%校正前系統的性能.
k0=40;%由kv=10s^-1,取得k0=40
n1=1;d1=conv(conv([1 0],[1 1]),[1 4]);
figure(1);sys=tf(k0*n1,d1);
[mag,phase,w]=bode(sys);
figure(1); margin(k0*n1,d1)
hold on
figure(2);
sysc=feedback(sys,1);
step(sysc)

%求滯后校正器，取wg1=1.5s-1, beta=10, 1/T1=0.1 wg1.
wg1=1.5;beta=10;
T1=1/(0.1*wg1);
betat=beta*T1;
Gc1=tf([T1 1],[betat 1])

%串聯滯后校正器的系統傳函
sys1=sys*Gc1
wg2=1.5;
num=sys1.num{1};
den=sys1.den{1};

%求超前校正器，已知wg2
na=polyval(num,j*wg2);
da=polyval(den,j*wg2);
g=na/da;
g1=abs(g);
h=20*log10(g1);
alpha=10^(-h/10);
T2=1/(wg2*(alpha)^(1/2));
alphat=alpha*T2;
Gc2=tf([alphat 1],[T2 1])

%校正后系統的性能.
sopen=sys*Gc1*Gc2;
hold on
figure(3);
bode(sopen)
margin(sopen)
sclose=feedback(sopen,1);
hold on
figure(4);
step(sclose)

%比較三張圖
Gc=Gc1*Gc2;
hold on
figure(5);
bode(Gc,sys,sopen)
margin(sopen)
legend('Gc','sys','sopen',-1)