poles of feedback connected systems

Dear all,
is it possible to determine the poles of the combination of two transfer functions in a feedback loop when you know the poles and zeroes of the
two individual transfer functions?
I've two small SISO transfer functions G1 and G2, from which the poles and zeroes are known. Know I connected them in a (positive) feedback loop and the new transfer functions is G1/(1-G1*G2). Is it possible to determine the poles of this new transfer function directly from the poles and zeroes from G1 and G2, without having to calculate the new transfer function?
Thanks in advance.
Johan Morren Delft University of Technology The Netherlands
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Johan wrote:

Yes it is, assuming that the transfer functions are rational. Separate G1 and G2 into their numerator and denominator. Call N1/D1 = G1, and N2/D2 = G2, with N1, etc., being pure polynomials. Now your transfer function is (N1/D1)/(1 - (N1/D1)*(N2/D2)). Multiply top and bottom by the denominators and see what you get.
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Tim Wescott
Wescott Design Services
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Tim Wescott wrote:

What you get is the new transfer function. My answer is "No it's not, but the so-called hard way is easy."
Jerry
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On Wed, 5 Jan 2005 16:14:13 +0000, Tim Wescott wrote

That's fine but of course you will stiill have to find the roots of the resulting denominator polynomial D1*D2 - N1*N2.
I have written a Root Locus plotting program that when given all the open loop poles and zeros, generates the loci of the closed loop poles as the loop gain is varied from zero to infinity. If you specify a gain value it will show you the positions of all the CL poles for that gain You can download a free copy of the program from :
http://www.biemke.freeserve.co.uk
AAR
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