y = {[0.419]};
z = {[1 0 0 0]};

x = tf(y,z)
rlocus(x)

t_s = 1;
zeta = -log(0.15)/sqrt((pi)^2 + log(0.15)^2)
omega_n = 4/(t_s*zeta)

sgrid(zeta, omega_n)
axis([-10 10 -9 9])

% Real zero = -2.86    Damping = 1     Frequency = 2.86
% C = 78.143 * (1 + 0.35s)/1
omega_f = 2*pi;
t_p = 0.231;
k_bb = 0.419;

OS = [0.2 0.15 0.10 0.05]
t_s = [4 3 2 1]

for i = 1:4
    fprintf('Line %d\n', i);
zeta = -log(OS(i))/sqrt((pi)^2 + log(OS(i)))
omega_n = 4/(t_s(i)*zeta)
z = omega_n*omega_f / (-omega_n + omega_f*omega_n*t_p + 2*omega_f*zeta)
k_c = omega_n^2 / (t_p*k_bb*z*omega_f)
fprintf('-------------------\n');
end