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Assume I have a system with open-loop gain G = (s+1)^2/s^3. This system has a negative feedback with feedback factor 1. I plot the open-loop gain by Bode and see that the phase margin Pm = 21.3877 at frequency 1.4656Hz.

enter image description here

Next I calculate closed-loop gain Acl = G/(1+G) and then check the step response of this closed-loop function. The plot in matlab shows that it rings at 0.21Hz NOT 1.4656Hz. It really made me confused. Why the ringing frequency is 0.21Hz not at the crossover frequency 1.4656Hz?

enter image description here

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    \$\begingroup\$ 1.47 rad/s is not 1.47 Hz \$\endgroup\$ – τεκ Feb 10 '18 at 0:39
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Your bode plot uses angular frequency \$\omega = 2 \pi f\$.

1.47 rad/s = 0.23 Hz

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