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Transfer function of a system is given as
Polar plot of the same system is
Gain margin (in dB) of the system is ______. (Important - Enter only the numerical value in the answer)
Polar plot of the same system is
Gain margin (in dB) of the system is ______. (Important - Enter only the numerical value in the answer)
Correct answer is between '9,10'. Can you explain this answer?
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Transfer function of a system is given asPolar plot of the same system...
Gain margin (GM) and Phase margin (PM) from the polar plot:
Let us consider the polar plot as shown below,
Figure: A polar plot of a stable system
Gain margin (GM):
The frequency at which the polar plot crosses the negative real axis is called a phase cross-over frequency (ωpc).
Let 'a' be the point of intersection and it is the magnitude at the phase cross-over frequency.
⇒ a = | G(jωpc) H(jωpc) |
And, we know that
Gain margin (GM) = 1 / |G(jωpc) H(jωpc)| = 1 / a
Gain margin in dB = 20 log (1 / a)
Calculations:
In the Given polar plot;
Phase margin (PM):
The frequency at which the polar plot crosses the unit circle (formed with the radius of the critical point) is called again cross-over frequency (ωgc).
From the polar plot, we can observe that
Phase margin (PM) = 180 - ∠G(jωgc) H(jωgc)
Let us consider the polar plot as shown below,
Figure: A polar plot of a stable system
Gain margin (GM):
The frequency at which the polar plot crosses the negative real axis is called a phase cross-over frequency (ωpc).
Let 'a' be the point of intersection and it is the magnitude at the phase cross-over frequency.
⇒ a = | G(jωpc) H(jωpc) |
And, we know that
Gain margin (GM) = 1 / |G(jωpc) H(jωpc)| = 1 / a
Gain margin in dB = 20 log (1 / a)
Calculations:
In the Given polar plot;
Phase margin (PM):
The frequency at which the polar plot crosses the unit circle (formed with the radius of the critical point) is called again cross-over frequency (ωgc).
From the polar plot, we can observe that
Phase margin (PM) = 180 - ∠G(jωgc) H(jωgc)
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Transfer function of a system is given asPolar plot of the same system isGain margin (in dB) of the system is ______. (Important - Enter only the numerical value in the answer)Correct answer is between '9,10'. Can you explain this answer?
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