Stability and Control of UAVs A Preliminary

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16 Νοε 2013 (πριν από 3 χρόνια και 11 μήνες)

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Stability and Control
of UAVs


A Preliminary
Study


Mathew Wolcott
1

and

Rat
neshwar

Jha
2



Unmanned Aerial Vehicles (
UAVs
)

are typically rotorcraft or airplanes and are used in
many applications, including surveillance, terrain mapping, military combat, an
d environmental
monitoring. Since there are a variety of tasks, there is also a variety of design and innovation in
UAVs.
This paper presents some
preliminary

studies related to flight dynamics and control of
UAVs, so that more complex aspects of UAVs ma
y be studied in future. It gives background
information on a generic aircraft, flight dynamic equations of motion
,

and the design of
controllers for improving the aircraft characteristics to satisfactory levels
.

T
he equations of motion
of

an aircraft

fo
r both longitudinal and lateral motion
s were
employed for the simulations (Ref 1)
.
The EOM were coded using MATLAB
. To model the
motion of aircraft
,

the static (




C

,
C

,
C
n
L
), control (
,
C

,
C
n
r
e



), and dynamic stability (
p
p

C

,
C
n
)
derivatives
were

used. These
are
aerodynamic

properties that each individual

aircraft has an
d can
be found through
experiments or computations
.
For these preliminary studies, derivatives were
obtained from Ref 1.
The ability to estimate

an
d simulate

the pitching moment (M), angle of
attack (

), sideslip angle (

), and the angle that the elevator, rudder, and ailerons have been
adjusted to (
,

,

,
a
r
e



)
was a
cq
uired
so that flight dynam
ics may be controlled.

An F
-
104A Starfighter aircraft was used
as a generic UAV
. It was excited with an initial
displacement to see w
h
ether it was inherently stable or not, both laterally and longitudinally.
Under normal circumstances, it was stable, a
nd so the displacement of the varying motions
approached zero after time. In the longitudinal case, the static
pitch

derivative
was negated to
create instability, which is common in modern aircraft. When the aircraft was unstable
,

the
motion diverged unl
ess controlled by the elevator

automatically
.
A controller using LQR
technique was

designed
to
automatically deflect
the elevator to stabilize the aircraft, with the goal
of
making

the aircraft underdamped in its motion. The motion of the ailerons and ru
dder was also



1

Class of 2007, Department of Mechanical and Ae
ronautical Engineering, Clarkson University
,
Honors Program, Oral Presentation


2

Associate Professor, Department of Mechanical and Aeronautical Engineering, Clarkson
University

simulated to provide greater damping in the lateral case. Though it was not
laterally
unstable, the
performance could be increased with control surface movement. It increased the damping in
lateral motion, but it was still underdamped.

Two

example
s

simulation results (one each from
longitudinal and lateral cases
)

are

provided. The pitch angle is the degree of rotation at which an aircraft is pointed in the vertical
plane in a body fixed reference frame.

We can show how pitch angle is chang
ed in a stick fixed
case, where no control is used, how it changes in an unstable case, and how it can be controlled
using an elevator.



Figure 1: Pitch angle can be controlled with the elevators.


We can see that the stick fixed
(stable)
case is lightly

damped and has some overshoot, though it
does approach zero over t
ime. The unstable case decreases
pitch angle
nonlinearly and
approaches infinity over time. The state controlled case is more heavily
damped than

the stick
fixed case,
i
t has
a
little ove
rshoot
,

and quickly approaches zero.


We can also look at some lateral qualities. The heading angle is the degree an aircraft has
rotated in the horizontal body plane.



Figure 2: The controlled case approaches zero quickly


The stick fixed case is ve
ry lightly damped, but since it is stable it approaches zero

over time
.
The controlled case is still underdamped, but has very few oscillations and stabilizes quickly.

The knowledge
that was

gain
ed for
this
paper

will form a foundation for more research
o
ver the following school year
s
.
This research may involve UAVs, aeroelasticity, and the use of
smart structures to control stability and motion. ANSYS, a programming language may also be
learned to assist in the future.
The final paper will present detai
ls of the simulation
, and include
all aspects of longitudinal and lateral motion discussed
.






References:

1.

Nelson, R.C., 1998, Flight Stability and Automatic Control, Second Edition,
Boston, McGraw Hill