This is what I have so far, and it is driven by the fact my professor says he does not want to see overly similar code as the others in my class... But I dont know how to find the dominant poles from this without a for loop like so many of my classmates will have... Any Ideas?
num=[3 3];
den=[conv([1 0],[conv([1 4],[1 7])])]
Gs1=tf(num,den)
hold on
rlocus(Gs1)
GS1=zpk(Gs1)
%%
R=[-0.1:-0.3:-5.8];
I=i*[0.01:0.01:0.5];
[Re Im]=meshgrid(R,I);
p=Re+Im;
p_s=sort(p);
%% angle from double pole at zero
Theta=180-angle(p);
Ts=sort(Theta);
%% distances from -7 to possible poles on Re axis
P4=-7;
P4d=P4-real(p_s(1,1:20));
%% distances from -4 to possible poles on Re axis
P3=-4;
P3dA=P3-real(p_s(1,1:13));
P3dO=real(p_s(1,15:20))-P3;
P3d=[P3dA,0,P3dO];
%% distance from zero poles to prime pole possible
P1_2=real(p_s);
%% Angles from "dP" to -4
ThP3A=atan2(imag(p_s(1:50,1:13)),P3dA);
ThP3O=180-atan2(imag(p_s(1:50,15:20)),P3dO);
ThP390=90*ones(1,50)';
ThP3=[ThP3A,ThP390,ThP3O];
%% Angles from "dP" to -7
ThP4=180-atan2(imag(p),P4d);
%% Finding Angle Deficiencies
ANGDef=180-ThP4-ThP3-2*Ts;
AngN=ANGDef/2;
xprime=1./tan(180-AngN);
x=[0:-.3:-5.8];
a_val1=x+xprime
