Ecole Nationale de l’Aviation Civile

(1)

www.enac.fr

The French civil Aviation University

Fixed-wing UAV with transitioning flight capabilities:

Model-Based or Model-Free Control approach?

A preliminary study.

Jacson M. O. Barth Advisors:

Jean-Marc Moschetta (ISAE) Jean-Philippe Condomines (ENAC)

2018

Jacson M. O. Barth 1

(2)

www.enac.fr

Outline

1 Introduction Problematic Objective

2 Background State of the art Model-Free Control Control architecture

3 Simulation results Transitioning flight Forward flight

Uncertain parameter analysis

4 Conclusion

Jacson M. O. Barth 2

(3)

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What is a hybrid UAV ?

MAVion Dark-Knight

Wingtra Cyclone

Jacson M. O. Barth / Introduction 3

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Problematic

Identification Modeling

Wind-tunnel campaigns Costly and time consuming Attitude control

Position control Navigation

Jacson M. O. Barth / Introduction / Problematic 4

(5)

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Objective

Control the entire flight envelope Great disturbance rejection Uncertain parameters

Adaptable to different hybrid UAVs

Jacson M. O. Barth / Introduction / Objective 5

(6)

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State of the art

Proportional Integral Derivative (PID)

[...] Although simple to tune without the knowledge of the model, PID controllers are limited in terms of disturbance rejection [...]

Linear Quadratic Regulator (LQR)

An accurate model of the system is required.

Incremental Nonlinear Dynamic Invertion (INDI)

INDI uses teste flight data to tune the control coefficients. Of course, to do this, the MAV needs to be flying with predefined

control parameters.

Jacson M. O. Barth / Background / State of the art 6

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Model-Free Control

Unmodeled State Dynamic

Estimator Feedback

Control

y _d u y m

F ˆ _y

Figure – Overall Model-Free Control schema.

Jacson M. O. Barth / Background / Model-Free Control 7

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Model-Free Control

MFC principles

y ^v _m = F + –u (1)

s ² Y m (s) ≠ sy m (0) ≠ y ˙ m (0) = F

s + –U (s) (2) 2Y m (s) + 4s dY _m (s)

ds + s ² d ² Y _m (s) ds ² = 2F

s ³ + – d ² U (s) ds ² (3) 2Y m (s)

s ³ + 4 s ²

dY m (s) ds + 1

s

d ² Y m (s) ds ² = 2F

s ⁶ + – s ³

d ² U (s)

ds ² (4)

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Model-Free Control

Estimator F ˆ = 5!

2T ⁵

⁄ t

t ≠ T [(T ≠ ‡) ² ≠ 4‡(T ≠ ‡) + ‡ ² ]y m (‡)d‡

≠ [ –

2 ‡ ² (T ≠ ‡) ² ]u(‡)d‡ (5) Control-loop

u = ≠ F ˆ

– + y ^(v) _d + K(›)

– (6)

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Model-Free Control

≠ + K d

²

dt

²

y _d •

Unmodeled State Dynamic

•

• ¨ y _d

› _y

u

y _m M F C _y

_d

_≠>u

F(t) ˆ 1 + – + ≠

Figure – Detailed Model-Free Control schema for a second-order system.

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Control architecture

Desired • trajectories

vxd

vyd

vzd

vxc

vyc

vzc

Mixing

Td!!n

MF Cd!!

MF C✓d!n

MF Cd!

MF Cvx

MF Cvy

MF Cvz MF Cx

MF Cy

MF Cz

Td

d

✓d

d

!n !

n+

n

!2

!1

1 2

Attitude stabilization Velocity

Control Position

Control Wind

Disturbances

•(,✓, ) (vx, vy, vz)

(x, y, z)

Figure – MFC architecture for Hybrid UAVs.

Jacson M. O. Barth / Background / Control architecture 11

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Hover-forward flight

1

2

3

4 Figure – Typical flight modes of Hybrid UAVs : 1-Take-Off ; 2-Transition ; 3-Forward ; 4-Hover.

Jacson M. O. Barth / Simulation results / Transitioning flight 12

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Hover-forward flight (LQR vs MFC)

t= 0s t= 18s

t¥28s

0 10 20 30 40 50

≠210121416182002468

Time (s)

Forwardspeed(m/s)

Desired forward speed Scheduled LQRMFC

0 10 20 30 40 50

0 10 20 30 40 50 60 70 80 90 100

Time (s) Pitchangle(¶)

◊d- MFC MFC

◊d- LQR Scheduled LQR

0 10 20 30 40 50

≠900

≠650

≠400

≠150 100 350 600 850

Time (s)

Motorrotations(rad/s) MFC

Scheduled LQR

0 10 20 30 40 50

≠30

≠25

≠20

≠15

≠10

≠5 0 5

Time (s) Elevons(¶)

Scheduled LQRMFC

0 10 20 30 40 50

≠4

≠2 0 2 4 6

Time (s)

Winddisturbance(m/s) Windu

Windw

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Hover-forward flight (LQR vs MFC)

Table – LQR vs MFC : RMSE - Hovering flight

y Scheduled LQR MFC SI Units

Pitch angle (With wind) 4.8131 3.2893 [

^¶

] Forward speed (With wind) 0.3170 0.2293 [m/s]

Table – LQR vs MFC : RMSE - Entire flight envelope

y Scheduled LQR MFC SI Units

Pitch angle (No wind) 3.0646 1.5131 [

^¶

] Forward speed (No wind) 0.8699 1.4613 [m/s]

Pitch angle (With wind) 4.5357 2.7858 [

^¶

] Forward speed (With wind) 1.8349 1.4700 [m/s]

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Forward flight

1

2

3

4 Figure – Typical flight modes of Hybrid UAVs : 1-Take-Off ; 2-Transition ; 3-Forward ; 4-Hover.

Jacson M. O. Barth / Simulation results / Forward flight 15

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Forward flight

cliquer ici

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Forward flight - actuators

0 20 40 60 80 100

≠850

≠600

≠350

≠100 150 400 650 900

Time (s)

Mot or s (r ad /s )

Ê

r

Êl

0 20 40 60 80 100

≠30

≠20

≠10 0 10

Time (s) Fl ap de fle ct ion s (

¶

)

”

l

”

r

Figure – Propeller speeds (Ê

l

< 0 and Ê

r

> 0) due to counter-rotation sense and the elevon deflections (”

l

and ”

r

), convention negative for pitch-up.

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Uncertain parameter analysis

Table – Fixed-Wing specifications Parameters Cyclone Dark-Knight SI Units %

Mass 0.852 0.586 [Kg] 45.39

I

xx

0.0036 0.0072 [Kg m

²

] 52.3 I

yy

0.0036 0.0072 [Kg m

²

] 52.47 I

zz

0.0036 0.0072 [Kg m

²

] 51.2 Propeller radius 0.2032 0.1524 [m] 33.33

Mean Chord 0.17 0.175 [m] 2.94

Wingspan 0.88 1 [m] 13.64

Wing area 0.1496 0.175 [m

²

] 16.98

Jacson M. O. Barth / Simulation results / Uncertain parameter analysis 18

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Uncertain Parameter Analysis

≠40≠20 0

20 40 0 500 1,0001,500 0

20 40 60

East (m) North (m)

Altitude(m)

Cyclone Dark-Knight

0 20 40 60 80 100

≠14

≠7 0 7 14 21

Time (s) Rollangle(¶)

„dCyclone

„Cyclone

„dDark-Knight

„Dark-Knight

0 20 40 60 80 100

0 5 10 15 20

Time (s) Pitchangle(¶)

◊dCyclone

◊Cyclone

◊dDark-Knight

◊Dark-Knight

0 20 40 60 80 100

8 10 12 14 16 18 20

Time (s)

Forwardvelocity(m/s)

Desired forward velocity Cyclone Dark-Knight

0 20 40 60 80 100

≠4

≠2 0 2 4 6

Time (s)

Eastvelocity(m/s)

Desired east velocity Cyclone Dark-Knight

0 20 40 60 80 100

≠4

≠2 0 2 4

Time (s)

Zvelocity(m/s)

Desired Z velocity Cyclone Dark-Knight

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Uncertain Parameter Analysis - Actuators

0 20 40 60 80 100

≠1,200

≠800

≠400 0 400 800 1,200

Time (s)

Propellerspeeds(rad/s) Cyclone

Dark-Knight

0 20 40 60 80 100

≠50

≠40

≠30

≠20

≠10 0 10 20

Time (s) Flapdeflections(¶)

”lCyclone

”rCyclone

”lDark-Knight

”rDark-Knight

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Perspectives

Forward-hover transition Stability analysis

Position control Navigation Real flights

Jacson M. O. Barth / Conclusion 21

(22)

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Acknowledgments

François Defaÿ Leandro Lustosa

(23)

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Ecole Nationale de l’Aviation Civile

Fixed-wing UAV with transitioning flight capabilities:

Model-Based or Model-Free Control approach?

A preliminary study.

Jacson M. O. Barth Advisors:

Jean-Marc Moschetta (ISAE) Jean-Philippe Condomines (ENAC)

2018

Outline

1 Introduction Problematic Objective

2 Background State of the art Model-Free Control Control architecture

3 Simulation results Transitioning flight Forward flight

Uncertain parameter analysis

4 Conclusion

What is a hybrid UAV ?

MAVion Dark-Knight

Wingtra Cyclone

Problematic

Identification Modeling

Wind-tunnel campaigns Costly and time consuming Attitude control

Position control Navigation

Objective

Control the entire flight envelope Great disturbance rejection Uncertain parameters

Adaptable to different hybrid UAVs

State of the art

Proportional Integral Derivative (PID)

[...] Although simple to tune without the knowledge of the model, PID controllers are limited in terms of disturbance rejection [...]

Linear Quadratic Regulator (LQR)

An accurate model of the system is required.

Incremental Nonlinear Dynamic Invertion (INDI)

INDI uses teste flight data to tune the control coefficients. Of course, to do this, the MAV needs to be flying with predefined

control parameters.

Model-Free Control

Unmodeled State Dynamic

Estimator Feedback

Control

y d u y m

F ˆ y

Figure – Overall Model-Free Control schema.

Model-Free Control

MFC principles

y v m = F + –u (1)

s 2 Y m (s) ≠ sy m (0) ≠ y ˙ m (0) = F

s + –U (s) (2) 2Y m (s) + 4s dY m (s)

ds + s 2 d 2 Y m (s) ds 2 = 2F

s 3 + – d 2 U (s) ds 2 (3) 2Y m (s)

s 3 + 4 s 2

dY m (s) ds + 1

s

d 2 Y m (s) ds 2 = 2F

s 6 + – s 3

d 2 U (s)

ds 2 (4)

Model-Free Control

Estimator F ˆ = 5!

2T 5

⁄ t

t ≠ T [(T ≠ ‡) 2 ≠ 4‡(T ≠ ‡) + ‡ 2 ]y m (‡)d‡

≠ [ –

2 ‡ 2 (T ≠ ‡) 2 ]u(‡)d‡ (5) Control-loop

u = ≠ F ˆ

– + y (v) d + K(›)

– (6)

Model-Free Control

≠ + K d

dt

y d •

Unmodeled State Dynamic

•

•

¨ y d

› y

u

y m M F C y

≠>u

F(t) ˆ 1 + – + ≠

Figure – Detailed Model-Free Control schema for a second-order system.

Control architecture

Figure – MFC architecture for Hybrid UAVs.

Hover-forward flight

1

y _d u y m

F ˆ _y

y ^v _m = F + –u (1)

s ² Y m (s) ≠ sy m (0) ≠ y ˙ m (0) = F

s + –U (s) (2) 2Y m (s) + 4s dY _m (s)

ds + s ² d ² Y _m (s) ds ² = 2F

s ³ + – d ² U (s) ds ² (3) 2Y m (s)

s ³ + 4 s ²

d ² Y m (s) ds ² = 2F

s ⁶ + – s ³

d ² U (s)

ds ² (4)

2T ⁵

t ≠ T [(T ≠ ‡) ² ≠ 4‡(T ≠ ‡) + ‡ ² ]y m (‡)d‡

2 ‡ ² (T ≠ ‡) ² ]u(‡)d‡ (5) Control-loop

– + y ^(v) _d + K(›)

y _d •

¨ y _d

› _y

y _m M F C _y

_≠>u