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transfer function of 2nd order system

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Saad_111

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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.
 

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barry

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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

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

barry

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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
 

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