Question regarding Gain/Phase Margins and Bode Plots

Main Question or Discussion Point

Hi

While going through http://eprints.iisc.ernet.in/archive/00013500/01/lec_6_web.pdf, I came across the following two statements (on page 3), for a system with loop gain = $G(s)H(s)$:

1. Open GH loop must be stable for designing via Bode Plots.

2. If for GH, gain crossover < phase crossover for open loop, closed loop will be stable.

The gain crossover frequency is the frequency at which the gain is unity or 0db. If it is less than the phase crossover frequency (at which phase is 180), then as the frequency increases from 0, the gain becomes unity before the phase becomes 180 degrees. So intuitively, the Nyquist plot does not pass through or encircle (-1 + j0). The closed loop system is therefore stable. Is this correct?

Thanks.

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Anyone?

Be careful it is for empirical rules!

If you use an open loop unstable plant how can you tell if gain crossover < phase crossover or not where the phase information is flawed by the unstable frequency ?

In reality under some assumptions it is possible to stabilize an open loop unstable system but not with Bode plots. At least try Sisotool in MATLAB

Thanks trambolin.