Finding natural frequency and damping from buck converter transfer function

[Brianrofl]

Homework Statement

Here is the transfer function of a buck converter I derived:

What I need to do next is obtain equations for w₀ and ζ. I know how to do this for equations that follow the general form:

But in this case I just can't figure out exactly how to do it. How do I find a value for w₀ that satisfies both the 3rd term in the denominator and the numerator?

The Attempt at a Solution

I've tried a bit of algebraic manipulation using different values for w₀ but without much luck. I know -- I hate to ask for help without showing any of my own work -- but I'd actually rather just be pointed into the right direction with this. It's something I've never really been able to do, and google searches on the subject were always useless because the transfer functions examples start with follow the generic form shown above.

Thanks.

 

[jaus tail]

Maybe you'll have to split the transfer function. Like 1 + sRC as (1/Den) + (sRC/Den) and then proceed. Just a guess.

 

[rude man]

Good guess jaus!
As for the OP: what is "d"?