Re: How Tune PID in octave using Frequency Response data

[Torsten Lilge]

On Tue, 2020-07-28 at 23:18 +0200, N wrote:
> > 
> > 
> > For a stability analysis of the closed loop based on the Nyquist
> > criterion, you need the frequency repsonce (nyquist()) of the open
> > loop,
> > not of Gry (jw), which represents the closed loop.
> > 
> > Torsten
> 
> It must be the closed loop, if using the open loop feedback gains are
> not included in the analysis.
> 
> With open loop frequency response it should however be possible to
> calculate closed looop frequency response.

The feedback gain is in F(jw) since this is the frequency response of
the PID controller (with gain). Therefore:

"Assessment of the stability of a closed-loop negative feedback system
is done by applying the Nyquist stability criterion to the Nyquist plot
of the open-loop system (i.e. the same system without its feedback
loop)." [1]

There are also forms of the criterion that are using the open loop
frequency response with gain 1 and where the number of closed loop poles
with positive real part can be determined depending on the open loop
gain.

Torsten


[1] https://en.wikipedia.org/wiki/Nyquist_stability_criterion