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6.2011-6407

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AIAA 2011-6407
AIAA Guidance, Navigation, and Control Conference
08 - 11 August 2011, Portland, Oregon
Analysis of Aircraft Multiple Engine Configurations for
Fault Tolerant Control
Downloaded by UNIVERSITY OF ADELAIDE on October 27, 2017 | http://arc.aiaa.org | DOI: 10.2514/6.2011-6407
Mario G. Perhinschi*, Frederick Beamer†
West Virginia University, Morgantown, WV, 26506
In this paper, a formal framework is presented that allows to analyze the potential of
using engine thrust control for aircraft actuator failure accommodation. Three sets of
parameters have been identified as critical: number of engines and their position, engine
thrust and throttle dynamics, and type and severity of the actuator failure. A mathematical
model was developed that allows to determine the values of some of the parameters when the
other are imposed and to construct envelopes under actuator failure conditions. A
Matlab/Simulink simulation environment was built including the model of a large transport
that can accommodate up to ten engines. Failures on the rudder, left or right aileron, or left
or right elevator were implemented. The simulation environment was used to verify the
analytical results and demonstrate the fault tolerant capabilities of multiple engine
configurations.
Nomenclature
φ, θ, ψ
δjC
FB
FE
FTi
=
=
=
=
=
M Cj
= moment produced by the failure of an aerodynamic control surface
M ei
= moment produced by the ith engine
M Fj
= moment produced by aerodynamic control surface j
M Nj
=
N
=
O
=
OXYZ
=
OEXEYEZE =
the Earth
Pi
=
PiXTiYTiZTi=
RF
=
! OPi
r
=
! OPi
r
=
A
~r OPi
=
Euler Angles
commanded deflection of control surface j
fixed body reference frame with respect to the aircraft
Earth reference frame
fixed body reference frame with respect to the ith engine
nominal moment produced by an aerodynamic control surface
number of engines
center of mass of the aircraft
system of coordinates in relation to FB with the origin at the mass center of the vehicle.
system of coordinates in relation to FE with the origin at an arbitrary reference point on the surface of
point of application of thrust for the ith engine
system of coordinates in relation to Pi for each engine
reference frame
position vector of the point of application of thrust
[ ]
[ ]
[!r ]
= position vector of P1 with respect to P2 with respect to SC FA
~r P2P1
SC
= tensor matrix of r 2 1
= system of coordinates
A
P2 P1
*
†
A
position vector with respect to a coordinate system associated to reference frame A.
component vector with respect to reference frame FA of the skew symmetric tensor ~r OPi .
!P
P
Associate Professor, Dept. of Mechanical and Aerospace Engineering, AIAA Senior Member
Graduate Student, Dept. of Mechanical and Aerospace Engineering
1
American
Instituteand
ofAstronautics,
Aeronautics
Copyright © 2011 by authors. Published by the American Institute
of Aeronautics
Inc.,and
with Astronautics
permission.
!
Ti
= thrust vector of engine i
!
∆Ti
= thrust for control produced by engine i
!
!
VA
= components of vector V with respect to FA
XMYMZM = system of coordinates with respect to FTi
Subscripts
e
= elevator or stabilator
a
= aileron
r
= rudder
c
= canard
f
= flaps
L
= “left” in conjunction with the control surfaces
R
= “right” in conjunction with the control surfaces
Downloaded by UNIVERSITY OF ADELAIDE on October 27, 2017 | http://arc.aiaa.org | DOI: 10.2514/6.2011-6407
[]
I.
Introduction
A
ircraft actuator failures or malfunctions have been identified throughout the years as a leading source of
accidents for all classes of aircraft1-4. Significant research efforts have recently been directed towards
developing fault tolerant control laws that can accommodate actuator failures5-9 and increase the safety of aircraft
operation. Actuator failures can be completely compensated if enough control redundancy is available. Depending
on their number and location, aircraft engines can provide some level of control redundancy that under certain
conditions can be critical. This capability has been investigated only in a limited manner10-14.
A prior study in automatic adaptive control has utilized neural network algorithms to assess and compensate
for damages to aerodynamic control surfaces by using engine control10. This study demonstrated that propulsion
control could provide additional control authority and redundancy when necessary but also exhibited the limitations
due to slower engine response.
Further research has been undertaken at West Virginia University (WVU) in developing a simulation
environment for the design and evaluation of direct and indirect adaptive flight control laws with built-in fault
tolerant capabilities15. This system is designed to accommodate aerodynamic control surface failures and critical
sensor failures through artificial neural network augmentation and control re-distribution among healthy actuators.
However, the additional control redundancy and the use of the aircraft engines as control mechanisms are not
investigated.
In this paper, a general framework is developed for the analysis of the control redundancy potential of
aircraft engines and possibly other ad-hoc propulsive devices. The model presented offers the analytical tools for
the design of emergency control laws that could use engines to accommodate aircraft actuator failures. A
preliminary control system utilizing expert knowledge in a fuzzy logic control architecture is developed and used for
demonstration within the Matlab/Simulink simulation environment.
The paper is organized as follows. The multiple engine model for fault tolerant control is described in
Section II. A brief analysis of the engine compensation for specific actuator failures is presented in Section III. The
WVU simulation environment is described in Section IV followed by a discussion of the fault tolerant control laws
in Section V. Simulation results are presented in Section VI for several typical actuator failures. Finally, some
conclusions are summarized in Section VII followed by acknowledgements and a bibliographical list.
II.
Multiple Engine Model for Fault Tolerant Control
A. Reference Frames and Systems of Coordinates
The following reference frames (RF) and systems of coordinates (SC) associated to them are used within this
paper:
Earth reference frame denoted by FE is assumed to be inertial. The associated system of coordinates
O E X E YE Z E is defined with the origin (or base point) at an arbitrary reference point O E on the surface of the
Earth, with EZ E along the local vertical, positive down, EX E arbitrarily oriented within the flat surface of the
Earth and EYE perpendicular and according to the right-hand rule.
Body reference frame denoted FB is fixed with respect to the aircraft, which is assumed a rigid body. The system
of coordinates OXYZ has the origin at the mass center of the vehicle O with the longitudinal axis OX positive
2
American Institute of Aeronautics and Astronautics
forward, the vertical axis OZ positive downward, and the lateral axis OY positive to the right of the pilot. The
orientation of the three axis with respect to FE is defined by the Euler angles ϕ , θ , ψ .
Engine #i reference frame denoted FTi is defined for each aircraft engine. Note that for the purpose of this paper,
Downloaded by UNIVERSITY OF ADELAIDE on October 27, 2017 | http://arc.aiaa.org | DOI: 10.2514/6.2011-6407
“aircraft engine” include not only the conventional hardware used for vehicle propulsion but also any thrustproducing devices that can be used for control. The system of coordinates Pi X Ti YTi Z Ti is assumed to have its
origin at the center of mass Pi of the engine, which also corresponds to the point of application of the thrust. The
orientation of Pi X Ti is assumed along the thrust vector. The orientation of the engine SC is generally defined with
respect to FB by corresponding Euler angles for each engine: θ i and ψ i .
B. Vector Notations and Transformations
!
The components of a vector V with respect to a SC O A X A YA Z A in RF FA are denoted as:
!
V A = vx v y vz T
[] [
]A
(1)
Let the components of the same vector in another SC O B X B YB Z B , associated to the same RF or a different one
be:
!
V B = vx v y vz T
(2)
B
!
!
then:
(3)
V A = L AB V B
where L AB is a 3x3 transformation matrix depending on the trigonometric functions of position angles ϕ , θ , ψ of
CS A with respect to CS B.
!
The position vector of point P1 with respect to point P2 (origin of vector arrow is at P2 ) is denoted as: r P2P1
and its components with respect to a SC in RF FA are:
! P2P1
T
(4)
r
A = r x r y rz A
!
The associated tensor ~r P2 P1 is defined such that for an arbitrary vector V we have:
! P2P1 ! ~ P2P1 !
×V = r
⋅V
r
(5)
[] [
[]
[]
[ ] [
]
]
and in components with respect to FA :
[
! P2 P1 !
×V
r
] [
A
= ~r P2 P1
] []
A
!
⋅V
A
 0

=  rz
− ry

− rz
0
rx
ry 

− rx 
0 
A
 Vx 
⋅ Vy 
 Vz 
(6)
A
C. Engine Force and Moment Compensation
The moment produced by one engine that can be used for control can be expressed as:
!
!
!
M ei = r OPi × ∆Ti
(7)
! OPi
is the position vector of the engine center of mass with respect to the center of mass of the aircraft and
where r
!
!
∆Ti is the amount of thrust available for control. In this preliminary analysis, the effects of ∆Ti on vehicle
acceleration will be neglected.
!
Let the moment produced by the failure of one aerodynamic surface be M Cj . This is the “missing” moment that
must be compensated for and is simply the difference between the aerodynamic moment produced by the control
surface under normal conditions and the one produced under abnormal conditions:
!
!
!
M Cj = M Nj − M Fj
(8)
Assuming a linear relationship between aerodynamic moment and control surface deflection, equation (8) becomes:
!
!
!
dM Nj
dM Fj
M Cj =
δ jC −
δ jF
(9)
dδ j
dδ j
3
American Institute of Aeronautics and Astronautics
where δ jC is the commanded deflection of control surface j, actually achieved under normal conditions and δ jF is
!
!
dM Nj
dM Fj
and
represent the derivative of the aerodynamic
the deflection reached under failure conditions.
dδ j
dδ j
Downloaded by UNIVERSITY OF ADELAIDE on October 27, 2017 | http://arc.aiaa.org | DOI: 10.2514/6.2011-6407
moment vector with respect to aerodynamic control surface deflection at normal and abnormal conditions,
respectively. Note that a failure may affect either or both the deflection and the aerodynamic characteristics
represented by the control derivative. To achieve failure accommodation, the total moment for control produced by
all engines must balance the total moment produced by all failed surfaces:
!
!
m dM
m !
n !
dM Fj
Nj
(10)
∑ M ei = ∑ M Cj = ∑ ( dδ δ jC − dδ δ jF )
j
j
j=1
j=1
i =1
Let the components in body axes of the moment derivative vector with respect to surface j deflection, be at normal
condition:
!
T
T
 dM Nj 
 dM Nx dM Ny dM Nz  Notation
M
 =

M yδ j
M zδ j 
(11)

x
δ
=
j

N
N
N  B
dδ j
dδ j 
 dδ j 
 dδ j

B
B
and under abnormal conditions:
!
T
T
 dM Fj 
 dM Fx dM Fy dM Fz  Notation
M

 =

M
M
(12)

x
y
z
δ
δ
δ
=
j F
j F
j F

B
dδ j
dδ j 
 dδ j 
 dδ j
B
(
(
) (
) (
) (
) (
)
)
B
Then the compensating engine moment must be, in body axes components:
!
!
m  dM 
 dM Fj 
n ! 
Nj
 δ jC − 
 δ jF )
∑ M ei  = ∑ ( 
 dδ j 
i =1
 B j=1  dδ j  B
B
Using Eqn (7), Eqn (13) can be re-written as:
!
!
m  dM 
 dM Fj 
! 
 n ! OP
Nj
i
 δ jC − 
 δ jF )
× ∆Ti ) = ∑ ( 
∑ ( r
 dδ j 
i =1
 B j=1  dδ j  B
B
( ) 
!
( ) 
∑ {[~r ] [∆T ] }
( ) 


r  ∆T  
(M δ ) 
 



− r  ∆T   = ∑  (M δ ) 


0   ∆T  
 (M δ ) 


(13)
(14)
( ) 
( ) 
( ) 
(M ) 
δ



− (M δ ) 


 (M δ ) 




N
F

OPi
δ
δ
(15)
i B
jC
jF 
B
N
F

i =1

F B
N B


 0
− rzi
x j
x j

yi
xi
n 
m
N
F


0
δ jC
δ jF 
(16)
∑  rzi
xi
yi
y j
y j
N
F

i =1 − r
j=1
r
xi
zi B
 yi
z j
z j

B
F B
N B

From equation (16) it can be seen that there are three sets of parameters that need to be evaluated when analyzing
the potential of using thrust to compensate for actuator failures. These three sets are:
!
• Number of engines n and their locations as determined by the vectors r OPi ;
!
• Amount of additional thrust available for control from each engine ∆Ti ;

 M xδ j

= ∑  M yδ j
j=1 
 M zδ j

n
m
M
 xδ j
−  M yδ j

 M zδ j

(
)
• Type and severity of the failure as measured by the deflection offset δ jC − δ jF and the alteration of the
control derivatives due to failure.
Furthermore:
cos(ψ i ) cos(θ i )
∆Txi 
!
 sin(ψ ) cos(θ )  ∆T
 ∆T  = L
T
∆
=
(17)
BTi
i Ti
i
i 
i

 yi 


 ∆Tzi 
sin(θ i )
[ ]
B
B
and:
4
American Institute of Aeronautics and Astronautics
)
)
)
(
(
(
)
)
)
(
(
(


M


M xδ j 
ryi  cos(ψ i ) cos(θ i )
xδ j 





m
N
F




0
− rxi   sin(ψ i ) cos(θ i )  ∆Ti  = ∑  M yδ j  δ jC −  M yδ j  δ jF 
(18)
N
F





=
j
1


rxi
0  
sin(θ i )
 M zδ j 
B
 M zδ j N  B

B

F B



An analysis can be performed by determining the necessary values for some of the parameters when the others
are imposed. It can be seen from equation (18) that the engine can be used to produce control moments by changing
the location of the point of application of the thrust ( rxi , ryi , and rzi ), by changing the orientation of the thrust
 0

∑  rzi
i =1 − r
 yi
n
− rzi
Downloaded by UNIVERSITY OF ADELAIDE on October 27, 2017 | http://arc.aiaa.org | DOI: 10.2514/6.2011-6407
vector ( θ i and ψ i ), and/or by changing the magnitude of the thrust ( ∆Ti ). Some of these options might not be
practical. The model also allows to determine, given a certain propulsion system configuration, the severity of the
failure that can be handled.
III.
Analysis of Engine Compensation for Specific Actuator Failures
Let us assume that the aerodynamic control surface j is stuck at a deflection δ jF . This means that the
aerodynamic characteristics of the control surface are not altered; therefore:
!
!
dM Nj dM Fj
=
dδ j
dδ j
and the moment due to the failure is:
!
!
dM Nj
δ jC − δ jF
M Fj =
dδ j
(
)
(20)
Eqn (18) becomes:


ryi  cos(ψ i ) cos(θ i )

m



− rxi   sin(ψ i ) cos(θ i )  ∆Ti  = ∑  δ jC − δ jF
 j=1 

rxi
0  
sin(θ i )
B

B


Let us assume that the aircraft is equipped with two identical engines (n =
symmetrically, such that:
! OPR
T
r
B = rx ry rz B
! OPL
T
r
B = rx − ry rz
 0

∑  rzi
i =1 − r
 yi
n
− rzi
0
(
[ ] [
[ ] [
∆TxR 
[∆T! R ]B = ∆TyR 
 ∆TzR 
B
]
[ ]T
!
= L BTR ∆TR
R
(19)
(
)(
(
)
)
)
 
M
 xδ j N  
 
 M yδ
(21)
j N
 

 M zδ j  
N B 

2, left = L, right = R) located
]B
cos(ψ R ) cos(θ R ) 
ε 
not 1R
=  sin(ψ R ) cos(θ R )  ∆TR = ε 2R  ∆TR


ε 2R 
sin(θ R )
B
B
cos(ψ L ) cos(θ L )
ε 
not 1L
!
= LBTL ∆TL T =  sin(ψ L ) cos(θ L )  ∆TL = ε 2L  ∆TL
L

 ∆TzL 

ε 2L 
sin(θ L )
B
B
B
∆TxL 
[∆T!L ]B = ∆TyL 
[ ]
(22)
(23)
(24)
(25)
A. Elevator Failure
Let us assume that the left elevator is locked at a deflection δ eLF . The failure will affect the pitching and the
rolling moment, while it is assumed that the effects on the yawing moment are negligible. Under these conditions
and omitting the subscript N for simplicity, Eqn (21) becomes:
 0 − rz − ry  ∆TxL 
 0
− rz ry  ∆TxR 
M xδ eL 
 

 



 = (δ

δ
)
r
0
r
T
r
0
r
T
−
∆
+
−
∆
−
(26)
yL 
eLC
eLF M yδ eL 
yR 
x 
x 
z
 z
− r
 0 
0   ∆TzR  B ry rx
0   ∆TzL  B
 y rx
B
B
B
Furthermore:
5
American Institute of Aeronautics and Astronautics
(
)
 − rz ∆TyR − ∆TyL + ry (∆TzR − ∆TzL ) 
M xδ eL 




 rz (∆TxR + ∆TxL ) − rx (∆TzR + ∆TzL )  = (δ eLC − δ eLF ) M yδ eL 
− r (∆T − ∆T ) + r ∆T + ∆T 
 0 
xR
xL
x
yR
yL  B
 y
B
or, using equations (24) and (25):
− rz (∆TR ε 2R − ∆TL ε 2 L ) + ry (∆TR ε 3R − ∆TL ε 3L )
M xδ eL 




ε
ε
ε
ε
δ
δ
(
)
(
)
(
)
r
T
T
r
T
T
=
−
∆
+
∆
−
∆
+
∆
R 1R
L 1L
x
R 3R
L 3L 
eLC
eLF M yδ eL 
 z
 − r (∆T ε − ∆T ε ) + r (∆T ε + ∆T ε )
 0 
R 1R
L 1L
x
R 2R
L 2L  B
 y
B
Downloaded by UNIVERSITY OF ADELAIDE on October 27, 2017 | http://arc.aiaa.org | DOI: 10.2514/6.2011-6407
(
(27)
)
(28)
This is a system of three equations with nine unknowns ( rx , r y , rz , ∆TR , ∆TL , θ R , ψ R , θ L , and ψ L ). Let us
assume that changing the direction of the thrust vector is not used for control; therefore the engine Euler angle are
constant and respectively equal in magnitude and symmetric for the left and right engine. As a consequence:
ε 1R = ε 1L = ε 1 , ε 2R = −ε 2L = ε 2 , and ε 3R = ε 3L = ε 3
(29)
and the number of unknowns (or variables that can potentially be used for control) is reduced to five ( rx , r y , rz ,
∆TR , ∆TL ):
− rz (∆TR + ∆TL )ε 2 + r y (∆TR − ∆TL )ε 3 


 rz (∆TR + ∆TL )ε 1 − rx (∆TR + ∆TL )ε 3 
 − r (∆T − ∆T )ε + r (∆T − ∆T )ε 
R
L 1
x
R
L 2
 y
M xδ eL 
= (δ eLC − δ eLF ) M yδ eL 
(30)
 0 
B
B
Note that if the axes of the engines are parallel to the aircraft longitudinal axis then ε 1 = 1 , ε 2 = ε 3 = 0 , and the
compensating engine moment is:


0
2 ! 


(31)
∑ M ei  =  rz (∆TR + ∆TL ) 
i =1
 B 

− ry (∆TR − ∆TL )
B
In this case, the rolling effects of the failure can not be compensated and an undesirable yawing moment is produced
unless ∆TR = ∆TL = ∆T . The pitching effects of the failure can be compensated if the engines are located off the
body-axes horizontal plane ( rz ≠ 0 ). Then:
2rz ∆T = (δ eLC − δ eLF )M yδ eL
(32)
Collective thrust
To compensate for the rolling effects of the failure, ε 2 ≠ 0 and/or ε 3 ≠ 0 .
( ∆TR = ∆TL = ∆T ) or differential thrust ( ∆TR ≠ ∆TL ) can be used. For the collective thrust case, Eqn. (30)
becomes:
M xδ eL 

 − 2rz ∆Tε 2


r ∆Tε − r ∆Tε  = (δ
δ
)
−
(33)
1
x
3
eLC
eLF  M yδ eL 
z
 0 


0
B
B
The following conditions result as necessary for rolling compensation:
rz ≠ 0 , ψ R = −ψ L ≠ 0 , and θ R = θ L ≠
π
2
Assuming that the devices considered are the actual aircraft main propulsion system, then ψ R = ψ L ≠
ε 1 ≠ 0 . Pitching compensation capabilities are maintained if:
θ R = θ L = 0 or rx = 0
⇒
rz ∆Tε 1 = (δ eLC − δ eLF )M yδ eL
or:
rz ε 1 ≠ rx ε 3
⇒
(rz ε 1 − rx ε 3 )∆T = (δ eLC − δ eLF )M yδ eL
(34)
π
2
, and
(35)
(36)
For the differential thrust case, considering that ε 1 ≠ 0 for the actual main aircraft propulsion system, the
yawing effects are avoided if:
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American Institute of Aeronautics and Astronautics
r y ε 1 = rx ε 2
(37)
Assuming that the differential thrust control is symmetric, that is ∆TR = − ∆TL = ∆T , then engine compensating
moment becomes:
2r y ∆Tε 3 
2 ! 


0
(38)
∑ M ei  = 

i =1
 B 

0


B
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The following conditions result as necessary for rolling compensation:
r y ≠ 0 and θ R = θ L ≠ 0
(39)
However, to maintain pitching moment compensation capabilities, ∆TR ≠ − ∆TL and Eqn. (30) becomes:
− rz (∆TR + ∆TL )ε 2 + r y (∆TR − ∆TL )ε 3 
M xδ eL 
 r (∆T + ∆T )ε − r (∆T + ∆T )ε  = (δ


R
L 1
x
R
L 3 
eLC − δ eLF ) M yδ eL 
 z


 0 
0
B
The additional conditions for both rolling and pitching compensation result to be:
rz (∆TR + ∆TL )ε 2 ≠ r y (∆TR − ∆TL )ε 3
rz ε 1 ≠ rx ε 3
(40)
B
(41)
(42)
B. Aileron Failure
Let us assume that the left aileron is locked at a deflection δ aLF . The failure will affect primarily the rolling and
– to some extent - the yawing moment, while it is assumed that the effects on the pitching moment are negligible.
Following the same procedure as for the elevator failure, we obtain an equation similar to Eqn. (28):
 M xδ 
− rz (∆TR ε 2 R − ∆TL ε 2L ) + r y (∆TR ε 3R − ∆TL ε 3L )
aL




(43)
 rz (∆TR ε 1R + ∆TL ε 1L ) − rx (∆TR ε 3R + ∆TL ε 3L )  = (δ aLC − δ aLF ) 0 
M

 − r (∆T ε − ∆T ε ) + r (∆T ε + ∆T ε )
R 1R
L 1L
x
R 2R
L 2L  B
 y
 zδ aL  B
Assuming again that changing the direction of the thrust vector is not used for control and considering Eqn. (29), we
obtain:
M xδ 
− rz (∆TR + ∆TL )ε 2 + r y (∆TR − ∆TL )ε 3 
aL




(44)
 rz (∆TR + ∆TL )ε 1 − rx (∆TR + ∆TL )ε 3  = (δ aLC − δ aLF ) 0 
M

 − r (∆T − ∆T )ε + r (∆T − ∆T )ε 
R
L 1
x
R
L 2 B
 y
 zδ aL  B
Since a compensatory rolling moment must be produced, differential vertical and/or lateral thrust components are
necessary. Let us assume that differential symmetric thrust is used, that is ∆TR = − ∆TL = ∆T . Then:
 M xδ 


2ry ∆Tε 3
aL




0
0
=
(
δ
−
δ
)
aLC
aLF 



M

− 2r ∆Tε + 2r ∆Tε 
y
1
x
2 B

 zδ aL  B
The additional conditions for rolling compensation are:
θ R = θ L ≠ 0 and r y ≠ 0
Yawing compensation is provided if:
r y ε 1 ≠ rx ε 2
(45)
(46)
(47)
C. Rudder Failure
Let us assume that the rudder is locked at a deflection δ rF . The failure will affect primarily the yawing and – to
some extent - the rolling moment, while it is assumed that the effects on the pitching moment are negligible.
Following the same procedure as for the elevator failure, we obtain an equation similar to Eqn. (28):
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American Institute of Aeronautics and Astronautics
M xδ 
− rz (∆TR ε 2R − ∆TL ε 2 L ) + ry (∆TR ε 3R − ∆TL ε 3L )
r




(48)
 rz (∆TR ε 1R + ∆TL ε 1L ) − rx (∆TR ε 3R + ∆TL ε 3L )  = (δ rC − δ rF ) 0 
M 
 − r (∆T ε − ∆T ε ) + r (∆T ε + ∆T ε )
R 1R
L 1L
x
R 2R
L 2L  B
 y
 zδ r  B
Assuming again that changing the direction of the thrust vector is not used for control and considering Eqn. (29), we
obtain:
M xδ 
− rz (∆TR + ∆TL )ε 2 + r y (∆TR − ∆TL )ε 3 
r




(49)
 rz (∆TR + ∆TL )ε 1 − rx (∆TR + ∆TL )ε 3  = (δ rC − δ rF ) 0 
M 
 − r (∆T − ∆T )ε + r (∆T − ∆T )ε 
R
L 1
x
R
L 2
 y
 zδ r 
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B
B
Since a compensatory yawing moment must be produced primarily, differential longitudinal thrust components are
sufficient provided the distance from the engine to the vertical plane of symmetry is large enough. Let us continue
to assume that differential symmetric thrust is used, that is ∆TR = − ∆TL = ∆T . Then:
 M xδ 


2r y ∆Tε 3
r




0
0
=
(
δ
−
δ
)
(50)
rC
rF




M 
− 2(r ε − r ε )∆T 
y 1
x 2

B
 zδ r  B
Eqn. (50) shows that if the location and the orientation of the two thrust vectors are fixed, then differential thrust
commands can be determined to produce compensation of the yawing moment. The necessary thrust is:
(δ rC − δ rF )M zδ r
∆T =
(51)
− 2( r y ε 1 − r x ε 2 )
However, it might be necessary to compensate for the residual moment on the lateral channel by using the aileron.
If the engine thrust differential is known as well as the moments produced by the failed rudder and assuming that
there is no change in the thrust vector, then Eqn. (49) can be used to find the engines positions. Solving for rx, ry,
and rz yields:
M xδ r ε 1 

δ rC − δ rF
rx =
(52)
 −1
2M zδ r +
(∆TR − ∆TL )ε 2 
ε 3 
ry =
(δ rC − δ rF )(M xδ r ε1 + M zδ r ε 3 ) ε 2
−
(∆TR − ∆TL )ε 1ε 3
ε1
(53)
rz =
 2M zδ r ε 3
 ε
+ M xδ r  − 3

(∆TR − ∆TL )ε 2  ε 1
 ε 1
(54)
IV.
δ rC − δ rF
WVU Simulation Environment
An advanced simulation environment has been developed at WVU to support the design, evaluation, and
validation of various aircraft fault-tolerant control laws15. Matlab and Simulink are used to ensure maximum
portability and flexibility. The dynamic model of a large transport aircraft is interfaced with the Aviator Visual
Design Simulator (AVDS) simulation package16 to provide visual cues when used directly on a desktop computer.
Flight control laws controlling the throttle level to each engine utilize fuzzy logic to compensate for abnormal flight
conditions under actuator failures. The main components of the WVU simulation environment are presented in
Figure 1. The primary five modules are:
• Aircraft Model Module
• Control System Module
• Aircraft Sub-System Failure Models
• Fuzzy Logic Throttle Controller
• User Interface
The aircraft dynamic model can be flown using a joystick or a set of pre-recorded command time histories.
User-friendly graphical user interface menus are used to set the conditions for the simulation scenarios, including a
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variety of options related to the architecture of the control laws, failure type and magnitude, and input/output
content. An example of the user interface provided by the AVDS visualization and the monitoring of relevant
engine parameters using Simulink scopes is presented in Figure 2.
A multi-engine large transport aircraft model has been developed for the investigation and analysis of utilizing
engine thrust to accommodate for aerodynamic control surface failures. The aerodynamic model is based on generic
values of the stability and control derivatives17 for a representative aircraft in this class. This simulation
environment allows for the study of two to ten engines to be added to the aircraft at specific locations in relation to
the aircrafts center of gravity. The model allows for the determination of engine placement, engine thrust, or
maximum control surface deflection failure to be fixed while the remaining parameters are determined.
Furthermore, the airplane model is easily adaptable for any other type of fixed wing aircraft.
The interface allows for the selection of a nominal conditions flight scenario or a control surface failure scenario
(Figure 3). The user then is allowed to choose the type of pilot input, from pre-recorded maneuvers to live joystick.
If the user selected the control surface failure scenario, then the particular failed surface may be selected and the
failure time and magnitude specified. Next, the user is allowed to specify the number of engines as well as the
engine placement (Figure 4). For certain engine configurations default values may be presented. Finally, the
Simulink model is opened. From here the AVDS program and relevant scopes can be opened and monitored as seen
in Figure 2.
Figure 1. General Architecture of the WVU Simulation Environment
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Figure 2. Interface of the WVU Simulation Environment
Figure 3. Simulation Scenario Selection
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Figure 4. Engine Selection and Position Menu
V.
Fuzzy Logic-Based Engine Control for Actuator Failure Accommodation
Fuzzy logic is a form of multi-value logic that operates with statements that can be true, false, or anywhere in
between and can be used to model the knowledge, experience, and modus operandi of a human operator18. Fuzzy
logic allows avoiding the rigidity of classic logic and the mathematics associated to it and facilitates modeling of
processes characteristic to living matter, such as intelligence.
In general, the flow of a fuzzy logic-based controller consists of three major modules18,19: fuzzification, inference
engine, and defuzzification. The crisp measurements from the sensors, or linguistic variables, must be converted
through the fuzzification process into a fuzzy input that represents the degree to which the crisp measurements
belong to each of the fuzzy sets defined by the linguistic values – an attribute associated with the linguistic variable
such as small, very small, large, etc. This takes place in the fuzzification module. Then the fuzzy input is used to
create a fuzzy output or command according to the set of condition rules provided by an expert operator in the form
of “IF – THEN” rules18-20. This is equivalent to translating the control rules from natural language into fuzzy logic.
The module in which this operation is performed is the inference engine. The fuzzy command represents
membership values of the output to fuzzy sets defined by the linguistic values associated with the command. This
information must then be converted back into a crisp value, within the defuzzification module, and used directly as
command signals.
A simple fuzzy logic-based controller was implemented in the WVU large transport aircraft model for the
purpose of illustrating the fault tolerant capabilities of propulsion devices in the presence of actuator failures. The
control strategy consists of commanding the attitude angle and angular rate on the three body axes using engine
throttle. As a result, the controller has two linguistic variables – attitude angle error between pilot command and
actual angle and the rate of change in this error. The crisp value from each linguistic variable is fuzzified using five
linguistic values – Large Negative, Negative, Zero, Positive, and Large Positive. There are two types of
membership functions utilized – a trapezoidal shape and a triangular shape. For the attitude angle error, both
trapezoidal and triangular membership functions are used, while for the rate error, only trapezoidal membership
functions. The membership functions for the inputs can be viewed in Figure 5. The output command uses triangular
shaped functions. See Figure 6 for the output membership functions and surface plot.
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Figure 5. Input Membership Functions for Attitude Angle Error and Attitude Angle Rate Error
Figure 6. Output Membership Functions and Surface Plot
The two 5-dimesional input linguistic variable vectors produce a five-by-five grid for all possible combinations.
This grid is used to formulate the inference rule matrix presented in Table 1 for the yaw channel. The output
linguistic variable is additional throttle deflection and can take seven linguistic values - Large Negative, Negative,
Small Negative, Zero, Small Positive, Positive, and Large Positive. For example, cell (2,3) corresponds to the
following inference rule: if the yaw angle error is “Zero” and the yaw error rate is “Negative”, then the additional
throttle deflection must be “Small Positive”. Within the inference engine module, the fuzzy command is generated
for each engine irrespective of its relative position to the center of gravity. The output from the inference engine is
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American Institute of Aeronautics and Astronautics
passed into the defuzzification module where the fuzzy values from the inference matrix are converted into a crisp
throttle alteration command. This command is then passed into an additional module that alters each individual
engine throttle command. The pilot throttle command is assumed to be the same for each engine. The alteration
from the fuzzy logic controller either increases or decreases this value based on the engine’s location with respect to
the aircraft's center of gravity and the required compensating moment.
Table 1. Inference Rules Matrix
Yaw Error
Large
Negative
Negative
Zero
Positive
Large Positive
Large Positive
Positive
Small Positive
Zero
Positive
Small Positive
Zero
Small Negative
Small Positive
Zero
Small Negative
Negative
Zero
Small Negative
Negative
Large Negative
Small Negative
Negative
Large Negative
Large Negative
Yaw Error Rate
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Large Negative
Negative
Zero
Positive
Large Positive
Large
Positive
Large Positive
Positive
Small Positive
Zero
VI.
Simulation Results
The model was exposed to two levels of actuator failure in addition to a nominal flight test, while using a twoengine configuration. Furthermore, it was tested at each level of failure using the fuzzy logic engine throttle control
engaged and disengaged. The failures considered were stuck rudder actuator at +10 and +15 degrees. The nominal
conditions test was conducted in order to establish a baseline for the aircraft as seen in Figure 7.
Figure 7. Nominal Conditions Flight Data Results
When the aircraft was exposed to the +10 degree stuck rudder actuator, it was still controllable while the fuzzy
logic controller was engaged. When the aircraft was flown without the controller engaged, it became uncontrollable.
These results can be viewed in Figure 8. When the model was exposed to the +15 degree struck rudder failure, it
was uncontrollable with and without the fuzzy logic controller engaged as seen in Figure 9. Two solutions were
examined. The first possible solution tested was to move the engines farther from the aircraft’s centerline. From the
proposed model, it results that in order to compensate for a rudder stuck at 15 degrees, the engines must be located
at a distance from the centerline equal to [6 14.5 2.25]. The original engine position was [rx ry rz] = [8 ±13 2.25]
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meters. It was moved to [rx1 ry1 rz1] = [5 ±15 2.125] meters. Using this approach, the aircraft was controllable while
using the fuzzy logic controller. It remained uncontrollable when the fuzzy logic controller was disengaged. This is
seen in Figure 10. The second approach kept the engines in the nominal engine configuration but the engines
maximum thrust was increased to 120%. It was found using Eqn. (51) that 113% thrust increase was necessary for
controllable flight. The increase in thrust allowed the aircraft to remain controllable while the fuzzy logic controller
was engaged and the aircraft remained uncontrollable when the controller was not engaged as displayed in Figure
11.
Figure 8. 10 Degree Rudder Actuator Failure, FL Engaged and Disengaged
Figure 9. 15 Degree Rudder Actuator Failure, FL Engaged and Disengaged
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Figure 10. 15 Degree Rudder Actuator Failure, Engines Moved, FL Engaged and Disengaged
Figure 11. 15 Degree Rudder and Actuator Failure, Thrust Increased, FL Engaged and Disengaged
VII.
Conclusions
A model was developed that can be used for the analysis of fault tolerant capabilities of engine throttle control
laws in the presence of aerodynamic control surface failures. A Matlab/Simulink simulation environment was built
that allows for the simulation of a large transport aircraft with a variable number of engines at different locations and
with different orientations.
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American Institute of Aeronautics and Astronautics
This framework can be used for the evaluation of the failure accommodation potential of any given engine
configuration, to determine fixed characteristics of the propulsion system necessary to be able to compensate for
actuator failure of a specified severity through differential throttle, and design fault tolerant engine control laws in
terms of engine throttle, translation, and rotation. The effectiveness of the approach was illustrated through an
example simulation.
The proposed model allows to effectively determine the maximum failure deflection that can be accommodated
by a given configuration, the required engine position for a specified failure magnitude and engine power, and the
maximum thrust needed to compensate a certain actuator failure if the location of the propulsion device is fixed.
Acknowledgment
This work has been supported in part by NASA under Cooperative Agreement no. NNX09AF64G.
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