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BODE PLOT SUMMARY

# BODE PLOT SUMMARY - GAIN AND PHASE MARGIN-The gain margin...

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GAIN AND PHASE MARGIN -The gain margin is defined as the change in open loop gain required to make the system unstable. Systems with greater gain margins can withstand greater changes in system parameters before becoming unstable in closed loop. -The phase margin is defined as the change in open loop phase shift required to make a closed loop system unstable. The phase margin also measures the system's tolerance to time delay. If there is a time delay greater than 180/Wpc in the loop (where Wpc is the frequency where the phase shift is 180 deg), the system will become unstable in closed loop STEADY STATE ERROR

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Bandwidth Frequency -The bandwidth frequency is defined as the frequency at which the closed-loop magnitude response is equal to -3 dB. However, when we design via frequency response, we are interested in predicting the closed-loop behavior from the open-loop response. Therefore, we will use a second-order system approximation and say that the bandwidth frequency equals the frequency at which the open-loop magnitude response is between -6 and - 7.5dB, assuming the open loop phase response is between -135 deg and -225 deg. -THE GREATER THE BANDWIDTH THE SMALLER THE RISE AND SETTLING TIMES. -To change the Bandwidth frequency for open loop response . Adding proportional gain From the bode plot above, we see that the phase margin can be greater than about 60 degrees if w is less than 10 rad/sec. Let's add gain to the system so the bandwidth frequency is 10 rad/sec, which will give us a phase margin of about 60 degrees. To find the gain at 10 rad/sec, you can try to read it off the Bode plot (it looks to be slightly more
than -40 dB, or 0.01 in magnitude). The

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