Finding the damping ratio (zeta) of an nth order system from a transfer function

[twillkickers]

I am having trouble with some of my homework. I am not quite sure how to find the damping ratio from a third order system when the transfer function (of s) is the only information supplied. Could anyone help me with this? I would like a method that would work with any nth order system, although my current problem is third order.

Also, I must find the damping ratio WITHOUT using differential equations to convert the transfer function to a function of time.

Here is a transfer function that may be used as an example:

s/2 + 1
-------------------------
(s/40+1)[(s/4)^2+s/4+1]

Thanks to anyone who is willing to contribute!

 

[DaveE]

While this may not be the system damping that you are asking about, the canonical form for a quadratic pole pair (simple resonance) looks like this:

$$ H(s) = \frac{1}{(1 + (2 \xi_o) (\frac{s}{\omega_o}) + ( \frac{s}{\omega_o})^2)} $$

Different people define damping for complex systems in different ways, which usually confuses me. I prefer to only associate damping with a specific resonance. So a system might have more than one damping coefficient.

 

[Joshy]

Are you allowed to use just dominant poles?