken the planning of several activities for this celebration. As one of several projects headed by Stephen Kahne, creation of a summary of historic control textbooks was undertaken by Janos Gertler, while a celebratory event and an IFAC Foundation are also planned by Rolf Isermann and Pedro Albertos and collaborators.

The IFAC 50 Team, in particular, Janos Gertler, did an excellent job to prepare this wonderful collection of historic control textbooks. The IFAC family deeply appreciates the hard work of many individuals who have made this book possible.

This book also reminds us that we have to be prepared for the next 50 years of I FAC.

February 2006.

Wook Hyun Kwon

President of IFAC 2005-2008

Historic Control Textbooks

CONTENTS

B R A S I L . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Contr61e Automatico- Teoria e Projeto P. Castrucci EDUSP, S. Paulo, SP, Brazil, 1969

Principios de Controle e Servomecanismos C. Pascoli Bottura Guanabara Dois, Rio de Janeiro, RJ, Brazil, 1982

CHINA, P E O P L E ' S R E P U B L I C OF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

Fundamental Theory of Automatic Control Translated from Russian (A.A. Voronov) by J.R. Xu, B.W. Wan, Z.T. Wang,

S.Q. Zheng 1957

Fundamentals of Automatic Control Translated from Russian (V.V. Solodovnikov, ed.) by Z.T. Wang 1957-59

Servomechanisms Huitang Chen 1961

Fundamentals of Automatic Control Theory Liu Bao 1963

C Z E C H R E P U B L I C ( C z e c h o s l o v a k i a ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

Servomechanisms Z. Trnka In Czech, SNTL Prague, 1954

Foundations of Automatic Control V. Strejc, M. Salamon, Z. Kotek and M. Balda In Czech, SNTL Prague, 1958

Elements of Control Loops M. Balda, V. Strejc and M. Krampera In Czech, SNTL Prague, 1958

Dynamics of Controlled Systems J. (~ermak, V. Peterka and J. Z,~vorka In Czech, ACADEMIA Prague, 1968

xi


D E N M A R K . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Automatisk Kontrol J. R. Jensen Polyteknisk Forenings Forlag, 1956

Notes on the Measurements of Dynamic Systems J. R. Jensen Servoteknisk Forskningslaboratorium, 1958

F I N L A N D . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Basics of Servomechanisms E. Laurila Published in 1954

Theoretical Background of Control Engineering, Vols. 1-2 H. Blomberg Helsinki University of Technology, 1963.

F R A N C E . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Technologie et calcul pratique des syst~mes asservis P. Naslin Dunod, 2 nd edition, 1958

Methodes Modernes d'Etude des Systemes Asservis J.-C. Gille, P. Decaulne, M. Pelegrin Dunod, 1960

Commande optimale des processus R. Boudarel, J. Delmas, P. Guichet Dunod, 1967

G E R M A N Y . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Die selbstt&tige Regelung (Feedback Control) A. Leonhard Springer Verlag, 1940, 1949, 1957

Dynamik selbstt&tiger Regelungen (Dynamics of Automatic Feedback Control)

R.C. Oldenbourg and H. Sartorius R. Oldenbourg Verlag, 1944, 1949, 1951

Kleines Handbuch technischer Regelungsvorg~nge (Compact Handbook of Engineering Control Processes)

W. Oppelt Verlag Chemie, 1954, 1956, 1960, 1964, 1972.

45

53

63

87

o ~

Xll


H U N G A R Y . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Automatika (Automation) (Lecture notes) A. Frigyes and I. Nagy Tank6nyvkiad6, 1954, 1957

Szabalyoz,~sok Dinamik,~ja (Dynamics of Control Systems) F. Csaki Akademiai Kiad6, Budapest, 1966

Automatika (Automation) F. Csaki and R. Bars TankSnyvkiad6, Budapest, 1969, 1971, 1974, 1983, 1986

ITALY ..........................................................................................

La Regolazione delle Turbine Idrauliche Giuseppe Evangelisti Nicola Zanichelli Editore, Bologna, 1947

Teoria della Regolazione Automatica Giorgio Quazza ANIPLA, 1962

Lezioni di Controlli Automatici- Teoria dei Sistemi Lineari e Stazionari A. Lepschy and A. Ruberti Edizioni Scientifiche SIDEREA, Roma, 1963

Elementi di servomeccanismi e controlli Sergio Barabaschi and Renzo Tasselli Zanichelli, Bologna, 1965

J A P A N . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Jidouseigyo no Riron to Jissai (Control Theory and Practice) Takeshi Samukawa 1948

Jidouseigyo Nyumon (Introduction to Control Theory) Keisuke Izawa 1954

Jidouseigyo Rironi (Automatic Control Theory) Yasundo Takahashi 1954

111

125

149

xiii


K O R E A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Automatic Control Analysis and Control Devices H.Y. Cheon, B.S. Hong and C.B. Park 1976

Linear Control System Engineering J.S. Kim 1988

N E T H E R L A N D S . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Elementaire Theorie van de Automatische Procesregeling, (Elementary Theory of Automatic Process Control)

J. Stigter Kluwer, Deventer, The Netherlands, 1962

Regeltechniek en Automatisering in de Procesindustrie (Control and Automation in Process Industry)

P. M. E. M. van der Grinten Prisma-Boeken, Utrecht/Antwerpen, 1968.

Regeltechniek J. C. Cool, F. J. Schijff, T. J. Viersma Agon Elsevier, Amsterdam/Brussel, 1969.

N O R W A Y . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Reguleringsteknikk (Control Engineering) Vol. 1 J. G. Balchen Tapir Book Company, Trondheim, 1963

Reguler ingsteknikk Vol. 2 J. G. Balchen Tapir Book Company, Trondheim, 1967

Reguleringsteknikk Vol. 3 J. G. Balchen, Magne Fjeld, Ole A. Solheim Tapir Book Company, Trondheim, 1970

P O L A N D . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Fundamentals of Control Systems - Volume I" Linear Systems P. Nowacki, L. Szklarski and H. G6recki Polish Scientific Publishers, Warszawa, 1958

Fundamentals of Automatic Control S. W~grzyn Polish Scientific Publishers, L6d~- Warszawa- Krak6w, 1960

163

173

189

2 0 3

xiv


R U S S I A (Soviet Union) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Foundations of automatic regulation" theory V. V. Solodovnikov (editor), Moscow, Mashgiz, 1954.

Lectures on the theory of automatic control M. A. Aizerman Moscow, Fizmatgiz, 1958.

Elements of the theory of automatic regulation A. A. Voronov, Moscow, Voenizdat, 1954.

Some problems in the theory of stability of motion N. N. Krasovski, Moscow, Fizmatgiz, 1959.

SPAIN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Teorfa de los Servomecanismos (Servomechanism Theory) A. Colino 1950

S W E D E N ......................................................................................

L. yon Hamos Svenska bokfSrlaget Bonniers. Stockholm 1968.

Reglerteori (Control Theory) K. J. AstrSm Almqvist \& Wiksell, Stockholm 1968.

S W I T Z E R L A N D . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Die Regelung von Dampfanlagen (Control of Thermal Power Plants) P. Profos Springer-Verlag Berlin/G6ttingen/Heidelberg 1962

T U R K E Y . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Servomekanizmalarin Prensipleri Translation, by M. 0IgOr, of Principles of Servomechanisms

(G. S. Brown and D. P. Campbell, John Wiley, 1948) Istanbul Technical University, 1962

Otomatik Kontrol Ders Notlari (Automatic Control Course Notes) M. N. Ozda,~ Istanbul Technical University, 1978

213

233

241

249

253

XV


UNITED KINGDOM ........................................................................

An Introduction to Servomechanisms A. Porter, London: Methuen, 1950, 1952, 1954, 1957

An Introduction to the Theory of Control in Mechanical Engineering R. H. Macmillan, Cambridge, England" Cambridge University Press, 1951

Servomechanisms J .C. West, London: The English Universities Press, 1953

UNITED STATES OF AMERICA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Network Analysis and Feedback Amplifier Design H. W. Bode Van Nostrand Company, Inc., New York, 1945.

Theory of Servomechanisms H. M. James, N. B. Nichols, and R. S. Phillips McGraw-Hill Book Company, Inc., New York, 1947.

Engineering Cybernetics H. S. Tsien McGraw-Hill Book Company, Inc., New York, 1954.

Automatic Feedback Control System Synthesis J. G. Truxal McGraw-Hill Book Company, Inc., New York, 1955.

Sampled-data Control Systems J. R. Ragazzini and Gene F. Franklin McGraw-Hill Book Company, Inc., 1958.

Stability by Liapunov's Direct Method. With Applications J. La Salle and S. Lefschetz Academic Press, New York, 1961.

Adaptive Control Processes" A Guided Tour R. Bellman Princeton University Press, Princeton, New Jersey, 1961.

Linear System Theory. The State Space Approach L. A. Zadeh and C. A. Desoer McGraw-Hill Book Company, New York, 1963.

Optimal Control M. Athans and P. L. Falb McGraw-Hill Book Company, New York, 1966.

261

275

xvi

EARLY CONTROL TEXTBOOKS in

BRASIL

Contr61e Automdtico- Teoria �9 Projeto

Plinio Castrucci EDUSP, S. Paulo, SP, Brazil, 1969

Principios de Controle e Servomecanismos Celso Pascoli Bottura Guanabara Dois, Rio de Janeiro, RJ, Brazil, 1982

Contributed by

Plinio Benedicto de Lauro Castrucci Celso Pascoli Bottura

Universidade de Sio Paolo UNICAMP, Campinas SP

Jos~ C. Geromel

UNICAMP, Campinas SP

Sociedade Brasileira de Atomdtica

Brasil


Contr61e Autom~itico- Teoria e Projeto

Plinio Castrucci EDUSP, S. Paulo, Brazil, 1969

This textbook derived its existence from lectures given at Escola Politrcnica da Universidade de S. Paulo, starting in 1961, to all the electrical engineering students. Chapters 1 to 10 were taught regularly in a two-semester course, during the fifth year of the engineering curriculum. Laboratory sessions for frequency and transient analysis, and compensation design, applied to electrical servos and regulators, were held during the second semester of the course.

A brief list of the chapters, with short comments added, is as follows"

Introduction

1. Feedback and Control

Part I - Linear Systems

2. Analysis of Linear Systems (transfer function, poles and zeros, frequency response, Routh criterion)

Part I I - Linear Feedback Systems

3. Quality Criteria (closed loop transfer function, stationary and transient errors, sensitivity to parameters)

4. Root Locus Method (rules, spirule, advantages of a "new root locus" defined in a plane y - s -1)

5. Frequency Response Method (Nyquist criterion, stability margins, Nichols chart)

6. The Central Problem in the Design of Servo-Systems ( lead, lag and general compensators, load compensation, field forcing, etc)

7. Modulated Signal Systems (amplitude modulation and sampling) (synchros, amplitude modulation with suppressed carrier, sampling and extrapolation, Z- transform, stability)

8. Digital Signal Systems ( binary codes, components, a digital servo)

Part I I I - Nonlinear Systems

9. Describing Functions (concept, saturation, dead zone, etc)

10. Phase Plane Analysis (isoclines, Lirnard method, parameter time, singular points, limit-cycles, analysis of on-off servos)

2 Brasil


11. Introduction to the General Stability Theory (state space, relative and asymptotic stability, sign-defined functions, Lyapunov theorems, introduction to domain research)

Part IV- Logical Systems

12. Boolean Algebra (concept, relay circuits, simplification and Veitch maps)

13. General Method of Design (design principles: from cause-effect map to sequence diagram to equations to relay circuit)

14. Modem Realizations (transistor logic, design with NORs and NANDs)

Appendices:

Small Laplace transform list; Multiple loop Nyquist criterion; Measurement techniques; Passive compensation circuits, Tustin's theorem on power gain versus time constant)

Proposed problems

References

Later editions developed into three titles: Linear Control, Nonlinear Systems and Digital Control.

Contributed by

Plfnio Benedicto de Lauro Castrucci Escola Polit6cnica, Universidade de S~o Paolo

Brasil

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Principios de Controle e Servomecanismos

Celso Pascoli Bottura Guanabara Dois, Rio de Janeiro, R J, Brazil, 1982

Work on this book was started in 1965 while the author was teaching at ITA (Instituto

Tecnol6gico de Aeromiutica) Sao Jose dos Campos, SP, Brazil and it was completed in 1972

when he was already was at UNICAMP (Universidade Estadual de Campinas), Campinas, SP,

Brazil). After some initial problems with publication, a Preliminary Edition was published at

UNICAMP in 1980, and finally the book was published by Editora Guanabara Dois in 1982.

It is a classical control textbook for a sixteen week undergraduate course, with one or two three

hour sessions weekly, including both analog and digital control analysis and design with a

frequency approach.

Contents:

- Introduction

- Feedback control systems: Linear Analysis

- Feedback control systems: Linear Synthesis

- Multivariable control

Contributed by

Celso Pascoli Bottura School of Electrical and Computer Engineering, UNICAMP

Campinas SP, Brasil

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10 Brasil

EARLY CONTROL TEXTBOOKS in the

PEOPLE'S REPUBLIC OF CHINA Fundamental Theory of Automatic Control

Translation from the Russian original by A. A. Voronov Translated by J. R. Xu, B. W. Wan, Z. T. Wang and S. Q. Zheng Date of publication" 1957

Fundamentals of Automatic Control Translation from the Russian original by V. V. Solodovnikov et al. Translated by Zhongtuo Wang Date of publication" 1957-59

Servomechanisms Author: Huitang Chen Date of publication" 1961

Fundamentals of Automatic Control Theory Author: Liu Bao Date of publication" 1963

Material collected and processed by

Xiao Deyun and Zheng Dazhong

Tsinghua University Beijing, P.R. China


Fundamental Theory of Automatic Control Russian original written by A. A. Voronov Chinese translation by Jun-Rong XU, Bai-Wu WAN, Zhong-Tuo WANG and Shou-Qi

ZHENG. Published in 1957.

The author of the book "Fundamental Theory of Automatic Control" is A.A. Voronov from the Soviet Union.. The book was translated into Chinese by four Chinese university lecturers: Jun-Rong XU, Bai-Wu WAN, Zhong-Tuo WANG and Shou-Qi ZHENG.

The second edition of this book in Russian was published in 1954 by the Military Publisher, Ministry of Defense, Soviet Union. The textbook was based on the teaching material the author gave for graduate students and scientific researchers of Moscow Bauman High Technology University and for students of Moscow Molotov Power and Energy Institute in 1948-1952.

The translated manuscript in Chinese of the very book had been used as teaching material for students in the Department of Electrical Engineering, Jiaotong University, Shanghai, since the beginning of 1955 by XU and WAN. This was the earliest control theory course taught in China. The book was published by the Electrical Power Publisher in 1957 with 470 pages and 2 impressions and the total number of copies of the book was about 10,000.

The book in Chinese was widely used as a textbook or reference for undergraduate students in Electrical Engineering as well as others over 15 years. It became one of the most important books for linear control theory in China.

The book was focused on linear control theory. It gave some simple mathematical preparation like Laplace transformation, theory of complex variables for students that were not familiar with. Its outstanding characteristic was that it paid attention to the basic concepts of the control problem. For example, it gave a good explanation to the linearization of a nonlinear plant or element such as prime mover, d.c. generator, two-phase induction motor etc. To explain the real meaning of frequency characteristics the book introduced the concept of harmonic excitation to control systems; to prove the amplitude-phase stability criterion it used the diagram of rotation of each vector denoted by (j(o-Sin) in numerator and denominator instead of the strict

mathematical proof. Another outstanding characteristic was that it also paid attention to some practical problems, which evidently were very important like the steady state behavior of the control systems, differential equations of plants and elements of different kinds and different nature. The book addressed not only the control problems in electrical engineering but also in mechanical and aviation engineering. Very detailed examples were given to illustrate the theory such as: electronic voltage regulator, servo system of radar station, prime mover speed control by centrifugal governor, carbon-pile voltage regulator etc. Enlightening questions were available for students at the end of each chapter.

Contents Preface Introduction Chapter 1 General Concepts Chapter 2 Basic Concept of Statics of Control Systems

12 China


Chapter 3 Plants and Elements Equations in Automatic Control Loop A. Controlled plants B. Sensitive elements of controllers C. Prime movers D. Amplifiers E. Stabilizing elements Chapter 4 Equations, Transfer Functions and Frequency Characteristics of Elements and

Systems Chapter 5 Stability of Linear Dynamic Systems Chapter 6 Examples to Study Stability of Automatic Control Systems Chapter 7 Study on Transient Quality of Control Systems Appendixes References

Contributed by Prof. Wan Baiwu

Xi'an Jiaotong University, Xian, China

China 13


14 China


A Typical Page from the Book "Fundamental Theory of Automatic Control" Schematic diagram and mathematical description of a selsyn servosystem with amplifier-dc

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China 15


Fundamentals of Automatic Control Russian original written by a collective of authors (V. V. Solodovnikov, Editor) Chinese translation by Zhongtuo Wang Published in 1957-1959

The Russian book "Fundamentals of Automatic control" was published in the year 1954 by the Publisher of Mechanical Engineering of the former Soviet Union and imported to China in the year 1955. The Chinese translation work started from 1956 by Mr. Zhongtuo Wang, a young teacher at Dalian Institute of Technology, China. It was published by the China Publisher of Electrical Power Engineering in three volumes. Volume one come out in the year 1957 in 5100 copies, volume two in 1958 in 5100 copies, and volume three in 1959 in 5780 copies. Later, in the year 1960, the second printing of volume one and two come out in 4620 copies each. From the year 1958, it was becoming the main textbook of the course "Theory of Automatic Control" in many famous universities of China. The Chinese translation was also exported to Korean Democratic Republic from 1960.

From the year 1961, the book was assigned as textbook in some departments of several key universities and was republished by the China Publisher of Industry in 7620 copies each volume.

As a standard text, it contains not only the linear theory of control systems in detail, but also some chapters about the problems of nonlinear theory as well as statistical theory of control systems. The authors were distinguished scholars in control theory of the former Soviet Union like M. Aizerman, A. Voronov, A. Krasovsky, A. Lerner, A. Letov, B. Petrov, G. Posperov, V. Solodovnikov (Editor in chief), Y. Zipkin, etc.

The main content of the book includes two parts: Part one: Introduction. Linear Theory. There are four divisions"

1. Mathematical descriptions of control systems (8 chapters). 2. Stability analysis (6 chapters). 3. Performance analysis. System Synthesis. Discrete systems (7 chapters). 4. Statistical analysis (4 chapters).

Part two: Some problems in nonlinear theory. There are four divisions: 1. Phase space and its applications (6 chapters). 2. Approximate analysis of the periodical process (3 chapters). 3. On-off systems (3 chapters). 4. Graphical analysis of nonlinear systems (2 chapters).

This textbook had a major influence on the education of control theory from the year 1958 to 1966.

Contributed by Prof. Wang Zhongtuo

Dalian University of Technology, Dalian, China

16 China


The Front Covers of the Book "Fundamentals of Automatic Control"

China 17


A Typical Page from the Book "Fundamentals of Automatic Control"

The control system of an aircraft compressor and the differential equations describing the dynamics of the system

. . . . . . . . .

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18 China


Servomechanisms Author: Huitang Chen Published in 1961

The author of the book "Servomechanisms" is Mr. Huitang Chen. This book was written based on the author's lecture notes for the course of "Servomechanisms" in Xi'an JiaoTong university in the fall of 1958. It was published as a national unified textbook by the People's Educational Press in July, 1961 after being evaluated and recommended by the National Unified Textbooks Committee. Revised twice, this book has 3 editions. By the time of July 1964, when the 3 r~ edition of the book was printed the 4 ~ time, the book had a total printing of over 11.5 thousand copies.

The history of writing this book is as follows: During the early 1950s, we learned from the Soviet Union and began to set up the specialty of "Electrification for Industrial Enterprises" in China .A course named the "Theory of Automatic Regulation" was arranged in the program. The textbooks we used were those translated from the textbooks of the Soviet Union. For example, the book "Theory of Automatic Regulation" by Voronov was adopted. This book mainly described the basic principles of automatic control. By the time of the mid 1950s, another specialty called "Automation and Telemechanics" was established. In order to strengthen the students' ability of design and let them grasp the practical systems, the course "Servomechanisms" was included in the program. As the teacher of this course, I deeply felt the deficiencies of that time, namely that we had overemphasized learning from the Soviet Union while ignoring new achievements made by America and the European countries, such as the root-locus method, M-N graph and methods of investigating servomechanism in a statistical context, etc. Therefore, most of the contents in my teaching materials came from the textbooks of America and the European countries. Meanwhile, some advanced methods developed in the Soviet Union were also included, such as time-optimal relay control, time-optimal servomechanisms, synthesis of systems based on the desired frequency response etc. Therefore, this book gave a brand new look to China of that time and was widely used nationwide. It was also very popular with engineers and technicians. It made great contributions by educating many specialists of a generation in automation. Many of those who now are academic leaders in the fields of automatic control remember the influence this book had on them.

China 19


Contents Chapter 1. Introduction

1-1. Definition & fields of application of servomechanism 1-2. Brief history of servomechanism 1-3. Examples of application

Chapter 2. Fundamental theory of servomechanism 2-1. Structure and work principle of servomechanism 2-2. Simplest servomechanism 2-3. Proportional control system 2-4. Differential control system 2-5. Differential &integral control system

Chapter 3. Components of servomechanism 3-1. Selsyn 3-2. Measurement of angular error using selsyn 3-3. Dual-speed error measurement system 3-4. False zero-point of dual-speed system 3-5. Signal selection for dual-speed system 3-6. Rectifier selector 3-7. Neon-lamp selector 3-8. Selector with electronic tube and relay 3-9. Phase demodulator of servomechanism 3-10. Servosystem with amplifier 3-11. Servosystem with magnetic amplifier 3-12. Electrohyraulic servosystem

Chapter 4. General design methods for servomechanism 4-1. Transfer function 4-2. Steady state error of servosystem 4-3. Amplitude-phase characteristic of open-loop system 4-4. Nyquist stability criteria 4-5. Synthesis of system basing on analytic formula of open loop transfer function 4-6. Synthesis of system basing on frequency response of closed-loop system 4-7. Synthesis of system basing on logarithmic characteristic 4-8. Synthesis of system basing on desired logarithmic characteristic 4-9. Synthesis of system basing on root-locus method

Chapter 5. A. C. servomechanism 5-1. Specific points of A.C. servomechanism 5-2. Requirements to the A.C. compensation network 5-3. Practical diagram & its design of A.C. compensation network 5-4. Design example of A.C. servomechanism 5-5. Practical A.C. servomechanism 5-6. Conclusion

20 China


Chapter 6. Time-optimal servomechanism 6-1. Concepts of time-optimal servomechanism 6-2. Determination of the form of optimal process 6-3. Building of time-optimal servomechanism 6-4. Example

Chapter 7. Selection of power element of servomechanism 7-1. Introduction 7-2. Load characteristic 7-3. Torque, speed and power demanded by the load 7-4. Determination of torque, speed and power for the power element 7-5. Motor-load gear ratio selection for total inertia 7-6. Influence of gear ratio to the total inertia

Chapter 8. Experimental methods for research of servomechanism 8-1. Introduction 8-2. Determination of dynamic characteristic using infra-low frequency device 8-3. Determination of system parameters basing on transient diagram by oscilloscope

Chapter 9. Relay servomechanism 9-1. General relay servomechanism 9-2. Linearized relay servomechanism 9-3. Time-optimal relay servomechanism

Chapter 10. Statistical dynamics of Servomechanism 10-1. Necessity of research using statistical method 10-2. Fundamental knowledge of possibility theory 10-3. Stationary random process 10-4. Response of system to the random signal 10-5. Calculation of integral of error spectrum density 10-6. Conclusion

Appendix

Contributed by Prof. Chen Huitang

Tongji University, Shanghai, China

China 21


The Front Cover of the Book "Servomechanisms"

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22 China


A Typical Page from the Book "Servomechanisms" An example of a time-optimal servomechanism for an automatic compensator by using nonlinear

state feedback of velocity

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China 23


Fundamentals of Automatic Control Theory Author: Liu Bao Published in 1963

"Fundamentals of Automatic Control Theory" was written by LIU BAO, published by Shanghai Science and Technology Publisher in 1963 with 568 pages and 3 impressions and the total number of copies printed is 16,500.

This book was written based on the lecture notes of Liu Bao for the senior course on automatic control in the Department of Mechanical Engineering at Tianjin University between 1956 and 1966. In 1956 this course was one of the earliest courses on automatic control taught in China. It had been used as a college textbook and also as reference material by engineers and research people in the field of automatic control. In the early 60's, many Chinese research workers read this book to improve their ability to deal with practical control problems.

This book provided 127 footnotes to point readers to the original sources of theories and rules, to help them understand different methods proposed by different authors and to help them find various references in English, Russian, Chinese and other languages.

The References of this book is not only a list of related books and papers, it is also an explanation and introduction of books, papers, journals, handbooks in the control field from the 40's to the early 60's. They are arranged in eight sections: basic mathematics; linear systems; automatic control theory; statistics; sampled data control systems; nonlinear systems; others; journals and conference proceedings.

Contents Preface Chapter 1 Introduction

1-1 The action principle and types of automatic control systems 1-2 The characteristics of automatic control system 1-3 Method to derive the motion equations of system and its elements Chapter 2 Solving and studying motion equations of linear automatic system

2-1 The frequency characteristics 2-2 Application of Fourier transformation 2-3 Application of Laplace transformation 2-4 Transfer function, unit response function, impulse response function

Chapter 3 Componential elements of automatic control system and their coupling 3-1 A period element 3-2 3-3 3-4 3-5 3-6 3-7 3-8 3-9

Vibrating element Integral element Amplifier element First order derivative element Second order derivative element Dead time element Different kinds of coupling of elements Different forms of system transfer function

24 China


Chapter 4 Stability of automatic control system 4-1 The fundamental idea of stability 4-2 Rouse-Hurwitz stability criterion 4-3 Mihailov stability criterion 4-4 Nyquist stability criterion 4-5 Analyzing stability by log frequency characteristics 4-6 Stability of multi-loop system 4-7 Remainder of stability 4-8 Stability of automatic control system with dead time element 4-9 The structure stability of automatic control system

Chapter 5 Quality analysis of automatic control system 5-1 Quality index for the automatic control systems 5-2 Integral appraisal method

5-3 Relationship between system quality and distribution of zeros and poles of transfer function

5-4 Root locus method 5-5 Frequency method 5-6 Methods to draw different characteristic curves

Chapter 6 Stabilization, correction and synthesis of automatic control system 6-1 Correction of automatic control system 6-2 Fundamentals of servo system synthesis 6-3 The extension of frequency method 6-4 Synthesis of multi-input multi-loop systems 6-5 Synthesis by the distribution of system poles and zeros 6-6 Application of root locus method in system analysis 6-7 Comparison of different synthesis methods

Chapter 7 Analysis and synthesis problem of control system under random process action

7-1 Some fundamental conceptions of probability 7-2 Correlation function and spectral density 7-3 Statistical method to calculate the dynamic characteristics of the controlled object 7-4 Dynamic precision of automatic control system 7-5 Synthesis of system under random process action

Chapter 8 Nonlinear automatic control system 8-1 General statement 8-2 Types of nonlinear characteristics in automatic control system 8-3 Basic idea about phase locus method 8-4 Phase diagram of nonlinear system 8-5 Point turning method 8-6 The method of improving system dynamic quality by use of nonlinear characteristics 8-7 Harmonic balance method 8-8 Analysis of nonlinear system under random inputs

Appendixes I h-function table II To find Lm/W+-/and arg(W+-)from log frequency curves Lm/W/and arg/W+-/ III Table of P,Q functions

China 25


IV Table of sinx/x, cosx/x V Calculating table to derive integral formula Jn VI Table to find phase frequency characteristic function from log amplitude frequency

characteristics References

Index

Contributed by Prof. Liu Bao

Tianjin University, Tianjin, China

26 China


The Front Cover of the Book "Fundamentals of Automatic Control Theory"

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China 27


A Typical Page from the Book "Fundamentals of Automatic Control Theory"

A new method to synthesize a control system by drawing frequency characteristics from the system's unit step response

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28 China


CZECH REPUBLIC (Czechoslovakia)

Servomechanisms Trnka Z. In Czech, SNTL Prague, 1954

Foundations of Automatic Control v

Strejc V., M. Salamon, Z. Kotek and M. Balda In Czech, SNTL Prague, 1958

Elements of Control Loops Balda M., V. Strejc and M. Krampera In Czech, SNTL Prague, 1958

Dynamics of Controlled Systems v

Cermdk J., V. Peterka and J. Zavorka In Czech, ACADEMIA Prague, 1968

Contributed by

Vladimir Strejc

Czech Technical University Prague, Czech Republic


Servomechanismy

Trnka Z. In Czech, SNTL Prague, (1954), pp. 372, Fig.274, Tab. 5.

The book is devoted to the linear theory of positional servomechanisms of electrical and mechanical controlled systems. The author originally wrote the book for students of the department of Electrical Engineering at the Technical University in Prague. These students were familiar with the mentioned systems by that time and could easily accept an extension of lectures to the automatic control of servomechanisms. It was a right premise and, consequently, the book got in a short time a very high popularity. In the USA several books appeared after the Second World War concerning this subject, so that the evolution at the Technical University actually followed a general development.

In the first chapters the ways of formulating the differential equations for electrical and mechanical linear systems are briefly reviewed. The author then designs a most simple linear positional servomechanism, solved first by means of conventional procedures in time domain. Using this example, different solutions are demonstrated, which are deeply elaborated in the next chapters introducing the frequecy characteristic in a complex plain and in logarithmic coordinates. The reader can recognise the main parts of servomechanisms as well as their behaviour when a sudden step change, input speed change or sinusoidal input occurs.

The Laplace transform is briefly presented. The basic positioning servomechanisms with derivative and integral of the control error are solved by means of the Laplace transform. The resulting differential equations are at most of the third order.

The next part of the book is devoted to the elements of servomechanisms. Principles, operation and Laplace transforms of the most common positioning servomechanisms are explained.

The following part of the book presents the synthesis of servomechanisms. The author mentions the stability cost functions which are frequently used and go directly to the desired result. Besides the complete Nyquist cost function, Michailov-Leonhard and Hurwitz criterions, important for a rapid verification of stability, are introduced.

The other part presents the algebra of block diagrams and procedures of designing a control by means of graphs in the complex plain and in logarithmic coordinates. It is mentioned that the procedure of graphs in logarithmic coordinates is for the synthesis of linear systems most rapid. It holds particularly for control loops where it is not necessary to ascertain the stability of arrangements with unstable inner loop.

Another part deals with experimental determination of elements of servomechanisms and of complete systems. The aim is to get responses to arbitrary input time signal with the help of the frequency characteristic. Some numerical examples of linear positional servomechanisms are given, e.g. servomechanism with viscous damping, servomechanism controlled by error and its integral, one with viscous damping corrected by imperfect integrating circuit, modification of the frequency characteristic by differentiating circuit and design of control loop stabilised by feedback.

Non-linear servomechanisms are treated only partly due to the difficulties in the solutions. Only the principle of solutions in the phase plain is mentioned. Parasite changes appearing at the "linear" servomechanisms are discussed.

30 Czechoslovakia


Prof. Ing. Dr ZDENI~K T R N K A

SERVOMECHANISMY

Schvdleno vSmosem ministerstva gkolstvi ze dne 17. b(ezna 1954 e. j . 19.079/54-S/4

jako celostdtni vysoko~kolskd udebnice

PRAHA 1954

STATNI NAKLADATELSTVI TECHNICKI~ LITERATURY

Czechoslovakia 31


vinuti (obr~izek 18,18). Tim se dos~me stejn6ho 6~inku, jako u z~ivitu nakr~rko.

To plat/ov~em jen pro selsyny pou~.it6 pro pt~im3~ p~enos 6I~u v zapojeni podle obr~zku 18,16. U selsynfi p0u~it3~ch jako polohov6 transform~tory by z~ivity nakr~tko rugily a je 16pe zde pou~.it rotorfi bez vyj~d~en3~ch p61fi, nebo~ vyjfid~en~i magnetick~ osa rotoru vyvol~iv~ momenty i u selsynfi zapojen3~ch podle obr~zku 18,15 jako polohov~ transform~tory.

Z

Obr. 18,17. Rotor selsynu' se z~vitem nakr~tko (z), kter9 po- tla~uje p~i6nou sio~-

ku pole.

Obr. 18,18. Vinuti rotoru selsynu s nevyj~id~en3;'mi p61y. Diametr~ln~ polo2en6 body virmti jsou spojer~y

nakr~tko.

Ozna~ime-li v~chylku selsynu vysila~e ~ a v~chylku selsynu pfijima~e q~, je odchylka poloh obou selsynfi ~p = % -- % a moment pfisobici na selsyn pfijima~ ]e M = Kq~. Pro pohyb selsynu p}ijima~e plati diferenci~lni rovnice

d"q~ dq92 ff clt ~ q- B - ~ = Kq~ (18,12)

d2~. dc?2 J ~ q-- S -~- -+- Kq~ = K% (18,13)

kde J je moment setrva~nosti rotoru p~ijima~e, B je konstanta tlumeni (indu- kovan3~mi proudy p}i pohybu). M~ime zde opfit diferenci~ilni rovnici harmo- nick~ho pohybu tlumen~ho. Rovnici transformujeme a zavedeme op~t pfiro- zenou frekvenci o9. a konstantu pom~rn~ho tlumeni a (viz vztahy 12,20 a 12,21)

(p'- + 2ao Z, + oo ) =

q~(p) = pO. _+_ 2aco~p -+--oJ~ (18,14)

Mfime zde stein6 vztahy jako u servomechanismu s viskosnlm tlumenim, ale p}im6 spojeni dvou selsynfi pro p~enos flhlu neni servomechanismus, nebof

184

32 Czechoslovakia

Historic C

ontrol Textbooks

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33


Foundations of Automatic Control v

Strejc V., M. Salamon, Z. Kotek and M. Balda In Czech, SNTL Prague, (1958), pp. 275, Fig. 214, Tab. 2.

After the first international meeting of experts in automatic control in Heidelberg in 1956, it was decided in the former Czechoslovak Republic to publish four basic books. These had to address the general theory of automatic feedback systems, the elements used in control loops, practical industrial applications and the calculation of the mathematical models of controlled systems.

This book refers to the first subject. After an introduction in Section A describing the control loop and main and auxiliary variables as well as dimension-free equations, the book deals with linear, continuous, discrete and non-linear control loops and with mathematical models of controllers and controlled systems including the measurement of their dynamic behaviours.

In section B, Linear control loops, the reader can find all basic aspects of systems starting with the solution of linear differential equations in time domain and by Laplace transformation. Attention is given to transfer functions, frequency response and step response characteristics including logarithmic Bode plots. Closed control loops differentiate command control and compensation of disturbing variable. All standard stability criterions are mentioned in intelligible form. Cost functions for optimum process control are focused on linear, quadratic and optimum module control actions.

In addition to single-input single-output (SISO) systems applying only four main control variables of the control loop (command, controlling, controlled and disturbing variables), the authors consider branched SISO systems with auxiliary variable measured on the controlled system, with auxiliary controlling variable, with measuring of the disturbing variable and finally with auxiliary variable measured on a controlled system model. Multi-input multi-output (MIMO) systems are for illustration confined to two inputs and two outputs.

Section C, Discrete controlled systems, describes the theory of two-step control and pulse control with step proportional to control error. Attention is paid to their transient responses, stability conditions and optimum responses. Particular solution concerns e.g. the speed of controller valve positioning, process control with transport lag of the controlled system and controllers with derivative and flexible correcting actions. Section D, Non-linear control systems, is devoted to the main elements appearing in a real control loop, such as saturation, dead-zone, hysteresis and relay non-linearities affected possibly by dry friction.

Section E, Models of controllers and controlled systems, are used for real systems simulation. In the early years after the Second World War it was possible to meet mechanical, hydraulic and pneumatic integrators used for mathematical models of the simulated control loops. The importance and flexibility of electronic elements were soon proven, a development properly recognised in this section.

The last section F, Measurement of dynamical characteristics of control loop elements, by conventional instrumentation facilities, describes briefly the different possibilities. Measurement results serve to calculate the step response or frequency characteristics.

34 Czechoslovakia


ING. VLADIH[R STREJC �9 ING. DR. MIROSLAV SALAMON

I NG. ZDENEK KOTEK, kand. tech. v~d

D O C. I N G. M 1 LA N BA L DA, kand. tech. v~d

Z A K L A D Y TEORIE SAlVlOd: I N N I~ REGULACE

PRAHA 1 958

STATNi NAKLADATELSTV i T E C H N I C K ~ L ITERATURY

Czechoslovakia 35

H i s t o r i c C o n t r o l T e x t b o o k s

OPTIMZkLN][ REGULAONI POCHOD 95

je kvadratiek~i regula6ni plocha

1

1 0 p ~ .....

2

- - (d~ - - 2 d o d~) C 2

C 1

d~ 0

C3

i q ca O~ I

1 1 c., 0 i i 0 q ca I

do ~ ~ + (d; - - 2 dod~l c~ + qd.; 2 (c~ c.~c~ - - c'; )

Podobnb bychom nalezli kvadratickou regula~nl plochu pro n = 4

p -_= d~ (qc~ - - ca)

2, c~ (qc,,.c~ - - c~ - - c~ q)

_:. c~(d~ - - 2 d~da) § c a (d~ - - 2 dod~) + d.] (c.,c 3 - - q q )

~) (C1C2C 3 ~ C~ ~ C~ C4)

p . . . . !LZ_o_ + 2 c~ z 5

a pro n = 5

§

(21.61)

(21.62)

(d;i - - 2 d2d4) z a .+- (d'.,. - - 2 d f l 3 § 2 dod~) z 2 -~ (d~ - - 2 dodo_) z 3 -+-, d~ z,

2z5

Z 0 -':'= ClC2C 3 - - C~ - - C~ C 4 ~ C1C 5

(21.63)

21 --- C 1 C 2 ~ C 3

Z 2 =-= CIC 4 --C 5

Z 3 ---= C3C 4 ~ 02C 5

Z 5 --- Z1Z 2 ~ Z~

Je dflle2it~ uvSdomit si, ~2e fysiks rozm~r po~itan6 plochy musl b3~t [sec], nebof hodnota pom~rnd odchylky regulovand veli6iny je bezrozm~rns Kontro]ou fysik{tl- nich rozm~rfl si p~,i prM~tickj, ch vy'poStech mflgeme st~]e ov~fovat spr~,,wlost po~etni- ho postupu. -

Podobn~ bychom mohli sestavit vztahy pro regula~:ni plochu i pro funkce J ( p ) vy,~.~iho i'fidu. Nazna~.en 3) po6etnl postup ms tu neobySejnou v~hodu, ~e neni tfeba, hledat kofeny polynomfl i~l(p) a X(p), jako u jinX'oh po~.etnich metod, kterd jsou prs z t~ehto dflvodfl pro praktickou aplikaci neupot%biteln6.

Zn~me-]i vztahy pro kvadratickou regula6nl plochu, je dalai ur6ovs podmlnek pro optimalni regula('n~ pochod ji~ snaring.

Zavedeme-li nov(. ozna6eni

s o + r o = u [ (21..64)

81 _k Fi == U I

3 6 C z e c h o s l o v a k i a


Elements of Control Loops

Balda M., V. Strejc and M. Krampera In Czech, SNTL Prague, (1958), pp. 474, Fig. 498, Tab. 40, Encl. 2.

The book describes all the important elements used in industrial control loops. The aim is to show, for each physical or chemical variable, the different sensors applied in practical solutions, together with their mathematical description. After the introduction in section A, dealing with basic knowledge of control, section B concerns measuring devices of controllers.

The first Subsection enumerates sensors for measuring level of liquids, starting with different kinds of floats and ending with the application of radioactive isotopes. Subs. 2 deals with pressure meters based on deformations or on float, piston, diaphragm or on electric resistance. Subs. 3 specifies flow meters for gases, liquids and vapours, by some kind of narrowing in the pipe line, e.g. by orifice gauge, and then measuring the pressure. Other mechanical devices are the Pitot tube and the rotameter. Likewise an electromagnetic induction meter for conductive liquids is mentioned.

Subs. 4 is dedicated to temperature measurements. Characterised are liquid-, gas-, dilatation-, bimetallic- and pressure-type and resistance thermometers. A great attention is paid to thermocouples. Finally heat radioactive sensors are considered.

The next Subs. introduces sensors for the continuous measurement of gas humidity. Mentioned are mechanical hydrometers, psychrometers, electrolytic moisture meters and others. The following Subs. deals with continuous measuring of density. Liquid density sensor may apply a vessel suspended on elastic input and output tubes. Next possibility for gases and liquids is based on measuring of hydrostatic pressure. Another way for liquids is the application of the law by Archimedes. Density of flammable gases can be established by the increase of their kinetic energy. An additional possibility is the measuring of internal friction of gases or measuring of sonic speed of gases and liquids and others. A separate problem is posed by the continuous measuring of viscosity. The respective means are e.g. capillary viscosity meters, rotary meters and those based on free fall of particles in case of liquids.

Next Subs. describes sensors for continuously taking the chemical composition of liquids and gases. A great number of instruments and methods are enumerated starting with measuring the penetration of infrared radiation of characteristic wavelengths, colorimeters, refractometers and others using different physical principles. The last example is based on measuring the changes of electroconductivity of solutions by chemical reactions. Another Subs. provides important information about continuous measuring of pH; the basic approach is followed by introducing the titrimetric curve and chemical equilibrium as the way of measuring pH.

The last Subs. is dedicated to the measuring of revolutions, by mechanical, hydraulic, air- operated and electric speedometers including speedometers based on eddy current.

The short section C informs about the remote transfer of controller simple well-tried electric procedures.

variables specifying the

Section D deals with three term controllers, differentiating proportional, integral and derivative actions and all useful combinations, as well as with mechanic, pneumatic, hydraulic, electronic

Czechoslovakia 37


and magnetic amplifiers. The next part is devoted to compensators such as self-acting electromechanical and electronic potentiometers and measuring bridges. At the end, different kinds of feedback are mentioned.

Section E concerns driving mechanisms and control valves. Described are pneumatic, diaphragm and piston drives, solenoid and electromagnetic drives and finally electro-servomotors. The second part of this section describes first the characteristic forms of valve cones and then sizing the valves including the calculation of their pressure drop.

Section F specifies the design of different kinds of continuously acting controllers taking into account the structure of the controlled system itself. The discontinuously acting controllers are represented by on-off and pulse- controllers.

The last part of the book, sections H, I and J concerns controlled systems.

38 Czechoslovakia


Doc. I NG. MILAN BALDA, kand. tech. v~d,

ING. VLADIMIR STREJC a ING. MILOSLAV KRAMPERA

PRVKY REGULA(~NiCH

OBVOD0

PRAHA 1 958

STJkTNI NAKLADATELSTVI TECHNICKr LITERATURY

Czechoslovakia 39


108 M~ralCf (~LENY REGULATORI.~7

Sklen~,ns trubice je upevnfina v kovovdm pouzd2e pouze spodnim koncem, t ak2e tlak mfi~e hornim spojenlm pflsobit na trubici i zven~i. Rotalnetr ms nahof'e induk6ni vysila6., kterdho se vfibec u t,~e, chto pNstrojfi hodn5 pou'21v~i.. Dole je pi"ipojena stavo.

znakovs vysokotlaks armatura s ukazatelem polohy plo. - - vgtku, ur6ens pro mlstni s]edov~ni prfitoku. Je-]i mS~ens

lA.t.ka neprfihledns mfi~e b3',t mlstni ukazatel naho~e had v~'stupnim hrdlem a jeho vnitf'ni prost, or se pak vyplni

[ vhodnj-m plynem. Rotametrfi s vysila(.em netze pou~it pro tak mald prfi-

toky jako rotametrfl bez vysila6e a se sklen~,nou trubiei~ _ TlakovA ztr~ita rotametru je pfibli~n5 st,filA, a je v pod-

stat6 ur~ov~hla vShou plovSku a plochou jeho prfimfitu do roviny kolmd k ose rotametru. PNrfistek kinetiekd energie se opfit m~ni na potenei~ilni energii tlakovou jen v ne- patrndm rozsahu, vzhledeln k nA.hldmu velkdmu roz~i~eni prfl~ezu po v?stupu z mezikru~i.

Nepf-ihli21me-]i k vlivu tf-eni a pf'itokovd rychlosti, millieme zAkladni rovnici rotametru odvodit vehni jedno- du~e. Ozna~ime-li vfihu plovSku, zmen~enou o vztlak, P a plochu, prfim~tu plov,4ku do roviny. kolmd k ose rotametru, Fv, bude stSls;" diferenSni tlak Ap na mezikru~.i dSn vztahen~

P A p .............

El i ~

Obr. 11.19. Magneticl@ pi'r polohy plov~kw"

rot ametru

t

t t! J,

z ~,eho2 podle Benmulliho rovnice t)]y'ne st~il~i, vychh)st prfitoku ll3ezero]l

] / "2 g P v

V OznaNme-li prom6ntivou ploehu mezikru~A F. bude

v rovnovA{n):'eh stavech plovAku platit pro objemov):- prfit:ok Q

Q =- F K. ~l 1.27) kde k.onstanta

.K.,_=.v__l/~2g P 7 Fv

Ze vztahu (.27) mfi~eme pro maxim~lni a minims , prfitok ur6it v3/-stupni a vstupnl prflm~r trubice a za pou-

~iti tdho~ vztahu k6t, ovat v~'~ky mezi obSma, prfif'ezy hod- Obr. 11.20. R otametr notami prfit , o k u .

s induk&aim vysfla6em P~i praktick6na provedeni v~ak vliv tf-eni, pf'itokov6 ryehlosti ani pom6rfi proud6nl a u plynfi t62 kompresibility

nemfi~eme p~ehli~et, lZozsM1 a pflsobeni t6ehto vlivfi (s v , j imkou pNtokov6 ryctalosti) zs na Reynoldsov6 6islu (viz odst. 11.1), na tva.ru plovs na pom6ru zfi'2eni a. na exponentu adia, batick6 expanse (jde-li o pl3my nebo pAry). P~esnou zfi, vislost prfltoku na, poloze plov~ku tedy mfi~eme zjistit jedin6 cejehovAnim, Ji~ p~i na, vrhov'Ani rotametzfi v~ak s t~mito vlivy musime poNt, at a Ndit se podle dosavadnich v3~-- s l e d k f i praktick3~ch m ~ e n i .

40 Czechoslovakia


K : O M P E N ' S ~ T O R Y 3.3"1

Celkov~ odpor potenciometru Po vypo~teme, d61ime-li celkov/~ rozsah v milivoltech, odpovidajici rozsahu m~en6 tepioty, prochgzejic[m proudem v miIiamp~Srech. Pak

P0----- EM:Sm~ - - EMSmm il

Proto~e velikost odporu potenciometru je ds p o u ~ i t ~ vinutim, vvpo6teme po- t[~ebnj? gunt

PPo R ~ : P- - 'Po

Nyni zns v~echny odpory m~ficiho obvodu ~ n~ R~. Proto~e v ~ k sou6ty odpor0 obou v6tvi mum bj~ stein6 velik6, bude

Rs = (R~ -I- R ~ ) - - ( R , -I- P0)

Tim je vypo6ten cel:~ m6Hc[ obvod. Zb~'vs ur6it odpory R~ a R: 7 a~ Rto. Odpor reostatu R~ volime tak, aby srazil nap6t[

6erstv6ho 6IAnku (asi 1,7 V) na p~adovanou hocknotu asi 1,02 V. PH napAjeclm prou-

< 2 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . / . . . . . . . /

O br. 27.7. Blokov6 schema etektronick6ho potenciometru- 1 ~ v i b r a t o r , '2 ~ z e s i [ o v a 6 ~ a p ~ B i , 3 ~ z e s i l o v a ( , v ~ - k o n u , 4 ~ b a l a , I ~ n i m o t o . t ~ e k

du 10 mA bude tedy odpor reostatu asi 70 ohm ft. Odpor/2 vje tlumieim odporem v obvodu galvanom6ru a ms vliv na jeho eitlivost.. Podle velikosti odporu vedeni thermo- 61Anku volime jeho velikost 15 a~ 30 ohmfi; pH vehni dlouh6m vedeni s v,Aky-m odporem se c/vky R 7 nepou'2iv~.

Odpor R10 se zapojuje pH kontrole mechanick6 nuly pi"istroje paraleln6 ke gab, ano- m~ru. MA hodnotu 20 a~ 50 ohmfi. Odpory R s a R~ tv.oH d61i6 napbt.I pH standardisaci nap~ti baterie na ochranu galvanom~ru pi:ed p~-et[~enim. R s = 1.0 a~ 50 oh.v.~t, R9 == 0 a:~ 60 ohm fl.

27.2:.2 E t e k t r o n i e k 6 s a m o 6 i n n 6 p o t e n c i o m e t r y a mf~stky

Elektronick6 kompensAtory jsou zalo~eny na stejn6m prineipu jako pHstroje elektromeehanick6, 5I[sto galvanom6ru s meehanieky'm vyva~ovaeim fistrojim v~ak pou~.:ivaji elektroniek6ho zesilova~e, kterr nap'~ji balan~ni m otorek. Balan~n~ motorek se otA61 ve smyslu odpovidajiein~ polarit6 vsgupnlho signAtu a ot:A,6i b6~2eem poteneio- metru P tak dlouho, a~ je mOHei obvod op6t v rovnovti, ze. S pohybem balan6nlho motorku .je svAzAn pohon ukazatele na st.upniei a pi"evody na dalgi 6leny regula6nlho

Czechoslovakia 41


Dynamics of Controlled Systems

(~erm~ik J., V. Peterka and J. Zfivorka In Czech, ACADEMIA Prague (1968), pp. 584, Fig. 320, Encl. 1 printed table.

This book is devoted to the procedure of establishing a mathematical model by mathematical- physical analysis. A detailed analysis of electric machines was already carried out in this way, but math. models of thermal systems were elaborated only partly and incompletely. The authors elaborated a large and difficult subject in a form accessible to readers and experts in automatic control opening and facilitating the solution of identification problems. The authors could not present all possible systems. First of all it was needful to concentrate the analysis on typical cases. On the other hand, the reader must be aware of the fact, that no math. model can completely cover reality in all coherence.

Chapter 1 is gives the reasons for math. models calculation.

Chapters 2 to 16 present particular systems as dynamics of liquids level in open tanks, transient states of free level of foamed steam-water mixtures, transient process influenced by controlling organs, nonstationary liquid discharge, hydraulic servo-motors and their dynamic equations, single and double acting hydraulic servomotors, experimental establishment of their time constant, linear hydraulic tracking systems with a high control precision and dynamic behaviour of hydraulic tracking servomotors.

Pressure dynamics of air-like gases in tanks and their transfer through narrowing, nonstationary flow of liquids trough a pipe, equation of continuity, power and kinetic energy, sonic waves in pipeline, pipe presentation as a sequence of resistances and capacitances, simplified single- capacity model.

Dynamics of heat transfer through a thin wall, detailed solution of the heat transfer dynamics and transfer function of the heat flow sensor, heating and cooling of monophasig liquids in case of perfect stirring, mixing heat exchangers, stirring heat ex-changers, recuperating heat exchangers, temperature dynamics of liquid flowing trough a pipe, tubular heat exchanger, transcendental transfer function and its approximation.

Steam-liquid mixtures, dynamics of pressure in drum boilers, level dynamics in closed systems under pressure, dynamics of steam-water zone of a single throughput boiler, the dynamics of engines like steam turbine with a superheater, turbine with warmed up steam, engine speed dynamics.

Nonstationary states of composition determined by physical and physico-chemical actions. Dynamics of plate rectifying columns, equations describing the dynamics of a plate, analytical as well as analogue and digital solution of a dynamical equation set of a column and dynamics of filled rectifying columns and their dynamic and static equations.

Dynamics of chemical reactors working continuously or periodically, tubular reactors and chemical composition in the reactor influenced by temperature changes. Nuclear reactors, kinetic equation of the reactor, simplifications and simulation of nuclear reactors.

42 Czechoslovakia


JIl~i CERM,~K VA, CLAV PETERKA Jl.~t ZAVORKA

DYNAMIKA V"

REGULOVANYCH SOUSTAV

v tepelnO

energetice

a chemii

ACADEMIA

~a~,, mdaI~';.~tvt ( e~koslovenske akademie r id

Praha 1968

Czechoslovakia 43


16.3 PRENOSOVI~ FUNKCE REAKTORU

529

Linefirni p?enos reak toru v oblasti nulovdho v~'konu

Vgimneme si nyni .a~kterS, ch ptenosovS'ch funkci reaktoru, p?edevgim vgak nejjednoduggiho linearizovan~ho pr'enosu reaktoru, kterS' je priwfi v obtasti nulovdho v~konu. Oblast nulovdho vS'konu znamenfi, 2e reaktor je sice kritickS,, ale v pod- stat~ nedod~iv,-i teplo chladivu a tak6, 2e kinetika kritickdho reaktoru nepodldhfi (v uva2ovandm/~ase) 2~idnS, m Zlllel.lfilll vlivem fyzikfilnich procesfl a zmfin v moder~i- toru, palivu, struktui~e atd.--- p~'edpoktdd~ime tedy tdm~[ ,,idefilni" rcaktor. De41e pfedpokl~idgtme, ~.e podil zpo~.d~n3i;ch neutronfl t l je realS,, (mengi ne2 0,01) a ~e 8k nebude vetgi ne;~li maxim~iln~. ,,/2 a pomern6 odchylky taN(,)/Nol =< 0,05.

Prevedeme-li po flprav~ ob~ rovnice ('.49) a (.50) v odchylkovdm tvaru z 6asov6 oblasti do oper~itorovdho tvaru, budou platit tyto vztahy"

m

8k ~ /'i AN(s)+ ~).i kRi(s), AN(s) = 7oo'V~ - 700 " , (.1)

, AR,O) = ~'-' ,~,','(~) - :., AR,(:). 02) To

Dosadime-li nyni z rovnice (.2) v}raz

/'-' ~:',.'(s) [SL..~ ~ ] ~R,(,) = To (.3)

do rovnice (.1), dostfi.vlime vztah

respektive

= ~ N o + . . . . . . . . L-i- To s 5. i m]

[ 1~ ~:,,] 5k ~:"(s) ' + 7 0 , ~ j : 700 No , -)

a odtud dostanmne po fiprav~ pi~enos ,,idefilniho" reaktoru v oblasti nulov6ho v}'ktnu jako vztah mezi pi~ebytkem reaktivity 8/, a pom~rnou zm~nou mnof~stvi r,..:utro~fa AN(t)/No, v anglosask6 literatui~e zpravidla zna~en:' takto"

G(s)= AN(s)/NOsk = 1 ITos I +--VTo~t 1 ~, . (.6)

44 Czechoslovakia


DENMARK

Automatisk Kontrol Jens R. Jensen Polyteknisk Forenings Forlag, 1956

Notes on the Measurements of Dynamic Systems Jens R, Jensen Servoteknisk Forskningslaboratorium, 1958

Contributed by

Mogens Blanke

Technical University of Denmark Lyngby (Copenhagen), Denmark


Early Automatic Control Education in Denmark

The development of the field in Denmark dates to 1949 when the Civ.Ing. (later Professor) Jens R. Jensen held a course in "Automatisk Kontrol" for engineers, organized by the Danish Engineering Association (Dansk Ingenicrforening). The lecture notes were the result of developing interest in the area of servomechanisms rapidly followed by industrial demand and research interest in control of machines, industrial mechanisms and processes.

In January 1956, the Danish industry founded the "Servoteknisk Forskningslaboratorium" as an independent research institute funded by industry. With Jens R. Jensen in charge of a few research engineers and a workshop assistant, the small team was busy bringing the latest theoretical developments into practice. Much effort was dedicated to the dynamic modelling of control objects and the measurement of response characteristics. The efforts included equipment to do correlation analysis to measure the dynamic characteristics for example of heat exchangers. Analog computers were built to support simulation, Jens R. Jensen constructed a frequency response calculator stick, cipher computers were brought into work in factory automation. Industrial undertakings included the overall control and servomechanisms used to cut steel profiles at the Burmeister and Wain shipyard.

Teaching of students of the "Den polytekniske La~reanstalt, Danmarks tekniske HCjskole" was another of the tasks of the new institute and the activity in research and teaching gradually dominated that of assistance to industry. The institute became a laboratory of the "Danmarks tekniske HCjskole" and named "Servolaboratoriet".

The original lecture notes from 1949 were rewritten in 1956 and were used to teach automatic control theory. Subjects included P and PI control for systems with one and two time constants, with integration, systems with time delay, stability analysis and design for stability using the frequency domain and root locations in the complex plane, Routh-Hurwitz criterion, feed- forward compensation. Control was treated for two-variable systems, exemplified by simultaneous temperature and flow control on page 44 and a general controller architecture on page 46. The use of complex zeros to shape phase responses are shown on page 121.

A second book was used to teach measurement of dynamic characteristics, the area that later developed into system identification. The "Notes on the Measurements of Dynamic Systems", Parts I and II from 1957 and 1958 respectively, show how correlation analysis was done using thermocouple multipliers. A digital correlation machine was subsequently constructed and the seven frequency binary test signal was invented by Jens R. Jensen.

References

Jens R. Jensen: Automatisk Kontrol. 1. udgave 1949.

Jens R. Jensen: Automatisk Kontrol, 2. udgave, 1956. Servoteknisk Forskningslaboratorium, Danmarks Tekniske HCj skole.

Jens R. Jensen: Notes on the Measurement of Dynamic Characteristics of Linear Systems. Part I, 1957. Servoteknisk Forskningslaboratorium, Danmarks Tekniske HCjskole.

Jens R. Jensen and M. Drost Larsen: Notes on the Measurement of Dynamic Characteristics of Linear Systems. Part II, 1958. Servoteknisk Forskningslaboratorium, Danmarks Tekniske HCjskole.

46 Denmark


Denmark 47


44,,

1+ s.'r= k,~ ,

�9

F i g . 39.

Ved h jmlp af de i e t f o r e g ~ e n d e a f s n i t ang ivne r e g l e r kan d e t t e

d iagram omformes r e d f . e k s o a t f l y t t e de t a n d e t summat ionspunkt i n e d e r -

s t e s l o j f e hen f o r a n de t f e r s t e s , m m a t i o n s p u n k t og regne de t o s l e j f e r

om t i l en e n k e l t b lok

,,,o R , . . . . .

'~ZR

,, ..... t

t + ~t +,,,,,,,, st= k4 k 5

,

] _ ~ o

klk 2 , . , . . . . .

I + k; k 2 .....

Fig . 40.

sore kan p y n t e s l i d t , h~ i s v i i n e d e r s t e b l o k i n d f e r e r d e f i n i t i o n e r n e i

f o r m l e r n e (20) og (31) og y d e r l i g e r e i n d f e r e r

~3 K~'= k4k . ~4 = i*K i

~R I .....

Fig . 41.

t+~; I+ ~.r,~

.... " r2m

KI Qm

'+K, ' + = r 2 zx~

48 Denmark


46.

anvende en kombina t i on af ~ben s l ~ j f e t e k n i k ( k o m p e n s a t i o n ) og l u k k e t

s l o j f e t e k n i k ( a u t o m a t i s k k o n t r o l ) .

. =

S!

Xb

S 2 L . X k /

F

Fi g. 42.

Man mAler f o r s t y r r e l s e n s s t e r r e I s e og a f l e d e r h e r a f e t s i g n a l , hvor -

med s y s t e m e t pAvi rkes e t p a s s e n d e s t e d , f . e k s , pA d e t s t e d , hvor f e j l e n

dannes . D e t t e a f l e d e d e s i g n a l ska l da t i l n ~ r m e l s e s v i s have en sAdan

k a r a k t e r , a t de t p~ de t s t e d i s y s t e m e t , hvor f o r s t y r r e l s e n g r i b e r ind ,

u d v i k l e r e t s i g n a l , de r n e t o p oph~ver f o r s t y r r e l s e n s i n d f l y d e l s e , sA-

i edes a t r e s t e n af s y s t e m e t , f o r t r i n s v i s den k o n t r o l l e r e d e s t e r r e l s e ,

ikke m~rker noge t t i l f o r s t y r r e l s e n . I d e t f o r s t y r r e l s e n s b e t y d n i n g

i f e l g e f i g . 36 e r e k v i v a l e n t reed en v i s e n d r i n g af r e f e r e n c e n , v i l d e t -

te f z l g e I i g kunne o p f y l d e s , nAr de t af f o r s t y r r e l s e n a f l e d e d e s i g n a l i

f i g . 42 g i v e r en l i g e sA s t o r men modsat e n d r i n g i r e f e r e n c e n , d . v . s .

man mA t i l s t r e b e

1 D -- - AB

1

I p r a k s J s kan denne i n d s t i l l i n g n~ppe ho Ides h e l t n o j a g t i g t over

l~nge re t i d s r u m s men b l o t den ho ldes reed en beskeden n s j a g t i g h e d , f . e k s .

20% opnAs dog, a t den o v e r s k y d e n d e f o r s t y r r e l s e , som den a u t o m a t i s k e

k o n t r o l mA modvi rke , r e d u c e r e s t i l ca . en f e m t e d e l , h v i l k e t a t t e r b e t y -

d e r , a t de opstAede a f v i g e l s e r r e d u c e r e s t i l en f e m t e d e l , h v i l k e t meget

vel kan v~re v~rd a t rage reed.

Det kan ogsA s t i l I e s op pA den made, a t de t s i k k e r t o f t e kan b e t a l e

s i g a t anvende bade kompensa t ion og a u t o m a t i s k k o n t r o l , i d e t man da f o r

en g iven k o n t r o l n z j a g t i g h e d kan n o j e s reed e t d l r l i g e r e k o n t r o l s y s t e m .

S p e c i e l t kan d e t mAske i t i l f e l d e , hvor k o n t r o l o b j e k t e t ikke er dimen-

s i o n e r e t reed h e n b l i k pA a u t o m a t i s k k o n t r o I , og hvor d e t e r u m u l i g t a t

d i m e n s i o n e r e e t t i l s t r ~ k k e l i g t godt a u t o m a t i s k k o n t r o l s y s t e m , ve re den

e n e s t e udvej t i l opnAelse af en onske t r e s u l t e r e n d e n ~ j a g t i g h e d .

Denmark 49


123

NAr e t ne tvmrks n u l p u n k t e r og p o l e r e r k e n d t e , s~ e r a m p l i t u d e - og

f a s e k a r a k t e r i s t i k k e r n e k e n d t (pA na r on n u m e r i s k f a k t o r p~ a m p l i t u d e k a -

r a k t o r i e t i k k e n ) . Hvis man i n d s k r m n k e r s t g t i l m i n i m u m f a s e f o r s k y d n t n g s -

ne tvmrk gmlde r d e t omvendte ogs~. En g i v e n a m p l t t u d e k a r a k t e r i s t i k e l l e r

en g i v e n f a e e k a r a k t e r i s t i k bes temmer e n t y d i g t f o r d e l i n g e n af n u l p u n k t e r

og p o l e r . At d e t m A Tnre s & l e d e s , ken Tel t kke " u m i d d e l b a r t " i n d e e s r e d

b o t r a g t n t n g a f f . e k a , f i g . 24 9 omend d e t mAske ken synes r i m e l i g t . Det

ken i m i d e r t i d b e v i s e s Ted h j n l p af n o g e t kompleks f u n k t i o n s t e o r i . Der

ken u d l e d e s mange f o r m l e r f o r den t n d b y r d e s sammenhmng mellom a m p l i t u d e -

og f a e e k a r a k t e r t s t t k k e r og f o r s k e l l i g e e g o n s k a b e r Ted dem. H. U. Bode

he r b e s k m f t i g e t s i g indgAende hermed og b r i n g e r en f o r m e l s a m l i n g og k u r -

v e r t t l hJmlp r e d n u m e r i s k e b e r e g n i n g e r t s i n bog, l i t t e r a t u r p u n k t 21.

'IT

0

-'i'r'

-2'IT

o~

2'1.

IHC' I

l | . . . . . . . . . . . . .

o~g HO)

28 .

Eksempela Vi t a n k e r es e t ne tvmrk

med to r e e l l e p o l e r i v e n s t r e h a l v p l a n

og to k o m p l e k s e , k o n j u g e r e d e n u l p u n k t e r .

De to n u l p n n k t e r t ~ n k e s b e l t g g e n d e meget

t e t r e d den im&ginmre a k s e , t t i l f a l d e

1) i v e n s t r e h a l v p l a n . De to p o l e r og

d e t n e d e r n t e n u l p u n k t v i i g i v e f o r h o l d s -

v i a "langsomme N v a r i a t i o n e r i bade am-

p l i t u d e og f a s e , nAr s g e n n e m l e b e r den

imaginmre akse i r a 0 t i l oo. Men i d e t

omrAde, hvo r co o m t r e n t e r l ig den ima-

g inmre vmrdi af n u l p u n k t e r n e og a l t s &

p a s s e r e r f o r b i d e t e v e r s t e n u l p u n k t , v i l

de r komme e t s t e r k t f a l d og d e r e f t e r em

s t m r k t s t t g n t n g i a m p l i t u d e k a r a k t e r t s t i k -

ken, og f a s e n , d e r e l l e r s i r a b e g y n d e l -

sen e r a f t a g e n d e , v i i i n d e n f o r e t snm-

v e r t i n t e r v a l a f co Tokse o m t r e n t x, se

f i g . 28, k u r v e r n e mmrket 1 ) . V t n k e l -

t i l v m k s t e n f o r co gAende i r a 0 t i l oo e r

n u l , da de t o p o l e r og de t o n u l p u n k t e r

i v e n s t r e h a l v p l a n ophmver h i n a n d e n i

denne h e n e e e n d e . I a n d e t t i l f e l d e 2)

t e n k o r v i os de to n u l p u n k t e r f l y t t e t

l i g e s& l a n g t t i l h e , r e f o r den i m a g i -

nmre akse . Det g i v e r samme a m p l i t u d e -

50 Denmark


Denmark 51


21

M, ea, surement 0f,~.a system of a Break Frequenc]r of 0,,,.0008 c/,e

The arrangement is shown in Fig. 11.

220 V

~o/2e -

Square wave

tarot" [ sin ~t coscot

Thermistor bridge

couple m, u/tipl1"er

Pot. H Electror~ recorder integrator Recorder

Fig.~ I.

The system consists of a container through which water

flows at a constant rate. The water is electrically heated,

and the temperature is measured by means of a thermistor

bridge.

Since it is not a simple matter to vary the heating

power sinusoidally, a square wave input is used. The re-

ference voltage is a sine wave in phase with or 90 ~ out of

phase with the first harmonic of the square wave. The higher

harmonics of the square wave are regarded as noise.

The output of the multiplier as well as the integral of

the output are recorded. The registrations obtained correspond

to Figs. 6 and 7 on pages 9 and 10 in Part I, and samples

of the registrations are shown in Pigs. 12 and 13o

Por demonstration purposes only three points of the

52 Denmark


FINLAND

Basics of Servomechanisms Erkki Laurila Published in 1954

Theoretical Background of Control Engineering, Vols. 1-2 Hans Blomberg Helsinki University of Technology, 1963.

Contributed by

Antti J. Niemi, Heikki Koivo, Raimo Ylinen

Helsinki University of Technology Helsinki, Finland


Background

Instruction and research of control engineering was initiated in Finland by Dr. Erkki Laurila (1913-98), Professor of Technical Physics at the Helsinki University of Technology, who from the academic year 1946-47 onwards devoted a part of his lectures to theoretical fundamentals of control. The other parts consisted mainly of methods of industrial measurements and control applications, and of fine mechanics which were related to his earlier work in the Finnish instrument industry. A Laboratory of Technical Physics serving the listed subject areas was also planned and soon set up, for experimental illustration of related phenomena and industrial controllers, and for individual constructions related e.g. to thesis works.

The 3rd year students of control engineering were already familiar with electron tube amplifiers, and Prof. Laurila could therefore use these for introduction into the concept of feedback and, further on, into that of stability and transients of feedback loops. Since the relay and proportional controllers dominated the practical applications of automatic control, they were also presented, and the models of the latter type were then augmented with reset (integral) and rate (derivative) elements. Simplified models of some basic industrial processes were taken for representations of the control objects. Transfer function models of control components and loops were introduced by him at the end of the 40's, after the integral transformations had been included in the mathematics courses.

During his first years of instruction, Prof. Laurila expanded the part of control engineering further and introduced electronics as another subject of lectures, while fine mechanics and instrument constructions, except industrial controllers and servo mechanisms, were taken over by another teacher. His lectures on control were occasionally accompanied by written sheets, and existing American and German textbooks were recommended for wider information. He obviously preferred to bring first his earlier and parallel studies on electronics of solid matter and rarefied gases to the form of two textbooks in Finnish, which were published in 1948 and, with Mr. L. Saari, in 1950.

Another pioneer in control engineering education in Finland is Dr. Hans B lomberg (1919-). He was appointed Professor of Theoretical Electrical Engineering at Helsinki University of Technology in 1956 with duties in Swedish, which is the other official language in Finland. Control engineering was at that time a new field of interest to electrical engineers and Professor B lomberg decided to specialize in it. Over the next decade his laboratory, called the Automatic Control Laboratory, was the centre of control engineering education and research in Finland.

54 Finland


Basics of Servomechanisms

Erkki Laurila Published in 1954

Erkki Laurila's textbook on control, entitled Basics of Servomechanisms, was published in 1954. It contained four chapters: 1. Introduction, 2. Mathematical and experimental methods of servomechanisms, 3. Linear servomechanisms, and 4. Nonlinear servomechanisms. Chapter 1 introduces the concept of automatic control as a feedback system. Two motivating examples are used: temperature control in a water tank and position servo as a typical linear servomechanism. In the latter case basic concepts of steady-state error and effect of damping are discussed. In the second chapter Laplace transform is introduced as a tool to treat linear, time-invariant differential equations. This leads to the introduction of the transfer function concept and further, to frequency domain presentations in the form of Bode and Nyquist diagrams.

Chapter three forms the core of the textbook. Linear servomechanisms are first characterized, then their stability issues are analyzed using e.g. Nyquist criterion. For design purposes, phase margin and gain margin are introduced as measures of degree of stability. To stabilize and improve the system performance, phase-lag and phase-lead networks are treated and examples are given to illustrate the design steps. Electric networks are used as basic compensators. In addition to servos, also pneumatic and hydraulic actuators are discussed and their transfer functions derived. Here and elsewhere, Laurila points out analogies between different systems. The chapter concludes with a discussion on elimination of disturbances. Linear servomechanism is used as a case study and block diagrams strongly support the analysis.

Chapter four studies nonlinear servomechanisms. The motivation comes from common nonlinear actuators like relays, relays with hysteresis and saturating actuators. Phase plane and describing function are explained as basic analysis tools. The use of describing function to specify self- oscillation and also as a design tool to avoid oscillation is briefly explained. The last topic in the book is sampled-data servosystems. These arise naturally from the idea of using contactor type of servosystems- digital computers are not mentioned. The treatment of the topic is rather cursory.

Although Erkki Laurila's textbook is only 100 pages long, he is able to summarize the key ideas and techniques in a concise manner. The reader is introduced to a new field of control engineering and is easily convinced of the usefulness of the approach.

Finland 55


VALTtON TEKNtLLiNEN TUTI(IMUSLAI,TO~$ ,~. . . . . . . . . . . . . . . . . . S . . . . . . . . . . . - . . . . . I i _ IILL LL | m l ' - - . . _ J I , I 1 , , 1 . J J I

T | e d e i t u t 11 3tl

SERVOTEKNI IKAN PERUSTEET

ERKKI L A U R I L A

H | L S I N K I 1954

56 Finland


verrannollinen. Takometripiirin a~ava~o oietetaan hltvi~i- vLn pieneksi .

Kuva 4,5

Kuvaan merkityiiia suureilla on seuraavat arvot:

= .. = ' = 0,002.0 K v 12 e F 2700(V/A) i c rg

R c - 8 0 D R F - 7 , 7 5 9 r m ffi 0 , 0 1 0 0

L c = 8 H y L F ffi 2 4 , 4 H y i m m a x - 1250A

Rq ffi 1,06D eg ffi 18,5.(V/A). i~ e t - 1 (V/rads'l)'-u

Lqffi 0 ,318 Hy e m ffi 40 (V/ rad s '~) . ,Ou J ffi 1 8 0 0 k g m 2 ] r a d 2

v i ~ t 6 m o m e n t t i T = 3 6 ( N m / r a d A)" i A

V o ~ m e k i r j o i t t a a e r i suu re i t t en v ~ i l l ~ va l l i t s eva t y h- t~lOt suo raan L - m u u n n e t t u ~ :

Ec = Kv(Ei - Et ) Ec _ Ec L c

I c ffi - =,:~-,:,,,:-::~ ....... =:-~,~ T I -" --- = 0, I s R c + S L c Rc(I+TIS) �9 :Re

k~ F I c k F Lq E F ffi -- ......... I c T2 = ' - . ffi 0 , 3 s

Rq+SLq 1 + T3s Rq

EF ....... E F I F : ........................... : T3 :LF ffi 3,2s

R F +s L F R r (I + Z :3 s) R F

Eg ffi kgI F

77

Iii Ill ll I II IIII I II IHIIIIIIIIIIIIIIgl[ll r I I I II . . . . . . . . . . LI

Finland 57


dP ar �9

~ r

r' a r ,B" " , , - i I - - t

Kuva 60

te lymetodi ikka keh/ tet ty jo huomat tavan p i t k ~ e , ja se mu i s - tut taa s u u r e s t i y l e i s p i l r t e / s s ~ Ltneaaris ten s e r v o s y s t e e - mien ~ t t t e l y t a p a a . Tarko i tuksenmuka tsuussy t s tA kAyte-

h - m u u n n o k s e n oheLta n ~ s s A p r o b l e e m o i s s a ns. z- muunnosta . Aikamuuttujan r( t ) z -muunnos saadaan lausu- tuksl L-muunnoksen avul/a

jolloin L-muunnoksen l a u s e k k e e s s a es i /ntyv~ �9 - s T korva- taan z: l la . Kaavas sa eslintyv& | T ( t ) o n

4 - "

8T(t ) = ~ I ( t - n T ) ] ~ i - - m .

z -muunnoksen kAytt66n pe rus tuen voidaan nAytejonosystee- mien ~ I t t e l y s s l l turvautua I / n e a a r l s t e n s y s t e e m l e n yhtey- dessl t kmytettyJ& graaf i~/a menete!mUt muis tu t tav i /n mene - te lmi /n .

SikKti kuinn&ytejonon aikavAli T on hyvin pient v e r r a t t u - na ohja t tavan s y s t e e m l n m ~ I r U v l l n aikavakloihln, voidaan s e rvosys t eemiA ~ i t e l l & Xineaarlsena. R i (Z) :n vas taava a i -

99

58 Finland


Theoretical Background of Control Engineering, Vols. 1-2

Hans Blomberg Helsinki University of Technology, 1963.

Because Professor Blomberg gave his lectures in Swedish but most of the students were Finnish speaking, he started already in the very early phase to use duplicates of his lecture notes in teaching. Those lecture notes were collected to a book Hans B lomberg: Theoretical Background of Control Engineering, Vols. 1-2, Helsinki University of Technology, 1963. This book was theoretically oriented; later on Professor Blomberg and his staff moved to more general systems theory.

The whole set of these lecture notes was never used as a textbook of the basic course in control engineering, because this was taught by other teachers and Professor Blomberg himself gave lectures in advanced methods of control engineering.

Volume 1 of the book contains four chapters. Chapter one is an introduction to control systems and their properties starting from some physical control systems. Then in chapter two the concepts of transfer function and block diagram algebra are introduced. Chapter three gives more examples of real control systems, in particular of those of electrical circuits and motors. Finally, in chapter four the discussion of properties of control loops is started from static error coefficients. The volume has also an appendix with introduction to Laplace transform.

Volume 2 is a direct continuation of chapter four in volume 1 and contains only one chapter and two appendices. The consideration of static errors is first completed. Then stability and instability definitions as well as their connection to location of poles are introduced. The traditional stability tests, like Routh-Hurwitz test and Nyquist test with several examples are presented. Also the construction and use of root locus for control design are considered. Finally, the properties of control systems in time domain using step responses and frequency responses as well as responses to stochastic inputs are discussed.

The first appendix of volume 2 contains a comprehensive introduction to Fourier transform and spectral theory of deterministic and stochastic signals and the second appendix presents the basic stability definitions of Ljapunov.

Finland 59


T E K N I S K A H O G S K O L A N Kompendium n:o 169

REGLERINGSTEKNIKENS TEORETISKA GRUNDER

Del 1

Prof. Hans Blomberg

Svensk-finsk ordf6rteckning c]v

Diphing. Seppo Rickman

Helsingfors 1963

60 Finland


s-planet

s=+jR

8=+J

I t,OlR f

-'r -5 / 'r~

,~-J 61 !

!

C I

I

- co<~-61i

,r adie R

z-planet (GH-planet)

%

till ~0-

~ . . . i

3J"

2 j '

~ungef~rlig Lbild av C 1

\

=GH(J~), W,a,.Z co

\

\

1

~'%+%R+%.,-%.,

~o=,1

W

gr adie M I

~ o ~, o,7/o. o 7

w=_+2 2 ' /

/ b /

--3 z=GH(jw ) Iger bilden

L%~<oo 1 { ~ % ) '' ~,, (~o R)

Fig. 4.8.3-2

Till~mpning av

Konturen C (bild a)

Nyquists st abilitetskriterium,

i s-planet ~r avbildad 8ver

exempel 2.

funkt i onen

2O i z-planet. Bilden b visar resultatet.

Finland 61


62 Finland


FRANCE

Technologie et calcul pratique des syst~mes asservis P. Naslin Dunod, 2 nd edition, 1958

Mdthodes Modernes d'Etude des Syst6mes Asservis J.-C. Gille, P. Decaulne, M. Pelegrin Dunod, 1960

Commande optimale des processus R. Boudarel, J. Delmas, P. Guichet Dunod, 1967

Contributed by

Marcel Staroswiecki Ecole Polytechnique Universitaire de Lille

France

Jean-Claude Trigeassou and Patrice Remaud

Ecole Supdrieure d'lngdnieurs de Poitiers France

Michel Kinnaert Universitd Libre de Bruxelles

Belgium

Background


In 1960, the classical theory of linear control systems was well established, following developments in Germany and in the United States during World War II. In France, it was disseminated through textbooks originally written in French, like

M. Bonamy, Servomgcanismes, Thdorie et Technologie (Masson, 1957),

J.-C. Gille, P. Decaulne, M. Pelegrin, Thdorie et Technique des Asservissements (Dunod, 1956), Thgorie et Calcul des Asservissements (Dunod, 1958),

P. Naslin, Les Systkmes Asservis (Ed. de la Revue d' Optique, 1951), Technologie et Calcul Pratique des Systkmes Asservis (Dunod, 1958),

or translated from American English

�9 H. Chestnut, R. Mayer, Servomdcanismes et R~gulation (Dunod, 1956)

and from German

�9 W. Oppelt, Manuel des Rdgulations Techniques (Eyrolles, 1957).

On a related subject, the book

M. Pelegrin, Machines it calculer ~lectroniques arithmdtiques et analogiques (Arithmetic and analog electronic computers) (Dunod, 1959)

deals mainly with the application of the first electronic computers to closed loop systems used in aircrafts, or used to simulate the dynamics of these complex systems. M. Pelegrin, French aeronautics engineer, was also a graduate of MIT (1949) in the domain of electronic computing. From 1954, he was responsible for teaching computers at Ecole Nationale Sup~rieure de l'Adronautique. This book reproduces his teachings for young aeronautics engineers, also specialists of automatic control for aircrafts. The two types of computers used at that time are presented, analog computers necessary for simulation purpose, and arithmetic computers, in order to perform complex computations or to incorporate them in closed loop systems. Though the technologies presented are all obsolete nowadays, this book gives evidence on the natural links between automatic computing and control in the fifties. Moreover, it gives numerous examples of computers manufactured by French companies of this time. Since 1950, France was able to produce the analog and digital computers needed by the army and industry, thanks to several companies, like "SociEtal d'Electronique et d'Automatismes" (SEA), and "Compagnie des Machines BULL". It is also important to note that these companies had been created by (or developed with the help of) pioneering control engineers (like P. Naslin and H.F. Raymond).

64 France


Technologie et calcul pratique des syst~mes asservis (Technology and practical design of feedback systems)

P. Naslin Dunod, 2 nd edition, 1958

About the book

This text book originates from a lecture given in 1953 by P. NASLIN to the Belgian Society of Mechanical Engineers. The text of this lecture was first published in France by DUNOD. Then, this first edition was enlarged, mainly with the numerous papers of the author published in the French journal "Automatismes", created in 1956. This second edition, published in 1958, constitutes a reference text book on automatic control, for the interest of the different technical examples presented, as well as for the pedagogy of the author in order to convince French engineers of the relevance of this new science.

This book is divided into three main parts:

Part. 1 Principes et technologie des syst~mes asservis (Principles and technology of feedback systems)

- Chapt. 1 Notion de syst~me asservi (page 3) - Chapt. 2 Transmission des informations. Systbmes de modulation (page 22) - Chapt. 3 Les 6tages de puissance des servomdcanismes (page 32) - Chapt. 4 Les syst~mes asservis ~ variables multiples (page 50) - Chapt. 5 Syst~mes asservis ?~ commande num6rique (page 65) Part. 2 Th~orie simplifi~e et calcul pratique des syst~mes asservis lin~aires et non lin~aires (Simplified theory and practical design of linear and nonlinear feedback systems)

- Chapt. 6 Propri6t6s des syst~mes lindaires. Notion de transmittance (page 87) - Chapt. 7 Stabilit6 des syst6mes asservis lin6aires (page 131) - Chapt. 8 PrEcision des syst~mes asservis lin6aires (page 153) - Chapt. 9 Mdthodes de correction des systbmes asservis lin6aires (page 181) - Chapt. 10 Calcul pratique des r6gimes transitoires (page 244) - Chapt. 11 Analyse harmonique des syst6mes non-lin6aires filtr6s (page 257) - Chapt. 12 Etude exp6rimentale des syst~mes asservis (page 276) Part. 3 Etude de quelques organes technologiques: moteurs, amplificateurs, organes de mesure (Description of some technological components: motors, amplifiers and sensors)

- Chapt. 13 Servomoteurs (page 285) - Chapt. 14 G6n6ratrices amplificatrices (page 301) - Chapt. 15 Amplificateurs magn6tiques (page 310) - Chapt. 16 Amplificateurs ~ tubes ~ gaz (thyratrons et ignitrons) (page 339) - Chapt. 17 Amplificateurs ~ tubes t~ vide. Modulateurs et d6modulateurs (page 369) - Chapt. 18 Calcul analogique. Simulateurs (page 396) - Chapt. 19 Mesure 6lectrique des grandeurs cindmatiques (page 414)

France 65

About the author


P. NASLIN, graduate of "Ecole Polytechnique" and "Ecole Sup6rieure d'Electricit6", was a pioneer in the introduction of automatic control in France after 2 nd World War. He greatly contributed, with the help of his teachings in engineering schools, his papers in technical journals, his lectures and his numerous books, to the diffusion of a modern approach to deal with closed loop systems, towards an audience composed of engineers from various origins. As he stated in the foreword of this book, his main objective was to demonstrate the fundamental functional identity between the controllers of steam engines and the negative feedback of electronic amplifiers. The originality of this book, one of the first to be published in France, is to be based on numerous examples, taken from different technological domains, in order to demonstrate the universality of the feedback concept.

Moreover, P. NASLIN deliberately decided to simplify theoretical developments, in order to facilitate the understanding of this new system methodology. Thus, he uses essentially the p Heaviside operator for the writing of differential equations and his demonstrations are mainly based on the frequency response. In all his other books, he made a great effort to be comprehensible to a large audience, by favouring approximate (but rigorous) techniques and methods in order to avoid sophisticated mathematics. Thus, he developed original techniques, particularly for the synthesis of feedback systems. He is the creator of the method "Polyn6mes normaux ~ amortissement r6glable" (normalized polynomials with tunable damping), also called in France "Naslin polynomials" (comparable to the normalized polynomials of Whiteley or those of Graham and Lathrop).

P. NASLIN is the autor of several textbooks in automatic control like: "Les r6gimes variables dans les systbmes lin6aires et non lin6aires" (Dynamics of linear and nonlinear systems) published by DUNOD in 1962 (500 pages) and "Introduction ~ la commande optimale" (DUNOD). He also wrote two textbooks dealing with discrete event systems: "Circuits logiques et automatismes ~ s6quences" which was published three times by DUNOD, and "Construction des machines s6quentielles industrielles" with co-author P. GIRARD in 1973, where an original method for the analysis of sequential systems is presented, this approach being a precursor of French normalized GRAFCET (based on graph theory and Petri nets). He is also the author of a book on electronic computers "Principes des calculatrices num6riques automatiques", which is the fruit of his experience in the development of the French computer industry.

Moreover, he is not only the brillant author of numerous books in all fields of control, he has also been responsible for a reference collection on automatic control published by DUNOD: "La biblioth~que de l'automaticien", composed of 40 titles. Thus, he is at the origin of the publication in French of the major books related to control, originating from the USA and the USSR.

Contributed by Jean-Claude Trigeassou and Patrice Remaud

Ecole Sup6rieure d'Ing~nieurs de Poitiers 86022 Poitiers Cedex France

66 France


~:,~, ..

iii~:.i i i i ; : : : ! ....

. . . . . . . . . . . .

TECHNOLOGIE ET

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. . . . . . P. N A S L I , N AnciQn ~6|6v@ de l ' ~co le Poty technique e l de. I 'E. S. E,

..!ng6nieur.~miilifolire en �9 :din I ' ~ m m Q n t Profi~sseur:b !.'~icole n a t i o n a l e Su l~r i | eure de ! * A r m e m e n t

et ~ |:*lnstitut s v ~ r ~ e u r d ~ ; M o t ~ r i a v x e J ::de Io Cons|tutt i , .on mic:onique. ..

DEUXiEME EDiTiON ENT|~REMENT 'REFONDUE

ET AU.GMiENTs

P A R T S

/ ~ . RUE B O N A P . A R T E : | 6 * |

19B8

i

France 67


~A #o O ~rs Os uR

s NiVgAU C O~,~tT DE CA/~IU/?A.TEOtg FREm D$.PI4ONO6~ApI4s

Fig, I-11. - - Exemples d~ syst~mes a~servis ~l~nental~s ~ action dtrecte.

The functional identity of different closed loop systems based on the feedback concept

t t#or~o~ co#ri#u J g~ctr~r/~v Mt~e~f ] ~_or~ut~ 5tmg A oountf ~o~'rr.#e

I 0 t

,o,. = .,.. ~_~-XI;.~, - , -- =-o,=,. = ;=~ I t " o , ' , ,~,,,'',,', ~ Y I T I ! ...................... ~ ~ ' - - ~ I

" ~ . . . . 17,+,=-1~ v L_I l+, 1%

4=: a N, a] =

Hude

. . ~ d r

T/9; + Vt~mArf Ue t4YL~.AULtOU~ (2",

~ n ~ = di~,t kY.J lal,.~ 0 ~e ~4ui~e

~Sl>etrt h.~drctuhO~

Woett- L~O~ord

6 i . & a l r , . , 61ndratn~

, t O Amplidge~ |

EIn.~AY,~GES g~EC~O~6u(ri~tES

vAte~ar~ tngcAoiouE

~ MOt~ o~ifiojre

|

AMPL/F~CATEU~'5 PNEU~AT~UES__

|

F i g . I l I - 1 . - - Prtnclpaux dtages de puissance utgi~s darts 1r servomdcanismes.

Power actuators c o m m o n l y used in servomechanisms: different technologies (electricity,

mechanics , hydraulics, pneumatics) .

68 France


~iiii!ii[!ii:i

ii iii,i iiii!iiiiitE::

PIROPI~II~'I~S I)E$ I~YS'I'~:MES LIN]~A]rtES. NOTION DE 'rltANsMrrT:LNCE 119

E n d6~signant, a v e e l e s i n d i c e s c o n v c n a b l e s , par 1 [ R les ddb i t s d a n s l e s 6 tran- g l e m e n t s par -un i t~ de d i f fdrence de p r e s s i o n e t par 1 / C la v a r i a t i o n de pres s ion

F':Ig. V 1-27.

d a n s les r 6 c i p i e n t s par uniCa! de d 6 b i t d'air, le p r o c e s s u s e s t ddcr i t par les 2 6 q u a t i o n s s u i v a n t e s :

d t } l 1 ~ o - t2}1 -J'}l . . . . 1}~ d t - - R 1 C ~ R ~ & .

d P s _ . tz~l - - - l"n d t ~ R ~ C a "

vo ~ v, ~ v2

.... T T (Z)

P vo R, v, ~ x ~ v~

| Fig. Vl-28, - - Cascade de deux 6rages du premier degr6 (a) ax, ec couplage et (b)

sans couplage.

iiii!!iiiii% i,:it:,~

iiiiiii!iiiiiiiiii!ii+i!!~iii~it~i::

Cascading of first order systems is presented (originating from electricity or pneumatics, with eventual coupling)

France 69

i!!:ii: "?:'

" > :i,

ii~iW

7!i~i!iii': '~ �9

:!i ) :

~7~!!~: �84

i!~iil .. . .

!!!!!i!i!~!ii!~7 .........

!i7i!711 ~

ii!iiiii!iTL; !i1711!!i~!~i!,: iiiiiiii:i~i:i,: i!i!iiiTi!ii:


~'rAII iLTTI~ DES SYSTi~,XlES A~.~.En'vl~ I.IN'J~AIRE5 147

Considt~rons par e x e m p l e le sys tbme de la figure VI-36, dou6 d'une chalne de reaction principale de fonct ion de transfert unitd et d'une chaine de r6ac- tion secondaire [~2- On commencera par analyser le ~ ' s ~ m e l h $ , - S i cette boucle ne comporte pas d'dldments instables , sa fonct ion de transfert ne pr6sentera pas de p61e h partie rdelle pos i t i ve et le nombre de tours dan~ le

_LI

0 7~

j ~ 2 Q

k(':,p + i)

(D Fig. VI 1-16. - - Application dti r d.e Nyquist-Gauchy

b un systbi i ie c o n i p o ~ ui l iquenient d'orgal ies .stables.

i i:i" iiiiiiiiiiiTii!~i~:: ~ :, ~ii7~17.i7',iii7

!iiiiii!iiiii~ii+, ,~

i i::iiii:: i77111~iiii!71:!!iiL:i :::i ~

sens direct de sa courbe de N y q u i s t , Cauchy autour du po int cr i t ique nous fournira le hombre de. poles de sa transn: i t tance cn boucle fermde, ~ parties r6elles pos i t ives , Ce nombre de p61es est dgal au nonlbre de toul~ que dol t faire darts le sens inverse la courbc de N y q u i s t - C a u c h y de Ia boucle principale autour du point crit ique pour que le sys t6me comple t soit stable,

Use of Nyquist stability criterion

70 France


s z ~ ~ "~. =

~ g , .

~ s ~

r4 g ~

�9 ~ ~ .~ ~ ,

- ~3.o

I1ti t1~

•

ItI1~11

~ s

4"i

6

I

L

, ~ .

~ . ~

~.~

..4.~

.~ I! o

,x~ u t ,...

~_2, •

x

~'y.

c~ P..

~4 ~ . " 2

. ,~ ,~. ~.~,

.2:-"

c ~

These two pages illustrate the approximate determination of the step response of a closed loop using frequency response.

France 71


M~thodes Modernes d'Etude des Syst~mes Asservis

J.-C. Gille, P. Decaulne, M. Pelegrin Dunod, 1960

The specific aim of the book by Gille, Decaulne and Pelegrin was to collect later research results, which extended the classical ones and opened new application areas, and which were only available through separate and fragmented papers in journals and conferences, generally written in English, in order to make them available to a general technical audience under a synthetic and didactic form. Its content was used by the authors for lectures at Ecole Nationale Sup6rieure de l'A6ronautique de Paris, and at Graduate level at the Facult6 des Sciences de Qu6bec.

The foreword of the book carefully states the mathematical background which is required from the reader: complex numbers, complex exponential, Laplace transform, decomposition of rational fractions. Matrix notation is used exceptionally, in very limited occurrences. The book is divided into four independent sections.

Section 1 presents the new analysis techniques associated with poles and zeros of the transfer function. These techniques, due to W. Evans, E. Guillemin and J. Truxal, are not believed by the authors to replace the classical harmonic approach, but they are credited with offering a new view of the problem, and stated as a nice complement to classical approaches. Closed loop analysis of linear mono-variable systems and the synthesis of a closed loop regulator are the main topics addressed in Section 1.

Section 2 addresses the statistical analysis of closed loop systems. Stochastic inputs are presented, and the design and optimization of linear systems is addressed. The methods presented in Section 2 follow from the works of C. Shannon and N. Wiener, Y. Lee and G. Newton in the United States, V. Solodovnikov in USSR, and M. P61egrin in France.

The third section gathers several extensions of the harmonic approach to multivariable systems and to sampled data systems. Arguments given by the authors to justify this extension are related with the practical implementation of closed loop control, by using analogue or digital computers. The section relies on the works by F.-H. Raymond (France), M. Colomb, E. Udsin, J. Ragazzini, L. Zadeh, W. Linvill, L. Sittler and J. Truxal (USA), Ja. Cypkin (USSR).

The last section is devoted to non-linear problems, the methods selected according to their interest for practical applications of closed loop systems, and graphical analysis being preferred to algebraic approaches. Transient behavior, first harmonic, second order state space, on-off regulators, and stability theory (Poincar6, Ljapunov) are the main topics. Research on non-linear systems was already very active, and Section 4 builds on results from USSR (Ja. Cypkin, B. Naumov, N. Bautin, A. L~tov, M. Ajzerman), Germany (W. Hahn, E. Pestel and K. Magnus), England (P. Nikiforuk and J. West) and France (B. Hamel).

The book contains a glossary in five languages (French, English, Russian, German and Spanish).

Contributed by


72 France


T E C H N I Q U E S D E L ' A U T O M A T I S M E

MIRTH 0 D ES MO O ERN ES D'ETUDE DES

SYSTEMES ASSERVIS PAP,

J.-C. GILLE Ing~nieur de I 'A i r

Master of Ar ts

M. PELEGRIN ing~nieur de I 'A i r Oocteur ~s Sciences

P. D E C A U L N E lng~nieur de l ' A i r Master of Science

: 1 . 9 6 0

France 73


TABLE DES MATII~RES

A v a n t - p r o p o s . . . .

I ' I~ | , :M lf:~l.ll': } ' . \ I :F I ' i 1.;

T E C H N I Q U E S D E S P O L E S E T Z E R O S D A N S L E P L A N D E L A P L A C E

( : 1 1 .~, P I ' [ ' } { I.: ] ,

I . I i . ' ; I ,:;

t :11 . \ i~, l ' i ' l l I,: "~.

2 , L "2.2 "2.:+

,I, .11%.Pl ' i ' t~ l , ' , ")+,

L a c o n f i g u r a t i o n des p61es e t des z ~ r o s

('.;is ,l(",: .~x.qfr ,llt l , rotr l i ( , r (~t +I~, ,q,, 'oe~l ortl t ' t , .

I ' , ~n6tl~,.)<i( ' (lt '.s |)61t,..~ t ' l z("r,~)s . .

L e l i e u d e s p61es o u l i e u d ' E v a n s

l'~\~:m[,I<':< . . . . . . . . . . \ t ) t ) / i < ' :+ l i t )+ l il I;, s l ; i i + i l ' i l , ~ +"t fi I t t'(~zz'l|H.+t~s:.~li't)~i.

7 I+;

.)~') �9 . ,.,

C o m p e n s a t i o n e t s y n t h + s e c lans le p l a n de L a p l a c e . ( M e t h o d e de G u t l l e m i n e t T r u x a l )

'{.l t:}i<~ix tJ<' l;i i't),l,'i.it+en ,it, Ir+tn~.sl'~+~rl et~ l~ott{'Ic l ' t 'rtii,"t ' . . . . . . .li) '~.'~ l)r de. l;l ft:~+it'ti()rt +I,, tl';nll~l'r t'In l,O]l,'lt'. 't~tjv~,j'tt, t,l ~I,,

l ' ( ; ~ i ( ' : ) I I O t l U I ' i + t ? [ ( + t { [ ' . . . . . . . -I 'i',

l ) l - : t N l l : : . ~ l l ' ; I ' , . \ I ~ T I I "

M I ~ T H O D E S S T A T I S T I Q U E S

( ,~\ , ,~ ' ,~{ , : I. E n t r ~ e s a l ~ a t o i r e s . N o t i o n s s u r les s p e c t r e s de { r ~ q u e n e e er l a t l t e o r i e de I ' i n f o r m a t i o n

1. i N ( ) l i ' t ~ t l <le s l ) { ' v l ['(' , t l ' f r 6 ( | t ~ o t ~ , ' e . . . . . _,1 .1.'2 t { e [ ; t t i o l l l ' ( ) l l i l : t r l l ( , r l l ; i l ( , , : t l ) l ) i i < ' : t l i i ) t , s . . +;'.)

l . I N ( ~ t i l , } , s S i l l ' 1;i { l l ( ;o l ' i ( . ' (]L~ I ' i l l [ ' l ) l ' l F ] ~ l { i ( ) l l . . . . . 7 [

Cri t /+res s t a t i s t i q u e s . O p t i m i s a t l o n e t s y n t h ~ s e des s y s t ~ m e s a s s e r v i s

~1(+11~,)<l~+' 'tl~, \ \ ' h q ] t ' r . . . . . . . . . . q,~ . . \ l ~ l l i < ' ; t l i t ) l l , l l , I;t l l l t ; I I I t)(t~' l i t : ~ \ i~ ' t l~ '~ ' . . . . . <.)(I

. . . . . . ~-)

I' ~ [ i .k | ) l . l t ~ i-. ~) .

I l n ~ a i r e s %. I -,. '2 ;).;:} 7). I ~'~.~) ft ' . ' t l ' ] l l ' ] l I.'-.il) II . .

( ' ,~ .\ P V ~ ' l ~ - : ( ; .

l ; l ~;.'2 (',.:~ ~;1

E X T E N S I O N S D E S M I ~ T H O D E S L I N I ~ . ~ i I : I E S

A s s e r v i s s e m e n t s ~ p l u s i e u r s v a r i a b l e s

~ V . , , , l i ' l ' i l ( ' ~ ,tit'. o ' ~ ) r } l l Z l : i l l , l ( ; f i l ; ( + ; , i l ' + ' s in l)Ii:.~i('tnrs \ ' ; l l ' j ; l [ , l . l , s . l ;c;l ' i ; l i l i(~tl. ,'l;+,'-~il'i,';tli,,rl. ~'xl'lzll~l~'.-. . . . . . Nt , .~ , l i (~LS ";~.11' It"."- ' ~ ' ; t ~ t " t l ~ l l l t ' 1 | l ' ~ . : 1 1 ) ; 1 ~ . ~ ' i l t 1 | ~ ' ~ I'1 ' ~ i l l l l l l i ; l | t ' l l F ~ . . . ( l l l l ' i , t I l l l ' S I | l t p l " 4 ,[]a' I it,;+,t+it' ,,;+:tt6;':tl,'. . .

IUI

74 France


V I I i ' L . X F l I . l ' i I | t ' ; S 5 l . X l ' l l ; l i l ' ] , g

(_:ItAPITRI': 7 . - . . . . F o n c t i o n s de t r a n s f e r t d e s s y s t ~ m e s l l n 6 a l r e s p u l s e s

7.1 S ' r I i n d a i r e s it d c h : ~ ] l t i l l o n t i a g e o u l)~tlst~s. 7. '2 1-~1 t . r a v i s f o r m a t i o ~ l e n z . . . .

. . . . i i!) �9 12,;

('xx.~Pvr)~v, 8 . - - R 6 p o n s e e n t r e q u e n c e et s y n t h ~ s e d e s a s s e r v l s s e m e n t s p u l s e s

8.1 A n a L y s t ; h a r m o n i q u e de.s s y s t t ' : m e s l.))tlsd.s . . . . . . 13:) 8.2. A P l ) l i t ' a t i o n h ]a s t a b i l i l . 6 (;los a s s e r v i s s e i n ( , ~ ) ' l . s t)n~lsds 147) 8 . 3 NoLiot~.,: .,stir l~t synLl - ,Ssc t i e s a s s e r v i s s e ) n ( , ) ) t s i)ttls6.~ . . . . . . . t 4 9

Q U : k T I A I I ~ ; M E I ' A f t ' l ' l IV.

A S S E R V I S S E M N N T S N O N L I N I ~ A I R E S

(;,t:~, p , 'raE 9. - - G@nera l i t6s . t t @ g i m e s t r a n s i t o i r e s

9.1 9.'2 9 . 3

(;tv.~.n,v'r)t r: 10 .

1 () . i .I (.). 2 Iq).3 1 0 . 4 10.5 I 0.r

( ; 0 , n d r a l i t d s s u r l e s s v s t . ~ r n e s a s s e r v i s ilOll l i l t d a i r e s . . . . . 15:) H O g i m c l r ~ i ] s i l o i r e ~.les a s s t ' r v i . ~ s e r n c t ~ l s l ) ~ r p l u s o u m o i ~ l s . I61i R 6 g i r r t e t . r a n s i t o i r e , d e s a s s e r v i s s e m o , ~ t s p o s s 6 d a n t ~,x~ ('.qd, r n e n t n o n

l i n 6 a i r e . . . . . . . . 1 72

(',tIAl'l'rl-,tN I I.

! l . l 11 .2 ! 1.3 11..1

L ' a p p r o x i m a t i o n d u p r e m i e r h a r m o n i q u e

P r i n c i p e ( le l a m 6 t h o d e . . . . . . . . . . G a i n 6 q u i v a l e n t d e s o r g a n e s tlOll livl(}uiro.s u s u e l s ~

S t ab i l i t (7 ; d e s a s s e r v i s s e m e n t s ~ t~r~ ~)t'~:t~(', n o n lit~(;:~iv'('. P e r f o r m a n c e s e l t ' () i l l l)ol |g~t ti(.)ll . . . . . C o m p l d m c n t . s ( l i v e r s ,

C o n c l u s i o ~ . . . . .

- L a m ~ t h o d e d u p l a n de p h a s e

l.t3 J ) l ~ t d ' e x i e l l s i o ) t ('~ l)l~as( ' . . . . . . . . . . . . . A l l p l i e a t . i o ~ t h q~mlqtit , . 's s . v s t 6 v n e s a s s t , r v i tnt)rt lit~d~til'o.~ s i ~ l ) l , , ~ . Gdn(}r~tlis~l. i()t~ " l '( 'sj):~('(: (l~' l ) ] l a s e . . . N o t i o n : . ; s~tt' l ' (>l)Iit t)i . , , ; t l i())t t~o)~ ]i)~(3~vi)'(,. . . .

q ; t t A ] ' t ' ) ' ~ 1 '2 . - - - O s c i l l a t i o n d e s a s s e r v i s s e m e n t s p a r p l u s o u m o i n s

1'2.1 I n t r o ( i t l e l i o ) ) . . 1 2 . ' 2 ( . )s( ' i l l ; t l i () l~s l i t )vt ' s t i e s rdff t l l ts l)i~r [;lit.s. or) tnLt)i)ns .I'2.:'~ ()s( ' i l l~tli()t) .~ foI ' t ' l :e~ 111'.'.; ~s:.;t 'vvis.,;(:)))~')tls l)a)" l.~]~s t)~t ]~t()i))s 12..1 SL;t l j i l i l . ( ' t i e s o. , : t ' i l l~tt i t) l ts . �9 .

1 2 . 5 Appl i r :+~l . ion it ]:t l i n d + t r i . ~ a t i o n p a r l . )a l~y~g-e . Co)~t~l~nsit)t~.

C,)~,~v~'rnv3 13. M ~ t h o d e s g ~ n 6 r a l e s de m 6 c a n i q u e n o n l i n 6 a l r e

13.1 G 6 n 6 r a l i l 6 s . . . 1 3 . 2 P o i l l t S sin)g~nli(,rs (,I , :y( ' l 'es li))~il(, 13.: t 31(. ' . l l~odes ;~)t;~13-ti(l~)t's . . . . . . . . . . . . 1 3 . | 1-161)ot~s(:~ (,)t frdqtn(:t~c.es ii()11 lit|(;~0irt, s (os(~ii l ; t ' l i () ,)s fc)r( 'd( 's) . .

(:)).~ v)'r)~E 1-1. - S t a b i l i t 6 n o n H n 6 a i r e . C o n c l u s i o n

14.1 N o t i o ~ l s (It', s i a l ) l i l t . t ; . .~i a l ' ) i l i t 6"

. . . .

I.I.'2, ) I , e s t l~d .or i :m( ,s d e l_dapL,,~()v s t , r l()r'al(-" 14 .3 I,~t )n("l ,hode. t i i re ( ; t ( : t ie l..i~I)~)~)t),,'. �9 . .

1,1..1 b l ~ l , i l i t ( " (It 's rd,.zin~('.~ i)et 'n);t t~t,t~ts l)l,ns ,,zd.r~('v:,t~x 1:1.5 S I ~ I ) i l i I ( : t it: . ~ t r u ( ' l ) i v c . 14.(; C o ) ~ c l u s i ( n l gdz~dr~l(: . . . .

~

: t r~ne : r e / . . - - L e c r i t O r e (le l - l a l l - , S ~ t r l o r i u s . . . . . . . l n n c , r e I I . - .... T l ~ d o r i e d e t ' o l ) t i m i , s a l . i ( m tic, \Viq:)~o.v. . . t t ~ t t e . r e . I l l . Q u e l ( l u e s rd.-.ntll.al.s d e e a l c u l rtlul.vit.it-:l . . . . I . e x i t l t J e t,)l (.'.in( t l av~gl tes tl(,s I('I'IIIPS let.:l~))i(lue.s ,n.g~,Is (t 'A. i t l ( ) l t t~ l i , I~ i , : . l l i l ) l i o g r a l ) h i e . . . . . . . . . . . . . . I n d e x d e s n o m s e i t d s . . . . . . . . . . . . . . t r i ( l e x a l p l ) : ~ b d t i ( I z l e (to~ I l l :~l i6r t '~ . . . . . . .

1 7)~ 1,qr i,)i) I (.)8 ...)()!)

2"21 "23"L "23 "2

2 5 3 "23t; .,7~) :2S'2 "-'.~7

"2 t)'2

:t2 "2

351 :3719 :lG2 :~7q;

3!) 1

3 9 -, I( )3

- i l l 1 1 7 4 4 5

1 5 5

France 75


LIE(' DI'.'. r Pt')LES 35

2.3.2 Asserv issements �9 s tab i l i t~ cond i t ionne l l e .

D ' a u t r e s s y s t . 6 m e s a s s e r v i s , a u c o n t r a i r e , sonl ; s t a b l e s p o u r c e r t a i a e s p l a g e s de v a r i a t i o n d u g a i n e n b o u c l e o u v e r t e , c ' e s t - - h - d i r e l o r s q u e k s a t i s f a i t h de s c o n d i t i o n s t c l l e s q u e

1,~< k < /,'~" , avec l ,~ # O.

I ls s e n t d i t s c o t ~ d i t i o t ~ n e t l e m e n t s l a b l e s . L e e a s le p l u s i m p o r t a n t de t e l s s y s t 6 m e s est. ce lu i d e s a s s e r v i s s e m e n t s i n s l a b l e s en b o u c l e o t t v e r t e , c ' e s t - ' h - d i r e d e n t la f o n c t i o n d e t r a n s f e r t e~ b o u c l e o u v e r L e a de s p61es "h p a r L i e r6e l l e p o s i t i v e . O n p e u t d o n n e r c o m m e e x e m p l e s les a v i o n s instabl~.~s p i l o t 6 s , les s y s t 6 r n e s h b o u c l e s s u p e r p o s 6 e s q u a n d l ' a s s e r v i s s c m e n t , i n t . e rne e s t i n s L a b l e , e t c . . .

P o u r ees systr a u m o i n s u n e b r a n c h e d u l i eu d e s p61es p a r t p o u r k - - 0 d ' u n p o i n t du d e m i - p l a n de d r o i t c . i~lle c o u p e a l o r s l ' a x e i m a g i n a i r e ( k - - k ~ . ) e t p r d s e n t e u n e p o r t i o n st.ai.)le. Si k a u g - m e n t e e n c o r e , le l i eu r e p a s s e d a n s le d e m i - p l a n de d r o i t e ( p o m p a g e ) .

L ' e x e m p l e 2 . 2 . 5 c i -~ tessus d ta iL c o n d i - L i o n n e l l e m e n t s t a b l e d a n s ie ca s d ' u n av io r t i n s t a b l e ( v o i r fig. 2 -22) .

( )n p e a t i m a g i n e r d e s a s s c r v i s s e m e n L s a s t .ub i l i t6 c o n d i t i o n n e l l e p o s s 6 d a n t p l u - s i e u r s p l a g e s de s t a b i l i t 6 (cf. f ig. 2 -23 ) . I ls se r e n c o n t r e n t . ~ssez r a r e m e n L en p r a t i q u e .

. . f

f

1;~t~. '2-23. ~ Asservissement h sLabilil6 condi t ionnel le eomple•

2,3.3 A u t r e s cas possibles.

D ' a u t r e s cas p e u v e . n t st; r e n c o n t . r e r ( ' ) . A ins i , il p e a t a r r i v e r q u ' u n e br:ancb.e c n t i 6 r e du lieLn , ] ' E v a n s , de k = 0 h k in f in i , s o i l

s i t u6e d~bns le d e m i - p l a n tie d r o i t e . O n a a l o r s a f f a i r e h ~rn s y s t 6 m e i n s t a b l e q u e l q u e so i t sex1 g a i n en ])ou(.qe o , ~ v e r t e : c ' e s t un ca s p a r t i c u l i e r de ce q u e les a u t e u r s s o v i 6 t i , l u e s

r ~

l:tt;. 2-24. -..- l . ieu d ' E v a n s d 'un asserwissemcnt i 11 trins~.q II C[II eii t instable.

FiG. "~~-.a.~ __ -ksservissement i, sLabilit6 paradoxale .

(t) Pour plus de d6tails sur ees eas complexes, x'oir Theorie el Ccdcul des Asservissen~et~ls, w 14.3.2 (pp. 2'55-259).

76 France


A S S E R V I S S I'.'M E N T S P I ' I . S ~:S 123

7.1.3 Transform6e de Laplace d'une fonction du temps (~chantillonn~e.

Si on ne s ' int6resse q u ' a u x valeurs de la sortie s(t) aux ins tants d '6ehant i l lonnage 0, T, 2 T,... (Fig. 7-7) eL non h la connaissance compl6te de s(t), il est possible d ' ob ten i r une relat ion simple entre l 'entr6e 6chantiIlonnfie eL la sortie 6chantil lonn6e.

F~o. 7-7

P a r appl ica t ion du prineipc de superposi t ion au syst~me lin6aire H(p) on sail qu 'on peu t ob ten i r la r6ponse s(t) par sommat ion des r6ponses du syst6me pour chaque impul- sion. D'od, en appc lan t h(t) |a r6ponse du sys tbme ~ une impuls ion uni ta i rc (~) �9

s(t) _-_ e ( o ) h ( t ) o < t < v

s(t) -- e(O)h(t) q- e (T)h( t --. 1") T :--~:" t < 2 7"

s(t) = e(O) h(t) + e(T) h(t - T) 4" e(2T) h(t--'27/'11 2 T ~--~t< 3 T

etc., el, aux ins tants d '6ehant i l lonnage �9

s(o) = e(O)h(o)

s(T) -- e(O)h( T) %. e( T)h(O)

s(2 T) --= e(0)h(2 T) + e( T)h( T) + e(2 T)h(O)

s(nT) -= ~ e(mT)h [(n m) T ] ,

Or, d 'apr6s l '6quat ion (7-2)" ao

S*(p) -- s(0) + s(7") e--TP + s(2 T) e - - ' r P �9 . . . . ~ s(n T) e

D'ou �9 n--, O0 OO

S*(p) = ~_r ~ e(m T)h [(n m) "('] c,~nTp.

On peut, v6rifier h par t i r de cet te express ion q u e :

S*(p) -- [e(0) -+- e ( T ) e - - r v + -..3 [h(O) + h ( T ) e - - r ~ -- . . .] = E*(p)[ l*(p)

ofa H*(p) est la t ransform6e de Laplace par 6ehanLillonnemenL assoei6e h la r6ponse impulsionnelle h(t) ou, ce qui revient au m6me, ~ la fonetion de transfert . H(p). En d 'au t res termes, en ne considdrant que des trans/ormdes de Laplace et fonctions de trans/ert pulsdes : la trans[ormde de la sortie d 'un sysl~me lindaire pour une entree ~chantillonnde est simplement la trans]ormde de l'enlrde multipli~e par la /onclion de transfert du syst~me, e x a e t e m e n t comme dans le cas des syst6mes eont inus :

S*(p) = E ' (p) H*(p). (7-6)

(t) La fonction h{t) est la r~ponse impulsionnelle du syst~me, l~,appelons que sa transform~o de L~place est la f o n c t i o n do trans fer t du s y s t ~ m e :

It(p) ~ (_~ h(t) et quo h(t) est la d~riv6e de la r~ponse uni ta ire q(t).

F r a n c e 7 7

His

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ontr

ol T

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ooks

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78

Fra

nce


Commande optimale des processus

R. Boudarel, J. Delmas, P. Guichet Dunod, 1967

This is a series of four books devoted to a new approach in the design of control problems, namely by using optimal control. Optimization approaches and Variation Calculus are known for long, and early applications to Control were developed by Hall and Sartorius, Wiener and followers. However, the practical interest of optimization based design for control applications rose drastically after World War II, when handling of constrained and non-linear problems became really possible. The enormous amount of papers dealing with optimal control, their heterogeneity, and the very small number of synthesis books for an engineering public justify the undertaking of writing this series, where the accent is put on a synthetic approach which highlights the main ideas, and develops in parallel continuous and digital approaches, while treating in detail the problems associated with numerical computation. The authors rely on the expertise gained by the Research Group on Optimization of the Centre d'Etudes et de Recherches en Automatismes at Ecole Nationale Sup6rieure de l'A6ronautique, and on the huge experience developed through many industrial and military contracts in aerospace and naval applications. They had also been teaching the material of their work in fairly prestigious institutions: Ecole Nationale Sup~rieure de l'A~ronautique (Paris), Ecole Nationale Sup~rieure d'Electrotechnique, Electronique, et Hydraulique (Toulouse), Institut National des Sciences Appliqu6es (Toulouse), D6partement de G6nie Electrique de l'Universit6 Laval (Qu6bec).

The four books of the series are"

1 �9 Concepts fondamentaux de l 'Automatique (Fundamental Concepts in Control), which sets the basic models, properties and tools (state space representation and basic system properties, stochastic variables, Markov processes),

2 �9 P r o g r a m m a t i o n n o n l indaire , (Nonlinear Programming), which addresses finite dimensional optimization, with applications in parameter identification and digital control,

3 �9 Programmation dynamique (Dynamic Programming), centered on control problems, with special emphasis on stochastic processes and computational aspects,

4 �9 M~thodes variationnelles (Variational Methods), which parallels classical Variation Calculus with Pontryagin's maximum principle.

Each of the three last volumes is illustrated with a number of completely solved application problems.

France 79


Table of Contents

Introduction Chapter 1

Volume 1 -Fundamental Concepts in Control

Part I Deterministic concepts

Notions on Process Control 1.1 Process 1.2 Process control 1.3 Mathematical model and identification 1.4 Optimization methods 1.5 Synthesis of a control system

Chapter 2 Process representation using the state vector 2.1 State vector 2.2 Differential systems 2.3 Recurrent systems

Chapter 3 State space representation of linear systems 3.1 Introduction 3.2 Identifying a n th order state equation 3.3 Model validity 3.4 Discrete time linear systems 3.5 Systems with multiple inputs and outputs

Chapter 4 Discretization of a continuous time state space equation 4.1 Introduction 4.2 Problem definition 4.3 Numerical integration methods 4.4 Non stationary linear systems 4.5 Time invariant linear systems

Chapter 5 The adjoint of a linear system 5.1 Adjoint operators 5.2 Adjoint system 5.3 Applications

Chapter 6 Observability - Controllability 6.1 Definitions 6.20bservability of linear time invariant systems 6.3 Controllability of linear time invariant systems 6.4 Relation with the transfer matrix 6.5 Other systems

Chapter 7 Reachable domains 7.1 Definitions 7.2 Properties 7.3 Borders of reachable domains at a given time

Chapter 8 Sensitivity 8.1 Introduction 8.2 Sensitivity with respect to the initial state

80 France


8.3 Sensitivity with respect to parameters 8.4 Linear systems

Chapter 9 Stability 9.1 Introduction 9.2 Notion of stability 9.3 Mathematical definition of stability 9.4 Ljapunov functions 9.5 Linear time invariant systems 9.6 Example

Part II Stochastic concepts

Chapter 10 Introduction 10.1 From deterministic to stochastic systems 10.2 Concepts associated with stochastic systems 10.3 The optimization problem formulation

Chapter 11 Representation of a stochastic continuous time signal 11.1 The notion of stochastic function 11.2 First order statistics 11.3 Second order statistics 11.4 Correlation functions 11.5 Correlation spectrum 11.6 White noise 11.7 Transmission of a stochastic signal through a linear element 11.8 Multivariable signal

Chapter 12 Representation of a stochastic discrete time signal 12.1 Definition of a stochastic discrete signal 12.2 First order statistics 12.3 Second order statistics 12.4 Correlation spectrum 12.5 Particular signals 12.6 Transmission of a stochastic signal through linear elements

Chapter 13 Discrete Markov processes 13.1 Markov process with discrete states 13.2 Markov process with continuous states 13.3 Study of the stochastic linear recurrent system

Chapter 14 Continuous Markov processes 14.1 Markov process with discrete states 14.2 Markov process with continuous states 14.3 Study of the stochastic linear differential system 14.4 Discretization of a continuous process

Contributed by


France 81


/ f

�9 ~

L

C O M M A N D E O P T / M A L E

O E P R O C E U

82 France


L A B O R A T O t R E D ' A U T O M A T I Q U E U.. :iver~it& L ib re de Bruxetles

TECHNIQUES DE L'A~flllilA~16M~ence, er C o l l e c t i o n p u b l i d e sous la d i r e c t i o n de j l . ~ . ( l r M . P I~LEGRIN

COMMANDE OPTIMALE DES

PROCESSUS TOME I

C o n c e p t s f o n d a m e n t a u x de I ' a u t o m a t i q u e

PAR

R. B O U D A R E L J. DELMAS Ing6nieur A .M. et E.S. E, Ing6nieur E. N. S. E. E. H.T., Master of Sciences

Centre d'l~tudes et de Recherches en Automatisme

P. GUICHET Ing6nieur A .M. et E.S. E,

Master of Sciences C ie internationale pour I ' lnformatique

PREFACE DE

J.-Ch. GILLE Ddpartement de g6nie dlectrique, Universit~ Laval, Ou6bec

Professeur honoraire, Ecole nationale supdrieure de I 'A6ronautique

: 1 . 9 6 ?

France 83


16 CONCEPTS D I ~ ~ I N I S T E S [CHAP. If]

11.2.1 Repr&sentation par une ~quation d'~tat

a) STRUCTURE

ConsJd6 rons c o m m e f o r m e s t a n d a r d "

•(t) ----- F i x ( t ) , e(O, t], (3) s ( 0 = Gl-x(t), tJ,

off la p r e m i e r e 6 q u a t i o n voctor ie l le r un sys t~me diff~rentiel d u p r e m i e r ordr�9 avec los h y p o t h e s e s su ivan tos "

G es t u n e f o n c t i o n u n i v o q u o ,

F es t uric f o n c t i o n c o n t i n u e e t sa t i s fa i san t ~ la c o n d i t i o n do Lipsch i tz .

N.B. - - g a p p e l o n s quo F sa t i s fa i t ~ la c o n d i t i o n do L ipsch i t z s ' i l ex is te uno c o n s t a n t e k pos i t ive tel le que , p o u r t et e(t) fix6s, on ai t �9

I[F[xl ( t ) , e ( t ) , t] -- F [x2 (t), e(t), t]ll <k[ Ixx (t) -- x2 (011,

que l s que so i en t x t e t x2 a p p a r t e n a n t h l ' e n s e m b l e des 6 ta ts admiss ib le s . L a va r i ab l e x(t) des 6 q u a t i o n s (3) a la p ropr i~ t~ du v e c t e u r d ' 6 t a t . E n effet,

r tous savons~que p o u r u n x(to) et u n e(to, t) d e n n i s , la s o l u t i o n do l ' 6 q u a t i o n diff~rent ieI le x(t) est un ique , m o y e n n a n t los h y p o t h e s e s p r~c6den tes ( t h~o r~me de C a u c h y ) ; e t la so r t i e s(t) est a lo r s d~finie d ' u n e fa~on u n i q u e si G est un i - voque . Auss i nous a p p e l l e r o n s (3) ~ q u a t i o n d ' 6 t a t du sys t~me en p r~c i san t << sous f o r i n t diff6rentiol le >> si o n veu t la d i s t i n g u e r de Ia f o r m e (2).

b) I m ~ T

U n e c lasse tr~s i m p o r t a n t e de p roces sus p h y s i q u e s pout 8 t re ropr~sentde p a r u n m o d ~ l e m a t h 6 m a t i q u r d u type (3). Le p r inc ipa l a v a n t a g e d ' u n e tel le r ep re - s e n t a t i o n est d ' a v o i r a p p o r t 6 une uni t6 darts l ' 6 t u d r do cos sys t~mes ; lo l e c t e u r d~jh u n peu f ami l i e r ave~ l ' a u t o m a t i s m e sal t q u e los p r o b l ~ m e s de s tabi l i t~ e t d ' o p t i m i s a t i o n p a r e x e m p l e s e n t a c t u e l l e m e n t t o u j o u r s abo rd6s , d ' u n e mard~re th~or ique , h p a r t i r de ce t t e r ep r6son ta t ion .

U n au t ro int~rSt es t de c o r r e s p o n d r e exp l i c i t emon t avec le s ch6ma do s imu- l a t i o n c o m m e ind iqu6 f igure IL2 oft les d o u b l e s t r a i t s i nd iquon t qu ' i l s ' a g i t dc p lus iours var iab les .

C) NON-UNICIT~ DE LA REPRb_SENTATION

I1 ost A p e u pros 6vident q u ' u n sys t~me pou t 6tro r ep r6sen t6 p a r diff~rentos 6 q u a t i o n s a y a n t la m ~ m e s t r u c t u r e que (3) m a i s oft los voc teurs d ' ~ t a t s e n t diff6ronts. I1 suffit p o u r cola de cons id~ror u n n o u v e a u vec tou r d ' 6 t a t y ( t ) 1i6 A x( t ) p a r uno f o n c t i o n b i u n i v o q u r d~r ivablo �9

x f t ) - - T [ y ( t ) ] .

84 France


R E P ~ A T I O N DES P R O C E S S U S P A R LE V E C T H U R D ' I ~ T A T

Lea 6 q u a t i o n s (11.3) s ' 6 c r i v e n t :

I ,~ ffi F [rr.y(O:l *(O,q ~ [ ~ " .~(t) ---- T I 9 ( 0 ,

s(t)~- G [rEy(t)], t]L

17

H x (to) o

F x o . 11.2. - - - S i m u l a t i o n d ' u n e ~ g l u a t i o n d ' 6 t a t

D ' a p r b s les h y p o t h 6 s e s su r T, la m a t r i c r des d6r iv6es par t io l les [OT/Oy] existe (d6r ivabi l i t6) e t a d m e t u n e inve r se Coiun ivoc i t6 ) ; los 6 q u a t i o n s pr6c6- d c n t e s p e u v e n t so m e t t r e sous la fo r rne :

y ( t ) ffi ~ E r ( 0 , e ( t ) , t ] ,

s ( t ) - ~ [ y ( t ) , t ] ,

qui est a n a l o g u e / ~ (3). P o u r la r e p r 6 s e n t a t i o n d ' u n p rocesaus p a r u n mo d ~ le m a t h 6 m a t i q u e d u

type (3), le cho ix d u v e c t e u r d ' 6 t a t se ra gu id6 p a r la s impl ic i t6 des 6 q u a t i o n s et p a r la s ign i f ica t ion p h y s i q u e des c o m p o s a n t e s d u v e c t e u r d '~ ta t .

/1 .2 .2 ~ t a t s pa r t i cu l i e r s

C e r t a i n s 6 ta ts pa r t i cu l i e r s j o u e n t u n r61e i m p o r t a n t . N o u s les a p p e l l e r o n s :

~tat maintenable

C ' e s t u n 6 ta t tel q u ' o n pu isse t r o u v e r u n e en t r6e e(t) qu i le laisso i n c h a n g 6 sur u n in te rva l l e de t e m p s . Ces 6 ta t s s a t i s fon t la r e l a t i o n impl ic i t e :

s: = f i x ( t ) , e ( t ) , t] = o. (4 )

A u n d o m a i n e d ' e n t r 6 e s admiss ib l e s , c o r r e s p o n d a lo r s u n d o m a i n e d ' 6 t a t s m a i n t e n a b l e s .

France 85


O B S E R V A B I L I T I ~ - - - COMMANDABILITI~ 95

V I . I . 3 Int~rSt de c e s n o t i o n s

Si o n c o n s i d ~ r e u n r 6 x l u a t i o n v e c t o r i e l l c d ' 6 t a t S q u e l c o n q u e d e l a f o r m e (1) o n p e u t t o u j o u r s la d 6 c o m p o s e r e n q u a t r e p a r t i e s c o m m e r e p r 6 s e n t ~ f i g u r e VI . 1 :

- - u n e p a t t i e o b s e r v a b l e e t c o m m a n d a b l e g0c, - - u n e p a t t i e o b s e r v a b l e e t n o n r So, - - u n e p a r t i e c o m m a n d a b l e e t n o n o b s e r v a b l e So, - - u n e p a t t i e n o n o b s e r v a b l e e t n o n c o m m a n d a b l e S ' .

FtG. VI . 1. - - D 6 c o m p o ~ i t i o n c a n o n i q u e d ' u n s y s t ~ m e

E x e m p l e

D a r t s l ' 6 q u a t i o n d ' 6 t a t s u i v a n t e -

Yet --" x t + 2 x 2 + x a + e t + e 2

Yc 2 = - - x 2 + x , t + e a + 2 e 2

~3 = -- 2 x 3 (2)

5~a "-- -xa

S --- X 2 + X , t

il e s t 6 v i d e n t q u e "

- - x~ e s t r e t n o n o b s e r v a b l e ,

- - x2 e s t c o m m a n d a b l e e t o b s e r v a b l e ,

x 3 e s t n o n c o m m a n d a b l e e t n o n o b s e r v a b l e ,

- - x , e s t n o n c o m m a n d a b l e e t o b s e r v a b l e .

L a n o t i o n d ' o b s e r v a b i l i t 6 e s t i m p o r t a n t e da r t s le p r o b l 6 m o d u r d ' u n m o d u l e d u t y p e ( l ) p o u r r e p r 6 s e n t e r l ' 6 v o l u t i o n d ' x m p r o o e s s u s r6el . E n r t l ' 6 t a t d ' u n sys t /~me es t , o o m m e n o u s l ' a v o n s vu , u n c o n c e p t a b s t r a i t ; s u r u n

86 France


GERMANY

Die selbstt~itige Regelung (Feedback Control) A. Leonhard Springer Verlag, 1940, 1949, 1957

Dynamik selbstt~itiger Regelungen (Dynamics of Automatic Feedback Control)


Kleines Handbuch technischer Regelungsvorg~inge (Compact Handbook of Engineering Control Processes)


Contributed by

Manfred Thoma

University of Hannover Germany


Die selbsttiitige Regelung (Feedback Control)

A. Leonhard Springer Verlag, 1940, 1949, 1957

The first edition of the book A. Leonhard: Die selbsttiitige Regelung in der Elektrotechnik (Automatic Feedback Control in Electrical Engineering) was published in 1940 by Springer-Verlag. Already two years later it was out of print. However, in 1944 a reprinted version of the book was published in the USA. Instead of printing a new edition, A. Leonhard suggested at that time to the publisher to write a new more general control engineering book which is not restricted to the field of electrical engineering. At the beginning of 1944, the new version of the manuscript was ready to be forwarded to the publisher. However, due to war and postwar circumstances the edition with the title" Die selbsttiitige Regelung- Theoretische Grundlagen mit praktischen Beispielen (Automatic Feedback Control- Theoretical Fundamentals with Practical Applications) was delayed until 1949. The delay, however, gave the editor the chance to include newly published results, like the Nyquist's Stability Criterion and the Logarithmic Plots (Bode Diagrams). The second revised and last edition of altogether 376 pages and 319 illustrations was published 1957.

At that time, most of the published books in Control Engineering paid increased attention to the mathematical part. In contrast, A. Leonhard's book rested much more on practical applications; in other words, the application of different mathematical methods was used to solve engineering problems (physical modeling).

The content of the last edition of the book is split into four major parts (A-D):

Part A considers fundamentals like different feedback control structures and objectives. Besides, the classical behavior of linear, time-invariant control components is presented in order to enable the reader to understand the basic principles and to apply them. In addition, the principal behavior of control components with dead-time is discussed.

Part B considers the design of mainly single input control system structures. Time responses and sinusoidal responses are used to characterize the transient behavior of feedback control systems. In addition, the reaction of control systems with discontinuous nonlinear control elements is studied.

The stability of feedback control systems is the subject of Part C. Different stability criteria (Routh-Hurwitz, Nyquist and Logarithmic Plots) of linear closed loop systems are presented. In case there are simple nonlinear elements in the loop, the stability analysis is to represent a nonlinear device by a describing function which is easier to handle.

The last Part D treats the problem how to choose the parameters of a closed loop system in order to improve the control behavior. Particular attention is given to the minimization of the transient response of linear feedback control systems with a step input. The optimal system is one that has the minimum control area. In that case the value of the control area is given by an integral error.

88 Germany


Of great practical value are the engineering examples- accompanied by considerable discussion - in each chapter. Some of them serve to extend the scope of the material of the text; others show design applications.

The characteristics in the time and frequency domain of linear, continuous-time controller and control components are tabulated in the appendix. The compilation of the tables includes, in the time domain, ordinary differential equations, their solutions and step responses and, in the frequency domain, transfer functions and polar plots.

The book addressed to practicing engineers and advanced students quickly in the field.

became a standard

Germany 89


Die selbstt~tige Regelung Theoretische Grundlagen mit

praktischen Beispielen

u

Professor Dr.-Ing. A. Leonhard Stuttgart

Z w e i t e n e u b e a r b e i t e t e A u f l a g e

Mi t 319 Abbildungen

Springer-Verlag Berlin / G6ttingen / Heidelberg

1957

90 Germany


58 3. Verhalten yon Einzelgliedern (Regelgliedern) des Regelkreises

E r m i t t l u n g des scheinbaren Gesamthubes in Abb .8 angedeute t . Die G1. (22) gilt nun genau so wie fiir z/H z auch fiir w/Hw, wit miissen uns nur dari iber k lar sein, dal3 dabei Hw verschieden ist, je n a c h d e m in welchem Bereich der K u r v e n b ~ h n wit ~rbeiten. Bei der Behand lung

eines wirklichen Regelvorganges ist selbst- versti~ndlich dieser Gesamthub, auf den tier Kolbenweg dami t bezogen wird, yon groBer Bedeu tung .

I~egelglieder, bei denen der Zusammen- hang zwischen E i n - u n d Ausgangsgr6Be durch die allgemeine Schwingungsgiei- chung (13b) darges te l l t werden muB, wie bei den beiden behande l t en Beispielen, tre-

Abb . 8. Z u s a m m e n h a n g z w i s c h e n der ten verh~ltnism/il3ig selten auf. Meistens Ste l lung des R i i ck f t ih rpunk tes

(I, Abb.5) und tier des Arbeitskomens ]iegen die Verh~ltnisse so, dab sich die allgemeine G1. (13b) durch Wegfall eines oder

auch zweier Glieder auf der l inken Seite vereinfacht . Die wicht igs ten F~lle sollen nun besprochen werden.

b) Weg-Geschwindigkei tss teuerung, Regelglieder mit Ausgleich. ~Tir be t rach ten zun~chst nochmals die beiden Anordnungen (Abb. 1 und 5), vereinfachen sie aber etwas. Bei Abb. 1 vernachl~ssigen wir die Selbst- indukt ion im Ankerkreis , so dab die e lekt romagnet ische Ze i tkons tan te T b ~-0 wird. Den mi t t e lba ren Regler (Abb. 5) vereinfache~ wir dadurch ,

t [ - - - - ~ o

i Abb. 9. Mi~te lbarer 01d ruck -Reg le r als Beispie l eincs Regelg l iedes m i t Weg-Geschwind igke i t s -

s t eue rung (Regelg l ied m i t Ausgle ich)

Abb. 10. R e g l e r m i t E I e k t ro - S te ue rmo to r

dal~ wir nach Abb. 9 yore Steuerkolben, der vom Mel]werk verstel l t wird, unmi t t e lba r den Arbei tskolben steuern. Das gleiche Ersa tzschema gilt auch fiir die Anordnung (Abb.5), wenn die Verstel lgeschwindigkeit des Haupts teuerk01bens sehr grol3 ist, so dab Ty ~ T z wird. Abb. 10 zeigt ein en tsprechendes Verstel lwerk aber mit E lek t ro -S teuermotor . I n beiden F ~ l l e n - - N e b e n s c h l u l ~ m o t o r mit vernachlKssigbar kleiner Anker induk- t ivi t~t , Verstel lwerk des ind i rek ten Reglers mit Riickfi ihrung nach

Germany 91


Regelglieder mit :Beeinflussung nur durch die Stellgr6Be selbst 59

Abb. 9 und 10 ~ k6nnea wir in der Differentialgleichung (13b) T b = 0 setzen, so dal3 sieh die Restgleiehung ergibt"

a' T~ + a = e. (23)

Bei der Anordnung nach Abb. 1 ist Ta naeh S. 52 eine Anlaufzeit- konstante, bei der nach Abb. 9 entsprechend S. 57 die scheinbare halbe SehluBzeit des Kolbens.

Der Frequenzgang ffir den jetzt einfaeheren Fall 1/iBt sieh sofort naeh G1. (14) angeben, in der T b = 0 gesetzt wird-

1 . . . . ~ .

= ~ ~ o~ T~ +~ (24)

mit der Kurve (Abb. 11), einem ~~--~~.fa Halbkreis. ,, .. ,~ - - - fa~ e.

+d

_ a J : = o o .......... _~=:0 .1.

t

Abb. 11. Frequenzgang eines Verstellgliedes Abb. 12. Ubergangsfunktion eines Regelgliedes mit Weg- Gesehwindigkeitssteuerung mit Weg- Gesehwindigkeitssteuerung

Die Differentialgleiehung der Ubergangsfunktion ergibt sieh aus G1. (23) mit e8 aufde r reehten Seite. Die LSsung und damit die Gleiehung der ~bergangsfunkt ion selbst lautet (mit riehtig eingesetzter Integra- t ionskonstante)- ( - , )

a = e 8 1 - - e ra (25)

Abb. 12 zeigt diese ~bergangsfunktion. Einer sprungar t igen~nderung der Eingangsgr6Be folgt also hier die AusgangsgrSfle erst allmi~hlich nach und erreicht asymptotisch nach einer ExponentiMfunktion einen neuen Wert . Da bei diesen Regelgliedern durch die Stellgr513e s, wenigstens bei mechanischen Anordnungen, sowohl die Stellung oder der Weg a als auch die Verstellgeschwindigkeit der AusgangsgrSBe a' beeinflul3t wird, kSnnen wir yon einer Weg-Geschwindigkeitssteuerung sprechen. M~n heil3t solche Verstellglieder auch Glieder , ,mit Ausgleich".

M s Ausgleichswert (q) eines Regelgliedes bezeichnet man das Ver- hgltnis yon Eingangsgr5Bengnderung (y) zu der durch sie im Beharrungs- zustand bewirkten Ausgangsgr613eni~nderung (x), wobei mit den tat- siichlichen Gr613en, nicht mit den bezogenen zu rechnen ist. Es wird also

y q - x (25a)

92 Germany


2 2 2 9. Ermitt lung des Regelvorganges bei nichtlinearen Regelgliedern

u n d d a m i t T c

~o (, + 1) o --/~,~ § ( ~ o - - #,~) e r , ~/~,~ (1 - - D~) + ~ o D ~ . (25)

I )abe i is t q~n0 die l~egelgr6Be zu :Beginn d e r S c h r i t t z e i t n ( t - - 0 ) und T c

~(n+~)0 a m E n d e , also a m Anfang de r Sch r i t t z e i t n ~ 1. Fi i r e T, is t /91 gese tz t .

D a n a c h G1. (19) a u c h d e r Z u s a m m e n h a n g zwi schen /~n+~) und/~.,~ b e k a n n t ist , ni~mlich

~b~(n ~- 1) ~-- ~tLn - - ~ 0 9 ( n - - 1)0 (26)

/ I 0,08-

o,,o~ /

o, oz

1

J I f

.... ] i

I I ! I S ! J ! l i i t

f 5 I

I t i ! t t

I ~ ------

J J J

Abb. 16. Regelvorgang bei einer Regelung. Schema entspreehend Abb. 15

k a n n die I n t e g r a t i o n schr i t twe i se du rchge f f ih r t w e r d e n e n t s p r e c h e n d Abb. 16.

q~3o - - #2 (1 ~ D1) + q~2o D1

(27)

~ o - - /~ (n-1) (1 --- D1) -{- qO,n--1)o D1

Bei de r Abb 16 ist ffir T~ = 1,0 u n d fiir ~ = 2 a n g e n o m m e n , so d a b ~ ~ 1

r ,

D1 - - e r, -_ e - 1 _~ 0,37 wi rd . Bei B e g i n n des Vorganges soll eine S t S r u n g a u f g e t r e t e n sein, die e incr A b w e i c h u n g de r bezogcnen S teuer - grSBe ~1 = 0,1 en t sp r i ch t . D e r B e z u g s w e r t ffir # is t so gew:s wic oben a n g e g e b e n (# = 1 g ib t l e tz t l ich a u c h ~ = 1).

D e r Abb . 16 ist zu e n t n e h m e n , d a b bei d e m a n g e n o m m e n e n W e r t T s T c

fiir u bzw. ffir die bezogene w i r k s a m e Vers te l lze i t (G1.21) T~ ~ z T 3

G e r m a n y 93


Regelung mit Schrittregler 223

1 = - - ~ - - - 0 , 5 der Rege lvorgang gu t ged~mpf t verl~uft . W ~ h r e n d aber

bei einer Rege lung nach Schema Abb. 15 u n d Verwendung eines s t e t i g e n Reglers die Rege lschwingung unabh~ngig yon der gew~hl ten Verstellzeit im_mer gedi~mpftverli~uft, bes t eh t je tz t mi t Schr i t t regler bei zu kleiner Ver- stellzeit , also zu grol]em W e r t ffir ~ die Gefahr "con t )endelungen, also ,con Labfl i t~t . Die Grenze der Stabi l i t~ t is t d a n n erreicht , wenn en t sp rechend Abb. 17 Regelgr61~e ~ u n d Steuergr61~e/z bei j e d e m Schr i t t ihr Vorzeichen wechseln, ihre Gr6Be aber be ibehal ten . I n d iesem Fal l wi rd

Cf (n + l ) o - - ~ %~o u n d /Un+l-----~/z~.

Oa aber nach G!. (27)

und Abb. 17. Regelvorgang bei e inem

Schema en t sp rechend Abb. 15. Labi le r Be t r i eb .

l~Bt sich der Grenzwer t yon ~, bei d e m die Pende lung en t sp rechend Abb. 17 auf t r i t t , e infach e r rechnen . Es wi rd

l + D x * ~ - ~ 2

1 - - D t bzw.

( T~j ) Tc ~-- Te 1 - - D 1 __~ Te = ~gT 1 T, 2(1 Q-D1) T1

Abb. 18 zeigt die Grenz-

werte -con , die n ieh t g

un t e r s e h r i t t e n werden diirfen, :Te

abh~ngig yon ~/-~ .

S ehr i t t regler werd e n hi~ ufi g so ausgeffihrt , dab die Sehr i t t - h6he n ieh t s te t ig mi t der Rege labweiehung wiiehst, son- d e r n in Stufen. Die Sehri~ge der VVippen 6 in Abb. 13 ist in d iesem Fal l in mehrere Stufen unterteilt , , so d a b die Schr i t th6he ffir verschiedene

0,8

O,7

I o,8- o,5

0,3

(2s)

T c

1 - - e 2',

Te ) " 2 l + e

(29)

. . . . . . . . . . . . .

m

. . . . . .

. , , / ~/oh// ~ ,,3 ~

"

I 1 ~ ............

o 42 0,~ 0,6 g,a Zg 1,2 ~,g Z~ 7,8 2,g

Abb. lB. Grenzwer t fiir bezogene Stel lzei t bei einer Regelung en t sp rechend Abb. 15

Abweichungsbereiche kons tant bleibt. Dami t bleiben aber u und T8 nicht kons t an t , sonde rn ver laufen abh~ngig yon der Rege labweichung

* I)ieses Ergebnis kann auch mit.Hilfe der :Differenzrechnung [39], [89] auf die aber nicht eingegangen werden soll, gefunden werden.

94 Germany


Dynamik selbstt~itiger Regelungen (Dynamics of Automatic Feedback Control)


The first edition of the classic R.C. Oldenbourg and H. Sartorius: Dynamik selbstt~itiger Regelungen, 1. Band (Dynamics of Automatic Feedback Control, Volume 1) was already published in January 1944 by the R. Oldenbourg Verlag. Actually, the manuscript was more or less completed already in 1942. Since the book was rather quickly sold out a reprinted version was made available in 1949. A pirate edition was even published in 1948 in the USA by the American Society of Mechanical Engineering. In addition, in 1949 a Russian version was on the market in the Soviet Union. Finally, the second and last edition, published in 1951, was translated into Japanese in 1953. This demonstrates clearly that the contributions of R.C. Oldenbourg and H. Sartorius in the field of automatic control were international recognized rather early.

The first volume is characterized by the subtitle: General and Mathematical Basic Foundation, Continuous and Discontinuous Control, Nonlinearities. The authors actually intended to write a second volume on optimal control problems. However, for some reason, the second volume never materialized.

The 258 pages and 118 illustrations of the last edition are split into six chapters (I-VI).

Chapter I provides a short introduction to control systems. The purpose of this chapter is to describe the general approach, to give definitions and to formulate the mathematical background.

A lengthy presentation in Chapter II deals with the structural and mathematical description of feedback control systems. For linear, time-invariant systems, three methods are derived based on differential equations, on frequency responses, and on transfer functions. Mathematically there is no fundamental difference between the three methods. However, depending on the standpoint and/or the practicability point of view, they have to be considered differently. The idea was to present a general way to characterize the transient behavior of all kind of automatic control systems, independent of the equipment and the technological peculiarities.

Chapter III is dedicated to continuous-time processes. Besides a classification into proportional (static) and integral (astatic) compensators, the authors also address the delay- time of simple systems with distributed parameters. Substantial attention is paid to the improvement of the response of feedback compensated systems.

In Chapter IV systems with simple nonlinear characteristics are investigated. Mainly based on practical mechanical equipments, the time response and the stability behavior of two cases are considered. The first one is a servomechanism with threshold and the second one with hysteresis, caused by components with friction. Since a closed form solution does not exist,

Germany 95


the integration of the differential equation has to be done stepwise. Note that the describing function was not really known at that time and therefore was not mentioned.

Two types of non-continuous control systems are studied in Chapter V. The authors considered first the transient behavior of feedback systems with bang-bang controllers. The main part is dedicated to step (sampling) control actions. In this case, linear difference equations are used in order to characterize the dynamics of these sampled data systems. The stability domain is already characterized by the inside of the unit circle. The authors also pointed out already that, with the help of a bilinear transformation, the Routh-Hurwitz criterion could be applied for stability determination.

The last Chapter VI considers the appropriate application of diverse control strategies by comparing them in particular continuous and sampled data control systems.

The aim of the book was to derive and present various mathematical methods for analysis and synthesis purposes of feedback control systems. But very little attention was paid to engineering applications. Therefore the book met with the approval of control scientists. However, the text contained a number of ideas that were new at the time and were pointing into future directions.

96 Germany


D Y N A M I K S ELBSTT;~TIG ER R E G E L U N G E N

1. B A N D

A L L G E M E I N E U N D M A T H E M A T I S C H E G R U N D L A G E N

S T E T I G E U N D U N S T E T I G E R E G E L U N G E N

N I C H T L I N E A R I T ~ T E N

VON

DR.-ING. RUDOLF C. O L D E N B O U R G

UND

DR.-i N G. H A N S S A R T O R I U S

MIT 112 BILDERN UND EINER TAFEL

2. AUFLAGE

VERLAG V O N R. O L D E N B O U R G

M U N C H E N 1951

Germany 97


w 38 Die S t a b i l i t a t des R e g e l v o r g a n g e s 57

anlage versuchsm/if.~ig vorliegt. Die Ergebnisse werden gew6hnlich in Form von Integralgleichungen erhalten, t t ier erweist sich nun die Laplacetransfor- marion als ein i~ul]erst wertvolles Hilfsmittel, da mit ihr die Auswertung dieser Integra]gleichungen ohne Schwierigkeit nahezu mechanisch erfolgen kann.

w 38 Die Stabilit~i~ des Regelvorganges Die ~bergangsfunktion des aufgetrennten Regelkreises sei bekannt und werde mit qg(t) bezeichnet. Mit Hilfe des Duhamelschen Integrals (w 17) ist es mSglich, den zeitlichen Ver- lauf der Ausgangsgr6Be z 1 (t)anzugeben, der yon einer beliebigen Zeitfunktion z(t) verursacht wird [Gleichung (17.8)]. Es ist:

z, (t) - -d - i ~ ( ~ ) z ( t - ~)a~. ( 3 8 . 1 )

0

Soll sich nun im Stabilit~tsgrenzfall eine einmal eingeleitete, etwa als sinus- f6rmig angenommene Zustands/inderung gerade yon selbst aufrechterhalten, so mul3 bei wieder geschlossenem Regelkreis :

z --~ ~ z 1 ( 3 8 . 2 ) t

sein, also" z (t) ~ d f dt~ cf (~) z (t - - ~)d ~. ( 3 8 . 3 ) # 0

Diese nun in Gestalt einer Integralgleichung erscheinende Stabilit/~tsbedingung sagt aber nichts anderes aus als die bereits gefundenen Bedingungen. Man kann sich davon iiberzeugen, wenn man auf beide Seiten der Gleichung (. 3) die Laplacetransformation anwendet:

I ; 1 d. - f ( ~ ) z ( t - - ~ ) d ~ �9 (3S. 4 )

o

�9 Naeh dem /~altung, ssatz der Laplaeetransformation (Anhang I a) wird Glei .....

chung (.4)" z(p) = - - p . ~ [q~(t)]- z(p). (38.5) .....

Nach Gleichung (16.3) ist die Laplacetransformierte der ~Jbergangsfunktion nichts anderes als der durch p dividierte komplexe Frequenzgang:

~[(p(t)] ~- ~(p)/p. (38.6}

Damit nimmt Gleichung (.4) die Form der bekannten Stabilit~tsbedingung des Regelvorganges an:

~ ( p ) --1-- I = 0. ( 38 .7 )

w 39 Der Regelverlauf Zur Ermit t lung des vollsti~ndigen Regelverlaufes ist es erforderlich, dal3 die Ubergangsfunktion des Teiles der Regelstrecke bekannt ist, der zwischen St6r- und Me[3stelle liegt. Wn" wollen sie mit q~z(t) bezeichnen. Dann ist die Aus-

98 G e r m a n y

Histor ic Control Textbooks

126 III. Stetige Regelungen

I )ami t geht die Stammgleichung (.30) in folgende dreiwertige Funkt ion fiber"

ya _ _ 3 h y q - 2 - - 0 , ( 6 5 . 3 4 )

Y die in Bild 61 dargestel l t ist. l ~ a Es ist hieraus zu ersehen, dab

2 y und dami t A nur dann l durchwegs reelle Wer te an-

. , .............. : ...... h nehmen, wenn h ~_ I(65.35) 3--~ wird, da k stets reell sein soil.

Aus den Gleichungen (.32) und (.35) folgt als Bedingung fill" drei reelle Wurzeln"

- 3 - 2 -1

Bild 61- Die dreiwertige FIunktion: yS-- 3 hy + 2 = 0 3 k 2 ~ ( A e / 3 - B ) .

I)iese Ungleiehung ist offenbar nur dann erffillbar, wenn

Ae/3 ~ B >__ O.

(65. 36)

~65.37)

Bea.chtet man nun, dab fiir A2/3 ---B nach G]eichung (.36) k -~ 0 sein mul3, so folgt aus (.37) und (.31)

C ~ (A/3)a (65.38)

als weitere notwendige (abet nicht hinreichende !) Bedingung dafiir, dab sgmt- liche Wurzeln der Stammgleichung reell werdenl) . Der zweite Teil unserer Aufgabe, n~imlich die Entscheidung, wann die ]?lgche [Gleichung (.28)] ein Minimum wird, gesta]tet sich sehr einfach, wenn man in einer rgumlichen Darstel lung die Flgche als Funk t ion der beiden Pa ramete r A und C aufzeichnet (Bild 62). In der A C-Ebene ist die Kurve C = (A/3) a ein-

gezeichnet. Da. fiir A und C F die Bedingung (.38) erfiillt

sein mug, und auBerdem beide Kons t an t en positiv sind, k o m m t nur der Bereich der A C-Ebene fiir unsere Be t r aeh tung in ]?rage, der zwisehen der Grenzkurve und der A-Aehse liegt. Lgngs der Grenzkurve ist

*A t ~ - die Flfi.che"

F / ( M Tz) = (A - 1 ) / ( A / 3 ) a,

lgngs der A-Achse-

Bild 62: Zur Ableitung der Bedingung fiir kleinste Regel- fl~iche ffir den Regelkreis nach Bild 60 (Fldchenrelie/) F l ( M m z ) = ~ .

a) Die notwendige und hinreichende Bedingung wird bekanntlich yon der Diskriminant~ geleistet, welche ffir den Fall der Gleichung (.30) lautet:

A zB ~ + 1 8 A B C - 4 A a C - 4 B 3 ~ 2 7 C 2 ~ 0 .

Germany 99


196 V. Unstetigo Rogelungen

mar ion in den Grenzen yon 1 bis oo, also aus Gleichung (.21): o o

F/To -= ~ ' F n l T v . (87.23) r~=l

Als einfaches Beispiel wollen wir nun noch die Regelfl/iche der Regelung des w 86 fiir den Fal l ermit te ln , dab die StSrung nicht im A b t a s t m o m e n t (v - - 0 ) , sondern im Ze i tpunk t ~ = Tst erfolgt.

m

-~ t s t

ii I , i

7 f t

Bild 94: Zur Bestimmung der :Flacho bei beliebigem StSrzeitpu_nkt

Wir w/~h}en die in Bild 94 gezeigte Interva,lleinteilung. Dann ist die Regelfli~che- o o

F I T c = F o / T c @ , ~ E n / T o . (87.24) n= l

Fiir die Anfangswerte z 0 und z i gelten die folgenden, leicht able i tbaren Be- s t imm ungsgleichungen �9

Z 0 : M (1 --- D 1-~st) /

z~ = M ( D (1 - - D r-~s') @ [1 S (1 - -D~-~s ' ) ] . (1 - - D)) j �9 (87.25)

Wel te r folgt mi t den Gleichungen (86. 3) und (86.4) nach Berechnung der Summat ionskons t an t en Ci und C u aus den Anfangswerten z 0 und z i"

z 2 - - z i (w i -{- w2) - - Zo .W i �9 w 2. (87.26)

Ffir die Flfichen der Anfangsinterva]le finder man unschwer [Gleichungen (.6) und (.7)]"

F ~ / T c ----- z~ ([1/(1 ~ D)] - - ( T z / T c ) ) ~ z o ( [D / (1 - - - D)] - - ( T z / T c ) ) } (87.27)

F 2 t T c = z2 (I1/(1 - - D)] - - ( T ~ I T c ) ) - - z~ ([D/(1 - - D)] - - ( T , / T c ) )

und 1--vS~

F o / T e = f M (1 - - D~)d'c = M[1 - - r s t ~ ( T z l T c ) (1 - - Di-:~st)]. (87.28) 6

100 Germany


Kleines Handbuch technischer Regelungsvorg inge (Compact Handbook of Engineering Control Processes)


Already in the Spring of 1947, W. Oppelt published his first booklet of 118 pages on feedback control systems. It had the title: Grundgesetze der Regelung (Principles of Control). It was printed by the Wolfsburger Verlagsanstalt under war and postwar circumstances as "Notdruck". In other words the paper and the printing were of very low quality. The same publishing house did put out in 1949 a second booklet of 144 pages with the title: Stetige Regelungsvorg~inge (Continuous Control Processes). Though the manuscript was forwarded to the publisher together with that of the first published book, publication took for the above mentioned reasons two years longer. While the first booklet did deal with basic mathematical methods, the second booklet did concentrate on applied matters. Hence these two booklets formed the basis for the well known book: Kleines Handbuch technischer Regelungsvorg~inge (Compact Handbook of Engineering Control Processes) which was for the first time published in 1954 by Verlag Chemie. Altogether there were five improved and extended editions (1954, 1956, 1960, 1964, and 1972) and one improved reprint in 1967. The fifth and last edition had 770 pages and almost 950 illustrations. Beyond that, the handbook was translated into Czech, French, Hungarian, Polish, Rumanian, and Russian. Even the two booklets were translated into Japanese.

The concern of all of Oppelt's books was to make the new and interdisciplinary thinking wider known to applied engineers. He knew that an abstract theory, detached from real applications, would frighten off the reader. That is why he did collect an immense number of examples of all imaginable engineering areas and, at that time already, of biological and economical processes, in order to underline the common attributes. Most of the illustrations of the examples were drawn in excellent form and clearness by W. Oppelt himself- he was in this respect really adept! The tremendous worldwide success of the book is due to an appropriate limitation of the mathematical tools used.

The content of the last edition of the textbook is divided into eleven chapters (I-XI).

Chapter I presents the introductory material like the problem and the method of attack. It is mainly based on a collection of physical systems and their block diagram models.

Chapter II supplies the background needed for the mathematical analysis of linear, time- continuous systems used in the book. Both time and sinusoidal responses are presented in order to characterize the transient behavior of control elements.

The next two chapters pay attention to quite a number of controlled processes (plants) and controller devices. Both the dynamic behavior and the design of engineering system examples are presented.

In Chapter III various controlled components are considered, arising mostly from industrial applications in the fields of mechanical, electrical, automotive, chemical or process engineering. All these processes are characterized by block diagrams and signal flow graphs.

Germany 101


Besides, a short introduction considers the fundamentals of random processes in automatic control.

The structure of controller devices is the topic of Chapter IV. A tremendous selection of mechanical, electrical, electronic, pneumatic, hydraulic and other designs are considered.

While the topics of the two previous chapters are treated independently of each other, now in Chapter V attention is paid to closed loop control systems, in which the functional components (plant and controller) are connected. The dynamic behavior and, in particular, the stability conditions of linear systems on one hand, and the synthesis methods on the other hand are considered by applying both time and frequency domain methods. Up to this point just simple SISO feedback systems are considered. Of course, the simple systems are used for the purpose of establishing definitions, a method of analysis, and the technique of computation.

Naturally, the systems are generally more complex such as interconnected multi-loop control or MIMO systems. Therefore in Chapter VI attention is now focused on complex control systems. For example, the advantages and disadvantages of feed-forward and cascade configurations are pointed out. Consequently, the control strategies are derived for a number of complex industrial systems.

In the preceding chapters, the analysis and design techniques discussed were mainly restricted to linear continuous-time feedback control systems. However, all practical systems are nonlinear to some extent and most of the commonly used tools and terminologies for linear systems are no longer valid. Nevertheless, there is a class of systems in which nonlinear elements are even intentionally introduced in order to improve system performance. The on-off or relay type servo-systems are common examples.

The next two chapters consider first systems with nonlinear characteristics and, subsequently, systems with a discontinuous nonlinearity. In the main part of Chapter VII the sinusoidal describing functions for simple isolated nonlinear elements, such as saturation, threshold and pre-load, are derived. The effect of nonlinear elements on the stability of closed loop control systems is studied afterwards.

Chapter VIII covers discontinuous control processes. At the beginning, attention is given to the dynamic behavior of feedback systems with switching and programmed controllers. Next the phase plane method and its application are studied. Then a short introduction to sampled- data control systems follows, and finally some typical examples how to apply time-optimal switching curves in the state space are presented.

The last three Chapters are dedicated to rather new developments. Chapter IX contains remarks on computer logic, on functional design of digital computers, on digital computer technology, and on digital control systems. Simulation devices and analog computer applications are addressed in Chapter X. A short introduction to adaptive control systems is the subject of the last Chapter XI.

The textbook was mainly addressed to advanced students and practicing engineers. The work is a classic which quickly became the standard in the field. A large number of figures and numerouss tables are characteristic for the book.

102 Germany


B[JCHER DER TECHNIK Herausgeber- Dr.-Ing. Alfred Kuhlenkamp

. . . . . . . . . . . . . . . . . . . . . . . . . ,,,

NOTDRUCK

Dr.- Ing. Win/ried Oppelt

Grundgesetze der Regelung

Mit 32 Bildern und 28 Tafeln

W O L F E N B t 3 T T E L E R V E R L A G S A N S T A L T

W O LF E N B I~TTE L- HAN N O VE R

1947

G. m. b. H.

Germany 103


BUCHER DER TECHNIK Herausgeber- Dr.-Ing. Alfred Kuhlenkamp

Dr.-Ing. Winfried Oppelt

�9 qI~F. e ~ Stettge Regelvor~ange

Wissenschaftliche Verlagsanstalt K. G. Hannover i n G e m e i n s c h a f t m i t

Wolfenbiit teler Verlagsanstalt G. m. b. H. Wolfenbiit tel

1949

104 Germany


Winfried Oppelt

Kleines Handbuch technischer Ftinfte, neubearbeitete

und erweiterte Auttage

Regelvorgange

1. Auflage 1954 2. neubearbeitete und erweiterte Auflage 1956 3. neubearbeitete und erweiterte Auflage 1960 4. neubearbeitete und erweiterte Auflage 1964 Verbesserter Nachdruck der 4. Auflage I967 5. neubearbeitete und erweiterte Auflage 1972

+ Verlag Chemie

Germany 105


•

S Z

W

• w

I:t

106 Germany


186 Regelstrecken

:3z r....

.x22

r~o = W&nmebitanz [ -t72

c o

-..... (D

abgef[Jhrf dutch Sfrahtung

2 ~ 20_.~_~ 273 ~ ~3

Tempera fupen: t ~

y yez

-&

..g22

....... ] Wb'rrne-Speicherung | im Guf in den Wand I

_ 1 / "~ 1 . . . .

! ' I ' l P o 3 :jv-~- ; .o; cZ v~ Wa'pme.,,,bitanz

- . im 6u f:

abgef(ihnf dutch S frahtung

/ aus der Wand

Zu-uncl Absfnahtun9 am Guf

. . . . . . . . . . . . I . . . . . . i ,

,,I ~ H H H ~'nm ilanz /, . . . . . . . . . . . _ _ _ _ _ i Hol l igko i fon / I ~ - f - [ P ~ ...... . -4 ........

! i zugor / . . . . I o,~ " , Q I I Sft~ahlung 7 1 .............. i ]

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!A ]

Die ,,dicke" Wand. Bei den bisherigen Betrachtungen hatten wir angenommen, dab die Tempera tur im Innern der Wand an allen Stellen dieselbe sei. Dies kann als N~iherung fiir verhiiltnism/il3ig dtinne W~inde angesetzt werden. Die Wandtempera tu r ergibt sich dann aus der Speicherw~irme der Wand, die als Unter- schied zwischen den zu- und abs t r6menden W~irmefltissen aufgenommen werden mu6. Bild 19.2i zeigt diese Zusammenh/inge. Dort ist der an den Wandungen iibergehende W~irmefluB angesetzt zu

Q h : aA(O~--~12), (19.14)

wo;bei ~ die W~irmetibergangszahl ist. Aus dem Signalflul3bild ergibt sich durch Zusammenziehen ein Verz6gerungsverhalten 1. Ordnung, Bild 19.21 rechts.

Germany 107


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110 Germany



HUNGARY

Automatika (Automation) (Lecture notes) Andor Frigyes and Istvdn Nagy Tank6nyvkiadb, 1954, 1957

Szabdlyozdsok Dinamikdja (Dynamics of Control Systems) Frigyes Csdki Akad~miai Kiad6, Budapest, 1966

Automatika (Automation) Frigyes Csdki and Ruth Bars Tank/~nyvkiad6, Budapest, 1969, 1971, 1974, 1983, 1986

Contributed by

Ruth Bars and Istvdn Nagy

Budapest University of Technology and Economics Budapest, Hungary


Introduction

The Electrical Engineering Faculty (School) at the Technical University of Budapest was founded in 1949, with specialisations in power engineering and telecommunication. Professors coming from the Mechanical Engineering Faculty and from industry became responsible for creating the profiles of the new departments. Excellent experts worked on incorporating the most up-to-date knowledge into engineering education. From the very beginning, the departments combined three activities" education, research and industrial projects. Research and industrial experiences fertilised the material of engineering courses.

The instructors worked with great enthusiasm on creating the Hungarian engineering literature. A great number of university lecture notes and textbooks were published in the first years that later served generations of electrical engineers.

At the Department of Electrical Machines and Drives, a strong school was created guided by Professors Pill K. Kovfics and Istv~in Rficz. Combining new concepts with traditional methods in discussing the operation and control of electrical drives, they created new approaches which - through their books and publications - became internationally appreciated and cited.

The subject of feedback control systems was taught at the Technical University of Budapest (TUB) in Hungary based on the so called German tradition using the time domain up to the end of the 1940' s. The teachers involved in the subject were mechanical engineers. At the beginning of the 1950's, younger members of faculty became responsible for teaching feedback control systems. They had read a number of recently published English books such as

James, H.M.-Nichols, N.B.-Philips, R.S." Theory of Servomechanisms. New York, McGraw-Hill Book Company, Inc., 1947.

Brown, G.S.-Campbell, D.P." Principles of Servomechanisms. New York, John Wiley and Sons, Inc., 1948.

Chestnut, H.-Mayer, R." Servomechanisms and Regulating System Design, New York, John Wiley and Sons.

The subject "Automation" appeared in the curriculum already in 1953, the lectures given by Professor Andor Frigyes. The first lecture notes were published in 1954 by Andor Frigyes and Istvfin Nagy (see below). The lecture notes were the advent in the University teaching of modem control theory in Hungary. The course of feedback control systems was based on the books listed. It is interesting to note that the Hungarian instructors did not have the English edition of the James-Nichols-Phillips book. Only the Russian translation of the book was available at that time and they studied this edition.

Two new Control Departments were established, arising from the Department of Electrical Machines and Drives. The Department of Automation (now Department of Automation and Applied Informatics) was established in 1961 under the direction of Professor Frigyes Cs~iki. The Department of Process Control (now Department of Control Engineering and Information Technology) was established in 1964, headed by Professor Andor Frigyes. Both departments offered basic and advanced control courses. The departments had a close link with the Research Institute of Automation (SzTAKI) of the Hungarian Academy of Sciences and with industry.

112 Hungary


Dr. Frigyes Cs~iki Dr. Andor Frigyes

Professor Frigyes Cs~iki had an impressively immense activity in control research and education. He was the founder of the Hungarian control literature. His books gave an overview and also a deep discussion of different areas of control theory. His most important scientific contribution was a systematic presentation and supplementary work over an extremely wide range of disciplines. A number of his books have been translated into English, German and Russian. These books served the control education and research community as basic reference sources and textbooks for a long time. Till now they are considered as a bible of control ideas. He recognized and called attention of his colleagues to upcoming new trends and ideas. His always up-to-date knowledge immediately affected the control curriculum and control research at the department. His books achieved a wide international reputation. Two of his books, one co-authored with Ruth Bars, are presented below.

Csfiki wrote a book on state-space methods for control systems, which was used both in basic and advanced control courses. (Csfiki Frigyes" Fejezetek a Szabfilyozfistechnikfib61, Allapotegyenletek. Mfiszaki K6nyvkiad6, Budapest, 1973.) This book has been translated into German and English (Die Zustandsraum-Methode in der Regelungstechnik, AkadEmiai Kiad6, Budapest, 1973, State-space Methods for Control Systems, AkadEmiai Kiad6, Budapest, 1977).

His main book, bible of Hungarian control engineers, was Modem Control Theories, Cs~iki Frigyes: Korszerfi Szab~ilyoz~iselmElet, Nemline~iris, Optim~ilis 6s Adaptfv Rendszerek, Akad6miai Kiad6, Budapest, 1970. It has been translated into English and Russian (Modem Control Theories, Nonlinear, Optimal and Adaptive Systems, Akad6miai Kiad6, Budapest, 1972, Sovremennaja Teorija Upravlenija, Nelinejnije, Optimalnije I Adaptivnije Sistemi, Izd. Mir, 1975,.). This book, reflecting immediately the newest ideas, attracted much attention in the international control community.

Hungary 113


Automatika (Automation) (Lecture notes)

Andor Frigyes and Istvfin Nagy Tankiinyvkiad6, 1954, 1957 (402 pages)

In the Introduction, the concept, notion, classification and history of control were treated. The structure of control loop closed the chapter (26 pages).

The next chapter was a long one describing the most frequently applied components of the control loop. First the electric and then the hydraulic and pneumatic components were discussed. Among the sensors the resistive, inductive and capacitive ones, the control transformer, the phase discriminators and the speed sensors were described. After the voltage and current stabilizators the notebook covered the topics of vacuum-tube amplifiers, tiratron-tube, magnetic amplifiers, saturable reactors, dc generators and the amplydin. Among the actuators the dc and the ac servomotors were treated. The descriptions of hydraulic and pneumatic components concluded the chapter (122 pages).

Next in the second volume of the notebook the authors dealt with theoretical tools of the control systems such as: Laplace transformation, transfer function, frequency characteristic, Nyquist diagram, time response, weighting function, Faltung theorem (convolution), proportional, integrator and differenciator elements, block diagram technique and classification of control systems: 0, 1 and 2 type systems (92 pages).

The next chapter dealt with the stability problem. First it described the physical background. Routh-Hurwitz, Mihajlov and Nyquist stability criteria were included and even the proof of the Nyquist criterion was given (34 pages). A separate chapter described the Bode diagram technique, (24 pages). The quality measures such as overshoots, steady-state error, control time, M curve, phase margin etc. were inserted in the next chapter (31 pages). The problem and methods of design were mainly treated by approximate amplitude Bode diagrams, (24 pages).

The last chapter presented a number of applications in the field of feedback control systems. Some of the examples were: temperature control by pneumatic elements, speed control of steam turbine, excitation control of turbine generator by magnetic amplifier, speed control of a Ward- Leonard system, etc. (48 pages).

114 Hungary

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118 Hungary


Szab~ilyozfisok Dinamikfija (Dynamics of Control Systems)

Frigyes Csfiki Akad~miai Kiad6, Budapest, 1966

Cs~iki Frigyes: Szab~ilyoz~isok Dinamik~ija (Dynamics of Control Systems), is a comprehensive book. The first chapter summarizes linear control theory. The second part gives basics of optimization. The third part discusses in detail the analysis and design of stochastic control systems. The forth part is a detailed analysis of sampled-data control systems. This book was used as a textbook for advanced control courses between 1966 and 1980. It still has actualities.

Hungary 119

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Frigyes Csaki and Ruth Bars Tankonyvkiado, Budapest, 1969, 1971, 1974, 1983, 1986

Hungary 121


The textbook Csfiki-Bars: Automatika was the first textbook for the basic control course. The book covered the following topics: historical introduction to control, basic concepts and structures, open- and closed-loop control, control examples, analysis in the time-, operator and frequency domain, characteristics of typical elements (lag, second order oscillating element, dead time, etc.), transfer functions, static and dynamic response, stability, PID compensation, models and control of electric machines, analog simulation, etc. Outlook, new trends" state-space methods, nonlinear control systems, optimal control, sampled-data control systems, computer control, stochastic control systems, adaptive control.

122 Hungary


A fentiek miatt a heltid6s szabalyoz~is stabiliz~itasa, illetve min6s~gjavit~isa igen

fontos feladat. A rendszer alkalmas m6don v~ilasztott integr~il~isi id6~illand6j6 soros integr~il6

taggal kompenz~ilhat6 (10.3-4. ~ibra). Az tm Yi,t (]w:) ered6 felnyitott k~r Nvou~sx-diagramj~inak

3~ meghatfiroz~is~it a i0.3-5. ~ibra mutatja. 2~ Allapitsuk meg az integral6 tag kritikus

/ " [ . " ~ , (/~a) integr~il~isi id6~illand6j~t, amelyre a szab~i- / I~u \~ .~ ~ ~'~OoJ) lyoz~is ~ppen a stabilit~is h.at~ir~ira keNi.

10.3-3. tJbra. Holtidtis szabfilyoz~is NYQtaS-r-diagramja

i0,3-4. ~bra. HoltidiSs szab~ttyozAs integral6 taggal kompenz~lhat6

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val6s tengelyt (mivel ezen a k~rfrekvenci~in mindk6t tag f~iziseltol~isa -90~ Ha az abszolfit 6rt6k l-ndl kisebb, a rendszer stabilis. Teh~it"

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Hungary 123


[tt x a t ~i)lapotvektor. u a szab~lyozott szakasz bemen6jeleib6I (a beavatkoz6- jetekb61 wtgy a i'n6dt~sitott jellemz6kb61) alk(~tott vektor, x,. a szab~ilyozott szakasz kimcn(iieteib61. ~ szabhlyozott jellemz6kb61 alkotott vekttw. (Jgy u( t )=x~,( t ) 6s x,ly):= x~(t),) Az f 6~ g vektorFfiggv6r~ycket l\)tytonosnak t~telezz~ik fel. A line,iris

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~ ( t ) - Ax( t ) I -Bu( f ) . (16. I-3) x.,.(t) = C x ( / ) -~,- D u ( t ) .

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x.,. =~ C x t Du. (16.1-4)

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V6gfil rnegemlitji.ik, bogy az egyvaltoz6s, ;lltaJld6 param&erd line'/iris szab~ilyozott

szakasz cgycrlletei : = A x I bu.

v -- c ~ x i du, (16.1-5)

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fs~rm',itrix), d pcdig skal~r. Most u 6s x, is ~k~tf~r. A nemfil~eAris r'cnd~zer hathsv'hzlatfit a I6.1-1. fibra muiatja be. A 16.1-2, Abr~n

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124 Hungary


ITALY

La Regolazione delle Turbine Idrauliche

Giuseppe Evangelisti Nicola Zanichelli Editore, Bologna, 1947

Teoria della Regolazione Automatica

Giorgio Quazza ANIPLA, 1962

Lezioni di Controlli Automatici- Teoria dei Sistemi Lineari e Stazionari

Antonio Lepschy, Antonio Ruberti Edizioni Scientifiche SIDEREA, Roma, 1963

Elementi di servomeccanismi e control l i

Sergio Barabaschi and Renzo Tasselli Zanichelli, Bologna, 1965

Contributed by

Alberto Isidori Universita degli Studi di Roma "La Sapienza"

Sergio Bittanti Politecnico di Milano

Claudio Bonivento and Giovanni Marro University of Bologna


La Regolazione delle Turbine Idrauliche

Giuseppe Evangelisti Nicola Zanichelli Editore, Bologna, 1947, 280 pages.

For a period about fifteen years, from the time of its appearance in 1947 until the early sixties, "La Regolazione delle Turbine Idrauliche", by Giuseppe Evandeglisti, was the only book written in Italian covering in a systematic manner problems and methods of automatic control. While the main purpose of the book was to address a variety of problems arising in the regulation of hydraulic power plants, the book covers in a rigorous and extensive form a number of topics that eventually became classical topics of any textbook in control, such as mathematical modelling, Routh-Hurwitz stability criterion, Laplace transform, steady state and transient analysis, etc.

Giuseppe Evangelisti (1903-1981) became Professor of Hydraulic Constructions at the University of Bologna in 1939. At that time, as a scientist and engineer, he had achieved a great international reputation in this field for his brilliant results on the theory of the water hammer phenomenon and on the design of hydraulic power plants. In the forties, new scientific curiosities brought him in touch with methods of analysis and design developed within the emerging areas of Automatic Control and Computer Engineering, which he specifically applied to the problem of the regulation of hydraulic turbines. Evangelisti promoted a lot of relevant pioneering initiatives in Italy and abroad, in these areas. He was one of the scientists that signed (1956) the famous Heidelberg resolution "in favour of an international union of Automatic Control", he founded (1957) the "Centro Calcoli e Servomeccanismi" at the University of Bologna (whose activities eventually merged into the Department of Electronics, Computer and Systems), he was a member of the first IFAC Council (1958) and very active in the scientific preparation of the first IFAC Congress in Moscow (1960). He taught regular courses of Automatic Control in the period 1960-1965 at the University of Bologna, for which he prepared a comprehensive set of lecture notes (1961).

"La Regolazione delle Turbine Idrauliche" covers material for the most part based on his personal research work during the difficult war period 1942-44. It is organized into nine chapters and covers the entire problem of the design of hydroelectric power generators. A first part of the book is devoted to the development of mathematical models of each individual subsystem (the turbines with their regulation devices, the supplied electric power network, the surge tank and the outflow pipe). The intermediate part of the book presents the mathematical tools for the analysis of stability and performance. Finally, the solution of the whole regulation problem is addressed in detail.

The first chapter reviews in detail all basic control schemes for the regulation of water turbines, whose components are then thoroughly analyzed and modelled in the second chapter, in the form of sets of first order differential equations. Among these schemes, one can recognize the classical proportional-integral-derivative feedback controllers realized by suitable connections of mechanical and oleo-dynamic devices. The next three chapters are devoted to what we would call today "automatic control theory". Chapter 3 covers the use of state-space representation, from general nonlinear models to the analysis of small oscillations via linear approximation, the Routh-Hurwitz stability criterion and Laplace transform. Chapter 4 covers the analysis of forced

126 Italy


and transient response and Chapter 5 presents in detail approximation methods and algorithms for the numerical computation of solutions. The next three chapters describe how the general methods of analysis and design presented in Chapters 3-5 can be effectively used in a variety of problems dealing with the regulation of hydraulic turbines. Finally, the book is concluded by a ninth chapter dealing with a full nonlinear analysis of the regulation problem under large perturbations.

Contributed by

Claudio Bonivento and Giovanni Marro University of Bologna

Italy

Italy 127


GIUSEPPE EVANGELISTI ORDIN'ARIO DI COSTRUZIONI IDR&ULICHE NELL~UNIVERSIT~ DI BOLOGNA

LA REGOLAZIONE

DELLE TURBINE IDRAULICHE

N I C O L A Z A N I C t t E L L I E D I T O R E

BOLOGNA 1947

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Teoria della Regolazione Automatica

Giorgio Quazza ANIPLA, 1962 (263 pages)

Born in Mosso, a small town not far from Biella, Italy, in 1924, Giorgio Guazza began his studies in engineering in the Politecnico of Turin in November 1941. He was an outstanding student; however, the dramatic war events of those days led him to join the Italian Resistance Movement. While continuing to study, he was already engaged in the Resistance in the mountains of the Italian Alps. It was there, on December 4, 1944, that he was taken prisoner during a roundup. After a period in a prison camp in Bolzano, he was sent to the concentration camp of Mauthausen, where he had to remain until May 1945 when the camp was liberated. Weakened by the internment, he was then down to his last physical resources. After a period of rehabilitation, he resumed his studies in the summer of 1945, and during the period from September 1945 to November 1946 he was able to pass all the remaining 25 exams. He presented his thesis on the stability of large power transmission lines in December 1946. He then spent a period of time in a Turin company working at the control of electrical machines, and then moved to the USA for three years (1950 - 1953), working first at MIT and then at the Brooklyn Polytechnic Institute. His studies focused on the emerging theory of servomechanisms, and for this he obtained his Doctorate degree in 1953.

Upon his return to Italy, he worked again as a control system designer in industry, until he joined the Italian Electrical Power Agency (ENEL) in Milan in 1964. Here he created the Automatic Control Research Center (Centro Ricerca di Automatica - CRA) in 1967, the purpose of which was to cope with control problems in the Italian electricity generation system. His research activity ranged from servomechanisms and analogue computing to speed governors for thermal and hydro-electric power systems. Soon, he became an internationally acknowledged expert in on-line power system control.

To put those years into perspective, let us mention some events taking place in Italy. In April 1956, an international meeting was organized at the Museum of Science and Technology in Milan, the Convegno Internazionale sui Problemi dell'Automatismo, held under the aegis of the Italian National Research Council (CNR). As chronicled in the newspapers of those days, the enthusiasm and expectations for control and automation were so remarkable, not only among specialists but also in the common people, that the conference had more than 1000 participants. Giorgio Quazza (then 32) attended the presentations with tremendous interest, and this experience had a deep impact on his engineering evolution. Also in 1956, the first exhibition on control and automation named the Biennial Italian Automation and Instrumentation (BIAS) was held. Last but not least, the Associazione Nazionale per l'Automazione (ANIPLA) was founded (again in 1956). This association has been very active, establishing a significant link between academia and industry, through the organization of conferences on various application areas and many tutorials for control engineers in industry.

At the end of the '50's and early '60's, ANIPLA invited Giorgio to give courses for the associates and it was the publisher of the first volume written by Giorgio, Teoria della Regolazione Automatica (1962), a comprehensive text of 263 pages on most aspects of basic control methods. The summary of the volume is as follows. 1: Analogies between electrical, mechanical, thermal and pneumatic phenomena; 2: Control systems in open loop and closed

Italy 131


loop; 3: Performance of control systems; 4: Closed loop control systems; 5: Determining the static and dynamic characteristics of a control loop; 6: Improving the time response of a system with partial feedback. 7: Systems with partial feedback and many controlled variables; 8" Non- linear systems and discontinuous control. Appendix" Complex functions, Laplace Transforms, Stability criteria, Relationship between the phase diagram and the attenuation diagram, Root locus method, Correlation between transient response and frequency response, Distributed parameter systems, Sampled data systems.

Meanwhile, at the Technical University of Milan (Politecnico di Milano) a group of young and active researchers in control was growing up and invited Giorgio to give some specialization courses for engineers. The volume Introduzione alla Ottimizzazione dei Processi, published in 1964 by Tamburini Editore, Milan, was prepared for such courses. This volume (119 pages) presents first the role of optimization in control, by describing methods such as Kuhn and Tucker, Arrow and Wolfowitz, and then turns to calculus of variation, Pontryagin maximum principle, and dynamic programming. The copyright page of each copy of this book carries the hand-written signature of the author.

C O P Y m ~ q ~ , ~ l l * | ~ ~ ! 9 6 4 o T A , I ~ U . B U ~ I . N | m a ~ . l D | ~ r O B E m, p ~ ,

T a t t e . I.~- c o p s d ~ J ~ b o . n o p o r t a ~ - ~ l o f i r . : m a d e l : s

The involvement of Quazza in the Politecnico culminated in 1971, when he was called to teach a regular course, Process Control, for students in their fifth year in Electronic Engineering. For this course, he prepared his third book, with the same title, (CLUP, 1973). It covers many aspects of process control, and has been used for decades by many students.

While directing the CRA of ENEL and teaching at the Politecnico di Milano, Giorgio Quazza was also very active in IFAC, where he had come to be appreciated by everybody as a genuine gentleman. He first served as Vice-Chairman of the Technical Committee on Systems Engineering (1969- 1972), then as Chairman of the Technical Committee on Applications (1972 - 1975) and in 1975 was elected to the Executive Council. In all these tasks he was appreciated not only for his efficiency, but also for his humor and presence. But, to the regret of all, a mountaineering accident in 1978 robbed IFAC and the control engineering community of one of its most illustrious and hardworking members. His corpse was found in a deep crevice after days of continuous search on August 11 th. Giorgio was planning to cross the glacier Ventina of Mount Rose, from Ayas to Zermatt, in the company of a close friend. The friend could not reach him, so he decided to make the crossing alone. In Zermatt he had an appointment with Professor John Coales, former president of IFAC, for a trip together in the mountains.

Giorgio Quazza will be remembered as one of the towering figures of control engineering of the past century, and a man of many qualities, the most eminent being that he was a person upon whom anyone could place complete reliance in time of trouble, as written in his obituary (Automatica, Vol. 15, 1979).

Contributed by

Sergio Bittanti Politechnico di Milano, Italy

132 Italy


f , , , , , , ,~ , , ,~ , , ,~ . . . . . . . . . . . . . . ,~,~,,,,~ , , , ~,-.~

PO LITECNI CO DI MILANO

CORSO DI CULTURA DI TECNICHE DELL'AUTOMAZIONE

TF.ORIA DELLA REGOLAZIONE AUTOMATICA

A CUR_& DI

GIORGIO QUAZZA

A N I P L A 1962

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Lezioni di Controll i Automat ic i - Teoria dei Sistemi Lineari e Stazionari (Lectures on Automatic Control- Linear and Time-lnvariant Systems)

Antonio Lepschy, Antonio Ruberti Edizioni Scientifiche SIDEREA, Roma, 1963

The first edition of the book "Lezioni di Controlli Automatici - Teoria dei Sistemi Lineari e Stazionari " (Lectures on Automat ic Control - L inear and Time-Invariant Systems ) by Antonio Lepschy and Antonio Ruberti was published in 1963 (in two volumes); the second edition (in one comprehensive volume) appeared in 1967. The late Antonio Ruberti (who after having been Rector of the University of Rome was appointed Minister for Higher Education and Scientific Research, and then European Commissioner for Scientific Research in Bruxelles) was at that time a professor of Automatic Control with the School of Engineering of the University of Rome. Antonio Lepschy was a professor of Automatic Control at the University of Trieste. The book has been used as a textbook for automatic control courses not only at the Universities of Rome and Trieste but also in many other Italian Universities.

The book is divided into three parts. The first one has an introductory style and presents the notion of control and a classification of control actions. Two appendixes supply a short history of automatic control and the terminology of control systems and components. The second chapter discusses the role of control in the field of automation and in the context of cybernetics.

The second part of the volume deals with the theory of linear time-invariant systems described by input-output relations. First the temporal behaviour of a linear time-invariant system is analysed by discussing the properties of the associated differential equation and by evaluating the free and the forced response of the system. Next the analysis in terms of Laplace transform is developed and the analytic and graphical representations of the transfer functions are discussed.

The third part is devoted to the analysis and synthesis of feedback control systems. Block diagrams, signal flow graphs and their algebra are introduced, emphasizing their use in modelling and analysis of feedback loops. A chapter is devoted to stability analysis: the Routh and Hurwitz criteria and the Nyquist criterion are introduced and discussed in detail; the meaning of stability margins for feedback systems is discussed. The steady-state and transient response to canonical inputs (in particular to the unit step) and the concepts of system promptness and precision are discussed, introducing the notions of loop type, rise time, overshoot, settling time etc. as well as indexes like ISE, ITAE etc.

Next, the problem of assessing the closed-loop behaviour starting from the analytic (poles and zeros) and/or graphical properties of the open-loop transferences is addressed. The root locus method and the use of the Nichols chart (and of other similar loci of the G(jco) plane) are presented.

The last chapters of the book are devoted to the problem of controller synthesis. The standard PID controllers and the relevant tuning formulas are presented; the lag-, lead- and lag-lead actions are discussed and the procedures for computing their parameters are illustrated. A chapter

Italy 137


was devoted also to the so called direct synthesis methods. Some notions about control system synthesis with two degrees of freedom are also presented.

Soon after the first edition of the book was published, the authors edited a textbook on control system components (A. Lepschy, A. Ruberti (eds): Componenti dei Sistemi di Controllo; vol. I "Strumentazione", vol.II "Amplificatori e Motori", Edizioni Scientifiche Siderea, Roma, 1964). Later Antonio Ruberti and Alberto Isidori published a book on system theory discussing the state variables approach (A. Ruberti, A. Isidori, Teoria dei Sistemi, Boringhieri, Torino, 1979).

Contributed by

Alberto Isidori Universita degli Studi di Roma "La Sapienza"

138 Italy


Prof. Ing. Antonio LEPSCHu Inc. di Controlli Automatici Universit~ di Trieste

Prof. Ing. AntonzoRUIIERTI Inc. di Controlli Automotici Universit~ di Roma I

LEZIONI DI

CONTROLLI AUTOMATICI

TEORIA DEI SISTEMI LINE ARI NORMAI..I

VOLUME I

Edizi0ni ~, i , . t i , i . . S ID E R E A

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Italy 141


Elementi di servomeccanismi e controlli

Sergio Barabaschi and Renzo Tasselli Zanichelli, Bologna, 1965

In 1948, Sergio Barabaschi (born 1930 in Parma, Italy) enrolled in the Technical University of Milan (Politecnico di Milano) as a student of Engineering. During his studies, around 1950, he had the chance of reading a book by Leonhard on Regelungstechnik. It was this book that triggered his interest in "applying electronics to non-electronics", as he still refers to it today. He investigated this possibility in a conversation with the Rector, the geologist Gino Cassinis, and, following his suggestion, decided to move to the State University of Milan, where he completed his preparation with two additional years of Physics. His goal to write his thesis on control was achieved, in 1952, under the supervision of Emilio Gatti (born 1922 in Turin, Italy, now an IEEE Life Fellow). The subject was the control of the delay of certain trains of impulses.

In January 1953, he started working at CISE (Centro Informazioni Studi ed Esperienze), an advanced private research institution established in 1946 in Milan. The objective of CISE was to explore the possibilities offered by nuclear science for the generation of electric energy. The specific task of young Barabaschi was the design of the hydrogen temperature control of a small pilot plant for the production of heavy water. The project's leader was Mario Silvestri, a professor of technical physics in the Politecnico di Milano, who had a special gift for the depth and broadness of his technical and non technical knowledge. Barabaschi then moved on to the development of a dynamic simulator of a nuclear reactor under the coordination of Emilio Gatti, with whom, in June 1955, he visited Caltech in the US to present their result.

In April 1956, he took part in the Convegno Internazionale sui Problemi dell'Atomatismo, held in Milan, where he met many scientists including Leonhard, the author of Regelungstechnik.

In those times, there was increasing interest in nuclear reactors as a new source of energy, thus a center, the Nuclear Research Center (CRN - Centro Ricerche Nucleari), was created in Ispra, a town approximately 50 km north of Milan. Barabaschi moved to that Center where the primary goal was to set up the first Italian nuclear reactor, called ISPRA-1. In 1956, he spent a period at Allis Chalmers in Buffalo, N.Y., US, to prepare the control specifications for the new reactor.

On his return to CRN, he worked for some three years on the development of the Laboratory of Servomechanism and Control of that Centre, where more than 30 technicians and 20 engineers were employed. Among these engineers, there was Renzo Tasselli (born 1934), who joined in 1957. The task of that laboratory was twofold. One goal was to provide tools for the design of reactor control systems, and the other the development of precise motion control systems tools to operate the robotic arms that were to be used for handling radioactive material. Barabaschi made a major contribution to the development of the robot Mascot-1 (Manipolatore Automatico Servocomandato e Transistorizzato).

On March 25, 1957, the Treaty Establishing the European Community was signed in Rome. On the same occasion, the Treaty Establishing the European Atomic Energy Community (EURATOM) was also signed. It was then that Italy proposed the Ispra Center as a location for EURATOM, moving two laboratories, including the Laboratory of Servomechanism and Control, to another location. The Laboratory directed by Barabaschi moved to the Centro Nucleare della Casaccia (some 20 km north of Rome) in 1963. Here Barabaschi remained until

142 Italy


1975, when Ansaldo, a major Italian company located in Genoa, asked for his assistance in the design of nuclear reactors. Sergio Barabaschi then began commuting between Rome and Genoa. It was during this years that Renzo Tasselli passed away in a tragic car accident in 1978.

The years from 1980 to 1993 marked a new period of life for Barabaschi. He joined the Ansaldo Company in Genoa full time, where he was called to work on automation and control, the passion of his life. In 1994, however, the Minister of University and Research, Salvini, asked for his assistance in Rome as Under-Secretary at that Ministry. From this the step to European commitments was short; from 1996 to 1998, he served as President of the European Industrial Research and Management Association, located in Paris, and subsequently as President of the European Science and Technology Assembly in Brussels until the year 2000. Finally he acted as Vice President of the European Council of Applied Science and Engineering (operating in Paris, at Acad6mie de France) until 2004.

The story of the book Elementi di servomeccanismi e controlli is as follows. Together with Tasselli, Barabaschi started working on the book in 1961 (during that period both authors were working at CRN in Ispra). The text was completed some three years later when Barabaschi and Tasselli were at La Casaccia and eventually published in 1965 by Zanichelli- Bologna.

The idea was to write a text on control in the easiest way possible, with strong emphasis on instrumentation, actuators and transducers, in order to supply an effective aid for the training of technicians. The volume consists of 747 pages and contains a huge number of photographs, block diagrams and drawings of various type, especially figures of transient behavior, Nyquist, Nichols and Bode plots, and so on. This required a incredible amount of work since most of these drawings had to be hand-made by the authors.

The book is organized in 23 Chapters plus 4 Appendices as follows. After an introductory chapter on automatic control, some basics of differential equations are introduced in elementary terms, with a number of electro-mechanical examples. Then first-order and second-order systems are dealt with in Chapters 3 and 4 respectively. Transfer functions are the subject of Chapter 5, while feedback is dealt with in the subsequent chapter. The steady state behavior is then studied, followed by stability analysis. The specification requirements and the main compensation methods are treated ~ in Chapter 10, and then attention turns to "Nonlinear System Theory". This is indeed the title of Chapter 11, where various topics are treated including the concept of describing function. The remaining 12 Chapters are devoted to the components of control systems, transducers (of velocity, acceleration, force, temperature, pressure, level, flow), amplifiers (based on electronic tubes and on transistors), magnetic amplifiers, motors, hydraulic and pneumatic systems as well as mechanical components. There are also 4 appendices (Fourier analysis, Laplace transforms, Proofs of root locus rules and Nyquist criterion).

This book was a great success selling more than 30.000 copies in the subsequent ten years.

Contributed by

Sergio Bittanti Politecnico di Milano

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148 Italy



JAPAN

Jidouseigyo no Riron to Jissai (Control Theory and Practice) Author: Takeshi Samukawa Date of Publication: September 1948

Jidouseigyo Nyumon (Introduction to Control Theory) Author" Keisuke Izawa Date of Publication: May 1954

Jidouseigyo Rironi (Automatic Control Theory) Author: Yasundo Takahashi Date of Publication: October 1954

Contributed by

Katsuhisa Furuta

Tokyo Denki University Japan


Jidouseigyo no Riron to Jissai (Control Theory and Practice)

Takeshi Samukawa JSME(Japanese Society of Mechanical Engineers), September 1948 Tokyo Japan

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150 Japan


The author was a control engineer who worked for an Askania Japan Co. from 1935 to 1944. His health condition was not good in the time of World War II and he became a lecturer of Tokyo Institute of Technology by the recommendation of Professor Shigeo Sasaki. He engaged in writing his thesis to submit as the Doctoral Dissertation to Tokyo Institute of Technology, but unfortunately passed away in December 1945. The degree was not awarded. The contents were so new at that time for the Japanese engineers that the Japan Society of Mechanical Engineers (JSME) published the thesis as a book. The preface was written by Prof. S. Sasaki. The original handwritten dissertation itself was a treasure for his family, therefore it was hand transcribed by his friend for publication. Since most of the research was done while he worked for a German related company and in the time of World War II, the references were several German papers, and a few American/English papers. Unfortunately, he was not known due to his short life but he was one of the researchers in control engineering in the pre-history of control engineering in Japan.

The book consists of two volumes. The first volume had the following four chapters in 202 pages.

Chapter 1, Introduction

Chapter 2, Structure and Classification of Control Systems (Static and astatic, Set point and servo control, Feedback and feed forward)

Chapter 3, Elements of Control Systems (Electric and mechanical sensors, Actuator valves, controller)

Chapter 4, Control Theory (Control methods, Stability degree, Control error and inverse response, Remarks on control methods, Dead time, Dead band, Friction and stiction, On-off control, Theory and practice.) Most of the mathematical models of plants are represented by differential equations. In this section, Hurwitz stability condition and Nyquist stability criterion are described. Dead time and nonlinear elements like dead zone, hysteresis and others were also considered.

The second volume has the following two chapters in 210 pages.

Chapter 5, Various Control Problems (Control of rotational velocity, Control of pressure, Pressure control theory, Control of flow rate and pressure difference, Servo control I (Flow rate and pressure), Servo control II (Position and angle), Level control, Temperature control, Moisture control, Composition control, Directional control of vehicle, Trajectory control, Electric control)

Chapter 6, Evaluation of Control Theory through Experiments and Remarks on Previous Control Theory (Artus, Tolle, Oppelt, Stein-Wunsch)

The book was owned by the late Professor K.Izawa and its manuscript has been found.

Typical pages of the book are shown below. The first gives controlling function. The second shows the transient response and the third one is explaining the dead zone.

Japan 151

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Jidouseigyo Nyumon (Introduction to Control Theory)

Keisuke Izawa Corona Publishing Co., May 1954 Tokyo Japan

The author was said to be the first control researcher receiving the Doctor of Engineering Degree in control engineering. He was born in Gunma Prefecture in 1925 and graduated from Department of Measurement, The University of Tokyo, in 1948. He wrote the book "Introduction of Automatic Control" in 1954 at the age of 29. After serving as a lecturer at the University of Tokyo, he became an associate professor at Tokyo Institute of Technology in 1954 and full professor in 1962. He was an associate professor at Purdue University. He attended the first meeting of IFAC in Heidelberg, and attended the IFAC Congresses until he passed away by an automobile accident in March 1970. He was a very energetic and very active researcher in control theory. His research interest was bang-bang type control and he showed that the sampled data system with a bang-bang type element has the aperiodic like chaotic response.

The book was revised 4 times and has been the best sold book in control theory in Japan. It contains 6 chapters, addition and appendix. The uniqueness of the book is the introduction of the slide rule to calculate the gain and phase of linear systems, which was commercially sold by the Hemmi Slide Rule Campany. The following introduction of the book is based on the last version.

The first chapter describes the basic idea of the control and its brief history. Chapter 2 presents the fundamental ideas of control theory like Laplace Transform, Block Diagram, Frequency Response, Loop Transfer Function and Closed Loop Transfer Function, Slide Rules for computation of the gain and phase of the frequency characteristics, the calculation of the frequency characteristics from the transient response and the transient response from the frequency characteristics. Chapter 3 gives the stability and its condition, Routh condition, Hurwitz condition, Leonhard condition, Root Locus and Logarithmic Root Locus method. Chapter 4 gives control performance and characteristics such as parameters of steady state error, transient response, frequency characteristics, and r.m.s condition. He studied the gain and phase margins of the loop transfer functions for past examples and from their results their choices for servo mechanisms and process control are given. Chapter 5 presents the synthesis problem of control systems. The objective and procedure of control system synthesis are described first, then tuning of the gain, addition of compensation, cascade control system, and series and feedback compensation are written. The feedback compensation is shown to compensate the time delay, which describes the basic principle of the Smith Predictor. The synthesis problem is studied using a process model as an example, and cascade control is applied. Chapter 6 deals with discontinuous control including the bang-bang type and discrete-time control. Examples of discontinuous systems are given. Then the discrete-time control system is explained including Z- transform. The additional materials include the Routh condition and its calculation, the dynamics of gear train, how to choose P, PI, PID and I controller for the given process model, and correlation function.

Japan 155


156 Japan


Thus the book covers almost all control approaches for single input single output systems before the introduction of state space. The book was the most popular control textbook for a long time, until the author passed away, and it was translated into English (Introduction to Automatic Control, Elsevier, 1963).

The book had been a best seller in engineering books, and was especially useful for process control engineers. It is now out of print but had been read by many control engineers for a long time.

Slide rule explanation in the book

Japan 157

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158 Japan

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Japan 159


Jidouseigyo Rironi (Automatic Control Theory)

Yasundo Takahashi Iwanami Syoten, October 1954 Tokyo Japan

160 Japan


Professor Yasundo Takahashi is considered as one of the pioneers of control engineering in Japan, together with Professor Yoshikazu Sawaragi. He was a professor of control engineering of The University of Tokyo, then became a professor t the University of California at Berkeley in 1958. After retirement from UC Berkeley in 1979, he worked for Toyohashi University of Technology till 1982. He was a member of the IFAC Japan NMO, National Committee of Automatic Control, Science Council of Japan, in 1957. He received the Oldenburger Medal in 1978. He passed away in October 1996. His first book on automatic control was published in 1948 by Kagakugizyutsusya Publishing Co. The company was located at Kanazawa City in Toyama Prefecture. The contents of the book were unique in the sense that a template for drawing the Bode Diagram was given. Later he published a book on computation of automatic control problems using Personal Computer, with the same company. But the book was not read widely so here we shall introduce the book published by Iwanami Syoten, one of the biggest publishers in Japan.

The book is 240 pages including the appendices. Chapter 1 is the introduction giving examples and the basic idea of automatic control. In the example, the servomechanism of the lathe is discussed. Chapter 2 is the representation of dynamics of linear systems. Transfer function and frequency characteristics including Bode diagram are described. A brief explanation of Laplace transform is given in the appendices. Chapter 3 gives examples of lower order systems. Chapter 4 handles the connection of systems using block diagrams. Series and parallel connection of the systems and the idea of P, I, D control are included. Chapter 5 presents higher order systems. The distributed parameter system like heat transfer is described. Dead time is also mentioned. Chapter 6 presents the characteristics of control systems. Steady state control errors and stability are analyzed. Hurwitz condition is given. Various PID tuning methods from the time response including Ziegler-Nichols are discussed. Chapter 7 deals with the frequency characteristics of single loop systems. The computation of the closed loop frequency characteristics from loop frequency characteristics is explained. The Ziegler-Nichols PID tuning based on frequency characteristics is presented. Describing function is also discussed. Chapter 8 discusses multi-loop systems including two controlled variables using the example of the pressure and level control of a boiler. Chapter 9 gives the computation of statistical characteristics like auto and cross- correlation functions. Chapter 10 deals with sampled-data control systems. Z-transform and frequency characteristics are given. Appendices are Laplace transform and pulse transfer function.

The author mentioned that the contents were from his lectures at undergraduate and graduate courses. The level is quite high for those days and the book can be used even currently if state space considerations are added. After he retired from the University of California, he published a revision of the book with Iwanami Shoten.

Professor Yasundo Takahashi was a mentor of control researchers in Japan just after World War II. His group studying automatic control became the Society of Instrument and Control Engineers.

Japan 161

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KOREA

Automatic Control Analysis and Control Devices H.Y. Cheon, B.S. Hong and C.B. Park 1976

Linear Control System Engineering

J.S. Kim 1988

Contributed by

Oh-Kyu Kwon

Inha University, Inchon, Korea


Introduction

Hangeul, the Korean alphabet, was invented in 1443 during the reign of King Sejong of the Joseon Dynasty. It is composed of 10 vowels and 14 consonants. The 'Hunminjeongeum,' a historical document which provides instructions to educate people using Hangeul, is registered with UNESCO. UNESCO awards a "King Sejong Literacy Prize" every year in memory of the inventor of Hangeul.

When the first control textbooks came out in English (e.g. Theory of Servomechanisms, by H. M. James, N. B. Nichols and R.E. Phillips, published in 1947), Korea was under difficult times just after gaining national independence from Japan. It took about 30 years after the first English control book was published that the first Korean book on automatic control was written in Hangeul. Until then, almost all control books in Korea were translated versions of books originally written in English.

Contributed by

Oh-Kyu Kwon School of Electrical Engineering

Inha University, Inchon, Korea

164 Korea


Automatic Control Analysis and Control Devices

H.Y. Cheon, B.S. Hong and C.B. Park 1976

The oldest Korean control textbook was written in 1976 by H.Y. Cheon, B.S. Hong and C.B. Park, which is shown in Figure 1, 2, and 3 and its title can be translated into English as Automatic Control Analysis and Control Devices. It dealt with the classical control techniques including PID control. But it is hard to say that this is a fully Korean book since it used Korean only for postpositional words and all the terminologies and most of contents were written in Chinese characters, as shown in the figures.

Contents :Automatic Control Analysis and Control Devices (H.S. Cheon, 1976)

Chapter 1. Introduction ................................................................................................... 1 Chapter 2. Terminologies in Control Systems ................................................................ 7 Chapter 3. Linear Systems and Differential Equations ................................................ 16 Chapter 4. Laplace Transformation .............................................................................. 37 Chapter 5. Transfer Function ........................................................................................ 59 Chapter 6. Block Diagram and Transfer Function ....................................................... 75 Chapter 7. Signal Flow Graph .................................................................................... 100 Chapter 8. Error Constants and Sensitivity ................................................................ 127 Chapter 9. Stability ..................................................................................................... 145 Chapter 10. Analysis and Design Objectives in Feedback Control Systems .............. 155 Chapter 11. Nyquist Analysis ...................................................................................... 165 Cha~ter 12. Root Locus Analysis ................................................................................ 187 Cha~ter 13. Bode Plot Analysis ................................................................................... 208 Cha~ter 14. Nichols Chart Analysis ............................................................................ 228 Cha~ter 15. Automatic Control Devices ...................................................................... 248 Chapter 16. Automatic Control Apparatus .................................................................. 289 Chapter 17. Analog Computer ..................................................................................... 311 Appendices ................................................................................................................. 343

Index ............................................................................................................................ 348

Korea 165

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168 Korea


Linear Control System Engineering

J.S. Kim 1988

In the strict sense of the word, the first Korean control textbook was published in 1988 by J.S. Kim when the 24 th Olympic Game was held in Korea. Figures 4-6 show the book cover and the Table of Contents of Kim's book. Its title is to be translated in English as Linear Control System Engineering, and an English translation of the Table of Contents is included below. This book has an important meaning in that it is fully written in Korean and uses Korean terms in control engineering. It covers modern control theory and multivariable systems as well as the classical subjects. It has been widely used as a textbook and a reference in Korean literature and provided a motive to publish a Korean dictionary of terminology in electrical and control engineering.

Contents : Linear Control System Engineering (J.S. Kim, 1988)

Chapter 1. Chapter 2. Chapter 3. Chapter 4. Chapter 5. Chapter 6. Chapter 7. Chapter 8. Chapter 9.

Introduction to Control Systems ................................................................... 1 Mathematical Background ............................................................................ 18 Mathematical Modelling of Dynamic Systems ........................................... 55 Performance and Stability of Feedback Control Systems ......................... 106 Root Locus Method ................................................................................... 150 Frequency Response of SISO Control Systems ....................................... 175 Frequency Response and Stability Robustness of MIMO Systems .......... 221 State-space Analysis of Linear Dynamic Systems .................................... 271 SISO Control System Design .................................................................... 311

Chapter 10. Control System Design Using Eigenvalue/Eigenvector Structure ........... 354 Chapter 11. LQ Control System Design ...................................................................... 399 Chapter 12. Kalman Filter ........................................................................................... 454 Chapter 13. MIMO Control System Design Using Model Reference Compensator ..... 487 Chapter 14. Digital Control Systems ........................................................................... 537 References .......................... , ........................................................................................ 575 Index ............................................................................................................................ 579

Korea 169


iii. i i �84184184 I�84 �9 i ~ ~i~ ~ii iii i ~ i~ ~ ~i ~�84

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170 Korea


1.1

1.2

1.3

1.4

1.5

1.6

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,~]~t ~-~ ~ , ~ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

~ t ~ l - - ~ ~ J ~ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

~11o-I,q ~1 ~1 ~--~+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

~l ~ ~ 1 ~ ~ol ~ ~ - o ~ - . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

~I,~I,~1 ~2 ~1 ~3 ;~1 ;~ ~1 - . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . t3

2. 1 x] ~ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

2.2 ~ ~ 7~1~ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

2. 3 Laplace ~-~&t- . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

2. 4 ~ Laplace tO_ ~1: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

2 .5 ~ @~1-,__~- ~ "o1~r ~-I z] Lap lace ~ l ~ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

2.6 u , ~ ~o~] ~_~ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

2.7 ~J ~o ~- ~ ~,~ ~t ~,~ ~3 ~ ~ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

2. 8 ~ ~ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 2. 9 ~ - ~ ~ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

2.10 ~--~--~.~/~vm] ~-] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

2. 11 Eucl idean @ 73~] x~ ~ ; ] - @ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

2.12 2~]- ~ ~ - ~;~s~e_~ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

2.13 x1~- ]~4 ~o~ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

2. 14 - 7 ~ ~] ~-] ~- Jacobian ~,~ ~ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

2.15 ~-]-~]- ~ _ o } 5:_~ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

~ ~ l l . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

@ -~ ~-11 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

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THE NETHERLANDS

Elementaire Theorie van de Automatische Procesregeling (Elementary Theory of Automatic ProcessControl)

J. Stigter Kluwer, Deventer, The Netherlands, 1962.


P.M.E.M. van der Grinten, Prisma-Boeken, Utrecht/Antwerpen, 1968.

Regeltechniek J.C. Cool, F.J. Schijff, T.J. Viersma Agon Elsevier, Amsterdam/Brussel, 1969.

Contributed by

Paul Van den Hof

Delft University of Technology Delft, The Netherlands


Elementaire Theorie van de Automatische Procesregeling (Elementary Theory of Automatic ProcessControl)

J. Stigter Kluwer, Deventer, The Netherlands, 1962, ll0pp.

The writer of this book is an engineering advisor and lecturer at a polytechnic school in Dordrecht, The Netherlands. He had a background in Mechanical Engineering, presumably from the Technical High School in Delft (currently Delft University of Technology).

The book discusses the elementary concepts of open-loop and closed-loop control, block diagrams and closed-loop transfers, first for static systems, and then for first-order and second- order dynamical systems. The frequency response function is introduced and Bode diagrams are analyzed, as well as polar (Nyquist) diagrams and Nichols diagrams. Stability and control performance (gain and phase margin) are explained using the Nyquist diagram, while the effects of P, I and D actions are explained. At the end of the book some nonlinear phenomena are discussed: actuator limitations, dead zone, hysteresis, friction. Typical examples include mixing systems and level control systems.

174 The Netherlands


E L E M E N T A I R E T H E O R I E

V A N DE A U T O M A T I S C H E

P R O C E S R E G E L I N G

,'~ r. j. S T : G T E R . : w . .

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N~ V, : : T G E V E R S M A A T S C H A P P I ]

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E. K L U W E R

The Netherlands 175


I N H O U D

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.:. Ze(/rC..!ch.T.;: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ] ;

4 . L " , y t r t . g . ,~ .~7z tu t t r . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ', 2

~ , f c'tP,'J~, r ~ t l ~ . I r r d " . ' d ~ l R L ~ I "~ , . ~ . . . . - . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4. Vr' jheid.<:2r:~d<;~ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ~. 6 7- V,.<,rb:. ' : /dc~ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . : 7

H o o f d s t u k II. Rc'cv!. '-,:::::: ~::~ !-,i,:,k.-ci~e:r,a

",. if,:.'. ,~.:,:,.k:c&::'.:::~' ............................................................ ~ 9 ::. D~, ._~c::,,a,~. k r i ; ~k [ c , : : , - , . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . :

:.-7. L,: neid,"l/cz, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2

4. S :o r in .~en . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 ~. Tcr',':,,k~q'~::'ditu.C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2. 4

H o o f d s t u k I I I , A~:aivse van s: , : ,ru~cp.

: . H~:t :t~:,,.'<~udc ~..:.~;'n,..t,.~: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . "7 ", L),:' >pr,n~4/un<tic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2S

.~ . ~ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

.:. D~' ';,,,":~,!~L, ............................................................... 2S

-. ~s .,.:lh','t.r S~;j1~,:z~;,/ ............................................. 2c:.

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H o o f d s t u k IV. Ovcrbrc::~i: :~!>.ver! '<uzdins van [ ineaire sys:emc~;

:.. t ,:~cn ~~:n v[',:rbrea.'ffa~L:;:'erlt,:,udmyen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 ;,.. ~r,.3z~r o~ r;,.~:dc-,:>rdc.~';,.;te:n:m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

3. Ecr.~te-,.,rd-:_~v.,tv,r . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ~;5 I- T:i' :'.:&*-orde:: vs,,:m,.i'n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ~9 S. S~:rtescf',;.i'k~'hv,::4 ~:'~u ~: ,> : t t~mt 'n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 3

H o o f d s t u k V. D~,:'~::;r.z::~t~er: ~. M e t hc, d,"d'u.'4r~.~;n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 6

2 . H e r U d:,'~r,::' d r , s ' r ( . , : : ! . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ~ 4

.~,. H o t a,.,:h,>isda.,:.,r(:,~ ....................................................... 57

;:. V,~.,r,~e,Gt,~n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5s

H o o f d , ~ t u k VI. S ~ a b i l ~.'~:

:. P,.'ri,ds ~',m d,: r~:Sp,t:.,':~- . ............................................. ~ !

2. Rr t t~ ~,::~',:~ r ' ~d~q[t';rz~', . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ~.:j,,

.~. .R~'d:r;'tt~: ~'~. ,n : t , ~ r m T c n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ~:~: ' Gr,:;'hsci:;' ~,~;r.,r'~.teL/in,. r,or" d< r .nd ,~a .v .dr ;'cr~g,_'rki,uq 6 5 15. '~ ' " : : , : t : : q ~ ' , : ' r i ' o " , d i r z . k ' " . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 09 ;;" V, ' rS~' !~r t tP: :'~;.:~ d~ <',,ahih:t,:~t "7C.

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Is de hoekfrequentie van de storin~ A?r '"A of '"I; dan levert de rcgclaar

een verbetering. Voor '"A ' " +"B

treedt versiechtering op. Een duidelijk beeld hiercan verkrij~,t men door de afwijkingsverhouding A.V. als functie ,,'an de frequentie (op lo~aritmische., schaai) uit re zetren (fig. VI-I5}.

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In fig. VI - i6 is bet polaire diagram getckend voor een regelkrlng met propor- tionele regeling. Her hieruit berekende verloop van de A.V. :s weergegeven in fig. VI-I7. Maken we de overbrengingsverhouding van de regelaar 2.5 ,naal zo groot, dan verplaatsen we her punt ( - - I . jo) naar P. d.x.~.z. ( - -o ,4 , j o). Vanuit dit punt wordt nu dus I Gr ~ + ~,emeten, waarbii de afstand OP 0,4 als nieuwe schaaleenhmd tc gebruikcn is. In fig. VI - t7 is her resultaat met gestippc1- de lijn weergegeven.

7o

178 T h e N e t h e r l a n d s



P.M.E.M. van der Grinten, Prisma-Boeken, Utrecht/Antwerpen, 1968. 257pp.

This is the first of two books that Paul van der Grinten wrote on control. The second one, "Statistical Process Control" with J.M.H. Lenoir, written in 1973, was used as lecturing material by the author in his courses for students from Technical Highschool Eindhoven, until the beginning of the 80's.

Paul van der Grinten, finished his PhD thesis "Stochastic Processes in Measurement and Control" in 1962, under the supervision of Professor Onno Rademaker. Later, when working at DSM (Dutch State Mines), he was appointed as part-time professor in Eindhoven, where he was teaching courses on stabilizing control systems and statistical methods in control. He was also involved in the editorial board of Automatica in the very early days.

In the book, properties of dynamical processes are treated in terms of differential equations and Laplace domain representations. Basic control operations as PID control are treated and analyzed in their time response effects. Dynamic stabilizing control systems are considered under the influence of stochastic type of disturbances. Examples include typical processes from process industry: mixing and heating processes as well as (petro-)chemical processes.

The Netherlands 179


DR. IR. P. M. E. M. VAN D E R G R I N T E N

R E G E L T E C H N I E K EN

A U T O M A T I S E R I N G IN DE

P R O C E S I N D U S T R I E

P R IS M .~, - B O E K E N

U T R E C H T , A N T W E R P E N

/

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184 The Netherlands


Regeltechniek

J.C. Cool, F.J. Schijff, T.J. Viersma Agon Elsevier, Amsterdam/Brussel, 1969.

This is a full-size textbook, 486pp, written by one of the early professors in control/hydraulics of Delft University (Viersma), and by one of his lecturers (Jan Cool) who later became a professor at the same university. It was used (in several new editions) at Dutch universities until the eighties, and in Dutch polytechnic schools all through the nineties.

It extensively discusses transfer function representation and properties of first order and second order systems with time delays, Bode and Nyquist diagrams and PID control, Nyquist stability criterion as well as the tuning of (PID-)controllers. Examples are from process control and from servo systems, among which hydraulic systems. Later chapters include stochastic processes and non-linear phenomena.

The Netherlands 185

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188 The Netherlands



NORWAY

Control Engineering (Reguleringsteknikk) Vol. 1 Jens G. Balchen Tapir Book Company, Trondheim, 1963

Control Engineering (Reguleringsteknikk) Vol. 2 Jens G. Balchen Tapir Book Company, Trondheim, 1967

Control Engineering (Reguleringsteknikk) Vol. 3

Jens G. Balchen, Magne Fjeld, Ole A. Solheim Tapir Book Company, Trondheim, 1970

Contributed by Jens G. Balchen

Norwegian University of Science and Technology Trondheim, Norway



Jens G. Balchen Tapir Book Company, Trondheim, 1963

At the Norwegian Institute of Technology, Trondheim, Norway (now Norwegian University of Science and Technology, NTNU), an Associate Professorship of Control Engineering was established in 1954 and a Control Engineering Laboratory was instituted at the same time with a staff of laboratory and teaching assistants and technicians. Regular courses in Control Engineering Fundamentals were offered to students from various departments in 1955 based on Norwegian notes prepared as the course progressed. These notes were printed in two volumes at the Laboratory from 1957/58 and were used until 1963 when the first issue of Jens G. Balchen: Control Engineering (Reguleringsteknikk) Vol. 1, 1963, was published by Tapir Book Company, Trondheim.

This little book (256 pages) has been printed in a large number of editions with many modifications and additions and used as the text for the introductory course in Control Engineering.

From 1999 the book has been transformed into: Jens G. Balchen, Trond Andersen, Bjarne A. Foss: Control Engineering, Vol. 1, Tapir Book Company, 1999, (568 pages).

The Control Engineering Laboratory was in 1962 converted into a Division (Institute) of Control Engineering within the Faculty of Electrical Engineering and in 1972 the Department of Engineering Cybernetics was established with 5 professorships.

Control Engineering, Vol. 1, 1963 (CE 1963) was based on classical theory of control systems with Laplace transforms and frequency response methods applied to analysis and synthesis. It contained some original contributions which became popular two decades later.

One such contribution was the development of the frequency response H-- (H-infinity). This development is shown in CE 1963, pages 187-193.

Another unique contribution of CE 1963 was the frequency response based analysis of effects of limitations (saturation) in feedback control systems (see CE 1963, Ch. 11, pages 227-236).

To fill the need for a textbook on equipment for practical implementation of industrial control systems, Associate Professor Ole A. Solheim wrote the book:

Ole A. Solheim: Instrumentation Engineering, 1966, Tapir Book Company, which was reprinted in many updated editions.

190 Norway


REG U LERI NGSTEKN I KK

Grunnlag for dimensjonering av linemre reguleringssystemer

Jens G. Balchen Professor i Reguleringsteknikk

Norges tekntske hmgskole Trondheim

Vol. I

TAPIRS FORLAG TRONDHEIM 1963

Norway 191


228

.11.2:. .... Metning. ~ (Amplitudebegrensning).

I fig. 11. I er det skissert noen statiske karakteristikker

for typiske elementer fra reguleringsteknikken. De er alle karak-

terisert ved at de hat en svre og nedre begrensningsverdi, mer

eller mindre skarpt definert. Slike elementer eller fysikalske

relasjoner kan forekomme p~ de forskjelligste st| i regule-

ringssystemer.

l X ~ ~ '~-...1 .

. . . . . . . . . . = i - " , i i 1

~------ ,~ p --------~ . . ;

~ ,21 i ....

k o n s t _ ~ i~ L

X 1! 1

R e g u t e r i n g s v e n t i l E lek t ron r~ r

. . . . / i I _ i k e s t r 6 m s g e n e r a t o r

Fig. 11.1

Noen enkle eksempler ps forekomst av ett slikt element i sy-

stemer, som forovrig kan beskrives med line,re relasjoner (trans-

ferfunksjoner H), er vist i fig. 11.2. Samtidig er de mest be-

tydningsfulle inngangs- og utgangsvariable antydet. Ved hjelp

av analysemetoder for linemre systemer kan vi ns lettvint finne

ut betingelsene for at metning ikk____~e skal inntre. Vi kan derimot

ikke uten videre finne ut hva sore skier dersom metning inntrer.

K jenner vi formen pA den inngangsvariable, kan vi, i alle

fall for enkelte former, lettvint finne formen p~ signalet (x)

I'oran det element der metningen inntrer. En vesentlig ting er at

signalenes stsrrelse (amplitude) over alt i linemre systemer vil

vmre proporsjonale. Har vi funnet formen av x for ~n storrelse

av den inngangsvariable, kan vi derfor lettvint finne akkurat den

192 Norway


229

amplitude av inngangssignalet som vli medfere metning p~ ett eller

annet tldspunkt. I tilfeller der slik metning medfsrer d~rligere

ytelse av systemet har vi dermed fAtten viktlg opplysning.

x(',.) / - =_

O

L_L_%"

- - - i ~ 4 ! . . . . .

.... J , .... L

Fig. 11.2

1 I. 3~ . . . . U n d e r s ~ k e ! ~ S e. ~ ~idsplane t.

Iet line~rt system kan vi, som nevnt, i prinsippet finne

responsen hvor som helst, forutsatt at den (eller de) inngangs-

variable er gitt. Selv om vi, for A bestemme forekomsten av met-

ning, bare trenger A kjenne maksimalverdien av responsen, kan det

imidlertid medfsre svart tidskrevende beregninger, dersom disse

foretas i tidsplanet.

Antar vl at det element som kan gA i metning er slik at det

innenfor sitt lineere omrAde har en forsterkning ilk I, finner vi

for de tre systemene som er skissert i fig. 11.2:

X S y s t e m a" - ( ~ ) = : ~ ( ~ ) d ~ - N =

r 1 + HIH 2

X System b: ~(s) =-H3.H4.HI.N der N =

I + HIH2H4

(11.1)

( i ~. 2 )

N o r w a y 1 9 3



Jens G. Balchen Tapir Book Company, Trondheim, 1967

During the 1960s there was a rapid growth in the enrolment of students who wrote their Masters- and Doctoral Theses at the Division of Control Engineering. Therefore a number of courses were developed covering advanced topics of control systems theory such as:

- Theory of Discrete Control Systems - Theory of Nonlinear Control Systems (Liapunov Theory, Harmonic Balance) - Stochastic Methods in Linear Control Systems Analysis and

Identification of System Parameters -Optimal Control Theory

The first 3 of these topics were dealt with in:

Jens G. Balchen: Control Engineering, Vol. 2, 1967. (CE 1967)

Special attention should be paid to the development of the w-transform in Discrete Control Systems Analysis (in CE 1967 w is replaced by q). The z-domain variable is transformed by a bilinear transformation

2 z-1 1 + wT/2 w = - - - or z = - -

T z+l 1 - wT/2

Modeling the system in the w-domain rather than the z-domain leads to some very convenient results which make analysis and synthesis of discrete control systems nearly identical to that of continuous control systems (see CE 1967 pages 27-35).

194 Norway


REGULERINGSTEKNIKK BIND 2

Videregliende reguleringsteknisk teori

Jens G. Balchen Profe.or i Reguleringstekntkk

Norges tekniske hqskote Trondheim

TAPIRS FORLAG Trondhelm 1967

Norway 195


27

dier p& enhetssirkelen, det vil si, z = 1-e j~ (hvilket er ensbe-

tydende med ~ velge s = jw). Derved kan en tegne en kurve for

vektoren A(z), som selvsagt blir identisk med den som er vist i

fig. 1.17 for A*(s). Stabilitet erda gitt av denne kurves belig-

genhet i forhold til det kritiske punkt -I + j0, som uttrykt i

Nyquist's stabilitetskriterium. Innsetting av z = 1-e j~ i A(z)

(so,, for eksempel gitt i (1.48)) er imidlertid ikke smrlig hensikts-

messig, idet det medfsrer endel tallregning. Denne siste metode

til stabilitetsundersokelse er derfor ikke s~rlig ~ foretrekke frem-

for undersokelse i s-planet.

Det finnes imidlertid et tredje alternativ som skal belyses

nmrmere.

1.9. q - t r a n s f o r m .

Ved~ innfere den bilinemre transformasjonen

T I + ~.q

z - T ( 1 . 6 5 ) 1 - ~ . q

finner vi at utsiden av enhetssirkelen i z-planet blir transfor-

mert til h.h.p, i q-planet, og innsiden av enhetssirkelen til v.h.p.

i q-planet. Ved denne transformasjon bibeholdes dessuten A(q)

som en ras jonal funks jon dersom A(z) er en rasjonal funksjon.

Vi firmer ogs~ ved sammenlikning av z-plan og q-plan at v.h.p.

i s-planet blir transformert til v.h.p, i q-planet, og tilsvarende

for h.h.p. Sammenhengen mellom s og q er vist grafisk i

fig. 1.19, der koter for konstant absolutt dempning, frekvens og

relativ dempning i s-planet er inntegnet i q-planet.

Ganske spesielt finner vi

Ts 2 z - I 2 e - I 2 T

q = u + j v = " ~ ' z + I = ~ " T s = . ~'Tg ~'s (1.66) e + 1

som red innsetting av s = j~ gir

196 Norway


2 8

q T - p lan jvT

aT= 0,6

uT

q �9 U+ jV

s �9 o' , jW

-3

Fig. i. 19.

2 e q= jv=~. e

jwT

jwT - 1

+ 1

( 1 . 6 7 ) gir

T _z) W.~' = arctg ( v . 2

2 2 e ~. =..,G .....

T jwT 2

e

- e

=.

+ e

jwT 2

2 wT

2

(1.67)

(~.68)

Norway 197


198 Norway



Jens G. Balchen, Magne Fjeld, Ole A. Solheim Tapir Book Company, Trondheim, 1970

After the (CE 1967) had been published in 1967, it was evident that there was a need for a new textbook covering "modem control theory" with particular emphasis on optimal control theory and aspects of practical implementations in computer control of multivariable processes. CE 1970 is completely based on state space descriptions of multivariable dynamic systems and has individual chapters on Modal Control, Optimal Control based on the Pontryagin Maximum Principle, Dynamic Programming, Optimal State Estimation (Kalman Filtering), Modal and Optimal Control of Distributed Parameter Systems.

CE 1970 was used for many years in graduate courses at the Department of Engineering Cybernetics together with a variety of books from international publishers. It was regarded among the students to have high pedagogical quality. An example of this is the derivation of the optimal discrete state estimator (Kalman Filter) in CE 1970 pages 269-273.

It has been a declared policy of the Department of Engineering Cybernetics to have available textbooks like CE 1963, CE 1967 and CE 1970 in the Norwegian language together with international books in order that the mother tongue professional language shall stay competitive.

Norway 199


269

6.3. 0ptimal d i s k r e t t i l s t a n d s e s t i m e r i n g . [8][9][101

I kapittel 5.9 har vi utviklet den optimale tilstandsestimator

(Kalmanfilter) for et kontinuerlig system. Samme type betraktnin-

get som derer gjort kan legges til grunn for utvikling aven

optimal tilstandsestimator for et diskret system beskrevet med

likningene

x(k+l) = r + A(k)u(k) + fl(k)v(k)

z(k) = D(k)x(k) + w_(k) (6.3-~)

For et slikt system kan vi, tilsvarende det som er gjort i kapittel

5.9, definere kovariansmatriser som fr

E((xCk)-x_-) CxCk)-x_-) T ) = X(k) der E(x(k)) = x

E((_v(k)-_~)(v(j)-v_-) T) = V(k)Skj

E ( (w_ (k) -w_) (w(j)-w_-)T) = W(k)6k j

der E(v(k)) = v~ (6 .3-2)

der E(w_(k)) = w_-

I (6.3-2) ha t vi a n t a t t at v(k) og w(k) er d i s k r e t e h v i t s t ~ y - p roses se r . Det te kommer t i l u t t r y k k red funksjonen

6kj , k, j

Vi skal ogs~ anta at v(k) og x_~(k) er ukorrelerte. Dette gfir

fram av at

E[w(k)v_(j) T] = 0

I (3.2-77) er det utledet et uttrykk for hvordan kovariansmatrisen

av responsen avet kontinerlig dynamisk system vil bli nSr det

200 Norway


270

u t s e t t e s fo r en s t o k a s t i s k p '~v i rkn ing . Vi f~ r da

X(t) - | T t

( t - t o ) + f ~ ( t - ~ ) c v c T ~ T ( t - T ) d~ (3.2-77)

to (6.3-3}

Dersom p r o s e s s e n er d i s k r e t , kan v i ved ~ innfCre t o = kT

og t = (k+l)T der T = t a s t e p e r i o d e , f~

X(k+l) - r T + a ( k ) V ( k ) a ( k ) T (6.3-4)

I e t d i s k r e t sys tem v i l en g j e r n e d e f i n e r e to f o r s k j e l l i g e t i l s t a n d s e s t i m a t e r -

x = a p r i o r i e s t i m a t e t av x(k) fCr m~l ingen l ( k ) u t n y t t e s

^

x = aposterioriestimatet av x(k) etter at m'$1ingen

y(k ) e r u t n y t t e t

Med d e t t e som u t g a n g s p u n k t kan en t i l s v a r e n d e de t som er g j o r t i ^

k a p i t t e l 5.9 f i n n e e t o p t i m a l t e s t i m a t x red ] m i n i m a l i s e r e obj ek t funks j onal en

J = E[(x(k)-x-)T(~)-~(x(k)-x_-) + ( ~ ( k ) - D x ) T w - ' ( E ( k ) - D ~ ) ] (6.3-S)

Det estimat sore derved fremkommer refereres ofte til som et

"minste kvadraters-minimumilvarians estimat". Derved kommer en

frem til et resultat sore kan presenteres i folgende sekvens"

1. Et a p r i o r i - e s t i m a t x~(k) og den t i l s v a r e n d e k o v a r i a n s m a t r i s e

X(k) a n t a s k j e n t f r a de t foreg~ende t i d s p u n k t ( k - l ) .

2. N'$r m~lingen (y(k) f o r e l i g g e r ved t i d s p u n k t e t k, beregnes ^

a p o s t e r i o r i - e s t i m a t e t x(k) og den t i l s v a r e n d e k o v a r i a n s - A " -

m a t r i s e X(k) ved h j e l p av formlene

A x(k) -- x_-(k) + K(k)(z(k)-DCk)x~(k)) (6.3-6)

Norway 201


271

der K(k) = .X(k)D T(k) [D(k)X(k)D T(k)+W(k)l

A

X(k) = [ I - K ( k ) D ( k ) l X ( k )

- i ( 6 . 3 -7 )

(6.3-s)

3. Apriori-estimatet x(k+1) og tilsvarende kovariansmatrise

X(k+1) red neste tidspunkt (k+l) beregnes av

\

x_(k+l) = o ( k ) ~ ( k ) + A(k)u(k) + f~(k)_~(k) (6.5-9)

som er en anvende l se av ( 6 . 3 - 1 ) , og

- - A

X(k+l) = ~ (k )X(k ) r T(k) + g(k)V(k)S2 T(k) (6 .3 -10 )

som er en anvendelse av (6.3-4).

Det diskrete Kalmanfilter kan med fordel illustreres med et

blokkdiagram som vist i figur 6.5-I. Figuren viser tydelig at

filteret best&r av en diskret modell av prosessen basert p5 (6.3-I)

som leper i paralell med den virkelige prosessen eksitert av

p'$dragsvektoren. Nodellen genererer et estimat (~(k)) av

m~levektoren og deter differansen mellom dette estimatet og den

virkelige m&levektor (y(k)) ved samme tidspunkt sore gjennom den

tidsvarierende matrisen K(k) sCrger for oppdateringen av

tilstandsestimatet ved tilbakekopling. Dersom K(k) skulle v~rt

null, ville vi f~tt det tilfelle sore ofte refereres til reed

betegnelsen "ballistisk" som er karakterisert ved at modellens

beregninger er fullstendig uavhengige av den virkelige prosessens

respons. Deter lett 5 vise at dette tilfelle vil oppst& etter

en tid dersom prosessforstyrrelsene v_(k) = 0 og nSr modellen er

en perfekt representasjon av den virkelige prosess. Det eneste

sore da er forskjellen mellom prosessens og modellens oppfOrsel er

at begynnelsesbetingelsene for prosessen er ukjente, men virkningen

av disse vil etter hvert dr

202 Norway


POLAND

Fundamentals of Control Systems - Volume I" Linear Systems

Pawef Nowacki, Ludger Szklarski and Henryk G6recki Polish Scientific Publishers, Warszawa 1958

Fundamentals of Automatic Control

Stefan W~grzyn Polish Scientific Publishers, Lbd~- Warszawa- Krakbw, 1960

Contributed by

Wladislaw Findeisen Ryszard Gessing

Warsaw University of Technology Warsaw, Poland

Silesian Technical University Gliwice, Poland


Fundamentals of Control Systems - Volume I: Linear Systems

Pawel Nowacki, Ludger Szklarski and Henryk G6recki Polish Scientific Publishers, Warszawa 1958

The idea of this textbook, entitled in Polish ,,Podstawy teorii ukIad6w regulacji automatycznej", came from Professor Pawel Jan Nowacki, who was later to become president of IFAC (1969 - 1972). The book had to be a comprehensive text for students of control engineering, from the mathematical background up to practical examples. Indeed, the first two chapters of the book introduce the reader to Fourier and Laplace transforms along with some elements of the theory of complex variables, permitting to understand the use of transfer functions and block diagrams for the description of control systems. The relations between frequency response and time response are elaborated here in practical detail.

The next chapter covers stability assessment of feedback systems; it is in this respect quite comprehensive, presenting not only the Routh-Hurwitz and the Nyquist criteria, but also the Russian approaches of Mikhailov and Neimark.

Chapter four is devoted to design methods of control loops on the basis of frequency response, using predominantly logarithmic characteristics. The authors pay attention to practical tools, such as the Nichols chart, as well as to the synthesis of series and parallel correctors for improvement of the control loop behaviour.

The last two chapters of the Nowacki & al. textbook are hardware oriented. The student gets introduced to components of electrical control systems, such as sensors, amplifiers and servomotors, and then receives a description of two examples: a Ward-Leonard drive controlled by an amplidyne and the control system of an electric mine-winder with asynchronous motor.

The book in its whole was written in the years 1956 to 1958. Professor Nowacki suggested that chapters 1 and 2 be written in collaboration with Dr. Henryk G6recki from the Mining Academy in Cracow, while he himself was a professor at the Warsaw University of Technology, and remained to be the main author. Dr. G6recki used to travel by train from Cracow to Warsaw and stayed with Professor Nowacki as his guest. The co-authors discussed the content of the book and worked till small hours. Then Dr. G6recki wrote chapters 3 and 4 at home and Professor Nowacki read and approved the manuscript. Chapters 5 and 6 were composed by Dr. G6recki and Professor Ludger Szklarski of the Mining Academy in Cracow.

Later on the three authors worked jointly on Volume II of the book, which was to appear in 1962 with the same publisher. The volume covers the issues of performance criteria, theory of multidimensional and non-stationary systems, as well as discrete systems, nonlinear systems, and some elements of optimal control.

Back in 1958 the Nowacki - Szklarski - G6recki textbook on control systems was practically the first to be written by Polish authors; it was, however, not alone on the market. A parallel and considerable effort was put into bringing to the Polish reader several important foreign books on control. The following translations into Polish were published in roughly the same time:

204 Poland


G.S. Brown and D.P.Campbell, Principles of Servomechanisms (Polish 1957)

A.A. Feldbaum, Electrical Systems of Automatic Control (original in Russian, Polish 1958)

W.Oppelt, Kleines Handbuch technischer Regelvorg~inge (Polish 1958)

J.C. Gille, M. P61egrin, P. Decaulne, Thdorie et technique des asservissements (Polish 1961).

As a result, the student, as well as the engineer in Poland had a fair insight into different schools and approaches to control systems and a good choice. This fact makes it also difficult to assess the impact of the Nowacki-Szklarski-Gorecki textbook alone; it is worth mentioning, however, that it was printed in 3000 copies.

Table of Contents

Control terminology in English, German, Russian and Polish

1. General isssues 1.1. Introduction 1.2. Elementary notions and elements of control systems 1.3. Characteristics of control systems

2. Mathematical foundations of control theory 2.1. The Fourier transform 2.2. The Laplace transform 2.3. Methods of calculation of roots of characteristic equations 2.4. Elements of the theory of complex variable 2.5. Calculation of the inverse Laplace transform 2.6. Calculation of residues 2.7. Block-diagrams of control systems 2.8. Relations between spectral characteristic and unit-step response 2.9. Approximate calculation of step response from transfer function 2.10. Approximate calculation of transfer function from step response

3. Stability assessment of feedback control systems 3.1. Introduction 3.2. The Routh and Hurwitz stability criteria 3.3. The Mikhailov stability criterion 3.4. The Nyquist criterion 3.5. Domains of stability and the Neimark criterion

4. Logarithmic amplitude and phase characteristics in application to analysis and synthesis of linear control systems

4.1. Application of logarithmic amplitude and phase characteristics 4.2. Notions and units in logarithmic amplitude and phase characteristics 4.3. Stability analysis of linear system with a single feedback loop 4.4. Logarithmic amplitude and phase characteristics of typical elements 4.5. Approximate logarithmic amplitude characteristics for single loop systems 4.6. Application of the Nichols' chart to systems with several feedback loops 4.7. Relation between break-off frequencies and the error coefficients

Poland 205


4.8. Introduction to the synthesis of correctors 4.9. Log amplitude and phase characteristics for an optimal transient process 4.10. Determination of desired logarithmic amplitude characteristics 4.11. Typical logarithmic amplitude characteristics and their classification 4.12. Nomograms for the synthesis of correctors 4.13. Determination of the relations needed for the synthesis of correctors

4.14. Application of nomograms to synthesis of non-typical logarithmic amplitude and phase characteristics

4.15. Synthesis of series correctors 4.16. Properties of the logarithmic amplitude characteristic of a series loop

element shunted by a corrector 4.17. Synthesis of parallel correctors 4.18. Synthesis of mixed (series and parallel) correctors

5. Components of control systems 5.1. Electro-mechanical analogies 5.2. Typical components of control systems 5.2.1. Introduction 5.3. Complex components of control systems 5.3.1. Sensors 5.3.2. Summing devices 5.3.3. Amplifiers 5.3.4. Servomotors 5.3.5. Stabilizers, dampers and accelerators 5.3.6. Feedback elements 5.3.7. Controllers

6. Practical examples of control systems 6.1. Ward-Leonard drive controlled by an amplidyne 6.2 Amplidyne controller applied to electric mine-winder with an asynchronous

motor

Bibliography

Contributed by

Wladislaw Findeisen Warsaw University of Technology

Warsaw, Poland

206 Poland


: . : ( . . : . . . . . " . . . . . " - . .

Lu R SZKL~ ~:.H.ENm:-s G o ~ e x x "~:~'~ P A W E L N O W A C ~ D G E ' . . "~.: ""~:~ . . . . . . . .~. ~.; . . . . . i . ~ ....

. . : . ~ . . , 7 ~ - - " . . . . �9

i~i T M A T Y C " :~::. - R E G U L A C J i ~ A U ~ 0 ZNEJ":i:~I,(,.~:~ n

�9 . , ~* .. , . , _ , - .

" - : "" ~ . . . . . . . . ~:" ' " ', ~ - - i: ...... i . : ; , !~ i

, " . . .... . . - : : . ~ . : .... : . - . . . . . . . :~, - ~ i I . : , : : �9

I

Poland 207


3.5. Ohszary ,stabiln, o~ci. Ka'yterium N e j ~ l ~ a 139

Obliczamy r6wnanie (3.5.27): M(s)

T(s) = = - - G ( s ) N(s)

i podstawiamy w rfim s = j co.

Punkt T0= 1 +j0 powinien lezed na zewn~trz krzywej - G(jo~), czyli wewn~trz obszaru stabilno~ci, j e~li uklad zamkniety jest stabilny. Wa- runek ten o czywigcie jest wa~ny w6wczas, gdy uldad otwarty jest stabilny.

.

~ d ~ - ~

Rys. 3.5.7

Jak widad z rys. 3.5.6 i ~e wzoru (3.5.26), rozwa2ali~my tutaj r6wna~ie

- G(s) = + 1 (3.5.30)

zamiast, jak to si~ czyni normalnie przy kryterium Nyquista--Michajtowa,

rSwnania G(s) = -- 1. (3.5.31)

W naszym przypadku otrzymali~my krzyw~ bed~c~ zwierciadlanym odbiciem krzywej wyraionej r6wnaniem (3.5.31) wzgl~dem osi j V i naszym punktem krytycznym jest punkt (+ 1 + j 0) zamiast (--1 + j 0).

Przejdziemy teraz do interpretacji kryterium Michajlowa za pomoc~t analizy obszaru stabilno~ci.

Zat6~.my, ~e ,dane jest r6wnanie charakterystyczne uMadu zamlmi~-

tego M(s)+ N(s )= O . (3.5.32)

Wprowadzimy teraz parametr T(s) zamiast zera:

M(s) + N ( s ) = T(s) . (3.5.33)

R6wnanie (3.5.32) jest oczywi~cie wSwczas szczeg61nym przypadkiem rbwnania (3.5.33). Nast~pnie zaktadamy w rdwnaniu (3.5.33) s - - j w i w y - kre~lamy krzyw~

T(joJ) -- U(co) + jV(o~) = M(jo.,) + N(j o~) . (3.5.34)

208 Poland


Fundamentals of Automatic Control

Stefan W~grzyn Polish Scientific Publishers, L6d~- Warszawa- Krak6w, 1960

Carrying the Polish title "Podstawy Automatyki" it was one of the first books written by Polish authors, devoted to Automatic Control. The first edition appeared in 1960 and was authored by Stefan W~grzyn in cooperation with his graduate students and collaborators Z. Bubnicki, A. Bukowy, Z. Cichowska, R. Gessing, Z. Pogoda, A. Macura, A. Skrzywan and T. Szweda; it was issued as a paperback textbook. The content was based on lectures read by Professor Stefan W~grzyn at the Electrical Engineering Faculty of the Silesian University of Technology in the period 1954- 1959. The textbook covered basic notions of control such as dynamics of linear systems, systems with feedback, stability, quality of control, continuous-time and sampled data systems, multivariable systems, nonlinear control, systems with dead zone relay, on-off control, peak-holding control, an introduction to digital control, as well as stochastic models and their application to automatic control.

A corrected second edition was printed in a similar paperback form in 1961; its cover is shown in the attached picture. A copy of the first edition was hard to come by.

On the basis of the 1960 and 1961 textbook editions a wide-circulation handbook "Control Fundamentals" was elaborated by Stefan W~grzyn, the first edition of which appeared in 1963. The content of the book was in principle the same as that of the textbook previously mentioned; however, the individual chapters were elaborated more carefully, corrected and modified. In particular, the chapter devoted to digital control was enlarged so as to become a separate part of the book. As a whole, the 1963 book is divided into four parts: the first is devoted to linear systems, the second- to nonlinear systems, the t h i rd - to digital control and the fourth - to stochastic control.

A second edition of the 1963 book, amended and enlarged, appeared in 1972. It contains a new part covering complex control systems, where problems related to identification, digital control algorithms and structures of complex control systems are described. A chapter devoted to optimal control was also added. The new problems were elaborated by Professor W~grzyn in cooperation with M. Bargielski, K. Na~cki and O. Palusifiski.

Following 1972, the book had several new editions or just new printings, the last in 1980. In 1978 entirely new material was added, namely a chapter devoted to real-time computer control. It was elaborated in cooperation with A. Wolisz and T. Czach6rski.

In general, it is beyond any doubt that the work of Stefan W~grzyn and his collaborators has influenced the control education in Poland more than any other single achievement. There is no formal evidence, but it certainly was used by students in places other than the Silesian University of Technology, as well as by control engineers all over the country. Due to continuous changes and amendments the book was on the market for a period of over 20 years, up to the 1980' s.

Contributed by

Ryszard Gessing Silesian Technical University

Gliwice, Poland

Poland 209


P ()D S TAW Y A U TO M ,.A~I' Y K [

Praca zbiorc)wa pod redakej~l

STEFANA W i'~GRZYNA

Wydan[e drngie

1%1 PAN sTW(.)WF: W'fDAWNtCTWO NAI_!KOWE

LODZ ..... WAI1SZA~,V.~, _ KRAKOW

210 Poland


z(~) = ~ (~.5o)

Element taki nazywamy elementem bezlnercyjnym. W ukZadaeh rze- czywlstych ka~dy element posiada pewn~ inerc J~ i w zasadzle nle ma idealnego elementu bezinercyJnego o funkcjl przeJ~clab~- d~cej liczb~ sta~ rzeczywlst~ k. PoJ~ciem tym operujemy Jed- nak bardzo czssto. Na przyk~ad dane s~ dwa elementy pracuj~ee w uk~adzie ~ancuchowym, przy czym staZa czasowa Jednego z nlch jest du2o wi~ksza, anlieli drugiego. Mo~emy w6wczas przyJ~6~2e jeden z element6w jest bezinercyJny i przy obllczenlu wypadko- weJ funkcJi przej~cia uwzg~dni6 tylko sta~ czasow~ druglego.

Zgodnie z wzorem (2.39) charakterystyka cz~sto~cl elementu inercyjnego pier~szego rz~du jest r6wn~

k _ k -iarc tq m r (2 .51 ) e

+ J ~ ~ - V4 + J T ~

Wykres tej char~cterystyki na p~aszczy~nie K(p) przedstawiony jest na rys. 2.23.

i I r,, [ i (i ~O)]

k (~,jo,) (k,joj ~-,~O-~2j :a)--,~ T, T ~ : o - aJ~a I

@}

b)

Rys. 2.23. Charakterystyki cz~sto~liwo~cl element6w In~reyj- nych pierwszego rz~du, T t < T 2 : a) stala ezasowa T I , b) stala

ozasowa T 2 30

Poland 211


212 Poland



RUSSIA (Soviet Union)

Foundations of automatic regulation: theory V. V. Solodovnikov (editor), Moscow, Mashgiz, 1954, 1117 p.

Lectures on the theory of automatic control M. A. Aizerman Moscow, Fizmatgiz, 1958, 520 p.

Elements of the theory of automatic regulation A. A. Voronov, Moscow, Voenizdat, 1954, 471 p.

Some problems in the theory of stability of motion

N. N. Krasovski, Moscow, Fizmatgiz, 1959, 211 p.

Contributed by

Boris Polyak

Institute for Control Problems Russian Academy of Sciences

Moscow, Russia


Introduction

Studies in the field of automatic control in Russia have a long history, starting from the seminal paper by I. Vyshnegradski (1876) and work of the famous mathematician P. Chebyshev (1871). The fundamental contribution to the theory is due to V. Lyapunov (1892), who developed the basic approach to the analysis of stability of nonlinear systems. Perhaps the first textbook on automatic regulators was the lecture course by the great Russian expert in mechanics N. Jukovski (1909). In the Soviet period automatic regulation attracted a lot of attention due to its role in industrialization of the country. In 1934, the Commission on Remote Control and Automation was founded, later it was transformed into the Institute of Automation and Remote Control of the Soviet Academy of Sciences (1939); the journal "Automation and Remote Control" was established in 1936. Some textbooks on automation in specific areas were published, e.g. for power machines (E. Nikolai, 1930), thermal processes (S. Gerasimov, 1937), electrical devices (B. Domanski, 1938), heating equipment (Yu. Kornilov, 1938), construction of automatic regulators (V. Lossievski, 1942). After the war, numerous Western books on control (such as MacColl, 1947; Lauer, Lesnik and Matson, 1948; Oldenburg and Sartorius, 1949; Gardner and Burns, 1949; James, Nichols and Phillips, 1951) were translated into Russian (we refer to the year of the translation); at the same time, original Russian textbooks appeared. Among the first were the following:

1. Yu. Kornilov, V. Piven', Foundations of the theory of automatic regulation, Moscow, Mashgiz, 1947.

2. M. Aizerman, Introduction to dynamics of automatic regulation of motors, Moscow, Mashgiz, 1950.

3. A. Voronov, Elements of the theory of automatic regulation, Moscow, Voenizdat, 1950. 4. Z. B lokh, Regulation of engines, Moscow, Gostechteorizdat, 1950. 5. B. Domanski, Introduction to automation and remote control, Moscow, Gosenergoizdat,

1950. 6. K. Krug, Transition processes in linear electrical circuits, Moscow, Gosenergoizdat,

1948. 7. M. Meerov, Foundations of automatic regulation of electrical machines, Moscow,

Gosenergoizdat, 1952. 8. E. Popov, Theory of automatic regulation, Leningrad, LKVVIA, 1952.

Below, we describe three textbooks of the early 1950's which played a fundamental role in teaching and research, being the stimulating examples for imitation for many years; the fourth sample is a textbook of 1986, which represents the high standards of that period.

We survey some Russian textbooks which played the main role in the development of research and education in this country. There were many others; some of which were even more widespread. The textbooks authored by E. Popov, M. Meerov, A. Netushil, V. Besekerski, Ya. Tsypkin, Ya. Roitenberg are worth mentioning. There also existed numerous textbooks covering some selected topics of automatic control. Of course, the attempt to survey all of them requires much more effort...

214 Russia


Foundations of automatic regulation: theory

V. V. Solodovnikov (editor), Moscow, Mashgiz, 1954, 1117 p. (Fig. 1.)

The contributors to the book include M. Aizerman, V. Voronov, L. Goldfarb, A. Krasovski, A .Lerner, A. Letov, F. Mikhailov, B. Petrov, V. Petrov, V. Solodovnikov and Ya. Tsypkin (for the full list of authors see Fig.2). Actually this is not an ordinary textbook- this huge volume can be called Encyclopedia of Automatic Regulation, and for a long time it played the role of THE BOOK for Soviet researchers and students. Most of the distinguished Soviet scientists in the field of control (with few exceptions - e.g.A. Feldbaum, A. Lur'e) were invited to join the team, which had a common understanding of the subject, techniques and tools of this science.

The monograph has some real-life examples and applications, but mainly it is focused on theory. Two other volumes are intended to cover practical recommendations and applications to various areas of industry.

The book consists of two parts - linear and nonlinear systems, respectively. Each part is divided into four sections, while a section includes several chapters. The structure looks very reasonable; all principal topics of the theory are addressed, and even a contemporary reader can encounter a lot of stimulating ideas.

Section 1 contains basic notions of control; the language of differential equations and transfer functions is used in parallel, and Laplace transform is exploited as the main technique.

Section 2 is devoted to stability of linear systems. Graphical tools play a significant role, and Mikhailov, Nyquist and Bode plots (known is Russian as the method of logarithmic frequency characteristics) are described in detail. The topic which is not well known for Western researchers is the so called D-decomposition (Chapter 11) - the separation of the stability domain in the parameter space. The approach goes back to Vyshnegradski and was developed by Yu.Nejmark (1948); the boundary of the stability domain in the 2D parameter plane can be expressed explicitly.

One of the results by A. Aizerman and F Gantmacher (Fig.3) reads as follows. Consider the characteristic polynomial P(s)=D(s)+M(s), where degD=n, degM= m; q,t,f are numbers of zero, real positive and unstable roots of D; r is the integer part of f/2; M is Hurwitz polynomial. Under these assumptions there exist D, M such that P is stable if and only if the following conditions hold: m>q+t-1, n+m>4r-1 (provided m>0 is even and f is even; for other situations the last condition vary). This result implies the existence of block diagrams which do not possess stability under arbitrary values of parameters involved (structural instability).

Very interesting is Section 3 -"Performance analysis and design". Of course, in 1954, no theory of optimal control existed, but the role of the performance index and specifications is expressed very clearly. Mainly the suggested tools rely on the Bode plot or on pole-zero location. Nevertheless Chapters 20 and 25 deal with integral quadratic performance index. For instance, the plot in Fig.4 exhibits the level sets of such an index as functions of the parameters k and T,

Russia 215


describing a model of the electrical device (potentiometer); this allows to choose optimal values of the parameters k=7.5, T=0.15. Chapter 21 addresses the theory of pulse systems and provides stability criteria for discrete-time models.

The theory of regulation under random disturbances is studied in Section 4. The basic notions of stationary random processes and their applications to control systems are given first (Chapters 22, 23). Less traditional is Chapter 2 4 , - the disturbances are not assumed to be random, but rather arbitrary bounded; the problem is to find the worst possible disturbances that lead to the largest deviation of the output. This so called problem of accumulation of disturbances was first studied by Bulgakov (1946). Of course, it is a typical problem of constrained optimal control.

Nearly half of the volume (Part 2) is devoted to nonlinear systems. This line of research was traditional for the Russian school; classical contributions of Lyapunov, Andronov and Krylov- Bogolubov can be mentioned. We focus just on a few challenging results addressed in this part of the book.

Chapter 31 "Improving dynamic properties of automatic regulation by use of nonlinear controls" is written by A. Lerner; note that it is published a few years earlier than the first papers on the Pontryagin maximum principle. The author starts with the formulation of the problem of time- optimal control for linear or nonlinear systems subjected to constraints on some of the derivatives (which may be considered as controls). Without rigorous analysis, he claims that the control variable should take boundary values only (the bang-bang principle); the instants of switching are found from a system of nonlinear equations (it is assumed that there are just n switching instants, where n is the order of the system). No general theory is provided; however several examples are discussed and optimal processes in the phase plane are obtained (see, e.g. Fig. 5). Note that simultaneously the papers on optimal control of linear systems were published by A. Feldbaum.

Various approximate methods for analysis of periodic regimes are considered in Section 6 (the method of small parameters, method of harmonic balance). Relay systems and self-oscillations in them are the subject of Section 7. The final Section 8 addresses graphical and numerical methods for calculation of time-response in time-varying or nonlinear systems.

216 Russia


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Lectures on the theory of automatic control

M. A. Aizerman Moscow, Fizmatgiz, 1958, 520 p. (second edition), (Fig.6).

The first edition of the book was published in 1956, its material was originally selected and used in lecture courses for engineers and was oriented towards practical applications. Later, the content of the course was revised to serve as a textbook for students. It became a standard for numerous other textbooks on automatic regulation.

The book consists of five chapters and two appendices. Four chapters are devoted to linear systems, the last one deals with nonlinear systems. The input-output description of single-input single-output systems and the frequency-domain approach are prevailing; however the state space language arises in some cases. Consider, for instance, Fig.7; this is the analysis of a linear system plus one scalar nonlinearity (the so called absolute stability problem). The linear part is given in state space form.

In 1949, M. Aizerman formulated the following conjecture: if nonlinearity belongs to a sector (Fig. 8) and the linearized system is stable for all linear characteristics in this sector, then the nonlinear system is stable as well. This Aizerman conjecture is true for n<2, however in 1958 (the year of publication of the textbook) V .Pliss constructed a counterexample for n=3.

The contents of the chapters are as follows. Chapter 1 deals with automatic regulators (examples, terminology, feedback, types of regulators are provided). Basic notions are presented in Chapter 2 (block diagrams, transfer functions, frequency response, the construction of mathematical model from empirical data). Stability of linear systems is analyzed in Chapter 3; the main techniques are based on D-decomposition (see above); Michailov and Nyquist plots are considered as particular cases of the approach. Performance is the subject of Chapter 4. There are many practical recommendations on how to deduce properties of the time response from the transfer function characteristics; a lot of attention is paid to numerical and graphical construction of time response. The last Chapter 5 deals with self-oscillations and forced oscillations in nonlinear systems. Relay systems are considered as examples.

The presentation is clear and rigorous, however, at the engineering level - not all statements are validated, while all of them are explained and illustrated by examples.

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Elements of the theory of automatic regulation

A. A. Voronov, Moscow, Voenizdat, 1954, 471 p. (second edition) (Fig. 9).

The first edition was published in 1950; note that "Voenizdat" means "Military Publishing House." The role of automation was well understood in military applications, this is why research in the field of automatic regulation had strong support from defense institutions. The author had a rich experience in giving lectures at Moscow Higher Technical University (Bauman MVTU) and Moscow Power Institute. These two Moscow universities were leading institutions in teaching automatic regulation. Later, the author published several textbooks on special topics in control, and the book under consideration was revised and divided into two volumes. To summarize, A. A. Voronov was one of the most popular and acknowledged authors in the field of automatic control. His books are well written and combine simplicity and rigor.

The book has peculiar features of the time when it was created (the last years of the Stalin era). The first phrase in Introduction reads: "I. V. Stalin in his work of genius 'Economic problems of socialism in the USSR' points out..." and a long citation (having no direct relation to automatic regulation) follows. On the same page we find reference to Marx and Engels, the next two contain three citations from Stalin again. Later, a long survey of Russian contribution to the field is presented; Western inventors and researchers are mentioned only in the negative aspect (for instance, Watt is said to have reinvented his regulator 18 years after Polzunov). At that time, this was the mandatory requirement for any scientific book...

The content of the textbook under consideration is close enough to Aizerman's (see above), but the nonlinear part is lacking. There are also many simplified real-life examples, and a lot of pages contain figures of specific devices and regulators (Fig. 10 ).

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Some problems in the theory of stability of motion

N. N. Krasovski,

Moscow, Fizmatgiz, 1959 (211 p.)

There are several reasons to distinguish this book among many others, which are in between a research monograph and a textbook (such compromise was highly typical for the Soviet literature of that period).

The author is the founder of the famous Sverdlovsk (now Ekaterinburg) school on automatic control. It includes such prominent researchers as Yu. Osipov (President of the Russian Academy of Sciences), A .Kurzhanski (Head of the Russian National Committee on Automatic Control), the late Academician A. Subbotin and many others. It is worth mentioning that research activity in the Soviet Union was concentrated mainly in Moscow. However there were scientific centers beyond Moscow, and in the control field two of them were of the top level - Sverdlovsk and Leningrad (some research activity took place also in Kiev, Gor'kii, Kazan and other cities). The Leningrad scientific school (A. Lur'e, V. Yakubovich, A. Pervozvanski, V. Fomin, A .Fradkov, G. Leonov) has long traditions, going back to the brilliant St.-Petersburg mathematicians, while the Sverdlovsk school was created from the beginning, and the role of N.Krasovski is hard to overestimate.

The book (Fig. 11) is devoted to the stability of motion. This direction of research (originated by Lyapunov, as has been mentioned above) was highly popular in the Soviet literature of that period. Such publications as N. Chetaev, Stability of motion, Gostekhizdat, 1956; M. Aizerman, F. Gantmacher, Absolute stability of regulated systems, AN SSSR, 1961; V. Zubov, Methods of A. M. Lyapunov and their application, LGU, 1957; A. Letov, Stability of nonlinear regulated systems, Gostekhizdat, 1955; A. Lur'e, Some nonlinear problems in the theory of automatic regulation, Gostekhizdat, 1951; I. Malkin, Theory of stability of motion, Gostekhizdat, 1952; V. Pliss, Some problems in the theory of stability in whole, LGU, 1958; E. Barbashin, Introduction to stability theory, Nauka, 1967, played a fundamental role in the development of stability theory, and even among them the book under consideration takes a top-level position.

Indeed, the book contains a lot of facts and techniques available in stability theory by that time. They are presented in simple and explicit form. All the statements are accompanied with proofs; however, the style is very far from formal. Many new results are presented, among them the important Barbashin-Krasovski theorem on the existence of Lyapunov function, stability under disturbances bounded in L~ norm, stability of time-delay systems (Fig. 12) and so on.

Later N. Krasovski contributed to the theory of optimal control (see his book Theory of control of motion, Nauka, 1968), to game-theoretical approach to control and to many other areas.

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' .:.:...:~,:.

~. . ...,~.~,~::.~::.::,:::.....:~.e~ .:.~,~,:~;.~....~<~.~ ~

............ ~,..,~.~.

~:~:,~,,:~s,,~,~ ............................... ~... ................... ~

..

..

..

..

..

~

........................... ~. .................

...~ ................. ~

....... ~:~.:.~,:::,~,,,:::,:,~,~,~:::,::.

" ~

~ ~

o o

~ 4

= &

~ :;,':

? ~ ~

L ..

§

~ o

~, i -~

~ 1

Figu

re 12

232 R

ussia


SPAIN

Teoria de los Servomecanismos (Servomechanism Theory) Antonio Colino Published in 1950

Contributed by Javier Aracil

Escuela Superior de Ingenieros Universidad de Sevilla, Spain


Teoria de los Servomecanismos (Servomechanism Theory)

Antonio Colino Published in 1950

The first book published in Spanish (at least as far as I am aware) on what is known today as Control Engineering is Teorfa de los Servomecanismos (Servomechanism Theory) by Antonio Colino. It is well known that the field of Engineering that has come to be known as Automatic Control came about as a result of the study of a type of electromechanical feedback system, servomechanisms. It is worth noting that this book was published in 1950, just a few years after the first books on this subject came out in English (e.g. the classic Theory of Servomechanisms, by Hubert M. James, Nathaniel B. Nichols and Ralph E. Phillips, published in 1947).

Colino's book was an introduction to this new field of engineering for the Spanish-speaker scholar. He had to deal with the translation of new terms, especially feedback, for which he aptly proposed the Spanish word realimentaci6n. It should be mentioned that, since 1972, Antonio Colino has been a member of the Spanish Royal Academy of the Language, the most important Spanish linguistic institution. The prologue to the book was written by one of the most illustrious Spanish engineers of the 20 th century, Esteban Terradas, who perceptively pointed out how important automatic control would be for engineering in the 20 th century. Colino's proposal was accepted and since then engineers in Spain-automatic control engineers and electrical engineers alike- have used the term realimentaci6n.

This acceptance was based as much on the use of the term (which, ultimately, justifies a term's adoption) as its appropriateness given that the prefix re- in realimentaci6n means "once more". Some authors use the word retroalimentaci6n. I think, however, that realimentaci6n gives a better sense of what happens in this process. As realimentaci6n connotes, the system is fed again with the results of the actions previously taken. This is exactly what we want the term to represent; thus, I think Colino's proposal was excellent and that it demonstrates great awareness of the Spanish language.

Even today, the index of the book comprises the programme for an introductory course on the theory of automatic control of linear systems - specifically, on the classic methods based on the study in the frequency domain- and it includes the typical subjects for such a course: transfer functions and their graphic representations, stability criteria (specifically, Nyquist' s), and other such topics. The book was used as a textbook and from it the Spanish engineers of the 1950's learned the fundamentals of automatic control.

234 Spain


CONSEJO SUPIRIOIt DE INVESTIGACIONES CIENTIFICAS PATRONATO JUAN DE LA CI~I.VA

INSTITUTO NAC[OiqAL DE ELECI'RONICA

TEORIA DE LOS

S E R V O M E C A N I S M O S POR

A. COLINO In|emtero ludust r is

Con pr~logo de E. TERR. A D A S

v~,a,~ i r . . "'*- "41r "i

" �9 .~

M A D R I D z 9 5 o

Spain 235


I N D I C E

P~iginas

PR6LOC, O . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

I.---INTRODUCCI6N"

i. S~omeca~isrnos . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2. A ctuacidn de un servo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 3. Servo con er162 tacomk, trica . . . . . . . . . . . . . . . . . . . 19 4. Estabilizacidn con la derivada dd error . . . . . . . . . . . . . . 2 I 5. Cierre de la introd~ci6n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

II.--FUNDAMENTOS MATEMATICOS DE ~ TEORiA DE LOS SERVOS :

I. Sistemas l~neales e~ctromec(~nicos . . . . . . . . . . . . . . . . . . 25 2. Serie e integral de Fourier . . . . . . . . . . . . . . . . . . . . . . . . 26 3. Tra~ormada de Laplace . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 4, Soluci~n de un s i s t e ~ de ecuaciones ~ntegro.difere~v

cia~es 1nediante la tmnsformada dO Laplace . . . . . . . . . . . 30

5. ~ ~ f o r ~ d a s @ i c ~ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

III.---TEORiA MATEM.~TICA DE LOS SERVOS:

I. Composici6n de ~ [unciones de trammi 'bn . . . . . . . . . 33 2. Coefivientesde error . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 3. Estabiii, lad de un servo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 4. Trans[ormaci6n de repreuntaciones. . . . . . . . . . . . . . . . . . . 38 5. Crilerio de N ~ u i s t . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 6. Condic:wnes compte~nentavias ~ ta es t~ 'u tad de un

servo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 7. Otros ~n~todos para d estudio de Ia estabdidad y ac-

tuaci6n de un servo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

236 Spain


,,,,,,,,,.:. -::::~ : :~ .7 - -_=- - - -

! V . . . . r , , o m ~ ~ DE :~,$ SERVO~~N~OS"

z M~dor dd ~,~ 45 2 . ~ t ~ a . . . ........... . ............. . ......................... . . . �9 . . . . . . . . . 49 3- A ~ ~ s y ~ n ~ los ~ ~ t ~ ~ .... 5~

V : ~ T ~ z A ~ : D ~ D ~ G ~ M A DE NYQUisT"

I ~u~~s de t r a n ~ i ~ n 65

~ Nyq a . . . . . . . . . . . . . . . 6 8 2. del d:i ~ ~ de u t .. . . . . . . . . . : . . . . . . ; : . . . . . . ~ .~ i . ~ ~ :~ ~ : ~ , ,

3. ~ db y ? ~ s ~ log, ~ ............................................ 73 4. E! d '~yra~ ~ d i f w a d o de N y q ~ en cooHcnad~

db y ? 78 ..

\,: i ~ C o ~ E c c 6 s DE LOS SERV:~

~. C o ~ 4 n t l o n ~ s s ~ e d c m ~ o de ~ o s c ~ e c - "-t~es. .......... . ..... . ................. . .......... ............. ..................... :e3

~. ,C~ec~on de ~ ias f re~~c ias . . . . . . . . . . . . . . . . . . . . . ....... . . 84 3. ~ e c c i d n ,~ ~ ~ f r e ~ : ~ . . . . . . 86

~e'" . . . . ~ p l e 88 5- ~ ~ e c a ! ~ ~ s con c o ~ t t e alNrna . . . . . . . . . . . . . . . . . . . . . .... 91

6, Circuitos c~ectores con p~tadora . ............................ 93

AP~NDIC~"

.......... " a ~ ~ s 95 ]. T e ~ d e l o s . ........................ . . . . . . . . . . . . 2. ~ ~ en~e k a ~ n N n y ia fase ......................... 3 .... El ~ ~ o del ~ o ~ los ~ s ............................................... 97 4. ~ o s ~ t ~ o s por b n ~ s . . . . . . . . . . . . . . . . . .. ~

B x ~ ~ : F | A i O I ~, ~ ~ :~ ,~ ~ ~ .~, ~: .~: , , . ~ ,~ :~, ~ ~ ~ ~: .~ .r ~ ~ ~ :~ ~t ~ ~ �9 ~ ~ :~ ~ ~ :~ ~ ~ ~ ~t ~ ~ ~ :~ ~t ~t ,m: �9 �9 .~.

Spain 237


Tendremos en un s e ~ o ~ncil lo

O s = G e ; ~ - - 0, - - O,

luego en funci6n de la entrada se obtendr~

1 - I - G 8 , ~ 1 -+-G 0,

La funci6n Go ( P ) - - G (,p)

1-+- G (p) es la transmisi6n conjunta del ser-

vo, que liga la salida con la entrada, teniendo en cuenta los e fe~- tos de !a ~rea!imentaci6n.

r Servo con circuito ~ la reaIimentaci6n (figura 3.3)-

, ............. __:._ ,~..~ - . . . . . . . . . . . . . . . . . . . . :_.~

. . . . . . . . . . . . . . . . . . . . . . .

Fig. 3.3.--Se~o con circuito en la realimentacidn.

De la figura se deduce

0, = G1 ~ ; ~ - - 0 , - - - G2 0,

GI

Este tipo de servo no es muy empleado, porque p u ~ e producit error ~ r m a n e n t e (v~a~ la teorla de e r ro r~ en i ~ servos).

~) Ser,Jo c ~ doyle 1,eatimentaci6n.~Este t i ~ de ~ r v o es mucho m~is empleado ( r~u~rd~e la ~mbilizaci6n con t ac~ metro). (Figura. 3.4.)

~ It 0 ' J - ~ ...... "~ . . . . . . . . . . . . . -----~L_ ~ I

?

.

Fig. 3.4,~erpo c ~ dob!e realimentaci6n.

34

238 Spain


/ p~mo p

_

Fig. 3.7.--Diagrama de Nyquist.

En resumen: el criterio de Nyquist permite simplemente,

trazando el lugar geomdtrico de G (oj), conocer si un servo es

estable o inestable, segdn encierre o no el punto - -1 . Pot ser

G (p) una funci6n de p con coeficientes reales G (to 2) y G (--of),

son sencillamente conju~adas, y basta trazar G ( ~ ) d - o~ -- 0 a = ~o ya que la figura de ~ = o a ~u = --- ~ es ta mera i, magen

de la curva anterior en el eje real.

Hay clue hacer observar que G (t~j) no es m~.s que la res-

puesta a una funci6n exponencial e/t~ty, por lo tanto, inedible

experimentalmente en sus dos componentes de amplitud y fase,

Io que permite el trazado experimental del diagranm de Nyquist

de un servo ya construido. 6. Condiciones complementa.rias a ta de estabilidad en un

servo.--Para enjuiciar la actuaci6n de un servo no es sufir conocer si es o no estable; es ademtis precis<) conocer otras ca- racterlstieas, eomo son el tiempo de formaci6n de la salida, forma de dsta, etc.

En realidad, para llegar a un conocimiento exacto seria pre-

ciso hallar la inversi6n de

G(p) e, (t) e, i + G(;)

39

Spain 239


240 Spain



SWEDEN

Reglerteori (Control Theory) Laszlo yon Hamos Svenska bokf6rlaget Bonniers. Stockholm 1968.

Reglerteori (Control Theory) Karl Johan Astr6m Almqvist \& Wiksell, Stockholm 1968.

Contributed by

Karl Johan Astr6m

Lund Institute of Technology Lund, Sweden


242 Sweden


Reglerteori (Control Theory)

By Laszlo von Hamos Svenska bokfiirlaget Bonniers. Stockholm 1968.

Swedish education in automatic control began in 1949 at the Royal Institute of Technology (KTH) in Stockholm. The first courses were given by Laszlo von Hamos, who worked for the Robot Weapons Bureau (Robotvapenbyr~n) at the Swedish Air Force. Laszlo von Hamos became the first professor of automatic control in Sweden in 1959. He also the Swedish representative who signed the Heidelberg resolution that led to the creation of IFAC. The control group at KTH had two experienced teaching assistants, Gunnar Attebo from K~ille, a Swedish process control company and Bengt Sj6berg from Saab Aircraft. The broad industrial base of the teachers gave a sound industrial perspective inspired from both aerospace and process control applications. The course was also complemented by laboratory exercises.

The book Reglerteori developed from the course material that von Hamos taught at KTH since the early 1949s. The book has 18 chapters: Introduction. Classification of control systems. Analysis of control systems by solving differential equations. Alternative ways to describe dynamics of feedback loops. Differential equations for control components. Combination of linear blocks. Graphical representations of transfer functions (Bode, Nyquist and Nichols plots). Overview of dynamical properties of blocks with simple differential equations. Methods for computing transient responses. Algebraic stability analysis (Routh-Hurwitz criteria). Root-locus. Stability analysis based on transfer functions (the Nyquist theorem). Static accuracy. Dynamic accuracy. Improvement of system properties (compensation). Overview of nonlinear systems. Simulation using analog computing. Overview of advanced control methods (multivariable, adaptation, optimization, learning, computer control). There are appendices on Laplace transforms and exercises. In recommendations for further reading there are references to the textbooks by D'Azzo and Houpis, Dorf, Naslin, Oppelt and Takai. The book gives a good coverage of classical control theory emphasizing modeling in terms of block diagrams and Laplace transforms, design based on root locus, Bode and Nichols charts and simulation based on analog computing.

It is interesting that in the early 1950s there was a controversy among the teachers at KTH about the best way to teach dynamics of linear systems. One professor in electromagnetics was a strong advocate of the Heaviside operation calculus, other professors in mechanical engineering advocated the Laplace transform. A hybrid, called the s-multiplied Laplace transform was also used by one professor. A reflection of the controversy was that von Hamos used the variable p instead of s as the argument of the transforms.

Sweden 243


o

i i -

O~:t i O,m "]

0, . - - - 8

--12

0,1:- - 44

-..t5

*-t6

Fig. 7" 1I. Nichols-d:iagram reed kurvskaror ]6r konstan:t M i dB och konstant N i grader. Kurvan G~ h~rr6r #dn typexempel 3:2 sd att ]iguren iir en motsvarighet till fig, 7: 5.

s~edes endast fita G0(jo~) p~ ett genomskinligt papper och trans- latem bladet pamnellt reed In [Gl-axeln fills Go-kurvan kommer att beam M-kurvan med det 6nskade v~det. AnmRrkas b~Sr, art kurvan Go l~mpligen konstrueras i ett Bode-diagram p~ ovan angivet s~tt, varefter den 6verf6rs till Nicholsdiagrammet.

!02

244 Sweden


Sweden 245


Reglerteori (Control Theory) o

By Karl Johan Astr~im Almqvist \& Wiksell, Stockholm 1968.

o

Karl Johan Astr6m was appointed professor in Automatic Control at the newly established engineering school Lund Institute of Technology in 1965. Prior to that, he had worked for IBM Research under Jack Bertram, a class-mate of Kalman, Franklin and others from Columbia University. Returning to university/kstr6m carried with him early experiences from computer

o

control and a perspective on the American university scene. Returning to the university Astr6m developed a new course in control that integrated classical control with the emerging state space approach. The advantage with such an approach is that it introduces two key approaches to control in a unified framework. The course was supplemented with exercises, and laboratories that were integrated with lectures. A book based on the new course was published in 1968. The book has five chapters: Introduction, Dynamical Systems, Reachability and observability, Analysis of Feedback Systems, Stability and Design. The introduction paints a broad perspective on control, its ideas and practical application. The section of dynamical systems starts with state space models and continues with input-output descriptions. The treatment of reachability and observability leads up to Kalman's representation theorem which gives a nice way to present the classical difficulty of pole-zero cancellation. The chapter on analysis presents classical concepts of sensitivity functions, Bodes relations and error coefficients. Stability is treated both from the Lyapunov point of view and as input-output stability. The particular methods include Routh- Hurwitz criterion, root-locus and the Nyquist theorem, practical stability and margins are also discussed. The chapter on Design treats specifications and control system design both from the viewpoints of classical compensation as well as state feedback and observers.

246 Sweden


6 : 5

) ) ~ ~ t _ . _ . j " i ~ " ! i ) _. ! - 7 i,,' I.' I i a

i ) , ~ __ �9 I li 1 . . . . . . . - 7 " : - ~ ,~ ;~ u �9 x i Y

I I ' ~ ~ ' " ~ " ~ " ~ ~ " ~ I ~ ] I : I

Fig. 5.1. Block~hem f6r en ~ t o r ~ r ~ pb ~ p p l i n g och rekonstr~tion av icke mittbara tiUstAn~variabler m~ eft ~ ~ f l ~ r .

d BL

u . . . . ~ +L~' + u" +./~' (&25)

Vi firmer ~ledes att det s l u ~ ~ s ~ e t ~ ~v o ~ g ~ 2n. S ~ m e ~ ~ler &r e g ~ r d ~ ~ mstrisem~ A - B L och A - K C . ~ t f61jer ~dare av (5.25) att tillstAndet ~ ej ~r styrbart rare sig ~ u T en~ x r. J~mf~r reed ~ a l ~ n i a v e r t 3:6. ~ moder sore genereras ~d ~ o ~ t m ~ o n e n av ill.tAn&. vafiable~ ~ ~ 1 ~ ej st~bam.

Enligt Kalmans uppdelninguats (sats 3:6.1)k&n det ~terkopplade systemet uppdelas p& det s~tt sore ~ i fig. &2. ~ignal-ut~gnal .re~onen ~ ~' och z' till y ges av

r(8) = o [ a I - A + BL]-~B[U'(a) +LX'(a)]

0ved6ringsfunktionen ~r sAledes entydi~ best~md a v A, B, C och L. Den heir o ~ n d e av h ~ m~W~en K v~js. Man kan ~ att a ~ o g a ~r~llanden g&l!er oavsett hut t i ~ n d s v ~ a b l e r n a r e k o ~ e ~ , ~ moder sore ird6rs i observeraren blir alltid icke styrbara.

Den regulatorstrukmr ~m visas i fig. 5.1 ~ m ycke~ flexi~l. Den k ~ o c ~ anv&ndas ~d reglering av fle~a~_abla system. F6r art dimen~on~ regtflatom kr~vs kunskap om m a t n ~ A, B och C, sore kan erh~l~ ur en matematisk modell av processen. Vidare m~te m&t~rna K oeh L best~mmas. F6r eft s t y r ~ s~tem m ~ en i ~ ~ l get ~ 5.1 ett L ~ n t art det slutna s ~ m e t f~r ~ a poler. Det finns ock~ ut~dgningar av sat~ 5.1 till tier. variabla system. Val av ma~sen K p&ver~ ejdet slutna sys~mets 6vet-

9,- As~r6m: ~l~ori 257

Sweden 247


248 Sweden



SWITZERLAND

Die Regelung yon Dampfanlagen (Control of Thermal Power Plants) Paul Profos Springer-Verlag Berlin/G6ttingen/Heidelberg 1962

Contributed by

Adolf H. Glattfelder and Walter Schaufelberger

ETH (Federal Technical University) ZLirich Switzerland


Die Regelung von Dampfanlagen (Control of Thermal Power Plants)

Paul Profos Springer-Verlag Berlin/Giittingen/Heidelberg 1962

Paul Profos received his Diploma Degree at ETH in 1936 and his Ph. D. in 1943 with a dissertation on "Vektorielle Regeltheorie". In this early work, he used vectors in the complex plane and frequency response techniques. Paul Profos worked for about twenty years in industry, already during his Ph. D., with Sulzer Brothers Limited. He joined ETH in 1958 as Full Professor.

In his book on "Control of Thermal Power Plants" he summarises the practical and theoretical work done in industry with the goal to make it explicitly available to practicing engineers.

The motivations to this book were the rapid changes in the construction of thermal power plants from 1945 to around 1960. It marks the transition from traditional drum boilers with natural circulation to once-through steam generators which opened the way to a substantial increase in steam pressure, steam temperature and steam mass flow and thus in unit power output. However, such once-through steam generators could no longer be operated safely in manual control mode, but required a high performance control system. It could no longer be designed by the traditional rules of thumb, but required a systematic approach based on mathematical models.

A key case was the super-heater control. As the steam temperature came close to the limit of the materials, dynamic responses became much more critical. Aging or the threat of ruptures required better theoretical insight and consequently Profos developed his "kappa-D" theory to improve temperature control. Possibilities of oscillations and instability in other parts of the plant (evaporators, parallel tubes) were also investigated. Already at that time, control engineering was seen as an integrating technology.

Soon after the book appeared, systematic simulation studies performance of the controlled systems.

became routine in order to guarantee

The book focuses on modelling. Its main elements are transparent physics, and well chosen assumptions leading to simple mathematical models. They are given as low order differential- difference equations and/or transfer functions. The control systems are described by structures and block-diagrams where Profos uses the then new IFAC graphic symbols. Typical controller settings and simulations of closed loop responses are not presented, as the needed technologies were not yet available at the time.

The book is addressed to practicing engineers and advanced students and quickly became the standard in the field. It adheres to the slogan of Profos "Es gibt nichts praktischeres als eine gute Theorie" (,,Nothing is more practical than a good theory.").

250 Switzerland


Die Regelung von Darnpfanla gen

Von

Dr. Paul P rofos o. P r o f e s s o r

a n d e r E i d g e n S s s t s c h e n . T e c h x ~ s c h e n : H o e h s e h u l e Z~ i r i ch

Mit 320 Abbildungen und Tabellen

i

S p r i n g e r - V e r l a g B e r l i n / G ~ t t i n g e n / H e i d e l b e r g

1962

Switzerland 251


7.3 Dyn.amise, hes Verhalten von Vorw/irnler- und l.:~bert~itzersystemen 167

n e b e n a b e r alle n o c h ein G h e d e n t h M t e n , das die s c h o n Ir f iher er- w ~ h n t e k o m p l i z i e r t e t~ranszendente , , F ( r m f u n k t ~ o n n u n in de r B i l d u n g

F = - 1 - - ~ . D I . + ~ , - - e (7.145) e n t h ~ l t (~" = 1).

Die A n w e n d u n g der L , ~ L A c E - R f i c k t r a n s f o r m a . t i o n d a r a u f l iefer t (fiber d ie ~ s u n g y o n F a l t u n g s i n t e g r a l e n )

9, [/] ~--- L.-:' {/~"} = e - ~ D - r J0 (2 | , / ~ ) + f J0 (2 V d � 9 (7.146) o ..

Die d e r i n e n t h a l t e n e B E S S E L - F u n k t i o n Jo i s t n u r f iber e inen Tei l des p r a k t i s c h ben .6 t ig ten A r g u m e n t b e r e i c h e s t abe l l i e r t . Ff i r den f ibr igen Be re i ch s ind R e i h e n e n t w i c k l u n g e n zu H i ~ e zu n e h m e n .

Die dc r Form/unktion e n t s p r e c h e n d e T e i l f i b e r g a n g s f u n k t i o n legg i m w e s e n t t i c h e n d e n Ver l au f de r U~bergangs funk t ion be i T e m p e r a t u r -

e S 0 , 5 , i "~ .................... : ............... 9 .............................. i ~ .........

O lO 20 25 r~Ke. t

Ab.b. 7 .40 S e h a r d e r t ' . ~ b e r g a n g s f u n k t i o n e n , e n t s p r e e h e n d d e r F o r m f u n k t i o n ~,xz(t), mi t ~:b a l s P a r a m e t e r

s t 6 r u n g les t . Sie ist , a n a l o g d e m F r e q u e n z g a n g der F o r m f u n k t i o n , n u r . . . . . . . . . . v o n d e m einzigen Parameter :~.D abh/ingig.: Es l~Bt, s ich d a h e r a u c h h ie r die G e s a m ~ h e i t der a u f t r e t e n d e n Te i l f ibe rgangs fu I~k t ionen ( lurch eine ~ : _ - ---2)[~ ....... FH [rl

in A b b . 7.40 fi ir bezogenes Z e i t m a 6 _K_____

d a r g e s t e U t " . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ~ . . . . . . . . . . . . . . . . . . . . - - - : : : : : : : : :::

Z u r B e r e c h n u n g de r ~ b e r g a n g s - 2 'r �9 ~ , _ ~ funkCion fi ir T e m p e r a t u r s t 6 r u n g ist: a . b b . 7 .41 B l o c k : s e h e r t l a z u r :Bildung d e r

n u n n o e h :die d e m Te i l f r equenz - { ? b e r g a n ~ f u . n k t i o n f t i r Tempera:turstfrun~ . . . . . . . . a u s d e n T e l i f l b e r g a t t g s f u n k t t o ~ t e n 7.,~.(t)

g a n g a~ (s. G1. (7 .135) )en t , s p r e c h e n d e ~nd :.,Hr Te f l f i be rgangs funk$ ion YI [t] zu ber t ick- sicht, igen. Diese h a t - - w i e be re i t s bei de r B e t r a c h t u n g .des F r e q u e n z - g a n g e s k.onstat ier~ - - r e inen T o t z e i t c h a r a k t e r (vgl. Abb . 7.41).

252 Switzerland


TURKEY

Servomekanizmalarin Prensipleri Translation of Principles of Servomechanisms

G. S. Brown and D. P. Campbell, John Wiley, 1948 ml

Translated by M~inir UIg~ir Istanbul Technical University, 1962

Otomatik Kontrol Ders Notlari (Automatic Control Course Notes)

=m

Mehmet Nimet Ozda,~ Istanbul Technical University, 1978

Contributed by

A. Talha Dinib~it~in

Do~lu,~ University Istanbul, Turkey


History. Education in Automatic Control in Turkey started about 50 years ago at Istanbul Technical University (ITU). In 1953, Prof. Mtinir Olgtir started teaching the course "Servomekanizma" at the Faculty of Electrical Engineering at ITU. In 1955, Prof. Mehmet

, ,

Nimet Ozda~ started teaching the course "Automatic Control" at the Mechanical Engineering Faculty of ITU. At that time, there were no textbooks written in Turkish for these courses. Both professors, therefore, initially prepared and used their personal course notes, and those students who knew foreign languages made use of relevant textbooks written in foreign languages.

Servomekanizmalarin Prensipleri

Translation of Principles of Servomechanisms G. S. Brown and D. P. Campbell, John Wiley, 1948

e e

Translated by Miinir Ulgiir Istanbul Technical University, 1962

Professor Ulgtir recommended the textbook "Principles of Servomechanisms by G. S. Brown and D. P. Campbell, John Wiley, 1948" to his students who knew English. He later translated this book and had it printed by ITU in 1962. Starting in 1962, he used this book as a textbook for the course "Servomekanizma". The first textbook in the field of Automatic Control in Turkish to be used in Turkey was this translated book.

The Turkish title of this 400-page textbook "Principles of Servomechanism", translated by Prof. Olgtir is "Servomekanizmalarin Prensipleri" and it is a 427-page book.

The contents of the translated textbook are the same as the original one. The main titles of these contents are:

1. Outline of Subject

2. Dynamics of Elementary Control Systems

3. Transient Response Using the Laplace Transform

4. Sinusoidal Response of Closed-Loop Systems

5. Systems Diagrams, Equivalent Circuits and Block Diagrams

6. Introduction to Synthesis, Determining the Gain Constant K

7. Methods of G Function Synthesis- Linear Coordinates

8. Methods of G Function Synthesis - Logarithmic Coordinates

9. Systems Subjected to Multiple Disturbances

10. Experimental Studies in Servomechanisms

11. Method for Approximating the Transient Response from the Frequency Response

Table of (sin x)/x

Problems

Bibliography Index

254 Turkey


T. C~ iSTANBUL TEKNIK tJN|VERSITESI

Kt)TDPHANES|

Sayl : 492

S E RVOME KA N iZMA LA RI N i PRENS PLERi

Kapall.(~evrim Konfrol Sisfemlerinin Dinamikleri ve Senfezleri

YAZANLAR: GORDON S. BROWN, PROFESSOR OF ELECTRICAL ENGINEERING

DIRECTOR, SERVOHECHANISHS LABORATORY MASSACHUSETTS INSTITUTE OF TECHNOLOGY

DONALD P. CAHPBELL, ASSISTANT PROFESSOR OF ELECTRICAL ENGINEERING MASSACHUSETTS INSTITUTE OF TECHNOLOGY

(~EVIREN :

H. HONIR OLGOR, PROFESOR. ELEKTRIK FAKOLTESi. JSTANBUL TEKNIK CINIVERSITESl

BERKSOY MATBAASI ISTANBUL -- 1 9 6 Z

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Otomatik Kontrol Ders Notlari (Automatic Control Course Notes)

o o

Mehmet Nimet Ozda~

Istanbul Technical University, 1978

Professor Ozda~ developed his personal course notes and then the Mechanical Engineering Faculty of the Istanbul Technical University printed those notes under the title "Otomatik Kontrol Ders Notlari" in 1978. This was the first printed material in the Turkish language for automatic control education.

Otomatik Kontrol Ders Notlari is 254 pages long and contains 262 figures and 5 tables. The main section titles are"

1. Introduction to automatic control

2. Modeling of dynamic systems

3. Transient response analysis

4. The Laplace transform

5. Analog computers

6. Measurement

7. Comparison

8. The controller

9. Performance of closed-loop systems

10. Frequency response methods

11. Closed-loop frequency response

12. The stability of linear feedback systems

13. The Root-Locus Method

14. The Nyquist Criterion

15. Performance criteria

Turkey 257


i.T.O. MAKiNA FAKOLTESi OTOMATIK KONTROL

eo o l

KORSUSU

OTOMATiK KONTROL DERS NOTLARI

Prof. Dr. M. ~limet OZDA$

i.T.U. MAKiNA FAKOLTESi OFSE T ATOLYESi

1978

258 Turkey


Su halde ampl i t i id le r orant IGi i elde etmek i~ in , Io9ar i tmik diyagram da her b i t te r im in cebr ik toplam0 altnacak demektir.

g ib i t e r i a l e r i n yukaroda b e l i r - a+ j c ~ : 2

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260 Turkey



UNITED KINGDOM

An Introduction to Servomechanisms Porter, A., London: Methuen, 1950, 1952, 1954, 1957

An Introduction to the Theory of Control in Mechanical Engineering Macmillan, R.H., Cambridge, England" Cambridge University Press, 1951

Servomechanisms

West, J.C., London: The English Universities Press, 1953

Contributed by

Stuart Bennett

The University of Sheffield Sheffield, United Kingdom


An Introduction to Servomechanisms

Porter, A., 1950, London: Methuen. (Second edition 1952, reprinted 1954 and 1957)

This was the first text book on control systems published in the UK and it was widely used on university and technical college courses. Arthur Porter, an influential figure in the development of automatic control in the UK during the 1940s, served as secretary to the Servomechanisms Panel, a wartime government organization responsible for coordinating work on servomechanisms [1]. As secretary to the panel he was aware of the major developments in the UK and met most of leading control people including Arnold Tustin, A L (John) Whiteley, L. Jofeh and Frederic C Williams. Immediately prior to the war Porter had been awarded a Commonwealth Fellowship which enabled him to spend two years working at MIT with Vannevar Bush's group. And in the early part of 1945 he spent some time in the USA gathering information for a government report on industrial applications of automatic control [2].

Porter, like Harold Locke Hazen and Gordon S Brown, had come to control systems through his involvement with the building and operation of differential analyzers. He recalls that in 1932, as an undergraduate reading physics at the University of Manchester, he read a paper by E C Bullard about solving second order differential equations using a moving coil galvanometer and decided that for his final year project he wanted to do something related to "calculating machines" [3]. Douglas R Hartree had recently returned from a visit to Bush at MIT and wanted to build a mechanical version of the Bush differential analyzer and Porter's interest was welcomed" he was given the task of building a capstan torque amplifier. His involvement with the differential analyzer continued during his MSc and PhD and his interest in control was strengthened through an enquiry from Albert Callender of Imperial Chemical Industries about using the differential analyzer to solve equations relating to automatic control of temperature in a chemical process.

On returning to the UK, in 1939, he had hoped to join P M S Blackett, then at Manchester, but was directed instead to join the Admiralty Research Establishment at Teddington, he subsequently moved to join B lackett's Operational Research Group and then in March 1942 was made head of the fire-control section at the Air Defence Research and Development Establishment at Malvern.

In 1946 he was appointed as Professor and Head of Instrument Technology at the Royal Military College of Science (RMCS), Shrivenham, and it is from this period that the text book emerged. In 1946, with L Jofeh, he gave a series of lectures on servomechanisms at Northampton Polytechnic Institute in London and at the RMCS he gave a course on servomechanisms to second year students studying Engineering Physics. These lectures formed the basis of the book. The first edition of the book had eight chapters: Closed-sequence control systems; Basic equations of linear servo systems; Transient and steady-state behaviour; Harmonic response diagrams; Lag correction and stabilization; Notes on some non-linear problems. In the second edition a chapter on Digital Servomechanisms was added. He avoided the use of the Laplace transform because he wrote "...it tends to surround the subject with a mathematical cloak which

262 United Kingdom


sometimes mystifies rather than clarifies", instead he used an "essentially classical treatment" with an emphasis on physical principles.

The structure of the book is one which was to be followed many times in subsequent years: system modelling, transient and steady state behaviour; frequency response; methods of compensation and stabilization; and some discussion of non-linear systems. In dealing with transient and steady state behaviour he covers classical and operational methods of solution and error classes and also, not surprisingly, suggests that the differential analyser and the newer forms of electronic servo-simulators are valuable means of determining transient behaviour.

The section on harmonic response covers the use of the "response vector locus" diagram (Nyquist) and the "log-gain" diagram (Bode), and he mentions the use of the inverse response vector diagram. He uses the diagrams to deal with stability and gain and phase margins but does not mention M and N circles or the Nichols approach. When it comes to modifying the system to improve performance he covers "lag compensation by pre-correction" i.e. feed-forward; "integrals of correction" i.e. use of a lag network; "derivatives of correction" i.e. lead network; and "subsidiary loops". The favoured method, in Britain, for stabilising and modifying servosystem performance was the use of subsidiary feedback loops which "provide a powerful method of stabilizing servo systems" Porter argued, and which can be used to "compensate dynamic lags", "stabilize the system" and "increase the speed of response" and such systems used feedback signals from generator field windings or a tachometer generator.

The addition of servo-control to previously manually operated systems during the early years of the war had quickly shown up problems of non-linear behaviour arising from static friction, saturation of amplifiers and servo-motors, and backlash in gearing throughout the loop. The chapter on non-linear problems derives from work on these problems" the major contributions made by Tustin and the several studies of the problems were done on the differential analyser at University of Manchester are mentioned.

Although Porter's book remained in print and was in use until the 1960s it dated quickly with respect to methods of analysis and design. As a text book its value was in some of the descriptions and modelling of components and in the physical insight into the behaviour. I also think on re-reading the book that what must have come through to students was the enthusiasm and authenticity of the author: this is a book written by someone who had struggled to make things work and knew intimately the problems and limitations.

Before publication of the book, Porter left RCMS and took up the post of Director of Science Research at Ferranti Ltd, Canada. He returned to England briefly in 1955 when he took up the post of Professor of Light Electrical Engineering at Imperial College, London returning to Canada in 1958 as Dean of Engineering at the University of Saskatchewan. In 1961 he took up the post as Head of Industrial Engineering at the University of Toronto which he held until 1975. From 1975 until 1981 he was chair of the Royal Commission on Electrical Power Planning, Ontario.

[1] A. Porter, "The servo-panel - a unique contribution to control systems engineering, Electronics and Power, pp. 330-333, 1965.

United Kingdom 263

[2]

[3]


A. Porter, "The application of control systems in industry," Ministry of Supply, London Interdepartmental Committee on Servomechanisms Publication 2, October 1945. A. Porter, "Building the Manchester differential analyzers" a personal reflection," lEE Annals of the History of Computing, pp. 86-92, 2003.

264 United Kingdom


I n t r o d u c t i o n to

S E R V O M E C H A N I S M S

by

A. P O R T E R M . S c . , P h . D .

Professor of Light Electrical Engineering at the Imperial College of Science

W I T H 79 D I A G R A M S

L O N D O N - M E T H U E N & C O . L T D .

N E W Y O R K - J O H N W I L E Y & S O N S , I N C .

United Kingdom 265

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An Introduction to the Theory of Control in Mechanical Engineering

Macmillan, R.H., 1951, Cambridge, England: Cambridge University Press.

Robert Hugh Macmillan graduated in 1941 from the University of Cambridge in Mechanical Engineering Sciences. He then served in the Technical Branch of the RAF until 1947 when he joined the staff of Cambridge University where he established a small control research group which he directed until 1953 when he was succeeded by John F Coales. In 1946 Macmillan had attended the series of lectures on servomechanisms at Northampton Polytechnic Institute in London given by Arthur Porter and L. Jofeh. This book appears to have been written during 1948-9 in that, although not published until 1951, the preface is dated 1949. Porter read the first draft of the book and Macmillan acknowledges the help received. The style of the book and the author's voice is that of an academic: it is clear that Macmillan had studied carefully the literature on the subject, and attempted to draw from it, as he states in his introduction, "the methods, principles and philosophy of control" rather than being concerned with "specific applications." He says that he has not made any attempt "to include those facts and figures which would be necessary...to provide a handbook for the technician or the designer."

As he was teaching students who were studying Engineering Science it is no surprise he argued that all engineers should study automatic controls and that "the theory of control...by touching upon so many branches of applied engineering science...acts as a unifying influence, which is welcome in these days of excessive specialization." He comments that "once the basic principles have been grasped" then the methods of analysis can be widely applied even to such diverse subjects as "economic controls and the control of infectious diseases." By way of an explanation of the title Macmillan says that he has used examples largely drawn from mechanical systems because electrical systems "...tended to monopolize the present literature."

In arguing for a study of the theory of control he writes:

"There seems...to be a regrettable tendency amongst some practising engineers to regard the mathematical analysis of control systems with distrust; they prefer the 'common sense and experience' to a careful examination, although practicable methods of making such a study have now been available for some years. This attitude is perfectly reasonable provided that only a low standard of performance is demanded of the controls used; but as soon as we wish to attempt to find the best possible controller for a given job, exact analysis becomes essential. The apparent obscurity of control theory can be attributed largely to the early specialist control engineers who succeeded in surrounding much of their work with an aura of mystery, enhanced by an excessively illogical and confusing nomenclature..."

And then succinctly he lays out the aims in studying the theory of control"

"...the first is to gain a clear understanding of the mode of operation of such controls; the second is to enable us to estimate the performance of a proposed control system; and the third is to gain some insight into the design of a control which will attain a specified performance."

And indeed the book does meet these aims.

The first five chapters, using simple mathematics, no more than that required to solve simple differential equations with constant coefficients, provide the reader with all that is needed to

United Kingdom 267


model and determine the stability, transient and harmonic response of simple control systems; and because he also explains, with a numerical example, Whiteley's standard forms, the reader has some guidance on the values of the coefficients needed in order to obtain an acceptable performance for systems of various class and degree. Throughout he uses, as an example, a hydraulic control system described by the equation

D( I +D /8)( l +D /12) 0o - KO where 0= 0/ - 0o

and I remember that when I was a student we did numerous examples on this system and it commonly appeared in examination questions.

In chapter 6 he covers the use of the harmonic response function and provides an introduction to the use of the Laplace transform. In the final chapter he gives a graphical method for finding the roots of the characteristic equation, the use of the harmonic response locus, the inverse harmonic response locus, amplitude and phase plots and, although he does not use the term, Nichols charts. In using the harmonic response locus he shows how to use M and N circles. The book ends with a short but informative historical survey, an extensive bibliography and appendices on complex numbers and the Laplace transform.

The book was reprinted in 1955 and it remained in widespread use until the middle of the 1960s.

In the academic year 1950-51 Macmillan was a Visiting Assistant Professor at MIT and in 1955 he gave a series of talks on Automation in the BBC programme "Talking about Science"; he also gave a series of popular lectures at the Royal Institution. These talks and lectures were subsequently published, in 1956, as a book Automation: Friend or Foe? [1]. Macmillan was appointed as Professor of Mechanical Engineering at the University of Swansea in 1956 and in the early 1960s joined the Motor Vehicle Research Association as its Director. He was an editor of the first volume of the series Progress in Control [2].

[1]

[2]

R. H. Macmillan, Automation: Friend or Foe ? Cambridge: Cambridge University Press, 1956. R. H. Macmillan, T. J. Higgins, and P. Naslin, "Progress in Control Engineering," in Progress in Control Engineering, vol. 1. London: Heywood and Company, 1962.

268 United Kingdom


A N I N T R O D U C T I O N TO

THE T H E O R Y OF C O N T R O L

IN M E C H A N I C A L ,

E N G I N E E R I N G

BY

R. It. M A C M I L L A N Lecturer in the Engineering Department of th~

University of Cambridge

Ill

C A M B R I D G E AT THE U N I V E R S I T Y P R E S S

1955

United Kingdom 269


w 30] MODIFIED FORMS OF RESPONSE LOCVS 155

Cartesian co-ordinates; the resulting locus has # as the variable frequency parameter. On such a chart one can draw contours of constant M and r (just as on the Nyquist diagram); the form of these contours is shown in fig. 30.5, which is, of course, another transformation of the Nyquist or Y-plane.*

We can very easily determine the change of loop gain necessary to make the locus tangential to any required M contour, thus giving the desired maximum overall dynamic magnification. It is only necessary to shift, the locus parallel to the 2 axis by the required amount; in practice it is convenient to have the chart of fig. 30-5

3o[, r r l r ~ I r r r r i For sa t i s fac to ry | I u" I p~ I

10

8 " , " "', ---=;

--- I 0 ,' ~ \ ', '

-90 ', t

I / / ,' , , ,, ', "30 / / t - 1 5 0 ,

-- 20 ~ a - 120 - 6 0 '

I ! , i ! I I ' ' ' ' --L'f

I .: 1 t : , t , , , , -30 ' ~ L J. _ _ _ _ _ . i ~ . ' ' ' '

- 2 . - ~ - ~ - ! ;~. 0

Phase sh i f t

Fig. 30.5. M and r contours on the h ~ diagram.

plotted on a transparent overlay, so that the appropriate gain can be found instantly by trial. The condition for stability on the Cartesian #~r chart is that the locus shall cross the ~ = n line below the point h = 0 (i.e. where h is negative); if it does not do this Mmax. would become very large.

Yet one other way of plotting the harmonic response function has been used; here the/~# and ~/z graphs are replotted with h and ~k as polar co-ordinates instead of Cartesian, as in the diagram which we have been considering. The result is a Nyquist locus with I Y(i(~ to a logarithmic scale (i.e. attenuation rather than amplification is used for the radius); such a locus has certain advantages over the direct form of Nyquist diagram, but we shall not discuss them as the polar #l/r locus is seldom used.

* I t has recently been pointed out by MacLellan that if the scales used for the ~r plot are such that equal lengths are used for 9 db. and 60 ~ then the graph is an orthogonal transformation of the Y(ioJ) plane. When using those scales it is thus possible to construct from the ~ = 0 contour an orthogonal grid of u and w contours, to determine the transient response of the system.

270 Un i t ed K i n g d o m


Servomechanisms

West, J.C. 1953, London: The English Universities Press.

John Clifford West wrote this book as a text for undergraduate university students while a lecturer in the Electrical Engineering at the University of Manchester. He graduated from the University of Manchester in 1943 and served in the RNVR until 1946 when he returned to Manchester as a lecturer. In 1947 he gave a final year undergraduate course in control~the first undergraduate course in the subject in the UK. He was encouraged by the then Professor of Electrical Engineering, Frederic Calland Williams, to start a small servomechanisms laboratory and one of the first research topics Williams proposed was the position control of a rotating magnetic drum for use as a memory store for the digital computer.

Before the war, Williams, together with Arthur Porter, had worked on curve follower input devices for the Manchester University Differential Analyser. During war Williams, who was a practically minded inventor as well as an academic, worked for the Telecommunications Research Establishment on a number of aircraft tracking problems. One of his inventions was the Velodyne- a dc motor and tacho-generator combination which can be used for accurate position and speed control. It was used in position control systems for small radar sets and also as an integrator in electro-mechanical analogue computers. After the war, Williams became interested in the embryonic digital computing and he was a leading figure in the development of the Manchester computer. Commercialisation of the computer required the provision of back up storage mechanisms.

With this background it is not surprising that the West book introduces automatic control through electrical drives for position and speed control. The first five chapters proceed at a gentle pace with considerable emphasis on the student gaining an understanding of the physical behaviour. Very early in the book he introduces the student to the use of the phase-plane diagram~it is used in the first instance to explain the effects of coulomb friction. And throughout the book he reminds the student that the linear equations used in the analysis do not provide a full description of the behaviour of real systems, for example, he writes:

"In practice there are limits and saturation effects. A servo-motor has a maximum torque, it has therefore a maximum acceleration. It has also a maximum safe speed which must not be exceeded in designing the system. The amplifiers also work within amplitude limits, beyond which there ceases to be a linear relation between input and output. The output power that the amplifier can deliver to the motor is also limited. These factors cannot enter into the simple linear equations, but they play an important part in the performance of the systems." [p. 72]

West briefly mentions the classical methods of solution of differential equations but quickly moves to a simple treatment of the servomechanism as a "network" and explanation as to how a network can be described by a transfer function r where p - o'+ jco. He then observes that in the rest of the book it will not "be necessary actually to solve the differential equations." There then follows a standard treatment of stability using Routh-Hurwitz, and the frequency response approach with an explanation of the Nyquist criteria. He also

United Kingdom 271


272 United Kingdom


explains the use of the gain-frequency diagram (he does not refer to this as the Bode plot although he references Bode's work). He explains clearly gain and phase margins and minimum phase networks.

The next chapters (11 and 12) lead the reader through the different methods of dealing with the problems of speed control, and in particular 'droop'. And with methods of reducing droop including integral action and the use of PID control. The effect of integral action 'wind-up' is described. Then follow chapters covering measuring devices, static amplifiers, rotary amplifiers and servo-motors. At first glance these seem to be standard treatments describing the devices and deriving appropriate transfer functions but a closer reading reveals a deep understanding of the practical issues and limitations of the devices when used in control systems. In chapter 18, dealing with steady-state accuracy of position control systems, he writes "IT]he best system can only reduce the error signal to zero, if the signals themselves are inaccurate, then the final positioning will be inaccurate. Thus the final limitation on the accuracy of position control systems rests on the accuracy of the measuring or monitoring devices."

The final two chapters of the book cover non-linear behaviour and give a brief introduction to methods of analysis and design of such systems, including treatment of 'bang-bang' control. And it is in the area of non-linear systems that West's major research contributions were made: In particular in 1956, with the dual input describing function [1 ]. He produced a book on non-linear control in 1960.[2]

In the Introduction he comments that the 1939-1945 war had led to the invention and development of many automatic control devices together with a rapid advance in the theory of control such that "...the whole subject is becoming of primary importance." It is possible, he argues "...to start from a few basic principles and build up a comprehensive theory of control" but "[T]he engineer...must be able to go from the abstract to the concrete, must be able to design a specific system for a given job." That the book succeeded in providing an excellent grounding for the student engineer needing to learn both the theory and how to move from the abstract to the concrete is one reason for its longevity~it remained in print until the late 1960s (the fifth reprint is dated 1965). Another reason, I think, is because it unfolds like a story of discovery. One can imagine John West in the lecture room encouraging the students to work out for themselves the next steps in the story.

John West moved to Queen's University Belfast in 1957 as Professor of Electrical Engineering and then in 1965 to University of Sussex as Dean of School of Applied Sciences. In 1979 he was appointed as Vice-Chancellor, University of Bradford and retired from this position in 1989. He served as the President of the Institution of Electrical Engineers in 1984 and was appointed as an Honorary Fellow of the Institution in 1992. John West has been active in retirement and arising from one of his many activities, in the year 2000, his name was added to the Roll of Distinguished Philatelists.

[1]

[2]

J. C. West, "Forty years in control," Institution of Electrical Engineers Proceedings-A, vol. 132, pp. 1-8, 1985. J. C. West, Analytical techniques for non-linear control systems. London: English Universities Press, 1960.

United Kingdom 273


10] GAIN-FREQUENCY C H A R A C T E R I S T I C S 1 0 9

curves, and is shown in Fig. 49. This is, of course, an approximate straight-line segmented characteristic, the true one having the comers rounded as shown dotted in the same figure.

The slope of the characteristic where it crosses the unity gain (zero db.) axis gives an indication of the phase angle at this frequency. Since the slope is 12 db. per octave for a small frequency range and 6 and

o \ / . . L .1_ . . . . . ~ T a , T§ . . . . . .

~ ab/oe~ cl

C

FIG. 48.--COMPONENTS OF EQUATION 139.

. . . . . . I , . a - ' X . .,, I . , - -

I . . . . . . . . . ' _ - ' '-:.~.~ ~ I -r -~a. "~S b' ! "%

b/oo

FIG. 49 . - -TI - IE SUM OF CURVES a, b, c AND d IN FIG. 48.

18 db. on either side, the first estimate of the equation in approximate form (equation (137)) would indicate all angle of 180 deg. Thus the system, if not unstable, would be highly oscillatory. It was shown in Section 9.6 that the phase margin should be of the order of 30-40 deg., i.e., the phase angle should be 140-150 deg. at unity gain. This corres- ponds to a slope of 9-10 db. per octave. Hence the system can be improved over that of Fig. 49 if it is possible to reduce the slope. The advantages of this approximate form are, first, that it is easy to draw

274 United Kingdom


UNITED STATES OF AMERICA

Contributed by

Peter Dorato

University of New Mexico Albuquerque, NM, USA

Karl Johan Astr6m Lund Institute of Technology

Lund, Sweden (Engineering Cybernetics, H.S. Tsien)


Network Analysis and Feedback Amplifier Design Hendrik W. Bode Van Nostrand Company, Inc., New York, 1945.

Theory of Servomechanisms Hubert M. James, Nathaniel B. Nichols, and Ralph S. Phillips McGraw-Hill Book Company, Inc., New York, 1947.

Engineering Cybernetics Hsue-Shen Tsien McGraw-Hill Book Company, Inc., New York, 1954.

Automatic Feedback Control System Synthesis John G. Truxal McGraw-Hill Book Company, Inc., 1955.

Sampled-data Control Systems John R. Ragazzini and Gene F. Franklin McGraw-Hill Book Company, Inc., 1958.

Stability by Liapunov's Direct Method, With Applications Joseph La Salle and Solomon Lefschetz Academic Press, New York, 1961.

Adaptive Control Processes" A Guided Tour Richard Bellman Princeton University Press, Princeton, New Jersey, 1961.

Linear System Theory. The State Space Approach Lotfi A. Zadeh and Charles A. Desoer McGraw-Hill Book Company, New York, 1963.

Optimal Control Michael Athans and Peter L. Falb McGraw-Hill Book Company, New York, 1966.

276 United States


Network Analysis and Feedback Amplifier Design

Hendrik W. Bode Van Nostrand Company, Inc., New York, 1945

The Bell Telephone Laboratories (Bell Labs), established in 1925, was a major center in the United States for the development of electronic technology. This classical text on feedback amplifier design is part of the Bell Telephone Laboratory Series of books that reported the technological innovations developed at the Laboratories. Researchers at the Laboratories made fundamental contributions to feedback control. In particular in 1927, H.S. Black introduced the concept of feedback to design high accuracy electronic amplifiers, and in 1932, H. Nyquist developed a frequency-domain criterion for the stability of feedback systems. Researchers at the Laboratories, such as R.M. Foster, also made fundamental contributions to electrical network synthesis. Network synthesis played a key role in the early implementation of feedback controllers, since the only electronics available at the time, e.g. 1940s, were passive electrical elements such as resistors and capacitors, and vacuum tube amplifiers.

Actually the major part of this book is devoted to passive network synthesis. As indicated in the title, Bode's text combines network theory and feedback design. The feedback design theory is based on Nyquist stability theorem, and the text introduces related frequency-domain plots, now known as Bode plots to expedite the feedback design. The frequency-domain design techniques presented in Bode's text dominated feedback design theory up to the 1960s, when state-space methods were first introduced. This text also introduces the sensitivity function to measure the sensitivity of closed-loop transfer-functions to plant parameter variations. The problem of feedback sensitivity design becomes a central control problem in the years following the publication of this text. In this text Bode also relates the gain and phase of a transfer function through his now famous Bode gain-phase relations.

The same year that Bode's text was published, a text by another Bell Labs researcher, LeRoy A. MacColl, appeared in the Bell Lab Series, with the title Fundamental Theory of Servomechanisms. The MacColl text was not as detailed as the Bode text, but it covered much of the same frequency domain theory. Interestingly, it also had some discussion of sampled-data control and nonlinear control.

United States 277


Network Analysis an.d Feedb,ac.k Amplifier Design

HENDRIK W. BODE, Ph.D., Research Mathematician,

BELL TELEPHONE LABORATORIES, INc.

ELEVENTH PRINTING

D. V A N N O S T R A N D C O M P A N Y , INC.

TORONTO

PRINCETON, NEW JERSEY

NEW YORK

LONDON

278 United States


I N T E R S T A G E N E T W O R K D E S I G N 413

merit values in Fig. 17.7,4 and Curve II , to Fig. 17.7B. The gain and phase c u ~ e s for the remaining structures are shown in Fig. 17.9. Curves

- , _ , . . . . , ,

~ b

J

0 ( 2 0 . 4 0

L

l .........

G 0 . 1.o I

I I I

1.0 1.2 (;3/6}0

4 0 , - . . . . . . . . . . . . . . . / " I ..... t .

1 . . . . . . . . . . . . . . . . . . . . ~ . . . . . . . . ' .........

/ - x / , ~ v " z z ' .................... .....

. . . . . . . . . . . . . . . . Z / "

, ,,, , .... 0.8 1.0 1 . 2

Fxo. 17.8

I I I and IV refer respectively to the structures of Figs. 17.7C and 17.7/). The performance of the structure of Fig. 17.7E, which matches the ideal

0o closely to be shown by a separate curve, is indicated by the crosses.

This sample page illustrates an original "Bode plot" of magnitude and phase versus frequency.

United States 279


Theory of Servomechanisms

Hubert M. James, Nathaniel B. Nichols, and Ralph S. Phillips McGraw-Hill Book Company, Inc., New York, 1947.

During World War II, much new technology related to radar systems was developed at the Massachusetts Institute of Technology's Radiation Laboratory, established in 1940. Feedback was an essential part of radar systems, and when, after the end of the war, the results of the research done at the Radiation Labs were reported in the series of volumes referred to as the Radiation Laboratory Series, the above volume, edited by James, Nichols and Phillips, focused on those results relating to feedback and the design of servomechanisms.

In a chapter written by N.B. Nichols, W.P. Manger and E.H. Krohns, frequency-domain design principles are presented, including a new design plot, now commonly referred to as a Nichols chart. This volume also presents, for the first time in the USA, in a chapter written by W. Hurewicz, an analysis of sampled-data systems, including the concept of the z-transform for discrete-time signals. Another notable result reported in this volume was the application of Norbert Wiener's mean-square prediction theory to the design of feedback control systems in the presence of random disturbance signals.

Four years after the publication of the James, Nichols and Phillips volume, the two volumes of Chestnut and Mayer, Servomechanisms and Regulating System Design (John Wiley & Sons, 1951) were published. These two volumes, which included many of the results presented in James, Nichols and Phillips, were popular text books in the USA for control courses, because of their many examples and problems.

280 United States


THEORY OF

SERVOMECHANISMS

Edited by

t l U B E R T M. J A M E S PROFESSOR OF PHYSICS

PURDUE U N I V E R S I T Y

N A T t t A N I E L B. N I C H O L S DIRECTOR OF R E S E A R C H

TAYLOR INSTI~UMENT C O M P A N I E S

RALPH S. P I t I L L I P S ASSOCIATE PROFESSOR OF M A T H E M A T I C S U N I V E R S I T Y OF SOUTHERN C A L I F O R N I A

O F F I C E O F S C I E N T I F I C R E S E A R C H A N D D E V E L O P M E N T

N A T I O N A L D E F E N S E R E S E A R C H C O M M I T T E E

FIRST EDITION

THIRD IMPRESSION

N E W Y O B K . T O R O N T O . L O N D O N

M c G R A W - H I L L BOOK C O M P A N Y , I N C .

1947

United States 281

His tor i c Con t ro l Textbooks

S~c. 4.11 ] DECI B E L - P t t A S E - A N 6 % E DI AGRA MS 181

decibel v~due . ) F o r the C-contours the highest value of 1I"~[ is re~ched 90 + ~ + mr a n d in decibels equals where the phase margin is e q u M t.o ( o

20 1 og,,, t 1 ~sin 4"t.

32 0

28

24

;tO

16 ....

8 - - t-/

N 0 - -

-8

-12 ~

- 1 6 ......

- 20 --

- 2 4

2O

........ i -

. , , , , . . . . ....... ~=,,

i "

/

..,_ i J

, . , . < , -

|= . , , ,~1 L _.E,,~_

Phase margin in degrees 4 O 60 80.

~ . ~ ~ i ~ . . . . . . _

, , , ~

......... L ............... ! .

. 4 N ! ..............

! k .1 _

| i | i | i i i i i

1oo . . . . . . ,,,, ,, ,,,

. . . . . . . . . . . . . .

..:..: ..........

. . . . . . . .

~ r . . . . . . . . . . w . . r

--- ...... /

7 > ___/_~ X f

~ t ......

1

/ ..,

1 . . . .

7

f

\ , ,_ , , ,

_'V,,

-180 -160 -140 -120. -100 -80 -60 Angle in degrees

20 140 150 , , . ~ . . . . . . . : ; , ,

q , �9

t L

l, i" l ...... !.

, : : - . _ : . . . . . : . . . . . . . . . . = :

�9

i _ _

-40 -20

180

0.5

12

18

24

--50

lqG, ,t.27.. ........ C o n s t a n t - p h a s e - a n g l e and constant -ampl i f i cat ion contours ott the d e c i t ~ l - p h a s e - angle l o o p ( t i a g r a m .

It is obviously possible to transfer the M-contours and the ~-contours from this decibel-phase-angle diagram to the type of decibel-log-frequency graph discussed in Sec. 4-10. Then, after a study of the rammer in which the attenuation curve crosses the M-contours, it is possible to alter the gain and, if necessary, the s|mpc of the ~ttenu:~tion plot to

This page illustrates a "Nichols plot".

2 8 2 U n i t e d States


Engineering Cybernetics

Hsue-Shen Tsien McGraw-Hill, New York, NY. 1954.

This is a remarkable book written by a remarkable person. Tsien graduated from Jiaotong University in Shanghai. He moved to the US where he got his PhD from Caltech in 1939. Tsien became a prot6g6 of Theodore von Kfirm~in, and an active researcher in the emerging aerospace field. He contributed to basic research as well as to early experiments with rocketry in what was to become the Jet Propulsion Laboratory (JPL). Tsien was also heavily involved with military projects; he joined von Kfirmfin in Washington as a member of a small Scientific Advisory Group to the US Army. In 1946 he became professor at MIT, and in 1949 he returned to Caltech with consultancies at JPL and Aerojet Corporation. During the McCarthy era in the early 1950s he was accused of being a Communist and in 1955 he was deported to China where he became the leader of the Chinese missile program. Engineering Cybernetics was written in a transition period when Tsien had lost his security clearance, much of the aerospace research was closed to him and he turned his interest to research in other fields and to teaching at Caltech.

The early 1950s was also a transition period in the field of control. Development of classical control theory had reached a plateau, and the paradigm shift called modem control theory had not yet occurred. Recall that Bellman's book on Dynamic Programming, Kalman's paper on filtering and Pontryagin's book on Optimal Control were published in 1957, 1960 and 1962.

The book Engineering Cybernetics has 18 chapters. It gives an unusually broad coverage of the field of control. The first four chapters treat traditional servomechanism theory covering transfer functions, frequency response, the Nyquist stability theory and Evans root locus method in a nice concise way. The book then treats much material that was non-standard at the time. There is a short chapter on time varying systems that is motivated by linearization of rocket trajectories along a path. Non-interacting control with applications to turboprop engines, sampled data systems, and systems with time delays are covered in separate chapters. There is a good coverage of stochastic systems in two chapters which gives fundamentals of stochastic process and Wiener-Kolmogoroff filtering theory. A very interesting chapter on relay feedback describes classical results by Fltigge Lotz, describing functions, the idea of minimum time control and switching surfaces developed by Bushaw. A chapter on nonlinear control covers jump resonance, frequency entrainment and parametric excitation. There are three chapters on optimal control. One of them suggests that control design should be formulated as an optimization problem, another solves it using adjoint variables, and the third deals with self-optimizing control developed by Draper and Li. The last two chapters deal with ultra-stability in the spirit of Ross Ashby and reliability.

A person lucky enough to have read Tsien's book in the late fifties would have been very well prepared for the exciting development of control that took place in the 1960s. The book Thread of the Silkworm by Iris Chang gives a fascinating tale of the career of Tsien Hsue-Shen.

United States 283


E N G I N E E R I N G CYBERNETICS

H. S. TSIEN

Dan~ a~: ~ ~ r G u : e ~ . ~ m Jet P r ~ ~ ~ n C e ~ ~ q ~ n ~ l ~ t ~ ~ , of ~chnoio~ ' P~Mena, :C'aifforn~

MeG I ~ W - H iL/~L B OOK C 0 MPA N Y, I N C.

New York '~,ox:k.to ~ ~ d o n

1954

284 United States


C O N T H. O L D E S I G IN B Y P E I / T I.,:l = l / B A T I ( ) N ..... I" H: E O :.H Y 1. 7 9

m i s t i n g ear!:i.h, as s k e t c h e d in Fig.... i 3.. I. T h e p h m a r m o t i o n is p ~ s i . M e d u e :to ::the a b s e n c e of t h e cr(:~s C~:,rioii.:s fo.ree in t h e e q u a t o r i a l pla~:~.e. T h e eoordina~te sys tem, i.s f ixed wi.t,h r e e p e c t t o t h e ro t a ; t i ng e a r t h , i..e.:, i.t

a c tu al |. y r o t a t e s wi t h . . . . . . . . . . . . . . . . . . . . . t h e ~ n gn i a, r v e | o c i :t y :~1:, t h e s:l:~,e.e.~ d. of c a r t h ro ~ t.i on., In :the:~: equa : tor i a,l: ..:plan. e,.. t h e i:::m~i t ion o.f t h e veh.iele ~t an y. t;i m.e insta::w:~t t ::is spe~eified b y t h e : radius r ~md the,: a n g l e 0 f r o m th.e ~ st.:arti:ng:: p o i n t of t h e

Wing

T a ~ e :, o f f

Fmo 1.3.1

:~tination::

veh ic le , r~, is t h e r a d i u s of t h e e a r t h . :fl is t h e g r a v i t a t i o n M cons t an t : a t t h e smfface of :t~:he e a r t h with:~:::nlt t h e .... ' ............................... ......... ', .......... 1 :.:::~ .......... ,~ .... i.~et 1::' .J:~ a, nd. 0 be t h e f o r c e p e r unit~ m:a~::~ d u e t~.o thru.~t,, an:el ae:r~ty::m::~a.mie fo r ce s , e:~w ~ ...... : on. . . . . t h e vehi.ch:::~ i~:t |:Ira r a d i a ! ~ ..... t h e . . . . . . c:i .rcumferent:ial diree .....

i t y of t h e velf icle a r e

dO dt

! ! t dt dO : tt

. . . . . . . . . . . . . . k ,~'~ ] I

:= e a)

w h . e ~ t h e p l u s s ign in t h e s e c o n d t e r m s o.11 t h e r i g h t will be v a l i d fo r f l igh ts t o w a r d t h e e a s t , a n d t h e m i n u s sign. fo r f l i gh t s t o w a r d the. wes t ,

This page shows a good early example of an optimal control problem

U n i t e d S t a t e s 2 8 5


Automatic Feedback Control System Synthesis

John G. Truxal McGraw-Hill Book Company, Inc., 1955.

This text contains a very comprehensive presentation of most of the frequency-domain techniques for the design of control systems, available in 1955. It covers a wide range of topics, including Nyquist methods, root-locus methods, sampled-data systems, nonlinear systems, and statistical mean-square design methods. Due to the limitations in electronic hardware available at the time, a major focus in the text was on the design of controllers that can be implemented as RC networks. Thus control system synthesis was closely linked to network synthesis, as in the text of Bode. A key "synthesis" result reported in this text is the so-called Guillemin approach, which attempts to design controllers with poles limited to the negative real s-domain axis, so that the controller can be synthesized with an RC network. It was not until the introduction of operational amplifier chips in the 1970s, that control synthesis became disconnected from network synthesis. In this text Bode's sensitivity function is used as a key tool to design feedback systems that minimize the effect of plant parameter variations.

At the time this text was written, the Polytechnic Institute of Brooklyn was an important national center for systems and control research in the United States, with such researchers as L. Braun, I.M. Horowitz, E. Mishkin, A. Papoulis, and D.C. Youla, in addition to Truxal. Under the leadership of Truxal, extensive research was done on adaptive control systems, leading to the publication of the edited volume, Mishkin and Braun, Adaptive Control Systems (McGraw-Hill, 1961). In addition to adaptive control, the Polytechnic research group focused on the design of feedback systems that were insensitive to plant parameter variation. A key contribution in this area was made by Horowitz, with the introduction of sensitivity measures appropriate to large parameter variations. Details of Horowitz's frequency-domain design approach to feedback and uncertainty appeared in his text Horowitz, Synthesis of Feedback Systems (Academic Press, 1963). In the text of Paul Frank, Introduction to System Sensitivity Theory (Academic Press, 1978), most of the major results associated with sensitivity design, that dominated feedback theory since the publication of Bode's text, were summarized. In the 1980s, the term Robust Design largely replaces Sensitivity Design in control text books.

A note on the term Synthesis used in the Truxal, and other control texts. It is a term that the control community inherited from electrical network theory, where "synthesis" meant, design theory with an existence theorem and a computable algorithm to find a design solution, when one existed. The term analytic design is generally understood to be synonymous with synthesis, as defined this way. Analytic design is in sharp contrast to design by trial-and-error. Design techniques based on shaping of the Nyquist plots are inherently trial-and-error techniques. Most of the results, presented in the texts of Truxal and Horowitz, cannot be said to be synthesis results in the strict network sense. It was not until the introduction of state-space techniques and H methods that the term synthesis could be used in its strict sense for control design. An example of a control text where the term is used properly in its strict sense, is the text of Vidyasagar, Control System Synthesis. A Factorization Approach (MIT Press, 1985).

286 United States


AUTOMATIC

FEEDBACK CONTROL SYSTEM

SYNTHESIS

PROFESSOR JOHN G. TRUXAL

Department ol Electrical Engineering Polytechnic Institute o/Brooklyn

Brookl:un. New Yor~

McGRAW-HILL BOOK COMPANY, ING,

New York Toronto London

1955

United States 287


296 P O L E - Z E R O S Y N T H E S I S

2 and 3 is noteworthy, particularly in view of the apparently striking dissimilarity between the two system functions.

5.3. Determination of the Open-loop Transfer Function from the Closed-loop System Function. The second step in a synthesis along the lines suggested by GuiIlemin is a determination of the open-loop transfer function corresponding to the closed-loop system function chosen to meet the performance specifications. It is this step which wins the stumbling block to successful logical synthesis of servomechanisms before Guille-

+,..,E(s) t Gts)p(s) l C(s)

I .... ............ ....... 1 ...... I --e (s)= ~ R p(s)+q(s)

Fro. 5.16. Unity-feedback. single-loop feedback control system.

These unknown poles and zeros are

equ,~tion

C I f ~ (s) is written

p(s)/q(s),

min's work, for in its basic form this step involves the evaluation of the roots of a polynomial. The essential problem is illustrated in Fig.

c 5.16. ~ (s) is known, with the nu-

merator and denominator polynomials in factored form; the poles and zeros of the open-loop transfer function G(s) are to be found.

C related to the known ~ (s)by the

C G(s) (8) = 1. + G(s) (5 .52)

as the ratio of polynomials, p(s)/n(s) , and G(s) as

C p P/q - P (5.53) -~ ( s ) - n - 1 + p / q - p -t-------q

n(s) = p(s) -[-q(s) (5.54) q(s) = n(s) -- p(s) (5.55)

In other words, the zeros of the open-loop transfer function are identical with the zeros of the closed-loop system function, while the poles of the open-loop transfer function are the zeros of the polynomial n(s) -- p(s). In general, determination of these zeros involves solution of a polynomial of the degree of n(s). It was this problem of zero determination which, until Guillemin's work, discouraged design through this method of working from the over-all system inward toward the compensation networks.

The foundation for the success of Guillemin's method lies in the procedure he presented to ensure a simple solution to the zero-determination

J C problem. He proposed that the pole-zero configuration f o r ~ (s) be

chosen not only to meet the specifications, but also to ensure that all zeros of q(s) lie on the negative real axis. If this condition is satisfied, the zeros of q(s) can be determined graphically by plots of ~(s) and p(s) (polynomials with known zeros)for real values of s and by gra@hical sub- traction according to the equation

q(8) = n(s) - p(s) (5.56)

This page illustrates the Guillemin synthesis concept of moving from closed-loop to open-loop characteristics.

288 United States


Sampled-data Control Systems

John R. Ragazzini and Gene F. Franklin McGraw-Hill Book Company, Inc., 1958.

This is one of the first texts written in the United States on sampled-data control systems. The authors were both former faculty members at Columbia University, where there was a strong research focus on sampled-data control, led by Professor John Ragazzini. Researchers at Columbia University in this area included, J.E. Bertram, B. Friedland, E.I. Jury, R.E. Kalman, G. Kranc, and L.A. Zadeh. This text presents much of the results developed by these researchers, e.g., the multirate sampling theory developed by Kranc. It is also one of the first texts to introduce the digital computer for the implementation of sampled-data controllers, although it was many years before efficient and inexpensive digital computers were to be realized. At the present time, digital-computer controllers have largely replaced operational-amplifier analog controllers.

In 1958, the text of another ex-Columbia University researcher Eliahu Jury was published, i.e. Jury, Sampled-data Control Systems (John Wiley & Sons, 1958). For a long time these two texts were the mainstay of the sampled-data literature in the USA. In 1958, the text of Tsypkin, Theory of Pulse Systems (State Press, 1958), was published in the USSR and in 1972, the text of Jtirgen Ackermann was first published in German, later to be expanded and translated into English in the text Ackerman, Sampled-data Control Systems. Analysis and Synthesis, Robust Design (Springer-Verlag, 1985). Since 1958 many texts have been written in the USA on the subject, with the title Sampled-data Control replace by Digital Control, an example being the recent text of Franklin, Powell, and Workman, Digital Control of Dynamic Systems (Addison-Wesley, 1997). This reflects the improvements that have occurred in digital technology, and the focus on digital implementation of controllers. Two other terms that have replaced the term Sampled-data Control are Discrete-time Control and Computer Control, e.g. Ogata, Discrete-time Control Systems (Prentice-Hall, 1987) and Astrom and Wittenmark, Computer Controlled Systems (Prentice-Hall, 1984).

United States 289


S A M P L E D-DATA

C O N T R O L S Y S T E M S

John R. Ragazzini Dean, College of Engineering

New York University

Gene F. Franklin Assistant Professor of Electrical Engineering

Stanford University

McGRAW-HILL BOOK COMPANY, INC.

New York Toronto London

1958

290 United States


M U L T I R A T E SAMPLED SYSTEMS 247

E X A M P L E

As an example of the design principle outlined in this section, a second-order plant with zero-order hold is considered. The pertinent transfer function of the continuous element is

1 -- e "-sT'/n l G(s) = (9.86) s s(s + 1)

From previous calculeotions (see See. 7.8) it is known that the pulse transfer flmction of this system has two zeros, so tha t n = 2. If, for

n +, - - , , / l-o.~-Gs=;~I / ~ a 2 -"~---0:63--f '~l l .......... 1"1 -- ~ ? C

(a}

/ Input / Output, cIt} 1 ..... /

o i , , i'i ........... 0 1 2 3 4 5 6

Time (bt

Fi~. 9.14. (a) Block diagram and (b) step response of a multirate system designed for zero ripple.

purposes of this example, T is taken to be 2 sec, then the previously calculated pulse transfer function can be used, namely,

0.368z2-t(1 + 0.718z2 -~) (9.87) G ( z ~ ) = (1 - z.~ - ~ ) (, 1 - 0.368z~ -~)

Substituting from (9.87) into (9.85),

D(z:~) (1 -- z f ~)(I - 0 .368zf 1) �9 = 0 . 3 G S ( I . 7 = i S ) ( t - z , -~)

] - 0.35gz~ .... t = 0.632 (9.88)

A block diagram of this sy~:tem and the associated step response are shown in Fig. 9.14.

I t is possible to generalize the interpretation of the basic design equation given as (9.82) considerably beyond the step-response case worked out in detail in (9.85). In some cases it is desirable, and for plants with

This page illustrates a multirate sampled-data system with a discrete-time compensa tor .

U ~ i t e d S t a t e s 2 9 1


Stability by Liapunov's Direct Method. With Applications

Joseph La Salle and Solomon Lefschetz Academic Press, New York, 1961.

La Salle and Lefschetz were both researchers at the Research Institute for Advanced Studies (RIAS), a division of the Martin Company, located in Baltimore, Maryland, when this book was published in 1961. During the period 1955-1965, RIAS was one of the major systems and control research centers in the USA. The researches at RIAS included, in addition to La Salle and Lef- schetz, J. Hale, R. Kalman, H. Kushner, G. Szego, L. Weiss and M. Wonham. Many fundamental results in linear, nonlinear, and stochastic systems originated at RIAS.

The above text presents some of the basic nonlinear results of Liapunov, that became known in the USA through the 1st IFAC Congress held in Moscow in 1960. In particular the text presents Liapunov's direct method with applications to feedback control systems. Liapunov functions used in the direct method to establish stability of nonlinear systems are now widely used in the control community for the analysis and design of feedback control systems.

This text also introduced the interesting concept of Practical Stability, which requires system variables to not just be bounded, but to be bounded by pre-specified bounds. Practical stability applied to systems operating over finite-time intervals, leads to the concept of Finite-time Stability.

A discussion of Liapunov' s direct method and finite-time stability appears in the text of Wolf- gang Hahn, Theory and Application of Liapunov's Direct method (Prentice Hall, 1963), originally published in German in 1959. Liapunov's stability theory is now a standard component of most nonlinear control texts.

292 United States


3"tabl"ll"ty by

ID Ltapunov's Direct _?ffethod

With Applications

JOSEPH LA SALLE

and

SOLOMON LEFSCHETZ

RIAS, Baltimore, Maryland

(A Division o] The Martin Company)

1961

New York ACADEMIC PRESS London

United States 293


w 9. I, IAPUNOV'S STABILITY THEOREMS 37

'$ w 9. Liapunov Stability Theorems It is intuitively clear that if near an equilibrium state of a

physical system the energy of the system is always decreasing,

then the equilibrium is stable. Liapunov's theorems are a gen-

eralization of this idea. Liapunov functions are simply an extension of the energy concept. The central idea of the Liapunov method

H I I s . . i--- - - -- . , .

/ \ / / / \ / C : V s k \ \

\ / \ / - ~ / - % / .

I"

FIG. 13. FIG. 14.

is to detect stability for a system (FA) by means of properties of a Liapunov function V(x) and to do this, not directly from a knowledge of the solutions, but indirectly from the system (FA).

Our proofs will be given as geometric a form as possible. However, for clearness in applying the theorerris it is indispensable to formulate them in a precise analytic manner.

I. STABILITY THEOREM. I/ there exists in some neighborhood [2 o/the origin a Liapunov /unction V(x), then the origin is stable.

II. AsYMPvorIc STABILITY THEOREM. I [ - F is likewise positive definite in ~, then the stability is asymptotic.

The two theorems will be proved together. We rest them heavily upon the second geometric interpretation of a positive definite function V(x). The sketch (Fig. 13) is conveniently made for n = 2 but the reasoning is valid for any n.

This page illustrates Liapunov's stability concepts and Liapunov functions.

294 United States


Adaptive Control Processes: A Guided Tour

Richard Bellman Princeton University Press, Princeton, New Jersey, 1961.

Richard Bellman was a researcher at the RAND Corporation, in Santa Monica, California during the period 1953-1956. During this period of time the RAND Corporation was one of the major centers in the USA doing research in systems and control. Some of the notable researchers at RAND working in the systems and control area included, J. Danskin, S. Dreyfus, I. Glicksberg, O. Gross, R. Isaacs, and R. Kalaba. Many RAND reports were published by the above researchers. The report most directly related to the above text is report R-313, Some Aspects of the Mathematical Theory of Control Processes, published in 1958 and authored by Bellman, Glicksberg, and Gross.

Bellman made many contributions to mathematics and control theory, but he is probably most famous for his invention of the Principle of Optimality and its application to optimal control (Dynamic Programming). Pontryagin's Maximum Principle and Bellman's Dynamic Programming provided solutions to many optimal control problems related to space programs and military applications (RAND was supported largely by the USA Air Force during the above period of time). In Adaptive Control Processes, Bellman covered a wide range of topics related to dynamic programming. In particular he discussed the calculus of variations, optimal stochastic control, differential games, and adaptive control. The style of presentation in this text is very informal, hence the subtitle, A Guided Tour. More details on dynamic programming may be found in an earlier text written by Bellman, Dynamic Programming (Princeton University text, 1957). A very interesting sketch of Bellman's life and career may be found in his auto- biographical book, Eye of the Hurricane. An Autobiography, (World Scientific, 1984).

United States 295


ADAPTIVE

CONTROL PROCESSES:

A GUIDED TOUR

BY

RICHARD BELLMAN THE RAND CORPORATI01f

1961

PRINCETON UNIVERSITY PRESS

PRINCETON, NEW JERSEY

296 United States


:TERMINAL" COI~TROL

Markoviaa property described above. In this case, the basic property of optimal policies is expressed by the following:

P R I N C I P L E OF O P T I M A L I T Y . An optimal policy ha~ the property that whatever the initial state and the initial decision are, the remaining decision,s mu.~t constitute an optimal policy with regard to the state resulting from the .first decision.

A proof by contradiction is immediate.

3.9 Derivation of Recurrence Relation

Using the principle cited above, we can derive the recurrence relation of (3.21) by means of purely verbal arguments. Suppose that we make an initial decision ql. The result of this decision is to transform Pi into T(Pa, ql) and to reduce an N-stage process to an ( N - l)-stage process. By virtue of the principle of optimality, the contribution to the maximum return from the last, ( N - 1)-stages will be fN_l(T(Pl, ql)). This is the Markovian property discussed in 3.5.

Hence, for some ql we have

(3.22) f,,:(Pl) = g(P~, fl) + f,+'-x[T(Pl, fl)]. It is clear that this ql must be chosen to maximize the right-hand side of (3.22), with the result that the final equation is

(3.23) fu(Pl) = Max [g(Pl, ql) + fN-I[T(Pl, fl)]]. q~

Although we shall discuss these matters in much detail in Chapter V which is devoted to the computational aspects, let us make this preliminary observation here. Observe that the usual approach to the solution of the maximization problem yields a solution in the form [ql, % . . . , qu], the same one, of course, which is obtained as a result of our variational process. The approach we present here yields the solution in steps: first, the choice of ql, then the choice of % and so on.

The decomi)osition of the problem of choosing a point in N.dimensional phase space into N choices of points in one-dimensional phase space is of the utmost conceptual, analytic, and computational importance in all of our subsequent work. The whole book is essentially devoted to the study of various classes of multidimensional processes which can, by one device or another, be reduced to processes of nmch lower dimension, and preferably to one-dimensional processes.

3.10 "Terminal" Control

A case of some interest in many significant applications is that where we wish only to maximize a function of the final state PN" In this case, the sequence of return fimctions is defined by the relation

(3.24) fN(Pl) = Max g(p,~,). qi

57

This page illustrates Bellman's "optimality principle".

United States 297


Linear System Theory. The State Space Approach

Lotfi A. Zadeh and Charles A. Desoer McGraw-Hill Book Company, New York, 1963.

This is one of the early textbooks published in the USA that presented the state-space approach to linear systems, pioneered by R. Kalman in the late 1950s. Prior to the introduction of state- space methods, linear control theory in the USA was essentially limited to frequency-domain methods. This text covers topics such as stability, controllability, observability and realizability, for both continuous-time and discrete-time systems, and for both time-invariant and time-varying systems. For a number of years this text was the only in-depth text available on state-space methods, a subject that had become as important as frequency-domain methods in control theory. However after 1965, an increasing number of texts were published on the subject, e.g., DeRusso, Roy, and Close, State Variables for Engineers (John Wiley & Sons, 1965), Schwartz and Friedland, Linear Systems (McGraw-Hill, 1965), Brockett, Finite Dimensional Linear Systems (John Wiley & Sons, 1970), Chen, Introduction to Linear System Theory (Holt, Rinehart and Winston, Inc., 1970), Kailath, Linear Systems (Prentice-Hall, Inc., 1980), and so on. Presently, almost every text on control theory contains some state-space material.

298 United States


Linear Systen-~ Theory The State Space Approach

Lotfi A. Zadeh & Charles A. Desoer Department of Electrical Engineering University of California Berkeley, California

M c G r a w - H i l l Book C o m p a n y , Inc .

New York / San Francisco / Toronto / London

United States 299


33

35

36

S ta te E q u a t i o n s of "l'int,:-in.variant D i f f eren, t iat S y s t e m s 4.4

We observe that the state e<luatiol~.s 29 and 3t are not of the same form as the state equations of a s3;stem of the reciprocal differential operator type (5 .8 .32) , nor are they of the canonical form

x = A x + B u

y = C x + D u

Consequently, we cannot use Corollary 2.5 .36, as in Sec. 3, to show that x qualifies as a state vector of ~.

Although it is an easy mat ter to verify tha t x as defined by 19 has the state separation property 2 . 3 . I 9 , it will be instructive to demon- s~trate directly that x satisfies the four consistency conditions 1.6.5, 1 .6 .11, 1 .6 . I5 , and 1.6.85. This is what we shall do in the sequel.

D i r e c t v e r i f i c a t i o n t h a t x q u a | i f i e s a s a s t a t e v e c t o r

We have to verify tha t 2I is an input-output-s ta te relation for the system characterized by the input -output relation

y(t) = (bmp "~ + . . . + bo)u

To avoid being influenced by notation, let us express 21 in the form

y( t ) = (+(t - to),r~) - + - i ( p ) [ l ( t - io)u(t)] t >_ to

where ~ is an m-vector, a = (al, . . . ,ex~), ranging over e'L [In effect, ~ represents a point (state) in the state space Z of ~.] We employ the symbol ~ rather than x ( t 0 - ) in 35 because at this stage of our arg~mmnt we have not yet demonstrated that the components of (~ are the values of u and its derivatives at t o - .

Since 85 is a general solution for 33, it follows that 3..~ satisfies the mutual-consistency condition (see g,.8.2/~). Furthermore, since the response is uniquely determined by (~ and u(to,q, it follows tha t 34i satisfies the first ,~.lf-consistency condition also. Thus, it will suffice to show tha t 3~ satisfies the third self-consistency condition, since this condition implies the second self-consistency condition (see 1.6 .39) .

We can simplify the argument without losing its essential features by carrying out t.he verification for the case where m = 1. Actually, this is all tha t we shall need at a later point (Secs. 8 and 9) to develop an effective general technique for associating a state vector with a differential system of any finite order.

For m = 1, ;33 and 3~ become respectively

y = p u

y( t ) = ~6(t -- to) + p l(t -- to)u(t)

where for simplicity we have set bo = O, b~ = 1. We assume furthermore that u(t) is real-valued, which implies that a ranges over the real line ( - ~ , , ::,': ).

~21

This page illustrates state equations for linear systems.

300 United States


Optimal Control

Michael Athans and Peter L. Falb McGraw-Hill Book Company, New York, 1966.

The Calculus of Variations, Pontryagin's Maximum Principle, and Bellman's Dynamic Programming, theories expounded in the 1950s, as design techniques for optimal control, provided solutions to problems of special interest in the USA and the USSR. In particular, these methods provided the theoretical basis for the design of many control systems associated with space and military applications, applications that were of intense interest at the time, in both countries. The Maximum Principle and Dynamic Programming had special appeal, since these methods dealt directly with the problem of control signal constraints. In the USA texts on these methods began to appear in the 1960s. An early text, which presented the Calculus of Variations approach, was the text of Kipinak, Dynamic Optimization and Control A Variational Approach (M.I.T. Press, 1961). A more detailed and rigorous presentation of variational approach appeared a few years latter in the text of Hestenes, Calculus of Variations and Optimal Control Theory (John Wiley & Sons, Inc., 1966). In 1962, an English translation of the Russian text of Pontryagin, Boltyanskii, Gamkrelidze, and Mishenko, The Mathematical Theory of Optimal Processes (Interscience Publishers, Inc., 1962) was published. This text included a detailed presentation of the Maximum Principle. However, one of the first texts written by USA authors on the Maximum Principle was the text of Athans and Falb, published in 1966. By introducing a sign change in the Hamiltonian function which appears in the Maximum Principle, Athans and Falb actually refer to the Maximum Principle as the Minimum Principle. The text by Athans and Falb is notable for its detailed discussion of some key design problems, such as time-optimal and fuel-optimal control. It also contained many Examples and Exercises, which made it attractive as a course text.

In the 1960s most graduate programs in the USA offered a course on Optimal Control. Some other notable early texts on the subject include the texts of Leitmann, An Introduction to Optimal Control (McGraw-Hill Book Company, 1966); Lee and Markus, Foundations of Optimal Control (John Wiley & Sons, inc., 1967); and Bryson and Ho, Applied Optimal Control (Blaisdell Publishing Company, 1969). However optimal control theory had some important limitations. The optimization equations required the solution of difficult two-point boundary value problems. Also the theory, at least the deterministic theory, did not deal with uncertainties in system dynamics. Thus over time fewer graduate programs in the USA offered a full course on optimal control. However, one optimal control problem which endured was the Linear- Quadratic (LQ) control problem. Under the leadership of Athans, MIT became an important center for the study of LQ theory. LQ theory found many applications in industry because it applied to multivariable systems and software was available to solve the associated optimization equations (matrix Riccati equations). In the early 1970s, two texts appeared that focused on LQ theory, the text of Anderson and Moore, Linear Optimal Control (Prentice-Hall, 1971) and the text of Kwakernaak and Sivan, Linear Optimal Control Systems (Wiley-Interscience, 1972).

United States 301


OPTIMAL CONTROL An Introduction to the Theory

and Its Applications

MICHAEL ATHANS Assistant, Profe~sor Department of Electrical Engineering Massachusetts Institu~e of Technology

PETER L. FALB Associate Professor Information and Control Engineering The University of Michigan

McGRAW-HILL BOOK COMPANY New York/St. Louis~San Francisco~Toronto~London/Sydney

302 United States


288 Conditions for optimality

We observe that the only difference between the two special problems is the difference between the forms of the target set S. In the next section, we shall state the mininmm principle for these two problems.

Exercise fi-17 Formulate special problems 1 and 2 in full detail.

5-13 The M i n i m u m Principle of Pontryagin

We shall state the minimum principle of Pontryagin for the two special problems in this section. We shall, of course, suppose that all the assumptions of Sec. 5-12 are in force, and we shall also use the notation of Sec. 5-12. Before stating the theorems, we shall introduce some additional terminology and notation. In particular, we have:

Definition 5-10 Let H(x, p, u) denote the real-valued function of the n vector x, the n vector p, and the m vector u, given by

H(x, p, u) = L(x, u) + (p, f(x, u)) (5-391)

where f(x, u) is the function which determines our system [that is, f(x, u) is the right-hand side of the state equation] and L(x, u) is the integrand of our cost functional. We say that H(x, p, u) is the Hamillonian funclion (or, simply, the Hamiltonian) of our problem and that p is a costate vector.

We observe that, in view of our assumption CP1, the functions H(x, p, u) OH

and -0-x-(X, p, u) are continuous on R, X R, • l], where ~ is the closure of

OH in R,,. Moreover, we note that -0-~(x, p, u ) i s well defined and is given

by

OH (x, p, u) = f(x, u) (5-392) 0p

Now let us suppose that x0 is our initiM state and that to is our initial time. If ft(t) is some admissible control and if we let ~(t) denote the trajectory of our system starting from x0 = ~(to) generated by fi(t), then, for any function p(t),

OH ~(t) - ~:: [~(t), p(t), it(t)] = fib(t), it(t)] (5-393) op

In addition, if ~ is any n vector, then the linear differential equation

p(t) = OH [i(t) p(t), a(t)] OX

oL [ i (t) ~(t)l - ( ~ 0x ' \ t

!

[ i (t) , fi(t)] p(t) (5-394)

This page illustrates Pontryagin's "minimum principle".

United States 303


304 United States


historic control textbooks (ifac symposia series) (ifac symposia series)

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