# Oral-History:Karl Astrom

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ÅSTRÖM:
− So this is my thesis. Part of this was actually published in book form, and there was one interesting incident that I came to think about when you asked When I came back from the United States I also had to do a pass in the Swedish military. Then I was placed at the Research Institute of National Defense. I was applying the stochastic controls we had learned about inertial navigation systems. I had two months in the military service, which was very useful to apply what I had learned to a basic problem. There is a summary here, which was written in Swedish, and then the major part here has to be written -- you see it here, for example, "The Characteristics of a Stable Platform.” See, I have here the platform the gyroscope is on, and the fact is that you can orient the gyroscopes in many different ways, and then the interactions change in very different ways. In today's language it is a typical multi-variable control problem. Here are the references to the Draper lab results. Most of the things we did were actually written in English. Here is the analysis of the inertial navigation system with the pendulum effect. So it's a typical mixture of mechanics and control. Here you see the swing of the pendulum, and stuff like this.
+ So this is my thesis. Part of this was actually published in book form, and there was one interesting incident that I came to think about when you asked. When I came back from the United States I also had to do a pass in the Swedish military. Then I was placed at the Research Institute of National Defense. I was applying the stochastic controls we had learned about inertial navigation systems. I had two months in the military service, which was very useful to apply what I had learned to a basic problem. There is a summary here, which was written in Swedish, and then the major part here has to be written -- you see it here, for example, "The Characteristics of a Stable Platform.” See, I have here the platform the gyroscope is on, and the fact is that you can orient the gyroscopes in many different ways, and then the interactions change in very different ways. In today's language it is a typical multi-variable control problem. Here are the references to the Draper lab results. Most of the things we did were actually written in English. Here is the analysis of the inertial navigation system with the pendulum effect. So it's a typical mixture of mechanics and control. Here you see the swing of the pendulum, and stuff like this.

Line 947: Line 947:

− ÅSTRÖM:
It has a mixed story, because it was part of mechanical engineering and part of electrical engineering. Also because of the process control aspect it was a big part of chemical engineering. So it has taken many different shapes. There have also been places where, for example, like here in _____, we're centralized in control, so we have area responsibility for control. We do control for everybody.
+ ÅSTRÖM:
It has a mixed story, because it was part of mechanical engineering and part of electrical engineering. Also because of the process control aspect it was a big part of chemical engineering. So it has taken many different shapes. There have also been places where, for example, like here in [inaudible], we're centralized in control, so we have area responsibility for control. We do control for everybody.

Line 961: Line 961: NEBEKER:
Yes.
NEBEKER:
Yes.

+
=== Collected Papers on Billerud
=== === Collected Papers on Billerud
===

## Contents

Dr. Karl Aström was born in Sweden in 1934. He attended graduate school at the Royal Institute of Technology in Stockholm, where he received his masters degree in engineering physics in 1957 and his Ph.D. in mathematics and control in 1960. His research was on guidance control for military purposes, and he worked as a consultant for the Swedish defense department. Aström worked with accelerometers, gyroscopes, and the uses of feedback in navigation control. In 1961 he joined IBM Sweden, where he focused on using digital computers for industrial process control. For a year and a half he studied IBM control groups in the United States, and worked on stochastic control problems at the San Jose laboratories. Upon returning to Sweden, Aström worked on process control computers for use in a paper mill. In 1965 he joined Lund University's engineering faculty and created a curriculum for process control. He wrote a seminal textbook, Control Theory, which was published in 1968. Together with fellow faculty members and graduate students, Aström has made many practical applications of control theory, including work with artificial intelligence, ship steering, water treatment plants, and heating and air conditioning systems. He is the recipient of the Callender Silver Medal from the Institute of Measurement and Control in London, and is a Fellow of the IEEE.

The interview spans Astrom's career, focusing on his work with IBM and as a professor specializing in control theory. Aström discusses his education in Sweden, his work with the Swedish defense ministry, and his subsequent work with IBM and the Lund University. He describes his research in industrial process control, particularly his work with digital computers and stochastic control problems. Aström recalls his work with process controls for paper manufacturing, naval guidance systems, and other practical applications. He evaluates colleagues in the field, the development and impact of control theory, the relative merits of digital and analog computers, IEEE contributions to the control field, and new uses for control theory and feedback. He lists many peers, publications, and control theory centers which have decisively shaped the control field.

KARL ASTRÖM: An Interview Conducted by Frederik Nebeker, IEEE History Center, 6 September 1994

Interview # 228 for the IEEE History Center, The Institute of Electrical and Electronics Engineers, Inc., and
Rutgers, The State University of New Jersey

This manuscript is being made available for research purposes only. All literary rights in the manuscript, including the right to publish, are reserved to the IEEE History Center. No part of the manuscript may be quoted for publication without the written permission of the Director of IEEE History Center.

Request for permission to quote for publication should be addressed to the IEEE History Center Oral History Program, Rutgers - the State University, 39 Union Street, New Brunswick, NJ 08901-8538 USA. It should include identification of the specific passages to be quoted, anticipated use of the passages, and identification of the user.

It is recommended that this oral history be cited as follows:
Karl Aström, an oral history conducted in 1994 by Frederik Nebeker, IEEE History Center, Rutgers University, New Brunswick, NJ, USA.

## Interview

INTERVIEWEE: Karl Åström
INTERVIEWER: Frederik Nebeker
DATE: 6 September 1994
PLACE: Lund University, Lund, Sweden

### Childhood, family, and education

NEBEKER:
I'm talking with Professor Åström. This is Rik Nebeker. You were born in 1934.

ÅSTRÖM:
Yes.

NEBEKER:
In Sweden.

ÅSTRÖM:
Yes. In a small city called Östersund. It's actually in the geographical middle of Sweden, but it's something like five hundred kilometers north of Stockholm.

NEBEKER:
I see.

ÅSTRÖM:
In a certain sense, out in nowhere. Twenty thousand people living in the city. Very few other cities around.

NEBEKER:

ÅSTRÖM:
My father was a worker. He was a painter.

NEBEKER:
Was it usual for people in that area to go into academics?

ÅSTRÖM:
In a certain sense we had a very good school system, so if people had talents for school they were pushed into switching, jumping classes, and moving into other environments. The social environment was very good from that point of view. Stimulating people even if you didn't have a family tradition for the background.

NEBEKER:
Were you always interested in science, in technology?

ÅSTRÖM:
I think I was interested in literally everything. Even things like literature. I've always had very broad interests. But towards the end we had a system with real school, like Realschule in Germany, and Gymnasium, and towards the end I thought I was either interested in going into mathematics or science. But I could also have considered going into literature or something else. I had very, very broad interests.

NEBEKER:
Was the Gymnasium specialized for maths and science?

ÅSTRÖM:
Either you went for natural sciences, or for languages. You know, the classics: Latin and Greek.

NEBEKER:
Right.

ÅSTRÖM:
Or else you did mathematics or science. I went into the mathematics and science part.

### Royal Institute of Technology

NEBEKER:
And then you went to the Royal Institute of Technology.

ÅSTRÖM:
Yes. In Stockholm. We had an interesting subject called engineering physics, or in Swedish, Technische Physik. A strong motivation to go there was that it was the toughest place to enter. They only took in twenty students from all over Sweden. There were a couple of other people who have done this, you know, so it was something you strive for, to get high grades. You could make it.

NEBEKER:
I noticed that there was another Åström who went there six years or eight years before. No relation of yours?

ÅSTRÖM:
No, he was in electro-physics. No relation at all. Exactly. No, not at all. I'm an only child.

NEBEKER:
I see. So what years were those?

ÅSTRÖM:
I came there in 1953. Then I finished with my masters degree in 1957.

NEBEKER:
I see. In what?

ÅSTRÖM:
In engineering physics.

NEBEKER:
In engineering physics. Did that require a thesis of some kind?

ÅSTRÖM:
Yes, we did a masters thesis. I did mine on the dynamics of drops and bubbles. Mine was applied mathematics.

NEBEKER:
Mathematically describing drops?

ÅSTRÖM:
Well, the problem was for what happens if we have a tube like this and then an air bubble going up through this, and calculating the form of this.

NEBEKER:
I see.

ÅSTRÖM:
As pieces of art right now you can see the bubbles, and also they look like umbrellas. There's this almost circular shape, and then they're sharply cut off. You see, the idea was to try to calculate the shape mathematically. That's what I did for my masters thesis.

NEBEKER:
Did you check that there was agreement between what you calculated and what actually occurred?

ÅSTRÖM:
Yes, I did. We made some photographs.

NEBEKER:

ÅSTRÖM:
Yes, yes.

NEBEKER:
Were those tedious calculations?

ÅSTRÖM:
They were very tedious calculations because it was sort of a series expansion. You assume the form, calculate the pressure, and then with the pressure calculate the new form. I was very unfortunate because my professor thought that I just needed two terms, but it turns out that a lot of the terms vanished. So I think I went up to six or eight terms before it vanished. It was much harder work than any of us had anticipated.

NEBEKER:
I see. And how did you carry out the calculations?

ÅSTRÖM:
Well, I did it essentially analytically.

NEBEKER:
I see.

ÅSTRÖM:
Yes, pencil and paper. No numerics. It was analytical calculation. Then, of course, in the end I was checking it. That was not a computer at that time; it was done by mechanical calculators.

NEBEKER:
I see.

ÅSTRÖM:
Hard to believe in this day.

### Effect of WWII on educational systems

NEBEKER:
I suppose since your education was post-World War II, that the Swedish type of technical education may have had more of an English orientation, whereas earlier it had more of a German one.

ÅSTRÖM:
Actually, German was my first foreign language.

NEBEKER:
I see.

ÅSTRÖM:
I took English, French, and German. But the generation after me, the class after me, took English as their first foreign language.

NEBEKER:
I could see, in looking at the materials in Denmark, it was very clear that up until the war the technical community was oriented towards Germany.

ÅSTRÖM:
Not only technical, but the ideas; all teachers in university went to Germany.

NEBEKER:
Is that right?

ÅSTRÖM:
Also, if you think of Germany before Hitler, you had Göttingen and Heidelberg, and these places. It was very clear that people with high scientific ambitions always went to Germany. For example, people who became teachers, I think it was very typical that they tried to go to Germany for a while during their studies and then come back.

NEBEKER:
So you started with German as your principal other language.

ÅSTRÖM:
German was my first foreign language, and then I took English and French fairly shortly afterwards.

NEBEKER:
Did you use any non-Swedish textbooks in your technical education?

ÅSTRÖM:
When I started at the Royal Institute of Technology, in mathematics we had a choice between a book in Swedish, and then a French one, de la Vallé Poussin, "Course d'analyse infinitesimal", and a book by Courant. I picked the French one, because of a recommendation from my mathematics teacher at the Gymnasium. He thought that mathematics was nicely written in French. That was my first book in analysis.

NEBEKER:
Was it the case then that people looked more to the United States if they wanted to further their education?

ÅSTRÖM:
At that time, in 1953, it was very difficult to study abroad. When I was in the Gymnasium, there was the possibility to spend a high school year in the United States, and I actually applied for that, and I was appointed, but we basically couldn't make it, financially. There were a few people in Sweden who went to high school in the United States. When I went through the engineering school it was extremely rare that people went abroad.

### Naval service and defense projects; Ph.D. thesis

NEBEKER:
What did you do when you completed your masters degree?

ÅSTRÖM:
Actually, when I completed my masters I continued at the Royal Institute of Technology, to do my thesis. I actually started before completing my masters. I started fairly early in my career as a teaching assistant. I think it was certainly the second year. I was a teaching assistant in mathematics and mechanics, and things like that. Through that I was pulled into a very interesting defense project in Sweden. This was when Sweden had plans to make nuclear warheads. The Research Institute of National Defense was interested in inertial guidance both for missiles and for airplanes. At the time, I was doing a fair amount of teaching in the mathematical physics department. Our professor there had contracts with the defense. They set up a group which was called the Theoretical Inertial Navigation Group. I was dragged into this at a fairly early stage. So already when I was working towards my masters, I was involved in that. We had people from the United States come, like Draper and several of his co-workers. When I finished my masters degree I continued to do that. Right after my degree I went into the Navy to do my military service.

NEBEKER:
That was compulsory?

ÅSTRÖM:
That was compulsory.

NEBEKER:
How long did that last?

ÅSTRÖM:
It lasted a total of eighteen months. I did two months before going into the engineering school, and then I did a year afterward, and then I had a couple of periods later on that I had to go.

NEBEKER:
Right. Did that have anything to do with your --

ÅSTRÖM:
Oh, yes. I started to become an ABC engineer: Atomics, Biological, and Chemical. So I took the course for that for, I think, two months, but then I was switched over to electronics. I was trained to be in charge of all the electronics on one of the Swedish destroyers.

NEBEKER:
My goodness.

ÅSTRÖM:
They had plans to make twenty-four, but they only made two. So that was a very good technical education.

NEBEKER:
Yes, I can imagine. That was over the radar systems?

ÅSTRÖM:
That was sonar, radar systems, telephones, and things like that.

NEBEKER:
I can imagine that there were a lot of advances in those years in those fields.

ÅSTRÖM:
You know, there were a lot of advances in this technology. But I also had some interesting experiences, almost culture shocks in contact with real life at the military. I was put in charge of a group of enlisted seamen with little technical education. We had the responsibility of servicing radar, and other equipment on a ship. I was pleasantly surprised to learn that you could do this very effectively if you can read a schematic diagram, if you know Ohm’s law, and if you know that voltage at the anode of a vacuum tube goes down when the grid goes up. It came as a big shock to me that you could be extremely good at repairing radar with so little knowledge.

NEBEKER:
I see.

ÅSTRÖM:
Interesting experience.

NEBEKER:
How was the experience with those radar systems, with all those tubes?

ÅSTRÖM:
They of course had failure rates that were quite high. So it was essential to have a fairly large staff of people to run them. When we were out on exercises I was surprised to see how well you could get this equipment to function, even under fairly severe environmental conditions. It was a useful experience.

NEBEKER:
It sounds like it. And then --

### Ph.D. thesis and guidance systems

ÅSTRÖM:
Then I went back to the Royal Institute of Technology. I was working very intensely on these guidance problems.

NEBEKER:
You were employed?

ÅSTRÖM:
You see, at this time the attitude among us people was that none of us wanted to have fixed employment because we thought that would tie us down. So I was teaching at the university, and then I was a consultant to the defense.

NEBEKER:
I see, so a certain amount of your time.

ÅSTRÖM:
Yes, a certain amount of my time. I spent most of my time working on this defense problem, which I finally wrote my thesis on.

NEBEKER:

ÅSTRÖM:
The professor was a professor in hydro-mechanics. His name was Bengt Joel Andersson. He was an applied mathematician. The reason I was pulled into this [inertial guidance] was that I knew about gyroscopes. He had been in the mechanics department, then during the time I was there, he became a full professor in fluid mechanics. He was a very good applied mathematician. There were also many other good teachers around. At Stockholm those of us who were more interested in theoretical work also went to lectures at Stockholm University. There was a Professor Ulf Grenander in probability theory who was quite influential in my own career. He later became a professor at Brown University. We also had a superb mathematics professor, named Professor Hormander, who was doing his military service in Stockholm by giving lectures at the Royal Institute. Don't ask me how that worked, but that's what he was doing. So he was giving us fairly advanced mathematics courses that we went to.

NEBEKER:
You were taking these voluntarily?

ÅSTRÖM:
Yes, exactly. You see, at that time there was no regular graduate school like you have in the United States. The idea in Sweden was that you write a dissertation, and you defend it in public, and that's the only thing you have to do. If you needed you could take coursework, but it was not, you know, like the streamlined American Ph.D. programs.

NEBEKER:
But you knew that mathematics would be --

ÅSTRÖM:
Yes. And of course we were interested.

NEBEKER:
Including probability?

ÅSTRÖM:
Yes. You know, we actually had a very good course in probability theory at the engineering school. Topics like random processes and things we learnt already in the engineering school. When I started to work with gyroscopes to try to describe gyro drift and the errors of the navigation system, it was pretty clear that probability theory and things like this played a major role in that.

NEBEKER:
So that was already used to the theory of gyro systems?

ÅSTRÖM:
Well, yes. For example several of the M.I.T. reports and things like that were using the probability theory. At the instrumentation lab they had people like Davenport and Root, who were working on this, so we knew it was sort of a theory that somehow would match. It wasn't entirely clear how it would fit in, but it was pretty clear that in this direction there was useful stuff.

NEBEKER:
And these inertial systems that the defense department was interested in used gyroscopes?

ÅSTRÖM:
Yes. Gyros and accelerometers.

NEBEKER:
What sort of accelerometers?

ÅSTRÖM:
They were very high-precision devices, so they were typically like a hinge and pendulum with very low friction, and they were supported in a sort of fluid way, so you had very little friction, and then you had force feedback on it.

NEBEKER:
I see.

ÅSTRÖM:
So you really could measure acceleration with very large precision.

NEBEKER:
In all three degrees of freedom?

ÅSTRÖM:
Yes, exactly. You had one instrument for each direction, to measure three components. Then we had a gyroscopic platform to keep the directions --

NEBEKER:
You were designing such systems?

ÅSTRÖM:
Yes, we were designing such systems. At this time there was a conglomerate of the Research Institute of National Defense and several of the Swedish defense industries. We were brought up as some sort of theoretical people who would be involved in this development. By accident I became very closely related with Philips. I and an engineer from Philips were essentially putting a system together, and we went down to Philips' headquarters in Holland to get money from them to do research on this. We had some patents on it as well.

NEBEKER:
What was it a system for?

ÅSTRÖM:
It was something called Schuler tuning.

NEBEKER:
For a missile?

ÅSTRÖM:
Well, it was used both for missiles and for aeroplanes. So the system was designed to do both things. We came up with a couple of new system principles of doing these kinds of things. We designed the system, and Philips built the system and participated in test flights, things like that.

NEBEKER:
And you got some patents on this?

ÅSTRÖM:
Yes.

NEBEKER:
And it was actually sold?

ÅSTRÖM:
Well, what happened was that Philips was developing it, so Philips bought this. I had a patent jointly with a man at Philips, named Folke Hector. So Philips acquired this patent for us, and they built a couple of systems that were test flown. It never went into large scale production.

NEBEKER:

ÅSTRÖM:
Yes, my doctoral work was actually on the dynamics of gyro-stabilized platforms. So that was my thesis work. I was using the work I did for the defense department as my thesis.

NEBEKER:
Was that a theoretical thesis?

ÅSTRÖM:
The thesis itself was theoretical, but I had my thesis in 1960, I think, yes -- and then later on the hardware was built and flight tested a little bit later. So the ideas were proved later.

### Ph.D. thesis and Schuler tuning, navigational systems

NEBEKER:
I see. Can you describe for me a little bit what that work meant?

ÅSTRÖM:
In my thesis I was looking for a couple of theoretical problems. One contribution of the thesis was this new system principal for doing Schuler tuning. I can describe Schuler tuning for you on the board. If you had an accelerometer, you see, and if this accelerometer is changing [inaudible] a little bit, then of course you would pick up a bit of gravity. So then you would think that you were accelerating although you were standing still.

NEBEKER:
Right.

ÅSTRÖM:
If this is the center of the Earth, you would like to have the accelerometer all the time aligned orthogonal to the center, because then it will only pick up motions, and not misalignments. There was a very clever principle to do with this that was invented by a German named Schuler who was using things like this for the gyro compass. And you can think about it like this. If this is the Earth, and if you would just put an accelerometer on a gyroscope at that point, then it will remain fixed in inertial space.

NEBEKER:
Yes.

ÅSTRÖM:
So you can move that and the accelerometer will stand like this [incomprehensible]. But now, suppose that you put the accelerometer at a tangent. Then, you see, if you accelerate like this the tangent of the [inaudible] -- but if you could make a pendulum that would be as long as the [inaudible] here, then it is always pointing to the center of the Earth. Well, what does this mean? Well, if you take this, that is the pendulum length, that is going to be the radius of the Earth, and then it means that if you calculate the theory it turns out that the theory is the square root of the 'l' over 'e', which is called [incomprehensible] ... the same kind as a satellite [inaudile] ... So the trick was, if you could make a pendulum that had a period [incomprehensible] and then we just put the accelerometer sitting on this, you could get it to work. And, of course, the idea to [incomprehensible] ... that was already known by Draper. But what Draper has done was in navigation and the instrumentation. They had found one way to achieve this. We found another way to do the Schuler tuning. We actually did it by feedback. We put up the pendulum and then we put a little torque motor which was connected to the torque of the pendulum, and then you put a gyroscope here that is measuring the rate of change, and then we are feeding back the signal [inaudible]. Then we get something electrical by feedback that looks like [inaudible] inertia, and then you just increase it. This principle was one of the ideas that we patented with this guy in Philips and that was one contribution of the thesis.

NEBEKER:
I see.

ÅSTRÖM:
Another one had to do with the following thing. You put three gyroscopes on a platform and you get fairly complicated reaction forces because when the gyroscopes move, you know, they kick back.

NEBEKER:
Yes.

ÅSTRÖM:
I did a very careful mathematical analysis of this configuration, and I showed that I could deal with these reactions by arranging the gyroscopes in interesting geometrical configurations. And, of course, this was my first contact with feedback. Variable feedback means that you really only defined the characteristics of it. People didn't think we could do this because they said it was impossible to have such high feedback. So I rigged together a mechanical system with this thing, with mechanical feedback, and we could actually make theories in about five minutes with this one. It was only after all the people who did electronics, and then we made a very simple one to show we could actually do it. That was the one we brought down to Philips, to get money from them.

NEBEKER:
Was that used in any other work?

ÅSTRÖM:
I don't really know, because a lot of this material was classified. However, it was written up fairly early by some of the people at the instrumentation lab, so they thought it was a pretty decent idea.

NEBEKER:
I see.

ÅSTRÖM:
You can check this. There is a Professor at M.I.T. named Winston Markey in the aeronautics department. He worked fairly closely with us. He can give you a side view on that if you're interested. And also for the record you should have Folke Hector from Philips. He was about ten years older than I am, and he was, a very good electrical engineer, and we worked well together.

NEBEKER:
I see.

ÅSTRÖM:
I was much stronger in theory than he was, and he had much wider electrical engineering experience.

NEBEKER:
And you were actually building the system at that time?

ÅSTRÖM:
Yes. We also tested it, which was kind of fun. I must tell you about how we got the money from Philips because at that time I was very inexperienced. We were going down to Philips to get money. It was Hector and myself, and we went down to Philips' technical manager. At that time, Philips' research lab was really the research lab in Europe. They had a physics guy named Kasimir who was one of the leading physicists, and he was the one who grilled us. So of course we were very nervous coming there as young men talking to him, but we persuaded him to put up some money for it. Philips also let us have one of their company planes to test it, and the captain was extremely skeptical. During the first test flight it didn't quite work. On one of the later test flights, we were flying across Sweden and looking at church towers and then we came into fog. I was not on this flight, but Folke Hector told me that they told the pilot, "Well, in about one minute, twenty-five degrees to the left there will be a church tower." Sure enough it came up after the fog. So afterwards this guy started to believe it.

NEBEKER:
And it was in -- did you say 1960?

ÅSTRÖM:
In 1960 I did my thesis.

### IBM employment

NEBEKER:
What did you do then?

ÅSTRÖM:
Well, Philips actually had been after me to start work all the time, and I had been sort of reluctant to do this because I wanted my freedom. But I was dead set to start work with Philips on that -- to really, you know, go through and work with this.

NEBEKER:
Was that an important area for them? Navigational systems.

ÅSTRÖM:
Navigational systems were very important. They both had radar systems, so they had a military electronics division. They wanted me to work there and I knew the people very well. I still remember this because it was kind of traumatic. I went up there and then they asked what salary I wanted, and we couldn't agree on the salary, so I was very mad. What really made me mad was that they said, "Well, you know, this is what we are paying ordinary engineers." And I was really mad that he called me an ordinary engineer, so I just left. [Laughter]

NEBEKER:
And stayed on at the Royal Institute?

ÅSTRÖM:
No. I was going to be married, so I had got the feeling that I really wanted to have another experience, and just by accident I saw a little advertisement in the newspaper that IBM were setting up their Nordic laboratory. IBM research.

NEBEKER:
In Sweden?

ÅSTRÖM:
In Sweden. They wanted to have people who were going to look into the possibilities of using computers for process control. So I went up there and was interviewed by this guy. Already when we did the guidance systems I had got involved with computers. When we started, there was only one computer in Stockholm. It was a copy of a von Neumann machine called BESC. Because of the military involvement we actually got access to the computer. That was another attraction of my getting involved with this project.

NEBEKER:
The computer was yours just for doing some of the calculations for that?

ÅSTRÖM:
We used it to do some of the calculations and simulations. It didn't have an assembler, so you programmed in machine code. You run it yourself; you had paper tapes up around your arms. Also for the navigation system we wanted to go digital, but digital computers were not reliable enough and not light enough, so we were using some kind of hybrid analog pulse technology for the computations in the navigation system at the time. It was not because we were using pulses, but it was kind-of special purpose. It was obvious to me at the time, that to learn about computers was great, and there was no better place to learn than IBM.

NEBEKER:
IBM didn't have a laboratory at that time in Sweden?

ÅSTRÖM:
They were just setting up. I think I was employee number thirteen [thirty?]. Something like this. So they started in January and I think I was hired in February. Something like this.

NEBEKER:
In 1961.

ÅSTRÖM:
Ironically, two weeks after I accepted IBM the guy from Philips called and said, "Well, we reconsidered this. We will give you the salary you want." Of course it was very challenging with this military technology, but it was pretty clear at the time that Sweden was not going to make nuclear warheads. The robot guidance system that we were working on didn't really make sense if you didn't have warheads, because you couldn't get the precision you needed with regular warheads.

NEBEKER:
And that was the only application that really called for that?

ÅSTRÖM:
Well, there were actually two. There was also an aeroplane application. I think another interesting thing about my starting to work for IBM was looking at another application area.

NEBEKER:
So you accepted this position at IBM.

ÅSTRÖM:
Yes I accepted it. And I had a fantastic boss there.

NEBEKER:
Who was that?

ÅSTRÖM:
His name is Kai Kinberg. He was a Swede, but his father was involved in Swedish prohibition. He was a doctor. And of course that was not very popular, so he left Sweden and went to Switzerland, so Kinberg was essentially brought up in Switzerland. He used to work for the IBM research laboratory in Switzerland, and he was brought over to Sweden. He was a superb research manager. He really knew how to handle research.

NEBEKER:
So he was brought there to set up --

ÅSTRÖM:
He was brought there as lab manager, to set up the lab, and there were people coming from England, Denmark, and many places.

### IBM and industrial process control, digital computers

NEBEKER:
And what was the mission?

ÅSTRÖM:
The mission of the laboratory was to explore the use of the digital computer for industrial process control. One reason for putting this in Sweden was the pulp paper industry in Sweden.

NEBEKER:
It already was using sophisticated process control?

ÅSTRÖM:
Well, they were using a very simple manual process control. There was really, if you like, a clash of two cultures at that time. There was also another mission of the lab, and that was to try to figure out what a computer should look like, to be available to process control, which was by no means obvious. You see, in 1959, they put the first computer on an oil refinery, in Port Arthur, Texas. IBM saw this as a big growth area, so they were selling special purpose machines for this, and then they wanted to have a lab with that mission.

NEBEKER:
I see. Did they have a U.S. group working on this?

ÅSTRÖM:
Yes. The key group at that time was in IBM research which was started in Yorktown Heights, and they were doing projects in the area, so they were doing for example a project with DuPont. They did a couple of other projects.

NEBEKER:
I see.

ÅSTRÖM:
In the products division they also had people who were working on this.

NEBEKER:
And you, of course, were in touch with --

ÅSTRÖM:
Yes, the guy who was in charge of research was a guy named Jack Bertram, who he later became one of the vice-presidents of IBM, but he was in charge of the control activity. He came from the very famous control university. Columbia University at that time had a fantastic view of automatic control. I don't know if you know some people there. For example, it was led by John Ragazzini and Lotfi Zadeh, and Gene Franklin [who is now at Stanford] was a professor. Zadeh then went to Berkeley. Gene Franklin was doing a dissertation, and he has been the key control professor at Stanford, so at the time Columbia was a great place, and Jack Bertram came from there. Rudy Kalman also got his Ph.D. dissertation there. So Jack Bertram was working with these guys and he was in charge of control, and I had the very nice opportunity to spend about a year and a half in Bertram's group in the States.

NEBEKER:
During this period you were working for IBM?

ÅSTRÖM:
Yes. That was a great experience.

NEBEKER:

ÅSTRÖM:
Well, I'll tell you this. My first assignment was to look into a French project where they were going to use a computer to control a nuclear power station. So we were brought down to Paris to help the French people, because I had the background.

NEBEKER:
IBM France?

ÅSTRÖM:
IBM France was going to offer a computer system to EDF, Électricité de France, and I and another Danish guy were brought down to France to help them to line up this system. Of course, the key problem there was the reliability of the system.

NEBEKER:
Yes.

ÅSTRÖM:
But it gave us a really good experience to try to get the grasp on the reliability issues in process control problems.

NEBEKER:
This was a special purpose computer?

ÅSTRÖM:
Yes. You see at that time IBM had something called "special engineering," so they made special engineering equipment -- they were offering one of these to EDF. Incidentally, EDF decided not to use a computer, essentially because of the reliability issues. Then I was brought back and the lab had a fairly large study of a steel plant in Sweden, in [inaudible], where they were looking into the feasibility of using a computer. I did a little bit of work on that and then I was brought over to the United States for a year and a half, and when I came back I was put into a project where they were putting a computer in a paper mill.

NEBEKER:

ÅSTRÖM:
Yes. I came out to IBM Research in their mathematics department in Yorktown Heights. I was there for a couple of months, and then the group was transferring over to San Jose, so I had really the option either to stay and have connections to Columbia or else to go with the group to San Jose. And I decided to go with the control group to California. They had a research lab there with only about one hundred people working. The main activity there at the time was still the disk drive storage, which they are still big on in San Jose. They also had a group on hydraulic bearings, I think like this, they also had a physics group, and then they had the control group.

NEBEKER:
What specifically were you doing?

ÅSTRÖM:
I personally was working on stochastic control problems, which tied very nicely into what I had been doing in Sweden before, with gyroscopes and things like that. I actually did a little bit for the federal systems division on calmer filtering in gyroscopes, and they were developing some theory which we thought was appropriate to process control. I remember we also did a little bit of satellite work for federal systems division. It was essentially sort of free-wheeling research work.

NEBEKER:
Were you given the freedom -- to choose --

ÅSTRÖM:
Yeah, a lot of freedom to choose. Occasionally, you know, they came in and said, "Now, guys, we have got to get this done, so put away what you are doing right now and help us to solve this problem." For example, I was there when the first CDC computer was designed by Seymour Cray, and then I could really see how a big company like IBM responds when something magic happens. So, for example, Jack Bertram moved from the control field and into the computer field, so he actually became manager of one of the futuristic IBM projects that were designed to make the leap towards this. Jack Bertram also had fantastic connections. Zadeh was at Berkeley, and Gene Franklin was a close friend of Jack’s. He was at Stanford. So we had ample opportunities, you know, to interact with people at universities.

### Stochastic process control, digital control

NEBEKER:
I see. Could we maybe digress just a little bit?

ÅSTRÖM:
Yes.

NEBEKER:
I'd like you to tell me a little about stochastic process control. Where that first found application, and why.

ÅSTRÖM:
Well, you see, at that time I think it was something like this. Coleman had published his papers on economy, so we essentially knew how to get the information about a process. Then it was the question, "How can you put this back into the feedback?" At the same time, Coleman had also been working on a problem called the linear quadratic regulator, which essentially is an optimization problem, and then it was very natural to get the stochastic optimizing property. The linear quadratic regulator was deterministic, and he tried to combine this and make sort of a unified theory of that. There were people working on this at Stanford. We were working on this at IBM, and then we suddenly started to understand how these two things were fitting together. With my experience with the gyroscopes, I saw immediately that this was a very nice theory, for example, to deal with many of the problems we had in the navigation systems. Like initialization in navigation systems. You are switching the system off as a gyro compass to line it up initially when you start, and this theory perfectly fit into this. I actually did some work related to that. Also in process control, you have a lot of noisy fluctuations and things like this. It was quickly clear that that was a sort of very nice theoretical framework. You would like to reduce fluctuations as much as possible, so it was clear, you know, that the --

NEBEKER:
But it hadn't been widely --

ÅSTRÖM:
Well, the theory was not really worked out, and people had not really done any applications like this either.

NEBEKER:
How was the theoretical side of control theory affected by the availability of the computer?

ÅSTRÖM:
Drastically. You see, digressing a little bit, in my view control was created around 1940. That was really when the field of control came together. It came together in the shotgun marriage of war, and there were essentially three ideas. Or, simplified in my mind, it was ideas from industrial process control: PID regulators and such things, which had been developed by itself; auto-pilots both for ships and for aircraft which were built earlier; the ideas from feedback amplifiers, which came out of the telecommunications field. During the war, at the MIT instrumentation laboratory and the radiation laboratory, they had gathered people together who had all these components, and they were doing the systems for radar, the pointing of the guns, and gun sights.

NEBEKER:
Right.

ÅSTRÖM:
And then suddenly they saw exactly how all this would fit together. They started to write books about feedback control and it spread like wildfire all across the world. That, you could say, was the first wave, and it was characterized mathematically by LaPlace transforms, complex variables and things like that. What was so interesting about control was that there came a second wave of theory during the 1960s, which was inspired a lot by research in for the space mission, where you brought in totally different types of mathematics. You brought in probability theory. You got things like the Palmer [?] filter and other things, and you brought in calculus variations, like the dynamic programming and maxima principles. Then suddenly you got the computer to implement the physics and do the simulation. So in a certain sense you got a second wave, both with an influx of ideas and also with totally new tools like the computer.

NEBEKER:
And those ideas wouldn't have been so useful if you hadn't had the digital computer?

ÅSTRÖM:
Not at all. Absolutely not. Using a digital computer, it was necessary for you to re-work the basic theory because now you could do much better. Compared to using continuous analog computer, with the digital computer you could do much better. That was, say, the center of the work at Columbia University at the time. They were actually doing a lot of work that had to do with SAGE. You know, the early warning system.

NEBEKER:
Right.

ÅSTRÖM:
One pioneer of digital control at this stage is Eli Jury. He wrote, I think, the first dissertation on sample data systems. He did this at Columbia, and then he went to Berkeley quickly afterwards. Another one was Gene Franklin. Ragazzini was the other one for early digital control, and that was entirely motivated by the impact of the digital computer.

NEBEKER:
In the 1950s I would imagine that it looked like the analog systems would be the model of all control.

ÅSTRÖM:
Definitely.

NEBEKER:
I happened to see in Scientific American a couple of months ago about optic telescopes. As late as a decade or two ago they were still using analog computers for the control of those mirrors.

ÅSTRÖM:
Of course, it was the only way to get the calculation speed at that time.

NEBEKER:
Yet there were some people, in the 1960s anyway, who thought that the digital computer would eventually win out. I mean there must have been a lot of areas then that you couldn't get the speed.

ÅSTRÖM:
No. And, you know, I don't think anybody at the time anticipated the speed increase we are getting in the computers and the price reductions and all that sort of thing.

NEBEKER:
Did it look to you like digital was the way to go?

ÅSTRÖM:
Definitely. That wasn’t a very strong reason for me to go to IBM. There were several other reasons to go to work for this IBM lab, because I had the gut feeling that the computer was really going to have a drastic influence on whatever it would do from two aspects. Both as an analysis tool to carry out a lot of calculations. For example, we were using analog computers as simulators, but the idea was to use the digital computer to do this work, and also to automate control design, and also to use the digital computer integrated in the control system. To me at the time that was very clear. It came first in process control because in process control you did not have this critical speed; in process control you can use much slower sample rates. If you went to the military systems where you need the speed it was impossible. One thing I saw pretty clearly, was process control. That was the reason, I think, why industrial process control was really the hotbed of computer control.

### Success of computer control systems

NEBEKER:
I see. And was this actually finding much success in the marketplace?

ÅSTRÖM:
Yes. I think I'll show you some diagrams.

NEBEKER:
Okay.

ÅSTRÖM:
I picked up a book called Computer Control System Theory Design, written by myself and one of my co-workers at Lund, and here on page three you have a curve which shows the rate of introduction of computers for process control. The first one was installed in March of 1950. So, you see here, that is where it started, and here is a logarithmic scale. You see, here is the growth of computers and an estimate of the total number of computers. Now, process control is following this at the same time, the development. So, for example, at the time I started to work for IBM they had fantastic reactions of this exponential growth. Here at the beginning the numbers were actually not large, but it has essentially been exponential growth. IBM’s predictions were more optimistic, as you might imagine, but if you looked today, nobody would think about having a large chemical process, or any process like this without having the computer control. For example, when people started using computers to supervise, they were still using analog computers. Analog controllers for the local levels, for the reliability and other reasons. Then came what I call the direct digital control period, where you are replacing the analog hardware. Instead of having many analog controllers, you have one central digital controller. When the microcomputer came, of course, that had tremendous impact, because now suddenly they had technology that was tremendously useful. Today most controllers, I think, are actually based on microprocessors.

NEBEKER:
I see. But in the early 1960s IBM was selling computers to companies for process control?

ÅSTRÖM:
Yes. There were several companies who would do this, and IBM was a major player. In the labs I was associated with, there was a computer IBM developed that was called the IBM 1800. That was a very successful process control computer. At the time people thought you needed a special type of computer for process control. You know, you needed interrupts and other things. There was a big discussion about having the best computer, buying a computer, and so on. But what happened was that many of the features we found necessary to have for industrial process control also turned out to be tremendously useful in other purposes. So the computer architecture changed a lot, and many of the features that we found useful in the hard real-time applications made their way into the regular computers. While at the beginning people thought there would be many different types of computers, it turned out that the same sort of computers were useful for all sorts of purposes. In other words, many of the features we found useful in engineering systems were very useful for other research.

NEBEKER:
Was that IBM1800 designed specifically for use in process control?

ÅSTRÖM:
That was designed specifically for process control. But several of the concept designs also made their way into the 360.

### Control experiments at Billerud Paper

NEBEKER:
I see. And when you returned to IBM Sweden what did you work on?

ÅSTRÖM:
At that time, the laboratory I worked with had got a project with a pulp and paper company called Billerud. Billerud had a very far-sighted manager named Tryggve Bergek. He had, by himself, come up with the idea that computers could really be used very profitably to improve the production of paper. So he had been looking for partners. Incidentally, he had been talking to SAAB in Sweden at the time, over computers. But SAAB was not willing to undertake the project. And also, IBM had had several failed projects of this type, so they had the computers put in, but they [incomprehensible]. So then IBM decided to put research money into this laboratory in Sweden and to do a really serious case study of the theory. That involved installation of computers at the plants. Billerud wanted to have a working system, and IBM wanted to squeeze as many applications as they could into this computer. Process control, production planning, and quality control.

NEBEKER:
I see.

ÅSTRÖM:
I was put in charge of the control aspect for that project. I had been fortunate to have all this exposure to the theoretical development in the States of what they were doing there, and then suddenly we were faced with these real problems, in the real world.

NEBEKER:
I can imagine that must have been quite a culture shock.

ÅSTRÖM:
Yes, but it was very interesting. I spent a lot of time at the paper mill. I lived in Stockholm but we were continuously going out to the paper mill, working round the mill, figuring out what we should do.

NEBEKER:
What computer did you use?

ÅSTRÖM:
Originally there was a special-purpose machine. That, I think, was called 1710. It was the first one after 1600[?]. It had a small drum. If you need, later I can pick out some data on it. And later on they installed two 1800 computers. One of them is still running, good as gold. So they introduced those two.

NEBEKER:
What year was that?

ÅSTRÖM:
This was in 1963. So that was, say, from essentially the period 1963 until 1965.

NEBEKER:
That 1800 was installed in that period?

ÅSTRÖM:
I honestly don't remember. Could you switch this off, then I could go and get the files. [Tape is stopped]

### Ph.D. thesis and gyroscopes

ÅSTRÖM:

So this is my thesis. Part of this was actually published in book form, and there was one interesting incident that I came to think about when you asked. When I came back from the United States I also had to do a pass in the Swedish military. Then I was placed at the Research Institute of National Defense. I was applying the stochastic controls we had learned about inertial navigation systems. I had two months in the military service, which was very useful to apply what I had learned to a basic problem. There is a summary here, which was written in Swedish, and then the major part here has to be written -- you see it here, for example, "The Characteristics of a Stable Platform.” See, I have here the platform the gyroscope is on, and the fact is that you can orient the gyroscopes in many different ways, and then the interactions change in very different ways. In today's language it is a typical multi-variable control problem. Here are the references to the Draper lab results. Most of the things we did were actually written in English. Here is the analysis of the inertial navigation system with the pendulum effect. So it's a typical mixture of mechanics and control. Here you see the swing of the pendulum, and stuff like this.

NEBEKER:
Now, control theory traditionally was part of mechanical engineering. Is that right?

ÅSTRÖM:
It has a mixed story, because it was part of mechanical engineering and part of electrical engineering. Also because of the process control aspect it was a big part of chemical engineering. So it has taken many different shapes. There have also been places where, for example, like here in [inaudible], we're centralized in control, so we have area responsibility for control. We do control for everybody.

NEBEKER:
I see.

ÅSTRÖM:
Different systems have different advantages and disadvantages. But let's go back to the theory.

NEBEKER:
Yes.

### Collected Papers on Billerud

ÅSTRÖM:
I just found this when I picked the things up. You asked about the computers used to build it. I picked up the papers in here.

NEBEKER:
This is a project report?

ÅSTRÖM:
Well, what happened was that after we had done the report at Billerud I became invited with lots of people from all over the world to take part in this sort of showcase, and in connection with this we published a collection of reports of the major results.

NEBEKER:
This is the collection of papers?

ÅSTRÖM:
Yes. If I had been smarter I should have insisted that we write a book on this. Because at the time, this was really the front line of computerized process control, and essentially IBM was spreading out reports anyway, but had we been smart we should have made a book out of it.

NEBEKER:
This was public or private?

ÅSTRÖM:
Public domain stuff. Produced by IBM. Put together and distributed, but we really should have done a major book out of it.

NEBEKER:
It's called "Integrated Computer Control of Paper Machines". I don't see a date.

ÅSTRÖM:

NEBEKER:
That distinguishes it from most applications.

ÅSTRÖM:
Oh, yes.

NEBEKER:
To have this very large number of inputs.

ÅSTRÖM:
Yes. We had our own real-time operating system. So with this one we had one hardware interrupt, and then we made our own operating system which gives us several operating systems. It was based on the 1620 machine, and then they had made this special-purpose machine called the 1710, which was the core of the 1620, but then they had added the interrupt. So in here [referring to a report] they have the IBM 1710 SPS 2 system, and then we had a FORTRAN compiler for it, and there was a symbolic programming system. So there was some primitive software for it, but we actually had to do a lot of software work for it.

NEBEKER:

ÅSTRÖM:
Actually, they used it for several other process control applications. They did for example, the input-output device, which were always tailor-made.

NEBEKER:
But this was one of the pioneering projects?

ÅSTRÖM:
Yes, this was one of the pioneering projects for it. You see in here there is a system summary which tells really what we were doing. We had then the basic process control. We had the process data collection, the product supervision system, we had production planning, we had production evaluation -- this is something that we would call quality control today. Then we had, I say, a fairly large quality control box. In my control group we had been involved with the process control part and the quality control part. So these were the two things that we had to do at the time.

### Billerud and Theoretical Problems

NEBEKER:
I see. Can you sort of sketch out how this project went?

ÅSTRÖM:
It was a fairly large project. There could have been something like forty people altogether involved with it. I think there probably is a man-years estimates in here. Also we had several people coming through, because the IBM people wanted to use this to have the learning experience to learn about other things.

NEBEKER:
Yes.

ÅSTRÖM:
There was, so to say, a project leader, and this guy was Tage Frisk. He was a Swedish guy, and he was employed by the lab. My group was involved with process control and quality control, and we had an instrumentations group, and we had a group that was associated with production planning. So there were a couple of key groups that were working. There were people both from IBM and from the pulp and paper company. Another one of the key people we hired was a young engineer called Ule Olson, and he is currently in charge of the Swedish Pulp and Paper Research Institute, for example. So there were a lot of people who were kind of graduating out of this group. What we did in control was quite interesting from my point of view. This was the machine that was generating paper, continuously, all of the time. You would like to minimize the fluctuations you have in the quality variables of the paper, naturally. One of the key quality variables is the thickness of the paper. They measure these in quantitative ways. So that's one of the key parameters. Another key parameter is essentially the moisture of the paper, and you would like to keep both in small fluctuations.

NEBEKER:
And those are being continuously monitored?

ÅSTRÖM:
Yes. There is a meter rate gauge; the paper width could be as much as five to ten meters. It's a gauge that travels across and measures the average, both in moisture content and in thickness. And, of course, the possibility to do this depends on having this measurement. You use it as the primary measurement to adjust how much fiber you are putting into the machine. The benefits are very easy to understand in this case. There are long time delays and it's a fairly complicated procedure, but it goes like this. When you sell the stuff, you guarantee that a certain percentage of the production is going to be above this amount. There will always be something in here. But you guarantee for example that eighty percent of the production is going to be above this. Now, suppose that you can make this a much more concentrated distribution. You see, on the average you need much less fibers.

NEBEKER:
Yes.

ÅSTRÖM:
And, of course, this is something you can translate directly to money. So even small reductions and fluctuations means a lot in terms of money. You're talking about several hundred thousand dollars per year for a large machine. So it's a very nice control problem. Also, if you looked at the nature of the fluctuations, which I may have here --

NEBEKER:
For the tape, let me state that this is an article in the IBM Journal of Research and Development you wrote. It was published in July of 1967, called "Computer Control of a Paper Machine."

ÅSTRÖM:
Typically in here the fluctuations are random. Typically this is what they really looked like. So this was fitting very nicely into the sort of background stuff I had. For this project we really had two problems. First figuring out how to solve this control problem, and then characterizing both the dynamics of the system and the kinds of fluctuations. For this purpose we developed special measurement techniques. We perturbed the valves that were adjusting the amount of fibers coming in and then we analyzed what was happening. So based on this we were automatically developing the mathematics involved, you see. That later became something called system identification. We were actually developing both the mathematics behind this and the applications while we were doing this, and then we were trying it out immediately. We were tailor-making mathematical theory that was taking this result and then generating control strategies that were going to minimize this fluctuation. That was the strategy that I called the minimum variance control strategy, that I essentially developed in connection with doing this. A lot of my previous background, you could say, came together here on this specific project.

NEBEKER:
It's surprising that such interesting theoretical issues would come out of this.

ÅSTRÖM:
I think that is what is so fascinating about control. Here you have a strong connection between guidance and gyroscopic platforms, and manufacturing of paper. The same sort of mathematical framework really came out of work for this. I think I have some other papers that I could show you. We developed this measurement technique where we could just go out and make measurements from the process. From this we could determine current fluctuations. How much can we possibly reduce them by introducing this feedback, and is this worthwhile? If it was worthwhile we implemented it on the computer, then we went on. So that was kind of a cute project. Then we were using similar techniques for the quality control problem. We were analyzing the quality fluctuations and we could come up with, for example, much better measurement techniques because they just used to take one sample. Well, we showed that if you take a couple of samples, you roll off a couple of tons of the paper, you could really improve the estimate of many variables significantly. For this we were using Kalman filtering. There was a lot of pressure on this project, but the lab manager, Kinberg, was very encouraging. He could also have said "Why don't you use the proven techniques and get something working?" But they had a very, very open-minded attitude about, "Okay, well, by all means try to see if you can do something new. If you really can do some improvements, spend time on this and do it." That's why I said that they were fantastic research managers.

NEBEKER:
I see. It also must have required either the right kind of contract, or an understanding company that you were doing it with.

ÅSTRÖM:
Yes. I think there were really two reasons. Number one was that IBM was willing to put in research money; this project was quite an expensive one. Also, the manager of the paper company let us experiment with -- there was a lot of discussion, for example. We said that we would like to change this like that to aid production, and then we came up with the agreement that if they could not discover what we were doing with their normal quality control procedures, we could go ahead and do it. [Laughter]

NEBEKER:
So anything under that threshold!

ÅSTRÖM:
Yes, anything under that threshold was okay. We didn't know quite what the levels were. Occasionally there were some bugs, but they were quite understanding about it. All in all it was a great fun experience.

NEBEKER:
It sounds like a very important project for the history of process control.

ÅSTRÖM:
Well, I'm not the guy to judge, but it certainly influenced me a lot.

NEBEKER:
And IBM had some success in selling such systems?

ÅSTRÖM:
Oh, yes. I think there were really a couple of major outcomes of this. Number one, it was clear from this project that with this approach, with IBM hardware, and, say, IBM know-how, one could actually install systems like this in the process control situations. This project as a whole was a big success. Also it did several other things, because we did hacking [?] things with this special-purpose computer, and a lot of the things we saw were influencing the later project. At the time IBM was developing the 1800, and I don't now remember the timing for this, but that's also possible to check out. Several of the things we saw we were feeding back to the 1800 architecture guys. There were also several developing software tools that found their way into the IBM 1800 system. After we had finished this project with Billerud, they were replacing the 1710 computers with 1800 computers.

NEBEKER:
I see.

ÅSTRÖM:
This is a confidential report, so maybe we shouldn't --

NEBEKER:
This is an IBM report?

ÅSTRÖM:
Yes. The paper mill was actually called Gruvon, by the Billerud company. Billerud is now part of a large conglomerate in Sweden called Stora.

NEBEKER:
I see.

### Organization of Research at IBM

ÅSTRÖM:
When I joined IBM they had two pure research labs. One was Yorktown Heights, the other one Zurich.

NEBEKER:
Right.

ÅSTRÖM:
And then they started at the European laboratories. I think when we started everything was run out of Nice. So the Nice lab was guiding all of the other labs. At one period that I worked for IBM Paul Ganson [sic] was in charge of the European labs, and the Nordic lab was one of them.

NEBEKER:
Right. I think there were six labs under him.

ÅSTRÖM:
There was one in Vienna. And one in Hursley, in England. So Nice, Vienna, Hursley.

NEBEKER:
Germany, France --

ÅSTRÖM:
And one more. So that was the heyday of IBM. I really enjoyed working for IBM, and there were many things coming, for example, from the Swedish. For example, most Swedish industries were very hierarchic, so it was normal for a young engineer to not have very much responsibility. You had to work in a group of five or six people, you did this for five years, and got a little bit more responsibility. At IBM if you showed that you were ambitious and hard-working, you got any responsibility you wanted. You had these assessments, talks, twice a year. Tell them what you are doing, things like that, and be very frank in your assessment. That was very unusual for the Swedish environment at the time. Project management went like this: they put you on a short course to learn how to do the same things, and you were forced to account for your own expenses. Sometimes you are put on evaluation. It's where you put together a team, and you go out and you tear a project to pieces, analyze what it is. Many times you are at the receiving end of this process. It’s a fantastic news [?] for these people.

NEBEKER:
It sounds like your years there were good.

ÅSTRÖM:
It was very productive for me. So I really enjoyed working for the company. Also they decided if you did something wrong, you heard it immediately. If you did something great you got all these immediate benefits; the next salary came round. Company policies taught us that you can always go up. If I have a guy working for me who has a guy working for him, and you wanted to hire this guy, there was no way for me to stop this. If he thinks it’s a better job he can always go over you, and every manager has to have a second in command that can take over his responsibility for all his people.

NEBEKER:
I see.

ÅSTRÖM:
They teach you a lot about how you should work together.

NEBEKER:
How large was the Swedish group?

ÅSTRÖM:
I think it was probably something like four hundred people. You had to interview a lot of people when you were hiring. There was a lot of experience in there.

### Joining Lund University

NEBEKER:
Was it in 1965 that you were offered the professorship?

ÅSTRÖM:
Yes. You see, in Sweden we had a funny system with professorship appointments. When you say “professor” they are full professors. A department announces, "There is an opening for a professor." Then anybody can apply, and the faculty forms a committee to rate the applicants. They write a public report. The applicants rebut [?] if they think they are entitled to.

NEBEKER:
So the rating of the applicants is --

ÅSTRÖM:
Is public. Then the faculty votes. Typically you have three people who write evaluations. They say, "Is he competent to be a professor?" And that they rank them, one, two, three, four, five, six... They all three do this, and sometimes they agree, and sometimes they don't. Then the faculty votes. So I sent in my application. At that time I didn't think that I would get the job. I thought it was kind of interesting. I thought, "Why don't I do this?" I had a very nice situation with IBM, and I was actually offered to go back to IBM. research laboratories. So I was actually thinking of going back to IBM. research.

NEBEKER:
Yorktown Heights?

ÅSTRÖM:
Yorktown Heights, yes. Then I came out on top of this professorship. We weren't sure what we were going to do, my wife and I, but then we said, "Okay, let's go down and have a look at it." I was quite challenged to start from scratch and build up a new group.

NEBEKER:
I see.

ÅSTRÖM:
That was 1965. Then I requested a leave of absence to finish off this project. Lund is an old university, but engineering had never been taught here, so this called for a new engineering school around 1960. The rector for that was the rector of the whole institute, who I knew quite well. He was also around at this place, so I asked him, "Can I get leave?" He said, "Well, you see, why don't you come down and have _____?" I said, "Okay, I'll do that." So then we moved down here with the family, and I decided to work on average one day a week to finish what I had at IBM. We negotiated that. So I went down here and started to teach, and then I finished off the Billerud project. About a year, a year and a half, were very, very busy.

NEBEKER:
So it was decided shortly before then that there should be an institute for automatic control?

ÅSTRÖM:
They decided that they were going to have a school of engineering, and then they decided that they should have a chair in automatic control. They decided that this chair should be responsible for teaching all the courses in control for electrical, mechanical, whatever.

NEBEKER:
Was that unusual?

ÅSTRÖM:
No, that was the pattern in Stockholm, and that was also the pattern here in Gothenburg. What happened after that in Stockholm was that they got it spread out. If you are teaching to many schools you have to be wide, because otherwise they will introduce their own courses. It made sense to have a central group of control, because there was so much that ties it together. On the other hand, you must also spend a lot of effort to make sure that you service the needs individually in the departments. Originally we had the same course for everybody, and later on we changed it around, so we now have one course for electrical engineering, computer engineering, and engineering physics. So that's just one course for that. We have another course for mechanical engineering, electrical engineering, and chemical engineering. People learn more or less the same thing, but examples are different and they do things a bit differently. You are more abstract with electrical engineers; you start top-down. With mechanical engineers you do it more bottom-up. That's it. The key material is more or less the same.

NEBEKER:
I see.

ÅSTRÖM:
For example, in Denmark, which is just across the water, I think they have five professors of _____ engineering. We have here, two full professors. We have been quite efficient. If one can keep a central group, it's fairly cost-efficient. On the other hand, at a large place like MIT they have people in aeronautics, and electrical engineering, mechanical, and --

NEBEKER:
I see.

ÅSTRÖM:
So I don't think there is a perfect solution.

### Control system societies and journals

NEBEKER:
To digress from your career. If one looks at the area of control systems over the last decades, is there a single community, or are there separate communities, when you look at the literature and so on?

ÅSTRÖM:
I think there is a strong international community, called the International Federation of Automatic Control Engineering. So there is a strong international body. They were formed right after the war. Yes, I think they were formed more or less in 1957.

NEBEKER:
This is unaffiliated to any other technical society.

ÅSTRÖM:
Yes. It is unaffiliated. That's a professional society. Then they started international conferences. The first one was held in Moscow, 1960. A very exciting meeting which I had no chance to go to. Then they have a World Congress every third year. They typically run workshops, and symposia about --

NEBEKER:
And these were people in electrical, chemical?

ÅSTRÖM:
Electrical, mechanical, chemical, aeronautics, mining, automotives. So that's one major body. Then there are national organizations. So there is something called the American Automatic Control Council. They are the American national body for IFAC. They arrange the ACC, the American Control Conference, every year. So that's a big thing. There you also have electrical engineers, mechanical engineers, chemical engineers. So there is actually a forum for that.

NEBEKER:
I see. Do they have journals, these societies?

ÅSTRÖM:
IFAC has a journal called Automatica. The American Automatic Control Society doesn’t have their own journal. There has been talk of the ECC, European Control Conference. Also the ACC, the Asian Control Conference. The European runs every other year. The first Asian one was this year. That will also be held, probably, every other year. Then you have the electrical engineering community in the United States. IEEE, which has the Control System Society, and they run the Decision and Control Conference every year.

NEBEKER:
Right.

ÅSTRÖM:
Then they have the journals, the Control Systems Magazine, and then the Applications Journal, and the Transactions on Automatic Control. So they have the three journals. Then we have American ASME.

NEBEKER:
I see. They have their own control journal.

ÅSTRÖM:
Yes, and they have a control conference in connection with their yearly conferences.

NEBEKER:
I see.

ÅSTRÖM:
And then you have AIChE, American Institute of Chemical Engineers. They also have their own control group, and they don't have a separate journal, but there are always process control people there. They get people.

NEBEKER:
I see.

ÅSTRÖM:
There is yet another body, namely the ISA, the Instrument Society of America. That is more instrument engineers devoted to process control. They have their own journals, and they have their own meetings.

NEBEKER:
But not specifically for control instrumentation?

ÅSTRÖM:
Well, most of their work is industrial, typically for industrial process control. Then you have the AIAA, the American Institute of Aeronautics and Astrophysics. They have their own control journal, and they also have their own specialized meetings for controlling aerospace. So I think that is another thing that is important for teaching. Here you have, for example, a list. These are the large American institutes. Then, of course, there are other publishers.

NEBEKER:
Oh, there is also SIAM.

ÅSTRÖM:
Yes. Society of -- they have their journal of control.

NEBEKER:
This is a fascinating field. It touches all areas of engineering.

ÅSTRÖM:
Yeah.

NEBEKER:
Is the SIAM one more theoretical?

ÅSTRÖM:
That's mathematical. When I grew up, applied mathematics was essentially computer (?) mechanics. But nowadays it is also legitimate to do applied mathematics of systems engineering problems. This creates both advantages for control and disadvantages, because the things that tie it together are abstract things.

NEBEKER:
Yes.

### Control theory and mathematical fields

ÅSTRÖM:
You know, things like feedback. Things like principles. You can do like I have the advantage of doing. When things become abstract you can suddenly move things across. It's great for technology transfer. It's also great for educating systems people, because the successful control engineer must be able to communicate. He must be able to communicate, whether it's about the process or other things. So we help to educate people a little bit, which is in general useful in engineering. But it is also very difficult, because, for example, if you are doing electrical motors there is no question where electrical motors are situated. It has the disadvantage that you are not tied to general pieces of hardware. So it's kind of amorphous from that point of view. It grew out of the applications. If you look at the theory, say, from 1960, then people threw away a lot of the applications, and focused on the abstract. Viewing it as a pure mathematical thing.

NEBEKER:
Can you tell me how it relates to these more mathematical fields? For example, operations research, or --

ÅSTRÖM:
If you take operations research, that is typically, static problems. You do optimization, but you are not really considering dynamics. On the other hand, if you look at very large problems, like large linear problems, large optimizations. Things like this. I think a key element of control is that we have dynamic systems. So in a certain sense both of us are using optimization theory quite a lot. But typically control has been not so complex, not so many variables. On the other hand, it has been more complicated.

NEBEKER:
I see.

ÅSTRÖM:
With control, if you change something it doesn't show up immediately. It has dynamic features, so the effect of changes right now won't show up until later, and that is really what is causing the difficulties of control.

NEBEKER:
Is there a branch of applied mathematics called the control theory?

ÅSTRÖM:
Oh, yes.

NEBEKER:
That corresponds to operations research?

ÅSTRÖM:
Yes, there is. There is, and it goes either under the name of system theory or control theory.

NEBEKER:
I see.

ÅSTRÖM:
That is why, for example, there are several in the mathematics community who do control theory. For example you have the very famous one at Rutgers Hector Sussmann. He's an interesting guy so you should go and talk to him. He is in the mathematics department.

NEBEKER:
I see.

ÅSTRÖM:
He's been on optimization.

NEBEKER:
These people are inspired by the more applied types of work?

ÅSTRÖM:
Yes. For example, do you know Richard Bellman?

NEBEKER:
Yes.

ÅSTRÖM:
He has made very major contributions to the control of this dynamic programming. You have an equivalent in Russia called Ponktryol. Ponktryol was a pure mathematician of the Stedler Institute. He picked up the control problem, then he extended classical calculus of variations, and he formulated what's called the Ponktyagins maximum principle. You have the Lagrange equations in classical calculus of variations. Ponktryagins maximum principle is a direct descent from that. Then you have the other approach to that which is the Hamilton and Jacobi equation. Hamilton and Jacobi, were great researchers in mechanics who gave another view of calculus of variations. Bellman's dynamic programming can be seen as a direct continuation of the work of Hamilton and Jacobi.

NEBEKER:
I see.

ÅSTRÖM:
So that's the other way of looking at the calculus of variations. And then you have Lagrange, Montreal --

NEBEKER:
And these both are part of --

ÅSTRÖM:
Part of the control theory evolution.

### Relation of theory to practice

NEBEKER:
How does it look today? There is a body of theory that is nicely applied in different areas?

ÅSTRÖM:
There is a body of control that is widely applied, and widely in use. Also, as always happens in this field, people are solving practical problems without any theoretical coverage. There is theory developed that probably nobody will look at, you know, ten years from now. This, of course, may be prejudiced, but I think that in engineering there will always have to be, in the long range, some kind of usefulness.

NEBEKER:
Yes.

ÅSTRÖM:
When you develop theories, it's very hard when you start off to know what is really going to stay there and what is not. You can't see from the beginning, because you really have to work through a lot of things. So there is always a discussion in control of the gap between theory and practice.

NEBEKER:
That is something commented on?

ÅSTRÖM:
Oh, yes. It's called "the gap". [Laughter] It comes and goes in little ways, but you very often find in the evenings that you are discussing this. I think that's true all over electrical engineering.

NEBEKER:
I've heard people in operations research criticizing theoretical work, that it gets further and further from any useful applications, and the people close to the applications just dismiss a lot of the work.

ÅSTRÖM:
Yes.

NEBEKER:
And the same sort of thing happens?

ÅSTRÖM:
The same sort of thing happens in control. For example, if you look at IEEE, I have been involved in evaluating the IEEE Transactions document called the archive papers. I don't remember the exact thing, but you can probably dig them up somewhere. We did studies, for example, on the average readership of the paper. It is very clear that people in industry don't read this journal on control. That was the reason why. There were always discussions: "What should we do about this?" At the same time there are people out in industry who are doing good work which somehow doesn't get properly written up. They send work to the Transactions, and people say, "Oh, this is rough." And they say, "You have to rewrite it." People don't have time to write it up. That's why we started the applications part. That's also another reason why the control systems magazine was started to bridge the gap. I also think that the current American academic system has some difficulties within it. There is a tremendous pressure brought upon young professors in electrical engineering. You get your Ph.D. and you get a basic position, and you have three years to publish. You have to get research grants, you have to get graduate students, so what do you do? Well, you write papers on your Ph.D. dissertation. You start students working on sub-problems of your dissertation. It means a very tough time starting out.

NEBEKER:
Yes.

ÅSTRÖM:
Now, if this goes on for three or four generations it gets sort of watered down. You are typically evaluated by the number of publications you have had.

NEBEKER:
Yes.

ÅSTRÖM:
There is nothing as good as the American graduate school. I think that is a superb graduate education. But the system there has built into it this --

NEBEKER:
Conservatism?

ÅSTRÖM:
Conservatism, continuing this research line. I think we are in a much luckier position. When I got my professorship in Sweden in 1965, if I hadn't published a single paper nobody would have bothered. We have much less pressure brought on us, which really means that it is much easier for us to gamble. Also, with a professorship I have immediately a bunch of assistants. I can hire a bunch of Ph.D.'s to work with who don't have any research grants. We don't have so much research money. It's not easy to solve this problem, but I think certainly in Europe we have some advantages. It has been easier for us to gamble, to look at some more long-range things than to just keep on doing what we have before.

NEBEKER:
Does this mean that the American professors, assistant professors, and so on in this area generally tend to push further some line of thinking, as you were saying, rather than maybe look at some new areas of applications?

ÅSTRÖM:
No, it seems you can't because, you know, there is such variety. There are many, many people. But on average they are under much more pressure.

NEBEKER:
Circumstances for an academic may, in the United States, contribute to a greater gap between what is actually used in practice and what people are publishing.

ÅSTRÖM:
Yes.

### Numerical analysis

NEBEKER:
There are also these communities in statistics and operations in numerical analysis. Are they tied to control theory?

ÅSTRÖM:
Yes. There have been a couple of people who are lying in interface between numerical mathematics and numerical analysis, and since computers are becoming so important, we are using numerical algorithms daily in control theory. For example, simulations for design calculations. There are special problems that are quite interesting from a numerical point of view. I can give you a couple of examples. If you take numerical linear algebra, you are just trying to solve regular linear equations. That's standard numerical mathematics. There are some very interesting equations coming out in automatic control. One is called the Lyapunov equation. Another one is called the Riccati equations. They are a very nice extension of the standard linear algebra-type equations. A numerical analyst by training is Alan Laub. He is a Canadian originally, and he made a Ph.D. in numerical mathematics, and now he is a professor in electrical engineering at the University of Santa Barbara, and he is doing numerical analysis for control. They recently published a monograph. IEEE Press. "Numerical Linear Algebra Techniques for Systems and Control."

NEBEKER:
I see.

ÅSTRÖM:
Another one is Candoran [sic]. He is a European who did a Ph.D. at Stanford. Another interesting connection that also ties into numerical analysis at Stanford is that there's a very famous professor in numerical mathematics called Gene Golub --

NEBEKER:
Yes.

ÅSTRÖM:
He is the grandfather of this community. He has been working on what is called singular value analysis. This has a lot of applications in control. In simulations we have to solve differential equations. Also we often a have what are called differential algebraic equations, some differential equations from algebraic equations. There are several numerical analysts right now coming into that. Also in optimization, this has, from time to time, been a very large area. There have been people who are doing very interesting work in optimization problems. For example, devices like satellites.

NEBEKER:
Is this a case of the application areas stimulating theoretical work in certain instances?

ÅSTRÖM:
I think it actually goes both ways now. We needed to have high quality algorithms to solve ours, so we are learning from the numeric community. We are also sending away problems from our area which are useful for numerical analysis. Many of my graduate students are taking courses in numerical analysis. I recently had a very interesting dissertation between numerical analysis and control. I had a student who demonstrated that, if you have a typical numerical equation, you take a little step and then you go forward. Well, in there you have something called automatic step calculations. That is something used for control. You choose the step, and then you get an estimate of how big the error is, and then you would like to close the loop. There are dynamics involved. So he looked at this as a control problem, and he came up with some very interesting uses of adjusted algorithms.

NEBEKER:
For numerical analysis?

ÅSTRÖM:
For numerical analysis problems. So that's typical. For example, here we have one of our dissertations from 1992. It is called "Control of Error in Convergence in ODE Solvers" ODE is ordinary differential equations. This is a typical example of interaction between numerical analysis and control.

### Statistics and probability

NEBEKER:
That's very interesting. What about statistics and probability?

ÅSTRÖM:
There is a very strong connection. The key problem in control is dealing with disturbances. If there were no disturbances there would not be any control problems. There are many different ways of describing the disturbance. One of them is to describe disturbances as random processes. If we do this we naturally have to bring in random disturbance. On top of this, you could then formulate an optimization problem which involves random disturbances. Then you get stochastic control theory, which is the topic of one of the books I wrote in the 1970s, Stochastic Control Systems. One of the recent IEEE Control Systems Society awards was given to Harold Kushner for his contributions to stochastic control theory.

NEBEKER:
Is he a statistician?

ÅSTRÖM:
No, he is a professor at Brown University, and so he is a professor of automatic control, but he has been essentially devoted all of his life to stochastic control theory.

NEBEKER:
I see.

ÅSTRÖM:
And again, given very interesting contributions to both fields. This book I mentioned largely grew out of a lot of work in that field. I finished this in 1971 --

NEBEKER:
In 1971.

ÅSTRÖM:
It is about ten years afterwards I published this.

NEBEKER:

ÅSTRÖM:
Sort of. Incidentally, Richard Bellman worked quite a lot with me. I was lucky enough to keep in touch with him.

NEBEKER:
I actually met him.

ÅSTRÖM:
He came to Sweden, and my mathematics professor was his official guide, so I was his real guide. That was at the time I worked with IBM I got on really well with both him and his wife, and then later on I spent the summer of 1969 working at the University of Southern California, and he taught me many things. One thing he said was, "It's not enough to write papers. You should write books." He said, “If you write papers you always have to do things slowly, but if you've been working on a field for a while you should really write a book about it." That is very good advice. Then he said, "If you've done this then you summarize your ideas, and then you put it away. You start to work on something else, because it is closed. You should never work on the same problem forever because you are reaching the point of diminishing returns." Now, that's something I remember.

Then Manosovich [sic] was here in Sweden many times, so we had very good personal relations, and he used to give hilarious lectures. For example, I remember he was at Karolinska Institute, it is a famous medical center. He said, "Cancer now supports more people than it kills." And he said things like this, "Well, you in Sweden ought to give the Nobel Prize in physics to a professor coming from an obscure university in the Midwest who doesn't have a piece of equipment that weighs one hundred thousand tons and costs the same amount of dollars!" He has also written an autobiography called, Eye of the Hurricane, and I never have figured out whether that has really been published or not, but I have the manuscript. It is very interesting reading.

### Revamping program at Lund

NEBEKER:
Maybe we should get back to your career?

ÅSTRÖM:
Yes.

NEBEKER:
You took this position in 1965. You said that you continued to work part time.

ÅSTRÖM:
Yes, I did.

NEBEKER:
How did things go with this new institute here?

ÅSTRÖM:
I thought it was a very, very fascinating experience, because at the time in Sweden, control was taught in the classic style with Laplace transforms, and nobody cared about state transitions. I had been lucky enough to see all this development, and also there was very little emphasis on using computers. I actually gave the first course in Sweden on sample data systems when I was doing my military service in Stockholm. That must have been around 1961. When I came here I was filled with ideas, about how one should really do the application. To me that was a big challenge. Also I had a pretty good feel of how I should build up a research group, because of my experience with IBM. In the experimental investigation that we started to do, there were lots of theoretical issues. So I was coming essentially with my head filled with problems and ideas. There was also a very heavy squeeze on the curriculum, so we just had a very small software [?] control ______. We had one introductory course of very few hours, and then we had what was called an advanced course, also with very few hours. The first thing I did was design what I called a reasonable introductory course to control, which was blending in the classical stuff with the new style that I had learned. Then I fairly quickly wrote a book on that. This book is called Control Theory, and it appeared first in 1968.

NEBEKER:
1968, yes.

ÅSTRÖM:
The key idea of doing this was to do a reasonably basic course that mixed in the old with the new.

NEBEKER:
Were there not textbooks that did the new approach?

### Relation to Swedish industry

ÅSTRÖM:
Neither in the United States nor in Sweden were there any textbooks. So this was, it is safe to say, fairly unique. Then I started to build up a research team. Based on my IBM experience, we were starting off by doing a research program. I was thinking out programs, and I think I have some of those available. So in 1969 I wrote a program for research in automatic control here in Lund. We wanted, number one, to do research on a good international level and educate researchers that would have a good international standing, which means focus. On the other hand, we wanted to make sure that we have breadth enough to serve the industrial needs in Sweden. I also started to get funding so that we could invite a lot of people coming from the outside. The topics we decided to work on were system identification, to look at theoretical aspects of the experimental techniques that we had developed, adaptive control, numerical methods for control, and the applications. Most of the projects were methodology oriented, so we said, "Okay, we are going to develop new ideas and new concepts." But then we said that to keep honest we should at each time have a real control problem, an applications problem.

NEBEKER:
One that is actually implemented?

ÅSTRÖM:
One that is implemented, and one where we work with external people that have problems. There were a couple of reasons for doing this. First of all, you get very interesting tensions in a research group. We said when we do these problems we should always look at the problem first, and look at methodology later. So you get very interesting tensions between the guy who is trying to solve it and the theoretical guys. Secondly, by doing this we will also find problem areas in real life which we have no good feel for, which was a kick-back of the theory. These were essentially the guiding principles that we used.

NEBEKER:
You carried that out?

ÅSTRÖM:
Yes. That general philosophy is something that we are still sticking to.

NEBEKER:
Mainly with Swedish companies?

ÅSTRÖM:
Yes. This is more or less a time perspective of what we have been doing, starting here in 1965. These are the methodology things we have been doing, and down here are the applications.

NEBEKER:
I see.

ÅSTRÖM:
So, you started to ask about the applications. We started off in the pulp and paper industry, and these applied projects have a typical finish in mind. Very often the students involved with this will go into the industry where we work. When they do they hope to set up groups that are much more powerful than the groups we have.

NEBEKER:
I see.

ÅSTRÖM:
That's a typical thing that happens. But then what also very often happens is that after a while they find problems they don't have time to deal with. So they are often repeating the factors [?]. I didn't think this would happen, but things are recurring. We have also said that it is useful to change application areas over time. You know, to maintain a certain break within the groups. If you look, for example, we started off with the paper industry. We did a lot of work with the power industry later on. Our first Ph.D. dissertation had to do with control of power systems. Modeling a boiler, something like this. This is now recurring, so right now we are heavily involved with the power industry. Then there was a period when we were working with heating ventilation and air- conditioning systems. We have done work with ship steering, again with Swedish industry, and here we have some interesting products like adaptive auto-pilots and stuff like that. We have been working with control of waste water treatment plants. We have been working on microbiological systems with the chemical engineering departments, and we have a robotics project. These have all been done with Swedish industries. This is the local power company, for example. This we did with a group of several companies. This was done both with the Swedish ship testing faculty in Gothenburg, and with a local shipyard. When you came here maybe you saw this. How did you come in?

NEBEKER:
On the flygbåt.

ÅSTRÖM:
Well, when you go out, you will see a huge crane on the left, and that is where the shipyard is. Just now they only do submarines. So that's a variety of topics.

NEBEKER:
Has it worked in bringing new ideas to the more theoretically inclined?

ÅSTRÖM:
Oh, yes. Very typically here, what we notice when we work with a project is that we need to be extremely efficient in terms of engineering man-hours. In other words, if you work with outside partners and you're such a good teacher [?], we have to be very efficient in carrying out controlling it. This activity has started a project that we call CAC: Computer Aided Controller. In other words, we try to develop computer-aided tools to help us solve it. We started with this in the late 1960s and early 1970s. We were one of the first control groups who really got aboard this. We developed software to design control systems and analyze them. This is something where we later had quite a lot of interaction with General Electric. General Electric acquired essentially all of our design software into their central research department, and they spread it out. We had over a ten-year period a very strong interaction with General Electric. That is a typical example. We also worked on system magnification for about ten years. I stopped that because I had two very good former Ph.D. students who became full professors in this. One in Uppsala, and the other in _______. They were very interested in doing system magnification, so I said, "Okay, why don't you guys do that? We will reduce our research activity in that area, and instead move the activity over to _____ control." Another thing called automatic tune also came out of the applications, because we had largely the work of [incomprehensible] ... had fairly complicated controls.

### PID devices

ÅSTRÖM:

Are you familiar with what is called a PID? No? I'll show you what it is. I have a little box in my hand which is a PID controller. Proportional Integral and Derivative. It is the simplest control algorithm that was being used at the center of industrial process control. Out in real life about 90 to 95% of all control problems are solved by these controls. They have not attracted very much research attention for the past fifty years. Yet it is the standard device. We had been working with applications, and it was very clear. These controls have three parameters that you have to select. The proportional gain, the integral gain, and the derivative gain, and a [incomprehensible] ... He developed in 1942 some empirical instruments for this. Even so, it is not easy for people with very little education to do this. So then, of course, we saw this out there and thought, “Wouldn't it be nice if we could do something where we take this and simplify it?” We were using some of the ideas that he had, and some new ideas, to provide these with just a push-button. You push this button, and it works automatically. That was a typical problem that was inspired from the grass roots. In a certain sense you can say that it was not really considered kosher to look at this. It was beneath you.

NEBEKER:
Too simple.

ÅSTRÖM:

NEBEKER:
Yes.

ÅSTRÖM:
So as a result of this we have done a lot of research which relates to these devices. For example, this was done with one of my co-workers, Hector. We started to work on this around 1980. We came up with a couple of patents that were very useful. We persuaded a Swedish manufacturer to start to make them, and they put in a little research group here on the science park. This time we really know how to do this, and say, "You don't have any guys who can do this, you'll have to hire some guys." They hired one of our former masters students who was also in industrial engineering. He set up his own group in the science park here and we developed the devices. Now they are licensing this to many of the large component companies. That has been a nice project coming out from the graduates.

NEBEKER:
Your expertise in this was important?

ÅSTRÖM:
Yes. We had the background in system identification, but it required some new ideas. Of course they were simple devices, but we needed something extremely robust that can work over a very, very wide range of temperatures. So this is more like having your own axe. The other things we have worked with have been more like scalpels. We are trying to combine the axe and the scalpel for the next generation.

NEBEKER:
I see. Your own research has been in these different areas all this time?

ÅSTRÖM:
I think I follow the advice from Richard Bellman to try to change what you are doing. When I started I did a lot of work in stochastic probability. That got in a real boom from this Billerud project and changed direction. Then I worked very intensely on system identification for a while. This has become, in a certain sense, a standard field right now, so the International Federation of Automatic Control has a conference every third year dealing with system identification. We have been involved with them from the very start. The last one was actually held this summer in Copenhagen. So I worked very hard in system identification. After that I switched to focus a lot on adaptive control. All the time, more or less, I have been working on the theory of computer control systems, the theory required when you are putting computers into this. That has been going on for quite a while. Since 1980 we had been exploring quite intensely the impact of artificial intelligence and _____ computing. We are now looking into problems where we are trying to merge control and diagnostics. There is a strong push from the quality control side. But inside a control room there are many signals that will tell you a lot about how well the system is performing.

NEBEKER:
How is that anything new?

ÅSTRÖM:

NEBEKER:
I see.

ÅSTRÖM:
That is one example.

NEBEKER:
What areas have you been working on in recent years.

ÅSTRÖM:
The last ten years we have been doing a lot of work on automatic control. Where we are now merging control and diagnostics, we call this autonomous controlling, control with intelligence. We are trying to increase the level of information. This is one example. Before, we had control with three parameters. Now we have the [incomprehensible]. My colleague over here, Professor _____, puts a flag up saying now there is something funny happening with control. We are doing control so you can go up to him and say, "My friend, how are you doing?" Then he'll tell you, "Well, you know, I mean the upper percentage with respect to quality variables." So you try to add some features to the control.

### Computer-Aided Modeling

NEBEKER:
I looked at this article on computer-aided modeling, the review article you wrote. You talk about a number of languages that weredeveloped specifically for control. What has been the success of these?

ÅSTRÖM:
Well, you know, this relates to developments. We call this Computer Aided Control Engineering. This was work that we started in the 1970s. The simulator that we were doing here, that is still run commercially. There are something like several thousand licenses out in something like fifty different countries. This has now been superseded by using MATLAB. I have a couple of students right now who are working on computer support for modeling complex systems. To do the mathematical modeling of something like that is very time- consuming and very error-prone. Right now we are using object-oriented programming methods to try to develop new techniques for the modern approach. So that's one spin-off problem.

NEBEKER:
Modeling of systems is, of course, standard technique across the sciences, and I imagine across applications as well. Is that a field in its own right?

ÅSTRÖM:
I think that there are several universities offering, for example, courses on modeling. Of course, modeling can be anything.

NEBEKER:
Yes.

ÅSTRÖM:
But if you look at our field, modeling for doing control systems design, we are very well defined. You can always make a model a little bit better here, a little bit better there. But if we do control systems design, we can always relate it to: does this have any affect whatsoever on the performance of the control system? Or will it not? In a certain sense it is fairly easy for us to do when we have done a good enough job.

NEBEKER:
I see.

ÅSTRÖM:
But I think it is an important aspect of essentially all the engineering activity.

NEBEKER:
Has the work done in control systems, the system identification kind of work, proved useful in other types of modeling?

ÅSTRÖM:
Well, for example, there are many people working on environmental problems, you know, so several of the techniques that have come out of the control systems community have proven very useful in analyzing ecosystems and things like this. A faculty member who worked here also has been using them for medical purposes. His special category is the human balance system. He has been applying system identification techniques to get better diagnostic methods for doctors. So that's a little bit of process control.

### Biological systems as models

NEBEKER:
Has there been any input of ideas to control theory from biological systems?

ÅSTRÖM:
Oh, yes. You know, this brings up the whole issue of cybernetics. I think Wiener was probably the most prominent exponent who said we should really look at biological systems, and see what inspiration we can draw from them for control systems. I think that is a very useful and very interesting research area, because clearly the human being can do many very good control tasks that are difficult. We can just think of the child's learning to stand up, how you are grasping things. That’s typically what robotics people have to do.

NEBEKER:
Yes.

ÅSTRÖM:
There's clearly things going on in our body that would be very useful to incorporate into technical systems, which we don't know how to do. Wiener started this with cybernetics, and Ross Ashley, but it didn't get very far because it was too difficult. But they looked at things like neural networks. That's one sort of inspiration. I think one area that is very challenging for control is digital servos [servers?], when you try to do servo systems which are based on digital information and things like this. In the application areas that have to do robotics, and mobile vehicles, and things like that, I think there are many interesting ideas.

NEBEKER:
With the neural networks it seems to be inspiration only at a fairly abstract level.

ÅSTRÖM:
Yes.

NEBEKER:
Have there been cases of people looking at particular sensory systems and getting something useful out of it?

ÅSTRÖM:
Well, I know one example. There is a group at Cal Tech, [incomprehensible] he has been looking at the human eye, say the lower limits of what you call early vision. Then he has been trying to do analog VLSI, that is mimicking the lower levels of the visual system. He has, for example, large slices of silicon like this, which are really VLSI. They consume very little electrical power, and are very interesting sensors with integrated electronics in them. That is one area where there have been real interesting results.

### Impact of sensor technology

NEBEKER:
That reminds me of another big issue. We touched earlier on the question of what got the computer into control systems work. What about new sensors? That opens up possibilities.

ÅSTRÖM:
My feeling is something like this: whenever there is a new sense of technology coming up there are totally new control systems that apply. A very nice example I am familiar with is from the pulp and paper industry. You have the measurement of the basis weight and the moisture content of the paper that would really open up the possibilities to do an efficient paper machine, at the time that people were developing new instrumentation equipment. This was based on radioactive absorption, and infra-red and some other techniques. There were actually two new companies that were founded based on this idea. One was a company called Accray, in the United States, and the other one was Measurex, and they were both founded on the idea that they developed a new sensor technique. Then, and particularly with Measurex, they were both actually developing computer systems for paper machine control based on this sensor technology, and then they sold the whole package to the customers. That is a very typical example of this. I think another example, which goes even further, is the CD player. You know, if you take the CD player, that encompasses several technologies. One of them is a cheap laser measurement. Another one is the cheap scheme of coding the disc. The third component is efficient control systems to position the sweeping arm. That is a typical example where there are several technologies getting together and suddenly, you know, you have a new type of product.

NEBEKER:
It's satisfying when one can simplify a very complex historical development, for example, in saying that the electron tube was the enabling technology for a number of applications, or made the applications possible. Or the computer was an enabling technology because you could do these calculations fast enough, or whatever. Is it possible to see such simple ideas, themes, in sensing instrumentation over the last decade? Are there particular breakthroughs there in photocells, or charge-coupled devices, or whatever, that you have seen? That has opened up a new area of control systems?

### Impact of feedback theory and technology

ÅSTRÖM:
In sensors, it is not that strong a force. Let me answer this a different way. I thought you were going to ask me, are there any ideas in control that have been this important?

NEBEKER:
That's a very good question.

ÅSTRÖM:
Then I could say something about it! I think if you take the idea of feedback, for example Black at Bell Labs got a patent for the feedback amplifier, and they were working like crazy to try to make a linear electronic amplifier, because they needed this. When they make long telephone lines they need repeaters.

NEBEKER:
Right.

ÅSTRÖM:
These repeaters need to be tremendously linear, because when you have many of them, other wise you get distortion. It was not until Black invented the feedback amplifier that we were able to make this system. You can say that the invention of feedback was an enabling technology for the long distance telephones. Then, of course, feedback came back in, in many different places. If you look, for example, to the development of instrumentation, there was a very big step in instrumentation when people started to use what we called force feedback. I'll give you a new example of that, by picking up a piece of paper. Suppose that you are going to measure a pressure. You know, a simple way -- are you familiar with what is called a Bourdon tube? One way to do the pressure is this. Down here is a bellow which effectively you send in the air with, and this also has a swing action. You put in your sensor that is measuring the distance; you just put it here. To do this you have a measurement device that depends on the spring coefficient that is in here. It depends on the calibration of this measurement. That’s how a lot of instruments were done, say, before 1955. Now, I introduce a feedback, and you can do something like that. In here you put a hole, and now you use this only as a zero. You introduce a feedback, with an amplifier, that you put into this hole, you are now generating a current [?] ______ that is accepted by that. Now you are using this sensor only as the zero. You are not depending on the calibrations. You only need to generate the force that is matching this one. Then you have to measure what this current is.

NEBEKER:
Right.

ÅSTRÖM:
It's opposed [?] to this. You get rid of the spring coefficient. This is what's called force feedback.

NEBEKER:
So you are using the feedback to maintain a --

ÅSTRÖM:
Exactly, to maintain a certain position and then you measure the force required. This went like wildfire through the instrumentation world. Again, it is the use of an abstract idea. What you really do is get an order of magnitude’s improvement in performance. You can be very clever; for example, you can send this in as pulses.

NEBEKER:
What is the advantage of that?

ÅSTRÖM:
Well, then you can read pulse trains, and you just count the pulses. If you just extend the counting time you can increase precision tremendously. For example, if you buy an electronic scale for your bathroom, they are based on this pulse series. With cheap equipment in there, you can just increase precision by changing your time period. I'll give you another one. You mentioned the active optics. What is that? Well, you have a mirror in there, and instead of driving this to very high precision, you just make sure that you can really change all these little circuits, you see.

NEBEKER:
Right.

ÅSTRÖM:
So you apply feedback to this. What I think is so fascinating about control is that you have a couple of these principles, like feedback, which cut across a lot of things, and by applying them in the right instances, you can get tremendous improvements in things.

NEBEKER:
And, of course, as with this active optics, it is the availability of cheap microelectronics --

ÅSTRÖM:
Exactly

NEBEKER:
Yes, so you can replace a very expensive essentially mechanical technology with active electronics. I happen to have looked a bit at the history of seismographs, and there is exactly this idea that revolutionized the design of seismographs.

ÅSTRÖM:
Okay.

NEBEKER:
Is that why the electron tube had a large impact on control systems? Because you had a good amplifier?

ÅSTRÖM:
A good amplifier. It is interesting, you know. Early process control people were using pneumatic systems to do control. They had what was called the flapper valve, which was the means of amplifying. There is another very interesting example if you take analog computers. Vannevar Bush, when he made his analog computer, there were really two inventions? It was the ball and disc integrator, that was one thing. The other thing was what was called the torque amplifier. The torque amplifier was a mechanical device where you could have a little torque amplified to a large torque. So I think that could be an interesting theme. To take the role of amplifiers in technology.

NEBEKER:
It's amazing that so much depends on just being able to amplify.

ÅSTRÖM:
Exactly.

NEBEKER:
There were simpler kinds of electric amplifiers, going back to Edison, such as putting another carbon microphone in, but I guess because of the poor response of that it didn't keep going in applications that are going now in electrics.

### Operational amplifiers and transistorization

ÅSTRÖM:
You have another thing that is connected with that. That is the operational amplifier. You know electronics?

NEBEKER:
Yes, I know that.

ÅSTRÖM:
After World War II there was a guy named George Philbrick. I don't know if he was _____. That's the guy who made a device that nowadays we draw like this {I made a simple sketch}. It is an amplifier with two inputs. It was called the operational amplifier.. It’s an amplifier that can put out a lot of feedback. He took a couple of electron tubes and connected them together in a sort of special pattern, and then he had a very flexible amplifier that could serve so many purposes. I remember, when I came here as a professor, they had just been transistorized, and you could buy operational amplifiers for about two thousand Swedish crowns. They were used in analog control systems. Nowadays when they are transistorized you buy them for probably about one quarter of the price. That is a sophisticated continuation of the regular amplifiers.

NEBEKER:
Is it possible to characterize the impact of the transistor apart from its impact on computing, the impact of the transistor on control systems?

ÅSTRÖM:
Yes. I think one of the immediate impacts of the transistor was that we were really getting these cheap operational amplifiers.

NEBEKER:
Of course, at the beginning they weren't --

ÅSTRÖM:
No, no, at the beginning they were costing as much, but first of all you had miniaturization.

NEBEKER:
Right.

ÅSTRÖM:
They were also much more rugged to vibration.

NEBEKER:
Right, right. I can imagine that's important.

ÅSTRÖM:
These devices, the standard PID controller, went through very rapid development. They used originally to be implemented by pneumatic systems. So you had standardized pneumatic pipes, and the signal was going through pipes. Then you made them with transistors, and then you made them with operational amplifiers, and now you do it with microprocessors. So it's essentially the same mathematical function, that goes through a range of things.

NEBEKER:
Now, I can imagine that the ruggedization, if that is the word, of these devices could open up new areas of applications. And miniaturization? Was that important in industry? Certainly important in military, aerospace, communications --

ÅSTRÖM:
The miniaturized stuff -- what’s interesting about sensors is that if you can find a mass market [incomprehensible], then the sensors used for that market will be available at very cheap prices. If you look at cars, many have the sensors; something that is going to come out of increased car automation will be a collection of sensors that are going to be used for many other things. It would not have been possible to make cars that satisfy the American Environmental Commission if you had not had sensors. That is quite a nice example of the impact of a sensor combined with miniaturization. There are probably more.

### Influential books in the field

NEBEKER:
It is obvious that having the microprocessor makes it possible for these sophisticated control systems in everything, so I imagine that has opened up many areas of application of control theory. What about really influential books in control theory?

ÅSTRÖM:
If you look at the beginnings, there are two early books that have been tremendously important. One is a book coming out of the M.I.T. Radiation Laboratories, James Nichols Phillips Theory of Servomechanism. There is another interesting book by Chia. I don't remember the exact title. Tsien was this interesting guy who was working at Caltech during the McCarthy era. He was Chinese. He wanted to go back to China. It is called Engineering Cybernetics, and Tsien defected to China. He was the guy who created the Chinese Institute. His book on engineering cybernetics, which was published in 1954, was tremendously --

NEBEKER:
Influential.

ÅSTRÖM:
Yes. He had many of the ideas and many unusual things. Here we have the James Nichols book. That was from 1947. Then of course you had Gordon Brown, the creator of the Servomechanicals Laboratory at M.I.T. He had a book called Principles of Servomechanisms, in 1948. Another interesting early book was the Chestnut and Mayer book from 1965. Truckstan's [sic] book from 1955 was a cornerstone. These were all classical control theory, except for Tsien, who was amazingly far-seeing. He had examined [optimal control I believe], and other things. There were other books that I kind of liked. There is one by Newton Gould and Kaiser Analytical Design of Linear Feedback Controls, from 1957. That was one of the first that started to look at modern ways of designing control systems. Then, of course, you have the more modern approaches, like Pontryagin Boltyanskii Gamkrelidze and Mishchenko, The Mathematical Theory of Control Systems, which had published the Pontryagin maximum principle. You had Bellman's book on Adaptive Control, from 1961, which I thought was very inspirational.

NEBEKER:
It looks like in the fifteen years or so after World War II, you had this field very well laid out.

ÅSTRÖM:
Very well laid out. And then, of course, there had been ever later developments. We have the development of optimum control. There are two books in there, again two classics. One is this Athans Falb, Optimum Control Theory, 1966. There is another one by Bryson and Ho which is a very good book on optimum control theory. Then you had specialized books on system identification, you had books on adaptive control, you had books on system theory, and things like that. When you are really going to single out things you need a little bit of the history.

NEBEKER:
Yes. Looking back on it, do you agree with Richard Bellman?

ÅSTRÖM:
[incomprehensible] -- I read quite a few books myself. I think it is a big effort, but I do think it is worthwhile.

NEBEKER:
There are so many prominent researchers who don't do that.

ÅSTRÖM:
I also think it depends on what stage you listen. Certainly with the fields which are in the development stage. I personally would not say you should read everything to write another book [incomprehensible]. If I take my own experience, for example, this stochastic control theory. I know that it is still being used in other things. This book we wrote on computer-controlled systems, we're not going to make a third version of that. We have certainly done lots, and it's also interesting teaching. If I can really digest the material to the stage that the students can spend ten percent less time writing, that's a fantastic gain.

### Influential centers for control theory

NEBEKER:
What about the most important centers for the development of control theory?

ÅSTRÖM:
Well, if you look at the early stage of development, what took place at MIT during the war was tremendous.

NEBEKER:
Yes.

ÅSTRÖM:
There were also similar things happening in the Soviet Union. There is the Institute for Control Sciences in Moscow. A huge Institute, a lot of very talented people. That has certainly been over the years a very influential center.

NEBEKER:
Have their publications been widely read?

ÅSTRÖM:
They have a journal called Automatic and Telemechanica, and they have also published quite a lot of books there. They are essentially for research. That has certainly been a strong center. If you look at universities this becomes quite personal. Certainly the strong American Universities like MIT. Stanford has a kind of small group. Berkeley used to be a real powerhouse. In the early times I would say Columbia University was a very, very strong place, but that group was dispersed quickly. Caltech has a small number of people, but very good people, you know. In the Midwest--Illinois had a very strong center for the Coordinated Science Laboratory, with people like Bill Perkins, Joe Cruz, Petar Kokotovic, probably a few people I forget. That has always been a very, very strong place.

NEBEKER:

ÅSTRÖM:
Bell Labs was very influential in the early stage, and all through the war period. The Rand Corporation has been tremendously important. Another very interesting case is, of course, RIAS. RIAS was the Research Institute of Advanced Studies, in America. It was owned by the Martin Marietta company. Kalman was there with a mathematics professor from Princeton Lefschetz. They had a tremendously strong group in control, for about a period of ten years. Rudy Kalman was there, Harold Kushner was there, and many, many other people. What is interesting is that Martin Marietta really could have cornered the market of Kalman filtering in the aerospace industry. But the company didn't recognize that. Then this group moved over to Brown University in applied mathematics. So Brown University has been a very strong group in control theory. Harvard has always had excellent people. Right now they have Larry Ho, Roger Brocket, small but powerful.

NEBEKER:
Who was in Europe?

ÅSTRÖM:
In Europe, in the old times there was a very strong control group in Cambridge. Imperial College always had a very good group. Oxford has had a small activity, and Manchester has been very, very strong in applications. Zurich had a very good control group. If you go on to Germany, there are many good places. Darmstadt is one, and Munich had a very good control group. You should mention some people in Offenpfaffenhofen (DLR). Oppelt was one of the early pioneers of control in Germany in Darmstadt. Nowadays we have people like Ackermann and Isermann. In France you have a very successful group at INRIA, Institute Nationale Recherche en Informatique et Automatique. Very strong on the mathematical side. It's Professor Lions who was heading this [incomprehensible]. They have research efforts in Paris, Sophia-Antipolis, and in many places. Grenoble has had a good group in control. Holland has superb control groups, and they have also done something that is very unique. They have a graduate school for the whole country, so everybody goes to Utrecht once a week for Ph.D. courses. Belgium has a couple of good control places. Norway has a very strong group in control, led by Professor Balchen. He started before me and still is going. Finland is very strong in applications.

NEBEKER:
And other groups in Sweden?

ÅSTRÖM:
In Sweden we have the group in Lund. Most of the professors in control theory were either my students, or students of my students, so I'm a bit partial, but I would say internationally that Lund, and Linkoping, and Uppsala. If you take the people that are most well known, Leonnart Ljung in Linkoping is very well known, Bjorn Wittenmark in Lund and Torsten Soderstrom in Uppsala are well known.

### Military and industrial applications

NEBEKER:
How important have the military applications been to the development of control? If you were somehow to be able to remove that from this history...

ÅSTRÖM:
Yes. I don't think we would have developed the same way.

NEBEKER:
It was the radar effort initially?

ÅSTRÖM:
I would say the war effort. I mean, if you look to the situation before the war there was industrial process control. There were electronic amplifiers. There were auto-pilot machines. They were essentially the same things, but nobody notices this. Probably later the connection would have been made, but much progress was made during these five years of war. The same thing happened in England, in the Soviet Union, and to a certain extent the same thing happened in America. Then, of course, it got the second kick, through the space effort, which you can say is war-related.

NEBEKER:
Was that a major influence on control theory?

ÅSTRÖM:
Oh, it was a very major influence. People used to talk about what is called modern control, where you have optimization theory brought in, and you have a lot of non-linear stuff. That was by and large motivated by the space effort. All the early effort in adaptive control was motivated by doing flight control systems for supersonic flight. The conventional technique did not work when it got supersonic. There were too many things that were changing, so you had to do something. The research in adaptive control was entirely driven by the military. If you take DARPA, in the United States, it has had a tremendous influence. If you take agencies like the ONR and the Air Force establishment, they have funded a fantastic amount of research. I think the same is true for any problem solving [?]. I think the Kontryarkin maxima principle for linear control probably had to do with the Russian space effort.

NEBEKER:

ÅSTRÖM:
We should also give credit to other companies like the Control Data Corporation. There were several small computer companies in England like the English General Electric, and Ferranti. So there were several other computer companies, and, of course, all of them had a foot in the military as well. A lot of the work that happened in the process control field was essentially coming from this direction. There were also major chemical companies which were heavily involved, like Monsanto and DuPont. They had control groups in the early stages, which also influenced this development quite a bit.

NEBEKER:
Those were of course more in chemicals.

ÅSTRÖM:
Yes, they were in chemicals, but a lot of the areas for digital control were essentially coming through chemical process control, because that is where the applications were, that is where the computer companies were dealing. So there was a very nice synergy there, so -- I think that --

NEBEKER:
Oh, that's very interesting. I happened to notice the electrical engineering applications. I suppose aeronautical engineering was also developed a lot from control systems?

ÅSTRÖM:
At Stanford one of the key people is Professor Bryson. He is professor of aeronautics. At MIT they have always had a strong control group in the aeronautics department.

NEBEKER:
I wanted to ask you about people you have come in contact with, or worked with, or somehow got to know. Are there ones who really impressed you somehow or another?

ÅSTRÖM:
Oh, there are many people. What I am afraid of is that I may miss some. If you take the very early stage, I learned a fantastic amount from the professors I had while I was at college. You see, at that time we were only twenty people in my class after one year. We had professors who were lecturing, so _____ the guys _______, he was lecturing, you know. We met about, say, once a month to have small talks. From these people, I got a lot of attitudes and learned a lot from them. I think Professor Ulf Grenander was one of the most superb expositors of probability theory that I have ever come across. He taught me a fantastic amount of probability theory. Another person that I actually came across later on was Harald Cramer. He was a professor before Grenander, and then he became Chancellor of Swedish University. I had a little interaction with him, and learned a fantastic amount from the interaction I had with him. He was a brilliant man. He was very fast, and it was fun. Richard Bellman. When I was at IBM, Jack Bertram who I worked with, taught me very many things, both technical and also otherwise. Also Rudy Colman . Rudy Colman was associated with IBM.

NEBEKER:
Is that how you got to know him?

ÅSTRÖM:
That's how I got to know him. Another person I had a lot to do with over the years was A.L.I. Jury. He was the one who started ______, and I shared an office with him in Zurich when I was writing this book on computer control. He read through manuscripts and gave a lot of advice. I've been much involved with publishing, and there was a superb publisher named George Axelby. He was the editor of the IEEE Transactions on Automatic Control. He took over Automatica, which was the IFAC journal, and I would say that George Axelby really shaped the automatic control field. I've been editor under him for a long time. When you edit papers, when you work on how to deal with authors. When he was reading he wrote me remarks, and so on. One tremendous thing about working as a professor is that you always interact with bright young people. That is a very good thing. I am getting a little bit off track and there's probably many other people I should mention. But I've forgotten to now.

NEBEKER:
Is there anything you wanted to comment on?

### Labs in classroom teaching

ÅSTRÖM:

NEBEKER:
I can imagine also in control theory that because parts of it are abstract, you might not understand it when it is said.

ÅSTRÖM:
No, I think that is a very, very good point. Because I think it is very easy to get lost in the abstraction if one is not careful. But not if one has some experience that is deeply related to it. They also get a little feel for how well things work, and what things do.

NEBEKER:
Yes.

ÅSTRÖM:
So I think that is quite an important principle of control education.

NEBEKER:
Thank you.