Zeta and Wn Values for Control

Question

I have a transfer function for control theory lecture. So the transfer function which is fifth (5.) order. How can I find $\zeta$ and $\omega_n$ values ?

For example : ${50 \over 60s^5+45s^4+85s^3-25s^2-758s}$

Answer 1

Have you noticed that your system is unstable?

You have negative coefficients in dominator!

This is the factorized form.

$$H(s)={50\over 60 s(s-1.60182) (1.85211 + s)(s^2+ 0.499706 s +4.25833 )}$$

Your transfer function does not look like second order transfer functions. No approximation makes sense in this case.

Octave / Matlab:

>> % pkg load control
>> H=tf(50,[60,45,+85,-25,-758,0]);
>> step(H,10)