Determine the Gain and Phase Margins approximately for the f

Determine the Gain and Phase Margins approximately for the following Bode Plot: Assume that we subtract 90degree from the phase margin. Is the system stable, and does the plot encirle the point \"-1\"?

Solution

Phase margin =-180+<GH/gain cross over frequency

i.e when Magnitude plot crosses 0dB the frequency is 0.8 rad/sec

angle at that frequency is <GH=-120 degrees approximately

Phase Margin =-180+<GH=-180-120= -300 or +60 degrees

Gain margin:

Phase cross over frequency is when phase plot crosses -180 degrees is 5 rad/sec

Gain at that frequency is -5 dB

Gain Margin =0-gain=5 dB

b)If we substract 90 degrees from phase margin i.e 60-90 =-30,the phase margin will be negative

and the system is unstable

Now nyquist plot encircles -1 to indicate ploes in right half plane which makes the system unstable