Stability Margins using Bode and Nyquist:
The stability margins obtained from the open loop frequency response of the system, tells us if a system will be unstable if we close the feedback loop OR how much we can push the system before it will become unstable. Basically the bigger the positive gain and phase margins are the more stable the system is, usually we aim for a positive Gain margin of at least 10dB and a positive Phase margin of 60 degrees.
We can use Bode and Nyquist plots to calculate the gain & phase margins of a system. The gain and phase margins are defined as follows:
BODE PLOT:
NYQUIST PLOT:
Nyquist diagram showing where gain and phase margins are calculated for the second order system:
