Timeline for gain margin and phase margin - significance
Current License: CC BY-SA 4.0
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| Nov 7, 2019 at 23:55 | comment | added | fibonatic | @TimWescott Indeed, it also took me a while to construct $L(s)$ as an example where gain and phase margin isn't enough. However, why not use the modulus margin for those edge cases. Plus, as stated in my answer, the inverse of the modules margin is equal to the peak of the sensitivity. So a large modules margin (a rule of thumb is often 6 dB) also guarantees a smaller peak of the sensitivity and thus amplify noise not too much, which sounds like a reasonable design requirement. | |
| Nov 7, 2019 at 23:43 | comment | added | TimWescott | I think that for most otherwise sane plants, good gain and phase margins mean a good modulus margin. Certainly the close-loop response of the system you show here would have some sort of bad behavior -- either peaking (in the frequency domain), ringing (time domain), some really weird long over-unity bump in the sensitivity (frequency domain), or some equally weird time domain phenomenon where it almost settles out but then takes forever to finally get to target. Modulus margin is a good measure -- I've certainly applied it in the past, even though I'd never heard a name for it until now. | |
| Nov 7, 2019 at 0:07 | history | answered | fibonatic | CC BY-SA 4.0 |