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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

Reply to
Matthew Douglas Rogge
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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...

Reply to
Tim Wescott

On Thu, 1 Sep 2005 19:23:21 +0100, Matthew Douglas Rogge wrote (in message ):

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

Reply to
AAR

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