Re: dmargin

[Yves Piguet]

Hello,

> Could someone explain the gm value returned by dmargin in sysquake?
>
> http://www.calerga.com/doc/LME_dyn.htm#dmargin
>
> As shown in the example:
> (gm,psi,wc,wx) = dmargin(0.005,poly([0.9,0.9]))
> gm = [-2, 38]
> psi = []
> wc = [0, 0.4510]
> wx = []
>
> The gain margin is 38, as confirmed by matlab using allmargin function. However, what about -2 in gm?

If the gain of negative feedback is outside the range [-2,38] (less than -2 or greater than 38), the closed-loop system is unstable. In that case, with G(z) = 0.005/(z-0.9)^2, G(z)/(1+kG(z)) is stable if and only if -2 > k > 38.

Negative gains aren't very common, but if the open-loop system is unstable, the lower limit is positive (a zero feedback gain, i.e. no feedback at all, would leave the system unstable). If it is close to 1, the robustness is bad (a small gain decrease would make the closed-loop system unstable). For instance if you get gm = [0.9, 2], if the open-loop gain is decreased by more than 10%, the system becomes unstable. Expressed in dB, the "lower" gain margin is 20 log10(0.9) = -0.91 dB. Note that a negative lower gain margin cannot be expressed in dB, it's "too good".

Hth

Yves