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I would be greatful is someone could kindly enlighten me as to the correct interpretation of the appended bode plots.

My understanding when interpreting bode plots is that we desire 0 gain where the phase is equal to or exceeds 180 degrees (marginally stable / unstable).

In the attached figure 'bode simple' the relationship is clear. Good phase margins can be observed i.e. where the phase shift exceeds 180 deg the magnitude is less than one. where the magnitude exceeds 1 the phase is less than 180.

In the second figure ('bode_conf') the relationship is not at all clear to me.

Two things appear to be evident in this plot.

1) The phase is increasing below 5 rad/s and therefore

a. there is either a minimum phase zero in the system at aprox 0.1 rad/s; or,

b. there is an unstable pole in the system at this same frequency (positive phase)

2) For the frequency range 0.001-1.5 rad/s the magnitude of the response is greater than 0db (a gain ratio in exces of one) while the phase shift over this same frequency range exceeds 180 degrees.

I would therefore deduce from the bode plot that this system is unstable. Not so! All poles of the system remain in the left hand half plane of the s-domain.

I would be greatful of any insight into the correct interpretation of the latter bode plot.

The magnitude of the resposne clearly exceeds one at the initial phase crossover (w_180) and indeed for all frequencies 0-1.5 rad/s.

The significance of the second crossover?

Regards,

Jamie

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# Analysing bode plots. Stability

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