1.
Unzip the File F16Sim.zip
This will create a directory F16Sim and it will contain all the files needed to
perform the non

linear simulations
2.
Open MATLAB
3.
Change to F16Sim directory
4.
Mex
the file
nlplant.c
using
>>
mex
nlplant.c
The above will create an executable (with a .mexw32 extension) that can then
be embedded as a function in
Simulink
or used as just another function in
MATLAB. You should see “nlplant.mexw32” in your directory.
5.
Add “F16Sim” to MATLABPATH. Make sure you append the directory to the end of the
path

> “File”

> “Set Path”

> Select “With sub

folders option”

> Move to bottom

>
Save.
6.
Create a Project Work directory, “
AwesomeProject
”

> change to this directory and
perform/save designs here.
7.
>> runLinF16Sim
The following list of commands will create the transfer functions for
a)
Altitude
–
elevator, b) bank angle
–
aileron, c) pitch angle
–
elevator and d) yaw angle
–
rudder.
After you are done with runLINF16sim,
1.
sys =
ss
(A,B,C,D);
% Creates the large state space system object
2.
systf
=
tf
(sys);
% Converts the SS object to a Transfer Function object
3.
syshde
=
minreal
(
systf
(3,2));
% Pulls out the Altitude
–
Elevator TF
4.
sysphida
=
minreal
(
systf
(4,3));
% Pulls out the Bank
–
Aileron TF
5.
systhede
=
minreal
(
systf
(5,2));
% Pulls out the Pitch
–
Elevator TF
6.
syspsidr
=
minreal
(
systf
(6,4));
% Pulls out the Yaw
–
Rudder TF
7.
% Save into a file called design Project
8.
save
designProject
sys
systf
sysphida
systhede
syspsidr
syshde
Example:
Pitch

Elevator Transfer function:

154.5 s^2

114.6 s

1.452

s^5 + 21.99 s^4 + 38.67 s^3 + 50.51 s^2 + 0.684 s + 0.3423
Example (contd.)
Pitch

Elevator Transfer function:
systhede

154.5 s^2

114.6 s

1.452

s^5 + 21.99 s^4 + 38.67 s^3 + 50.51 s^2 + 0.684 s + 0.3423
>> damp(
systhede
)
Eigenvalue
Damping Freq. (
rad
/s)
i
)

4.20e

003 + 8.26e

002i 5.08e

002 8.27e

002
ii)

4.20e

003

8.26e

002i 5.08e

002 8.27e

002
iii)

8.91e

001 + 1.30e+000i 5.66e

001 1.57e+000
iv)

8.91e

001

1.30e+000i 5.66e

001 1.57e+000
v)

2.02e+001 1.00e+000 2.02e+001
•
The last
eigenvalue
corresponds to the actuator.
•
(
i
) and (ii) are characterized by low frequency and low damping (stable) and
correspond to the long period (
Phugoid
) mode.
•
(iii) and (iv) correspond to the short period mode.
•
DESIGN REQUIREMENT
: Increase short period damping to 0.707
•
See if the DESIGN REQUIREMENT can be met using a simple proportional gain (K).
•
Perform this analysis using the Root Locus method we just discussed in class.
•
Plot the step response for a unit elevator deflection using ‘
systhede
’ with and without
the control element.
•
Can you place the closed loop poles (short period only) such that they have a damping
of 0.707 and frequency of 2
rad
/s?
•
What happens to the other roots if you meet the above objective?
•
Document your analysis.
•
For those who have unstable
systhede
, you need to find a way to stabilize the
system as well as satisfy the DESIGN REQUIREMENT.
•
The following requirements can be used as a guideline for
your controller design for the project
•
Longitudinal Dynamics
•
Stable
Phugoid
(Long period)
•
Short period dynamics
•
Damping ratio between 0.5
–
0.85
•
Frequency between 2.0
–
5.0
rad
/s
•
Lateral

Directional Dynamics
•
Stable roll subsidence
•
Stable spiral
•
Stable Dutch Roll
•
Damping ratio
–
at least 0.3
•
Frequency
–
at least 1.5
rad
/s
•
Real part of the
dutch
roll poles
–
at least 0.35
•
Each team will design the following autopilots,
•
Pitch displacement autopilot (consider )
•
Altitude hold autopilot (consider )
•
hc
is the commanded altitude
•
It is desirable that the achieved altitude has less than 5
percent overshoot .
•
Roll autopilot to achieve a desired bank angle and a yaw damper
to improve the Dutch Roll Performance
HINTS:
•
Good pitch displacement can be achieved by using a PD
element in the feedback path and a PI element in the forward
path (after the summing junction).
•
Once the pitch displacement autopilot is done, consider
altitude hold autopilot with the pitch loop closed.
•
For the Yaw

Damper you may use in the feedback path
and a simple gain after the summing junction. Find appropriate
values for T and the Gain to get desirable properties.
)
(
)
(
s
s
e
)
(
)
(
s
h
s
h
c
1
Ts
s
PROJECT REPORT
1.
Cover page with names of the team members and signatures.
2.
The main body of the text should be formatted 11 pt, Times New Roman with 1 inch
margin on all sides.
3.
The following items must be summarized
–
Flight condition at with the design was
performed, Design requirements, Transfer functions employed for design, Analysis of the
transfer functions, Specific actions taken to improve performance, Choice of control
elements (why did you choose those elements), Final controller transfer functions,
Simulation results.
4.
Provide details of the contributions from each team member when you
are organizing the
report.
5.
For simulation, you will build a
Simulink
diagram using the Complete System with 4 control
inputs (Thrust, Elevator, Aileron, Rudder) and 12 outputs (North, East, Down, Roll, Pitch,
Yaw, Velocity,
AoA
,
AoS
, Roll Rate, Pitch Rate, Yaw Rate). Fix the Controls and all the other
States at the trim values obtained from earlier work. Add the control elements to this and
simulate the system. (See Figure)
DEMUX Block
V
1
Trim Thrust
1
Trim Rudder
1
Trim Elevator
1
Trim Aileron
s+0.1
s+1
Theta Feedback
Theta
1
Ref Altitude
R  Yaw Rate
Q  Pitch Rate
Psi
Phi
s+0.1
s
PI (altitude)
20s+0.2
s+0.1
PI (Theta)
P  Roll rate
North
H
East
Angle of SideSlip
Angle of Attack
x' = Ax+Bu
y = Cx+Du
12 State Aircraft
State Space
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