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A RECONFIGURATION SCHEME FOR FLIGHT CONTROL ADAPTATION TO
FIXED-POSITION ACTUATOR FAILURES
ROBERT S. EICK
A THESIS PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
MASTER OF SCIENCE
UNIVERSITY OF FLORIDA
Robert S. Eick
I dedicate this work to my family.
This research was inspired by the Intelligent Flight Control System (IFCS) flight
research project at NASA Dryden Flight Research Center (DFRC). The author thanks
John Burken of NASA DFRC for his support.
TABLE OF CONTENTS
ACKNOWLEDGMENTS . .
LIST OF TABLES ...
LIST OF FIGURES ........
A B STR A C T . . . . . . . . . .
1 INTRODUCTION ...............
2 REVIEW OF LITERATURE
2.1 Introduction ...............
2.2 The State of the Art ............
2.2.1 Fault Detection and Isolation (FDI)
2.2.2 Robust Control ..........
2.2.3 Fault-Tolerant Control .......
2.2.4 Robust Fault-Tolerant Control .
2.2.5 Robust Fault Estimation ......
2.2.6 Fault-Tolerant Control w/ FDI .
2.2.7 Supervision ............
2.3 Types of Redundancy . . .
2.4 Fault-Tolerant Control Methods .....
2.4.1 Passive Approaches . .
2.4.2 Active Approaches .. ......
3 PRELIMINARIES .. .............
3.1 Aircraft Flight Mechanics . . .
3.1.1 Aircraft Axis Systems .......
3.1.2 General Equations of Motion .
3.1.3 Linearized Equations of Motion
3.2 Neural Networks .. ...........
3.2.1 Artificial Neural Networks .
3.2.2 Design . ........
3.2.3 Areas of Applications . .
. . . . . .
4 FAULT DETECTION AND ISOLATION . ... ... .. 35
4.1 Failure Parameterization .. ... ............. 35
4.2 FDI via Artificial Neural Networks . . . . 37
4.2.1 Artificial Neural Network FDI Formulation . ..... 37
4.2.2 Artificial Neural Network Development . . . 38
5 THE STABILIZATION PROBLEM . . .. . . 42
5.1 The Nonlinear Trim Problem . . .. . . 42
5.2 The Linear Trim Problem . . . . . . 44
6 FAULT-TOLERANT CONTROL DESIGN METHODS . . 46
6.1 Fault-Tolerant Control Design Using LQR Theory .. . 47
6.2 Fault-Tolerant Control Design Using H, Theory . . . 49
7 APPLICATION TO AN F/A-18 . . . . . . 53
7.1 H healthy F/A -18 . . . . . . . 53
7.2 Failed F/A-18 . . . . . . . 57
7.3 Artificial Neural Network FDI . . . . . 60
7.4 Stabilization . . . . . . . . 61
7.5 Fault-Tolerant Control Nonlinear Simulations . . 62
8 CONCLUSION S . . . . . . . . 70
A LINEARIZED MODEL OF THE F/A-18 . . . . 73
B NOMINAL CONTROLLER DESIGN . . . . . 76
REFEREN CE S . . . . . . . . . 83
BIOGRAPHICAL SKETCH ............................. ..94
LIST OF TABLES
4-1 F/A-18 Control Surface Position Limits . . . . 41
7-1 Stabilization Results . . . . . . . 62
LIST OF FIGURES
1-1 American Airlines Airbus A300-600 . .
1-2 Flight 548 crashes in Queens, New York. . .....
1-3 Vertical Stabilizer of Flight 548....... . .....
2-1 General schematic of a reconfigurable control system with supervision
2-2 Venn Diagram of Reconfiguration Strategies .. .............
Taxonomy of Reconfigurable Control Methods ..... . . 15
Relationship between Earth axis system and body axis system . 22
A biological neuron . . . . . . . 30
An artificial neuron . . . . . . . 31
An artificial neural network . . . . . . 32
The structure of a full-state feedback control system . . . 36
Roll feature vectors for different failure position w . . . 39
F/A-18 flight control surface numbering scheme . . . 40
Reference closed-loop system . . . . . .. 49
Target M odel . . . . . . . . 50
Ho synthesis model . . . . . . . 51
H o analysis m odel . . . . . . . 52
Longitudinal responses: healthy aircraft . . . . 54
Lateral-directional responses: healthy aircraft . . . . 55
Control surface deflections: healthy aircraft . . . . 56
Longitudinal responses: failed aircraft . . . . 57
Lateral-directional responses: failed aircraft . . . . 58
Control surface deflections: failed aircraft . . . . 59
7-7 Lateral responses : LQR FTC .
7-8 Longitudinal responses : LQR FTC .
7-9 Control surface deflections : LQR FTC
7-10 Lateral responses : Hc FTC . .
7-11 Longitudinal responses : Hc FTC .
7-12 Control surface deflections : Hc FTC .
. . .. 6 4
. ... . 6 5
. ... . 6 6
. . .. 6 7
. . ... . 6 8
. ... . 6 9
Abstract of Thesis Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Master of Science
A RECONFIGURATION SCHEME FOR FLIGHT CONTROL ADAPTATION TO
FIXED-POSITION ACTUATOR FAILURES
Robert S. Eick
Chair: Richard C. Lind, Jr.
Major Department: Mechanical and Aerospace Engineering
This work considers the problem of redesigning a flight control system to achieve
acceptable stability and performance in the presence of a control surface failure. The
particular failure considered is the fixed-position or jammed actuator failure. This
is an especially difficult type of failure to overcome since the operational control
surfaces must be reconfigured not only to achieve the control objective but also to
compensate for a disturbance due to the failure. The proposed reconfiguration scheme
relies on three interdependent systems: a fault detection and isolation (FDI) system,
a stabilization system, and a fault-tolerant control system. FDI is developed using an
artificial neural network that monitors the feedback measurements of the flight control
system. Stabilization is based upon a least-squared optimization algorithm to determine
a new trim condition for the failed aircraft. Two fault-tolerant control techniques
are developed to complete the reconfiguration scheme. The first is a linear quadratic
regulator (LQR) approach and the second is an H, approach. In each approach the
effects of the jammed surface are treated as a measurable constant disturbance to the
system. For the LQR approach a controller is designed that balances the jammed
surface (disturbance rejection), and provides command-tracking. For the Ho approach
a two-step design process is used where first the feedforward part of the controller is
designed to achieve perfect trajectory following then the feedback part of the controller
is designed using H, regulator theory. The H_ approach relies on the use of a low-
pass filter in controller synthesis to limit the disturbance forces and accurately simulate
the effects of the jammed surface. The two methods, along with FDI and stabilization,
are demonstrated on a high fidelity nonlinear six-degree-of-freedom F/A-18 simulator.
Simulation results are presented with a significant control surface failure and show the
benefits on stability and performance using the developed reconfiguration techniques.
The LQR and H, methods achieved virtually the same results for the targeted failure
class with both regaining stability and restoring performance in all instances.
To achieve the safety goals in air travel it will be necessary to design flight control
systems that can compensate for failures and damage to aircraft. All modem aircraft
depend upon their flight control system to provide the handling qualities necessary for
successful flight. When a component of the flight control system fails or is damaged it
is desirable that the safety of the aircraft not be compromised. Reconfigurable controls
attempts to address this issue by developing reconfigurable control schemes that
enhance survivability and safety to allow an aircraft to be recovered in flight after it has
suffered component failure or damage. The primary benefit of reconfigurable controls
is the ability to significantly enhance flight safety. Beyond this, a reconfigurable
controller has the potential to restore desired stability and performance characteristics
so that a crippled aircraft can complete its mission and land successfully. With their
clear benefit in both military and civil aircraft, reconfiguration techniques and strategies
have become the focus of many investigators in recent years and are currently receiving
A reconfiguration scheme consists of three parts: a fault detection and isolation
(FDI) procedure, a reconfiguration logic, and a fault-tolerant control law. The FDI
procedure detects a failure and isolates it to a specific component of the system and the
reconfiguration logic adjusts the control law so that system stability and performance
are restored. This work focuses on developing a fault-tolerant control law and FDI
procedure for a specific class of aircraft failures. The resulting scheme provides a
fast and efficient method to detect failure and procedures to overcome the effect of a
control failure on stability and performance. The failure class analyzed throughout this
work is a fixed-position or jammed actuator failure, which results in a flight control
surface becoming inoperable. The goal of a reconfigurable controller for this failure
class is to reconfigure the control law to use the remaining operational control surfaces
in such a manner that the prefailure flying qualities are restored. The objective of this
work is to develop a reconfiguration scheme that is easily implementable into current
flight software and offers a measurable degree of reliability for the targeted type of
Analysis has shown that the probability of an actuator failure is extremely low,
however, in the event failure occurs, the most probable type of failure is the fixed-
position actuator failure . The success of a reconfigurable controller depends
crucially on the ability of the FDI module to promptly and accurately identify failure.
This work proposes the development of artificial neural networks to accomplish this
task. The function performed by the neural network for aircraft FDI is the mapping
of aircraft measurements into fault categories that describe which surface has failed
and at what position. Once the failure has been positively identified, the next step in
the proposed reconfiguration scheme is the development of a fault-tolerant controller
capable of using the FDI information to effectively restore stability and performance.
Fault-tolerance deals with the ability to complete a task satisfactorily (reliability)
and the likehood of conducting an operation safely without endangering the human
operators of the controlled system (survivability) . Two fault-tolerant control (FTC)
methods are developed and evaluated in this work. The first is a linear quadratic
regulator (LQR)-based technique while the second is an Ho-based technique. In
each approach the effects of the jammed surface are treated as a constant disturbance
to the system. While all nominal controllers have some inherent robustness to a
limited failure class, an appropriately designed reconfigurable controller should have
a much larger region of survivability. These proposed techniques and the ensuing
reconfiguration schemes appear to meet the challenges of the fixed-position actuator
failure well for both linear and nonlinear simulations.
1.1 Motivating Example
On November 12, 2001 an American Airlines Airbus Industry A300-600, Figure
(1-1) , Flight 587 en route from John F. Kennedy International Airport (JFK),
Jamaica, New York, sustained a catastrophic failure when the vertical stabilizer and
rudder separated from the fuselage shortly after takeoff [4, 5]. The 2 pilots, 7 flight
attendants, 251 passengers, and 5 persons on the ground lost their lives when the
aircraft broke apart and crashed into the residential community of Belle Harbor, New
York, Figure (1-2) . The resulting investigation examined many issues including the
adequacy of the certification standards for transport-category airplanes, the structural
requirements and integrity of the vertical stabilizer and rudder, the operational status
of the rudder system at the time of the accident, the adequacy of pilot training, and the
role of pilot actions in the accident.
Figure 1-1: American Airlines Airbus A300-600
It was determined that before the separation of the vertical stabilizer and rudder,
Flight 548 encountered two wake vortices from a Boeing 747, which had departed JFK
ahead of the accident aircraft. The two airplanes were separated by about 5 miles and
90 seconds at the time of the vortex encounters. During and shortly after the second
encounter, the flight data recorder (FDR) on the accident aircraft recorded several large
rudder movements and corresponding pedal movements to full or nearly full available
rudder deflection in one direction followed by full or nearly full available rudder
deflection in the opposite direction.1 The subsequent loss of reliable rudder position
data is consistent with the vertical stabilizer separating from the airplane. Among the
potential causes examined for this catastrophic failure were rudder system malfunction,
as well as flight crew action.
Figure 1-2: Flight 548 crashes in Queens, New York
The National Transportation Safety Board and Airbus engineers believe that
large side loads were likely present on the vertical stabilizer and rudder at the time
they separated from the airplane. Calculations and simulations show that, at the time
of the separation, the airplane was in an 8 to 100 airplane nose-left sideslip while
the rudder was deflected 9.50 to the right. Airbus engineers have determined that
this combination of local nose-left sideslip on the vertical stabilizer and right rudder
1 Preliminary information based on FDR data and an analysis of the manner in
which rudder position data is filtered by the airplane's system indicates that within
about 7 seconds, the rudder traveled 11 right for 0.5 seconds, 10.5 left for 0.3 sec-
onds, between 11 and 10.5 right for about 2 seconds, 10' left for about 1 second, and
finally, 9.50 right before the data became unreliable.
deflection produced loads on the vertical stabilizer that could exceed the airplane's
design loads. The Federal Aviation Administration (FAA) concluded that it was this
dangerous combination of sideslip angle and rudder position which resulted in the
complete lost of aircraft, crew, and passengers.
Figure 1-3: Vertical Stabilizer of Flight 548
While the vertical stabilizer and rudder appeared to separate cleanly from the
fuselage, Figure (1-3) , the flight controller was inadequately designed to regain
control of the crippled aircraft. The resulting configuration of leading edge flaps,
trailing edge flaps, ailerons, and elevators were incapable of countering the sudden roll
and yawing moment generated by the absence of the vertical stabilizer. Rolling upside
down and finally out of control the airplane succumbed to the increasing aerodynamic
forces as a massive engine, wing, and fuselage breakup scattered remains throughout
Jamaica Bay and Long Island New York. The tragedy of the Flight 587 accident
endures as another motivation in the emerging field of Reconfigurable Controls, which
aims to develop flight controllers which can handle failures such as this.
The purpose of this work is to propose an adaptive scheme in reconfigurable flight
controls capable of recovering desired performance and stability characteristics for an
aircraft experiencing a fixed-position actuator failure. Chapter 2 provides a review of
the current literature in the area of reconfigurable flight controls. The mathematical
details of aircraft flight mechanics and a non-technical introduction into artificial neural
networks is given in Chapter 3. Chapter 4 presents a fault detection and isolation (FDI)
procedure for fixed-position actuator failures using artificial neural networks. The
stabilization problem and aircraft fault modeling is reviewed in Chapter 5. Chapter 6
focuses on the theoretical development of fault-tolerant controllers using LQR-based
and Ho-based techniques. Both of these fault-tolerant control methods along with FDI
and stabilization results are combined in Chapter 7 to demonstrate the success of the
proposed scheme on a nonlinear F/A-18 simulation. Finally, Chapter 8 presents the
conclusions of this work.
REVIEW OF LITERATURE
In 1984 the Air Force Flight Dynamics Laboratory initiated the first research
program dedicated to the investigation of reconfiguration technology for flight control
systems with the Self-Repairing Flight Control Systems Program. The main objective
of this program was to significantly improve the reliability, maintainability, surviv-
ability, and life cycle costs of aircraft flight control systems through aerodynamic
reconfiguration and maintenance diagnostics. Special consideration was given to devel-
oping a reconfiguration strategy that uses the remaining control surfaces to substitute
for the lost force and moment generating capabilities when a single control surface
becomes impaired from failure or battle damage . Since this original initiative many
methods have been proposed to solve the reconfiguration problem for flight controls.
This chapter outlines the state of the art, which remains largely a theoretical topic with
most applications studies based upon aerospace systems.
The objective of reconfigurable controls is to detect a failure using the feedback
signals of the flight control system then reconfigure the control law in a fashion that
restores the desired stability and performance characteristics of the aircraft. There is
a substantial body of reconfigurable controls literature that includes applications in
hazardous chemical plants, the control of nuclear power plant reactors, space craft,
and the control of unstable fly-by-wire aircraft. Research into reconfigurable control,
however, is largely motivated by the control problems encountered in aircraft system
design. The goal of these researchers is to provide self-repairing capability to enable a
pilot to land an aircraft safely in the event of a serious malfunction .
The main requirement for any fault-tolerant controller as part of a reconfiguration
scheme is that, subsequent to a malfunction in the system, it should either maintain
some acceptable level of performance and stability or degrade gracefully. While
significant theoretical progress has been made in academia, few results have been
applied to real vehicles. The view is usually taken that the application of a complex
fault-tolerant controller is best applied to systems where the governing principles are
easily understood and verifiable. This "simplistic" approach has consistently caused
a reluctance within the field to experiment on systems which pose intolerable risks in
terms of safety, cost, instability or unpredictability. The general view is that simpler
controllers, with fewer components or lines of software code are intrinsically more
reliable and that further complexity would unnecessarily increase the overall risk of
failure during routine operation [10, 11].
The initial step in developing any reconfiguration scheme is determining the
limitations of the conventional feedback controller. Strategies for reconfiguration are
generally application-specific and are normally dependent on available equipment and
measurements. The task then becomes the design of a controller with suitable structure
to guarantee stability and satisfactory performance, not only when all components are
fully operational, but also in the case when sensors, actuators and other components
malfunction. Owen  referred to a control system with this structure as one that
possesses integrity or that has control loops that possess loop integrity, while Veilltette
et al.  and Birdwell et al.  prefer to use the term reliable control.
Figure (2-1) shows the general schematic of a reconfigurable control system
with four main components: the model (including the plant dynamics, actuators,
and sensors), the fault detection and isolation (FDI) module, the controller, and the
supervision module. The solid lines represent signal flow (commands, feedback,
etc.) while the dashed lines represent adaption (tuning, scheduling, reconfiguration,
or restructuring). The possible faults include malfunctions in sensors, actuators, or
Controller Actuators SDy s sensors upervlslon ---
r r I I
L- _-- - - - - - - -
Figure 2-1: General schematic of a reconfigurable control system with supervision
other components of the plant. The FDI subsystem constantly monitors the system's
performance and stability using the feedback signal of the closed-loop system and
the position commands to the actuators, then provides the supervision subsystem with
information about the onset, location and severity of any fault. Based on the system's
measurements together with FDI information, the supervision system will reconfigure,
tune, or adapt the controller to accommodate for the effects of the fault.
The relationship between the four main components of Figure (2-1) allows
the reconfigurable control problem to be solved in a very systematic manner. The
principles involved in the systematic design and development of a reconfigurable
controller are outlined by Blanke et al. . He demonstrated that the development
of each subsystem affects the development of the overall system, this interdependence
necessitates a comprehensive strategy for reliable and highly efficient control law
redesign. Ultimately, the design procedure is a multidisciplinary task involving relevant
science/technology, control theory and design, signal processing and human factors.
2.2 The State of the Art
Over the past two decades there has been an extensive investigation into many
possible solutions of the reconfigurable controls problem. Figure (2-2) depicts the
areas of greatest contribution and their interrelationship towards forming a complete
Figure 2-2: Venn Diagram of Reconfiguration Strategies
2.2.1 Fault Detection and Isolation (FDI)
With the development of powerful quantitative and/or qualitative modelling
tools and artificial neural networks the field of FDI has become very refined [16,
17,18,19, 20, 21,22, 23, 24,25, 26, 27,28, 29, 30, 31, 32, 33]. However, much of the
research has yet to be combined with fault-tolerant controllers to present a complete
reconfiguration strategy. The main issue to overcome with traditional methods for
FDI involves specification of all critical design conditions and/or extensive overdesign
for unpredicted or uncertain conditions. To date, as noted by Barron et al. , the
best FDI systems only consider a fraction of the operational fault conditions that
might be encountered and only a small portion of those that may be encountered are
actually used explicitly for design because the number of possible fault conditions is
very large. This fact severely inhibits the design of a global FDI system for complex
systems such as aircraft. It may also be important to identify the fault type and its
severity as well as the reason for the fault development. When these functions are
included along with FDI, the function performed is called fault diagnosis. Several
investigators, including Legg , Herrin , Bell , Hunt et al. , and Blanke
et al.  have discussed the use of failure mode effects analysis (FVMEA) techniques
to determine systematically how fault effects in components relate to fault inputs,
outputs, or elements within the components. FMEA is a bottom-up analytical process
which identifies potential hazards of a new system with the goal to anticipate, identify
and avoid failures in the design and development stages.
2.2.2 Robust Control
Robust control design has received much attention within the controls community
since the late 1970's. The few cases that have attempted to directly apply robust
control theory to reconfigurable controls usually have not considered the effects of the
faults on the control system [39, 40,41, 42]. Eterno et al.  and Stengel  note
that this passive approach to reconfigurable controls makes the fundamental assumption
that faults can be modelled as uncertainties. Admittedly, there do exist robust control
techniques that are suitable for a very specific class of failures that can indeed be
modeled as uncertainty regions around a nominal model. Any failure that does not
significantly degrade the system or push the system outside the stability radius given
by the robust controller will not compromise satisfactory stability and performance.
However, any controller with a large enough stability radius to encompass most failure
situations will likely be conservative and there is still no guarantee that unanticipated
failures could be handled. Despite this, several investigators, including Birdwell et
al.  and Veilltette et al. , have insisted that robust control theory can be used to
maintain acceptable system stability and performance when control loops malfunction
in a broad sense Most investigators, however, agree that a reconfigurable controller
will require additional loops and control structure. There are too many types of
common failures, such as actuator and sensor malfunctions, which cannot be adequately
modelled as uncertainty. These problems motivate the need for a controller that more
directly addresses the situation.
2.2.3 Fault-Tolerant Control
The area of fault-tolerant controls has attracted the attention of investigators
with increased frequency over the past few years. For example, Lane and Stengel
 and Ochi and Kanai  pursued the use of feedback linearization and Gao
and Antsaklis  described the use of pseudo-inverse methods. Adaptive control
approaches using artificial neural networks are consider by Calise et al. , Idan et
al. , Johnson and Calise , and many others. While Huang and Stengel ,
Morse and Ossman  and Jiang  have made important contributions based upon
model-following control principles.
2.2.4 Robust Fault-Tolerant Control
This area of reconfiguration has received only a minimal amount of attention.
Wu  addresses the problem of performance robustness during normal system
operation versus fault recovery. A prescribed performance level is optimized under a
detection criterion relating the measurements to specific faults. The specific designer is
largely free to choose one of a number of suitable FDI techniques. Jiang  discusses
how fault-tolerance can be achieved using eigenstructure assignment design.
2.2.5 Robust Fault Estimation
The joint design of robust controllers and fault estimation often leads to complex
interactions between the controller and fault estimator because the design freedom is
utilized to solve both problems simultaneously [55, 56, 57, 58, 59]. This fundamental
problem, however, is unavoidable as most studies in this area are based upon the idea
that the robust controller optimization and fault estimation designs are best combined,
for example, Tyler and Morari  use Ho optimization. An alternative way of
performing open-loop FDI with a separate controller design avoids the difficulties of
this design and provides much of the motivation for the next area.
2.2.6 Fault-Tolerant Control w/ FDI
The functions of FDI and reconfigurable control have been combined in a few
notable studies [60, 53]. It is widely accepted that the FDI function along with
redundant system design can prevent the development of more serious faults. When
fault detection and isolation is carried out using the open-loop approach the controller
affects the FDI robustness but not vice-versa [26, 61]. The controller's robustness issue
becomes de-coupled from the FDI unit design and allows for an increased freedom in
controller design and structuring. The main disadvantage with this de-coupling is the
adverse affects the detection delay has upon system stability as reported by Mariton
. The combination of the FDI system and control reconfiguration is a complex
issue and one study by Srichander and Walker  proposes a stochastic approach
to the stability analysis of some active fault tolerant control systems employing
FDI schemes. The main assumption here is that behavior resulting from randomly
occurring faults can be characterized dynamically by stochastic differential equations.
The stochastic differential equations vary randomly in time and the equations can be
analyzed using Markov theory. These stochastic approaches to robustness analysis are
an emerging theoretical field in reconfigurable control.
Different forms of selection logic and system management have been introduced
into fault-tolerant systems by various investigators including Rauch , Buckely ,
Eryurek and Upadhyaya , and Polycarpou and Vemuri . The function of
supervision is essentially the active form of fault-tolerant control in which fault
decision information is used to select the most suitable control function subsequent
to the declaration that a fault has occurred. Also essential to the operation of the
supervision system is the ability to determine whether a fault has determental effects
on the system's performance and stability serious enough to warrant controller changes.
Kwong et al. [68, 69] shows that the fuzzy model reference learning controller
(FMRLC) can be used to reconfigure the nominal controller in an F-16 aircraft to
compensate for various actuator failures without using explicit failure information.
Kwong then developed an expert supervision strategy for the FMRLC that used only
information about the time at which a failure occurs and showed that it achieved
higher performance control reconfiguration than an unsupervised FMRLC. Fierro
and Lewis  discuss a hybrid system framework which considers simultaneously
the control and decision-making issues. A continuous-state plant is supervised by a
discrete-event system which is based on a theory of linked finite state machines.
2.3 Types of Redundancy
As mentioned in the introduction, a reconfigurable controller should ideally be
developed using a systematic and integrated approach to design. Most papers only
consider problems which are based on mathematical models of the plant, but there are
also many non-mathematical challenges which require attention at every stage and in
all aspects of system design. Blanke et al.  paid attention to the development of
the overall concept of systematic design. His study demonstrated that the development
of a complete reconfiguration strategy requires an understanding of the structure of
the system, the reliability of different components, the types of redundancy available
and the types of controller function that are available or might be required. It is
impossible to ensure control reconfiguration without redundancy in the initial system.
Often the type and level of redundancy provided determines the way in which control
reconfiguration is enacted. Hence, a failed sensor or actuator in systems with varying
levels of redundancy will sometimes have dramatically different reconfiguration
schemes to overcome the failure.
There are two forms of redundancy associated with reconfigurable controls. Direct
redundancy is achieved by the use of multiple interdependent hardware channels
and analytical redundancy is achieved by backing up available measurements using
a mathematical model. Sometimes a combination of the two forms of redundancy
is necessary. Making the best use of both the direct redundancy and the analytical
redundancy provided by the system is a major task of reconfigurable control system
2.4 Fault-Tolerant Control Methods
Figure (2-3) shows the taxonomy of fault-tolerant control methods.
2.4.1 Passive Approaches
Passive approaches to fault-tolerance make use of robust control techniques to
ensure that a closed-loop system remains insensitive to certain faults [43, 44]. The
I II II
Interacting Adaptive I I Model
Multiple I Feedback Predictive
Models Linearization I I Control
U- L---_______-J L-_______ -- L_-_---- J
L- - -
Figure 2-3: Taxonomy of Reconfigurable Control Methods
impaired system continues to operate with the same controller and system structure, i.e.
the main objective it to recover the original system performance. Basically, the passive
controller will reject the fault only if it can be de-sensitized to the fault's effects just as
if it were a source of modelling uncertainty .
Among those who have extend their work on robust control to deal with passive
fault-tolerance are Horowitz et al.  and Keating et al.  who used quantitative
feedback theory, and McFarlane and Glover  and Williams and Hyde  who
employed the frequency domain approach based on Ho-norm optimization. Nett et
al. , Tyler and Morari , and Murad et al.  present robust design approaches
to integrated control and fault estimation based upon the so-called four parameter
controller. All of these passive fault-tolerant controllers are actually good examples
of baseline controllers that can be used as a basis for further fault accommodation
with active controllers. The original robustness is important during the detection and
2.4.2 Active Approaches
In active fault-tolerance, a new control system is designed using the desirable
properties of performance and robustness in the original system, but with the reduced
capability of the impaired system in mind. Active fault-tolerance has this title because
on-line fault accommodation is used. These methods differentiate themselves from
passive approaches in that they take fault information explicitly into account and do not
assume a static nominal model. In order to achieve reconfiguration or restructuring, an
active fault-tolerant system requires either a priori knowledge of expected fault types
or a mechanism for detecting and isolating unanticipated faults. This is essentially the
function of a fault detection and isolation (FDI) scheme.
Active approaches are divided into two main types of methods: projection based
methods and on-line automatic controller redesign methods . The latter involves
the calculation of new controller parameters in response to a control impairment, Gao
and Antsaklis  referred to this method as reconfigurable control. In projection-
based methods a new pre-computed control law is selected according to the type of
malfunction that has been isolated . Stengel  further classifies a reconfigurable
or restructurable system whose feedback action is changed automatically as a special
form of an intelligent control system. On-line restructuring or reconfiguration of
control is a topic of ongoing research.
220.127.116.11 Multiple model control (MMC)
There are several areas of multiple model controls that have achieved notable
success as fault-tolerant control techniques: Multiple Model Switching and Tuning
(MMST), Interacting Multiple Model (IMM), and Propulsion Controlled Aircraft
(PCA). The idea of multiple model control has received increased interest in the last
few years with Boskovic et al. [76,77,78,79,80,81,82,83,84], Kanev et al. [85,86,87],
Demetriou , Zhang and Jiang , and Maybeck . In MMST Boskovic et al.
 describes the dynamics of each fault scenario by a model, then designs a controller
for each fault scenario creating a massive parallel architecture. When a failure occurs,
MMST switches to the pre-computed control law corresponding to the failure situation.
The difficulty with this approach becomes one of choosing which model/controller
pair to switch to at each time instant. In IMM Zhang and Rong Li  and Munir and
Atherton  attempt to overcome this key limitation of MMST, rather than using the
model which is closest to the current failure scenario, IMM computes a fault model as
a convex combination of all pre-computed fault models and then uses this new model
to make control decisions. Burken and Burcham  develops PCA which is a special
case of MMST, where the only anticipated fault is total hydraulics failure and only the
engines are used for control. The PCA problem was taken up by the NASA Dryden
Flight Research Center [94, 95] in 1995 when they demonstrated successful landings
after complete hydraulic failure using a MD-11 and a F-15 with propulsion-only
18.104.22.168 Control allocation (CA)
Control allocation (CA) is the technique of producing the desired set of forces and
moments on an aircraft from a set of actuators. The purpose of control allocation is to
allow the design of control laws which do not directly consider actuator failures. The
output of the control law can be a set of desired forces and moments and the job of
the allocator is to select appropriate actuator positions which will achieve the desired
results. Bordignon and Durham  and Durham and Bordignon  addressed the
problem of control allocation with magnitude and rate limits on the actuators, Davidson
et al.  develops a control allocation technique for the extremely over-actuated
Innovative Control Effector (ICE) aircraft and Zhenyu et al.  looks at restoring as
much of the performance of the original system as possible after a actuator failure.
22.214.171.124 Adaptive feedback linearization via artificial neural networks
This section examines a method primarily developed by Calise et al. [48, 49, 50,
100, 101, 102, 103] involving a model reference adaptive control scheme using adaptive
feedback linearization with an artificial neural network to cancel inversion errors.
The approach splits the dynamics of the plant into three single-input-single-output
(SISO) subsystems for roll, pitch, and yaw. Each subsystem has a model reference
adaptive controller. Brinker and Wise  and Wise et al.  have contributed
by developing a control allocation technique that generates the desired roll, pitch, or
yaw moment specified by the controller using the available control surfaces. Wise et
al.  along with Calise [48, 102] have successfully demonstrated adaptive feedback
linearization using artificial neural networks on the Tailless Advanced Fighter Aircraft
(TAFA) and NASA's X-36.
126.96.36.199 Sliding mode control (SMC)
Shtessel et al. [105,108, 106, 107] used Sliding Mode Control (SMC) to develop
a robust controller that adaptively handles input magnitude and rate constraints.
The proposed controller is set up in a two-loop configuration with the desired result
of tracking a trajectory given by roll, pitch, and yaw angle. The outer-loop of the
controller takes roll, pitch, and yaw and provides angular rate commands to the inner-
loop, which is assumed to track the commands using the actuator inputs. There are two
benefits of this controller. First, it can handle all failures which modify the dynamics
of the plant less than the assumed uncertainty. Second, the on-line adaptation of the
boundary layer can handle partial loss of actuator surfaces, while avoiding limits and
integrator windup by reducing the tracking performance. The limitation of SMC is the
assumption that the input function is square and invertible. This limitation requires that
there must be one and only one control surface for every controlled variable and that
none of the control surfaces can ever be lost. Therefore, SMC is only applicable for
failures which cause a loss of effectiveness of the control surface, unlike the floating or
jammed surface failure scenarios.
188.8.131.52 Eigenstructure assignment (EA)
The concept of Eigenstructure Assignment (EA) was formally introduced by
Andry et al. . The idea behind the technique is to use state feedback to place
the eigenvalues of a linear system then use the remaining degrees of freedom to
align the eigenvectors as accurately as is possible. While the method for choosing
appropriate eigenvectors and eigenvalues is not well-defined for aircraft, Davidson
and Andrisani  highlighted the effects of the eigenstructure on flying qualities.
Other researchers who propose EA for use in reconfigurable flight control systems
are Konstantopoulos and Antsaklis , Belkharraz and Sobel , and Zhang and
184.108.40.206 Model reference adaptive control (MRAC)
The goal of Adaptive Model-Following Control (MRAC) is to force the plant
output to track a reference model. Although there are limitations of adaptive control
for reconfiguration, Bodson and Groszkiewicz  and Groszkiewicz and Bodson
 are attempting to apply it in slightly modified forms. First, a model structure
must be assumed. The types of failures addressed in reconfigurable control, however,
may well cause the plant structure to change drastically. Second, adaptive control
requires that the system's states change slowly enough for the estimation algorithm to
track them. However, faults may cause abrupt and drastic changes in the states moving
the system instantaneously to a new region of the state space. As a result, adaptive
control on its own is not enough to handle the general problem, but may well be an
important part of the reconfigurable algorithm.
220.127.116.11 Model predictive control (MPC)
Model predictive control has been proposed as a method for reconfiguration
due to its ability to handle constraints and changing model dynamics systematically.
Maciejowsku  designed a MPC controller that has an intrinsic ability to handle
jammed actuators without the need to explicitly model the failure. Failures can also be
handled in a natural fashion by changing the internal model used to make prediction
in either an adaptive fashion as done by Kanev and Verhaegen , a multi-model
switching scheme as done by Boskovic and Mehra , or by assuming a FDI scheme
that provides a fault model as done by Huzmezan and Maciejowski [117, 118]. The
MPC approach to reconfiguration has achieved some notable successes but there
are still fundamental issues that need to be examined. First, it is not clear how to
adjust the weights in the cost function for an arbitrary fault model. Second, choosing
performance targets is not a simple question. Finally, MPC requires an on-line
optimization which makes it difficult to implement as an aircraft controller where the
optimization must occur at high sampling rates and in fixed time. Also, there is no
guarantee that there exists a solution to the optimization problem for all time.
This chapter provides a review of the necessary technical background for an
introductory investigation of reconfigurable flight controls. While is it assumed the
reader has been exposed to these topics previously, a more in depth explanation of
these concepts can be found in a number of undergraduate texts [119, 120, 121,122].
3.1 Aircraft Flight Mechanics
The equations of motion for an aircraft in flight have changed little since their
original formulation by Lanchester (1908) and Bryan (1911) . The following
sections identify the various reference frames used to describe an aircraft's state,
provide an overview of the derivation of the general nonlinear equations of motion, and
describe the small-disturbance theory linearization technique.
3.1.1 Aircraft Axis Systems
The motion of an aircraft can be described using many different axis systems.
The three axis systems used here are the body-axis system fixed to the aircraft, the
Earth-axis system, which we will assume to be an inertial axis system fixed to the
Earth, and the stability-axis system, which is defined with respect to the relative wind.
Each of these systems is useful in that they provide a convenient system for defining a
particular vector such as an aerodynamic force vector, the weight vector, or the thrust
18.104.22.168 Body-Axis System
The body-axis system, (bl, b2, b3) in Figure (3-1), is fixed to the aircraft with
its origin at the aircraft's center of gravity. The bl axis is defined out the nose of the
aircraft, the b2 axis is defined out the right wing of the aircraft, and the b3 axis is
Figure 3-1: Relationship between Earth axis system and body axis system
defined down out of the bottom of the aircraft. These three axes form a traditional
right-handed orthogonal reference system.
22.214.171.124 Earth-Axis System
The Earth-axis system, (el, e, e3) in Figure (3-1), is fixed to the Earth with its
e3 axis pointing to the center of the Earth. Often, the el axis is defined as North and
the e2 axis is defined as East. The Earth-axis system is assumed to be an inertial axis
system for which Newton's laws of motion are valid. While this assumption is not
totally accurate, it works well for most aircraft problems where the aircraft is traveling
up to supersonic but not hypersonic speeds.
126.96.36.199 Stability-Axis System
The stability-axis system, (s1,s2,s3), is rotated relative to the body axis system
through the angle-of-attack and is used to study small deviations from a nominal flight
condition. The origin of the stability-axis is also at the aircraft center of gravity. The
sl axis points in the direction of the projection of the true airspeed onto the xz plane of
the aircraft. The s2 axis is out the right wing while the s3 axis is orthogonal and points
in accordance with the right-hand rule.
3.1.2 General Equations of Motion
The goal in this section is to develop the equations of motion which describe
the position and orientation of the aircraft in appropriate reference frames. This
development is essential in understanding how an aircraft behaves as well as the
dynamics and relationships between the various reference frames. The velocity of the
aircraft with respect to the body-axis system is given by
VB v (3.1)
The velocity VB does not include the effects of wind. Any vector in the Earth-axis sys-
tem can be transformed into the body-axis system using the following transformation
(note the notation used for trigonometric functions, Sp = sin4, Cp = cos4, T =- tan ,
CeOC S4S0SeCV C Sv CA SeC + S Sv
IEB= CoeS SseSVS +CCV C SoSV- SiCV (3.2)
S-SO SWCo CCo
where y, 0, 0 describe the orientation of the aircraft in the Earth-axis system. The
angle of attach, a, and sideslip, 3, can be defined in terms of the velocity components
of the body axis system. The equations for a and 3 are defined by
a = tan -
s u (3.3)
3u = sin1
/U2 + V2 + W2
The position of the aircraft is most often used for navigation; therefore, its dynamics
are given in the Earth-axis system as follows
rE = y (3.4)
Remember that z points toward the ground and is therefore negative for positive height.
As a result, the altitude or height is often used instead of z to describe the location of
the aircraft while in flight. The aircraft height is given by
h = -z (3.5)
The orientation of the aircraft is defined relative to the Earth-axis and is given by
the Euler angles (V, 0, 0). The Euler angles define the rotations from the Earth-axis
system to the body axis system. The ordering of the rotations is important and is done
according to a 3-2-1 Euler angle sequence. If the sequence is performed in a different
order other than V, 0, and 4, the final result will be incorrect. The accepted limits on
the Euler angles are
-900 <0 < 900 (3.6)
-1800 < < 1800
The angular rotation rates are defined relative to the body axis system as,
OB = q (3.7)
where p is the roll rate, q is the pitch rate, and r is the yaw rate. The angular rates
are related to the rate of change of the Euler angles by the following coordinate
p 1 0 -So p
q = 0 C, SpCo
Sr J (3.8)
1 S7Toe C To P
S= 0 C( -S( q
y 0 SS. CS' rJ
Note that when perturbations are small, such that (, 0, V) may be treated as small
angles, that is, < 15', then Equations (3.8) can be approximated as
The dynamics are derived from Newton's 2nd Law which states that the summation
of the external forces acting on a body is equal to the time rate of change of the
momentum of the body; and the summation of the external moments acting on the
body is equal to the time rate of change of the moment of momentum (angular
momentum). The force equation is given by
F=m ( + (x Vc) (3.10)
and the moment equation as
M= dt +(co) (Ico)) (3.11)
where Vc is the velocity of the center of mass of the aircraft, co is the angular ve-
locity and I is the moment of inertia tensor. The force vector which consists of the
aerodynamic forces and thrust forces acting on the aircraft is given by
F= y (3.12)
The equations can now be written in terms of the variables defined in this section. The
three force equations in the body-axis system are
X- mgSo = m (u + qw rv)
Y +mgCS = m (v +ru -pw) (3.13)
Z + mgCeC = m (w +pv- qu)
where rT is the angle between the x-body direction and the thrust vector, T. Assuming
that the mass distribution of the aircraft is constant, such as neglecting fuel slosh and
fuel bum, the moments and products of inertia do not change with time. The three
moment equations in the body-axis system are
L = IxxP Ixzr + qr (Izz Iyy) Ixzpq
M= Iy+rp(I -Izz)+Ix r2 ) (3.14)
N = -Ixz + Izz + pq (Iyy I) +Ixzqr.
where [L,M,N] are the rolling moment, pitching moment, and yawing moment acting
of the aircraft, respectively. These applied moments consist of aerodynamic and thrust
moments acting on the aircraft. The forces and moments are functions of the control
surfaces, thrust, and aerodynamics of the aircraft and can be written as functions of the
six linear and angular velocities (u,v,w,p,q,r) and the actuator positions.
188.8.131.52 Longitudinal and Lateral-Directional Equations of Motion
The six aircraft equations of motion, (3.13)-(3.14), can be decoupled into two sets
of three equations. These are the three longitudinal equations of motion and the three
lateral-directional equations of motion. This is convenient in that for many flight con-
ditions only three equations need to be solved simultaneously. The three longitudinal
equations of motion consist of the x force, y moment, and z force equations
X = m (u + qw rv) + mgSo
M= Iy+rp (I -z) +Iz (p2 2) (3.15)
Z = m (w +pv- qu) mgCoeC
The lateral-directional equations of motion consist of the x moment, y force, and z
L = Ixx Izr + qr (Izz Iyy) Izpq
Y = m (v + ru pw) mgCoSo (3.16)
N = -Iz+ Izz r+pq (Iy I,) + Ixqr
In addition to the six force and moment equations of motion, Equation (3.8) is required
to completely solve the aircraft problem because there are more than six unknowns due
to the presence of the Euler angles in the force equations. Recall, the three kinematic
p= -So + p
q = SCo* + C (3.17)
r = CqCo* SO
3.1.3 Linearized Equations of Motion
The nine aircraft equations of motion, (3.15)-(3.17), are nonlinear differential
equations. They can be solved with various numerical integration techniques to obtain
time histories of motion variables, but it is nearly impossible to obtain closed form
solutions. It is assumed that the motion of the aircraft consists of small deviations from
a reference condition of steady flight; therefore, the small perturbation approach can be
used to linearize the equations of motion and develop the closed form solutions around
trim conditions. Steady flight can be defined, for example, as one of the following:
steady wings-level flight = = = = 0
steady turning flight = 0 = 0, = turn rate
steady pull-up = = = 0, = pull-up rate
steady roll = t = 0, = roll rate,
where p =q r = V = = V = 0 and all control surface inputs are zero. There
are three possible methods for computing a linear model for small perturbations
around the trim or steady-state condition. The first is to replace any nonlinearities
in the general dynamics equation with their first order Taylor series approximations.
The second is to run an identification algorithm using data collected from either a
nonlinear model or the physical system. The final method, and one used throughout
this work, is to numerically compute the effects of small changes in state variables
and inputs on the state derivatives. This can be done, for example, by using a Matlab
linearization routine such as linmod on a nonlinear Simulink model. The benefits of
the linearization is that we can write the physical system in a convenient matrix form
where x E Rn is the state variables and u E RP is the control inputs. The system output
y E Rq is given by
y =Cx +Du (3.19)
The state, control, and output vectors are defined as follows
x = state vector (n x 1) (3.20)
The matrices A, B, C
u= input vector (p x 1)
y = output vector (q x 1)
are constant matrices and defined as follows
a12 .. aln
plant matrix (n x n)
bll bi2 bip
bnl bn2 1.. bnp
C\\ C12 *...* Cln
control matrix (n x p)
output matrix (q x n)
Cql Cq2 CqnI
where A is the plant matrix, B is the control matrix, and C is the output matrix. For the
aircraft considered throughout this work the D matrix is the null matrix.
3.2 Neural Networks
This section is intended to review and help the reader understand what artificial
neural networks are, how they work, and where they are currently being used. The
intent is to give a non-technical introduction; therefore, it does not go into depth with
mathematical formulas. A more detailed explanation is provided in [121,122].
3.2.1 Artificial Neural Networks
An Artificial Neural Network is a system loosely modeled on the human brain.
While neural networks do not approach the complexity of the brain, they are an an
attempt to simulate within specialized hardware or sophisticated software the multiple
layers of simple processing elements called neurons. Each neuron is linked to a certain
number of its neighbors with varying coefficients of connectivity that represent the
strengths of these connections. Learning is accomplished by adjusting these strengths
to cause the overall network to output appropriate results.
184.108.40.206 The Biological Neuron
Dendrites: Accept inputs
Soma: Process the inputs
Axon: Turn the processed inputs
Synapses: The electrochemical
contact between neurons
Figure 3-2: A biological neuron
The most basic components of neural networks are modeled after the structure of
the brain; therefore, a great deal of the terminology is borrowed from neuroscience.
The neuron is the most basic element of the human brain and provides us with the
abilities to remember, think, and apply previous experiences to our every action. The
power of the brain comes from the large number of neurons (approximately 1011)
and the multiple connections between them (up to 200000). All natural neurons have
four basic components, Figure (3-2), which are dendrites, soma, axon, and synapses.
Basically, a biological neuron receives inputs from other sources, combines them in
some way, performs a generally nonlinear operation on the result, and then outputs the
220.127.116.11 The Artificial Neuron
P w Y n f a
Figure 3-3: An artificial neuron
The basic unit of artificial neural networks, the artificial neuron, simulates the four
basic functions of natural neurons. That various inputs to the network, p, are multiplied
by a connection weight, w, these products are simply summed with a bias, b, then fed
through a transfer function, f, to generate a result, a. Referring to Figure (3-3), an
artificial neuron output is given by
a =f (wp +b) (3.26)
Even though all artificial neural networks are constructed from this basic building block
their architectures and applications are extremely diverse.
Designing a neural network consists of four important steps: arranging neurons
in various layers, deciding the type of connections among neurons within a layer as
well as among those in different layers, deciding the way a neuron receives input and
produces output, and determining the strength of connection within the network by
allowing the network to learn the appropriate values. The process of designing a neural
network is an iterative one.
Biological neural networks are constructed in a three dimensional way from
microscopic components. Artificial neural networks are the simple layering of artificial
neurons, which are then connected to one another. All artificial neural networks have
a similar structure of topology, Figure (3-4). Some of the neurons receive input, the
input layer, and other neurons provide the network's outputs, the output layer. All the
rest of the neurons are hidden from view, the hidden layer.
input input hidden output output
vector layer layer layer vector
Figure 3-4: An artificial neural network
When the input layer receives the input, its neurons produce output, which
becomes input to the other layers of the system, the process continues until the output
layer is reached and information is passed to the output vector. The determination of
the number of hidden neurons the network should have in order to perform its best
is often a process of trial and error. If the number of hidden neurons is increased
too much, the network will memorize the training set and will have problems in
The brain basically learns from experience, this is also true for artificial neutral
networks. Learning typically occurs through training or exposure to a truthed set
of input/output data where the training algorithm iteratively adjusts the connection
weights. For this reason, artificial neural networks are sometimes called machine
learning algorithms. The learning ability of a neural network is determined by its
architecture and by the algorithm chosen for training. The training method usually
consists of one of three schemes:
Unsupervised learning: The hidden neurons must find a way to organize
themselves without help from the external environment. In this approach,
there are no target outputs available for the network to measure its predictive
performance for a given vector of inputs.
Reinforcement learning: Reinforced learning is also called supervised learning.
The connections among the neurons in the hidden layer are randomly arranged,
then reshuffled as the network is told how close it is to solving the problem.
Instead of begin provided with the correct output for each network input,
reinforced learning only gives a grade. The grade is given by a teacher. The
teacher may be a training set of data or an observer who grades the performance
of the network results.
Backpropagation: This method has proved highly successful in training of
multilayered neural nets. The network is not just given reinforcement for how
it is doing on a task. Information about errors is also filtered back through the
system and is used to adjust the connections between the layers, thus improving
performance. A form of backpropagation is used in this work.
One can categorize the learning methods into yet another group: off-line or on-line.
Off-line: In the off-line learning methods, once the systems enters into the
operation mode, its weights are fixed and do not change any more. Most of the
current networks are of the off-line learning type. Off-line learning is used in this
On-line: In on-line or real time learning, when the system is in operating mode,
it continues to learn while being used as a decision tool. This type of learning
has a more complex design structure.
3.2.3 Areas of Applications
The first practical application of artificial neural networks came in the late 1950s,
with the invention of the perception network and associated learning rule by Frank
Rosenblatt . Rosenblatt and his colleagues built a network and demonstrated
its ability to perform pattern recognition. Today, neural networks are performing
successfully in a wide variety of problems including interpretation, prediction, di-
agnosis, planing, monitoring, debugging, repair, instruction, and control. Basically,
most applications of neural networks fall into the following five categories: prediction,
classification, data association, data conceptualization, and data filtering.
FAULT DETECTION AND ISOLATION
The purpose of this chapter is to develop an artificial neural network that can
be used in fault detection and isolation (FDI) of fixed-position actuator failures. The
failure class is briefly reviewed and defined mathematically then the procedure to
develop an artificial neural network is outlined.
4.1 Failure Parameterization
A flight control system is working properly if all the control effectors, i.e.,
leading edge flaps, trailing edge flaps, ailerons, stabilators, and rudders maintain the
state variables in the neighborhood of their desired values. A fault occurs when a
certain level of deterioration takes place in one or more state variable because of
permanent physical change, i.e., jammed or hard-over control surfaces. System failure
occurs when a fault or combination of faults lead to complete system deterioration
and a sudden termination of flight control. Faults may produce only poor or reduced
performance, but may also lead to catastrophic failure including loss of aircraft and
This work focuses on the case when a control surfaces freezes in a fixed-position
and does not respond to subsequent commands. This is an especially difficult type
of failure to overcome since the remaining actuators should be reconfigured not only
to achieve the control objective, but also to compensate for a disturbance due to
the failure. We assume that the failure is unknown but can be determined from the
feature history of state variables and position commands to the actuators. The failure
introduces a constant disturbances into the overall closed-loop system so that the
solution to the new control problem is far from trivial.
Figure 4-1: The structure of a full-state feedback control system
The hope is that a positive identification of the failed control surface and fixed-
position will facilitate the development of a revised control law to stabilize the failed
aircraft and reinstate optimal maneuvering performance. Referring to Figure (4-1),
let uc describes the signal generated by the controller and up the signal that enters the
actual plant through the control surfaces. The reason for making a distinction between
uc and Up is that control surface jamming is manifested by up assuming a constant
value even while u, varies with time. For simplicity, assume that in the case with no
failures u,(t) = Up(t). A fixed-position actuator failure is define as
up (t)= u (t) if t
where tf denotes the failure instant of the control surface and w is the value at which
the control surface has frozen. The proposed neural network will monitor a signal
consisting of state measurements and control surface position commands, uc, to
determine if the aircraft is operating properly, uc(t) = Up(t), or has suffered a control
surface failure, u, (t) Up (t). When a control surface has failed the neural network will
hopefully identify which control surface has failed and at what position the failure has
4.2 FDI via Artificial Neural Networks
4.2.1 Artificial Neural Network FDI Formulation
Traditional methods for FDI tend to employ mathematical state-space models of
the monitored system such as state observers and Kalman filters, which continually
estimate predicted state measurements. Fault detection is achieved in these methods by
comparing predicted to actual state measurements. The pivotal assumption with these
techniques is that the state-space model of the system is known positively. In reality,
state-space models are good assumptions at best. Being based on a mathematical
model, they can be very sensitive to modeling errors, parameter variations, noise,
disturbances, etc. For example, modeling errors can be interpreted as a fault, thus
producing false alarms, or hinder actual system degradation from being detected in
the first place. A mathematical model is simply a description of system behavior
and accurate modeling for a complex nonlinear system is very difficult to achieve in
practice even when the analytical equations of motion are known. For this reason,
fault detection and isolation by these methods is an imprecise science and has shown
to be quite difficult over the past 20 years. Hence, the development of a robust and
less model dependent method for fault detection and diagnosis for complex nonlinear
system is warranted. Artificial neural networks are an ideal solution to this problem
since they demonstrate several desired advantages: powerful nonlinear mapping
properties, noise tolerance, self-learning and parallel processing capabilities.
Artificial neutral networks have been proposed as solutions for a wide variety of
tasks. Among the most promising applications is that of pattern classification. Pattern
classification implies observing input data with the intend of recognizing specific traits.
This classification process facilitates the initiation of certain actions based on the input
data. The inputs representing a pattern are called the measurement or feature vector.
In fault diagnosis, the different types of faults occurring in the system may be viewed
as decision classes. The function preformed by a pattern recognizing neural network is
the mapping of the input feature vector into one of the various decision classes. Fault
detection and diagnosis can, therefore, be considered a pattern classification activity,
and, thus, the potential exists for fault detection and diagnosis using an artificial neural
4.2.2 Artificial Neural Network Development
Neural networks are excellent mathematical tools for dealing with nonlinear
problems, as they are designed to learn patterns of activities. A nonlinear system
can be approximated by a neural network given suitable weighting factors and an
architecture consisting of at least one hidden layer. The system model can be extracted
from historical training data using a learning algorithm that often requires little or no a
priori knowledge about the system. Learning is just determining the proper connection
strengths to allow the outputs nodes to achieve the correct target output for a given
feature vector. This adaptive nature of neural networks provides great flexibility for
modeling nonlinear systems by allowing the weights to be learned by experience,
thus producing a self-learning system. The default performance function for many
feedforward neural networks is the mean squared error, which is the average squared
error between the network outputs and the target outputs. A backpropagation training
algorithm is used to train the network. Learning proceeds by updating the network
weights in the direction in which the performance function decreases most rapidly, the
negative of the gradient. One iteration of the backpropagation algorithm can be written
xk+l = Xk + akgk
where xk is a vector of current weights, gk is the current gradient, and ck is the
learning rate. Learning begins by initializing all the connection strengths to small
randomly selected values. Then a training pattern of feature vectors composed of
simulated flight data is introduced into the input nodes of the network.
0 150 -
0 1 2 3 4 5 6 7 8 9 10
Figure 4-2: Roll feature vectors for different failure position w
The training data consists of roll angle, pitch angle, yaw angle, roll rate, pitch
rate, yaw rate, angle of attack, sideslip, and position commands to the control surfaces
for the unfailed case and a characteristic set of simulated failures for a given pilot
command. Figure (4-2) shows the roll angle feature history for five different failures
during a pitch doublet, the roll angle is zero for the unfailed case. The failures
occurred on the left leading-edge flap at positions denoted by w. As can be easily seen
by Figure (4-2) small changes in the failure position produce drastic changes in the
evolution of the roll angle of the aircraft. These results constitute historically rich flight
data to design a neural network for FDI. Once all these feature vectors are gathered
the input vectors are then propagated in a feed-forward fashion through the network
to produce output values. The outputs were compared to the desired target outputs to
produced a mean squared error signal. The connection strengths are then systematically
adjusted by the learning algorithm to reduced the mean squared error to a desired
value. After each training cycle, the neural network will know more about the system
dynamic behavior. Once the connection strength is properly determined to undershoot
the desired mean squared error, training is stopped and the neural network is ready
for fault detection and isolation. The output vector consists of two variables, namely
a surface identifier and a position indicator, i.e., the output vector [0; 0] corresponds
to the absence of any particular fault and [n;w] corresponds to the nth control surface
jammed at w.
Figure 4-3: F/A-18 flight control surface numbering scheme
The proposed neural network has the ability to detect a specific fault, control
surface and fixed-position, using pattern recognition techniques that activate an alarm
in the form of the output vector. It therefore acts as a pattern recognizer for the
detection of specific faults and classifies the faults accordingly. Figure (4-3) shows the
numbering scheme for the control surfaces of an F/A-18 aircraft and Table (4-1) lists
the position limits for each control surface, the maximum and minimum values are the
After the network is trained, fault detection and diagnosis is simply a matter of
presenting a new historically rich feature vector to the input nodes and reading the
output vector from the output nodes. The neural network can be tested by simulating
new flight data to produce a new input vector not in the original training pattern.
Table 4-1: F/A-18 Control Surface Position Limits
# Effector Position Limits
1,2 Leading Edge Flaps (lef) -3 < 8tef < 33
3,4 Trailing Edge Flaps (tef) -8 < 6tef < 45
5,6 Ailerons (ail) -25 < 8ai < 45
7,8 Stabilators (stb) -24 < 8hzt < 10.5
9,10 Rudders (rud) -30 < 8rud < 30
On-line fault detection and diagnosis can be achieved by using a system of delays to
produce the historical data necessary for the neural network to perform its calculation
THE STABILIZATION PROBLEM
This chapter presents the formulation of the stabilization solution which is one
of the most time-critical components of a reconfiguration scheme. A fixed-position
actuator failure can create a constant force and moment disturbance on the aircraft.
This constant force and moment can lead to a significant deviation from the desired
trim condition and leave the remaining control surfaces incapable of regaining control
of the aircraft. There are several suitable methods for returning an aircraft to a trim
condition following a failure which include the use of a regulator system with integral
control or, if the disturbance can be measured, in a linear trim subsystem through the
use of feedforward control. This work will focus on the development of the latter
approach which has the distinct advantage of rapid response to disturbances while
not adversely affecting the stability of the system. Its disadvantage is that any errors
between the approximated disturbance received through fault detection and isolation
and true disturbance will directly appear in the output. The following sections present
a formal description of the stabilization problem and describe a decomposition of
the problem which allows the use of a fast and efficient Matlab algorithm in the
solution [124, 125].
5.1 The Nonlinear Trim Problem
During normal flight, the motion of an aircraft with respect to the Earth-axis
system can, in general, be described by the nonlinear autonomous differential equations
x(t) = fo (x(t),u(t)) +
y(t)= h, (x(t),u(t))
where fo : R"xp F-+ Rn and ho : R"xp -+ Rq are nonlinear mappings, x(t) E R" is the
state variables vector, u(t) E RP is the input vector, (t) is a vector of unmeasurable
disturbances, and y(t) E Rq is the output vector. The orientation of the aircraft is
trimmed at the nominal values (x,, u,) when
fo (xn,u) =0
ho (x,,U) =0
During straight and level flight the nominal control settings u, are established which
maintain steady state flight (x = 0) with wings level at constant altitude, airspeed, and
heading. Following a fixed-position actuator failure, the aircraft dynamics are assumed
x(t) = fo (x(t),u(t)) + (t) +d
y(t) = h(x(t), u(t))
where d is a constant or slowly varying measurable disturbance vector. For our failure
class, d represents the constant disturbance that results from the nonzero deflection of
the failed control surface. Following a fixed-position actuator failure, a trim condition
fo (xn,n) +d = 0
ho (x, u) =0
The problem then becomes how to determine a solution (x,, un) which satisfies
Equation (5.4). The solution can be determined by using the Matlab trimming routine
trim on a nonlinear model of the aircraft's equations of motion at a desired flight
condition. It is only necessary to develop the proper constraints on the magnitudes of
the control surfaces and states to produce a feasible solution for implementation.
5.2 The Linear Trim Problem
Let the open-loop linearized dynamics of the healthy aircraft be described as
x(t) = Ax(t) +Bu(t) (5.5)
where x(t) E R" is the state variables vector, u(t) E RP is the control vector, A E R"x" is
the plant matrix, and B E Rn"p is the control matrix. Let the measurements be given by
y(t) = Cx(t) +Du(t) (5.6)
where y(t) E Rq is the output vector, C E Rqxn is the output matrix, and D E Rqxp is the
null matrix. Assume that a postfailure model of an aircraft at a chosen flight condition
is given by
x(t) = Ax(t) +Brur(t) + d (5.7)
where x(t) is the state vector of the linear aircraft dynamics and ur(t) is the vector of
available (i.e., failed surface is deleted) control surfaces deflections, and d is a vector of
constant disturbances that can be used to represent forces and moments generated by
a failed surface. For the general problem, the disturbance vector d may be measured
(e.g., by the use of an FDI algorithm) or unmeasurable. Let the key quantities that are
to be regulated in denoted by
y(t) = Cx(t) + Du,(t) (5.8)
Elements of y(t) might represent quantities such as altitude, bank angle, flight path
angle, and rotational rate perturbation. The objective of our problem will be to
automatically select u, (t) to guarantee that y(t) achieves some desired value in steady
state, yd(t). More precisely, the linear trim objective can be expressed as finding the
solution (x, Un) that guarantees
0 =Ax +Bu +d (5.10)
For this work, we will assume that the disturbance d is caused by a fixed-position
actuator failure which can be measured through FDI. We will further assume that the
disturbance takes the form
d= b,,ir (5.11)
where w is the difference between the jammed position of the failed control surface
and its nominal value, and b, is the column removed from the B matrix corresponding
to the failed control surface. Now define the model of an aircraft with a fixed-position
actuator failure as
x(t) = Ax(t) +Bu,(t) + b,, ,1 (5.12)
where x(t) E R" is the state vector, u,(t) E R 1 is the vector of remaining control
surfaces (i.e., failed surface is deleted), b,, i is the input to the aircraft caused by the
jammed surface w, and b, is the column in B corresponding to the jammed surface.
As with the nonlinear trim formulation, it is necessary to impose some constraints on
the allowable magnitudes of the states and control surfaces, (x,u), for which a solution
should be feasible. These constraints can be described as upper and lower limits on the
UL < U < UU
Equation (5.9) through (5.13) describe the main objectives of the linear trim problem.
That is, produce a control system that achieves stable flight at constant altitude with
certain specified states set to zero, while the deviation of all other states is minimized
from their desired values. Various norms and weighting matrices can be used to
determine the solution to this problem, the Matlab routine trim is demonstrated in the
FAULT-TOLERANT CONTROL DESIGN METHODS
The objective of this work is to develop a reconfiguration scheme that is reliable
and offers a degree of assured success for the targeted types of failures. The reconfig-
uration scheme is expected to stabilized the aircraft in the event of a control surface
failure and provide reasonable command-tracking performance.
To accomplish these goals, two approaches are investigated and evaluated in
this chapter. One is based on linear-quadratic regulator (LQR) methodology. In
this approach the effect of the jammed surface is treated as a measurable constant
disturbance to the system. An LQR controller is designed to stabilize the aircraft
(stabilization), balance the jammed surface (disturbance rejection), and provide
command tracking. The second method is developed by the author of this work,
which is based on an H, approach. Here the effect of the jammed surface is treated
as a constant disturbance which is bounded by a low-pass filter. A reference nominal
controller is designed for the healthy aircraft with all control surfaces operable.
This nominal controller is used as a target model in Ho synthesis to design a robust
controller which is capable of canceling the influence of the jammed surfaces and
reproduce as closely as possible the desired outputs of the healthy aircraft.
The problem formulation for the targeted type of failure is presented before each
fault-tolerant control method is developed in the following sections. Let the open-loop
linearized dynamics of the healthy aircraft be described in state variable form as
x(t) = Ax(t) +Bu(t) (6.1)
where x(t) E R" is the vector of aircraft states and u(t) E RP is the vector of control
surfaces. Let the measurements be given by
y(t) = Cx(t) +Du(t) (6.2)
where y(t) E Rq is the output variables available for feedback control. It is assumed
that a baseline control law has been designed based on (6.1) that provides satisfactory
stabilization and command-tracking performance of the aircraft. Suppose now that one
of the control surface actuators fails suddenly and jams at a position w. Let us rewrite
the entire postfailure system in state space form as
x(t) = Ax(t) +Bu,(t) + b,, 1 i (6.3)
where x(t) E Rn is the state vector, u,(t) E RP 1 is the vector of remaining control
surfaces (i.e., failed surface is deleted), b,, i is the input to the aircraft caused by the
jammed surface w, and bw is the column in B corresponding to the jammed surface.
6.1 Fault-Tolerant Control Design Using LQR Theory
LQR design methodology can be applied directly to Equation (6.3) assuming that
b,, 11 is a constant disturbance that can be eliminated by using integral control. While
that assumption is completely accurate and can produce desired results it is not the
approach taken here. The approach taken here is based upon a systematic procedure
in which the failure is identified through FDI, Chapter (4), and directly canceled by
finding a new trim condition, Chapter (5). The result is a new linear system which
directly considers the effects of the constant disturbance. This new linear system is
achieved by considering the results of our automatic trim algorithm
0 = Ax, +BUn +b,, i' (6.4)
where n, E R" is the vector of nominal aircraft states and n, E RP 1 is the vector of
nominal control surface deflections such that the state derivatives are identically zero.
Note that the trim condition (x,, u,) is only available for calculation when w is known
through some FDI procedure. By simply rearranging Equation (6.4) we can achieve an
expression for the constant disturbance in terms of the state matrices and trim condition
b,, = (Ax, +B,u,) (6.5)
By substituting this result into Equation (6.3) we find our new linear system is given by
x(t) = A (x(t) x,) +B, (u,(t) u,) (6.6)
The fault-tolerant control problem can now be stated as follows using LQR methodol-
ogy. Find the control u,(t) -u, that minimizes
J= f [(x x,)T Q(x ,) + (_- n)TR (u u) dt (6.7)
The optimal control that minimizes (6.7) is given by
u, (t) -u, = -R 1BTP(x(t) -x,) A -K(x(t) -x,) (6.8)
where P solves the algebraic Riccati equation
0 = ATP+PA QPBR 1BTP (6.9)
Assuming that the linearized model is valid the feedback law (6.7) guarantees that
the linearized closed loop system will be stable, and that the important states (6.2)
will approach their desired trajectories regardless of the constant disturbance. Integral
control can be added to the design process to minimize errors and improve tracking
performance. Thus the primary goals of stabilizing the aircraft (stabilization), balancing
the jammed surface (disturbance rejection), and providing command tracking will be
met by this LQR fault-tolerant design.
6.2 Fault-Tolerant Control Design Using H, Theory
This section develops the theory for aircraft tracking control for a class of aircraft
failures using H, control design methodology. The author uses a two-step process
of first designing the feedforward part of the controller to achieve perfect trajectory
following and then designing the feedback part of the controller using H, regulator
theory. The objective of the tracking problem is to get a plant output to track a desired
model signal. The design procedure will attempt to exploit the H--optimality criterion
for judging tracking performance while minimizing the worst case tracking error norm
over an admissible ball of disturbances. The resulting controller design is an innovative
technique for fault-tolerant controls in which H, methodology is applied directly to the
targeted failure class.
The desired model signal to be tracked is given by a reference LQR controller
design for the healthy aircraft (see Appendix B for controller design) shown in Figure
Figure 6-1: Reference closed-loop system
where P is the linearized F/A-18 model (see Appendix A), Kiqr is the feedback gains,
kiqr is the feedforward gains, and I is an integrator. The reference controller as shown
in Figure (6-1) presents some difficulties in our design process, since, in general, H_
design frameworks do not consider integral control. The problem is that H_ control
theory cannot be applied directly to a system that is neutrally-stable. H, synthesis
will attempt to stabilize the pole at s = 0 and such a pole in the reference closed-loop
system is not stabilizable. However, this obstacle can be overcome by implementing a
two-step design approach. First, the feedforward and feedback gains are designed using
LQR methodology to achieve desired trajectory following and disturbance rejection
criteria for the healthy aircraft. Then the plant model and feedback gains are removed
from the reference controller and used as a target model for H, synthesis. The target
model, T, is given by Figure (6-2).
Figure 6-2: Target Model
The goal is to design an H, controller that not only achieves the same tracking
performance of the baseline controller but one that is capable of rejecting a disturbance
caused by a jammed control surface. The problem can be set up as follows, let the
postfailure state-space form be given as
x(t) = Ax(t) +B,u,(t) +d (6.10)
where u, is the remaining control surfaces (i.e., failed surface is deleted), and d is a
disturbance force. The measurements y(t) are corrupted by noise such that
yn(t) =y(t) +wn (6.11)
Our objective is to design a control law so that the effect of the disturbance force d on
the state measurements of the aircraft is reduced over an extremely small frequency
range, 0 < co < 0.01, such that the resulting disturbance is modeled as a constant force
upon the system. A low-pass filter given by
Ww = --
is used to limit the disturbance force and achieve this goal. The result is a constant
disturbance upon the system which is magnitude bounded by the position value of the
jammed surface w. The synthesis model for H, design is shown in Figure (6-3)
Figure 6-3: Hc synthesis model
where wk is the control weight and Wp is the performance weight on the error signal of
desired measurements to actual measurements
e =yd -Y
The synthesis model shown in Figure (6-3) along with weighting functions wd, Wk, wn,
and Wp can be used to determine the sub-optimal H, controller, KH_, that minimizes
the worst case tracking error norm over a magnitude bounded disturbance force. Thus,
the primary goal of designing a controller that not only achieves the same tracking
performance of the baseline controller but one that is capable of rejecting a disturbance
caused by a jammed control surface will be met by this H, fault-tolerant design. The
implementation of the H, controller is shown in the analysis model in Figure (6-4).
Figure 6-4: Hc analysis model
APPLICATION TO AN F/A-18
In this final chapter the reconfiguration scheme proposed throughout this work
is demonstrated on a high-fidelity nonlinear F/A-18 simulation. The simulation
is based on the 6 degree-of-freedom equations of motion for a rigid body driven
by aerodynamic, propulsive, and gravitational forces. The aerodynamic model is
nonlinear and full independent control authority is available with realistic actuator
models including rate and position limits. A nonlinear controller is included with this
simulation that provides excellent performance and stability characteristics for a wide
variety of high-performance maneuvers over the entire F/A-18 flight envelope. This
controller is appropriate for the healthy aircraft and should not be altered; therefore,
fault-tolerance will be achieved by switching to a predetermined controller for recovery
and subsequent command following.
The failure scenario handled throughout this chapter involves a 2-inch longitudinal
stick motion that commands a pitch doublet during which the left trailing-edge
flap becomes stuck from a fixed-position actuator failure. It is assumed the failure
is unknown but can be overcome by combining the fault detection and isolation
procedure, Chapter (4), the stabilization procedure, Chapter (5), and either of the two
formulated fault-tolerant control procedures, Chapter (6).
7.1 Healthy F/A-18
In this section the normal response of the F/A-18 to a 2-inch longitudinal stick
doublet is reviewed for the unfailed case so that the reader can properly appreciate the
evolution from the unfailed baseline controller to the fault-tolerant controllers. The
maneuver is conducted in a 20 second simulation in which the pilot holds the stick at
its neural point from 0-3 seconds, pulls and holds the stick at a positive 2 inches from
3-6 seconds, pushes and holds the stick at a negative 2 inches from 6-9 seconds, then
returns and holds the stick to its neural point from 9-20 seconds.
0 5 10 15 20
0 5 10 15 20
Figure 7-1: Longitudinal
0 5 10
responses: healthy aircraft
Figure (7-1) shows the longitudinal responses to the 2-inch longitudinal stick
doublet in the unfailed case. The maneuver causes the aircraft to pitch upwards at 0.15
radians/second from 3-6 seconds, then pitch down-wards at -0.15 radians/seconds from
6-9 seconds. The aircraft pitches to a maximum 25 degrees then returns back to wings
Figure (7-2) shows the lateral responses to the 2-inch longitudinal stick doublet
in the unfailed case. The maneuver is essentially decoupled causing no response in the
lateral states. This is characteristic of the F/A-18 which is known to have excellent
5 10 15 20 0
Figure 7-2: Lateral-directional responses:
Figure (7-3) shows the control surface deflections commanded by the 2-inch
longitudinal stick doublet in the unfailed case. The leading-edge flaps, trailing-edge
flaps, and stabilators are used collectively to pitch the aircraft with the primary pitching
moment being generated by the stabilators. It is important to note that neither the
ailerons nor rudders are required to pitch the aircraft using the baseline controller in the
3 5 10 15 2(
0 5 10 15 20
-10 I I
0 2 4 6 8 10 12 14 16 18 20
10 I I I I I I I
Figure 7-3: Control surface deflections: healthy aircraft
0 2 4 6 8 10 12 14 16 18 20
7.2 Failed F/A-18
In this section we show the effects of the left trailing-edge flap failure on the
baseline controller. The maneuver is identical to the previous section with no attempt
by the pilot to correct for the severe deviations from the desired trajectory. While this
is not an ideal assumption, it is made in this case to simplify the fault detection and
isolation process and to guarantee full control authority is passed to the fault-tolerant
controller. The failure occurs at 4 seconds with the left trailing-edge flap becoming
stuck at approximately 3.96 degrees. While this failure may not sound severe the
effects upon performance and stability are devastating.
0 5 10 15 20 0 5 10 15 20
^ 20 :
0 5 10 15 20 0 5 10 15 20
Time, (sec) Time, (sec)
Figure 7-4: Longitudinal responses: failed aircraft
Figure (7-4) shows the longitudinal responses to the 2-inch longitudinal stick
doublet with a left trailing-edge flap failure at 4 seconds. The aircraft retains reason-
able responses for pitch angle and pitch rate during the maneuver. Once the aircraft is
commanded back to wings level it begins to pitch downward violently. At 20 seconds
the aircraft is pitched downward at a negative 16 degrees with increasing pitch rate and
total true airspeed.
5 10 15 20
0 5 10 15 20
5 10 15 20 0 5 10
Time, (sec) Time, (sec)
Figure 7-5: Lateral-directional responses: failed aircraft
Figure (7-5) shows the lateral responses to the 2-inch longitudinal stick doublet
with a left trailing-edge flap failure at 4 seconds. As previously shown, for the unfailed
aircraft's the lateral states are not excited by a pitch doublet. This decoupling is not
the case for a pitch doublet in which the leading-edge flap has failed. At 20 seconds
the aircraft has rolled completely on its side with a constant roll rate and a minimal
side-slip and yaw rate. The aircraft continues to roll and pitch until it is nose down.
Finally the aircraft impacts the ground in approximately 37 seconds (time of failure
plus 34 seconds) traveling just over Mach 1.
0 2 4 6 8 10 12 14 16 18 20
-5 7 ^ -- --- ---- --- -- -
0 1 16 18 20
0 2 4 6 8 10 12 14 16 18 20
0 2 4 6 8 10 12 14 16 18 20
0 2 4 6 8 10 12 14 16 18 20
12 14 16 18 20
Figure 7-6: Control surface deflections: failed aircraft
Figure (7-6) shows the control surface deflections for a 2-inch longitudinal stick
doublet with a left trailing-edge flap failure at 4 seconds. First, it is essential to notice
the effects of the failure on the left trailing-edge flap. This is shown by the red dashed
line in the second response. The position of the control surface remains constant after
the failure instant. Also notable is the excitation of the ailerons and rudders by the
feedback elements of the baseline controller attempting to counter the roll and yaw
moments generated by the failure. This is also apparent in the differential stabilator
deflection. Functioning with only nine operational control surfaces, the baseline
controller proves ill-equipped to handle the failure.
7.3 Artificial Neural Network FDI
The artificial neural network (ANN) proposed in Chapter (4) for fault detection
and isolation (FDI) of a fixed-position actuator failure is developed and evaluated
in this section for the proposed scenario. The network was designed in Matlab and
accepts as inputs five seconds of flight data sampled at 5 Hz. The measurements used
for creating the input feature vector are Euler angles, Euler rates, angle-of-attack, side-
slip, and position commands to the trailing-edge flaps, ailerons, stabilators, and rudders.
It was determined that the position commands to the leading-edge flaps, which are
primarily used for trimming the aircraft, were not producing a "rich" feature history;
therefore, they were not used for training the network or performing the FDI operation.
The removal of the leading-edge flaps position commands from the network design and
operation is without incident, since there exists ample measurements with "rich" feature
histories to generate desired results. As previously stated, the network is designed to
accept as input a vector composed of position commands and aircraft measurements
generated by the baseline controller; and output a vector identifying the failed control
surface and failed position in the event a failure occurs.
The network used for the scenario presented throughout this chapter was designed
to monitor flight maneuvers including pitch and roll doublets and wind-up turns. The
specifications of the network include: four layers with 312 neurons in the input layer;
156 neuron in the first hidden layer; 78 neurons in the second hidden layer; and 2
neurons in the output layer. The activation functions are constant throughout each
layer and are logsig, logsig, logsig, and pureline, respectively. The learning algorithm
selected was trainscg, which is a backpropagation technique where the network training
function updates weight and bias values according to the scaled conjugate gradient
method. The algorithm is capable of training any network as long as its weights, net
inputs, and activation functions have derivatives, which are satisfied by the design. The
network was designed and trained off-line with a fixed architecture. Once the desired
mean-squared error was achieved with the training algorithm the network weights and
bias were not changed during FDI operation. For the proposed scenario, five seconds
of flight data starting from the failure instant were input into the finalized network to
produce FDI results. The actual failure occurs on the left trailing-edge flap (control
surface #3) at a fixed-position of 3.96 degrees. The network results are given by
3.01 failed surface
ANN output = (7.1)
3.99 failed position
These results demonstrate the capability of an artificial neural network to perform
fault detection and isolation of fixed-position actuator failures. The first result, 3.01,
represents the identifier for the failed control surface and correctly identifies the
left-trailing edge flap (control surface #3) as the failed surface. The second result,
3.99, represents the identifier for the control surface position in degrees. This result
achieves the desired accuracy and positively identifies a left trailing-edge flap failure
with precision suitable to continue with trimming and fault-tolerant control. Acceptable
results for this simulation would have included a failed surface identifier of 0.25 the
actual integer value or a failed position identifier of 0.5 degrees the actual position
value. While these ranges were reached through the process of trial and error, they
have been determined to consistently facilitate desired results throughout the entire
The stabilization solution from Chapter (5) was implemented on the scenario
presented throughout this chapter using the fault detection and isolation (FDI) results,
Equation (7.1), from Section (7.3). The constraints placed upon the Matlab function
trim included returning the aircraft with the failed control surface back to wings level
flight at constant altitude, airspeed, and heading. This orientation can be expressed as
finding the nominal control surface position un such that
0 = Brun + brw (7.2)
while the nominal state vector x, is given by
0 = x (7.3)
Also, the allowable deflection of each control surface was constrained by the position
limits defined by the nonlinear simulation, which can be found in Table (4-1). The
results for a left trailing-edge flap failure at 3.99 degrees are given as
Table 7-1: Stabilization Results
8 tbi 1.18
8 tbr -0.850
These results can be easily verified by solving the equation representing the
aircraft with a control surface failure, Equation (5.12), using the appropriate x,, u,, and
w such that
0 = Ax, +Brun +b,, ~ (7.4)
7.5 Fault-Tolerant Control Nonlinear Simulations
The results included in this section show the implementation of the developed
reconfiguration techniques on a nonlinear F/A-18 simulation. The only alteration to
the nonlinear simulation, inaddition to the new fault-tolerant controllers, involved
permitting each control surface independent deflection rather than the traditional
collective or differential deflection of the baseline controller. The failure scenario
continues from the previous sections. While performing a pitch doublet the left
trailing-edge flap fails at 3.96 degrees at 4 second, resulting in an undesired roll, pitch,
and yaw motion. The task of the reconfiguration scheme developed throughout this
work is to positively identify that failure has occurred, determine the severity of the
failure, and then switch control from the baseline controller to a fault-tolerant controller
to regain stability and restore performance. The FDI procedure was performed off-line
using five seconds of flight data from 4-9 seconds with acceptable results to proceed
with control authority switching from the baseline controller to the fault-tolerant
controller at 9 seconds. Then, a 2-inch longitudinal stick doublet is initiated at 23
seconds to demonstrate the command-tracking capabilities of each fault-tolerant
controller on the nonlinear equations of motion. The goal here was to pitch the aircraft
without exciting any lateral states of the aircraft, just as in the unfailed case.
The following figures show the results for each control methodology. Figures
(7-7)-(7-9) show the control surface deflection and state responses using the LQR
fault-tolerant controller and Figures (7-10)-(7-12) show the control surface deflection
and state responses using the H, fault-tolerant controller. For the state responses,
the red dashed line is the desired performance of a healthy F/A-18 performing two
consecutive pitch doublets while the black solid line is the results achieved with each
fault-tolerant controller. In each case, the pitch moment is primarily generated by the
deflection of the stabilators about a new trim point. Similar results are achieved by
each fault-tolerant controller. The rise time during the commanded maneuver is slightly
slower than the desired healthy F/A-18. The maneuver is performed with zero steady-
state error and without producing any measurable roll angle or roll rate during the pitch
maneuver even though the left trailing-edge flap has failed. The desired results are
achieved, stability is restored, and command-tracking is performed.
0 10 20 30 40 0 10 20 30 40
0 10 20 30 40 0 10 20 30 40
Time, (sec) Time, (sec)
Figure 7-7: Lateral responses : LQR FTC
0 10 20 30 40
0 10 20 30 40
0 10 20 30 40
Figure 7-8: Longitudinal responses : LQR FTC
0 5 10 15 20 25 30 35 4(
I I I I I I I I
5 10 15 20 25 30 35 4(
100 5 10 15 20 25 30 35 4(
1 0 I I I I I I I
0 5 10 15 20 25 30 35 4(
S--5 I I I I I I-- -
0 5 10 15 20 25 30 35 4(
Figure 7-9: Control surface deflections : LQR FTC
0 10 20
0 10 20
Figure 7-10: Lateral responses : Ho FTC
< \< o
0 10 20 30 40 0 10 20
o I !
t 10 0 I -
0 10 20 30 40 0 10 20
Time, (sec) Time, (sec)
Figure 7-11: Longitudinal responses : Hc FTC
Figure 7-12: Control surface deflections : Hc FTC
-2 1 I I I
0 5 10 15 20 25 30 35 40
A reconfiguration scheme for flight control adaptation to fixed-position actuator
failures is expected to accomplish three tasks. First, the scheme must have a fast and
efficient method for identifying that a failure has occurred and the resulting effects
upon stability and performance. Second, the scheme must adjust the trim values for
command input so that level flight can be achieved. Third, the closed-loop system must
ensure command-tracking, despite the detrimental effects of the failure and reduction
in control effectiveness. The failure class analyzed throughout this work is a fixed-
position or jammed actuator failure, which results in a flight control surface becoming
inoperable. This work has introduced, developed, and demonstrated the necessary
concepts to satisfactorily achieve all three goals for the targeted failure class.
The reconfiguration scheme developed through this work is a systematic procedure
that attempts to maximize the tracking performance of the failed aircraft while
satisfying the stability requirements. As a result, the proposed scheme relied on three
interdependent processes: 1) fault detection and isolation, 2) stabilization, and 3)
command-tracking. The use of artificial neural networks proved to be an excellent tool
for identifying fixed-position actuator failures. These highly organized and versatile
architectures were readily suited to perform the fault detection and isolation (FDI) task
which maps state measurements into various failure classes. The results from the FDI
procedure facilitated the development of a feedforward trim solution to recover system
stability and two fault-tolerant control strategies to restore system performance. The
two fault-tolerant methodologies explored, LQR and Ho, assumed that the effects of
the failed surfaces would introduce a constant disturbance into the dynamical equations
governing the motion of the aircraft. The resulting theoretical development relied
on exploiting the robustness of each technique to directly address and overcome the
effects of the failure by as nearly as possible reconstructing the forces and moments
of the unfailed aircraft. The complete reconfiguration scheme was demonstrated on
a nonlinear simulation of an F/A-18 to show the potential of the two methods in
reconfigurable controls. The LQR and H, methods achieved virtually the same results
for the targeted failure class with both regaining stability and restoring performance in
The author of this work recognizes that several assumptions made throughout this
work limit its application into flight systems. For example, the solutions presented
throughout this work were developed using a single flight condition for a very specific
failure class. No consideration was given to expanding the results over the entire
flight envelope or into other failure scenarios. Furthermore, the standards used for
judging the fault-tolerant controllers design were exceptionally high. Success was only
defined by the the complete restoration of prefailure performance. In some situations
in which an aircraft has suffered a significant system failure, it may not be necessary
or even desirable to restore the performance to that of the healthy aircraft. Therefore,
a method for determine how much performance is desired after a specific failure
must be developed in conjunction with the pilots who fly the aircraft. Additionally,
the incorporation of a reconfiguration scheme into an aircraft will most likely not
be accomplished successfully post-production; rather, the tools for reconfiguration
must be integrated into the initial design concepts of the aircraft. The initial design
integration of reconfiguration technology may lead to design conflicts between normal
operation and the rare occurrence of many of the failures currently under investigation
in reconfigurable flight controls. Finally, a reconfiguration scheme will have to be
flight tested to prove its usefullness in real-world situations. Such testing on full-size
piloted aircraft is the essential step in demonstrating the promised benefits of the
In summary, the results achieved in this work demonstrate the ability of artificial
neural networks with linear control techniques to accommodate a very specific
failure class while restoring stability and command-tracking to an aircraft which has
experienced a significant control system failure. The methods developed here appear to
be very effective in achieving the major objective to develop a reconfiguration scheme
to accommodate fixed-position actuator failures.
LINEARIZED MODEL OF THE F/A-18
The following is a linearized model of an F/A-18 generated from a high fi-
delity six degree-of-freedom nonlinear simulator. Since the aircraft potentially
has ten independent control surfaces, it is an ideal candidate for control restruc-
turing and is used throughout this work for control synthesis. The flight con-
ditions for the linearized model are Mach = 0.8, height = 10,000 ft, (trim =
1.230, trim = 1.230, Ptrim = Ptrim = 00, and weight = 30,777 lbm. Let u =
(8iefj Fief, Stefi 8tef, Sail, 6ail, 8tbi &stb, 6rudi 6rudr,)T be the input vector of control
surfaces perturbations from the trim values, where 8tef, 8tefr are the left and right
leading-edge flaps, 8tef/, 8tef the left and right trailing-edge flaps, 8ail7, 8ailr the left
and right ailerons, 8 tb5, 6stbr the left and right stabilators, and 8rud,, 8rudr the left and
All of the control surface surface deflections are in degrees. The sign convention
is positive leading-edge flap deflection is up, positive trailing-edge flap deflection is
down, positive aileron deflection is down, positive stabilator deflection is down, and
positive rudder deflection is left looking forward. The surface trim values are 1.720
for the trailing-edge flaps, 1.120 for the stabilators, and 0" for the trailing-edge flaps,
ailerons, and rudders. Let the state vector for perturbations from the trim conditions be
x = (u w q vpr ) ,T where the components are, in order of appearance in x, forward
velocity, vertical velocity, pitch rate, pitch angle, side velocity, roll rate, yaw rate, and
roll angle. The units are in radians/second for angular rates, radians for angles, and
feet/seconds for velocities. The linearized dynamics of the F/A-18 at the preceding
flight conditions are given by
x(t) = Ax(t) +Bu(t) (1)
where x(t) is the state vector and u(t) is the vector of available control surfaces. The
dynamics of the A matrix are decoupled in the longitudinal and lateral directors, while
the B matrix is not. The first four states represent the longitudinal dynamics and the
second four represent the lateral dynamics such that
A= Alon at (2)
B= [B B2] (3)
-0.0209 0.0482 -18.3387 -32.1361
-0.0377 -1.8386 853.1909 -0.6901
Alone = (4)
0.0002 -0.0206 -0.9431 0
0 0 1.000 0
-0.3196 18.3106 -860.7181 32.13611
-0.0346 -6.9243 0.7349 0
0.0098 0.0044 -0.3233 0
0 1.0000 0.0215 0
The open-loop eigenvalues of the aircraft
NOMINAL CONTROLLER DESIGN
The design process followed to arrive at the reference state-feedback controller
used for the target model in the Ho design uses LQR methodology. Since the lon-
gitudinal and lateral dynamics are decoupled for the unfailed aircraft, we can design
controllers for them separately. See Appendix A for the linearized aircraft model for
x(t) =Ax(t) +Bu(t)
To decouple the inputs, we need to mix them to obtain
inputs. We do this as follows. Let
1 1 0 0 0 0 0
0 0 1 0 0 0
0 0 0 0 0 0 1
1 -1 0 0 0 0 0
0 0 1 -10 0 0
0 0 0 0 1 -10
0 0 0 0 0 0 1
0 0 0 0 0 0 0
differential and collective
Unew = Bmix u
where Unew = (6efc 8tefc 8stbc 8lefd 8tefd 6aild stbd 8rud) T, where the components are,
in order of appearance in Unew, collective leading-edge flaps, collective trailing-edge
flaps, collective stabilators, differential leading-edge flaps, differential trailing-edge
flaps, differential ailerons, differential stabilators, and collective rudders. The first three
mixed inputs represent the longitudinal control while the the last five mixed inputs
represent the lateral control. We can now scale the inputs to ease our controller design
such that 1 unit in each input is approximately equivalent in terms of importance. We
pick the scaling for the new inputs as follows
Up = S1 Unew (10)
S1 ^ diag[33,45,10.5,33,45,45,10.5,30] (11)
We then let
B = B (Bm,,) 1S (12)
be our new B matrix, which is mixed and scaled. We can follow the same reasoning
for the state variables such that
Xp = T1 -x (13)
Ti = diag [0.01,0.01, 1, 1,0.01, 1,1,1] (14)
then our new system matrices are
Ap= Ti -Aa T,1
Bp = Ti B1
and the linear aircraft model becomes
Xp = ApXp +Bpup (16)
We can now split the aircraft into longitudinal and lateral models and design controllers
for each individually.
The longitudinal model is given by
The states are the scaled versions of the longitudinal states, x = (u w q 0) and the
scaled inputs are u = (81ef, tef 8stbc) T. We would like to control the pitch angle in the
longitudinal axis. This is done by augmenting the system with an integrator on pitch
on =[ 0 0 0 1
y = 0 = Clon
Then our new longitudinal system becomes
x A,,o 0 x Bion
=z= + u
xI Clon O xi 0
We then proceed to design an LQR controller for this augmented model. We used
diag [0.0, 0.3,1.2,5.0,36.0]
The result is
Figure (B-l) shows the state responses to a pitch doublet, the black line represents the
nominal controller designed here while the red dashed line represents the nonlinear
5 10 15 20
0 5 10 15 20
10 15 20 0 5 10
Time, (sec) Time, (sec)
Figure B-1: Nominal Longitudinal Responses
The lateral model is
The states are the scaled versions of the lateral states, x = (vp r T) and the scaled
inputs are u = (Steffd 8efd 6sail td 8Brugdc) The goal we would like to achieve with
lateral design is automatically coordinated flight. One way to achieve this is by
controlling side velocity and roll angle so that a nonzero commanded roll angle with
zero-commanded side velocity will produce a steady turn. This is done by augmenting
the system with an integrator on side-velocity and roll angle. Let
1 0 0 0
Clat = (25)
0 0 0 1
Then our new lateral system becomes
S Alat 0 x Blat
=z= + u
I Clat 0 X 0
We then proceed to design an LQR controller for this augmented model. We used
Qla, = diag [0.01,0.001,50.0, 0.01,10.0, 1.0]
Riat = diag [1.0, 5.0, 1.0, 0.25, 1.0]
The result is
0.0000 0.0000 -0.0000 0.0000 0.0000 0.0000
0.0819 1.2723 -14.2166 8.9759 0.1520 8.5733
Klat= 0.2299 4.1653 -29.2495 30.0738 0.4254 29.3576 (30)
0.0315 1.3124 9.3172 10.2124 0.0568 10.6313
0.4417 0.4901 -230.8703 -4.1777 0.8727 -11.0881
Figure (B-2) shows the state responses to a roll doublet, the black line represents the
nominal controller designed here while the red dashed line represents the nonlinear
0 5 10 15 20
0 5 10
0 5 10 15 20
0 5 10 15 20
0 5 10
Figure B-2: Nominal Lateral Responses
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