%% branches of a root loci
clear all;
gain =1;
zeros = -8;
poles = [-2+2*j, -2-2*j, -12]';
L = zpk(zeros,poles,gain);

Ks = cat(1,logspace(-1,2,100)',logspace(2,4,100)'); 
[R] =  rlocus(L,Ks);


figure
plot(real(poles(1)),imag(poles(1)),'bx',real(poles(2)),imag(poles(2)),'kx',real(poles(3)),imag(poles(3)),'rx');
hold on;
plot(real(zeros),imag(zeros),'bo');
th = title('open loop poles and zeros');
set(th,'fontsize',20);
axis([-13 2 -40 40]);

%polt the real and imag axis:
plot([-13 2],[0 0],':');
plot([0 0],[-40 40],':');

%plot the asymptotes:
relative_degree = length(poles) - length(zeros);
alpha = (sum(poles) - sum(zeros))/relative_degree;
rs = [0.1:0.1: 100]';
for ell=1:relative_degree
    phi_ell = pi/relative_degree + 2*pi/relative_degree *(ell-1);
    line_ell = rs*[cos(phi_ell), sin(phi_ell)] + repmat([alpha 0],length(rs),1) ;
    ph(ell) = plot(line_ell(:,1), line_ell(:,2),'b:')
end;




pause(3);

for ii=1:length(R)
    roots = R(:,ii)+ 1e-16*j;
    plot(real(roots(1)), imag(roots(1)),'bx',real(roots(2)), imag(roots(2)),'kx',real(roots(3)), imag(roots(3)),'rx');
    titlestr = ['K = ',num2str(Ks(ii))];
    set(th,'string',titlestr);
    pause(0.01);
end;