perform the non-linear simulations

hardtofindcurtainUrban and Civil

Nov 16, 2013 (3 years and 7 months ago)

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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