From what I have studied so far, gain margin is defined as how much additional gain the system can be given before it becomes unstable, and this can be measured from the bode magnitude plot corresponding to the frequency at which the phase crosses -180 degrees.
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What if the phase plot is such that it becomes flat-looking at say -75 degrees, and never goes below that? Then how is the gain margin calculated? (i.e then will the phase crossover frequency be infinite?)
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If an open loop system's bode plot says that it has negative gain margin but positive phase margin, is the system unstable (and cannot be stabilized)?
EDIT:
How would the -180 degree phase crossover frequency point be determined here? For example, just by a Google search I got a few instances,
Best Answer
From a theoretical point of view...
If the loop phase never reaches -180 degrees then the gain margin is undefined. The gain margin is measured at -180 degrees loop phase. The phase margin is measured at the unity loop gain frequency and if this occurs at a frequency after the phase flattens off at -75 degrees then the phase margin will be +105 degrees. A pretty stable system in the closed loop I would say.
Negative gain margin means that a Nyquist diagram plot passes to the left of the -1+j0 point and so the system is unstable. The system should be stabilised by reducing the forward gain so that the gain margin becomes positive and the Nyquist plot passes to the right of the -1+j0 point when travelling in a clockwise direction.
Whether a system is stable or unstable when the loop is closed depends on what the value of the loop gain is when the loop phase is -180 degrees. This statement doesn't encompass the full Nyquist criteria but is a general guide.