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28-29 January 2010
AIRBUS Benchmark Overview
Final COFCLUO workshop
Presented by
Guilhem PUYOU1, Adrien BERARD2
1 Stability and Control Department2 Load and Aeroelasticity DepartmentAIRBUS
28-29 January 2010P
age 2
© AIRBUS FRANCE S.A.S. All rights reserved. Confidential and proprietary document. Contents
•A
IRB
US
motivations
•O
ne word about A
IRB
US
flight control philosophy•
Nonlinear benchm
ark�
Modelling
�Flight envelope &
Varying param
eters�
Criteria
•Integral benchm
ark �
Modelling
�Flight envelope &
Varying param
eters�
Criteria
•B
aseline pratices
28-29 January 2010P
age 3
© AIRBUS FRANCE S.A.S. All rights reserved. Confidential and proprietary document. Motivations
•N
on linear benchmark:
�N
on linearmodelling of rigid body
aircraft and control laws.
�Tw
o major issues:
–A
ssess performance in a non linear
framew
ork–
Validate full flight dom
ain protection�
AIR
BU
S expectations:
–A
lternative to the Monte-C
arlo approaches–
Reduce w
orkloadinduced by “m
anual” validation of flight domain
protection
•Integral benchm
ark:�
Linear modelling of flexible body
aircraft (including rigid one).�
Challenges:–
Manage high order
of state space representations–
Provide continuous
validation process on the whole param
etrical domain
–A
fast method for w
orst case search and identification of critical param
eters combinations
28-2
9 Ja
nuar
y 20
10P
age
4
© AIRBUS FRANCE S.A.S. All rights reserved. Confidential and proprietary document.
Flig
ht c
ontro
l law
s ph
iloso
phy
Pilo
ting
devi
ces
28-29 January 2010P
age 5
© AIRBUS FRANCE S.A.S. All rights reserved. Confidential and proprietary document. Flight control laws philosophy
Flight domain protection
Peripheral flight envelope
Protection laws activated
Permanent deflexion on stick is required to keep the
steady state
Norm
al flight envelope“N
ormal” law
activated
Protection not activated
Stick released or AP active w
ill not fly beyond this limit
Manoeuvring A/C
will fly at
this safe limit w
ith controls on stops
If exceptional upset brings the A/C
in this domain, protections are
deactivated and full authority is restored
Overspeed
Vc
Bank angle
ϕϕϕ ϕ
Load factorN
z
Pitch attitude
θθθ θ
Angle of attackLow
speedααα α
28-29 January 2010P
age 6
© AIRBUS FRANCE S.A.S. All rights reserved. Confidential and proprietary document. Flight control laws philosophy
Longitudinal axis control: Pitch control (1/2)
•Pitch norm
al law (N
zlaw
):�
Control the
flight pathof the aircraft, through
a load factordem
and. �
Load factor is limited
to [-1g ; 2.5g]in clean configuration �
Impulse on the
stick leadsto a flight path
angle change. Atconstant
speed, theflight path
angle remains roughly
constant, stick released.
+2.5gN
z-1g
28-29 January 2010P
age 7
© AIRBUS FRANCE S.A.S. All rights reserved. Confidential and proprietary document. Flight control laws philosophy
Longitudinal axis control: Pitch control (2/2)
Pitch control principle
Longitudinal stick deflection
Objective =
Pitch rate
28-29 January 2010P
age 8
© AIRBUS FRANCE S.A.S. All rights reserved. Confidential and proprietary document. Flight control laws philosophy
Longitudinal axis control: angle of attack protection (1/2)
•A
ngle of attackprotection (low
speed or stallprotection):�
Theobjectives of the
angle of attackprotection law
are:–
introduce static stability at lowspeed,
–protect the aircraftagainst stall,
–provide the
best possible manoeuvrability
when necessary
�The
angle of attack target is'alpha prot'w
ith neutral stick and 'alpha m
ax' with
full back-stick.
CL
(Cz)
Angle of attack ααα α
ααα αStall : Loss of lift and/or aircraft control (aural stall w
arning before)
ααα αm
ax : in AOA protection law
, AO
A reached with fully aft stick
ααα αfloor : activation (close to ααα α
floor) of alpha floor function
ααα αprot: entry in AO
A protection law
ααα αVLS : AO
A reached the Lowest Selectable Speed (VLS is com
puted in FMG
EC)
28-29 January 2010P
age 9
© AIRBUS FRANCE S.A.S. All rights reserved. Confidential and proprietary document. Flight control laws philosophy
Longitudinal axis control: angle of attack protection (2/2)
Stall protection
28-29 January 2010P
age 10
© AIRBUS FRANCE S.A.S. All rights reserved. Confidential and proprietary document. Flight control laws philosophy
Longitudinal axis control: high speed protection (1/2)
•H
ighspeed protection
�H
ighspeed protection law
limits the
possible speed/mach
excursionsbeyond
maxim
um speed (V
max) and M
ach number
(Mm
ax).�
The Vm
ax/Mm
ax target isV
MO
/MM
O stick free and (roughly)
VMO
/MM
O+15kts full forw
ardstick.
•Pitch attitude protection�
Enhance the effectivenessof angle of attack
and highspeed
protectionsin extrem
econditions, by lim
iting the aircraft dynamic
close to theangle of attack
and speed limits.
28-29 January 2010P
age 11
© AIRBUS FRANCE S.A.S. All rights reserved. Confidential and proprietary document. Flight control laws philosophy
Longitudinal axis control: high speed protection (2/2)
Hight speed protection
28-29 January 2010P
age 12
© AIRBUS FRANCE S.A.S. All rights reserved. Confidential and proprietary document. Flight control laws philosophy
Lateral axis control
•The objective of the lateral norm
al law is to control the
roll and yaw axis
of the aircraft, through roll rate and sideslip dem
ands.
•The m
ain features of the lateral normal law
are the follow
ing:�
the roll stickis translated into a roll rate dem
andat zero sideslip: the m
aximum
roll rate demand m
ust not exceed 15°/s.
�neutral spiral stability
must be achieved up to 33°
bank (constant bank angle with stick at neutral),
while positive spiral stability
must be restored
above 33° bank(bank angle com
es back to 33° w
ith stick at neutral)�
the maxim
um bank angle m
ust be limited to 66°
�the pedal inputcom
mands a com
bination of sideslip and roll angle
-15°/sdϕϕϕ ϕ/dt
+15°/s
βββ β+ kϕϕϕ ϕ
28-29 January 2010P
age 13
© AIRBUS FRANCE S.A.S. All rights reserved. Confidential and proprietary document. Flight control laws philosophy
Lateral axis control
Bank angle lim
it depends upon the condition :
•αprotlaw
•High speed protection
•External disturbance
Roll objectives
Roll rate value depends upon the condition :
•A
lpha prot
•E
ngine dissymetry
automatic
pitch trim
negative stick entry
(dpm)
positive roll rate dΦΦΦ Φ
/dt(m
ax 15°/s)
return to 33°
attitude maintained
33°
67°
when pilot
releases the stick
Bankangle
limit
67°
Bankangle
limit
pitch remain
constant
pitch compen
sation reduced
automatic
turn co-ordination
ΦΦΦ Φ> 0
dpm< 0
automatic
pitch trim
negative stick entry
(dpm)
positive roll rate dΦΦΦ Φ
/dt(m
ax 15°/s)
return to 33°
attitude maintained
33°
67°
when pilot
releases the stick
Bankangle
limit
67°
Bankangle
limit
pitch remain
constant
pitch compen
sation reduced
automatic
turn co-ordination
return to 33°
attitude maintained
33°
67°
when pilot
releases the stick
Bankangle
limit
67°
Bankangle
limit
pitch remain
constant
pitch compen
sation reduced
automatic
turn co-ordination
ΦΦΦ Φ> 0
ΦΦΦ Φ> 0
dpm< 0
dpm< 0
28-29 January 2010P
age 14
© AIRBUS FRANCE S.A.S. All rights reserved. Confidential and proprietary document. Benchm
arksN
on linear benchmark
Non linear Benchmark
double clickto launch scenario.m
WIN
D
SENSO
RS
PILOT O
RD
ERS
& IN
PUTS
yOU
TPUTS
AIRBU
S FRAN
CE S.A.S. 2007.
ALL RIG
HTS R
ESERVED
. C
ON
FIDEN
TIAL AND
PRO
PRIETAR
Y DO
CU
MEN
T.
CO
NTR
OL LAW
S
AIRC
RAFT
ACTU
ATOR
S
Control devices or pilot
model used to perform
«
hold » comm
and
Sim
plified actuators including first order
dynamic and position
and rate saturations
Flight dynamics
equations using quaternion and based on a N
N m
odelling of the aerodynam
ic coefficients
Main filters and delays
Full flight control law
system including
protections
28-29 January 2010P
age 15
© AIRBUS FRANCE S.A.S. All rights reserved. Confidential and proprietary document. Modelling
Control surfaces and actuators
Non linear Benchmark
1dq (deg)
Realized order
upulo
y
Saturation
Rate lim
iter
LIMU
P
LIMLO
1
0.1s+11st or 2nd order transfer function
1dqco (deg)
Com
manded order
28-29 January 2010P
age 16
© AIRBUS FRANCE S.A.S. All rights reserved. Confidential and proprietary document. Modelling
Flight Mechanics (1/3)
Non linear Benchmark
•Fundam
ental equation(V
velocity vector, Ωrotation vector)
�Forces
Mom
ents� �� �
� �� �∧
+∂ ∂
=V
t V
mF
��
��
()
()
I
t I
M
��
��
⋅∧
+∂ ⋅
∂=
FyA
ERO
FxA
ERO
FzA
ERO
MrA
ERO
Mp
AER
O
Mq
AER
O
FyA
ERO
FxA
ERO
FzA
ERO
MrA
ERO
Mp
AER
O
Mq
AER
O
Fzg
FygFzg
Fxg
mg
mg
Fzg
FygFzg
Fxg
mg
mg
�G
ravity
FxEN
G R
FxEN
G L
FxEN
G R
FxEN
G L
�E
ngines
•Forces and m
oments
�A
erodynamic loads
28-29 January 2010P
age 17
© AIRBUS FRANCE S.A.S. All rights reserved. Confidential and proprietary document. Modelling
Flight Mechanics (2/3)
Non linear Benchmark
•Focus on aerodynam
ic loads modelling:
•Local m
odellingof aerodynam
ic coefficients by neural networks:
�(M
ach,alpha,beta)domain for longitudinal coefficients
�(M
ach)domain for lateral coefficients
•Local m
odels dependencies:�
Longitudinalaerodynamic coefficients (C
y,Cl,C
n): alpha,beta,M
ach,q,altitude,centerof gravity position, horizontal tail plane deflexion, elevator deflexion, spoiler deflexion
�Lateralaerodynam
ic coefficients (Cx,C
z,Cm
) : alpha,beta,M
ach,p,r,altitude,centerof gravity position, inner ailerons deflexion, outer ailerons deflexion, rudder deflexion, spoiler deflexion
•G
lobalcoefficient computation by
local models interpolation.
Cx
V
S 2 1
Fx2
AIR
AER
O−
=C
l
V c
S 2 1
Mp
2A
IRA
ERO
AER
O=
Cy
V
S 2 1 -
Fy
2A
IRA
ERO
=C
m
V c
S 2 1
Mq
2A
IRA
ERO
AER
O=
Cz
V
S 2 1
Fz2
AIR
AER
O−
=C
n
V c
S 2 1
Mr
2A
IRA
ERO
AER
O=
28-29 January 2010P
age 18
© AIRBUS FRANCE S.A.S. All rights reserved. Confidential and proprietary document. Modelling
Flight control laws (1/2)
Non linear Benchmark
FLIGH
T MAN
AGEM
ENT
SYSTEMN
avigation P
erformances -Flight planning
Guidance
long term control
(~ 60s)
FLIGH
T GU
IDAN
CE &
AU
TO-THR
UST SYSTEM
Flight path & speed control
medium
term control
(~ 10s)
FLIGH
T CO
NTR
OL SYSTEM
Attitude &
acceleration control S
tructural modes dam
pingS
urfaces servo-loops short term
control (~ 5s)
Engines
Surfaces
SENSO
RS
Aircraft R
esponse
Piloting O
rders
Thrust Orders
Guidance
Objectives
ErtrtetErtertErtertttrrrreteeErterterttErtertete
ErtrtetErtertErtertttrrrreteeErterterttErtertete
NDND
Flight plan selection and optim
isationAltitude, slope heading
and speed selection
PFDPFD
ECA
MEC
AM
Attitu
de and acceleration piloting
RU
D TR
IM10,4
RESET
RU
D TR
IM10,4
RESET
0123F
0123F
0123F
0123FW
arning
Manual flight control law
validation benchmark
A/TH
R is provided for easier m
anoeuvre simulation
28-29 January 2010P
age 19
© AIRBUS FRANCE S.A.S. All rights reserved. Confidential and proprietary document. Modelling
Flight control laws (2/2)
Non linear Benchmark
•Pitch axis control: scheduling param
eters (Vc, Mach, cg)
•Lateral axis control: scheduling param
eters (Vc, M
ach)
•Speed control: scheduling param
eters (Vc, M
ach)
VMO
/MM
O
PRO
TECTIO
N
?PR
OTEC
TION
nzN
OR
MA
L LAWD
QE
?PR
OTEC
TION
DQ
OR
DER
S C
HO
ICE
INTEG
RATO
R
MAN
AGEM
ENT AN
D
ELEVATOR
D
EFLECTIO
N
CO
MPU
TATIO
ND
QM
OD
Q*
OIH
DQ
/THS
CO
UPLIN
G
LATE
RA
L NO
RM
AL
LAW
PE
DA
LS
MA
NA
GE
ME
NT
DRE
DPELEC
DRN
DPN
DPE
DP
/DR
O
RD
ER
C
HO
ICE
DPM
OA
LE*O
ALI*
OS
P1*O
SP2*
OS
P3*O
SP4*
OS
P5*O
SP6*
OLD
EGRY
D
LATE
RA
L K
INE
MA
TICS
Elevator
Horizontal tail plane
Ailerons
Spoilers
Rudder
Engine 1
Engine 2
AUTO
-THR
UST
SP
EE
D
TAR
GE
TP
I/MG
1
PI/M
G2
28-29 January 2010P
age 20
© AIRBUS FRANCE S.A.S. All rights reserved. Confidential and proprietary document. Flight envelope & varying param
etersFlight envelope
•N
ormal flight envelope
�Load factor: -1g < N
z< 2.5g in clean configuration and 0g < N
z< 2g in
high lift configurations�
Pitch attitude: -15° < θ
< 30°�
Angle of attack: -5° < α
< αprot
�A
ltitude: 0 < Zp< 41000 ft
�S
peed (in flight): Vα
prot < Vcas
< VM
O (=330 kts)
�M
ach (in flight): 0.2 < Mach < M
MO
(=0.86)�
Roll angle: -33° < ϕ
< 33 °�
Weight and
Centerof gravity location: w
ithin the weight and balance
diagram
•Peripheral flight envelope
�A
ngle of attack: -5° < α< α
max
�S
peed (in flight): Vα
max < Vcas
< VD (=365 kts)
�M
ach (in flight): 0.2 < Mach < M
D (=0.93)
�R
oll angle: -66° < ϕ< 66 °
Non linear Benchmark
28-29 January 2010P
age 21
© AIRBUS FRANCE S.A.S. All rights reserved. Confidential and proprietary document. Flight envelope & varying param
etersFlight envelope
Peripheral flight envelope
Norm
al flight envelopeO
verspeedVc
Bank angle
ϕϕϕ ϕ
Load factorN
zPitch
attitudeθθθ θ
Angle of attackLow
speedααα α
VD
MD
MM
O
VMO
ααα αprot
ααα αm
ax
-15°/ +30°33°
66°-1g / +2.5g
28-29 January 2010P
age 22
© AIRBUS FRANCE S.A.S. All rights reserved. Confidential and proprietary document. Flight envelope & varying param
etersFlight dom
ain
TO D
O
Non linear Benchmark
0
5000
10000
15000
20000
25000
30000
35000
40000100150
200250
300350
400450
500550
6 0
VTAS (kts)
Altitude (ft)
Mach
0.20.3
0.40.5
0.60.7
0.80.9
MM
O
VM
O
MD
VD
Vααα α
stallV
ααα αm
axV
ααα αprot
MM
OM
D
VMO
VD
Zpm
ax
28-29 January 2010P
age 23
© AIRBUS FRANCE S.A.S. All rights reserved. Confidential and proprietary document. Benchm
arksN
on linear benchmark
Non linear Benchmark
•C
riteria�
Unpiloted aircraft stability
�P
iloted aircraft stability�
Perform
ance assessment: Turn coordination
�M
anoeuvrability requirements: longitudinal axis
�Flight dom
ain protection (AoA
, Pitch, S
peed/Mach, R
oll, Load factor)
•C
onditions:�
For any initial flight conditions within the flight envelope
�For any pilot inputs
�For any w
ind perturbations within the certified set
�A
ssuming uncertainties on aerodynam
ic coefficients
28-29 January 2010P
age 24
© AIRBUS FRANCE S.A.S. All rights reserved. Confidential and proprietary document. Clearance problem
Unpiloted aircraftstability
•Initial pointA
ny trimm
ed point in the overall flight domain w
ithout pilot inputs.
•C
riteria�
Closed loop m
ust remain stable
�Stability can be relaxed to the existence of slow
ly divergent modes,
provided that the time of doubling
of the divergent variable is more
than 6s.
•U
ncertainties�
robustness to CG
data must be guaranteed.
Even w
ith wrong cg values used by the control law
s (between m
in and m
ax CG
values), the closed-loop stability must be guaranteed.
Therefore uncertain parameter to be considered is cg value in input of
the flight control laws. This value can vary from
the minim
um value to
the maxim
um value w
hatever the trimm
ed point value.
Non linear Benchmark
28-29 January 2010P
age 25
© AIRBUS FRANCE S.A.S. All rights reserved. Confidential and proprietary document. Clearance problem
Piloted aircraftstability
•Initial point
�A
ny trimm
ed point in the overall flight domain.
�C
onstant pedal input (so the sideslip will be zero or non zero) and the
right side-stick input necessary to maintain constant heading.
•C
riteriaS
tarting from the trim
med point w
ith deflected control devices, so sideslip and heading are both steady, and w
ith or without w
ind. The aircraft must
reach an other stable situation, within the norm
al flight envelope, when the
control devices are released or when the w
ind stops.
•U
ncertainties �
Global aerodynam
ic coefficients uncertainties: 10% on
(Cx,C
y,Cz,C
l,Cm
,Cn)
�W
ind gradient occurrence (gradient between [1;5kts/s], am
plitude<20kts, any orientation).
Non linear Benchmark
28-29 January 2010P
age 26
© AIRBUS FRANCE S.A.S. All rights reserved. Confidential and proprietary document. Clearance problem
Piloted aircraftstability
•M
anoeuvre
Non linear Benchmark
Longitudinal stick
Lateral stick
Pedals
Altitude hold
time
dpm
Release
Heading hold
time
dre
Release
Constant input
28-29 January 2010P
age 27
© AIRBUS FRANCE S.A.S. All rights reserved. Confidential and proprietary document. Clearance problem
Perform
ance assessment: Turn coordination
•Initial pointA
ny trimm
ed point in the normal flight dom
ain.
•C
riteriaFor any lateral stick input, w
ithout pedal input, the sideslip value must
remain low
er than 1° while the bank angle does not re
ach 33°.
•U
ncertainties�
Flight path angle value (included in the initial point selection).�
Constant lateral side stick value w
ithin devices capabilities.�
Global aerodynam
ic coefficients uncertainties: 10\% on
(Cx,C
y,Cz,C
l,Cm
,Cn).
Non linear Benchmark
28-29 January 2010P
age 28
© AIRBUS FRANCE S.A.S. All rights reserved. Confidential and proprietary document. Clearance problem
Perform
ance assessment: Turn coordination
•M
anoeuvre
Non linear Benchmark
Longitudinal stick
Lateral stick
Pedals
Flight path hold
No input
time
dpm
Constant input
28-29 January 2010P
age 29
© AIRBUS FRANCE S.A.S. All rights reserved. Confidential and proprietary document. Clearance problem
Manoeuvrability requirem
ents: longitudinal axis
•Initial pointA
ny trimm
ed point in the peripheral flight domain w
ithout pilot inputs.
•C
riteria�
low speed: pilot m
ust be able to modify short term
trajectory within the
flight envelope. When pulling the stick, the short term
Cz
response must
be compared to the natural aircraft capability:
�high speed: betw
een VM
O and V
MO
+15kts, nose-down authority m
ust rem
ain greater than 0.3g.
•U
ncertainties�
Global aerodynam
ic coefficients uncertainties: 10% on
(Cx,C
y,Cz,C
l,Cm
,Cn).
�Longitudinal side-stick constant input w
ithin the devices capabilities .
Non linear Benchmark
28-29 January 2010P
age 30
© AIRBUS FRANCE S.A.S. All rights reserved. Confidential and proprietary document. Clearance problem
Manoeuvrability requirem
ents: longitudinal axis
•M
anoeuvre
Non linear Benchmark
Longitudinal stick
Lateral stick
Pedals
No input
No input
time
dqm
Constant input
28-29 January 2010P
age 31
© AIRBUS FRANCE S.A.S. All rights reserved. Confidential and proprietary document. Clearance problem
Flight domain protection
•Initial pointA
ny trimm
ed point in the normal flight dom
ain without pilot inputs
•C
riteriaFor any pilot inputs and w
ind perturbations included in lower-described
subsets, the aircraft response must rem
ain in the following envelope :
�Load factor: -1g < N
z< 2.5g | no overshoot
�P
itch attitude: –
-15° < θ< 30°
–overshoot: low
er than 1 degree at high mach and low
er than 2 degrees at low m
ach (M
<0.5). �
Angle of attack: –
-5° < α< α
max
–overshoot: low
er than 1 degree at high mach and low
er than 2 degrees at low m
ach (M
<0.5). �
Altitude: 0 < Zp
< 41000 ft�
Speed (in flight): V
αm
ax <V
cas< V
D | no overshoot
�M
ach (in flight): 0.2 < Mach < M
D | no overshoot
�R
oll rate p must not exceed 15°/s.
�R
oll angle: -66° < ϕ< 66 °
Non linear Benchmark
28-29 January 2010P
age 32
© AIRBUS FRANCE S.A.S. All rights reserved. Confidential and proprietary document. Benchm
arksIntegral B
enchmark
Integral Benchmark
Kernel part of the law
s (w
ithout protections). R
oughly linear but scheduled
Sim
plified actuators including first order
dynamic and position and
rate saturations
State space representation
provided for several (V
c,Mach,M
ass,Fuel tanks) cases
Main filters and delays
28-29 January 2010P
age 33
© AIRBUS FRANCE S.A.S. All rights reserved. Confidential and proprietary document. Modelling
Naturalaircraft: basic equations
•Origin:
�S
tructural dynamics equation
�G
eneralized aerodynamic loads (m
ovement, turbulence, control
surfaces)�
Rationalization of generalized aerodynam
ic loads
Integral Benchmark
28-29 January 2010P
age 34
© AIRBUS FRANCE S.A.S. All rights reserved. Confidential and proprietary document.
Integral model
Aerodynamic m
odel
•steady and unsteady airforces
•methods of different accuracy
(DLM
, unsteady CFD
)
A
Modelling
Natural aircraft: D
ata computation
•finite elem
ents•stiffness•m
asses incl. fuel & payload
Structuralmodel
KM
Integral Benchmark
28-29 January 2010P
age 35
© AIRBUS FRANCE S.A.S. All rights reserved. Confidential and proprietary document. Modelling
Natural aircraft: State space m
atrices
Integral Benchmark
Rigid
modes
Flexiblem
odes
Delays
modes
Control surfaces
deflexion
Vertical and lateral
Wind
++
p, q, r, ϕ, θ, α,N
y,N
z, β
Flight m
echanics
Loads and accelerations
for ≠pts
Tx,Ty,Tz, M
x,My, M
z, N
z, Ny
All state m
atrices havethe sam
estructure butthe
statenum
ber canchange:consistency loss
28-29 January 2010P
age 36
© AIRBUS FRANCE S.A.S. All rights reserved. Confidential and proprietary document. Modelling
Natural aircraft: flight points and m
ass cases
•A
wide set of linear a/c m
odels are delivered covering: mass, cg,
fuel, speed, Mach num
ber�
State-space integral m
odel with som
e hundreds of states�
Flight points: 3 Mach w
ith 3 speed cases = 9 flight points�
Mass cases: 18 m
ass cases (described by ratios of fuel tank loads)�
2 flight situations: longitudinal and lateralŁ
324 integral models
Integral Benchmark
0.650.7
0.750.8
0.850.9
0.951
200
250
300
350
400
Mach num
ber
Vc (kts)
28-29 January 2010P
age 37
© AIRBUS FRANCE S.A.S. All rights reserved. Confidential and proprietary document. Benchm
arksIntegral B
enchmark
Integral Benchmark
•A
eroelastic stability criterion�
Eigenvalues stability–
max
i (Re(λ
i ))<α�
Stability m
argins requirement:
–A
llowable gain range: gains x2
–A
llowable phase range: [-90°,+90°]
•C
omfort in turbulence
�||T
wind→
acc, CL (s)||2 ≤
||Tw
ind→acc, O
L (s)||2•
Loads in turbulence•
Loads during manoeuvres
28-29 January 2010P
age 38
© AIRBUS FRANCE S.A.S. All rights reserved. Confidential and proprietary document. Clearance problem
Aeroelastic stability criterion
�Flutter curves analysis (frequency and dam
ping) …
�S
tability margins requirem
ent: A
llowable gain range: gains x2
Allow
able phase range: [-90°,+90°]
Integral Benchmark
28-29 January 2010P
age 39
© AIRBUS FRANCE S.A.S. All rights reserved. Confidential and proprietary document. Clearance problem
Load response to turbulence
•The target is to compute the variance of the load outputs.
•The variance is the area under the power spectral density (P
SD
)curve.•The variance can be w
ritten as the H2 norm
of the transfer between w
hite noise input and load outputs using a von K
arman
filter.
•Criteria:
The variance must not overshoot a given m
aximum
value. In practice, increm
ental results are used.
Integral Benchmark
28-29 January 2010P
age 40
© AIRBUS FRANCE S.A.S. All rights reserved. Confidential and proprietary document. Clearance problem
Com
fort criterion
•The target is to compute the variance of filtered accelerations.
•The variance is the area under the power spectral density (P
SD
)curve.•The variance can be w
ritten as the H2 norm
of the transfer between w
hite noise input and filtered acceleration outputs using a von K
arman
filter.
•Criteria:
The objective is to verify a certain improvem
ent (or to see worsening) in
comfort w
hen compared to the open-loop case.
Integral Benchmark
28-29 January 2010P
age 41
© AIRBUS FRANCE S.A.S. All rights reserved. Confidential and proprietary document. Clearance problem
Manœ
uvre criteria
•R
oll manoeuvre:
apply full roll stick. When p
max (m
ax roll speed) is reached, release the stick back to zero.p
max = 15°/s
•Pitch m
anoeuvre:pull (or push) the stick. W
hen 1.5g (or -1g) for incremental load factor is
reached, release the stick back to zero.•
Yaw m
anoeuvre:apply full pedal (rpedal). W
hen a given βm
ax (max yaw
angle, function of Vcand high-lift configuration) is reached, release the pedal back to zero. Integral m
odels use clean configuration.
•C
riteria:Theobjective is
to find faster the worstm
ass cases for the loadpoint of view
.
Integral Benchmark
28-29 January 2010P
age 42
© AIRBUS FRANCE S.A.S. All rights reserved. Confidential and proprietary document. Validation m
ethodsP
rogram
launchD
evelopment
launch1rst Flight
Certification
EIS
Feasibility studiesD
evelopment
Series
t
Major H
Q m
odel update after identification
Design methods
Linear design on rigid A/C
(normal law
s)
Linear design on flexible A/C
*
Nonlinear design (H
Q protection law
s)Fine Tuning
Linear analysis •H
Q:
OL/C
L stability, margins, frequency dom
ain response, tim
e-domain perform
ance (v.s. nominal dom
ain)•A
eroelastic:O
L/CL stability, m
argins•Loads :frequency dom
ain response
Validation methods
Nonlinear analysis
•HQ
:N
L margins (P
IO), tim
e-domain perform
ance (v.s. full flight dom
ain)•Loads :tim
e-domain perform
ance
Robustness analysis (gridding
based)R
obustness v.s. : more flight points, m
ore scenarios, aero-data uncertainties, delays, pilot dynam
ics
STR
(simulation test request)
FTR (flight test request)
1rst HQ
and Load m
odels
Failure cases analysis **
Out of C
OFC
LUO
scope
1rst Aeroelastic
model
Nonlinear design (Loads protection law
s)
*If necessary after analysis on aeroelastic m
odel
Program
launch
Developm
ent launch
1rst FlightC
ertificationE
IS
Feasibility studiesD
evelopment
Series
t
Major H
Q m
odel update after identification
Design methods
Linear design on rigid A/C
(normal law
s)
Linear design on flexible A/C
*
Nonlinear design (H
Q protection law
s)Fine Tuning
Linear analysis •H
Q:
OL/C
L stability, margins, frequency dom
ain response, tim
e-domain perform
ance (v.s. nominal dom
ain)•A
eroelastic:O
L/CL stability, m
argins•Loads :frequency dom
ain response
Validation methods
Nonlinear analysis
•HQ
:N
L margins (P
IO), tim
e-domain perform
ance (v.s. full flight dom
ain)•Loads :tim
e-domain perform
ance
Robustness analysis (gridding
based)R
obustness v.s. : more flight points, m
ore scenarios, aero-data uncertainties, delays, pilot dynam
ics
STR
(simulation test request)
FTR (flight test request)
1rst HQ
and Load m
odels
Failure cases analysis **
Out of C
OFC
LUO
scope
1rst Aeroelastic
model
Nonlinear design (Loads protection law
s)
*If necessary after analysis on aeroelastic m
odel
28-29 January 2010P
age 43
© AIRBUS FRANCE S.A.S. All rights reserved. Confidential and proprietary document. Validation m
eans
Program
launch
Developm
ent launch
1rst FlightC
ertificationE
IS
Feasibility studiesD
evelopment
Series
t
real-time
desktop sim
ulator
OC
ASIME (+ basic piloting devices and display)
EPOPE (+ piloting devices and display)
A/C –1 (+ real com
puters)
A/C 0 (+ real actuators and hydraulics)
Flight test A/C
Advanced Sim
ulators
A/C
MATLAB
, SIMPA*, ATO
SMA*, ATLAS*
MATLAB
, SIMPA*, ATO
SMA*, ATLAS*
•Analytical inputs
•Control designer in the loop
•Pilot m
odel in the loop
•Hum
an pilot in the loop
non real-time
desktop sim
ulator
*In-house software
Major H
Q m
odel update after identification
1rst HQ
and Load m
odels1rst A
eroelasticm
odel
Program
launch
Developm
ent launch
1rst FlightC
ertificationE
IS
Feasibility studiesD
evelopment
Series
t
real-time
desktop sim
ulator
OC
ASIME (+ basic piloting devices and display)
EPOPE (+ piloting devices and display)
A/C –1 (+ real com
puters)
A/C 0 (+ real actuators and hydraulics)
Flight test A/C
Advanced Sim
ulators
A/C
MATLAB
, SIMPA*, ATO
SMA*, ATLAS*
MATLAB
, SIMPA*, ATO
SMA*, ATLAS*
•Analytical inputs
•Control designer in the loop
•Pilot m
odel in the loop
•Hum
an pilot in the loop
non real-time
desktop sim
ulator
*In-house software
Major H
Q m
odel update after identification
1rst HQ
and Load m
odels1rst A
eroelasticm
odel
28-29 January 2010P
age 44
© AIRBUS FRANCE S.A.S. All rights reserved. Confidential and proprietary document. Baseline solution
•U
se of non-real time sim
ulator:�
Perform
ance assessment: analysis on fine grids providing calibrated pilot
inputs�
Worst case detection: M
onte-Carlo based analysis
Flight domain coverage
0 %100 %
$$$ $
Validation mean
Non-real tim
e sim
ulator
Real tim
e sim
ulator
Flight test A/C
Series A
/CS
eries A/C
Flight domain coverage
0 %100 %
$$$ $
Validation mean
Non-real tim
e sim
ulator
Real tim
e sim
ulator
Flight test A/C
Series A
/CS
eries A/C
28-29 January 2010P
age 45
© AIRBUS FRANCE S.A.S. All rights reserved. Confidential and proprietary document. Baseline
solution
Flight domain coverage
0 %100 %
$$$ $
Validation mean
Non-real tim
e sim
ulator
Real tim
e sim
ulator
Flight test A/C
Series A
/C??
Series A
/C
Flight domain coverage
0 %100 %
$$$ $
Validation mean
Non-real tim
e sim
ulator
Real tim
e sim
ulator
Flight test A/C
Series A
/C??
Series A
/C
•U
se of non-real time sim
ulator:�
Perform
ance assessment: analysis on fine grids providing calibrated pilot
inputs�
Worst case detection: M
onte-Carlo based analysis