# How to find system overshoot (Mp) from Bode diagram

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?  ## 1 Answer

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