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Subject: Re: The First NFB theory
Date: 17 Sep 2002 01:06:09 -0500
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On Tue, 17 Sep 2002 01:46:30 GMT, Chuck Simmons
>Kevin Aylward wrote:
>> "Steve Taylor" wrote in message
>> > 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
>> > > 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
>> > 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.
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
Here's a nice synopsis of historical developments in control theory.
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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