Autonomous Guidance and Control of Airplanes under
Actuator Failures and Severe Structural Damage
GirishChowdhary _,Eric N.Johnson , y
x
RajeevChandramohanz ,M. Scott Kimbrell ,AnthonyCalise
{
Georgia Institute of Technology, Atlanta, GA, 30318
This paper presents control algorithms for guidance and control of airplanes under actuator failures and severe structural damage. The presented control and guidance algorithms
are validated through experimentation on the Georgia Tech Twinstar twin engine, _xed
wing, Unmanned Aerial System.
Damage scenarios executed include sudden loss of all
aerodynamic actuators resulting in propulsion only ight, 25% left wing missing, sudden
loss of 50% right wing and aileron in ight, and injected actuator time delay.
A state
dependent guidance logic is described that ensures the aircraft tracks feasible commands
in the presence of faults.
The commands are used by an outer-loop linear controller to
generate feasible attitude commands. The inner loop attitude control can be achieved by
using either a linear attitude controller or a neural network based model reference adaptive controller.
The results indicate the possibility of using control methods to ensure
safe autonomous ight of transport aircraft through validation on a scaled model that has
characteristics of a typical transport category aircraft.
I.
Introduction
Fixed wing aircraft can be rendered inoperable by in-ight damage. Such damage may include actuator
failures, battle damage, structural failure, damage due to terrorist attacks, and damage due to high speed
impact. Lifting surface loss and control surface loss are examples of failures that make it extremely hard for
pilots to maintain stable ight and ensure that the aircraft is capable of landing successfully. Under such
circumstances, automatic control systems can be used for autonomously maintaining stable ight and aiding
the pilot in landing.
Commonly used closed loop ight control approaches assume a linearized dynamical model for the dynamics and use linear control methods (see for example 1,2). Under severe structural faults, however, the
dynamics of the aircraft are signi_cantly altered. For example, under an asymmetric wing failure, aircraft
will experience asymmetric lateral forces coupled with longitudinal motion that cannot be represented by
standard symmetric wing decoupled aircraft models. In order to maintain safe ight, such changes in dynamics, brought about by system faults, must be handled by the onboard controller. Fault Tolerant Control
(FTC) research aims at designing controllers that can mitigate such changes automatically and maintain
safe ight. Several recent reviews and textbooks have been published in this area (see e.g. 3,4,5,6 ). Three
types of failures have been studied: sensor failure, actuator failure and structural damage. Fault tolerant
control in the presence of sensor or actuator damage with online identi_ed failure characteristics were studied
in 3,7. Fault tolerant control in the case of structural damage, including partial loss of wing, vertical tail
loss, horizontal tail loss, and engine loss, has also been recently explored recently. 8,9,10 Crider explored
linear quadratic regulators for partial tail loss through a simulation study on a linear Boeing 747 model. The
method focused on linear decoupled longitudinal and lateral models with parameter variations. 11 Hallouzi
and Verhaegen used subspace identi_cation techniques along with model predictive control for simulation
_
Research Engineer II, School of Aerospace Engineering, AIAA member
Lockheed Martin Professor of Avionics Integration, School of Aerospace Engineering, AIAA member
z
Research Assistant, School of Aerospace Engineering, AIAA student member
x
Graduate of the School of Aerospace Engineering
{
Professor, School of Aerospace Engineering, AIAA member
y
1 of 25
American Institute of Aeronautics and Astronautics
study of elevator lock-in-place and rudder-runaway faults based on a linear Boeing 747 model. 12 Hitatchi
used H 1 robust control design techniques for damage tolerant control using propulsion only control. Simulation results on a linear Boeing 747 model and a nonlinear aircraft model were presented. 13,14 Yucelen
et al. proposed the derivative-free model reference adaptive control approach for adaptation in presence of
rapidly varying uncertainties. 15 ,16 They validated this approach through simulation on the NASA Generic
Transport Model (GTM) with aeroelastic e_ects. 17 Lombartes et al. used online system identi_cation in a
dynamic nonlinear model inversion scheme with the parameters of the inversion model identi_ed online. 18
They validated the method on a Boeing 747 model in simulation for several damage scenarios including
rudder runaway, stabilizer runaway, and rudder loss. Lunze and Ste_en use disturbance decoupling methods
to handle identi_ed actuator faults for linear models. 19 They assume that the fault only a_ects the control
e_ectiveness parameters and that a model of the damaged plant is known. Experimental results on a laboratory mounted helicopter-like experimental setup are presented. Boskovic et al. used retro-_t control for
fault tolerant control design under bounded fault-induced uncertainty. 10 Nguyen et al. used direct-indirect
adaptive control and recursive least squares based adaptive control for control of aircraft under simulated
30% loss of left wing of the NASA generic transport model. 9 Many other authors have also presented fault
tolerant control approaches using Model Reference Adaptive Control (MRAC) architecture. 20 ,21,5,22 Jourdan et al. demonstrated in ight MRAC based inner-loop attitude control in the presence of severe structural
faults on a UAV that was a reduced scale model of a F-18. 23 Faults considered included up to 60% wing
loss.
In most of the previously mentioned approaches, the focus was on inner loop adaptive/recon_gurable
attitude control given an attitude command or regulation in the presence of an initial attitude disturbance.
The outer-loop control, that is the generation of desired velocity and attitude commands to navigate to a
waypoint were exogenous inputs that do not explicitly take into account that failure has occurred, such as
inputs provided by a pilot. Under severe faults, the aircraft's capability to track commands is also severely
limited. Therefore, a key and a relatively unaddressed problem in guaranteeing safe ight in the presence
of damage is to ensure that the aircraft is commanded feasible attitudes and acceleration commands in the
presence of faults. The state dependent outer-loop guidance approach presented in this paper has been
speci_cally designed for subsonic aircraft, and uses estimates of the aircraft position, velocity, and attitude
measurements, along with air data measurements to continually modify the commands to help ensure that
safe ight is maintained. The guidance logic provides acceleration commands, which are converted to attitude
commands (roll, pitch, yaw). The inner loop attitude controller then generates the appropriate actuator
commands. A feedback is established between attitude guidance and acceleration guidance that ensures the
acceleration commands are modi_ed if the attitude commands exceed heuristically determined limits. For
example, forward acceleration is modi_ed to maintain level ight if the desired angle of attack command
exceeds a heuristically determined limit that typically avoids stall. This results in a cascaded inner-outer
loop architecture as depicted in Figure 1. The attitude controller can either be a linear PID type attitude
controller or a model reference adaptive controller.
An issue that arises when using adaptive methods, particularly for manned aircraft, concerns the e_ect
that adaptation might have on any existing stability margins. It is possible that an adaptive controller, designed to assist or augment an existing non-adaptive ight controller, might signi_cantly reduce the stability
margin of the non-adaptive ight controller in the event of an in-ight failure, and even in the absence of
failures in actuation or airframe damage. Calise and Yucelen derive a modi_cation term (namely Adaptive
Loop transfer Recovery (ALR)) that can be used with a wide variety of adaptive approaches that acts to
preserve the loop transfer properties of a non-adaptive controller in the absence and in the presence of damages. The principle is based on loop transfer recovery, similar to that employed in robust control design. In
the context of fault-tolerance, the ALR terms is described and ight-tested here for ensuring safe ight in
the presence of actuator time delays.
In this paper we present the details and ight test results of fault tolerant guidance and control algorithms.
All of the algorithms presented have been ight tested on the Georiga Tech Twinstar (GT Twinstar) twin
engine, _xed wing, Unmanned Aerial System. Damage scenarios executed include loss of all aerodynamic
actuators resulting in propulsion only control, 25% loss of left wing, sudden loss of 50% right wing, and
injected time delay. The contributions of this paper are summarized here:
1. Description and ight-test validation of a state dependent autonomous waypoint following guidance
approach that establishes a feedback between the outer-loop guidance and inner-loop attitude guidance
to ensure level ight when attitude commands exceed predetermined safe limits due to faults
2 of 25
American Institute of Aeronautics and Astronautics
Waypoints
Air-speed
measurement
Compute
Acceleration
commands
ax , a y , a z
Compute
attitude
commands
d , d , d
Inner-loop
attitude
controller
Figure 1.
The presented fault tolerant inner-outer-loop control architecture. The guidance logic provides the
aircraft with acceleration commands, which are then converted to desired attitude commands which are used
by the inner loop attitude controller to command appropriate actuator commands. The baseline linear inner
loop attitude controller can be replaced with a Model Reference Adaptive Controller.
2. Description and ight-test validation of inner-loop PID attitude controller with the state dependent
guidance approach of 1. for maintaining autonomous waypoint following ight in the presence of known
complete loss of all aerodynamic e_ectors and unknown loss of 50% of right wing and all of the right
aileron
3. Description and ight-test validation of an inner-loop model reference adaptive controller with the
state dependent guidance approach of 1. for autonomous waypoint following ight in the presence of
unknown severe structural faults including 25% left wing loss
4. Flight-test validation of the adaptive loop recovery method for mitigating unknown actuator time
delays
The guidance method presented here is based on a combination of the physics and heuristics of ying an
aircraft. As such, no theoretical proof of stability is presented for the cascaded outer-loop and inner-loop
guidance and control methods. However, the output of the guidance system, namely the desired accelerations
and attitudes, are hard-limited in the software. This indicates that the desired commands passed to the
linear or the MRAC attitude inner-loop controller are guaranteed to be bounded. It is well known that the
local stability of PID inner-loop attitude controllers with integrator windup protection and bounded desired
commands can be established with Lyapunov's second method (see for example Chapter 3.7 of 25). The
stability proofs of the inner-loop MRAC attitude control methods in the presence of parametric uncertainty
26
and bounded reference commands have been previously presented.
Therefore, it should be reasonable to
expect local stability of the cascaded closed loop system for an appropriate choice of gains. This intuition is
reected by the positive ight test results. Section III presents the details of the state dependent guidance
logic used. The details of a linear attitude controller are presented in Section IV, and results with the
linear attitude controller are presented in Section V. The details of the MRAC architectures are presented
in Section VI and ight test results with MRAC under structural faults are presented in Section VII. The
adaptive loop transfer recovery method is introduced in Section VIII and ight test results with injected
actuator time delays are presented in Section VIII.A. The paper is concluded in Section IX.
II.
The Flight Test Vehicle
Flight testing of fault-tolerant control algorithms for safe ight in the presence of severe structural
faults has been performed at the UAV Research Facility at Georgia Institute of Technology. These ight
tests were performed on the GT Twinstar _xed wing Unmanned Aerial System (UAS). The GT Twinstar
(Figure 2) is a foam built, twin engine aircraft based on the Multiplex Twin Star II model airplane. It has
3 of 25
American Institute of Aeronautics and Astronautics
been equipped with an o_-the-shelf autopilot system.The control algorithms discussed in this paper were
implemented on the autopilot system through custom developed software. The autopilot system comes with
an integrated navigation solution that fuses information using an extended Kalman _lter from six degree
of freedom inertial measurement sensors, Global Positioning System, air data sensor, and magnetometer
to provide accurate state information. 27 The available state information includes velocity and position in
global and body reference frames, accelerations along the body
x;y;z axes, roll, pitch, yaw rates and attitude,
barometric altitude, and air speed information. These measurements can be further used to determine the
aircraft's velocity with respect to the air mass, and the ight path angle. The Twinstar can communicate
with a Ground Control Station (GCS) using a 900 MHz wireless data link.
The GCS serves to display
onboard information as well as send commands to the autopilot.
Flight measurements of airspeed and
throttle setting are used to estimate thrust with this model. An elaborate simulation environment has also
been designed for the GT Twinstar. This environment is based on the Georgia Tech UAS Simulation Tool
(GUST) environment. 28 A linear model for the Twinstar in nominal con_guration (without damage) has
been identi_ed using the Fourier Transform Regression (FTR29 ) method by the authors. 30 A linear model
with 25% left wing missing has also been identi_ed.31
Figure 2.
The Georgia Tech Twinstar UAS. The GT Twinstar is a _xed wing foam-built UAS designed for
fault tolerant control work.
III.
State Dependent Outer-loop Guidance for Fault-Tolerant Operation
The task of the guidance system is to provide feasible acceleration and attitude commands such that the
aircraft can track a desired trajectory despite structural damage. Due to this reason, the guidance logic plays
a central role in ensuring safe ight in the presence of damage. In this section we describe a guidance scheme
designed to accommodate signi_cant faults. These faults include structural damage, and partial or complete
(known) failures of all aerodynamic e_ectors (propulsion only control). The guidance system is designed
to achieve a desired airspeed vdes , altitude hdes , and a prescribed course. These are typically speci_ed by
waypoint locations with associated speed and altitudes between any two waypoints. Special provision is also
included to y a holding pattern around a speci_ed point.
The guidance system is designed to calculate acceleration commands axG ;a yG ;a zG in the body x;y;z
axes given the desired waypoints, speed, and altitude using state-dependent guidance laws. The commands
are adapted to current ight condition by scaling them based on the measured airspeed.
A feedback is
established between attitude (inner-loop) guidance and acceleration (outer-loop) guidance that ensures the
acceleration commands are modi_ed if the attitude commands exceed heuristically determined limits.
A.
Speed Guidance
Speed guidance is concerned with providing an acceleration command
axG in the body x axis given a desired
forward speed. One simple approach is to set the forward acceleration to be proportional to the di_erence
3 v as
between the desired speedvdes and the measured airspeedvas: axG = v des
where _speed denotes a desired
_speed
4 of 25
American Institute of Aeronautics and Astronautics
time constant for speed regulation. However, this formulation ignores the coupling between the forward
airspeed and the angle of attack of an aircraft. In particular, it ignores the fact that the lift of an aircraft is
dependent both on its airspeed and its angle of attack, which in turn is related to azG . To account for this
coupling, the commanded speed is modi_ed by the vertical guidance through the variable vmod when angle
of attack limits are exceeded or due to a failure of longitudinal ight control (elevator). The modi_cation
term vmod is discussed in Section C. This term forms a feedback between the inner-loop attitude controller
and the outer-loop guidance to ensure that the aircraft is commanded feasible trajectories. This results in
the following expression for the desired forward acceleration command
vdes + vmod l vas
axG =
:
A)
_speed
B.
Vertical Guidance
The task of the vertical guidance is to provide a vertical desired acceleration command
azG given the desired
altitude. The desired altitude ( hdes ) and the desired altitude rate (h_des ) commands are found by interpolating
between current waypoints with current actual position. Letting _altitude denote a time constant associated
with the desired _rst order altitude response, and h denote the current altitude, the desired vertical speed
vs des is found based on the following equation
vsdes =
hdes l h _
+ hdes :
_altitude
B)
Here the term _altitude is the time constant for a _rst order command _lter on the desired altitude. It is
important to limit the vertical airspeed between attainable limits. This is achieved by estimating maximum
and minimum sustainable vertical speeds for the current airspeed, and by using them to limit vs des :
vs max =
( _t ; max l _t ; LPF )
( _t ; min l _t ; LPF )
;v smin =
;
gvasK P ax G
gvasK P ax G
C)
where the variableK P ax G is a constant gain which relates throttle changes to expected acceleration changes,
g
is the acceleration due to gravity, andvas is the measured airspeed. Note that the termgvasK P ax G scales the
limits with the measured airspeed vas . Furthermore, _t denotes the throttle command while _t ; LPF denotes
the predicted throttle position to maintain current ight condition. The variable
_t ; LPF is estimated using
the following Low Pass Filter (LPF):
( _t + sK
x PaxG l _t ; LPF )
__t ; LPF =
_thrustLPF
D)
where sx is the measured speci_c force in the direction of air-relative motion directly available through
accelerometer measurements and_thrustLPF is the time constant of the LPF. The LPF reduces the e_ect of
noisy accelerometer data or high frequency on throttle changes. Finally, the (positive down) vertical desired
acceleration commandazG is computed using a low pass command _lter with a time constant of _v s :
azG =
C.
l ( vs des l vs )
:
_v s
E)
Lateral Guidance
The prescribed course between any two waypoints is assumed to be a straight line. The cross track error
is de_ned as the distance from the current location to the course, and is de_ned to be positive to the right
of the course. To intercept the course from the current location, an intercept velocity is found using a _rst
order model with a desired time constant _intercept and the cross track error using the following equation
vintercept =
1 ecrosstrack
:
2 _intercept
F)
A lead angle 4 T intercept , which is the di_erence between the desired intercept path and the actual path of
the aircraft, is estimated by using an estimate of the ground speed vGS . This lead angle is used to control
the track angle of the aircraft for intercepting the desired path ( to eliminate cross track error):
vintercept
4 T intercept = sin 3 1
:
G)
vGS
5 of 25
American Institute of Aeronautics and Astronautics
It is important to ensure that the magnitude of 4 T intercept is limited from above in order to avoid it from
becoming excessively large (e.g. 30 deg), and limited below, in order to ensure that it does not diminish
very close to the desired waypoint. The desired track angle is:
Tdesired = Tcourse + 4 T intercept ;
H)
Tdesired is then converted to an air-relative track angle. If the aircraft is ying at zero sideslip, then this
would be the desired heading, otherwise, the desired heading needs to be adjusted by adding the estimated
drift angle 4 Tdrift to the desired track angle. The latter handles mind cross-winds if air-data measurements
are used to estimate 4 Tdrift . The estimated drift angle is de_ned as the angle between the direction of
movement through airmass and movement across ground. The desired track angle is found using
desired
= Tdesired + 4 T drift :
I)
The case when the drift angle exceeds 90 degrees in magnitude relates to the case when the aircraft has
negative ground speed (going backward), this case requires further modi_cations that are not discussed in
this paper. A lateral guidance acceleration command ayG is then found by comparing this air-relative track
angle desired with the actual track angle :
ayG =(
It is important to limit the magnitude of
excessive bank angles.
IV.
desired l
)
2vGS
:
_intercept j cos4 T drift j
_)
ayG to an experimentally determined reasonable value to avoid
Inner-loop Guidance and Linear Attitude Control
The guidance system provides the inner loop control system with acceleration commands in an air-relative
velocity frame. The task of the inner loop control system is to convert these commands to aileron, elevator,
rudder, and two throttle commands (for a twin engine aircraft).
A.
Roll Control
Desired roll angle ' des should be commanded to achieve the lateral desired acceleration commandayG and
the aircraft ight path angle (
). However, the control authority of the bank angle control law needs to be
scaled with the desired vertical acceleration azG in order to ensure that the aircraft does not loose altitude
due to excessive bank. This is achieved by the following equation:
'
des =atan2
sayG l azG + gcos
: _
0
)
The desired roll angle is used to _nd the aileron command _a using a Proportional-Integral-Derivative law
(PID):
_a = K P' ( ' des l ' ) l K D' ' _+ _a;I ;
)
where K p' and K d' ' _ are proportional and derivative gains respectively, and_a;I is the integrator state. The
aileron command is limited between the aileron deection limits. The integrator state is updated by
__a;I = K I' ( _a l _a;I )
_)
with the integration performed after limiting the aileron command.
This e_ectively provides an input
proportional to the integral of a sum of bank error and bank angle rate. The combined control law therefore
has built-in integrator windup protection. A similar strategy is used for the other axes. If the aileron is not
available due to damage, then the same formulation is used to calculate rudder deection, with di_erent gains
(and the computation given below for directional control is ignored). If no aileron or rudder is available, then
di_erential thrust command is found by using the same formulation but with di_erent gains. In all other
cases the di_erential thrust command is set to zero. Implementation of this architecture requires that the
aircraft control system estimate which actuators have become ine_ective. In the ight test results presented
here with actuator failures (Section V.B) the aircraft control system was assumed to have the knowledge
whether or not aerodynamic actuators are stuck, however, it does not know which actuators are stuck. In
practice, this can be achieved by monitoring actuation mechanism health, by measuring actuator deection,
or through comparison of the aircraft response to actuator commands to nominal response.
6 of 25
American Institute of Aeronautics and Astronautics
B.
Yaw Control
The yaw control has a PID form with built-in integrator windup protection similar to the roll control logic
described above. In the nominal case when the aileron is available, the rudder command is
_r =
K P ay
( ayG cos' + azG sin' l sy ) + _r;I
2
vas
_)
where K Pay is a selected proportional gain, and sy is the speci_c force experienced at the center of gravity
of the aircraft along the body y axis; found directly through accelerometer measurements transported to the
center of gravity. Letting K Iay denote a chosen integral gain, the integral term _r;I is updated by:
__r;I = K Iay ( _r l _r;I ) ;
)
with the integration performed after limiting the rudder command. When the aileron is not available, the
rudder is used for roll control as described in Section A.
C.
Pitch Control
The goal of the pitch control is to provide the required elevator deection to achieve the desired accelerations.
Letting K Paz denote the chosen proportional gain, the desired angle of attack command _ des is found by
the following expression
l K Paz
_ des =
( azG cos' l ayG sin' l sz ) + _ des;I :
_)
2
vas
The integral term _ des;I eliminates the steady state error and is updated using the integral gain K Iaz as
follows
__des;I = K Iaz ( _ des l _ des;I ) :
_)
The angle of attack command is then limited between a minimum and maximum value, based on expected
positive and negative stall angles. If the command is beyond these limits, then the commanded speed is
modi_ed to alter the desired forward speed by modifying the guidance commandaxG of (1) by updating the
variable vmod using the following equation
vmod = vas
r azG cos' l ayG sin'
l vdes :
sz
_)
This modi_cation assumes that the lift coe_cient will remain constant and changes the commanded speed to
achieve desired lift corresponding to requested acceleration. This formulation accounts for stall prevention
as well as for the case of elevator failure. In implementing equation 18 care was taken to prevent computing
the square root of a negative number by monitoring the sign of the term inside the square root. It is also
important to note that vmod was limited to an experimentally determined reasonable value, particularly on
the negative side. Elevator command _e is found by using a PID control law with K P_ and K D_ denoting
the proportional and derivative gains:
_e = K P_ ( _ des l _ ) l K D_ __+ _e;I :
_)
Letting K I_ denote the chosen integral gain, the integral term _e;I is updated using
__e;I = K I_ ( _e l _e;I ) :
D.
_)
Throttle Control
Symmetric throttle command is found by the following PI control law where
proportional and integral gains:
_t = K Pax ( axG l v_as ) + _t;I;
K Pax and K Iax denote the
_)
where v_as is the online estimated time derivative of the true airspeed. The integral term updated by:
__t;I = K Iax ( _t l _t;I ) :
_)
Di_erential throttle (described in the section on roll control) and symmetric throttle are combined to get
left engine and right engine throttle. Priority is given to symmetric throttle if they cannot both be satis_ed
within limits.
7 of 25
American Institute of Aeronautics and Astronautics
V.
A.
Flight Test Results with State Dependent Guidance and Baseline Linear
Controller
Asymmetric Structural Damage: Sudden 50% right wing failure
We present ight test results as the aircraft undergoes a 50% right wing loss (along with losing complete
right aileron functionality) in autonomous ight with the baseline non-adaptive controller and the statedependent adaptive guidance logic. Figure 3 shows the GT Twinstar in autonomous ight with 50% right
wing loss, resulting in a severe loss of control authority. The aircraft is put in an oval holding pattern about
a waypoint, the right wing is then ejected in mid-ight at about 2021 seconds using a speci_cally designed
ejection mechanism that is triggered from the ground. The aircraft onboard control system is not aware
of the fault, and the aircraft is expected to continue to track an oval holding pattern.
Accordingly, the
controller continues to use the same parameters as in the case of no faults. Figure 4 show the ground track
of the aircraft as the aircraft attempts to track a holding pattern about a waypoint. Figure 5 shows the
recorded altitude of the aircraft. Figure 6 shows the recorded angular rates. It can be seen that while the
aircraft is successful in maintaining ight, the angular rate has an oscillation. Particularly, oscillations in
angle of attack and roll are observed, which result in the oscillations in altitude seen in Figure 5. There are
also oscillations in yaw rate, however their time constant is much lower. It was observed that in order to
perform turns required to maintain the holding pattern, the guidance system forced the aircraft into stable
limit cycles due to the conicting requirements of maintaining forward speed, angle of attack, and turn rate.
This indicates that the onboard controller was not able to _nd a set of inputs corresponding to a steady
trimmed state. This is not unreasonable, given the asymmetric nature of the damage and that the right
aileron functionality is missing. Figure 7 shows the recorded control inputs. It can be seen that the rudder,
aileron, and throttle often saturate. In particular, the aileron saturates at its minimum value repetitively as
the aircraft tries to maintain level ight. The results indicate that the aircraft is able to maintain autonomous
ight in spite of the severe structural damage. The frequency and amplitude of oscillations observed were
found to be within acceptable limits for this type of aircraft and the rather extreme damage condition. It
may be possible to reduce the oscillations through appropriate choice of angle of attack limits and yaw rate
limits. Furthermore, online detection of fault and adjustment of controller parameters accordingly would
also help in reducing the oscillations.
Figure 3.
B.
GT Twinstar in autonomous ight after jettisoning 50% right wing.
Failure of all aerodynamic e_ectors: Propulsion only control
The presented algorithm is able to mitigate the complete loss of all aerodynamic e_ectors by using di_erential
throttle for control. This ight condition is termed as propulsion only control. Figure 8 shows the ground
track of the Twinstar UAS as it tracks an oval pattern in propulsion only control, while Figure 9 shows the
altitude. Figure 10 shows the control commands. At around 1055 seconds into ight, the loss of aileron,
elevator, and rudder actuators is simulated by keeping them constant; the control from this point onward is
accomplished by using only di_erential throttle. The last sub_gure in Figure 10 shows that the di_erential
8 of 25
American Institute of Aeronautics and Astronautics
Ground track of GT Twinstar, aircraft jettisons 50% right wing in mid flight
0
-100
North f t
-200
-300
-400
-500
-600
-300
Figure 4.
-200
-100
0
100
East ft
200
300
400
500
Ground track of GT Twinstar; aircraft jettisons 50% right wing in mid ight.
Aircraft altitude
215
210
205
altitude ft
200
195
190
185
180
175
1980
Figure 5.
2000
2020
2040
2060
2080
time seconds
2100
2120
2140
2160
GT Twinstar altitude; aircraft jettisons 50% right wing at 2021 seconds.
9 of 25
American Institute of Aeronautics and Astronautics
angular rate data corrected for bias
roll rate, rad/ s
0. 5
0
-0. 5
-1
-1. 5
1980
2000
2020
2040
2060
2080
2100
2120
2140
2160
2000
2020
2040
2060
2080
2100
2120
2140
2160
2000
2020
2040
2060
2080
flight time
2100
2120
2140
2160
pit ch rat e, rad/ s
1
0. 5
0
-0. 5
-1
1980
yaw rat e, rad/s
2
0
-2
-4
1980
Figure 6.
Measured angular rate data in autonomous ight; aircraft jettisons 50% right wing at 2021 seconds.
Controller inputs
rudder
0. 5
0
-0. 5
-1
1980
2000
2020
2040
2060
2080
2100
2120
2140
2160
2000
2020
2040
2060
2080
2100
2120
2140
2160
2000
2020
2040
2060
2080
2100
2120
2140
2160
2000
2020
2040
2060
2080
Time seconds
2100
2120
2140
2160
elevat or
1
0. 5
0
1980
aileron
0. 5
0
-0. 5
-1
1980
Throt t le
100
50
0
1980
Figure 7.
Recorded onboard control inputs; aircraft jettisons 50% right wing at 2021 seconds.
elevator, and aileron inputs are normalized; Throttle input is shown in percentage.
10 of 25
American Institute of Aeronautics and Astronautics
Rudder,
throttle only gets activated when the aerodynamic e_ectors are deemed failed. Figure 11 shows the angular
rate data. Despite increased oscillations in roll, the control performance of the UAS was found to be
satisfactory to enable automated landing.
Ground track
-100
-200
-300
North ft
-400
-500
-600
-700
-800
-200
Figure 8.
VI.
-100
0
100
200
East ft
300
400
500
600
Ground track of GT Twinstar in the propulsion only case.
Inner-loop Model Reference Adaptive Control
The inner-loop state-dependent attitude controller can be replaced with a MRAC attitude controller.
The adaptive controller is provided with attitude commands calculated using the inner-outer loop guidance
described in Sections III and IV. The Euler angle attitude commands are converted to a quaternion representation. The desired quaternion command is then calculated using techniques described in Section II of 32.
The idea is to calculate an error quaternion based on a quaternion product between the desired quaternion
33
and the conjugate of the measured quaternion.
The desired angular rate command is also calculated using
the desired velocity and measured acceleration. In the following, we describe the details of the adaptive
control architecture that converts the desired attitude and angular rate commands to actuator commands.
Let D x _< n be compact, and Let x ( t ) be the known state vector, let _ 2 < n denote the control input.
Note that it is assumed that the dimension of the control input is same as the dimension of • x . This is a
reasonable assumption for inner-loop attitude control of aircraft, where the angular rates p;q;r correspond
to the aileron, elevator, and rudder control inputs. In context of MRAC, this assumption can be viewed as
a speci_c matching condition. Consider the following system that describes the dynamics of an aircraft:
x•( t ) = f ( x ( t ) ; x_( t ) ;_ ( t )) ;
_)
In the above equation, the function f is assumed to be globally Lipschitz continuous in x; x_ 2 D x , and
control input _ is assumed to be bounded and piecewise continuous. Therefore, existence and uniqueness of
piecewise solutions to (23) are guaranteed. This assumption is easily satis_ed by most aircraft systems.
The goal of the Approximate Model Inversion (AMI)-MRAC controller is to track the states of a reference
model given by:
x•rm = f rm ( x rm ; x_rm ;r ) ;
_)
where f rm denotes the reference model dynamics which is assumed to be continuously di_erentiable in
x rm ; x_rm for all x rm ; x_rm 2 D x _< n . The commandr ( t ) is assumed to be bounded and piecewise continuous.
Furthermore, it is assumed that the reference model is chosen such that it has bounded outputs (x rm ; x_rm )
11 of 25
American Institute of Aeronautics and Astronautics
Aircraft altitude
220
215
210
altitude ft
205
200
195
190
185
180
1000
1040
1060
1080
time seconds
1100
1120
1140
Altitude in the propulsion only case. The aircraft begins propulsion only control at 1055 seconds
Controller inputs
rudder
0.5
0
-0.5
1040
1050
1060
1070
1080
1090
1100
1110
1120
1130
1050
1060
1070
1080
1090
1100
1110
1120
1130
1050
1060
1070
1080
1090
1100
1110
1120
1130
left
right
1050
1060
1070
1080
1090
Time seconds
1100
1110
1120
1130
elevator
0.4
0.3
0.2
1040
aileron
0.2
0
-0.2
1040
100
T rottle
h
Figure 9.
into ight.
1020
50
0
1040
Figure 10.
Actuator commands in the propulsion only case.
12 of 25
American Institute of Aeronautics and Astronautics
angular rate data corrected for bias
p rad/s
1
0. 5
0
-0. 5
1040
1050
1060
1070
1080
1090
1100
1110
1120
1130
1050
1060
1070
1080
1090
1100
1110
1120
1130
1050
1060
1070
1080
1090
time secods
1100
1110
1120
1130
0. 6
q rad/s
0. 4
0. 2
0
-0. 2
1040
r rad/s
0. 5
0
-0. 5
-1
1040
Figure 11.
into ight.
Angular rates in propulsion only case.The aircraft begins propulsion only control at 1055 seconds
for a bounded input r ( t ). Often a linear reference model is desirable, however the theory allows for a general
nonlinear reference model as long as it is bounded-input-bounded-output stable. When the actuators are
subjected to saturation, a nonlinear reference model may be required.26
Since the exact model 23 is usually not available, we choose an approximate model f^( x; x;_
_ ) which is
invertible with respect to _ such that
3
_ = f^ 1 ( x; x;_
_ ):
_)
where _ 2 < n is the pseudo control input, which represents the desired acceleration. Note that the choice
of the inversion model should capture the control assignment structure, however the parameter of that
mapping need not be completely known. This is important in guaranteeing that appropriate control inputs
are mapped to appropriate states. For example, the inversion model should capture the fact that a deection
in aileron a_ects the pitch rate, although the exact parameters of the relationship need not be known. It is
assumed that for every ( x; x;_
_ ) the chosen inversion model returns a unique _. This can be realized if the
dimension of the input _ is the same as the dimension of x•. In many control problems, and indeed in the
aircraft attitude control problem studied here, this is true. Hence, the pseudo control input satis_es
_ = f^( x; x;_
_ ):
_)
This approximation results in a model error of the form
x• = _ + _( x; x;_
_ )
where the model error _ : < 2n + k !<
n
_)
is given by
_( x; x;_
_ ) = f ( x; x;_
_ ) l f^( x; x;_
_ ):
_)
A tracking control law consisting of a linear feedback part _pd = l [K pK d ]T[ x x_], a linear feedforward
part _rm = •
x rm , and an adaptive part _ad ( x ) is chosen to have the following form
_ = _rm + _pd l _ad:
_)
De_ne the tracking error e 2 < 2n as e( t ) = [ x rm ( t ) l x ( t ) ; x_rm ( t ) l x_( t )] T . To derive the equation for
tracking error dynamics note that •e = •
x rm l x• = _rm l ( _ + _) due to (28). Substituting (29) we see that
13 of 25
American Institute of Aeronautics and Astronautics
"
e
•= _pd l ( _ad l _) and then, letting A =
#
" 0 #
I
, and B =
, the tracking error dynamics
l Kd
I
0
l Kp
are found to be34 ,26,35,36
e_ = Ae + B [uad ( x; x;_
_ ) l _( x; x;_
_ )] :
_)
The baseline full state feedback controller gainsK;p d are chosen such thatA is a Hurwitz matrix. Hence
for any positive de_nite matrix Q 2 < 2n _ 2n , a unique positive de_nite solution P 2 < 2n _ 2n exists to the
Lyapunov equation
A TP + PA + Q = 0 :
_)
Letting _x = [ x; x;_
_ ] 2 < 2n + k , it is assumed that the uncertainty _(_ x ) can be approximated using a Single
Hidden Layer (SHL) Neural Network (NN).
A.
Model Reference Adaptive Control using a Single Hidden Layer Neural Network
A SHL NN is a nonlinearly parameterized map that can be used for capturing unstructured uncertainties
that are known to be continuous and de_ned over a compact domain.37 Let _x denote the input to the SHL
NN, the output of a SHL NN can be given as
uad (_
x ) = W T_ ( V T x_) 2 < n 3 :
_)
In the above equation, W 2 < ( n 2 +1) _ n 3 , where n 2 is the number of hidden layer neurons and n 3 is the
dimension of the NN output, is the NN synaptic weight matrix connecting the hidden layer with the output
layer and has the following form:
0 _ w; 1
B w1; 1
W = B
..
B
B
.
@
wn;2 1
1
___ _ w;n 3
___ w1;n 3
..
..
.
.
___ wn;n2 3
C
C 2 < ( n 2 +1) _ n 3 ;
C
C
A
_)
where V 2 < ( n 1 +1) _ n 2 is the NN synaptic weight matrix, with n 1 being the number of inputs to the NN,
connecting the input layer with the hidden layer and has the following form:
0 _ v; 1
B v1; 1
V = B
..
B
B
.
@
vn;1 1
and x_ _<
n 1 +1
1
___ _ v;n 2
___ v1;n 2
..
..
.
.
___ wn;n1 2
C
C 2 < ( n 1 +1) _ n 2 ;
C
C
A
_)
. x_ contains the data on which the network trains x in and the constant bias term bv :
0
x_ =
B
B
bv !
= B
B
x in
B
B
@
bv
x in 1
x in 2
..
.
x in n 1
1
C
C
C 2 < n 1 +1 :
C
C
C
A
_)
Typically x in = x , however, the actuator deections and other states may also be used to train the NN.32 For
ease in notation, let z = V T x_ 2 < n2 , then the vector function _ ( z) 2 < n 2 +1 is given by:
0
B
_ ( z) = B
B
B
@
bw
_1 ( z1 )
..
.
_n 2 ( zn 2 )
1
C
C 2 < n 2 +1 :
C
C
A
14 of 25
American Institute of Aeronautics and Astronautics
_)
The elements of _ consist of sigmoidal activation functions, which are given by:
_j ( zj ) =
1
:
1 + e3 azj j
_)
SHL NN are known to be universal approximators.37,38 That is, for all _x 2 D , where D is a compact set,
there exists a number of hidden layer neurons n 2 , and an ideal set of weights (W _;V _ ) that brings the NN
output to within an _ neighborhood of the function approximation error. The largest such _ is given by
_ = sup W
_T
_( V
_T
x_) l _(_x ) :
)
x_) + _
~( x ) ;
!)
x_ 2 D
Hence the following approximation holds for all _x 2 D
_(_x ) = W
_T
_(V
_T
where D is compact, and __= sup x_2 D k_
~( x ) k can be made arbitrarily small given su_cient number of hidden
layer neurons.
The NN weight adaptation laws are given by: 39,40,32,35
_ =
W
V_ =
l ( _ ( V T x_) l _ 0( V T x_) V T x_) r T € w l k kekW
0
l € V xr
_ TW _T ( V T x_) l k kekV;
)
!)
where the last term in 40 is Narendra and Annaswamy'se-modi_cation term which is used to prevent weight
41
drift in the presence of sensor noise.
Figure 12 depicts the control architecture for MRAC control discussed
in this section. Pseudo Control Hedging 34,32 is used for mitigating actuator saturation. It should be noted
that for the above adaptive laws to hold, the reference model and the exogenous reference commands should
be constrained such that the desired trajectory does not leave the domain over which the neural network
approximation is valid. Under these assumptions, the closed loop MRAC architecture used here has been
shown to have guarantees of uniform ultimate boundedness. 26,35 Furthermore, ensuring that the state
remains within a given compact set implies an upper bound on the adaptation gain (see for example Remark
2 of Theorem-1 in 42). Note also that _ depends on _ad through the pseudocontrol _, whereas _ad has to
be designed to cancel _. Hence the existence and uniqueness of a _xed-point-solution for
_ad = _(_x;_ ad ) is
assumed. Su_cient conditions for this assumption are also available43 .44
VII.
Flight Test Results with MRAC
Results from a ight tests are presented as the aircraft tracks an oval pattern while holding altitude at
200 ft with 25% of the left wing missing. The GT Twinstar uses the guidance algorithm discussed in Section
III to ensure that the aircraft can track feasible trajectories even when it has undergone severe structural
damage. The adaptive control algorithm has a cascaded inner and outer loop design. The state dependent
guidance logic described in Section III, commands the desired roll angle, angle of attack, and sideslip angle
to achieve desired waypoints. The inner loop ensures that the states of the aircraft track these desired
quantities using the control architectures described in section VI. The SHL MRAC implementation has _ve
hidden layer neurons. The learning rates in equation 40 are set as €w = 1 and € V = 5 for the SHL MRAC
implementation while the e-modi_cation constant _ is set to 0.1.
A.
Flight Test Results Without Damage
In this section ight test results are presented as the aircraft operating in nominal conditions tracks four
waypoints arranged in a rectangular pattern. The ground track of the controller is shown in _gure 13. In
that _gure, the circles denote the commanded way points, the dotted line connecting the circles denotes the
path the aircraft is expected to take, except while turning at the way points.
While turning at the way
points, the onboard guidance law smooths the trajectory with circles of 80 feet radius.
Figure 14 shows
the altitude tracking performance of the SHL MRAC adaptive controller.
The inner loop tracking error
performance of the SHL MRAC adaptive controller is shown in _gure 15. The actuator input required for
the SHL MRAC adaptive controller is shown in _gure 16. The inner loop tracking performance and general
inner loop handling was found satisfactory.
15 of 25
American Institute of Aeronautics and Astronautics
xrm
xc
Reference Model
crm

fˆ  1

cmd
Nonlinear
Actuator Dynamics

f
x
+
erm

 
ad
Neural Network
Adaptation Law
pd
Figure 12.
B.
PD compensator
Neural Network Adaptive Control using Approximate Model Inversion
Flight Test Results With Damage
In this section ight test results are presented as the aircraft tracks four waypoints arranged in a rectangular
pattern with 25% of the left wing missing. The guidance and control laws remain unaltered in both nominal
ight and damaged ight, with the adaptive controller expected to mitigate the e_ects of the enforced
damage. Figure 17 shows the ground track of the aircraft with 25% left wind missing. Figure 18 shows that
the altitude tracking performance of the SHL MRAC adaptive controller. The cross-tracking and altitude
performance of the SHL MRAC controller when ying with damage remained comparable to controller
performance under nominal conditions (nominal performance was shown in Figures 13,14).The inner loop
tracking error performance of the SHL MRAC controller is shown in _gure 19. The actuator input required
for the SHL MRAC controller is shown in _gure 20.
The inner loop tracking performance and general
inner loop handling of the damaged aircraft was found satisfactory to attempt several successful automated
landings.
16 of 25
American Institute of Aeronautics and Astronautics
Ground track
cmd
SHL MRAC
0
−100
N
ort
h
ft
−200
−300
−400
−500
−300
Figure 13.
−200
−100
0
100
East ft
200
300
400
Flight recorded ground track for SHL MRAC under nominal conditions.
206
cmd
SHL MRAC
204
202
alt
itu
de
ft
200
198
196
194
192
0
5
10
15
20
time seconds
25
30
35
40
Figure 14.
Flight recorded altitude tracking performance for SHL MRAC and DFMRAC under nominal
conditions on the GT Twinstar UAS. The commanded altitude is at 200 ft.
17 of 25
American Institute of Aeronautics and Astronautics
0.5
ra
di
an
s
0
−0.5
0
5
10
15
20
15
20
15
20
time seconds
0.5
ra
di
an
s
0
−0.5
0
5
10
time seconds
innerloop errors
0.5
ra
di
an
s
0
−0.5
0
5
10
time seconds
Figure 15.
Inner loop tracking errors for SHL MRAC
Controller inputs
0.5
ru
dd
er
0
−0.5
0
5
10
15
20
25
5
10
15
20
25
5
10
15
20
25
5
10
15
20
25
0.4
el
ev
at
or
0.2
0
0
0.5
ail
er
on
0
−0.5
0
80
Th
rot
tle
60
40
20
0
Time seconds
Figure 16.
Actuator inputs for SHL MRAC
Ground track
cmd
SHL MRAC
0
−100
N
ort
h
ft
−200
−300
−400
−500
−600
Figure 17.
−200
−100
0
100
East ft
200
300
400
500
Flight recorded ground track for SHL MRAC with 25% left wing missing.
18 of 25
American Institute of Aeronautics and Astronautics
208
cmd
SHL MRAC
206
204
alt
itu
de
ft
202
200
198
196
194
0
5
10
15
20
time seconds
25
30
35
40
Figure 18.
Flight recorded altitude tracking performance for SHL MRAC with 25% left wing missing. The
commanded altitude is at 200 ft.
0.5
ra
di
an
s
0
−0.5
0
5
10
15
20
time seconds
25
30
35
5
10
15
20
time seconds
innerloop errors
25
30
35
5
10
15
20
time seconds
25
30
35
0.5
ra
di
an
s
0
−0.5
0
0.5
ra
di
an
s
0
−0.5
0
Figure 19.
Inner loop tracking errors for SHL MRAC
Controller inputs
1
ru
dd
er
0.5
0
0
5
10
15
20
25
30
35
40
5
10
15
20
25
30
35
40
5
10
15
20
25
30
35
40
5
10
15
20
Time seconds
25
30
35
40
1
el
ev
at
or
0.5
0
0
1
ail
er
on
0.5
0
0
100
Th
rot
tle
50
0
0
Figure 20.
Actuator inputs for SHL MRAC
19 of 25
American Institute of Aeronautics and Astronautics
VIII.
Adaptive Loop Transfer Recovery for Flight Control under Actuator
Time Delay
Actuator time delays can be induced due to unmodeled actuator dynamics and can worsen over time
due to actuator wear. Traditionally, aircraft control system designers have relied on phase and time delay
margins of linear controllers to guarantee robustness to unmodeled time delays. These concepts do not
directly extend to adaptive controllers because the closed loop is nonlinear. However, MRAC is designed to
track a linear reference model, which is typically chosen to satisfy the desired closed loop margins (gain and
time delay margins). The goal of the ALR approach is to design an adaptive law such that the states track
the reference model asymptotically, and the reference model margins are preserved to the maximum degree
possible.
In order to study the stability margins of the closed loop system, linearization about an equilibrium point
x_ of the adaptive law of (40) is typically required along with the assumption that the external commands
T
_ T @_( V_ x_) , where W;V
_ _ denote the frozen weights. Figure
are constant. Such an analysis involves the termW
@x_
21 shows the loop with the linearization and the weights frozen. If W = 0, and if the system were exactly
modeled as a linear system, then the margins calculated with the loop broken at x correspond to the margins
of the reference model. The bottom portion of the diagram shows the e_ect of the adaptive element in steady
_ = 0, V_ = 0). It can be seen that even with e( t ) = 0 and the weights constant, the
state (that is when W
adaptive term modi_es the margins of the reference model in an unknown way. Furthermore, when weights
are not constant, the feedback loop becomes nonlinear and it is not possible to use such a representation to
analyze the margins using this representation. However, it may still be possible to use this representation to
analyze the margins of the linearized system if the following constraint were approximately satis_ed
W T (t )
@_( V T x_( t ))
= 0;
@x_( t )
")
by modifying the adaptive law such that it satis_es asymptotically 42 as the modi_cation gain approaches
in_nity. 45
Linearized
system
x
-
+
𝐾ë
9
Figure 21.
Í
ò
ê:8 Í T;
òT
Visualization of the linearized adaptive system dynamics
This is achieved by adding a modi_cation term to the adaptive law of (40). Let
J (t ) =
20 of 25
American Institute of Aeronautics and Astronautics
1
T
T
_( t )) k2F
2 kW ( t ) _ ( V x
,
denote a cost function wherek:kF denotes the Frobenious norm. Minimization of this cost would mean that
the constraint in (42) is approximately satis_ed. Similar to other modi_cations for adaptive control, ALR
adds a term to the adaptive law in the direction of maximum reduction of this cost. Noting that
@J( t )
= _ ( V T x_) _ T ( V T x_) W;
@W( t )
#)
the modi_ed adaptive law for the outer layer weights W has the form:
_ = l ( _ ( V T x_) l _ 0( V T x_) V T x_) r T l € w k kekW l € a _ ( V T x_) _ T ( V T x_) W:
W
$)
In the above adaptive law, the last term is the ALR term with € a > 0 being the ALR gain. Theorem 1 in
T
@_( V x ( t ))
[42] shows that for a system a_ne in control with matched linearly parameterized uncertainty, if
@x( t )
has full column rank, there exists a € _a such that if € a > € _A x ( t ) asymptotically tracks the reference states
x rm . Furthermore, there exists k 1 and _ such that kW T_ (_
x ) k_ Ke1 3 _ { a t + OA =€ a). This means that
W(t) is driven into a subspace within which the constraint in ") is approximately satis_ed, exponentially
in time. The speed with which this happens is proportional to the ALR gain, and the accuracy to which the
constraint is satis_ed is inversely proportional to the ALR gain.
The ALR design procedure consists of selecting the ALR gain €w su_ciently large such that the cost in
(43) remains su_ciently small for all t>t 1 > 0, where t1 is also made su_ciently small by a su_ciently
large ALR gain. While a similar modi_cation term can be found for the hidden layer weightsV , it was found
that the approximate satisfaction of 42 can be achieved with only modifying the outer layer weights using
(44). It is further shown in [45] that increasing the ALR gain does not amplify the e_ect that sensor noise
has on the adaptive control law as compared to the e_ect sensor noise would have had if €a were equal to
zero.
A.
Flight Test Results using ALR under Actuator Time Delay
The e_ectiveness of ALR in handling time delay was tested in ight on the GT Twinstar aircraft.
Time
delay was injected in the elevator command until unacceptable performance was observed, which was characterized by limit cycles with high frequency and unacceptable magnitude.46 The time delay above which the
unacceptable performance was observed is referred to here as the time delay margin. It was found through
ight test results that the time delay margin without ALR was about 0
:08 seconds, and with ALR about
0:12 seconds. Figure 22 shows the evolution of pitch rate as time delay of:11
0 seconds is added and the ALR
term is toggled. As the time delay is added, we see the onset of undesirable limit cycles in the pitch rate, at
about 31 seconds into ight. When the ALR term is switched on a reduction in undesirable oscillations is
observed. At 65 seconds, the ALR term is switched o_ again, and we notice a reappearance of the undesirable
oscillations.
21 of 25
American Institute of Aeronautics and Astronautics
Time delay of 0.11
seconds added
1. 5
ALR turned
ON
pitch rate
Vehicle
performs
a turn
ALR turned
OFF
1
0. 5
0
-0. 5
-1
0
10
20
30
40
50
60
flight time
Time (sec)
Figure 22.
Evolution of pitch rate with injected time delay.
22 of 25
American Institute of Aeronautics and Astronautics
70
80
90
IX.
Conclusion
We described outer-loop guidance and inner-loop attitude control algorithms that ensure safe waypoint
following autonomous ight of a twin engine aircraft in the presence of severe structural damage or actuator
damage. A speci_cally designed state dependent guidance law for subsonic aircraft was described and used
to ensure that the aircraft is commanded a feasible trajectory in the presence of damage.
The guidance
law established a feedback between inner-loop guidance and outer-loop guidance to ensure that the aircraft
acceleration commands were modi_ed if the attitude commands exceeded predetermined limits. This provides
a simple way to ensure that the aircraft commands do not leave the safe-ight envelop. However, since no
fault detection algorithm is implemented onboard, the attitude limits must be conservatively chosen to ensure
reasonable compromise between performance in nominal conditions and safety with damage. With better
knowledge of the damage, a more accurate estimate of the feasible envelop could be generated online. This
is expected to improve the performance signi_cantly.
A baseline linear attitude controller with the state dependent guidance logic was tested in ight with 50%
of the aircraft's right wing jettisoned in mid ight. The baseline controller was also tested in a propulsion
only control scenario, in which all aerodynamic e_ectors of the aircraft were frozen. A single hidden neural
network based model reference adaptive attitude controller along with the state dependent guidance logic
was tested in ight with 25% of left wing missing. The Adaptive Loop Recovery modi_cation to adaptive
control was veri_ed in ight to allow the adaptive controller to tolerate larger actuator time delays. The
ight-tests were performed on the GT Twinstar UAV which is a small foam built airplane with aerodynamic
characteristics that resemble a typical transport category aircraft (twin-engine, propeller driven, un-swept
high mounted wings). This work highlighted the fact that outer-loop guidance methods that ensure feasible
trajectories are commanded to the aircraft are critical in ensuring safe autonomous ight in the presence of
faults. These results indicate the possibility of using autonomous ight control methods for ensuring safe
ight, and in some cases safe automated landing, of aircraft with severe structural damage.
Acknowledgments
This work was supported in part by NSF ECS-0238993 and NASA Cooperative Agreement NNX08AD06A.
The authors thank Jeong Hur, Research Engineer I at Georgia Tech. Jeong was the lead test-pilot for several
of the ight test results presented.
References
1
Etkin, B. and D., R. L.,
Dynamics of Flight, Stability and Control
, John Wiley and Sons, 1996.
Stevens, B. L. and Lewis, F. L., Aircraft Control and Simulation , John Wiley and Sons, 2003.
3
Patton, R. J. and Chen, J., \Fault-Tolerant Control Systems: The 1997 Situation,"
IFAC Symposium on Fault Detection
Supervision and Safety for Technical Processes , Kingston Upon Hull, UK, 1997, pp. 1033{1054.
4
Hajiyev, C. and Caliskan, F., Fault Diagnosis and Recon_guration in Flight Control Systems
, Kluwer Academic Publicshers, Norwell, MA, 2003.
5
Steinberg, M., \Historical overview of research in recon_gurable ight control,"
Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering
, Vol. 219, No. 4, 2005, pp. 263{275.
6
Zhang, Y. and Jang, J., \Bibliographical review on recon_gurable fault-tolerant control systems,"
Elsevier Annual Reviews
in Control , Vol. 32, No. 1, 2008, pp. 229{252.
7
Isermann, R., Fault-Diagnosis Systems: An Introduction from Detection to Fault Tolerance
, Springer-Verlag, Berlin,
Germany, 2006.
8
Nguyen, N., Krichnamumar, K., and Kaneshige, J., \Dynamics and Adaptive Control for Stability Recovery of Damaged
Asymmetric Aircraft,,"
AIAA Guidance, Navigation, and Control Conference and Exhibits
, August 21-24 2006, AIAA-20066049.
9
Nguyen, N., Krishnakumar, K., and Kaneshige, J., \Flight Dynamics and Hybrid Adaptive Control of Damaged Aircraft,"
AIAA Journal of Guidance, Control, and Dynamics
, Vol. 31, No. 3, 2008, pp. 751{764, doi: 10.2514/1.28142.
10
Boskovic, J. D., Prasanth, R., and Mehra, R. K., \Retro_t Fault-Tolerant Flight Control Design Under Control E_ector
Damage," AIAA Journal of Guidance, Control and Dynamics
, Vol. 30, No. 3, 2007, pp. 703{712.
11
AIAA, Control of Commercial Aircraft with Vertical Tail Loss
. AIAA 4th Aviation Technology, Integration, and Operation (ATIO) Forum, 2004, AIAA-2004-6293.
12
Hallouzi, R. and Verhaegen, M., \Fault-Tolerant Subspace Predictive Control Applied to a Boeing 747 Model,"
Journal
of Guidance, Control and Dynamics , Vol. 31, No. 4, July-August 2008, pp. 873{883, AIAA-33256-469.
13
Hitachi, Y., Damage-Tolerant Control System Design for Propulsion-Controlled Aircraft
, Master's thesis, University of
Toronto, Toronto, Canada, 2009.
2
23 of 25
American Institute of Aeronautics and Astronautics
14
Hitachi, Y. and Liu, H., \
H 1 -LTR Technique Applied to Robust Control of Propulsion-Controlled AircraftPropulsionControlled Aircraft," AIAA Guidance, Navigation, and Control Conf.
, Chicago, IL, Aug. 10-13 2009.
15
Yucelen, T. and Calise, A., \A derivative-free model reference adaptive controller for the generic transport model,"
AIAA
Guidance, Control and Navigation Conference , Toronto, Canada, August 2010, invited.
16
Yucelen, T. and Calise, A., \Derivative-Free model reference adaptive control," Vol. 34, No. 8, 2012, pp. 933{950.
17
Yucelen, T., Kim, K., Calise, A., and Nguyen, N., \Derivative-Free output feedback adaptive control of an aeroelastic
generic transport model," Guidance, Navigation, and Control conference , AIAA, Portland, OR, August 2011, AIAA-2011-6454.
18
Lombaerts, T. J. J., Huisman, H. O., Chu, Q. P., Mulder, J. A., and Joosten, D. A., \Nonlinear Recon_guring Flight
Control Based on Online Physical Model Identi_cation,"
Journal of Guidance Control and Dynamics
, Vol. 32, No. 3, 2009,
pp. 727{748, AIAA paper number 0731-5090, doi:10.2514/1.40788.
19
Lunze, J. and Ste_en, T., \Control Recon_guration after Actuator Failures using Disturbance Decoupling Methods,"
IEEE Transactions on Automatic Control
, Vol. 51, No. 10, October 2006, pp. 1590{1601.
20
Idan, M., Johnson, M. D., and Calise, A. J., \A Hierarchical Approach to Adaptive Control for Improved Flight Safety,"
AIAA Journal of Guidance Control and Dynamics
, Vol. 25, No. 6, nov-dec 2002, pp. 1012{1020.
21
Lavertsky, E. and Wise, K., \Flight Control of Manned/Unmanned Military Aircraft,"
Proceedings of American Control
Conference , 2005.
22
Kutay, A., Chowdhary, G. V., Calise, A., and Johnson, E. N., \A Comparision of Select Direct Adaptive Control Methods
under Actuator Failure Accommodation,"
Proceedings of the AIAA GNC Conference , Honolulu, HI, 2008, AIAA-2008-7286.
23
Jourdan, D. B., Piedmonte, M. D., Gavrilets, V., and Vos, D. W.,
Enhancing UAV Survivability Through Damage
Tolerant Control , No. August, AIAA, 2010, pp. 1{26, AIAA-2010-7548.
24
Chen, Z., Samarabandu, J., and Rodrigo, R., \Recent Advances in Simultaneous Localization and Map-building using
Computer Vision," Proc. of the AIAA Guidance, Navigation, and Control Conference and Exhibit
, 2008.
25
Haddad, W. M. and Chellaboina, V., Nonlinear Dynamical Systems and Control: A Lyapunov-Based Approach
, Princeton University Press, Princeton, 2008.
26
Kannan, S., Adaptive Control of Systems in Cascade with Saturation
, Ph.D. thesis, Georgia Institute of Technology,
Atlanta Ga, 2005.
27
Christophersen, H. B., Pickell, W. R., Neidoefer, J. C., Koller, A. A., Kannan, S. K., and Johnson, E. N., \A compact
Guidance, Navigation, and Control System for Unmanned Aerial Vehicles,"
Journal of Aerospace Computing, Information, and
Communication , Vol. 3, May 2006, AIAA paper number 1542-9423, doi: 10.2514/1.18998.
28
Johnson, E. N. and Schrage, D. P., \System Integration and Operation of a Research Unmanned Aerial Vehicle,"
AIAA
Journal of Aerospace Computing, Information and Communication
, Vol. 1, No. 1, Jan 2004, pp. 5{18, AIAA paper number
1542-9423 doi: 10.2514/1.4424.
29
Morelli, E. A., \Real Time Parameter Estimation in The Frequency Domain,"
Journal of Guidance Control and Dynamics , Vol. 23, No. 5, 2000, pp. 812{818.
30
Debusk, W., Chowdhary, G., and Eric, J., \Real-Time System Identi_cation of a Small Multi-Engine Aircraft,"
Proceedings of AIAA AFM , AIAA, Chicago, IL, 2009, AIAA-2009-5935.
31
Chowdhary, G., Debusk, W., and Johnson, E. N., \Real-Time System Identi_cation of a Small Multi-Engine Aircraft
with Structural Damage," AIAA Infotech@Aerospace , AIAA, Atlanta, GA, April 2010, AIAA-2010-3472.
32
Johnson, E. and Kannan, S., \Adaptive Trajectory Control for Autonomous Helicopters,"
Journal of Guidance Control
and Dynamics , Vol. 28, No. 3, May 2005, pp. 524{538.
33
Wie, B. and Barba, P. M., \Quaternion feedback for spacecraft large angle maneuvers," Vol. 8, 1985, pp. 360{365.
34
Johnson, E. N., Limited Authority Adaptive Flight Control
, Ph.D. thesis, Georgia Institute of Technology, Atlanta Ga,
2000.
35
Chowdhary, G., Concurrent Learning for Convergence in Adaptive Control Without Persistency of Excitation
, Ph.D.
thesis, Georgia Institute of Technology, Atlanta, GA, 2010.
36
Chowdhary, G. and Johnson, E. N., \Theory and Flight Test Validation of a Concurrent Learning Adaptive Controller,"
Journal of Guidance Control and Dynamics , Vol. 34, No. 2, March 2011, pp. 592{607.
37
Hornik, K., Stinchcombe, M., and White, H., \Multilayer Feedforward Networks are Universal Approximators,"
Neural
Networks , Vol. 2, 1989, pp. 359{366.
38
Suykens, J. A., Vandewalle, J. P., and Moor, B. L. D., Arti_cial Neural Networks for Modelling and Control of Non-Linear
Systems, Kluwer, Norwell, 1996.
39
Lewis, F. L., \Nonlinear Network Structures for Feedback Control,"
Asian Journal of Control , Vol. 1, 1999, pp. 205{228,
Special Issue on Neural Networks for Feedback Control.
40
Kim, Y. H. and Lewis, F., High-Level Feedback Control with Neural Networks , Vol. 21 of Robotics and Intelligent Systems ,
World Scienti_c, Singapore, 1998.
41
Narendra, K. S. and Annaswamy, A. M., \Robust Adaptive Control in the Presence of Bounded Disturbances,"
IEEE
Transactions on Automatic Control , Vol. AC-31, No. 4, 1986, pp. 306{315.
42
Yucelen, T. and Calise, A., \Kalman Filter Modi_cation in Adaptive Control,"
Journal of Guidance, Control, and
Dynamics , Vol. 33, No. 2, march-april 2010, pp. 426{439.
43
Kim, N., Improved Methods in Neural Network Based Adaptive Output Feedback Control, with Applications to Flight
Control , Ph.D. thesis, Georgia Institute of Technology, Atlanta Ga, 2003.
44
Zhang, T., Ge, S., and Hang, C., \Direct adaptive control of non-a_ne nonlinear systems using multilayer neural networks," American Control Conference, 1998. Proceedings of the 1998 , Vol. 1, jun 1998, pp. 515 {519 vol.1.
45
Calise, A. and Yucelen, T., \Adaptive Loop Transfer Recovery,"
Journal of Guidance Control and Dynamics
, Vol. 35,
No. 3, 2012, pp. 807{815, AIAA paper number 731-5090, doi: 10.2514/1.55835.
24 of 25
American Institute of Aeronautics and Astronautics
46
Kimbrell, S., Johnson, E. N., Chowdhary, G., and Calise, A., \A Process to Obtain Robustness Metrics for Adaptive
Flight Controllers," AIAA Guidance Navigation and Control conference
, AIAA, Chicago, IL, Aug 2009, AIAA-2009-5966.
25 of 25
American Institute of Aeronautics and Astronautics