What is gain margin, phase margin,
gain crossover frequency, and phase cross frequency? What is the practical use
of these parameters?
Gain Margin and Phase Margin are
the relative stability measures.
Think of both as safety
margins for an open-loop system which you would like to make
closed-loop.
·
That
is, if you are walking next to a cliff, you want a positive space or
"margin" of safety between you and a big disaster.
·
Hopefully,
that intuition may help keep you straight how gain and phase
margins are defined -- so that positive margins indicate there is still
a safety margin (before instability).
The gain and phase margin are two
metrics to tell you how close the system is to oscillation (instability).
Gain Margin: It is the gain which can be varied before the system becomes
just stable (i.e., after varying the gain up to a certain threshold, the system
becomes marginally stable and then further variation of gain leads to instability).
Gain Margin occurs at phase cross
over frequency(phase cross over frequency is the
frequency at which the phase angle G(s)H(s) -180 degrees)
Phase margin: It is the phase that can be varied before the system becomes
just stable (i.e., after varying the phase up to a certain threshold, the
system becomes marginally stable and then further variation of phase leads to instability).
Phase margin occurs at Gain Cross
over frequency.
Gain cross over frequency is the frequency at which the magnitude of the G(s)H(s) becomes
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