[sdiy] Pole Dancing

[Richie Burnett]

I too learned about Root Locus in Control Theory class.  Unfortunately it 
was only touched upon fairly briefly in Analogue Control and wasn't even 
mentioned in Digital Control!  I've always thought of RL as a "Control" 
thing, and the only place where I've seen it mentioned relating to audio was 
in Tim Stilson's paper "Analyzing the Moog VCF with Considerations for 
Digital Implementation."

BTW, it's interesting to plot the RL of a State Variable Filter.  The poles 
move along circular arcs in the SVF when the resonance amount is altered. 
This is in contrast to the X-shaped lines for the moog ladder in the Stilson 
paper.  And... I just noticed that you can do this with the Javascript 
simulator on your web page too, using the second feedback slider!  Neat! :-)

-Richie,



-----Original Message----- 
From: Neil Johnson via Synth-diy
Sent: Tuesday, January 24, 2023 8:35 AM
To: Donald Tillman
Cc: synth-diy mailing list
Subject: Re: [sdiy] Pole Dancing

Donald Tillman wrote:
> I wrote an article with a built in JavaScript root locus simulator. 
> Please enjoy:
>     https://till.com/articles/poledance/

Great tool!  There are several interactive tools like this online. One I 
like is
https://controlsystemsacademy.com/0019/0019.html
as you can plot poles and zeroes.

Nowadays there are libraries for Matlab, Octave, and Maxima for
plotting the root-locus (which, technically, are the lines - the loci
- that connect the poles - roots - and zeroes).

I had the pleasure of learning about RL under Sid Williamson while at
Surrey (or "Servo Sid" as he liked to call himself).  There are quite
a few satellites up there orbiting the Earth thanks to his control
systems (while not teaching he worked for Surrey Satellites).  He
would often claim he knew more about RL than Truxal (hmmmmmm......).
I do wonder if one of Sid's former students (not me) wrote the
wikipedia page on Root Locus.

Cheers,
Neil
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