Pflimlin, Soueres, Hamel - Hovering Flight Stabilization in Wind Gusts for a Ducted Fan UAV
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Transcript of Pflimlin, Soueres, Hamel - Hovering Flight Stabilization in Wind Gusts for a Ducted Fan UAV
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7/30/2019 Pflimlin, Soueres, Hamel - Hovering Flight Stabilization in Wind Gusts for a Ducted Fan UAV
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Hovering flight stabilization in
wind gusts for a ducted fan UAV
Jean Michel Pflimlin
Philippe SouresTarek Hamel
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Presentation outline
Introduction
System Modelling
Control design
Conclusion
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IntroductionBertin Technologies VTOL UAV history
American VTOL
UAVs
Kestrel
(Honeywell)
iSTAR (Allied
Aerospace)
Internal studies
SFER
Bertin VTOL UAV
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Reference frames Inertial frame I (NED - North East
Down) :
Body fixed A :
Dynamic representation
: Center of Gravity G position / Iv : CoG velocity vector/ I
R : transformation matrix from I to A :
: angular velocity vector of Arelative to I, expressed in A
System ModellingDynamic representation
[ ]Ibbb zyxR ,,=
[ ]T
Arqp ,,=
),,( 000 zyx
),,( bbb zyxxb
yb
zb
x0
y0
z0
Notations :
=
0
0
1
1e
=
0
1
0
2e
=
1
0
0
3e
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System ModellingControl inputs
Thrust intensity u = ~ (propellers RPM)
Control surfaces efforts
Fi effort of control grid i (Fi ~ i) Resulting efforts Fail et ail
(expressed in A)
It can be shown that
=
=4
1i
iail FF =
=4
1i
iiail FGA
ailail eL
F = .1
3
([ ]ail
TT
iiPPPF = =
1
4..1)(
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System ModellingWrenches acting on the system
Weight
Thrust
Control vanes
Wind perturbations
G
emgmgzP
==
0
. 30
r
Gai l
ail
ail
RF
=
.
G
b
eRu
zuT
== 0
..
.
3r
Gext
T
ext
extFRe
FF
=3.(
z0
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System ModellingDynamic equations
++==
+++=
=
).(
.
3
33
ext
T
ail
extail
FReII
RR
FRmgeeuRvm
v
(&
(
&
&
&
Kinematic equation of position
Newtons theorem expressed in I
Kinematic equation of attitude
Eulers theorem expressed in A
Null as long as yaw rate is keptto zero
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Control designObjectives Constraints Design
Objectives : stabilize the vehicle in hovering flight at a
constant position despite of wind gusts
Constraints : unknown aerodynamical efforts, but slowlyvarying
Design :
Full state feedback available [,v,R,] Non linear control design based on Backstepping
Adaptive control to estimate in real time unknown aerodynamic
efforts andextF extF.
s
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Control DesignControl model
+=
=++=
=
ext
T
ail
extD
DD
MReI
RR
FmgeeRuvm
v
3
33.
(&
(&
&
&
Pb : the control input ail acts on translational dynamicsand makes the system strictly non-minimum phase
Choosing a control point away from G allows to cancel
the term thanks to centrifugal forces
The control model is then given by :
ailR
extext FM .=
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Control DesignBackstepping process
3
4
2
1
i
i iS iS&
extextext
extextext
sD
MMM
FFF
~
~1
=
=
=
22
2
11
~
2
1~
2
12
1
extext MF
S
++
=
ext
T
extext
T
ext
D
T
MMFF
vkS
&&
&
~1~1
)( 012
111
+=
)(02 = Dvm
2
21221 += SS
2
3232
1+= SS
2
4342
1+= SS
ext
T
extext
T
ext
T
i
ii
MMFF
eRukS
&&
&
~1)(~1
).(
1
132
2
1
2
2
+
= =
133. = eRu
)(~1
)(~1
)(
232
23
3
1
2
3
extTextTextextText
T
i
ii
FMMFF
u
pu
qu
RkS
&&&
&
&
++
+=
=
24
=
u
puqu
R&
321
&&
&&
&
T
KMMFF
u
Iu
Iu
RkS
T
extM
T
extext
T
ext
l
mT
i
ii
4
433
31
1
3
4
1
2
4
)(~1
)(~1
))/(
)/(
(
=
=
+++
+=
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Final step of Backstepping :
Control Law
Adaptive filters
Ensures time derivative is
Control DesignDefinition of the control law
+
=
)()/(
)/(
31
1
T
r
l
m
n
R
rk
u
Iu
Iu
&&
=
Mext
ext
MF
3
&
&
2
452
1rSS += 2
4
1
2
5rkkS
r
i
ii=
=
&
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Control DesignControl law architecture
s
D
Dv
u
puqu
&
3.eRu
extF
extM
r
extF&
extM&
u&&l
m
n
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Control DesignCompensator implementation
u
S
D
Dv
R
ail
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Control designSimulation results
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ConclusionTo be continued
Decoupling of translational and rotationaldynamics in the control law design
Sensor fusion in order to give full stateestimation Attitude & Heading restitution system
INS/GPS Hybridization
Saturation constraints: stability domain analysisand control design involving saturations