A Root Locus Question

Hi,
I've got a question for all you pros. Say there's a system that has open loop poles and zeros that look as such:
| | | | ------x----0-----x-----0-------x---------x | | | | |
I know what the root locus looks like, but that's not the problem. I have to find out the rate that the closed loop poles that go to infinity do so as the loop gain increases. I also have to find how fast the closed loop poles that go to the zeros do so as K goes to infinity.
The locations of the poles and zeros are given as variables and they are looking for an analytical expression. Any ideas how to tackle this?
Thanks,
Matt
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Matthew Douglas Rogge wrote:

Since you say "they" I get the impression you're taking a class -- if so, this is the sort of question that profs and TA's are paid to answer. I'd suggest that you get your money's worth.
If you're doing self-study and you've just got a book to go from say so, and maybe someone'll be motivated...
--

Tim Wescott
Wescott Design Services
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On Thu, 1 Sep 2005 19:23:21 +0100, Matthew Douglas Rogge wrote

How do you define "rate" and "fast" ? If you can define those terms mathematically it might give a clue as to how find the answer.
I see several difficulties. The change of closed loop pole position with change of K will be:
a) particular to the locus branch
b) a function of two variables (sigma and omega) in the case of off-axis branches
c) a function of K itself rather than a constant
Why do you need these analytical expressions? Do they convey any useful information about the system itself ?
AAR
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