s=tf('s');
k=3;
kcrit=175/36;
kr1=0.35*kcrit;
kr2=0.8*kcrit;
T1=3;
T2=0.5;
T3=2;
K0=k/((1+s*T1)*(1+s*T2)*(1+s*T3));
Ks1=K0*kr1;
Ks2=K0*kr2;
Kscrit=K0*kcrit;
Es1=(1/(1+Ks1))*(1/s);
Es2=(1/(1+Ks2))*(1/s);
system1=tf([k*kr1],[3,8.5,5.5,1])

%%EX 4
Mw1=Ks1/(1+Ks1);
Mw2=Ks2/(1+Ks2);
% bodemag(Mw1)
% hold on;
%bodemag(Mw2)
% legend('M(w)k1','M(w)k2')
% k0st=isstable(K0)
% nyquist(Ks1)
% hold on;
% nyquist(Ks2)
% hold on;
% nyquist(Kscrit)
% legend('ks1','ks2','kscrit')
% impulse(Es1)
% hold on;
% impulse(Es2)

% % EX 6
% w1=0.194;
% w2=1.12;
% w3=1.92;
% sine21=w1/(s^2+w1^2);
% sine22=w2/(s^2+w2^2);
% sine23=w3/(s^2+w3^2);
% Mw11=Ks2*sine21;
% Mw12=Ks2*sine22;
% Mw13=Ks2*sine23;
% impulse(Mw13)

% EX 9 for kr2
qw1=1/(1+Ks2);
bodemag(qw1)