Re: 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 :-)
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If you look at what I did you might get some ideas.

http://dougs.homeip.net/qtoctave/bode1w.m

Doug Stewart

Thanks for your help! If I understood your code correctly, the following code should do the job:

Regards,

Lukas

## Copyright (C) 2004 Doug Stewart

## 

## This program is free software; you can redistribute it and/or modify

## it under the terms of the GNU General Public License as published by

## the Free Software Foundation; either version 2 of the License, or

## (at your option) any later version.

## 

## This program is distributed in the hope that it will be useful,

## but WITHOUT ANY WARRANTY; without even the implied warranty of

## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the

## GNU General Public License for more details.

## 

## You should have received a copy of the GNU General Public License

## along with this program; if not, write to the Free Software

## Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA

% 

%function     bode1w (n,d)

%n= numerator

%d=denominator

%

% This was written to help my students with Gain Margin and Phase Margin

%GM and PM lines are added to the Bode plot and 

%GM and PM values are printed on the screen.

## bode1w

## Author: doug 

## 

## 2004-09-27 doug 

## * Initial revision

## Rev #1  Nov 29 2004 Doug Stewart

## Rev #2 Sept 2005 Doug Stewart 

##              - Added the If for negative phase steps.

##              - and the DO loop

## Rev #3 Sept 2005 Doug Stewart

##              - used unwrap.m

function [gamma, phi, w_gamma, w_phi] = margin(sys);

% Get Frequency Response

[mag, pha, w] = bode(sys);

% fix the phase wrap around

phw = unwrap(pha * pi/180);

pha = phw * 180/pi;

% find the Gain Margin and its location

[x, ix] = min(abs(pha + 180))

if (x > 1)

gamma = "INF"

ix = length(ph);

else

gamma = 1/mag(ix);

endif

w_gamma = w(ix);

% find the Phase Margin and its location

[pmx, ipmx] = min(abs(mag - 1));

phi = 180 + pha(ipmx);

w_phi = w(ipmx);

endfunction