Trajectory Tracking for High Aspect-Ratio Flying Wings

7/29/2019 Trajectory Tracking for High Aspect-Ratio Flying Wings

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Trajectory Tracking for High Aspect-Ratio Flying Wings

Brijesh Raghavan, Mayuresh Patil and Craig Woolsey

1Department of Aerospace and Ocean Engineering,

Virginia Tech.

AIAA Atmospheric Flight Mechanics Conference and Exhibit

Honolulu, HI, August 2008

(Virginia Tech) HALE Trajectory Tracking AFM 08 1 / 18
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Outline

1 Introduction

2 Modeling

3 Results

4 Conclusions and Future Work

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Introduction

Motivation and Overview

High Altitude Long Endurance (HALE) flying wings designed for highaspect ratio and low structural weight

Exhibit high flexibility and significant static aeroelastic deformation in

flight

Previous work showed that a rigid flying wing model that accounts forstatic aeroelastic deformation at trim captures pre-dominant flight

dynamic characteristics of the corresponding flexible flying wing

Current work on design of a flight controller using a non-linear guidance

law and dynamic inversion for path-following

Results presented for a curved, rigid flying wing for a straight line and

circular path

Modification to controller proposed for flexible flying wings



4/18

Modeling

Overview of closed-loop simulation

Figure: Closed-Loop Schematic


d li


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Modeling

Modeling for simulation

Flying wing structure is modelled using a geometrically exact, intrinsic

beam formulation developed by Hodges

Small strain assumption, uses linear elastic law

Equations are augmented by intrinsic kinematic equations that relate

velocity and angular velocity to strain and curvature

Aerodynamic loads are modelled using a 2-D aerodynamics model

developed by Peters and Johnson

Aerodynamic model augmented to account for the effect of skin friction

dragPropulsive system consists of multiple engines along the span

Energy conserving, Finite-difference based discretization


M d li


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Modeling

Post-processing of state vector

State vector from the simulation module has 21 structural variables foreach node, and 6 unsteady aerodynamic variables for each element

Mass and moment of inertia properties specified for each element in the

FE model

Dynamic Inversion for flight control requires calculation of equivalentflight dynamic variables

These quantities are calculated in the mean reference frame which has its

origin at the CG

First part of post-processing module computes the following quantities at

each time instantr

cg, Icg, P, HM, Vcg, M

Second part of post-processing module calculates Euler angles of the

mean axis and inertial co-ordinates of the CG


Modeling
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Modeling

Controller Design

Figure: Closed-Loop Schematic

Figure: Differential Thrust


Modeling
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Modeling

Controller Design: Guidance Module

Ground path following based on work by Parket al.

ald = 2

Vg2

L1

sin

ahd = 2V2

(hc h)

L2h 2V

h

Lh

avd = Kvel(Vc V)

Va

d = a

dv cos a

dh sin

adladv sin + a

dh cos

Figure: Guidance Algorithm


Modeling


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Modeling

Dynamic Inversion

Equations of motion to be inverted

Mfaero +Mfg +

MfT = Mtotal(MVcg +

MMMVcg)

MM1MM2MM3

=

0 cosmi sinmi cos mi1 0 sin mi

0 sin mi cosmi cos mi

mi

mi

mi

Mmaero + MmT = MIcgMM+ MMMIcgMMCalculation of demanded rates

MVcg +

M

M

MVcg = C

MV Va

d

dmi = K(mic mi)

dmi = K(mic mi)

dmi = K( mi)MdM = K(

MMc MM)


Results


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Results

Parameters of Rigid Flying Wing

Table: Input parameters

b = 73.06 m CL = 2 CL = 1 CD0 = 0.01c = 2.44 m Cm0 = 0.025 Cm = 0 Cm = 0.25

Ixx= 4.15 kg m I

yy= 0.69 kg m I

zz= 3.46 kg m = 8.93 kg/m

L1 = 609.6 m Kvel = 0.001 K = 0.1 K = 1Lh = 6304.8 m CL0 = 0 xac = 0.0 m mex = 22.67 kg

Wing tip dihedral 5

Position of wing tip dihedral 12.19 m from wing tip

Aileron position outboard 12.19 m from wing tip

Radius of curvature of wing 219.45 m


Results


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Curved Rigid Wing: Straight Line path

0 100 200 300 400 500 60032

32.5

33

33.5

34

time in s

TinN

Thrust

(a) Thrust

0 100 200 300 400 500 6009.1

9.15

9.2

9.25

9.3

time in s

flapi

n

flap deflection

(b) Flap

0 100 200 300 400 500 6000.5

0

0.5

time in s

aileron

in

aileron deflection

(c) Aileron

0 100 200 300 400 500 6001

0.5

0

0.5

1

time in s

TinN

Redistributed thrust

(d) T(Virginia Tech) HALE Trajectory Tracking AFM 08 11 / 18

Results


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Curved Rigid Wing: Straight Line path

0 100 200 300 400 500 6000.04

0.03

0.02

0.01

0

0.01

0.02

0.03

0.04

time in s

in

roll angle of mean axis

(e) Roll

0 100 200 300 400 500 6003.78

3.79

3.8

3.81

3.82

3.83

time in s

in

pitch angle of mean axis

(f) Pitch

0 100 200 300 400 500 6001.5

1

0.5

0

0.5

1

1.5

time in s

in

yaw angle of mean axis

(g) Yaw

0 100 200 300 400 500 6005

0

5

10

15

time in s

ycoordinm

Y coord

flight path

commanded trajectory

(h) Y co-ord

0 100 200 300 400 500 6000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

time in s

heightinm

altitude in m

(i) Altitude(Virginia Tech) HALE Trajectory Tracking AFM 08 12 / 18

Results
http://find/


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Curved Rigid Wing: Circular path

0 100 200 300 400 500 60032

32.5

33

33.5

34

34.5

35

35.5

36

time in s

TinN

Thrust

(j) Thrust

0 100 200 300 400 500 6009.1

9.15

9.2

9.25

9.3

time in s

flapi

n

flap deflection

(k) Flap

0 100 200 300 400 500 6006

5

4

3

2

1

0

time in s

aileron

in

aileron deflection

(l) Aileron

0 100 200 300 400 500 60012

10

8

6

4

2

0

time in s

TinN

Redistributed thrust

(m)

T(Virginia Tech) HALE Trajectory Tracking AFM 08 13 / 18

Results


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Curved Rigid Wing: Circular path

0 100 200 300 400 500 6000

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

time in s

in

roll angle of mean axis

(n) Roll

0 100 200 300 400 500 6003.65

3.7

3.75

3.8

3.85

3.9

time in s

in

pitch angle of mean axis

(o) Pitch

0 100 200 300 400 500 6000

20

40

60

80

100

120

140

time in s

in

yaw angle of mean axis

(p) Yaw

0 1000 2000 3000 4000 5000 60000

1000

2000

3000

y coord in m

xcoordinm

ground track

flight path

commanded trajectory

(q) Ground Track

0 100 200 300 400 500 6002

0

2

4

6

8

10

time in s

heightinm

altitude in m

(r) Altitude(Virginia Tech) HALE Trajectory Tracking AFM 08 14 / 18

Results


15/18

Flexible Wing: Straight Line path

0 0.5 1 1.5 2 2.5 3 3.50

50

100

150

200

250

300

350

time in s

T

inN

Thrust

(s) Thrust

0 0.5 1 1.5 2 2.5 3 3.50

10

20

30

40

50

60

time in s

aileroni

n

aileron deflection

(t) Aileron

Figure: Control deflections for straight and level flight


Results
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Proposed Modification for Flexible Flying Wings

Figure: Closed-Loop Schematic for Flexible Flying Wings

Similar modification done by Gregory for a HSCT configuration


Conclusions and Future Work
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Conclusions

Path-following controller designed for a high-aspect ratio flying wing

using multi-step dynamic inversion and a non-linear guidance law

Results presented for a curved, rigid-wing case for tracking a straightline and a circular path

Future Work

Modify controller to make it work on the flexible flying wing

Augment controller for Gust Load Alleviation


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Thank you !

Questions ?

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Documents

Trajectory Tracking for High Aspect-Ratio Flying Wings