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Problems in teaching control-engineering
Problems in Teaching Control-engineering W. OPPELT General View on the Connection between Teaching and Development of a Technical Professional Field At the universities and technical colleges today the treatment of a technical professional field often lags far behind industrial development. This is partly because of the large funds which at present industry spends on development with the result that research is very thorough. The other reason is found in the pattern of teaching related to development. Engineers are educated for the future, the technical development of which is as yet unknown. Engineers now leaving the universities may still be working in the year 2000. There is no doubt that the environment then will be very different from that of today. Because of rapidly changing situations in the professional field it is necessary that the curriculum shall be drawn up in relation to the future direction of development. This is similar to the problem which a communication engineer finds by the separation of signal and noise. It is known that a solution of this problem causes a time delay. The creator of a curriculum is working under better circumstances than the above-mentioned communication engineer, for he knows that: Natura facit non salta. The laws of nature are valid always. Therefore, each curriculum must teach students the laws of nature. Further, the education of the coming generation should be such that it will be able to use these laws in new fields of technology of which the coming generation may take advantage. On the other hand the creator of a curriculum is limited. The time interval available for education depends on biological evolution of human beings and is therefore fixed. The increased scope of technological subjects under development cannot be compensated by longer education. Again, in the years 2000 and 3000 the period of education still must render people independent in their profession on or about their 25th year of life in order to make proper use of the following years which are those of highest efficiency. Further development of technical science cannot proceed by extending the period of education; it must therefore be apparent in the content of the lectures . There are changes in the relative importance of professional fields; certain subjects are dismissed, others arise. Existing Situation in Teaching in the Field of Control-engineering Automatic control-engineering is a young field, formed in the 30's. Now it is represented in almost every technical college, but its place in the curriculum and its coordination with other faculties varies, howeverl. ]n general, control-engineering is taught during the last two years of study and mostly it is considered a special field of study connected with the related field of application. For this reason in some schools there are parallel independent courses concerning the role of either mechanical, or electrical, or process engineering in the field of automatic control. These courses apply then only to a selected group of students of the above-mentioned technical professional fields. The whole field of control-engineering is already taught at
some places in a general form. Therefore, all students of mechanical, electrical, and process engineering, and of physics attend similar courses. The theory of control-engineering which is independent of its application is then the guiding line while the examples for application are taken from different fields. In the long run both these possibilities are unsatisfactory. The first possibility of holding special lectures closely connected with application does not get away from a purely descriptive version as, in general, the knowledge of the students is not sufficient for an exhaustive treatment and there is not time for broad preliminary studies. The second possibility-a common treatment of the control-engineering field-does not have these limitations but a significant proportion of the lectures must be devoted to obtaining sufficient basic skill in techniques such as those dealing with frequency response, Laplace transforms, etc. There is no doubt that within this arrangement the special problems of the control-engineering field can only occupy a part of the whole course 2 • A significant incorporation of the automatic control field in the curriculum is only possible if changes and new compendiums are also made in those fields which are closely connected with control-engineering. In what follows, consideration is given to those fields in which the presence of control-engineering can affect other technical fields. Future Incorporation of Automatic Control in the Curriculum Control-engineering components have inputs (where information is picked up) and outputs (with which they manipulate the energy flOW)3 . This characteristic therefore makes the controlengineering field a bridge between communication engineering on the one hand and energy engineering on the other. The necessary basis which describes the behaviour of such components is therefore to be found partly in the communication engineering field, namely when handling the transferfunction of communication systems (in the time domain, in the frequency domain, by characterization of a system using poles and zeros, by mathematical methods to go from frequency domain to time domain, etc.) This basis is also to be found in part in the field of energy flow and therefore closely related to the dynamics of mechanical engineering, fluid mechanics, heat engineering and 'classical' electrical engineering. Current handling of the basic control-engineering elements is split into many special fields. Their entity is therefore not evident to the learning students and much useful time is wasted by parallel handling in the different fields. A person who does not go into the field of automatic control in detail will not recognize the main essentials. He is only able to recognize either the part of communication engineering or the part of energy engineering or just the mathem~tical part of this matter. The components and considerations of automatic control will without doubt take a great, if not a decisive, part in the engineering fields of the future even if they are not concerned with automatic control problems in a narrower sense. Therefore, they should be taught as a central field of study in completeness
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to mechanical, electrical, chemical engineers and physicists. Such a field of study does not yet exist during the period of education. Its creation and content have to be newly set up but, in general, would only concern the linear part and therefore should be as follows: (a) Mathematical methodology of the transfer-function in an easy manner. The connection between frequency response, transient response and location of poles and zeros. (b) Interpretation of the physical laws in the form of operators and the immediate composition of the signal flow diagrams in order to derive the dynamic behaviour of the desired system. (c) Derivation of the transfer-functions and signal flow diagrams for the almost important mechanical, hydraulic, pneumatic, thermal and electrical systems 4 • (d) Stability conditions by use of algebraic methods and also in the frequency domain. (e) Derivation of the circuit diagram of an analogue computer from the signal flow diagram of the considered system. Such a central field of study should constitute a considerable easement to the different specialized fields. This would mean that, for example, students would have much better knowledge when they begin to study communication and data-transmission engineering so that the questions arising could be handled more efficiently. ]n addition the handling of the dynamic behaviour of electrical machinery and plants would get better preparation. However, such a central field of study would be especially effective for students of mechanical engineering. These students would thereby profit from the new style of representation as signal flow diagrams and the operational methods which hitherto have generally been confined to electrical engineering in default of sufficient knowledge. An essential addition may be expected for the dynamic handling of mechanical systems, vibration engineering, and of the dynamic behaviour of thermal and hydraulic systems. Finally the advantages conferred on all those fields by the widespread use of analogue computers are so obvious that it is hardly necessary to mention them. In order that imparted knowledge in such a field of study will come to fruition it is important to introduce it relatively early (undergraduate level). In the curriculum of German technical universities it should already be put in the third or fourth semester. The amount of two semesters each with two hours in a week (possibly with exercises and laboratory work also) should be sufficient. The time for this new lecture could be found in such a way that now many other lectures can be shortened because the fundamental knowledge is given by this central field of study. The name of this field of study is not so important as its content. It could be called: General System-engineering, or Automatic Control-engineering Fundamentals, or Treatment of the Dynamic Behaviour of Systems, etc . Annexing such a field of study to an institute for automatic control-engineering or an institute for communication engineering, or its complete detachment, is not so important as existence of such a central lecture everywhere.
Now a more decisive treatment is possible whereby higher mathematical operations as Laplace transformation, statistics, etc. can be used. For the linear treatment it would mean covering the following: (a) Detailed consideration of the problems of stability (e.g. root-locus method, D-factorizing, Liapunov methods, etc.). (b) Transient behaviour of a system by the use of different types of regulators, by different locations of the points of application of disturbances, etc. (c) Synthesis and optimal adjusting methods of a control system. (d) Multi-loop control systems. (e) Sampled-data control systems. Self-adjusting control systems. There would also be a place for the treatment of non-linear control problems and the detailed representation of their characteristics and the mathematical methods which are necessary for their handling. The narrower field of automatic control would also be the place for a theoretical and experimental handling of the components which here would find a sufficient platform in parallel to the central lecture, as control-components cannot be handled without close contact with the theory. An institute of automatic control-engineering will now be free for ha ndling the main problems of the field of controlengineering. The institute should for this reason possess sufficient equipment and comprehensive facilities.
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Treatment of Digital Systems The central field of study discussed above contains only analogues and simple linear systems. However, modern datahandling increasingly makes use of digital processes . The latter also find more and more use in the control-engineering field, so that education in this section is necessary also. The group working in this special field, however, is smaller than that in the analogue field as digital systems are mostly electrically operated systems; but their treatment as a whole should certainly be covered. An adequate lecture should be based on the logic-elements, the different types of storage, the analoguedigital converters V.V., and the elements of digital computer techniques. Whether the lecture should be more on the side of communication engineering or more on the side of controlengineering should be decided according to circumstances. References See: BROWN, G. S. Feed-back engineering-A challenging educational objective, in A. TUSTIN, Automatic and Manual Control. 1952. London. KINDLER, H. Regelungstechnik in Lehre und Forschung. Die Technik 14 (1959) 453 . COALES, J. F. The education of instrument technologists and control engineers. Process Control and Automation 6, May (1959) 192. RAYMOND, F. H. La formation des ingenieurs dans les techniques d'automatisme. Automalisme I (1956) 99 , cr. with article of discussion from AJSERMAN, M. A. Gegenwart und Zukunft der Regelungstechnik als Wissenschaft. Automat.
I
Telemeeh ., MoseolV 20 (1959) 257
The Field of Automatic Control in a Narrower Sense
3
When taking the elementary art out of the field of controlengineering there just remains the proper problems of automata.
~
Cr. with KUPFMikLER, K. Nachricht und Energie. Re/;elungstechnik 5 (1957) 226
OPPELT, W. Kleines Handhueh lee/mischer Regelvorgiinge. Verlag Chemie, Weinheim Bergstrasse, 1960. See §§ 17, 19, 20, 24 and 2~
Summary First the technical situation to date is described . In teaching controlengineering problems it is necessary to refer to some of the additional background. The paper deals with the desired situation. Pure mathe-
matical methods used in control-engineering fields should be taught in normal mathematical lectures (namely differential equations for transient response, frequency response and Laplace transforms.
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complex function theory, Boolean algebra, etc.). Dynamical behaviour in the fields of application should be treated in these courses (viz. dynamical behaviour of heat-exchangers in courses on thermodynamic problems, behaviour of synchronous machines in electrical problems, etc.) Courses in control-engineering depend on these two topics. Control-engineering lectures should therefore cover signal-flow theory (analogue and digital), feedback theory, stability problems, analysis and synthesis, non-linear control, sampled-data control, application of statistical theory, optimizing and self-adjusting control.
If the student knows this theoretical background, he can himself solve control problems in the desired fields of application. There is still another objective for control-engineering institutes. This is the general treatment of all the control components (mechanical, pneumatic, hydraulic, electrical, etc. analogue and digital) with which the student should also be able to deal. The paper gives in extenso the expected scope of the lectures, laboratory work and exercises. It makes a proposal for the equipment of a control-engineering institute at a technical university and shows some examples from the Institut flir Regelungstechnik der Technischen Hochschule Darmstadt.
Sommaire Pour I'enseignement de I'automatique, il est necessaire de se referer a un certain nombre de donnees prealables. Les methodes purement mathematiques utilisees en automatique doivent etre enseignees dans des cours normaux de mathematiques (equations differentielles pour la reponse transitoire, la reponse frequentielle et la transformee de Lapiace, theorie des fonctions de variables complexes, algebre de Boole, etc .. .. ). Le comportement dynamique dans les diverses applications doit etre traite dans le cours correspondant (comportement dynamique des echangeurs de chaleur dans le cours de Thermodynamique; comportement des machines synchrones dans le cours d'Electrotechnique). L'enseignement des asservissements derive des deux considerations precedentes.
Le programme de ce cours doit couvrir la theorie des schemas fonctionnels (analogique et digitale), la theorie de la reaction, les problemes de stabilite, d'analyse et de synthese, les applications de la theorie statistique, les contr61es a optimisation et a autoadaptation. Le rapport donne, dans son ensemble, le programme de ces cours, du travail de laboratoire, et des exercices. 11 donne une proposition pour I'equipement d'un institut de servomecanismes dans une universite technique, et donne l'exemple de I'Institut d'Automatique de I'Ecole Poly technique de Darmstadt.
Zusammenfassung Zuerst wird die heutige Situation auf dem Gebiete der Ausbildung in der Regelungstechnik geschildert. In ihr ist es notwendig, neben regelungstechnischen Problemen eine zusiitzliche Einfiihrung in die benotigten mathematischen Grundlagen zu geben. Dann wird die wiinschenswertc Situation geschildert. Dabei sollten die besonderen mathematischen Verfahren, die in der Regelungstechnik benotigt werden, als spezielle mathematische Vorlesungen unter diesem Gesichtspunkt zusammengefasst werden (z.B. Lineare Differentialgleichungen und ihre Obergangsfunktionen, Frequenzgange und Laplace Transformation, Funktionentheorie, Boolesche Algebra u. dgl.). Das dynamische Verhalten der Regelstrecken kann in die Vorlesungen der Anwendungsgebiete verwicsen werden (z.B. dynamisches Verhalten von Warme-Austauschern in die Vorlesungen der Warmetechnik, Verhalten von Synchron-Maschinen in Vorlesungen der Elektrotechnik). Die Vorlesungen der Regelungstechnik stunden jetzt zwischen·
diesen beiden Grenzgebieten und wurden folgendes enthalten: Signalfluss-Theorie (analog und digital), Theorie des Regelkreises, Stabilitatsprobleme, Analyse und Synthese des Regelkreises, Nichtlineare Regelung, Getastete Regelung, Anwendung statistischer Verfahren, Selbsteinstellende Regelkreise. Mittels dieses theoretischen Riistzeuges kann dann der Student einerseits die Regelprobleme in den verschiedenen Anwendungsgebieten losen. Andererseits kann er jetzt die Bauelemente der Regelungstechnik (mechanische, elektrische, pneumatische, hydraulische Elemente usw. , analoge und digitale Bauelemente) behandeln . Die Bearbeitung solcher Bauelemente unter gemeinsamen Gesichtspunkten ist , neben der Pflege der allgemeinen Theorie, die Hauptaufgabe flir regelungstechnische Institute. Die sich aus dieser Aufgliederung ergebenden Folgerungen werden im einzelnen auseinandergesetzt.
DISCUSSION S. I.
ARTOBOLEYSKI
(U.S.S.R.)
In my discussion I shall consider the question of training personnel working in the field of automation of technological processes and , basically, those fields of industry for which discrete, more correctly discontinuous operational processes, which, as a rule, are performed by machines, are characteristic. The variety of these processes is characteristic; processes identical in nature and giving the same final result may be carried out on various types of machines with various sequences of operations, i.e. the processes may have different structures. Therefore the designer and technologist has the problem of choosing the optimum form of automation for given specific conditions, and this choice should be made during the design or adjustment of the equipment. This choice requires the complex evaluation of possible alternatives according to a number of criteria, including technical-economic ones. From the point of view of cybernetic concepts, a technological process may be represented in the form of three streams: material (work pieces), energy and information. All three streams are interrelated and interact. The choice and design of optimal systems and the construction of the equipment is possible only on the basis of theoretical propositions establishing the character of the relationships between the streams.
The theory of automatic regulation, more correctly of automatic control, basically considers problems connected with the stream of information, considering that the operating conditions of the controlled objects and their dynamic characteristics are given. The proposal of Professor Oppelt in regard to changing the content of the courses in theory of automatic control in technical institutes, and the methodology of presenting them, will doubtless improve the education of future engineers in this field, but does not solve the above problems completely. Their solution requires the inclusion in the education of specialists of a discipline or section which can be termed the theoretical foundations of the automation of production processes (T.F.A.). The tasks of T.F.A. are broad, but they can be defined as the development of the theory and methods of constructing the operating algorithm of an automatic system carrying out a given technological process and the efficient realization of this algorithm. The control algorithm is obviously a component part of the functioning algorithm. T.F.A. should provide a complex consideration of the problem and, consequently, should use extensively the results of a number of such 'old' and 'new' scientific disciplines as, of course, the theory of automatic control, cybernetics, the theory of computers, etc. The development of T.F.A. can only be successful if it is developed as an inter-disciplinary subject. Practice shows that to develop
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automation the inter-disciplinary exchange of experience has tremendous significance; the theoretical basis of such an exchange should be one of the fundamental tasks of T.F.A. The development of a theory is only possible if the. basic structural elements of the objects studied have been estabhshed and their classifications and the physical factors defining the interrelations of these elements clarified. Scientific work carried out in the U.S .S.R. in recent years has permitted the solution of a substantial number of these problems with respect to discontinuous operating process ~~~hlnes. On this basis there have been formulated a number of diVISIOns of T.F.A.: (a) generalized theory of the dri~es of executive organs in machines; (b) generalized theory of machine control systems; (c) th~ory of automatic production lines; and (d) the theory of productiVity of machines and production lines. .. The basic propositions of T.F.A. are descnbed In the works of the author' ,2. The establishment of T.F.A. of machine processes has not only a pedagogic significance. A number of scientists in the U.S.S.R. and in other countries consider that the estabhshment of a special discipline treating the generalized theory of mode~n technological machines, extensively using feedback, electronICs, comput,ers, electrical-hydraulic and pneumatic dri.ves" etc., is very, pressl~g. Such a theory, in the opinion of these SClentlst~ , should UnIte speCialists of various scientific fields, who take part In the development of modern technological machines and automatic lines, . The complex solution of the scientific problems of automatIOn of productive processes is, of course, outsIde the. framework of our Congress, but, as was correctly sai? by Academlc,tan V. A, Trapeznikov, is the only correct and effectIve way of solVing them. T.F.A" as a complex discipline, ca~ .only. be de~eloped ~n. the baSIS of co-operative work of speclahsts In vanou~ ?Isclpllnes and an especially large role will be play~d b~ speclahsts In the field . of automatic control. I therefore felt It deSirable to draw your attentIOn to these problems.
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2
References ARTOBOLEVSKI, S. I. On the principles of automation of discrete technological processes, The Automation of Technological Processes, No. lIl, 1960 Academy of Sciences of the U,S.S.R . ARTOBOLEVSKI, S. l. The Calculatioll of the Productivity of Machines. 1951. Mashgiz,
B. A.
RYABOV
(U.S.S.R.)
A. V.
S.
We have heard the interesting report of Professor Oppelt, which, in my opinion, has discussed only one si,de of t~e complex process ?f educating or, more exactly, of forming engl~eenng spectah~ts In automatic control. The educational process IS more comphcated and does not consist only of theoretical subjects in the field of automatic control. The following questions are still not clear to me: . (I) Inclusion of the subject 'regulation fundamentals' In the curricula of all technical institutes requires a certain physicalmathematical minimum in the education of the students. How should this minimum be provided? What is its length in hours? What subjects should be inclu~ed? . , (2) Presenting the course regulatIOn fundamentals somewhat divorced from concrete examples leads to the reductIOn of such a course to a supplement to applied mathematics , Is this c~rrect? Is it pedagogically justifiable to present a technIcal subject Without the use of engineering examples? " (3) The further training of engineers is not discussed In the report. Where should the student become acquainted with special applications and where should project design be introduced, etc. ? In the technical institutes of the Soviet Union these stages of education are included in the institutes' curricula , in certain other countries it takes place in industry and in specialized ~n~titutes. It would be interesting to have the opinion of Professor Oppelt on this question,
FATEYEV
(U.S.s.R.)
The question raised by Professor Oppelt in his report is of great interest and has very great importance for the correct development of automation and its means, The training of engineers, whose work will be in the field of automation control, should be such that the engineer, entering industry after graduation, can quickly begin his work and the fulfilment of his purpose. The statement of the speaker on the training of engineers 40 years from now, i,e, in the year 2000, is not clear. Education should be so organized that the knowledge obtained by th~ engineer during his education should be utilizable as rapidly as possible. The thought expressed by the author of the re~ort: 'Therefore each curriculum must be designed to teach the coming generall?n the laws of ~ature, so that they will be able to apply these laws Independently In contributing to the progress of engineering science', should be acknowledged as completely correct. The reasonable, statement of ~he author on the impossibility of extending the penod of education should also be noted . I would now like to speak on the method of teaching the theory of automatic control. In our opinion control theory should be presented as the general theory of all problems arising in control processes, and not as the theory of regulating some ind~vidual industrial processes, Such a theory cannot and should not eXist: In a general theoretical course examples should, however, be given, which illustrate the individual results in automatic control processes, as for example is done in Professor Opp~lt's book, , . In the individual specialized faculties (chemical, mechanIcal engineering, etc.) it will be ~ecessary t~ establish courses on the automatic control of productIOn mechanIsms and processes as, for " example, is done in the technical institutes of ~h~ U,S.S.R. Furthermore, it is stated in the report that It IS necessary to hmlt ourselves to the presentation of the theory of linear systems---:a point of view with which it is difficult to agree. At the present time the requirements of practice are so g~eat and th~ theory of control, h~s developed so strongly that lu!utatlon to the llne~r theory alone IS In no way possible, although thiS theory IS the baSIS, . The students should be required to study on a compulsory basIs: questions of non-linear theory; questions of simulation; the use of control computers; and the theory of statistical methods. We agree with Professor Oppelt that study of control theory cannot be postponed to the end of the curriculum, The course should start not later than 2 or 2~· years before graduation, and should be preceded by a well-rounded preparation in mathematics, electronics and various magnetic-hydraulic, and other elements, G. GERASIMOV
(U.S.S.R.)
The conclusions expressed by the speaker are correct,. but not universally. It is possible to debate the place of a course In control theory; probably it is more useful to give it in the. later years, However, in general his recommendations are hardly SUitable for the training of engineers in all specializations, taking into . account modern differentiation of production. It appears more SUitable to have individual curricula for technologists (as such), technologists intended for the automation of some branch of production and, finally, engineers for the development of means ,of automa~ion, The first category should receive a sound ~echnologlca~ educatIOn and a sound training in the field of automatIOn. The third should ha~e a comprehensive education in mechanical .or electncal englneenng. For successful automation of a technological process Its technology should be studied fairly fully. It appears to us that in the later years the number of hours given to technological subjects and to subjects of automation should be approximately the same*.
* The mathematical foundations of automation need not be presented in a course on control theory, Such subjects as operational methods, principles of harmonic analysis, etc, can be conveniently presented in a course of mathematics. It should be remarked that the paper does not mention the necessity of the serious study of measurement problems encountered in some given field of technology. At the same time, in the proposed list of subjects nothing is said about measurement. However, sometimes measurements are decisive for questions of automation and should not be omitted.
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YE.
G.
SHRAMKOV
(U.S.S.R.)
The basic ideas described in Professor Oppelt"s paper deserve serious consideration and should be approved with certain minor reservations. Unfortunately, the paper does not reflect the position that, in the education of students in the field of automatic control, an important part is played by training in the field of electrical measurements in the broad sense of this concept, having in mind the methods and equipment available for the measurement of various types of physical quantities. I would like to take the opportunity of this Congress to emphasize once again the necessity of giving serious attention to electrical measurements and considering it as a field of automation and control. It is quite natural that students in the field of automatic control should be fairly deeply and extensively educated in the field of primary transducers (pick-ups) which in many respects determine the precision and reliability of operation of automatic instruments. This is the subject of measurement, in particular electrical measurement engineering.
V. N.
DOBKIN
(U.S.S.R.)
Today the concept of automatic control is already substantially broader than the concept of automatic regulation. Therefore, in solving engineering problems of automation, it is not only necessary to have knowledge of system dynamics, which Professor OppeJt includes in a course termed 'a course of automatic control', but also a number of other mathematical subjects. A group of my colleagues at the Institute and I consider that future specialists in automatic control must be given at least elementary knowledge of such mathematical subjects as the fundamentals of mathematical logic (which is at the root of the theory of finite automata), elements of variational calculus and linear programming (important in work on optimization), principles of mathematical statistics, certain numerical methods, etc. General knowledge of system dynamics and the basic concepts of the above mathematical subjects should be taught in the first half of the curriculum (during four or five semesters). It might be more correct to name this a course in mathematical methods in engineering. We share the view of Professor S. G. Gerasimov that problems of regulation and control, as such (i.e. questions of the interaction of control systems with the controlled objects), should be considered in higher courses (fourth or fifth year of instruction) after instruction in technological processes and technological equipment. It is important that these technological courses be supplemented to a sufficient extent by instruction on topics in the dynamics of production processes and the characteristics of their control. Professor OppeJt mentioned the basic difficulty in the training of specialists, which follows from the impossibility of extending appreciably the period of education, despite the increase in geometric progression, of the volume of knowledge required. It appears that a solution of this dilemma should be sought in the further specialization of engineers. The history of development of higher education confirms this tendency. An example might be the concept of the 'specialist in the field of automatic control', which is employed in the paper under discussion. Scientific engineering experience in the automation of production shows that already differentiation within this concept is necessary, at least along two lines, namely, specialists in means of automation (in whose training great weight should be given to industrial electronics and design subjects), and specialists in the application of these
means in the corresponding specific fields of industry (i.e. applications engineers), who require a fairly. extensive. technological training. It would be valuable to contmue, m the periodIcal press of various countries, the discussions begun at this section of the Congress. S.
N.
ZASEDATELEV
(U.S.s.R .)
The congress has not given adequate attention to questions of measurement. Actually, the development of automation is directly connected with the solution of problems of obtaining information, with the development of the theory and with the means of measurement. It is to be hoped that in the future I.F.A.C. will give suitable space to questions of measurement. DOMANSKI
(U.S.s.R.)
Does Professor Oppelt assume that it is necessary to introduce an additional course in mathematics or to revise fundamentally the existing courses of mechanics and automation? W. OPPELT, in reply. I should like to express my appreciation to our Soviet colleagues for their active participation and the interest which they have expressed in my paper. I consider that the problem of teaching should be considered dynamically, so to speak, for example, as the growth of a tree or the birth of new cells. The teaching process is limited by time, and it is therefore necessary to find a criterion for what is essential in the process. I have taken this point of view in the paper: teaching automatic control should begin as early as possible. This is advantageous because the teaching of further subjects may be based on the previous knowledge of automatic control. I do not intend to claim that a course in automatic control should be limited to an introductory course, on the contrary, it should be developed and deepened. In answer to Professor Domanski, I consider that it is necessary to broaden the mathematics courses. I agree with Docent Dobkin that in courses connected with the automatic control of technological processes, greater attention should be given to the process dynamics. However, I do not think that there is a contradiction between my proposition on the earliest presentation of the course and the necessity of deepening instruction in the courses in later years. It is very important that the student should know the appropriate mathematical techniques when he proceeds to a deeper study of automatic control. I agree with Professors Gerasimov and Shramkov on the necessity of strengthening instruction in courses on measurement. We have in Darmstadt an institute which trains measurement specialists. We consider that in the Federal German Republic the training of specialists in automatic control should not be carried on in industrial enterprises but in the schools. I agree that a course in automatic control should be considered a completely independent discipline, as, for example, mathematics. Further, I would like to state that the course in automatic control should be considered as a single unit, and not broken down into individual subgroups according to individual specialized applied sciences. I consider that courses in application of automatic control should be included in the corresponding specializations in the technical institutes, while the institutes training specialists in automatic control should teach the basic theory of automatic control more broadly.
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some places in a general form. Therefore, all students of mechanical, electrical, and process engineering, and of physics attend similar courses. The theory of control-engineering which is independent of its application is then the guiding line while the examples for application are taken from different fields. In the long run both these possibilities are unsatisfactory. The first possibility of holding special lectures closely connected with application does not get away from a purely descriptive version as, in general, the knowledge of the students is not sufficient for an exhaustive treatment and there is not time for broad preliminary studies. The second possibility-a common treatment of the control-engineering field-does not have these limitations but a significant proportion of the lectures must be devoted to obtaining sufficient basic skill in techniques such as those dealing with frequency response, Laplace transforms, etc. There is no doubt that within this arrangement the special problems of the control-engineering field can only occupy a part of the whole course 2 • A significant incorporation of the automatic control field in the curriculum is only possible if changes and new compendiums are also made in those fields which are closely connected with control-engineering. In what follows, consideration is given to those fields in which the presence of control-engineering can affect other technical fields. Future Incorporation of Automatic Control in the Curriculum Control-engineering components have inputs (where information is picked up) and outputs (with which they manipulate the energy flOW)3 . This characteristic therefore makes the controlengineering field a bridge between communication engineering on the one hand and energy engineering on the other. The necessary basis which describes the behaviour of such components is therefore to be found partly in the communication engineering field, namely when handling the transferfunction of communication systems (in the time domain, in the frequency domain, by characterization of a system using poles and zeros, by mathematical methods to go from frequency domain to time domain, etc.) This basis is also to be found in part in the field of energy flow and therefore closely related to the dynamics of mechanical engineering, fluid mechanics, heat engineering and 'classical' electrical engineering. Current handling of the basic control-engineering elements is split into many special fields. Their entity is therefore not evident to the learning students and much useful time is wasted by parallel handling in the different fields. A person who does not go into the field of automatic control in detail will not recognize the main essentials. He is only able to recognize either the part of communication engineering or the part of energy engineering or just the mathem~tical part of this matter. The components and considerations of automatic control will without doubt take a great, if not a decisive, part in the engineering fields of the future even if they are not concerned with automatic control problems in a narrower sense. Therefore, they should be taught as a central field of study in completeness
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W. OPPELT
to mechanical, electrical, chemical engineers and physicists. Such a field of study does not yet exist during the period of education. Its creation and content have to be newly set up but, in general, would only concern the linear part and therefore should be as follows: (a) Mathematical methodology of the transfer-function in an easy manner. The connection between frequency response, transient response and location of poles and zeros. (b) Interpretation of the physical laws in the form of operators and the immediate composition of the signal flow diagrams in order to derive the dynamic behaviour of the desired system. (c) Derivation of the transfer-functions and signal flow diagrams for the almost important mechanical, hydraulic, pneumatic, thermal and electrical systems 4 • (d) Stability conditions by use of algebraic methods and also in the frequency domain. (e) Derivation of the circuit diagram of an analogue computer from the signal flow diagram of the considered system. Such a central field of study should constitute a considerable easement to the different specialized fields. This would mean that, for example, students would have much better knowledge when they begin to study communication and data-transmission engineering so that the questions arising could be handled more efficiently. ]n addition the handling of the dynamic behaviour of electrical machinery and plants would get better preparation. However, such a central field of study would be especially effective for students of mechanical engineering. These students would thereby profit from the new style of representation as signal flow diagrams and the operational methods which hitherto have generally been confined to electrical engineering in default of sufficient knowledge. An essential addition may be expected for the dynamic handling of mechanical systems, vibration engineering, and of the dynamic behaviour of thermal and hydraulic systems. Finally the advantages conferred on all those fields by the widespread use of analogue computers are so obvious that it is hardly necessary to mention them. In order that imparted knowledge in such a field of study will come to fruition it is important to introduce it relatively early (undergraduate level). In the curriculum of German technical universities it should already be put in the third or fourth semester. The amount of two semesters each with two hours in a week (possibly with exercises and laboratory work also) should be sufficient. The time for this new lecture could be found in such a way that now many other lectures can be shortened because the fundamental knowledge is given by this central field of study. The name of this field of study is not so important as its content. It could be called: General System-engineering, or Automatic Control-engineering Fundamentals, or Treatment of the Dynamic Behaviour of Systems, etc . Annexing such a field of study to an institute for automatic control-engineering or an institute for communication engineering, or its complete detachment, is not so important as existence of such a central lecture everywhere.
Now a more decisive treatment is possible whereby higher mathematical operations as Laplace transformation, statistics, etc. can be used. For the linear treatment it would mean covering the following: (a) Detailed consideration of the problems of stability (e.g. root-locus method, D-factorizing, Liapunov methods, etc.). (b) Transient behaviour of a system by the use of different types of regulators, by different locations of the points of application of disturbances, etc. (c) Synthesis and optimal adjusting methods of a control system. (d) Multi-loop control systems. (e) Sampled-data control systems. Self-adjusting control systems. There would also be a place for the treatment of non-linear control problems and the detailed representation of their characteristics and the mathematical methods which are necessary for their handling. The narrower field of automatic control would also be the place for a theoretical and experimental handling of the components which here would find a sufficient platform in parallel to the central lecture, as control-components cannot be handled without close contact with the theory. An institute of automatic control-engineering will now be free for ha ndling the main problems of the field of controlengineering. The institute should for this reason possess sufficient equipment and comprehensive facilities.
(n
Treatment of Digital Systems The central field of study discussed above contains only analogues and simple linear systems. However, modern datahandling increasingly makes use of digital processes . The latter also find more and more use in the control-engineering field, so that education in this section is necessary also. The group working in this special field, however, is smaller than that in the analogue field as digital systems are mostly electrically operated systems; but their treatment as a whole should certainly be covered. An adequate lecture should be based on the logic-elements, the different types of storage, the analoguedigital converters V.V., and the elements of digital computer techniques. Whether the lecture should be more on the side of communication engineering or more on the side of controlengineering should be decided according to circumstances. References See: BROWN, G. S. Feed-back engineering-A challenging educational objective, in A. TUSTIN, Automatic and Manual Control. 1952. London. KINDLER, H. Regelungstechnik in Lehre und Forschung. Die Technik 14 (1959) 453 . COALES, J. F. The education of instrument technologists and control engineers. Process Control and Automation 6, May (1959) 192. RAYMOND, F. H. La formation des ingenieurs dans les techniques d'automatisme. Automalisme I (1956) 99 , cr. with article of discussion from AJSERMAN, M. A. Gegenwart und Zukunft der Regelungstechnik als Wissenschaft. Automat.
I
Telemeeh ., MoseolV 20 (1959) 257
The Field of Automatic Control in a Narrower Sense
3
When taking the elementary art out of the field of controlengineering there just remains the proper problems of automata.
~
Cr. with KUPFMikLER, K. Nachricht und Energie. Re/;elungstechnik 5 (1957) 226
OPPELT, W. Kleines Handhueh lee/mischer Regelvorgiinge. Verlag Chemie, Weinheim Bergstrasse, 1960. See §§ 17, 19, 20, 24 and 2~
Summary First the technical situation to date is described . In teaching controlengineering problems it is necessary to refer to some of the additional background. The paper deals with the desired situation. Pure mathe-
matical methods used in control-engineering fields should be taught in normal mathematical lectures (namely differential equations for transient response, frequency response and Laplace transforms.
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PROBLEMS IN TEACHING CONTROL-ENGINEERING
complex function theory, Boolean algebra, etc.). Dynamical behaviour in the fields of application should be treated in these courses (viz. dynamical behaviour of heat-exchangers in courses on thermodynamic problems, behaviour of synchronous machines in electrical problems, etc.) Courses in control-engineering depend on these two topics. Control-engineering lectures should therefore cover signal-flow theory (analogue and digital), feedback theory, stability problems, analysis and synthesis, non-linear control, sampled-data control, application of statistical theory, optimizing and self-adjusting control.
If the student knows this theoretical background, he can himself solve control problems in the desired fields of application. There is still another objective for control-engineering institutes. This is the general treatment of all the control components (mechanical, pneumatic, hydraulic, electrical, etc. analogue and digital) with which the student should also be able to deal. The paper gives in extenso the expected scope of the lectures, laboratory work and exercises. It makes a proposal for the equipment of a control-engineering institute at a technical university and shows some examples from the Institut flir Regelungstechnik der Technischen Hochschule Darmstadt.
Sommaire Pour I'enseignement de I'automatique, il est necessaire de se referer a un certain nombre de donnees prealables. Les methodes purement mathematiques utilisees en automatique doivent etre enseignees dans des cours normaux de mathematiques (equations differentielles pour la reponse transitoire, la reponse frequentielle et la transformee de Lapiace, theorie des fonctions de variables complexes, algebre de Boole, etc .. .. ). Le comportement dynamique dans les diverses applications doit etre traite dans le cours correspondant (comportement dynamique des echangeurs de chaleur dans le cours de Thermodynamique; comportement des machines synchrones dans le cours d'Electrotechnique). L'enseignement des asservissements derive des deux considerations precedentes.
Le programme de ce cours doit couvrir la theorie des schemas fonctionnels (analogique et digitale), la theorie de la reaction, les problemes de stabilite, d'analyse et de synthese, les applications de la theorie statistique, les contr61es a optimisation et a autoadaptation. Le rapport donne, dans son ensemble, le programme de ces cours, du travail de laboratoire, et des exercices. 11 donne une proposition pour I'equipement d'un institut de servomecanismes dans une universite technique, et donne l'exemple de I'Institut d'Automatique de I'Ecole Poly technique de Darmstadt.
Zusammenfassung Zuerst wird die heutige Situation auf dem Gebiete der Ausbildung in der Regelungstechnik geschildert. In ihr ist es notwendig, neben regelungstechnischen Problemen eine zusiitzliche Einfiihrung in die benotigten mathematischen Grundlagen zu geben. Dann wird die wiinschenswertc Situation geschildert. Dabei sollten die besonderen mathematischen Verfahren, die in der Regelungstechnik benotigt werden, als spezielle mathematische Vorlesungen unter diesem Gesichtspunkt zusammengefasst werden (z.B. Lineare Differentialgleichungen und ihre Obergangsfunktionen, Frequenzgange und Laplace Transformation, Funktionentheorie, Boolesche Algebra u. dgl.). Das dynamische Verhalten der Regelstrecken kann in die Vorlesungen der Anwendungsgebiete verwicsen werden (z.B. dynamisches Verhalten von Warme-Austauschern in die Vorlesungen der Warmetechnik, Verhalten von Synchron-Maschinen in Vorlesungen der Elektrotechnik). Die Vorlesungen der Regelungstechnik stunden jetzt zwischen·
diesen beiden Grenzgebieten und wurden folgendes enthalten: Signalfluss-Theorie (analog und digital), Theorie des Regelkreises, Stabilitatsprobleme, Analyse und Synthese des Regelkreises, Nichtlineare Regelung, Getastete Regelung, Anwendung statistischer Verfahren, Selbsteinstellende Regelkreise. Mittels dieses theoretischen Riistzeuges kann dann der Student einerseits die Regelprobleme in den verschiedenen Anwendungsgebieten losen. Andererseits kann er jetzt die Bauelemente der Regelungstechnik (mechanische, elektrische, pneumatische, hydraulische Elemente usw. , analoge und digitale Bauelemente) behandeln . Die Bearbeitung solcher Bauelemente unter gemeinsamen Gesichtspunkten ist , neben der Pflege der allgemeinen Theorie, die Hauptaufgabe flir regelungstechnische Institute. Die sich aus dieser Aufgliederung ergebenden Folgerungen werden im einzelnen auseinandergesetzt.
DISCUSSION S. I.
ARTOBOLEYSKI
(U.S.S.R.)
In my discussion I shall consider the question of training personnel working in the field of automation of technological processes and , basically, those fields of industry for which discrete, more correctly discontinuous operational processes, which, as a rule, are performed by machines, are characteristic. The variety of these processes is characteristic; processes identical in nature and giving the same final result may be carried out on various types of machines with various sequences of operations, i.e. the processes may have different structures. Therefore the designer and technologist has the problem of choosing the optimum form of automation for given specific conditions, and this choice should be made during the design or adjustment of the equipment. This choice requires the complex evaluation of possible alternatives according to a number of criteria, including technical-economic ones. From the point of view of cybernetic concepts, a technological process may be represented in the form of three streams: material (work pieces), energy and information. All three streams are interrelated and interact. The choice and design of optimal systems and the construction of the equipment is possible only on the basis of theoretical propositions establishing the character of the relationships between the streams.
The theory of automatic regulation, more correctly of automatic control, basically considers problems connected with the stream of information, considering that the operating conditions of the controlled objects and their dynamic characteristics are given. The proposal of Professor Oppelt in regard to changing the content of the courses in theory of automatic control in technical institutes, and the methodology of presenting them, will doubtless improve the education of future engineers in this field, but does not solve the above problems completely. Their solution requires the inclusion in the education of specialists of a discipline or section which can be termed the theoretical foundations of the automation of production processes (T.F.A.). The tasks of T.F.A. are broad, but they can be defined as the development of the theory and methods of constructing the operating algorithm of an automatic system carrying out a given technological process and the efficient realization of this algorithm. The control algorithm is obviously a component part of the functioning algorithm. T.F.A. should provide a complex consideration of the problem and, consequently, should use extensively the results of a number of such 'old' and 'new' scientific disciplines as, of course, the theory of automatic control, cybernetics, the theory of computers, etc. The development of T.F.A. can only be successful if it is developed as an inter-disciplinary subject. Practice shows that to develop
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W.
automation the inter-disciplinary exchange of experience has tremendous significance; the theoretical basis of such an exchange should be one of the fundamental tasks of T.F.A. The development of a theory is only possible if the. basic structural elements of the objects studied have been estabhshed and their classifications and the physical factors defining the interrelations of these elements clarified. Scientific work carried out in the U.S .S.R. in recent years has permitted the solution of a substantial number of these problems with respect to discontinuous operating process ~~~hlnes. On this basis there have been formulated a number of diVISIOns of T.F.A.: (a) generalized theory of the dri~es of executive organs in machines; (b) generalized theory of machine control systems; (c) th~ory of automatic production lines; and (d) the theory of productiVity of machines and production lines. .. The basic propositions of T.F.A. are descnbed In the works of the author' ,2. The establishment of T.F.A. of machine processes has not only a pedagogic significance. A number of scientists in the U.S.S.R. and in other countries consider that the estabhshment of a special discipline treating the generalized theory of mode~n technological machines, extensively using feedback, electronICs, comput,ers, electrical-hydraulic and pneumatic dri.ves" etc., is very, pressl~g. Such a theory, in the opinion of these SClentlst~ , should UnIte speCialists of various scientific fields, who take part In the development of modern technological machines and automatic lines, . The complex solution of the scientific problems of automatIOn of productive processes is, of course, outsIde the. framework of our Congress, but, as was correctly sai? by Academlc,tan V. A, Trapeznikov, is the only correct and effectIve way of solVing them. T.F.A" as a complex discipline, ca~ .only. be de~eloped ~n. the baSIS of co-operative work of speclahsts In vanou~ ?Isclpllnes and an especially large role will be play~d b~ speclahsts In the field . of automatic control. I therefore felt It deSirable to draw your attentIOn to these problems.
1
2
References ARTOBOLEVSKI, S. I. On the principles of automation of discrete technological processes, The Automation of Technological Processes, No. lIl, 1960 Academy of Sciences of the U,S.S.R . ARTOBOLEVSKI, S. l. The Calculatioll of the Productivity of Machines. 1951. Mashgiz,
B. A.
RYABOV
(U.S.S.R.)
A. V.
S.
We have heard the interesting report of Professor Oppelt, which, in my opinion, has discussed only one si,de of t~e complex process ?f educating or, more exactly, of forming engl~eenng spectah~ts In automatic control. The educational process IS more comphcated and does not consist only of theoretical subjects in the field of automatic control. The following questions are still not clear to me: . (I) Inclusion of the subject 'regulation fundamentals' In the curricula of all technical institutes requires a certain physicalmathematical minimum in the education of the students. How should this minimum be provided? What is its length in hours? What subjects should be inclu~ed? . , (2) Presenting the course regulatIOn fundamentals somewhat divorced from concrete examples leads to the reductIOn of such a course to a supplement to applied mathematics , Is this c~rrect? Is it pedagogically justifiable to present a technIcal subject Without the use of engineering examples? " (3) The further training of engineers is not discussed In the report. Where should the student become acquainted with special applications and where should project design be introduced, etc. ? In the technical institutes of the Soviet Union these stages of education are included in the institutes' curricula , in certain other countries it takes place in industry and in specialized ~n~titutes. It would be interesting to have the opinion of Professor Oppelt on this question,
FATEYEV
(U.S.s.R.)
The question raised by Professor Oppelt in his report is of great interest and has very great importance for the correct development of automation and its means, The training of engineers, whose work will be in the field of automation control, should be such that the engineer, entering industry after graduation, can quickly begin his work and the fulfilment of his purpose. The statement of the speaker on the training of engineers 40 years from now, i,e, in the year 2000, is not clear. Education should be so organized that the knowledge obtained by th~ engineer during his education should be utilizable as rapidly as possible. The thought expressed by the author of the re~ort: 'Therefore each curriculum must be designed to teach the coming generall?n the laws of ~ature, so that they will be able to apply these laws Independently In contributing to the progress of engineering science', should be acknowledged as completely correct. The reasonable, statement of ~he author on the impossibility of extending the penod of education should also be noted . I would now like to speak on the method of teaching the theory of automatic control. In our opinion control theory should be presented as the general theory of all problems arising in control processes, and not as the theory of regulating some ind~vidual industrial processes, Such a theory cannot and should not eXist: In a general theoretical course examples should, however, be given, which illustrate the individual results in automatic control processes, as for example is done in Professor Opp~lt's book, , . In the individual specialized faculties (chemical, mechanIcal engineering, etc.) it will be ~ecessary t~ establish courses on the automatic control of productIOn mechanIsms and processes as, for " example, is done in the technical institutes of ~h~ U,S.S.R. Furthermore, it is stated in the report that It IS necessary to hmlt ourselves to the presentation of the theory of linear systems---:a point of view with which it is difficult to agree. At the present time the requirements of practice are so g~eat and th~ theory of control, h~s developed so strongly that lu!utatlon to the llne~r theory alone IS In no way possible, although thiS theory IS the baSIS, . The students should be required to study on a compulsory basIs: questions of non-linear theory; questions of simulation; the use of control computers; and the theory of statistical methods. We agree with Professor Oppelt that study of control theory cannot be postponed to the end of the curriculum, The course should start not later than 2 or 2~· years before graduation, and should be preceded by a well-rounded preparation in mathematics, electronics and various magnetic-hydraulic, and other elements, G. GERASIMOV
(U.S.S.R.)
The conclusions expressed by the speaker are correct,. but not universally. It is possible to debate the place of a course In control theory; probably it is more useful to give it in the. later years, However, in general his recommendations are hardly SUitable for the training of engineers in all specializations, taking into . account modern differentiation of production. It appears more SUitable to have individual curricula for technologists (as such), technologists intended for the automation of some branch of production and, finally, engineers for the development of means ,of automa~ion, The first category should receive a sound ~echnologlca~ educatIOn and a sound training in the field of automatIOn. The third should ha~e a comprehensive education in mechanical .or electncal englneenng. For successful automation of a technological process Its technology should be studied fairly fully. It appears to us that in the later years the number of hours given to technological subjects and to subjects of automation should be approximately the same*.
* The mathematical foundations of automation need not be presented in a course on control theory, Such subjects as operational methods, principles of harmonic analysis, etc, can be conveniently presented in a course of mathematics. It should be remarked that the paper does not mention the necessity of the serious study of measurement problems encountered in some given field of technology. At the same time, in the proposed list of subjects nothing is said about measurement. However, sometimes measurements are decisive for questions of automation and should not be omitted.
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PROBLEMS IN TEACHING CONTROL-ENGINEERING
YE.
G.
SHRAMKOV
(U.S.S.R.)
The basic ideas described in Professor Oppelt"s paper deserve serious consideration and should be approved with certain minor reservations. Unfortunately, the paper does not reflect the position that, in the education of students in the field of automatic control, an important part is played by training in the field of electrical measurements in the broad sense of this concept, having in mind the methods and equipment available for the measurement of various types of physical quantities. I would like to take the opportunity of this Congress to emphasize once again the necessity of giving serious attention to electrical measurements and considering it as a field of automation and control. It is quite natural that students in the field of automatic control should be fairly deeply and extensively educated in the field of primary transducers (pick-ups) which in many respects determine the precision and reliability of operation of automatic instruments. This is the subject of measurement, in particular electrical measurement engineering.
V. N.
DOBKIN
(U.S.S.R.)
Today the concept of automatic control is already substantially broader than the concept of automatic regulation. Therefore, in solving engineering problems of automation, it is not only necessary to have knowledge of system dynamics, which Professor OppeJt includes in a course termed 'a course of automatic control', but also a number of other mathematical subjects. A group of my colleagues at the Institute and I consider that future specialists in automatic control must be given at least elementary knowledge of such mathematical subjects as the fundamentals of mathematical logic (which is at the root of the theory of finite automata), elements of variational calculus and linear programming (important in work on optimization), principles of mathematical statistics, certain numerical methods, etc. General knowledge of system dynamics and the basic concepts of the above mathematical subjects should be taught in the first half of the curriculum (during four or five semesters). It might be more correct to name this a course in mathematical methods in engineering. We share the view of Professor S. G. Gerasimov that problems of regulation and control, as such (i.e. questions of the interaction of control systems with the controlled objects), should be considered in higher courses (fourth or fifth year of instruction) after instruction in technological processes and technological equipment. It is important that these technological courses be supplemented to a sufficient extent by instruction on topics in the dynamics of production processes and the characteristics of their control. Professor OppeJt mentioned the basic difficulty in the training of specialists, which follows from the impossibility of extending appreciably the period of education, despite the increase in geometric progression, of the volume of knowledge required. It appears that a solution of this dilemma should be sought in the further specialization of engineers. The history of development of higher education confirms this tendency. An example might be the concept of the 'specialist in the field of automatic control', which is employed in the paper under discussion. Scientific engineering experience in the automation of production shows that already differentiation within this concept is necessary, at least along two lines, namely, specialists in means of automation (in whose training great weight should be given to industrial electronics and design subjects), and specialists in the application of these
means in the corresponding specific fields of industry (i.e. applications engineers), who require a fairly. extensive. technological training. It would be valuable to contmue, m the periodIcal press of various countries, the discussions begun at this section of the Congress. S.
N.
ZASEDATELEV
(U.S.s.R .)
The congress has not given adequate attention to questions of measurement. Actually, the development of automation is directly connected with the solution of problems of obtaining information, with the development of the theory and with the means of measurement. It is to be hoped that in the future I.F.A.C. will give suitable space to questions of measurement. DOMANSKI
(U.S.s.R.)
Does Professor Oppelt assume that it is necessary to introduce an additional course in mathematics or to revise fundamentally the existing courses of mechanics and automation? W. OPPELT, in reply. I should like to express my appreciation to our Soviet colleagues for their active participation and the interest which they have expressed in my paper. I consider that the problem of teaching should be considered dynamically, so to speak, for example, as the growth of a tree or the birth of new cells. The teaching process is limited by time, and it is therefore necessary to find a criterion for what is essential in the process. I have taken this point of view in the paper: teaching automatic control should begin as early as possible. This is advantageous because the teaching of further subjects may be based on the previous knowledge of automatic control. I do not intend to claim that a course in automatic control should be limited to an introductory course, on the contrary, it should be developed and deepened. In answer to Professor Domanski, I consider that it is necessary to broaden the mathematics courses. I agree with Docent Dobkin that in courses connected with the automatic control of technological processes, greater attention should be given to the process dynamics. However, I do not think that there is a contradiction between my proposition on the earliest presentation of the course and the necessity of deepening instruction in the courses in later years. It is very important that the student should know the appropriate mathematical techniques when he proceeds to a deeper study of automatic control. I agree with Professors Gerasimov and Shramkov on the necessity of strengthening instruction in courses on measurement. We have in Darmstadt an institute which trains measurement specialists. We consider that in the Federal German Republic the training of specialists in automatic control should not be carried on in industrial enterprises but in the schools. I agree that a course in automatic control should be considered a completely independent discipline, as, for example, mathematics. Further, I would like to state that the course in automatic control should be considered as a single unit, and not broken down into individual subgroups according to individual specialized applied sciences. I consider that courses in application of automatic control should be included in the corresponding specializations in the technical institutes, while the institutes training specialists in automatic control should teach the basic theory of automatic control more broadly.
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