Control Design for F-18 Longitudinal Dynamics

Student Name
Student ID Number
CONTROL DESIGN
Institutional Affiliation
F-18 Longitudinal Dynamics
Assignment
Date of submission
Question 1
2018

Open loop system modes
A system can be represented using the continuous time domain function or using
the state space. The state space uses matrix notation to represent a system of
signals. The standard state space representation is,
̇x= Ax+ Bu
y=Cx + Du
The open loop system mode does not have a feedback loop. Using MATLAB
software, the F-18 longitudinal dynamics is represented as
d
dt [V
α
q
θ ]=
[−0.0239 −28.3172 0 −32.2
−0.0003 −0.3621 1 0
0 −2.2115 −0.2532 0
0 0 1 0 ][V
α
q
θ ]+
[−3.8114 0.001
−0.0515 0
−2.8791 0
0 0 ] [δe
δr ]
[ γ
V ]= [0 −1 0 1
1 0 0 0 ] [V
α
q
θ ]
To compute the eigenvalues and eigenvectors,
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))
Question 2
1

The transfer function of the system is given based on the following relationship,
G ( s ) =K ( n ( s )
sk d ( s ) ) for a system of type K
2x2 system transfer matrix
G11 ( s )=−111.4 s3 +1534 s2 −1.11e04 s+1.046e04
s4−48.98 s3−53.64 s2+3871 s−625.1
G12 ( s ) =−7.061e05 s3 +1.881e07 s2−1.868e07 s−9.515 e 08
s4 −48.98 s3−53.64 s2+ 3871 s−625.1
G2 1 ( s ) = −287.2 s3+ 7640 s2+2038 s−741.6
s4−48.98 s3−53.64 s2 +3871 s−625.1
G22 ( s ) =−9.749e05 s3 +2.341e07 s2−4.209e07 s +2.954 e 07
s4−48.98 s3−53.64 s2 +3871 s−625.1
Question 3
Single input-single output systems for the transfer function G11(s).
G11 ( s )=−111.4 s3 +1534 s2 −1.11e04 s+1.046e04
s4−48.98 s3−53.64 s2+3871 s−625.1
Using the characteristic equation to determine the poles of the system,
poles=[-1.149;-8;-8.5;-9]; %place observer poles
2