# Phase margin of an already inverted system

1. ## Phase margin of an already inverted system

I am designing a feedback system, and I frequently see that phase margin is computed as the cross over frequency phase + 180 degrees, which tells me how far I am from -180 degrees at the cross over frequency, and so it tells me how close I am to the point that I've completely inverted my control signal.

In my case, my control signal is already inverted naturally, and so at DC frequency, I already have 0 phase margin technically according to these formulas.

So my question would be how do I find the phase margin of a system that starts at -180 degrees? Would I start at -180 degrees and see how close I am to -360 degrees as I approach my cross over frequency?

I've attached my Phase response of the plant and feedback sensor transfer functions combined to see what I'm talking about.

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2. ## Re: Phase margin of an already inverted system

A evryone knows, phase is cyclic with 360°. So in your diagram, presuming it's actually showing the overall loop phase, -360° would be the reference for phase margin. For valitidy of the simplified phase margin stability criterion, there must not be multiple crossings of the n*360° line.

In simple words, phase margin is the distance to the oscillation condition: Loop gain = 1 (gain understood as a complex quantity, describing both magnitude and phase).

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3. ## Re: Phase margin of an already inverted system

Thanks for the great answer. The loop phase shown is only my plant and my sensor combined . . my next step is to design the compensator, and I wanted to make sure I understood my situation correctly since I'm used to seeing reference to 0 degrees. I only have one unity gain crossing, and so I believe the phase margin criterion should be sufficient for stability.

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