%
% File on the use of Root Locus 
% as presented during the lecture 
% P. S. Shiakolas
% =================================================
% If you need more help on using the roor locus
% command use >> help rlocus
%
% also if you have the controls toolbox, experiment
% with the rlocus command/graphical environment 
% =================================================
%
% Define the numerator factors 
np1 = [1 3]; np2 = [1 1+3*i]; np3 = [1 1-3*i];

% Define the denominator factors 
dp1 = [1 0]; dp2 = [1 1]; dp3 =[1 2]; 
dp4=[1 4]; dp5 = [1 5+2*i]; dp6 = [1 5-2*i];

% Setup the numerator using conv command
% conv multiplies polynomials
num = conv(np1, conv(np2, np3) );

% Setup the denominator using conv command
d12 = conv(dp1, dp2) ; d33 = conv(dp3, dp3) ;
d34 = conv(dp3, dp4) ; d56 = conv(dp5, dp6) ;
den = conv( conv(d12, d33), conv(d34, d56) );

%enable zoom with mouse clikcs
zoom on
% plot the root locus [R,K] = RLOCUS(NUM,DEN)
[r, k] = rlocus(num, den);
rlocus(num,den); grid;
title('Root Locus for Lecture Example')