1
EE 5320 Project
1
Summer
2006
Design
and Analysis
of Aircraft Control Systems
Objective:
It is well known that the pilot’s efforts can be greatly reduced by introducing
feedback signals into the flight control channels. The determination of these feedb
ack
signals repr
esent
the control problem
s
discussed here.
The usual method of attack is to separate the aircraft’s equation of motion into two
uncoupled modes, a longitudinal and a lateral mode.
The technique
s
described in
this project
are
systematic an
d efficient method
s
for
designing multi

variable controllers based on well k
nown results in classical,
as well as
modern control t
heory. The methods would yield
multi

loop system
s
in which a linear
combi
nation of all aircraft states are
feed

back in each c
ontrol channel, consequently,
every feasible feedback path will be considered.
Important:
Final project report
(individually done)
w
ill be due
07/31/06
Midnight
.
Email the soft copy of the report to
jyotir@arri.u
ta.edu
, copy to
dvrabie@arri.uta.edu
,
and
pballal@arri.uta.edu
Sample report format is posted here
(
http://arri.uta.edu/acs/jyotirmay/EE4343/Labs_Projects/project
reportformat.doc
).
This document will be updated
frequently;
new steps will be added
along with the
relevant material covered in the class.
No intermediate repor
ts are required.
Project 1
weighs 100
% towards project grade.
2
Aircraft
Dynamics
are give
n by
(See appendix for the
definitions).
R
R
A
A
r
p
R
R
A
A
r
p
R
R
A
A
r
p
E
E
q
u
E
E
u
E
E
u
N
N
r
N
p
N
N
L
L
r
L
p
L
L
V
Y
V
Y
V
g
r
V
Y
p
V
Y
V
Y
M
q
M
M
u
M
V
Z
q
V
Z
u
V
Z
X
g
X
u
X
u
1
Primer
(Not for submission)
What are lateral and longitudinal dynamics of a system in
motion?
When lateral and longitudinal dynamics of a system in motion can be decoupled?
What
do Aircraft
system states
physically mean?
What
does phugoid motion
physically mean?
Project Assignment
For aircraft longitudinal dynamics
,
1.
Identify system states; classify them into rates and positions.
2.
Identify system control inputs.
3.
Write lin
ear system state
space equation in the form
Bu
Ax
x
.
4.
Make a signal flow diagram of aircraft longitudinal dynamics.
5.
Find the resolvant matrix.
6.
Obtain the characteristic polynomial.
7.
Find the system poles using the data in the Table 1, you will observe two shor
t
period
modes (
real poles), and a phugoid
mode (
complex pole pair).
8.
Find the damping and frequency of the phugoid motion
using the data in the Table
1
.
9.
The speed variations in aircraft longitudinal motion are often “trimmed” by a
separate throttle control
so that
u
can be assumed negligible. Thus we can use a
simplified dynamic model in which the state variables are
1
x
q
x
2
3
x
Using these state variables and aerodynamic coe
fficients of Table 3, find the gains
that place the closed loop poles in the pattern:
2
s
,
3
1
j
s
.
10.
Draw the block diagram of the closed loop system achieved in the previous
problem.
For aircraft lateral dynamics
11.
Ident
ify system states; classify them into rates and positions.
12.
Identify system control inputs.
3
13.
Write linear system state space equation
in the form
Bu
Ax
x
.
14.
Make a signal flow diagram of aircraft longitudinal dynamics.
15.
The eigen values for the
lateral motion of an aircraft consist, typically, of two
complex poles with relatively low damping, and a pair of real poles. The complex
pair defines a mode called dutch roll. One real pole, relatively far from the origin,
defines a mode called roll subs
idence, and a real pole near the origin defines the
spiral mode.
(The
latter is sometimes unstable

spiral divergence.) Using the data
given in table 2 find the four modes of the aircraft.
16.
A stability augmentation system (SAS) is to be designed for this air
craft using
two rate gyros, each of which measures one of the body rates
p
and
r
.Find the
transfer functions
( use the data given in Table 2).
)
(
)
(
s
s
p
A
)
(
)
(
s
s
r
A
)
(
)
(
s
s
p
R
)
(
)
(
s
s
r
R
Is it apparent f
rom these transfer functions why the ailerons are used for roll (
p
)
control and the rudder is used for yaw (
r
) control? Write your observations.
17.
Is the dynamic process controllable using only the ailerons?
( use the data given in
Table 2, write your observ
ations in support of the answer)
18.
Is the dynamic process cont
rollable using only the rudder
? ( use the data given in
Table 2, write your observations in support of the answer)
.
19.
The rudder is often used for turn coordination; we may thus assume a control law
for the rudder.
T
V
Y
p
V
Y
r
V
Y
V
g
V
Y
V
Y
p
r
A
A
R
R
1
1
(a)
Using the aerodynamic data of table 2, find the control law for the ailerons that
makes the sideslip decay constant
2
.
0
T
s and places the remaining poles at
1
s
and
3
1
j
s
.
20.
Combine the result with (a) to obtain the entire control law
Kx
u
.
4
Appendix A:
Aerodynamic Variables
and parameters
deflection
elevator
:
deflection
aileron
:
deflection
rudder
:
angle
yaw
:
angle
roll
:
rate
yaw
:
rate
roll
:
pitch
:
rate
pitch
:
speed
in
change
:
angle
slip
slide
:
attack
of
angle
:
E
A
R
r
p
q
u
Table 1
:
Aerodynamic parameters for AFT

16 on landin
g approach
Kt
V
139
0507
.
0
u
X
861
.
3
X
0
E
X
00117
.
0
V
Z
u
5164
.
0
V
Z
0717
.
0
V
Z
E
000129
.
0
u
M
4168
.
1
M
4932
.
0
q
M
645
.
1
E
M
Table 2: Aerodynamics data for a fighter aircraft
( Lateral Dynamics)
746
.
0
V
Y
006
.
0
V
Y
p
006
.
0
V
Y
r
0369
.
0
V
g
0012
.
0
V
Y
A
0092
.
0
V
Y
R
9
.
12
L
746
.
0
p
L
387
.
0
r
L
05
.
6
A
L
952
.
0
R
L
31
.
4
N
024
.
0
p
N
174
.
0
r
N
416
.
0
A
N
76
.
1
R
N
Table 3: Aircraft lon
gitudinal dynamics, simplified
1
V
Z
1
.
0
V
Z
E
5
.
0
q
M
5
M
9
E
M
14
X
1
E
X
5
EE 5320
Project 2
Summer
2006
Workshop: Contro
l System Design Tools
Real

Time Targets enables to run software models in real time on the desktop for rapid
prototyping or hardware

in

the

loop simulation
of control system and signal processing
algorithms.
This workshop’s objective is to develop an ability to create and control a real

time
execution entirely through software/hardware tools. Using these tools, a source code can
be generated, compiled; this
facilitates real

time execution on a Windows PC while
interfacing to real hardware using PC I/O boards.
I/O device drivers are included to support a selection of I/O boards, enabling attendees to
interface to sensors, actuators, and other devices for exp
erimentation, development, and
testing of real

time systems.
Demonstrations will include

interfacing with some of the electromechanical systems,
identification, modeling and design of controllers. Available implementation platforms
will be discussed.
Ke
y Features
Run models in real time on desktop PC.
Provides fast point

by

point processing of data for minimal latency, a requirement
in control system applications.
Works with PC I/O boards for real

time input and output.
Enables control of real

time mod
el execution directly from the software, creating
a "PC

in

the

loop" prototyping environment.
Enables signal acquisition and parameter tuning.
Includes a C compiler for building the real

time code.
6
Industrial Emulator
Spring

Mass Damper
Inverted Pendulum
Torsion Control System
Figure: Electromechanical Systems
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