3. For the unity feedback system in Fig-4, with G(s)=K/(s+1)(s+4)​ Design a PID controller that will yield at peak time of 1.2s and damping ratio 0.8 with zero error in step input. b. Use Matlab to verify your design.

clc

clear all 

close all

G= zpk([],[-1 -4],1);

GPD=zpk([-7.59],[],1.98);

Tc=feedback(G*GPD,1);

step(Tc)

stepinfo(Tc)

figure(2)

title(‘step response with PD controller’)

%PID controller simulation%

GPID=zpk([-0.5 -7.59],[0],2.17473);

Tpid=feedback(G*GPID,1);

step(Tpid)

stepinfo(Tpid)

figure(2)

title(‘step response with PID controller’)