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Given a bode diagram of loop transmission function, I have heard that it's possible to qualitatively assess the behavior of the system in time domain. These characteristics include delay time, settling time, overshoot and steady state error. My question is how?

For example, I know that the delay time in general increases when the relative degree of the system is increased. Are there any shortcuts like this that I can infer from bode plots? What parts in particular should I look for in a bode diagram?

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  • \$\begingroup\$ there a lot of formulas for that, research a little on the internet and you will find them \$\endgroup\$ – berto Mar 10 '16 at 4:00
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The response of a system is related to it's poles and zeros and static gains (transfer functions), which comes from the system's characteristic equation.

Also, there are plenty of info in the internet concerning how to "draw" a bode plot from a transfer function. For instance, a pole corresponds to a -3db gain decay from its frequency. Then if you look a bode plot and its gain only starts decaying on high frequencies, then you can assume you have fast poles and the time response will be fast.

So there's this relation:

characteristic equation <-> Transfer function <-> bode plot

So you can come from a bode plot, have an understanding about poles and zeros of the system's transfer function, then from here you can estimate settling time from the well known formulae.

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