F-18 Longitudinal Dynamics: Stability, Control and Plots

Consider the F-18 Longitudinal Dynamics.............................1
For system stability................................................3
for magnitude and phase plots.......................................4
For System Controllability..........................................5
Consider the F-18 Longitudinal Dynamics
A=[-0.0239 -28.3172 0 -32.2;-0.0003 -0.3621 1 0;0 -2.2115 -0.2532 0; 0 0 1 0]
B=[-3.8114 0.001; -0.0515 0;-2.8791 0;0 0]
C=[0 -1 0 1;1 0 0 0]
...Compute the open loop system modes
...To obtain the eigenvalues and eigenvectors
[V,D]=eig(A);
disp('EigenValues:')
disp(abs(V))
disp('EigenVector:')
disp(abs(D))
poles=[-1.149;-8;-8.5;-9]; %place observer poles
K=place(A,B,abs(poles));
disp(abs(K))
[t1 t2]=eig(A-B*K)
eig(A-B*K)
pls=[-0.05+0.09i,-0.05-0.09i,-1.05+1.1i,-1.05-1.1i];
L=place(A',C',pls')'
% To obtain the eigen value
eig(A-L*C)
Ac=abs(A-B*K-L*C);
Bc=L;
Cc=abs(K);
Gcss=ss(Ac,Bc,Cc,0);
Gc=tf(Gcss);
zpk(Gc)
A =
-0.0239 -28.3172 0 -32.2000
-0.0003 -0.3621 1.0000 0
1

0 -2.2115 -0.2532 0
0 0 1.0000 0
B =
-3.8114 0.0010
-0.0515 0
-2.8791 0
0 0
C =
0 -1 0 1
1 0 0 0
EigenValues:
0.9987 0.9987 1.0000 1.0000
0.0252 0.0252 0.0000 0.0000
0.0377 0.0377 0.0003 0.0003
0.0249 0.0249 0.0030 0.0030
EigenVector:
1.5124 0 0 0
0 1.5124 0 0
0 0 0.0966 0
0 0 0 0.0966
1.0e+05 *
0.0000 0.0012 0.0001 0.0009
0.0854 5.1051 0.3385 3.1935
t1 =
-0.0020 -0.9987 -0.0272 0.0483
-0.4652 -0.0065 0.1233 -0.1354
-0.6677 -0.0498 0.9859 -0.9820
-0.5812 -0.0059 0.1095 -0.1227
t2 =
1.1490 0 0 0
0 8.5000 0 0
2