For the Nichols plot shown, the system is:
For the Nichols plot shown, the system is: Correct Answer Stable
Concept of Gain Margin and Phase Margin:
1. The formula for Gain Margin (GM) can be expressed as:
GM = 0 – G dB
Where G is the gain. This is the magnitude (in dB) as read from the vertical axis of the magnitude plot at the phase crossover frequency (It refers to the frequency at which phase curve cuts the negative times the 180° axis in the plot).
2. The formula for Phase Margin (PM) can be expressed as:
PM = ϕ – (-180°)
Where ϕ is the phase lag (a number less than 0). This is the phase as read from the vertical axis of the phase plot at the gain crossover frequency (It refers to the frequency at which the magnitude curve cuts the zero dB axis).
Note:
1. For a Stable system: Bothe the margins should be positive.
2. For Marginal Stable System: Both the margins should be zero
3. For Unstable System: If any of them is negative.
Explanation:
In the Nichlos plot we can see,
When ϕ = -180° or at phase cross over frequency (ωpc)
Gain < 0 dB → -ve {-20 dB < gain < -10 dB}
Gain margin = 0 – (gain)ωpc = +ve
Similarly when gain = 0 dB or at gain cross over frequency (ωgc)
-150° < ϕ < -180°
PM = 180° + ϕ → +ve
So we can see Both gain margin and phase Margin is +ve hence system will be stable.
