transfer function of 2nd order system

[Saad_111]

Hi Control Engineers!
How to find natural frequency and damping ratio of the transfer function

G(s) = (s+3)/s(s+2)

i got the result on matlab as shown in attachment, but don't know how it comes, answer please.

 

[barry]

I think you need to read something rather than blindly dumping things into Matlab. You need to have an understanding of poles and zeroes.

For your system, you've got a pole at -j2 and 0. zeta (damping) has values of 1 and -1 because the poles lie on the j-axis (zeta is a function of the angle of the pole from the j-axis)

 

[Saad_111]

Poles are at 0 and -2 not at -j2. None of the pole is lying on j-axis

 

[barry]

Sorry, you're right about the pole at -2. Damping is related to the angle from the REAL axis, zeta=cos(angle). Since you angle is 0 (and 180), cos(0)=1,-1