I'm having trouble understanding the plot attached. The bode plot here shows the bode plot of a plant to be controlled with PID. So, if I want a phase margin of 30 degrees at the bandwidth frequency, then as shown on the picture, based on the formula (PM=180 + ...) my bandwidth after PID controller is applied is 30 hz, with a phase margin of 30 degrees at that bandwidth frequency (30 hz). Say now I want a phase margin of 50 degrees. From calculation this will then occur at the frequency corresponding to phase of -130 degrees, in the phase plot of the plant. But this is weird then; I will obtain the same frequency if I want, say, 60 degrees of phase margin (i.e. phase in plant of ~-110 degrees)! So the same frequency for different possible phase margins?

I'm confused.... Is it then the bandwidth that can give this phase margin is 0 i.e. not realisable? So there is a maximum phase margin that can be realised?

Bode plot of plant that wants to be PID controlled


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