Pflimlin, Soueres, Hamel - Hovering Flight Stabilization in Wind Gusts for a Ducted Fan UAV

7/30/2019 Pflimlin, Soueres, Hamel - Hovering Flight Stabilization in Wind Gusts for a Ducted Fan UAV

1/15

Hovering flight stabilization in

wind gusts for a ducted fan UAV

Jean Michel Pflimlin

Philippe SouresTarek Hamel


2/15

Presentation outline

Introduction

System Modelling

Control design

Conclusion


3/15

IntroductionBertin Technologies VTOL UAV history

American VTOL

UAVs

Kestrel

(Honeywell)

iSTAR (Allied

Aerospace)

Internal studies

SFER

Bertin VTOL UAV


4/15

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


5/15

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)(


6/15

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


7/15

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


8/15

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


9/15

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 .=


10/15

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

))/(

)/(

(

=

=

+++

+=


11/15

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=

=

&


12/15

Control DesignControl law architecture

s

D

Dv

u

puqu

&

3.eRu

extF

extM

r

extF&

extM&

u&&l

m

n


13/15

Control DesignCompensator implementation

u

S

D

Dv

R

ail


14/15

Control designSimulation results


15/15

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

Documents

Pflimlin, Soueres, Hamel - Hovering Flight Stabilization in Wind Gusts for a Ducted Fan UAV