# 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?

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