From: John Woodgate
Subject: Re: Historical question: negative feedback and the op amp
Date: Thu, 14 Nov 2002 19:39:45 +0000
Organization: JMWA Electronics Consultancy
Reply-To: John Woodgate
NNTP-Posting-Date: Thu, 14 Nov 2002 21:12:30 +0000 (UTC)
X-Newsreader: Turnpike (32) Version 4.01 <5Z8C9wtxbnpWyFnyfFzqmVF739>
I read in sci.electronics.design that Chuck Simmons
wrote (in <3DD3A4A5.688DDDDD@webaccess.net>)
about 'Historical question: negative feedback and the op amp', on Thu,
14 Nov 2002:
>Generally, a sampled system modelled by a system of n linear first order
>ODEs (the same as an nth order ODE) with constant coefficients gives
>rise to a quotient of polynomials say p(z)/q(z) where the degree of q(z)
>is n and the degree of p(z)<=n (deg(p)>deg(q) is non-causal). Assume
>that there is an FIR controller we wish to apply which is given by
>r(z)/z^k where r(z) is a polynomial of degree k. Obviously, the closed
>loop system including the FIR is stable if all of the zeros (roots) of
>z^k*q(z)-r(z)*p(z) are inside the unit circle. There will be n+k zeros
>of this polynomial. However, of the coefficients of this polynomial, we
>may select arbitrarily at most k+1 leaving n-1 coefficients to chance.
>In other words, we can force at most k+1 zeros inside the unit circle by
>selecting the coefficients of r(z) while the other n-1 can be anywhere.
>That is, give an arbitrary p(z)/q(z), we cannot, in general, stabilize
>it with an FIR.
Dat makes my brane 'urt! You can use the fir to shore up whatever it is
you need to stabilise. Unless it's a well shaft.
>An interesting point is that if n=1, we can always use an FIR. At n=2,
>we have one pole we cannot place.
I dunno, I fink a fir makes a very good pole. You place it in the garden
and fly a flag from it.
Regards, John Woodgate, OOO - Own Opinions Only. http://www.jmwa.demon.co.uk
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