Electronic Design

What's All This Negative Feedback Stuff, Anyhow?

Once upon a time, I worked as Director of Development at Philbrick Researches in Boston. I was reporting directly to George Philbrick himself. (I’ll have more stories to tell about him another day. One day George asked me, could I name the earliest example of a system with feedback? I thought for a second and then conceded, “No, I couldn’t.”)

George proceeded to tell me about some master clock builders who had designed many beautiful high-precision clocks back in the 14th or 15th century. (I’m trying to give you this from memory after a full 20 years.) They had a tedious procedure for trimming and adjusting the rate of the pendulum for each new clock to bring it up to the correct speed so that it agreed with a master clock.

But one of the master workmen decided to get smart and lazy. He added a little mechanical detector so if a new clock’s pendulum were to fall behind the reference, it would trip a cog that would then rotate the screw on the new pendulum and shorten it up, making it run faster. Of course, this was operated as a sampled-data system—it did not exactly work in real time. So if the pendulum’s speed was too far out of sync, the servo would not work. But the lazy fellow was able to do some first-order tweaking and then go home. When he came to work in the morning, the new clock’s pendulum would be perfectly matched with the reference.

WOW! Let’s give a cheer for 1550s technology. This is not only a feedback loop—it’s also one of the world’s first PLLs (phase-locked loops). That would, of course, be the first if there’s any truth to this story. I’ve searched a little and have not been able to confirm its validity, though. But maybe there’s an element of truth in there. Maybe I don’t have the century quite right. But, it’s an impressive story, and George did tell it to me.

The next week, when it was time for our meeting, I told George that I had an example of feedback that was older than his, by a large margin. He looked at me quizzically and I explained. When the ox or bullock was first tamed and domesticated thousands of years ago, it was found that if you put a ring through the nose of the ox, you could easily lead it with a gentle tug, and the beast would follow you closely. At first, the ox would follow closely to avoid pain in his sensitive nose, but eventually he would learn to follow because it was his job and habit.

Even a small child could learn to lead an ox pulling a heavy cart or sledge, by tugging lightly on a thin cord. So here is the original Unity-Gain Follower, with a high input impedance, and a low output impedance. Even if the ox didn’t pull the load quite far enough, he was still under control “inside the loop,” because even a child could tug a few more inches on the cord to get the load pulled up to exactly where he wanted it. I can’t tell if that feedback goes back 5000 or 6000 years or more, but it surely is a good example, and George had to concede to that.

In the early 1800s, steam engines were developed to a rather high degree of sophistication. To maintain speed, the governor was invented. The centrifugal force on a couple of rotating fly-balls was coupled in a linear motion that could open or close the throttle. The basic governor had finite gain, so if a load was applied, the engine would slow down and then work its way back up a little—but not all the way back, due to the finite gain. To obtain substantially perfect speed regulation, governors were devised with tricky mechanical linkages so that they had infinite gain. But some of these were unstable. Finally, improved designs had infinite dc gain, but a well-controlled dynamic response, to help keep the loop stable. To think all this stuff went on back in the 1880s! I can look up a whole bunch of these old designs in my old Encyclopedia Britannica, the 1891 edition. YES, 1891, not 1981!

Now, come to think of it, George Philbrick told me of a saw mill he designed when he was young. He said he designed it to idle at a moderately slow speed, to save on fuel and energy. But when a load was applied, it would speed up smoothly, so as to apply maximum power when the load was heaviest. Of course, any simple governor could not do this, because if it sensed the inertial load of the saw blade, it would speed up as it sensed the torque being sent to speed up the inertial load. It could not easily distinguish this from a lossy load, such as a log being cut by the saw teeth. This loop would normally oscillate with a vengeance, back and forth from the highest speed to a stall speed.

But, of course, George claimed he had designed a detector that could distinguish the difference between a dynamic load and a lossy load, and he could servo the loop with adequate stability. In theory, one could indeed do this. But when George was young (in the 1930s and 1940s), I doubt if the tools were easily at hand. Still, I would not want to bet him that he did not or could not do it. After all, in 1970 I designed an analog-to-digital converter that could easily have been built in the 1940s or earlier. But I still think George was pulling my leg.

In the 1930s, Mr. Harold S. Black devised his famous theories about negative feedback at Bell Labs. The best amplifiers of the time still had excessive distortion. When you cascaded 40 or 60 stages of amplifier, as you might do in a long-distance telephone line, the distortion kept building up. With the aid of feedback, the amplifiers’ distortion could be cut to negligible levels, even after many cascaded stages. The story of how Black became aware of the advances of negative feedback, while crossing New York harbor on a ferry-boat, was recounted a few years ago in the IEEE Spectrum and makes a fascinating read….

It was only a matter of time before this led to the analog computer and the operational amplifier. Now, we all know that a basic operational amplifier can integrate a signal. But in the early days of analog computation, even a single pentode could perform integration (see the figure). George Philbrick worked with many things of this type—crude, imperfect, but inspiring. Who invented the operational amplifier? Nobody argues that there was only one inventor, but there were groups of engineers who helped convert those crude, unidirectional current pumps into the familiar op-amp functions we know. And George was one of those pioneers.

During World War II, George worked with analog computing systems, training gunners to do a better job of aiming their guns at fast-moving planes. He found that if you inserted a controller circuit between the man and the gun, it could be tailored to improve the response and accuracy. He could also tailor this response to make the job more difficult, more awkward. He added lags to make it really difficult to aim the gun. Then after some more practice he removed the lags, and the gunner was now quicker and more accurate than ever. So this was used as part of the training.

George also devised controller networks that, under favorable conditions, could aim a gun at the correct angle ahead of the plane’s image—the “lead”—better than a human could. He designed controllers that were very good at adapting to any changes in the dynamics of the gun-aiming circuits.

However, there was one situation George said he could not handle with his controllers: If the gain reversed—if the knob that was supposed to make the gun to go the left made it go right—he could not accommodate that. These days, of course, you could design a computer that would detect this reversed response and then make it work right. But back in the 40s, it wasn’t so easy.

Now that reminds me of one of my pet experiments. Somebody told me that if you’re riding a bicycle, and you cross your hands on the handlebars, your servo will goof up and you will crash. I tried it. I crashed. I will concede that if you think really hard and lock up your shoulder with your arms, you may be able to steer the bike to servo things and not crash. But if you just let your arms push and pull, as if they were not crossed, well, I warn you now, it’s easy to crash a bike. Please do not hurt yourself. You do not really have to try it; just think about it. But if you go ahead with this endeavor, try it on a soft lawn where you won’t get ruined when you crash.

These days, there are so many examples of negative feedback that it’s almost preposterous to try to count them. If you have a VCR, the motors are driven at a precise speed by a loop controller. Radios have AFC and AVC loops. A refrigerator’s thermostat is a crude, bang-bang controller. Kids’ toys act as robots with feedback.

A single op amp may have two or three feedback loops. When we are driving our cars or riding our bicycles, if we get off center in our lane, we servo back to where we want to be. If the car’s speed errs from the bogey value, the speed control pulls it back to the right speed. There’s almost no limit to the amount of negative feedback that we use in a given day. And the more we think about the Good Old Days, the better we can appreciate how things work and how things got to be this way.

Now, I’m only writing about negative feedback. I was not intending to write about George Philbrick. Imagine what I’d had said if I had intended to write about George.

All for now. / Comments invited! / RAP / Robert A. Pease / Engineer

 

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