# Fast way to find system poles?

1. Apr 19, 2006

### Maxwell

Hey, I was wondering if there is a fast way to find the poles of a system - not using a calculator.

For example,

$$G(s) = \frac {30}{(s^2 + 6s + 20)(s + 2)(s + 13)}$$

I know two poles right off the bat: -2 and -13, but is there a way to get the poles from the quadratic quickly? Besides the using the quadratic equation, I mean.

I don't think there is, but for some reason I thought I saw someone taking the "b" term, in this example 6s, and halving it. So the pole would be 3. I don't think this is right, is it?

Thanks.

2. Apr 19, 2006

### FredGarvin

It's been a really long time since doing controls work for me. However, other than the quadratic formula, your idea of halving the b term seemed to give you the real component of the roots (they are complex roots). You would have to change the sign on the real part as well.

3. Apr 19, 2006

### Maxwell

Well for what I am interested in, I only need the real term. The imaginary part doesn't play a role in figuring out if a system has dominant poles.

Thank you for answering, this will save me much time.