What is the gain margin in a Bode plot?

In simpler terms, the gain margin tells us how much we can increase the amplification of the system without causing it to oscillate or become uncontrollable.

To find the gain margin on a Bode plot, you need to:

Identify the frequency at which the phase angle is exactly -180 degrees (180-degree phase shift).

Determine the corresponding gain value at that frequency.

The gain margin is then calculated as the inverse of the gain (in magnitude) at the -180-degree phase frequency, expressed in dB.

If the gain margin is positive, it means the system is stable and can handle additional gain without becoming unstable. On the other hand, if the gain margin is negative or very close to zero, the system is marginally stable, and any further increase in gain may lead to instability.

In control system design, a positive gain margin is desired to ensure stability and robustness in the presence of uncertainties or disturbances. Engineers often use the gain margin as one of the criteria to assess the stability of a control system and make design decisions accordingly.