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From: Phantom
Newsgroups: sci.electronics.design
Subject: Re: The First NFB theory
Date: 17 Sep 2002 01:06:09 -0500
Message-ID:
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On Tue, 17 Sep 2002 01:46:30 GMT, Chuck Simmons
wrote:
>Kevin Aylward wrote:
>>
>> "Steve Taylor" wrote in message
>> news:3d86106e$0$5810$fa0fcedb@lovejoy.zen.co.uk...
>> > Chuck Simmons wrote:
>> >
>> > > "On Governors" or something like that. 1876 I think. It gives the
>> > > stability criterion that all of the poles of the characterstic
>> equation
>> > > of the closed loop system must be located in the left half plane.
>> > >
>> > > Chuck
>> >
>> >
>> >
>> > J.C. Maxwell "On Governors" proc. Of the Royal society of London 16
>> 1868
>> >
>> > In Selected papers on mathematical trends in Control theory Dover New
>> > York 1964 pp 270-283
>>
>> So, what I would like to know was Nyquist aware of this? Did he steal
>> the idea?...
>
>It hardly matters. Stability conditions for ordinary linear differential
>equations with constant cofficients go back before Maxwell. Maxwell
>noted that a feedback system like a steam engine governor can be modeled
>with an ordinary linear differential equation with constant cofficients.
>Maxwell refined what was known about stability at the time with an eye
>to linear feedback systems.
>
>Today we mostly work with highly nonlinears systems which we pretend are
>linear. In this I am thinking of sampled quantized digital control
>systems which do not satisfy strict stability. I sometimes use a variant
>of what Maxwell wrote which is that I must place all of the eigenvalues
>of the system matrix inside the unit circle. It sounds different but is
>precisely the same as Maxwell's condition in his paper.
>
>Chuck
I've always thought it strange that Routh (of Routh-Hurwitz fame) beat
Maxwell in the Mathematical Tripos for 1854. Routh was Senior
Wrangler and Maxwell was Second Wrangler. I guess even Maxwell could
stumble.
http://www-g.eng.cam.ac.uk/125/noflash/1950-1975/control.html
Here's a nice synopsis of historical developments in control theory.
http://arri.uta.edu/acs/history.htm
As mentioned in this synopsis, the earlier developments had used the
system differential equations, whereas at Bell Labs in Nyquist's time,
the approach was a frequency domain approach.
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