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In some questions (in linear control theory) it is desired to design a controller to change the system overshoot (Mp), my question is:

Is it possible to find Mp or damping factor directly from Bode diagram without estimating the transfer function of the system?

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The question assumes there is one damping factor i.e. the transfer function is dominated by a 2nd order system. In practice there could be several interacting 2nd order systems so care has to be taken here.

Assuming it is dominated by a single 2nd order system, this diagram may be useful: -

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This picture allows you to calculate \$\zeta\$ by looking at the peak amplitude value in the bode plot. From this you can calculate \$\omega_n\$ using the 2nd formula. Once \$\omega_n\$ is known you can double check the value of Q (1/2\$\zeta\$) because, for a 2nd order filter like this Q IS the magnitude of the amplitude response at \$\omega_n\$.

Here's the bigger picture showing how the bode plot and pole zero diagram are related: -

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  • \$\begingroup\$ Thank you for answering. What about higher values of \$\zeta\$ where diagram has no peak value? \$\endgroup\$ – SMA.D Jul 14 '16 at 8:48
  • \$\begingroup\$ I don't know what you mean. \$\endgroup\$ – Andy aka Jul 14 '16 at 9:55
  • \$\begingroup\$ The 5th diagram that you showed has no peak. (You have marked it "amplitude Q at \$\omega_n\$") \$\endgroup\$ – SMA.D Jul 14 '16 at 11:00
  • \$\begingroup\$ Oh yes it does have a peak - look carefully along the 0dB line (Q=1) at about 0.7\$\omega_n\$ \$\endgroup\$ – Andy aka Jul 14 '16 at 11:03
  • \$\begingroup\$ Just another question, what is the \$\zeta\$ values in the 5 plotted diagrams (just to compare the order of peaks for different cases). \$\endgroup\$ – SMA.D Jul 14 '16 at 11:13

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