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From: Chuck Simmons
Organization: You jest.
X-Mailer: Mozilla 4.61 [en] (X11; U; Linux 2.0.33 i586)
Subject: Re: The First NFB theory
References: <email@example.com> <3D851052.693A7E50@webaccess.net> <%_lh9.25414$S32.firstname.lastname@example.org> <3D85F5EC.FB883081@webaccess.net> <email@example.com>
Date: Tue, 17 Sep 2002 01:46:30 GMT
NNTP-Posting-Date: Mon, 16 Sep 2002 18:46:30 PDT
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.
... The times have been,
That, when the brains were out,
the man would die. ... Macbeth
Chuck Simmons firstname.lastname@example.org
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