To help the control system lab experiment using MATLAB

1. Program : G(s)H(s)=
𝟑( 𝒔+𝟐)(𝒔+𝟑)
𝒔( 𝒔+𝟓)( 𝒔+𝟔)(𝒔+𝟖)
clc
clear all
clf
a=3*[1 2];
b=[1 3];
num=conv(a,b);
d=[1 0];
e=[1 6];
f=[1 8];
g=[1 5];
h=conv(d,e);
n=conv(f,g);
den=conv(h,n);
rlocus(num,den)
grid
output:

2. Program : G(s)H(s)=
𝟒(𝒔+𝟑)
𝒔 𝟑( 𝒔+𝟏)(𝒔+𝟐)
clc
clear all
clf
num=4*[1 3];
a=[1 0];
b=[1 0];
c=[1 0];
d=[1 1];
e=[1 2];
g=conv(a,b);
h=conv(c,d);
m=conv(g,e);
den=conv(h,m);
rlocus(num,den);
axis([-4 2 -4 4])
grid
output :

3. Program : G(s)H(s)=
𝟒𝒔
( 𝒔+𝟏)(𝟏+𝒔) 𝟐
clc
clear all
clf
num=4*[1 0];
a=[1 1];
b=[1 2];
c=[1 2];
g=conv(a,b);
den=conv(g,c);
rlocus(num,den);
axis([-4 0 -4 4])
grid
output :

4. Program : G(s)H(s)=
𝟐(𝒔+𝟏) 𝟐
( 𝒔 𝟐−𝟗)( 𝒔+𝟓) 𝟐(𝒔+𝟐)
clc
clear all
clf
p=2*[1 1];
q=[1 1];
num=conv(p,q);
a=[1 3];
b=[1 3];
c=[1 5];
m=[1 5];
n=[1 3];
g=conv(a,b);
h=conv(c,m);
k=conv(g,n);
den=conv(h,k);
rlocus(num,den);
grid
output :

5. Program: C(s)=
𝒔(𝒔+𝟐)
𝟏+(𝒔 𝟐+𝟐𝒔)(𝒔+𝟑)
clc
clear all
num=[0 1];
a=[1 0];
b=[1 2];
c=[1 3];
d=conv(a,b);
den=conv(c,d);
rlocus(num,den)
grid
output:

6. Program:
clc
clear all
clf
a=[-1 -0.5 ; 1 0];
b=[0.5; 0];
c=[1 -1];
d=[0];
rlocus(a,b,c,d)
grid
output: