AB-267 DYNAMICS & CONTROL OF FLEXIBLE AIRCRAFT

I N S T I T U T O T E C N O L Ó G I C O D E A E R O N Á U T I C A

I M A G E C R E D I T S : B O E I N G

F L ÁV I O S I LV E S T R E

L E C T U R E N O T E S

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S Y L L A B U S

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Summary

AB-267 DYNAMICS AND CONTROL OF FLEXIBLE AIRCRAFT

Recommended: AB-103 / MVO-30 (Aircraft Stability and Control)

Weekly dedication: 3h classes, 6h homework & learning

Summary: Free-body vibration - revision of modal analysis, and definition of mean axes. Derivation of EoM of flexible aircraft applying Lagrangian Mechanics. Generalised forces. 2D aerodynamics and strip theory. Propulsive and gravitational forces. Modal truncation and model reduction. Unified theory for flight mechanics and aeroelasticity. Flight simulation. Stability of elastic aircraft. Control law design for flexible aircraft and aeroservoelasticity. State observer design for flexible aircraft dynamics.

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Administrative

AB-267 DYNAMICS AND CONTROL OF FLEXIBLE AIRCRAFT

‣ Midterm exam #1 (50%) + list(s) of exercises (50%)

‣ Midterm exam #2 (50%) + list(s) of exercises (50%)

‣ Final exam (100%)

Collaboration: knowledge exchange with classmates is highly encouraged. HOWEVER, each student shall write down his or her own solutions. Copy of solutions or codes from others is prohibited!!!

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Bibliography

‣Waszak, M. R.; Schmidt, D. K., Flight Dynamics of Aeroelastic Vehicles. J. Aircraft, vol. 25, n . 6, 1988, pg. 563-571.

‣ Bismarck-Nasr, M. N. Structural Dynamics in Aeronautical Engineering. American Institute of Aeronautics and Astronautics, Inc., 1999.

‣Wright, J. and Cooper, J., Introduction to Aircraft Aeroelasticity and Loads (Aerospace Series). Wiley, 2008.

‣ Goldstein, H., Classical Mechanics. Addison-Wesley Publishing Company, Inc., 1980.

‣ Schmidt, D. K., Modern Flight Dynamics. Mc Graw Hill, 2012.

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aeroelasticity

Lagrangian mechanics

aeroelasticity

dynamics of flexible aircraft

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Work plan

‣ introduction

‣ (supersonic) review of systems of reference, RB flight dynamics & aeroelasticity

‣ definition of mean axes

‣ structural dynamics and modal superposition

‣ EoM of flexible aircraft applying Lagrangian mechanics, under small deformations

‣ 2D aerodynamics and strip theory

‣ QS and unsteady aerodynamic loads due to aircraft deformation

‣ simulation of flexible aircraft programming EoM in MATLAB

‣ trimming and linearisation, stability analysis

‣ aeroelastic oscillation suppression

‣ sensor positioning and aeroservoelastic stability

‣ flexibility-driven PIO5

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Introduction

What is a FLEXIBLE aircraft?

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Introduction

Helios: a prototype of a HALE aircraft powered by solar energy

https://www.youtube.com/watch?v=1NCOPLEJOl0 (look at 1’50’’)7

C O U R T E S Y: N A S A

“Thirty minutes into the flight the aircraft again encountered normal turbulence and then experienced an unexpected, persistent high wing dihedral configuration. As a result, the aircraft became unstable as pitch oscillations grew. Airspeed deviated from the normal flight speed, and the deviations grew with every cycle of the oscillation, soon exceeding the aircraft s design speed. The resulting high dynamic pressures caused the wing s outer wing panels to fail and the solar cells and skin on the upper surface to rip off. “

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Introduction

X-HALE: flexible prototype for flight testing, developed at UMich (Prof. Cesnik) - currently being reproduced at ITA

https://www.youtube.com/watch?v=QSZxoANusHU

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Introduction

Does it apply only to HALE or small aircraft?

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Introduction

Boeing 787 dreamliner

https://www.youtube.com/watch?v=StQneURTciU 1 0

I M A G E C R E D I T S : B O E I N G

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Introduction

Is that a new phenomenon?

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Introduction

Sailplane DG-300

https://www.youtube.com/watch?v=kQI3AWpTWhM 1 2

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I M A G E C R E D I T S : N A S A

Introduction

»

I M A G E C R E D I T S : C H A R L O T T E M C G I N N I S

Wright 1902 aircraft, Wright brothers

‣ warping wings to generate roll (inspired on birds)

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Introduction

Why does the flexibility increase?

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Introduction

Why does the flexibility increase?

‣ Breguet equation of range in cruise

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R =

r2

⇢S

2

TSFC

C1/2L

CD

⇣pWi �

pWf

⌘

fly at higher altitudes

more efficient engines

reduce drag for a given lift

CD = CD0 +1

⇡eARC2

L

increase AR!

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Introduction

What consequences does the increase in flexibility bring?

some examples…

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Introduction

Frequency separation band gets tighter >> stability concerns

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Drewiacki, Silvestre, Guimarães Neto, AIAA 2016* (accepted)

Guimarães Neto, PhD Thesis, 2014

increase in flexibility

dutch roll

elastic modes

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Introduction

Handling qualities - PIO due to airframe flexibility

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Drewiacki, Silvestre, Guimarães Neto, AIAA 2016* (accepted)

increase in flexibility

susceptible to PIO

notch-filtered

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−12 −10 −8 −6 −4 −2 0 2 4

0

20

40

60

80

100

120

140

160

180 0.0160.0320.05

0.075

0.105

0.15

0.24

0.4525

50

75

100

125

150

175

Root Locus (sensor at P2)

Real Axis

Imag

inar

y Ax

is

Mode 16Mode 14

Mode 12

Mode 8

Mode 5

Mode 2

aerodynamic lags

dutch rollshort period

Kr = 0.1Kr = 1.0

Introduction

AEROSERVOELASTIC stability

‣ control law may interact with elastic modes

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Introduction

FCL design: stability margin & performance reduction

2 0

G(s ) : ue to Kqq s

Open -L oop Phase (de g)

Open-L

oop

Gain

(dB)

G(s ) : ue to K θθ s

Open -L oop Phase (de g)

Open-L

oop

Gain

(dB)

G(s ) : Hr e f to H

Op en -L oop Phase (de g)

Open-L

oop

Gain

(dB)

−270 −180 −90 0 90 180

−20

−10

0

10

20

30

40

−1080 −720 −360 0

−30

−20

−10

0

10

20

−270 −180 −90

−20

−10

0

10

20

30

fi l te re dw ith η- SAS

0 10 20 30 400

2

4

6

8

10

12

T ime [s]

∆H

[m]

∆Hr e f

∆H

0 10 20 30 40−15

−10

−5

0

5

10

T ime [s]

∆α,∆θsand

∆δe[o]

∆α∆ θ∆ δ e

0 10 20 30 40−1

−0.8

−0.6

−0.4

−0.2

0

0.2

0.4

0.6

0.8

1

T ime [s]

∆n

z[g

]

c ock p itlast pax

0 5 10 15 20 25 300

2

4

6

8

10

12

T ime [s]

∆H

[m]

∆Hr e f

∆H

0 5 10 15 20 25 30−12

−10

−8

−6

−4

−2

0

2

4

6

8

T ime [s]

∆α,∆θsand

∆δe[o]

∆α∆ θ∆ δ e

0 5 10 15 20 25 30−2

−1.5

−1

−0.5

0

0.5

1

1.5

T ime [s]∆

nz[g

]

c ock p itlast pax

Silvestre et al, Journal of Aircraft 2016 (submitted)

D E C O U P L E D F C L D E S I G N

C O U P L E D F C L D E S I G N 7.1 dB to 10.9 dB

62.4o to 65.4o

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Introduction

Convinced that flexibility matters?

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Some advertising :)

We are…

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‣ X-HALE is currently under construction at ITA

‣ validation of integrated models with different levels of complexity (moderately and highly flexible AC)

‣ coupling of AE and FM modes

‣ new techniques for control without notch filters —|| AE in the loop

funded by

partners

F L I G H T P H Y S I C S I N O VA A E R O D E F E S A

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Desirable background

Let’s first quickly review some topics you may need during the course

‣ Reference systems & transformation matrices

‣ RB flight mechanics

‣ Aeroelasticity

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1st list of exercises

Solve exercises 2.1, 2.2, 2.9 of

Schmidt, D. K., Modern Flight Dynamics. Mc Graw Hill, 2012

Due: next Thursday, March 4th

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