#### celebrevida

##### Junior Member level 1

**Closed-Loop Stable for Negative Phase Margin?**

Consider the following T(s)=1/(1+G(s))

Let G=K(s+1)^2/s^3

Let's define wc=unity gain frequency & w180= -180 crossing freq

The loopgain G is very interesting.

If K=10, we see that w180=1 but Gain(w180)=26dB. The GM is negative but if we look at poles of T(s) or Nyquist, it is stable!

This means that you can be stable even with negative GM!

But if K=0.25, we see that wc=0.725 and the phase(wc)=-198deg. The PM is -18deg as we are -18deg pass -180deg. And indeed we see that the closed loop is unstable (poles of T(s) are RHP & Nyquist unstable)

This leads me to wonder, is it possible to be stable if we have negative PM with a different example?

(Since it is clearly possible to be stable with negative GM, I am wondering if it is also possible to be stable with negative PM instead.)

If not, then are we always unstable if phase is more negative than -180deg at unity gain and why?

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