main.m

clc;
clear;
A= [ 0 1 0 0 0 0
    -4.7059 -.0882 0 0 1.3588 0
    0 0 0 1 0 0
    0 0 0 -5 1.617 4.5
    0 0 0 0 -.9091 0
    0 0 0 0 0 -1
    ];
B=[0 0
   0 0
   0 0
   0 0
   1 0
   0 .8
    ];
C=[1 0 0 0 0 0;
    0 0 1 0 0 0;
    ];
D=zeros(2,2);
sys = ss(A,B,C,D);
tf(sys)
%Section 1:--------------------------
%s=tf('s');
syms s;
G= [(1.359/(s^3+0.9973*s^2+4.786*s+4.278)) 0;
    (1.617/(s^3+5.909*s^2+4.546*s)) (3.6/(s^3+6*s^2+5*s));
    ];
%Section 2:---------------------------
pzmap(sys);
%Section 3:---------------------------
J = jordan(A);
disp('Jordan Matrix of A is:');
disp(J);
%Section 4:---------------------------
F=(s*eye(6,6)-A);
phi=ilaplace(F);
syms t;
f= expm(A*t);
disp('Transition Matrix is:');
disp(f);
%Section 6:---------------------------
 Co=ctrb(A,B); %Controllability Matrix
 rCo=rank(Co);  %Rank of Controllability Matrix
 Ob=obsv(A,C);  %Observability Matrix
 rOb=rank(Ob); %Rank of Observability Matrix
 disp('Controllability Matrix:');
 disp(Co);
 disp('Rank of Controllability Matrix:');
 disp(rCo);
 disp('It is Controlable since it is Full-rank.')
  disp('Observability Matrix:');
 disp(Co);
 disp('Rank of Observability Matrix:');
 disp(rCo);
 disp('It is Observable since it is Full-rank.')
 %Section 7:-----------------------------
if isstable(G(1,1))
    disp('G(1,1) is Stable')
else
    disp('G(1,1) is not Stable')
end
if isstable(G(1,2))
    disp('G(1,2) is Stable')
else
    disp('G(1,2) is not Stable')
end
if isstable(G(2,1))
    disp('G(2,1) is Stable')
else
    disp('G(2,1) is not Stable')
end
if isstable(G(2,2))
    disp('G(2,2) is Stable')
else
    disp('G(2,2) is not Stable')
end
%Section 8:------------------------------------------
 e=eig(A);
 disp('Eigenvalues of A are:');
 disp(e);
 %Section emtiazi:-----------------------------------
p=[-8;     % desired poles
    -8;
    -7;
    -5;
    -11;
    -9;];
K=place(A,B,p);   % For feedback in the simulink simulation