OCST: Gain Margin

[Lukas Reichlin]

Dear Octave Community,

I wrote an objective function to optimize an Aström/Hägglund PID  
Controller numerically by fminsearch. Versions for Octave and Matlab/ 
SImulink can be found here:

http://n.ethz.ch/student/lukasre/download/optiPID/

The Octave control package is quite limited. However, I managed to get  
along quite easily except for one thing: the gain margin of a system.  
In Matlab, there's [gamma, phi, w_gamma, w_phi] = margin(sys). I  
couldn't think of a way to calculate the gain margin numerically. Is  
there any control systems engineer out there who knows how to  
implement an algorithm for the problem? Help would be very appreciated.

Regards,
Lukas

BTW: Despite I implemented the routine quite differently, the  
conformity of the results between Matlab and Octave is simply  
fantastic :-)