For the open loop transfer function Gs design a compensator

For the open loop transfer function G(s), design a compensator K(s) so that the closed loop unity feedback system will have 4% over shoot, and 4/3s settling time.

Solution

num1=[1 2];

den1=[1 4 3];

num2=[1 7 10];

d1=[1 1];

d2=[1 3];

d3=[1 5.1];

d12=conv(d1,d2);

den2=conv(d12,d3);

[cnum1,cden1]=feedback(num1,den1,1,1,-1);

[cnum2,cden2]=feedback(num2,den2,1,1,-1);

t=0:0.1:2; step(cnum1,cden1,t) step(cnum2,cden2,t)