Automatic Control Systems Homework Solutionclc clear A3 2 07

Solution

clc
clear
A=[-3 -2 -0.75 0 0;-3 0 0 0 0;0 2 0 0 0;0 0 1 0 0;0 0 0 2 0];
B=[1;0; 0; 0; 0];
C=[0 0 0 0 2.75];
n=size(B);
O(1,:)=C;
D(:,1)=B;
for i=2:n
O(i,:)=O(i-1,:)*(A);
D(:,i)=(A)*D(:,i-1);
end
if det(O)~=0
disp(\'Given system is observable\')
else
disp(\'Given system is not observable\')
end
if det(D)~=0
disp(\'Given system is controllable\')
else
disp(\'Given system is not controllable\')
end

O
det(O)
D
det(D)

RESULT:

Given system is observable
Given system is controllable

O =

0 0 0 0 2.7500
0 0 0 5.5000 0
0 0 5.5000 0 0
0 11.0000 0 0 0
-33.0000 0 0 0 0

ans =

-3.0197e+04

D =

1.0000 -3.0000 15.0000 -58.5000 252.0000
0 -3.0000 9.0000 -45.0000 175.5000
0 0 -6.0000 18.0000 -90.0000
0 0 0 -6.0000 18.0000
0 0 0 0 -12.0000

ans =

1296