ab-267 dynamics & control of flexible...
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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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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 F L ÁV I O S I LV E S T R E
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
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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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