<%BANNER%>

A Reconfiguration Scheme for Flight Control Adaptation to Fixed-Position Actuator Failures


PAGE 1

A RECONFIGURA TION SCHEME FOR FLIGHT CONTR OL AD APT A TION T O FIXED-POSITION A CTU A T OR F AILURES By R OBER T S. EICK A THESIS PRESENTED T O THE GRADU A TE SCHOOL OF THE UNIVERSITY OF FLORID A IN P AR TIAL FULFILLMENT OF THE REQ UIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE UNIVERSITY OF FLORID A 2003

PAGE 2

Cop yright 2003 by Robert S. Eick

PAGE 3

I dedicate this w ork to my f amily

PAGE 4

A CKNO WLEDGMENTS This research w as inspired by the Intelligent Flight Control System (IFCS) ight research project at N ASA Dryden Flight Research Center (DFRC). The author thanks John Burk en of N ASA DFRC for his support. i v

PAGE 5

T ABLE OF CONTENTS page A CKNO WLEDGMENTS . . . . . . . . . . . . . . . . i v LIST OF T ABLES . . . . . . . . . . . . . . . . . vii LIST OF FIGURES . . . . . . . . . . . . . . . . . viii ABSTRA CT . . . . . . . . . . . . . . . . . . . x CHAPTER 1 INTR ODUCTION . . . . . . . . . . . . . . . . 1 1.1 Moti v ating Example . . . . . . . . . . . . . . 3 1.2 Ov ervie w . . . . . . . . . . . . . . . . 5 2 REVIEW OF LITERA TURE . . . . . . . . . . . . . 7 2.1 Introduction . . . . . . . . . . . . . . . . 7 2.2 The State of the Art . . . . . . . . . . . . . . 9 2.2.1 F ault Detection and Isolation (FDI) . . . . . . . 10 2.2.2 Rob ust Control . . . . . . . . . . . . . 11 2.2.3 F ault-T olerant Control . . . . . . . . . . . 11 2.2.4 Rob ust F ault-T olerant Control . . . . . . . . . 12 2.2.5 Rob ust F ault Estimation . . . . . . . . . . . 12 2.2.6 F ault-T olerant Control w/ FDI . . . . . . . . . 12 2.2.7 Supervision . . . . . . . . . . . . . . 13 2.3 T ypes of Redundanc y . . . . . . . . . . . . . 14 2.4 F ault-T olerant Control Methods . . . . . . . . . . 14 2.4.1 P assi v e Approaches . . . . . . . . . . . . 14 2.4.2 Acti v e Approaches . . . . . . . . . . . . 16 3 PRELIMIN ARIES . . . . . . . . . . . . . . . . 21 3.1 Aircraft Flight Mechanics . . . . . . . . . . . . 21 3.1.1 Aircraft Axis Systems . . . . . . . . . . . 21 3.1.2 General Equations of Motion . . . . . . . . . 23 3.1.3 Linearized Equations of Motion . . . . . . . . 27 3.2 Neural Netw orks . . . . . . . . . . . . . . 30 3.2.1 Articial Neural Netw orks . . . . . . . . . . 30 3.2.2 Design . . . . . . . . . . . . . . . 31 3.2.3 Areas of Applications . . . . . . . . . . . 34 v

PAGE 6

4 F A UL T DETECTION AND ISOLA TION . . . . . . . . . . 35 4.1 F ailure P arameterization . . . . . . . . . . . . 35 4.2 FDI via Articial Neural Netw orks . . . . . . . . . 37 4.2.1 Articial Neural Netw ork FDI F ormulation . . . . . 37 4.2.2 Articial Neural Netw ork De v elopment . . . . . . 38 5 THE ST ABILIZA TION PR OBLEM . . . . . . . . . . . 42 5.1 The Nonlinear T rim Problem . . . . . . . . . . . 42 5.2 The Linear T rim Problem . . . . . . . . . . . . 44 6 F A UL T -T OLERANT CONTR OL DESIGN METHODS . . . . . . 46 6.1 F ault-T olerant Control Design Using LQR Theory . . . . . 47 6.2 F ault-T olerant Control Design Using H Theory . . . . . . 49 7 APPLICA TION T O AN F/A-18 . . . . . . . . . . . . 53 7.1 Healthy F/A-18 . . . . . . . . . . . . . . . 53 7.2 F ailed F/A-18 . . . . . . . . . . . . . . . 57 7.3 Articial Neural Netw ork FDI . . . . . . . . . . . 60 7.4 Stabilization . . . . . . . . . . . . . . . . 61 7.5 F ault-T olerant Control Nonlinear Simulations . . . . . . . 62 8 CONCLUSIONS . . . . . . . . . . . . . . . . 70 APPENDIX A LINEARIZED MODEL OF THE F/A-18 . . . . . . . . . . 73 B NOMIN AL CONTR OLLER DESIGN . . . . . . . . . . 76 REFERENCES . . . . . . . . . . . . . . . . . . 83 BIOGRAPHICAL SKETCH . . . . . . . . . . . . . . . 94 vi

PAGE 7

LIST OF T ABLES T able page 4–1 F/A-18 Control Surf ace Position Limits . . . . . . . . . 41 7–1 Stabilization Results . . . . . . . . . . . . . . . 62 vii

PAGE 8

LIST OF FIGURES Figure page 1–1 American Airlines Airb us A300-600 . . . . . . . . . . 3 1–2 Flight 548 crashes in Queens, Ne w Y ork . . . . . . . . . 4 1–3 V ertical Stabilizer of Flight 548 . . . . . . . . . . . 5 2–1 General schematic of a recongurable control system with supervision . 9 2–2 V enn Diagram of Reconguration Strate gies . . . . . . . . 10 2–3 T axonomy of Recongurable Control Methods . . . . . . . 15 3–1 Relationship between Earth axis system and body axis system . . . 22 3–2 A biological neuron . . . . . . . . . . . . . . . 30 3–3 An articial neuron . . . . . . . . . . . . . . . 31 3–4 An articial neural netw ork . . . . . . . . . . . . . 32 4–1 The structure of a full-state feedback control system . . . . . . 36 4–2 Roll feature v ectors for dif ferent f ailure position w . . . . . . 39 4–3 F/A-18 ight control surf ace numbering scheme . . . . . . . 40 6–1 Reference closed-loop system . . . . . . . . . . . . 49 6–2 T ar get Model . . . . . . . . . . . . . . . . 50 6–3 H synthesis model . . . . . . . . . . . . . . . 51 6–4 H analysis model . . . . . . . . . . . . . . . 52 7–1 Longitudinal responses: healthy aircraft . . . . . . . . . 54 7–2 Lateral-directional responses: healthy aircraft . . . . . . . . 55 7–3 Control surf ace deections: healthy aircraft . . . . . . . . 56 7–4 Longitudinal responses: f ailed aircraft . . . . . . . . . . 57 7–5 Lateral-directional responses: f ailed aircraft . . . . . . . . 58 7–6 Control surf ace deections: f ailed aircraft . . . . . . . . . 59 viii

PAGE 9

7–7 Lateral responses : LQR FTC . . . . . . . . . . . . 64 7–8 Longitudinal responses : LQR FTC . . . . . . . . . . 65 7–9 Control surf ace deections : LQR FTC . . . . . . . . . 66 7–10 Lateral responses : H FTC . . . . . . . . . . . . 67 7–11 Longitudinal responses : H FTC . . . . . . . . . . . 68 7–12 Control surf ace deections : H FTC . . . . . . . . . . 69 ix

PAGE 10

Abstract of Thesis Presented to the Graduate School of the Uni v ersity of Florida in P artial Fulllment of the Requirements for the De gree of Master of Science A RECONFIGURA TION SCHEME FOR FLIGHT CONTR OL AD APT A TION T O FIXED-POSITION A CTU A T OR F AILURES By Robert S. Eick August 2003 Chair: Richard C. Lind, Jr Major Department: Mechanical and Aerospace Engineering This w ork considers the problem of redesigning a ight control system to achie v e acceptable stability and performance in the presence of a control surf ace f ailure. The particular f ailure considered is the x ed-position or jammed actuator f ailure. This is an especially dif cult type of f ailure to o v ercome since the operational control surf aces must be recongured not only to achie v e the control objecti v e b ut also to compensate for a disturbance due to the f ailure. The proposed reconguration scheme relies on three interdependent systems: a f ault detection and isolation (FDI) system, a stabilization system, and a f ault-tolerant control system. FDI is de v eloped using an articial neural netw ork that monitors the feedback measurements of the ight control system. Stabilization is based upon a least-squared optimization algorithm to determine a ne w trim condition for the f ailed aircraft. T w o f ault-tolerant control techniques are de v eloped to complete the reconguration scheme. The rst is a linear quadratic re gulator (LQR) approach and the second is an H approach. In each approach the ef fects of the jammed surf ace are treated as a measurable constant disturbance to the system. F or the LQR approach a controller is designed that balances the jammed surf ace (disturbance rejection), and pro vides command-tracking. F or the H approach x

PAGE 11

a tw o-step design process is used where rst the feedforw ard part of the controller is designed to achie v e perfect trajectory follo wing then the feedback part of the controller is designed using H re gulator theory The H approach relies on the use of a lo wpass lter in controller synthesis to limit the disturbance forces and accurately simulate the ef fects of the jammed surf ace. The tw o methods, along with FDI and stabilization, are demonstrated on a high delity nonlinear six-de gree-of-freedom F/A-18 simulator Simulation results are presented with a signicant control surf ace f ailure and sho w the benets on stability and performance using the de v eloped reconguration techniques. The LQR and H methods achie v ed virtually the same results for the tar geted f ailure class with both re gaining stability and restoring performance in all instances. xi

PAGE 12

CHAPTER 1 INTR ODUCTION T o achie v e the safety goals in air tra v el it will be necessary to design ight control systems that can compensate for f ailures and damage to aircraft. All modern aircraft depend upon their ight control system to pro vide the handling qualities necessary for successful ight. When a component of the ight control system f ails or is damaged it is desirable that the safety of the aircraft not be compromised. Recongurable controls attempts to address this issue by de v eloping recongurable control schemes that enhance survi v ability and safety to allo w an aircraft to be reco v ered in ight after it has suf fered component f ailure or damage. The primary benet of recongurable controls is the ability to signicantly enhance ight safety Be yond this, a recongurable controller has the potential to restore desired stability and performance characteristics so that a crippled aircraft can complete its mission and land successfully W ith their clear benet in both military and ci vil aircraft, reconguration techniques and strate gies ha v e become the focus of man y in v estigators in recent years and are currently recei ving signicant attention. A reconguration scheme consists of three parts: a f ault detection and isolation (FDI) procedure, a reconguration logic, and a f ault-tolerant control la w The FDI procedure detects a f ailure and isolates it to a specic component of the system and the reconguration logic adjusts the control la w so that system stability and performance are restored. This w ork focuses on de v eloping a f ault-tolerant control la w and FDI procedure for a specic class of aircraft f ailures. The resulting scheme pro vides a f ast and ef cient method to detect f ailure and procedures to o v ercome the ef fect of a control f ailure on stability and performance. The f ailure class analyzed throughout this w ork is a x ed-position or jammed actuator f ailure, which results in a ight control 1

PAGE 13

2 surf ace becoming inoperable. The goal of a recongurable controller for this f ailure class is to recongure the control la w to use the remaining operational control surf aces in such a manner that the pref ailure ying qualities are restored. The objecti v e of this w ork is to de v elop a reconguration scheme that is easily implementable into current ight softw are and of fers a measurable de gree of reliability for the tar geted type of f ailure. Analysis has sho wn that the probability of an actuator f ailure is e xtremely lo w ho we v er in the e v ent f ailure occurs, the most probable type of f ailure is the x edposition actuator f ailure [ 1 ]. The success of a recongurable controller depends crucially on the ability of the FDI module to promptly and accurately identify f ailure. This w ork proposes the de v elopment of articial neural netw orks to accomplish this task. The function performed by the neural netw ork for aircraft FDI is the mapping of aircraft measurements into f ault cate gories that describe which surf ace has f ailed and at what position. Once the f ailure has been positi v ely identied, the ne xt step in the proposed reconguration scheme is the de v elopment of a f ault-tolerant controller capable of using the FDI information to ef fecti v ely restore stability and performance. F ault-tolerance deals with the ability to complete a task satisf actorily (reliability) and the lik ehood of conducting an operation safely without endangering the human operators of the controlled system (survi v ability) [ 2 ]. T w o f ault-tolerant control (FTC) methods are de v eloped and e v aluated in this w ork. The rst is a linear quadratic re gulator (LQR)-based technique while the second is an H -based technique. In each approach the ef fects of the jammed surf ace are treated as a constant disturbance to the system. While all nominal controllers ha v e some inherent rob ustness to a limited f ailure class, an appropriately designed recongurable controller should ha v e a much lar ger re gion of survi v ability These proposed techniques and the ensuing reconguration schemes appear to meet the challenges of the x ed-position actuator f ailure well for both linear and nonlinear simulations.

PAGE 14

3 1.1 Moti v ating Example On No v ember 12, 2001 an American Airlines Airb us Industry A300-600, Figure ( 1–1 ) [ 3 ], Flight 587 en route from John F K ennedy International Airport (JFK), Jamaica, Ne w Y ork, sustained a catastrophic f ailure when the v ertical stabilizer and rudder separated from the fuselage shortly after tak eof f [ 4 5 ]. The 2 pilots, 7 ight attendants, 251 passengers, and 5 persons on the ground lost their li v es when the aircraft brok e apart and crashed into the residential community of Belle Harbor Ne w Y ork, Figure ( 1–2 ) [ 6 ]. The resulting in v estigation e xamined man y issues including the adequac y of the certication standards for transport-cate gory airplanes, the structural requirements and inte grity of the v ertical stabilizer and rudder the operational status of the rudder system at the time of the accident, the adequac y of pilot training, and the role of pilot actions in the accident. Figure 1–1: American Airlines Airb us A300-600 It w as determined that before the separation of the v ertical stabilizer and rudder Flight 548 encountered tw o w ak e v ortices from a Boeing 747, which had departed JFK ahead of the accident aircraft. The tw o airplanes were separated by about 5 miles and 90 seconds at the time of the v orte x encounters. During and shortly after the second encounter the ight data recorder (FDR) on the accident aircraft recorded se v eral lar ge

PAGE 15

4 rudder mo v ements and corresponding pedal mo v ements to full or nearly full a v ailable rudder deection in one direction follo wed by full or nearly full a v ailable rudder deection in the opposite direction. 1 The subsequent loss of reliable rudder position data is consistent with the v ertical stabilizer separating from the airplane. Among the potential causes e xamined for this catastrophic f ailure were rudder system malfunction, as well as ight cre w action. Figure 1–2: Flight 548 crashes in Queens, Ne w Y ork The National T ransportation Safety Board and Airb us engineers belie v e that lar ge side loads were lik ely present on the v ertical stabilizer and rudder at the time the y separated from the airplane. Calculations and simulations sho w that, at the time of the separation, the airplane w as in an 8to 10airplane nose-left sideslip while the rudder w as deected 9.5to the right. Airb us engineers ha v e determined that this combination of local nose-left sideslip on the v ertical stabilizer and right rudder 1 Preliminary information based on FDR data and an analysis of the manner in which rudder position data is ltered by the airplane' s system indicates that within about 7 seconds, the rudder tra v eled 11right for 0.5 seconds, 10.5left for 0.3 seconds, between 11and 10.5right for about 2 seconds, 10left for about 1 second, and nally 9.5right before the data became unreliable.

PAGE 16

5 deection produced loads on the v ertical stabilizer that could e xceed the airplane' s design loads. The Federal A viation Administration (F AA) concluded that it w as this dangerous combination of sideslip angle and rudder position which resulted in the complete lost of aircraft, cre w and passengers. Figure 1–3: V ertical Stabilizer of Flight 548 While the v ertical stabilizer and rudder appeared to separate cleanly from the fuselage, Figure ( 1–3 ) [ 7 ], the ight controller w as inadequately designed to re gain control of the crippled aircraft. The resulting conguration of leading edge aps, trailing edge aps, ailerons, and ele v ators were incapable of countering the sudden roll and ya wing moment generated by the absence of the v ertical stabilizer Rolling upside do wn and nally out of control the airplane succumbed to the increasing aerodynamic forces as a massi v e engine, wing, and fuselage breakup scattered remains throughout Jamaica Bay and Long Island Ne w Y ork. The tragedy of the Flight 587 accident endures as another moti v ation in the emer ging eld of Recongurable Controls, which aims to de v elop ight controllers which can handle f ailures such as this. 1.2 Ov ervie w The purpose of this w ork is to propose an adapti v e scheme in recongurable ight controls capable of reco v ering desired performance and stability characteristics for an aircraft e xperiencing a x ed-position actuator f ailure. Chapter 2 pro vides a re vie w of the current literature in the area of recongurable ight controls. The mathematical

PAGE 17

6 details of aircraft ight mechanics and a non-technical introduction into articial neural netw orks is gi v en in Chapter 3. Chapter 4 presents a f ault detection and isolation (FDI) procedure for x ed-position actuator f ailures using articial neural netw orks. The stabilization problem and aircraft f ault modeling is re vie wed in Chapter 5. Chapter 6 focuses on the theoretical de v elopment of f ault-tolerant controllers using LQR-based and H -based techniques. Both of these f ault-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 w ork.

PAGE 18

CHAPTER 2 REVIEW OF LITERA TURE In 1984 the Air F orce Flight Dynamics Laboratory initiated the rst research program dedicated to the in v estigation of reconguration technology for ight control systems with the Self-Repairing Flight Control Systems Program. The main objecti v e of this program w as to signicantly impro v e the reliability maintainability survi vability and life c ycle costs of aircraft ight control systems through aerodynamic reconguration and maintenance diagnostics. Special consideration w as gi v en to de v eloping a reconguration strate gy that uses the remaining control surf aces to substitute for the lost force and moment generating capabilities when a single control surf ace becomes impaired from f ailure or battle damage [ 8 ]. Since this original initiati v e man y methods ha v e been proposed to solv e the reconguration problem for ight controls. This chapter outlines the state of the art, which remains lar gely a theoretical topic with most applications studies based upon aerospace systems. 2.1 Introduction The objecti v e of recongurable controls is to detect a f ailure using the feedback signals of the ight control system then recongure the control la w in a f ashion that restores the desired stability and performance characteristics of the aircraft. There is a substantial body of recongurable controls literature that includes applications in hazardous chemical plants, the control of nuclear po wer plant reactors, space craft, and the control of unstable y-by-wire aircraft. Research into recongurable control, ho we v er is lar gely moti v ated by the control problems encountered in aircraft system design. The goal of these researchers is to pro vide self-repairing capability to enable a pilot to land an aircraft safely in the e v ent of a serious malfunction [ 9 ]. 7

PAGE 19

8 The main requirement for an y f ault-tolerant controller as part of a reconguration scheme is that, subsequent to a malfunction in the system, it should either maintain some acceptable le v el of performance and stability or de grade gracefully While signicant theoretical progress has been made in academia, fe w results ha v e been applied to real v ehicles. The vie w is usually tak en that the application of a comple x f ault-tolerant controller is best applied to systems where the go v erning principles are easily understood and v eriable. This “simplistic” approach has consistently caused a reluctance within the eld to e xperiment on systems which pose intolerable risks in terms of safety cost, instability or unpredictability The general vie w is that simpler controllers, with fe wer components or lines of softw are code are intrinsically more reliable and that further comple xity w ould unnecessarily increase the o v erall risk of f ailure during routine operation [ 10 11 ]. The initial step in de v eloping an y reconguration scheme is determining the limitations of the con v entional feedback controller Strate gies for reconguration are generally application-specic and are normally dependent on a v ailable equipment and measurements. The task then becomes the design of a controller with suitable structure to guarantee stability and satisf actory performace, not only when all components are fully operational, b ut also in the case when sensors, actuators and other components malfunction. Owen [ 12 ] referred to a control system with this structure as one that possesses inte grity or that has control loops that possess loop inte grity while V eilltette et al. [ 13 ] and Birdwell et al. [ 14 ] prefer to use the term reliable control. Figure ( 2–1 ) sho ws the general schematic of a recongurable control system with four main components: the model (including the plant dynamics, actuators, and sensors), the f ault detection and isolation (FDI) module, the controller and the supervision module. The solid lines represent signal o w (commands, feedback, etc.) while the dashed lines represent adaption (tuning, scheduling, reconguration, or restructuring). The possible f aults include malfunctions in sensors, actuators, or

PAGE 20

9 Controller Actuators Sensors Supervision FDI Plant Dynamics F ault F ault F ault input Figure 2–1: General schematic of a recongurable 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 pro vides the supervision subsystem with information about the onset, location and se v erity of an y f ault. Based on the system' s measurements together with FDI information, the supervision system will recongure, tune, or adapt the controller to accommodate for the ef fects of the f ault. The relationship between the four main components of Figure ( 2–1 ) allo ws the recongurable control problem to be solv ed in a v ery systematic manner The principles in v olv ed in the systematic design and de v elopment of a recongurable controller are outlined by Blank e et al. [ 15 ]. He demonstrated that the de v elopment of each subsystem af fects the de v elopment of the o v erall system, this interdependence necessitates a comprehensi v e strate gy for reliable and highly ef cient control la w redesign. Ultimately the design procedure is a multidisciplinary task in v olving rele v ant science/technology control theory and design, signal processing and human f actors. 2.2 The State of the Art Ov er the past tw o decades there has been an e xtensi v e in v estigation into man y possible solutions of the recongurable controls problem. Figure ( 2–2 ) depicts the areas of greatest contrib ution and their interrelationship to w ards forming a complete reconguration strate gy

PAGE 21

10 Figure 2–2: V enn Diagram of Reconguration Strate gies 2.2.1 F ault Detection and Isolation (FDI) W ith the de v elopment of po werful quantitati v e and/or qualitati v e modelling tools and articial neural ne wtw orks the eld of FDI has become v ery rened [ 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 ]. Ho we v er much of the research has yet to be combined with f ault-tolerant controllers to present a complete reconguration strate gy The main issue to o v ercome with traditional methods for FDI in v olv es specication of all critical design conditions and/or e xtensi v e o v erdesign for unpredicted or uncertain conditions. T o date, as noted by Barron et al. [ 34 ], the best FDI systems only consider a fraction of the operational f ault conditions that might be encountered and only a small portion of those that may be encountered are actually used e xplicitly for design because the number of possible f ault conditions is v ery lar ge. This f act se v erely inhibits the design of a global FDI system for comple x systems such as aircraft. It may also be important to identify the f ault type and its se v erity as well as the reason for the f ault de v elopment. When these functions are included along with FDI, the function performed is called f ault diagnosis. Se v eral in v estigators, including Le gg [ 35 ], Herrin [ 36 ], Bell [ 37 ], Hunt et al. [ 38 ], and Blank e et al. [ 15 ] ha v e discussed the use of f ailure mode ef fects analysis (FMEA) techniques to determine systematically ho w f ault ef fects in components relate to f ault inputs, outputs, or elements within the components. FMEA is a bottom-up analytical process which identies potential hazards of a ne w system with the goal to anticipate, identify and a v oid f ailures in the design and de v elopment stages.

PAGE 22

11 2.2.2 Rob ust Control Rob ust control design has recei v ed much attention within the controls community since the late 1970' s. The fe w cases that ha v e attempted to directly apply rob ust control theory to recongurable controls usually ha v e not considered the ef fects of the f aults on the control system [ 39 40 41 42 ]. Eterno et al. [ 43 ] and Stengel [ 44 ] note that this passi v e approach to recongurable controls mak es the fundamental assumption that f aults can be modelled as uncertainties. Admittedly there do e xist rob ust control techniques that are suitable for a v ery specic class of f ailures that can indeed be modeled as uncertainty re gions around a nominal model. An y f ailure that does not signicantly de grade the system or push the system outside the stability radius gi v en by the rob ust controller will not compromise satisf actory stability and performance. Ho we v er an y controller with a lar ge enough stability radius to encompass most f ailure situations will lik ely be conserv ati v e and there is still no guarantee that unanticipated f ailures could be handled. Despite this, se v eral in v estigators, including Birdwell et al. [ 14 ] and V eilltette et al. [ 13 ], ha v e insisted that rob ust control theory can be used to maintain acceptable system stability and performance when control loops malfunction in a broad sense Most in v estigators, ho we v er agree that a recongurable controller will require additional loops and control structure. There are too man y types of common f ailures, such as actuator and sensor malfunctions, which cannot be adequately modelled as uncertainty These problems moti v ate the need for a controller that more directly addresses the situation. 2.2.3 F ault-T olerant Control The area of f ault-tolerant controls has attracted the attention of in v estigators with increased frequenc y o v er the past fe w years. F or e xample, Lane and Stengel [ 45 ] and Ochi and Kanai [ 46 ] pursued the use of feedback linearization and Gao and Antsaklis [ 47 ] described the use of pseudo-in v erse methods. Adapti v e control approaches using articial neural netw orks are consider by Calise et al. [ 48 ], Idan et

PAGE 23

12 al. [ 49 ], Johnson and Calise [ 50 ], and man y others. While Huang and Stengel [ 51 ], Morse and Ossman [ 52 ] and Jiang [ 53 ] ha v e made important contrib utions based upon model-follo wing control principles. 2.2.4 Rob ust F ault-T olerant Control This area of reconguration has recei v ed only a minimal amount of attention. W u [ 54 ] addresses the problem of performance rob ustness during normal system operation v ersus f ault reco v ery A prescribed performace le v el is optimized under a detection criterion relating the measurements to specic f aults. The specic designer is lar gely free to choose one of a number of suitable FDI techniques. Jiang [ 53 ] discusses ho w f ault-tolerance can be achie v ed using eigenstructure assignment design. 2.2.5 Rob ust F ault Estimation The joint design of rob ust controllers and f ault estimation often leads to comple x interactions between the controller and f ault estimator because the design freedom is utilized to solv e both problems simultaneously [ 55 56 57 58 59 ]. This fundamental problem, ho we v er is una v oidable as most studies in this area are based upon the idea that the rob ust controller optimization and f ault estimation designs are best combined, for e xample, T yler and Morari [ 56 ] use H optimization. An alternati v e w ay of performing open-loop FDI with a separate controller design a v oids the dif culties of this design and pro vides much of the moti v ation for the ne xt area. 2.2.6 F ault-T olerant Control w/ FDI The functions of FDI and recongurable control ha v e been combined in a fe w notable studies [ 60 53 ]. It is widely accepted that the FDI function along with redundant system design can pre v ent the de v elopment of more serious f aults. When f ault detection and isolation is carried out using the open-loop approach the controller af fects the FDI rob ustness b ut not vice-v ersa [ 26 61 ]. The controller' s rob ustness issue becomes de-coupled from the FDI unit design and allo ws for an increased freedom in controller design and structuring. The main disadv antage with this de-coupling is the

PAGE 24

13 adv erse af fects the detection delay has upon system stability as reported by Mariton [ 62 ]. The combination of the FDI system and control reconguration is a comple x issue and one study by Srichander and W alk er [ 63 ] proposes a stochastic approach to the stability analysis of some acti v e f ault tolerant control systems emplo ying FDI schemes. The main assumption here is that beha vior resulting from randomly occurring f aults can be characterized dynamically by stochastic dif ferential equations. The stochastic dif ferential equations v ary randomly in time and the equations can be analyzed using Mark o v theory These stochastic approaches to rob ustness analysis are an emer ging theoretical eld in recongurable control. 2.2.7 Supervision Dif ferent forms of selection logic and system management ha v e been introduced into f ault-tolerant systems by v arious in v estigators including Rauch [ 64 ], Buck ely [ 65 ], Eryurek and Upadhyaya [ 66 ], and Polycarpou and V emuri [ 67 ]. The function of supervision is essentially the acti v e form of f ault-tolerant control in which f ault decision information is used to select the most suitable control function subsequent to the declaration that a f ault has occurred. Also essential to the operation of the supervision system is the ability to determine whether a f ault has determental ef fects on the system' s performance and stability serious enough to w arrant controller changes. Kw ong et al. [ 68 69 ] sho ws that the fuzzy model reference learning controller (FMRLC) can be used to recongure the nominal controller in an F-16 aircraft to compensate for v arious actuator f ailures without using e xplicit f ailure information. Kw ong then de v eloped an e xpert supervision strate gy for the FMRLC that used only information about the time at which a f ailure occurs and sho wed that it achie v ed higher performance control reconguration than an unsupervised FMRLC. Fierro and Le wis [ 70 ] discuss a hybrid system frame w ork which considers simultaneously the control and decision-making issues. A continuous-state plant is supervised by a discrete-e v ent system which is based on a theory of link ed nite state machines.

PAGE 25

14 2.3 T ypes of Redundanc y As mentioned in the introduction, a recongurable controller should ideally be de v eloped using a systematic and inte grated approach to design. Most papers only consider problems which are based on mathematical models of the plant, b ut there are also man y non-mathematical challenges which require attention at e v ery stage and in all aspects of system design. Blank e et al. [ 15 ] paid attention to the de v elopment of the o v erall concept of systematic design. His study demonstrated that the de v elopment of a complete reconguration strate gy requires an understanding of the structure of the system, the reliability of dif ferent components, the types of redundanc y a v ailable and the types of controller function that are a v ailable or might be required. It is impossible to ensure control reconguration without redundanc y in the initial system. Often the type and le v el of redundanc y pro vided determines the w ay in which control reconguration is enacted. Hence, a f ailed sensor or actuator in systems with v arying le v els of redundanc y will sometimes ha v e dramatically dif ferent reconguration schemes to o v ercome the f ailure. There are tw o forms of redundanc y associated with recongurable controls. Direct redundanc y is achie v ed by the use of multiple interdependent hardw are channels and analytical redundanc y is achie v ed by backing up a v ailable measurements using a mathematical model. Sometimes a combination of the tw o forms of redundanc y is necessary Making the best use of both the direct redundanc y and the analytical redundanc y pro vided by the system is a major task of recongurable control system design. 2.4 F ault-T olerant Control Methods Figure ( 2–3 ) sho ws the taxonomy of f ault-tolerant control methods. 2.4.1 P assi v e Approaches P assi v e approaches to f ault-tolerance mak e use of rob ust control techniques to ensure that a closed-loop system remains insensiti v e to certain f aults [ 43 44 ]. The

PAGE 26

15 Propulsion Controlled Aircraft Interacting Multiple Models Adapti v e Feedback Linearization Control Allocation Model Predicti v e Control Multiple Models Switching and T unning Model Reference Adapti v e Control Sliding-Mode Control Eigenstructure Assignment Multiple Models Adapti v e Actuator Only Controller Synthesis Approaches Acti v e Approaches P assi v e Rob ust Control Recongurable Controls Figure 2–3: T axonomy of Recongurable Control Methods impaired system continues to operate with the same controller and system structure, i.e. the main objecti v e it to reco v er the original system performance. Basically the passi v e controller will reject the f ault only if it can be de-sensitized to the f ault' s ef fects just as if it were a source of modelling uncertainty [ 43 ]. Among those who ha v e e xtend their w ork on rob ust control to deal with passi v e f ault-tolerance are Horo witz et al. [ 71 ] and K eating et al. [ 72 ] who used quantitati v e feedback theory and McF arlane and Glo v er [ 73 ] and W illiams and Hyde [ 74 ] who emplo yed the frequenc y domain approach based on H -norm optimization. Nett et al. [ 55 ], T yler and Morari [ 56 ], and Murad et al. [ 57 ] present rob ust design approaches

PAGE 27

16 to inte grated control and f ault estimation based upon the so-called four parameter controller All of these passi v e f ault-tolerant controllers are actually good e xamples of baseline controllers that can be used as a basis for further f ault accommodation with acti v e controllers. The original rob ustness is important during the detection and reconguration interv al. 2.4.2 Acti v e Approaches In acti v e f ault-tolerance, a ne w control system is designed using the desirable properties of performance and rob ustness in the original system, b ut with the reduced capability of the impaired system in mind. Acti v e f ault-tolerance has this title because on-line f ault accommodation is used. These methods dif ferentiate themselv es from passi v e approaches in that the y tak e f ault information e xplicitly into account and do not assume a static nominal model. In order to achie v e reconguration or restructuring, an acti v e f ault-tolerant system requires either a priori kno wledge of e xpected f ault types or a mechanism for detecting and isolating unanticipated f aults. This is essentially the function of a f ault detection and isolation (FDI) scheme. Acti v e approaches are di vided into tw o main types of methods: projection based methods and on-line automatic controller redesign methods [ 51 ]. The latter in v olv es the calculation of ne w controller parameters in response to a control impairment, Gao and Antsaklis [ 47 ] referred to this method as recongurable control. In projectionbased methods a ne w pre-computed control la w is selected according to the type of malfunction that has been isolated [ 75 ]. Stengel [ 2 ] further classies a recongurable or restructurable system whose feedback action is changed automatically as a special form of an intelligent control system. On-line restructuring or reconguration of control is a topic of ongoing research. 2.4.2.1 Multiple model control (MMC) There are se v eral areas of multiple model controls that ha v e achie v ed notable success as f ault-tolerant control techniques: Multiple Model Switching and T uning

PAGE 28

17 (MMST), Interacting Multiple Model (IMM), and Propulsion Controlled Aircraft (PCA). The idea of multiple model control has recei v ed increased interest in the last fe w years with Bosk o vic et al. [ 76 77 78 79 80 81 82 83 84 ], Kane v et al. [ 85 86 87 ], Demetriou [ 88 ], Zhang and Jiang [ 89 ], and Maybeck [ 90 ]. In MMST Bosk o vic et al. [ 76 ] describes the dynamics of each f ault scenario by a model, then designs a controller for each f ault scenario creating a massi v e parallel architecture. When a f ailure occurs, MMST switches to the pre-computed control la w corresponding to the f ailure situation. The dif culty with this approach becomes one of choosing which model/controller pair to switch to at each time instant. In IMM Zhang and Rong Li [ 91 ] and Munir and Atherton [ 92 ] attempt to o v ercome this k e y limitation of MMST rather than using the model which is closest to the current f ailure scenario, IMM computes a f ault model as a con v e x combination of all pre-computed f ault models and then uses this ne w model to mak e control decisions. Burk en and Burcham [ 93 ] de v elops PCA which is a special case of MMST where the only anticipated f ault is total hydraulics f ailure and only the engines are used for control. The PCA problem w as tak en up by the N ASA Dryden Flight Research Center [ 94 95 ] in 1995 when the y demonstrated successful landings after complete hydraulic f ailure using a MD-11 and a F-15 with propulsion-only control. 2.4.2.2 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 allo w the design of control la ws which do not directly consider actuator f ailures. The output of the control la w can be a set of desired forces and moments and the job of the allocator is to select appropriate actuator positions which will achie v e the desired results. Bordignon and Durham [ 96 ] and Durham and Bordignon [ 97 ] addressed the problem of control allocation with magnitude and rate limits on the actuators, Da vidson et al. [ 98 ] de v elops a control allocation technique for the e xtremely o v er -actuated

PAGE 29

18 Inno v ati v e Control Ef fector (ICE) aircraft and Zhen yu et al. [ 99 ] looks at restoring as much of the performance of the original system as possible after a actuator f ailure. 2.4.2.3 Adapti v e feedback linearization via articial neural netw orks This section e xamines a method primarily de v eloped by Calise et al. [ 48 49 50 100 101 102 103 ] in v olving a model reference adapti v e control scheme using adapti v e feedback linearization with an articial neural netw ork to cancel in v ersion errors. The approach splits the dynamics of the plant into three single-input-single-output (SISO) subsystems for roll, pitch, and ya w Each subsystem has a model reference adapti v e controller Brink er and W ise [ 104 ] and W ise et al. [ 103 ] ha v e contrib uted by de v eloping a control allocation technique that generates the desired roll, pitch, or ya w moment specied by the controller using the a v ailable control surf aces. W ise et al. [ 103 ] along with Calise [ 48 102 ] ha v e successfully demonstrated adapti v e feedback linearization using articial neural netw orks on the T ailless Adv anced Fighter Aircraft (T AF A) and N ASA s X-36. 2.4.2.4 Sliding mode control (SMC) Shtessel et al. [ 105 108 106 107 ] used Sliding Mode Control (SMC) to de v elop a rob ust controller that adapti v ely handles input magnitude and rate constraints. The proposed controller is set up in a tw o-loop conguration with the desired result of tracking a trajectory gi v en by roll, pitch, and ya w angle. The outer -loop of the controller tak es roll, pitch, and ya w and pro vides angular rate commands to the inner loop, which is assumed to track the commands using the actuator inputs. There are tw o benets of this controller First, it can handle all f ailures 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 surf aces, while a v oiding limits and inte grator windup by reducing the tracking performance. The limitation of SMC is the assumption that the input function is square and in v ertible. This limitation requires that there must be one and only one control surf ace for e v ery controlled v ariable and that

PAGE 30

19 none of the control surf aces can e v er be lost. Therefore, SMC is only applicable for f ailures which cause a loss of ef fecti v eness of the control surf ace, unlik e the oating or jammed surf ace f ailure scenarios. 2.4.2.5 Eigenstructure assignment (EA) The concept of Eigenstructure Assignment (EA) w as formally introduced by Andry et al. [ 109 ]. The idea behind the technique is to use state feedback to place the eigen v alues of a linear system then use the remaining de grees of freedom to align the eigen v ectors as accurately as is possible. While the method for choosing appropriate eigen v ectors and eigen v alues is not well-dened for aircraft, Da vidson and Andrisani [ 110 ] highlighted the ef fects of the eigenstructure on ying qualities. Other researchers who propose EA for use in recongurable ight control systems are K onstantopoulos and Antsaklis [ 111 ], Belkharraz and Sobel [ 112 ], and Zhang and Jiang [ 113 ]. 2.4.2.6 Model reference adapti v e control (MRA C) The goal of Adapti v e Model-F ollo wing Control (MRA C) is to force the plant output to track a reference model. Although there are limitations of adapti v e control for reconguration, Bodson and Groszkie wicz [ 114 ] and Groszkie wicz and Bodson [ 115 ] are attempting to apply it in slightly modied forms. First, a model structure must be assumed. The types of f ailures addressed in recongurable control, ho we v er may well cause the plant structure to change drastically Second, adapti v e control requires that the system' s states change slo wly enough for the estimation algorithm to track them. Ho we v er f aults may cause abrupt and drastic changes in the states mo ving the system instantaneously to a ne w re gion of the state space. As a result, adapti v e control on its o wn is not enough to handle the general problem, b ut may well be an important part of the recongurable algorithm.

PAGE 31

20 2.4.2.7 Model predicti v e control (MPC) Model predicti v e control has been proposed as a method for reconguration due to its ability to handle constraints and changing model dynamics systematically Maciejo wsku [ 116 ] designed a MPC controller that has an intrinsic ability to handle jammed actuators without the need to e xplicitly model the f ailure. F ailures can also be handled in a natural f ashion by changing the internal model used to mak e prediction in either an adapti v e f ashion as done by Kane v and V erhae gen [ 86 ], a multi-model switching scheme as done by Bosk o vic and Mehra [ 76 ], or by assuming a FDI scheme that pro vides a f ault model as done by Huzmezan and Maciejo wski [ 117 118 ]. The MPC approach to reconguration has achie v ed some notable successes b ut there are still fundamental issues that need to be e xamined. First, it is not clear ho w to adjust the weights in the cost function for an arbitrary f ault model. Second, choosing performance tar gets is not a simple question. Finally MPC requires an on-line optimization which mak es it dif cult to implement as an aircraft controller where the optimization must occur at high sampling rates and in x ed time. Also, there is no quarantee that there e xists a solution to the optimization problem for all time.

PAGE 32

CHAPTER 3 PRELIMIN ARIES This chapter pro vides a re vie w of the necessary technical background for an introductory in v estigation of recongurable ight controls. While is it assumed the reader has been e xposed to these topics pre viously a more in depth e xplanation of these concepts can be found in a number of under graduate te xts [ 119 120 121 122 ]. 3.1 Aircraft Flight Mechanics The equations of motion for an aircraft in ight ha v e changed little since their original formulation by Lanchester (1908) and Bryan (1911) [ 123 ]. The follo wing sections identify the v arious reference frames used to describe an aircraft' s state, pro vide an o v ervie w of the deri v ation 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 man y dif ferent axis systems. The three axis systems used here are the body-axis system x ed to the aircraft, the Earth-axis system, which we will assume to be an inertial axis system x ed to the Earth, and the stability-axis system, which is dened with respect to the relati v e wind. Each of these systems is useful in that the y pro vide a con v enient system for dening a particular v ector such as an aerodynamic force v ector the weight v ector or the thrust v ector 3.1.1.1 Body-Axis System The body-axis system,b 1b 2b 3in Figure ( 3–1 ), is x ed to the aircraft with its origin at the aircraft' s center of gra vity The b 1 axis is dened out the nose of the aircraft, the b 2 axis is dened out the right wing of the aircraft, and the b 3 axis is 21

PAGE 33

22 Figure 3–1: Relationship between Earth axis system and body axis system dened do wn out of the bottom of the aircraft. These three ax es form a traditional right-handed orthogonal reference system. 3.1.1.2 Earth-Axis System The Earth-axis system,e 1e 2e 3in Figure ( 3–1 ), is x ed to the Earth with its e 3 axis pointing to the center of the Earth. Often, the e 1 axis is dened as North and the e 2 axis is dened as East. The Earth-axis system is assumed to be an inertial axis system for which Ne wton' s la ws of motion are v alid. While this assumption is not totally accurate, it w orks well for most aircraft problems where the aircraft is tra v eling up to supersonic b ut not hypersonic speeds. 3.1.1.3 Stability-Axis System The stability-axis system,s 1s 2s 3, is rotated relati v e to the body axis system through the angle-of-attack and is used to study small de viations from a nominal ight condition. The origin of the stability-axis is also at the aircraft center of gra vity The s 1 axis points in the direction of the projection of the true airspeed onto the xz plane of the aircraft. The s 2 axis is out the right wing while the s 3 axis is orthogonal and points in accordance with the right-hand rule.

PAGE 34

23 3.1.2 General Equations of Motion The goal in this section is to de v elop the equations of motion which describe the position and orientation of the aircraft in appropriate reference frames. This de v elopment is essential in understanding ho w an aircraft beha v es as well as the dynamics and relationships between the v arious reference frames. The v elocity of the aircraft with respect to the body-axis system is gi v en by V B u v wn r(3.1) The v elocity V B does not include the ef fects of wind. An y v ector in the Earth-axis system can be transformed into the body-axis system using the follo wing transformation (note the notation used for trigonometric functions, S fsin f C fcos f T ftan f etc.) l E B C q C y S f S q C yC f S y C f S q C yS f S y C q S y S f S q S yC f C y C f S q S yS f C yS q S f C q C f C qn r(3.2) where y q f describe the orientation of the aircraft in the Earth-axis system. The angle of attach, a and sideslip, b can be dened in terms of the v elocity components of the body axis system. The equations for a and b are dened by atan1 w u bsin1 v u 2v 2w 2 (3.3)

PAGE 35

24 The position of the aircraft is most often used for na vigation; therefore, its dynamics are gi v en in the Earth-axis system as follo ws r E x y zn r(3.4) Remember that z points to w ard the ground and is therefore ne gati v e for positi v e height. As a result, the altitude or height is often used instead of z to describe the location of the aircraft while in ight. The aircraft height is gi v en by hz (3.5) The orientation of the aircraft is dened relati v e to the Earth-axis and is gi v en by the Euler anglesyqf. The Euler angles dene 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 dif ferent order other than y q and f the nal result will be incorrect. The accepted limits on the Euler angles are 0y360 90 q90 180 f180(3.6) The angular rotation rates are dened relati v e to the body axis system as, w B p q rn r(3.7) where p is the roll rate, q is the pitch rate, and r is the ya w rate. The angular rates are related to the rate of change of the Euler angles by the follo wing coordinate

PAGE 36

25 transformations, p q rn r 1 0S q 0 C f S f C q 0S f C f C qn r f q yn r f q yn r 1 S f T q C f T q 0 C fS f 0 S f S1 q C f S1 qn r p q rn r(3.8) Note that when perturbations are small, such thatfqymay be treated as small angles, that is,15, then Equations ( 3.8 ) can be approximated as p q rn r f q yn r(3.9) The dynamics are deri v ed from Ne wton' s 2nd La w which states that the summation of the e xternal forces acting on a body is equal to the time rate of change of the momentum of the body; and the summation of the e xternal moments acting on the body is equal to the time rate of change of the moment of momentum (angular momentum). The force equation is gi v en by FmdV c d t wV c(3.10) and the moment equation as MdI w d t w I w(3.11) where V c is the v elocity of the center of mass of the aircraft, w is the angular v elocity and I is the moment of inertia tensor The force v ector which consists of the

PAGE 37

26 aerodynamic forces and thrust forces acting on the aircraft is gi v en by F X Y Zn r(3.12) The equations can no w be written in terms of the v ariables dened in this section. The three force equations in the body-axis system are XmgS qm uqwr vYmg C q S qm vr upwZmg C q C fm wpvqu(3.13) where f T is the angle between the x -body direction and the thrust v ector T Assuming that the mass distrib ution of the aircraft is constant, such as ne glecting fuel slosh and fuel b urn, the moments and products of inertia do not change with time. The three moment equations in the body-axis system are LI xx pI xz rqrI zzI yyI xz pq MI yy qr pI xxI zzI xzp 2r 2 NI xz pI zz rpqI yyI xx!I xz qr"(3.14) where#LMN$are the rolling moment, pitching moment, and ya wing moment acting of the aircraft, respecti v ely These applied moments consist of aerodynamic and thrust moments acting on the aircraft. The forces and moments are functions of the control surf aces, thrust, and aerodynamics of the aircraft and can be written as functions of the six linear and angular v elocitiesuvwpqrand the actuator positions. 3.1.2.1 Longitudinal and Lateral-Directional Equations of Motion The six aircraft equations of motion, ( 3.13 ) -( 3.14 ) can be decoupled into tw o sets of three equations. These are the three longitudinal equations of motion and the three

PAGE 38

27 lateral-directional equations of motion. This is con v enient in that for man y ight conditions only three equations need to be solv ed simultaneously The three longitudinal equations of motion consist of the x force, y moment, and z force equations Xm uqwr v!mgS q MI yy qr pI xxI zzI xzp 2r 2 Zm wpvqu%mg C q C f (3.15) The lateral-directional equations of motion consist of the x moment, y force, and z moment equations LI xx pI xz rqrI zzI yyI xz pq Ym vr upwmg C q S q NI xz pI zz rpqI yyI xxI xz qr (3.16) In addition to the six force and moment equations of motion, Equation ( 3.8 ) is required to completely solv e the aircraft problem because there are more than six unkno wns due to the presence of the Euler angles in the force equations. Recall, the three kinematic equations pS q y f qS f C q yC f q rC f C q yS f q (3.17) 3.1.3 Linearized Equations of Motion The nine aircraft equations of motion, ( 3.15 )-( 3.17 ), are nonlinear dif ferential equations. The y can be solv ed with v arious numerical inte gration techniques to obtain time histories of motion v ariables, b ut it is nearly impossible to obtain closed form solutions. It is assumed that the motion of the aircraft consists of small de viations from a reference condition of steady ight; therefore, the small perturbation approach can be

PAGE 39

28 used to linearize the equations of motion and de v elop the closed form solutions around trim conditions. Steady ight can be dened, for e xample, as one of the follo wing: steady wings-le v el ight f f q y0 steady turning ight f q0, yturn rate steady pull-up f f y0, qpull-up rate steady roll q y0, froll rate, where p q r V a b0 and all control surf ace inputs are zero. There are three possible methods for computing a linear model for small perturbations around the trim or steady-state condition. The rst is to replace an y nonlinearities in the general dynamics equation with their rst order T aylor series approximations. The second is to run an identication algorithm using data collected from either a nonlinear model or the physical system. The nal method, and one used throughout this w ork, is to numerically compute the ef fects of small changes in state v ariables and inputs on the state deri v ati v es. This can be done, for e xample, by using a Matlab linearization routine such as l inmod on a nonlinear Simulink model. The benets of the linearization is that we can write the physical system in a con v enient matrix form xAxBu (3.18) where x&R n is the state v ariables and u&R p is the control inputs. The system output y&R q is gi v en by yC xDu (3.19) The state, control, and output v ectors are dened as follo ws x x 1tx 2t. . x nt n rstate v ectorn1(3.20)

PAGE 40

29 u u 1tu 2t. . u pt n rinput v ectorp1(3.21) y y 1ty 2t. . y qt n routput v ectorq1(3.22) The matrices A B C are constant matrices and dened as follo ws A a 11 a 12'('('a 1 n a 21 . . . . . . . a n 1 a n 2'('('a nnn rplant matrixnn(3.23) B b 11 b 12'(')'b 1 p b 21 . . . . . . . b n 1 b n 2'(')'b n pn rcontrol matrixnp(3.24) C c 11 c 12'(')'c 1 n c 21 . . . . . . . c q 1 c q 2'(')'c qnn routput matrixqn(3.25) where A is the plant matrix, B is the control matrix, and C is the output matrix. F or the aircraft considered throughout this w ork the D matrix is the null matrix.

PAGE 41

30 3.2 Neural Netw orks This secion is intended to re vie w and help the reader understand what articial neural netw orks are, ho w the y w ork, and where the y are currently being used. The intent is to gi v e a non-technical introduction; therefore, it does not go into depth with mathematical formulas. A more detailed e xplanation is pro vided in [ 121 122 ]. 3.2.1 Articial Neural Netw orks An Articial Neural Netw ork is a system loosely modeled on the human brain. While neural netw orks do not approach the comple xity of the brain, the y are an an attempt to simulate within specialized hardw are or sophisticated softw are the multiple layers of simple processing elements called neurons. Each neuron is link ed to a certain number of its neighbors with v arying coef cients of connecti vity that represent the strengths of these connections. Learning is accomplished by adjusting these strengths to cause the o v erall netw ork to output appropriate results. 3.2.1.1 The Biological Neuron Figure 3–2: A biological neuron The most basic components of neural netw orks are modeled after the structure of the brain; therefore, a great deal of the terminology is borro wed from neuroscience. The neuron is the most basic element of the human brain and pro vides us with the

PAGE 42

31 abilities to remember think, and apply pre vious e xperiences to our e v ery action. The po wer of the brain comes from the lar ge number of neurons (approximately 10 11 ) and the multiple connections between them (up to 200000). All natural neurons ha v e four basic components, Figure ( 3–2 ), which are dendrites, soma, axon, and synapses. Basically a biological neuron recei v es inputs from other sources, combines them in some w ay performs a generally nonlinear operation on the result, and then outputs the nal result. 3.2.1.2 The Articial Neuron*,+ -,.p f *,+ -,.b / n a w Figure 3–3: An articial neuron The basic unit of articial neural netw orks, the articial neuron, simulates the four basic functions of natural neurons. That v arious inputs to the netw ork, 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 articial neuron output is gi v en by afw pb(3.26) Ev en though all articial neural netw orks are constructed from this basic b uilding block their architectures and applications are e xtremely di v erse. 3.2.2 Design Designing a neural netw ork consists of four important steps: arranging neurons in v arious layers, deciding the type of connections among neurons within a layer as well as among those in dif ferent layers, deciding the w ay a neuron recei v es input and

PAGE 43

32 produces output, and determining the strength of connection within the netw ork by allo wing the netw ork to learn the appropriate v alues. The process of designing a neural netw ork is an iterati v e one. 3.2.2.1 Layers Biological neural netw orks are constructed in a three dimensional w ay from microscopic components. Articial neural netw orks are the simple layering of articial neurons, which are then connected to one another All articial neural netw orks ha v e a similar structure of topology Figure ( 3–4 ). Some of the neurons recei v e input, the input layer and other neurons pro vide the netw ork' s outputs, the output layer All the rest of the neurons are hidden from vie w the hidden layer *,+ -0. *,+ -0. *,+ -0. *,+ -0. *,+ -0. *,+ -,. *,+ -,. *,+ -,. *,+ -,. *,+ -,. 1 1 1 1 132 4 4 4 4 465 7 7 7 7 7 7 7 798 1 1 1 1 132 4 4 4 4 465 1 1 1 1 132 : : : : :3; : : : : :3; < < < < <6= : : : : :3; < < < < <6= > > > > > > > >9? @ @ @ @ @3A B B B B BDC E E E E E3F G G G G GDH E E E E E3F @ @ @ @ @3A input v ector input layer hidden layer output layer output v ector Figure 3–4: An articial neural netw ork When the input layer recei v es 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 v ector The determination of the number of hidden neurons the netw ork should ha v e 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 netw ork will memorize the training set and will ha v e problems in generalization.

PAGE 44

33 3.2.2.2 Learning The brain basically learns from e xperience, this is also true for articial neutral netw orks. Learning typically occurs through training or e xposure to a truthed set of input/output data where the training algorithm iterati v ely adjusts the connection weights. F or this reason, articial neural netw orks are sometimes called machine learning algorithms. The learning ability of a neural netw ork is determined by its architecture and by the algorithm chosen for training. The training method usually consists of one of three schemes:IUnsupervised learning: The hidden neurons must nd a w ay to or ganize themselv es without help from the e xternal en vironment. In this approach, there are no tar get outputs a v ailable for the netw ork to measure its predicti v e performance for a gi v en v ector of inputs.IReinforcement learning: Reinforced learning is also called supervised learning. The connections among the neurons in the hidden layer are randomly arranged, then reshuf ed as the netw ork is told ho w close it is to solving the problem. Instead of be gin pro vided with the correct output for each netw ork input, reinforced learning only gi v es a grade. The grade is gi v en by a teacher The teacher may be a training set of data or an observ er who grades the performance of the netw ork results.IBackpropagation: This method has pro v ed highly successful in training of multilayered neural nets. The netw ork is not just gi v en reinforcement for ho w it is doing on a task. Information about errors is also ltered back through the system and is used to adjust the connections between the layers, thus impro ving performance. A form of backpropagation is used in this w ork. One can cate gorize the learning methods into yet another group: of f-line or on-line.IOf f-line: In the of f-line learning methods, once the systems enters into the operation mode, its weights are x ed and do not change an y more. Most of the

PAGE 45

34 current netw orks are of the of f-line learning type. Of f-line learning is used in this w ork.IOn-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 comple x design structure. 3.2.3 Areas of Applications The rst practical application of articial neural netw orks came in the late 1950s, with the in v ention of the perceptron netw ork and associated learning rule by Frank Rosenblatt [ 121 ]. Rosenblatt and his colleagues b uilt a netw ork and demonstrated its ability to perform pattern recognition. T oday neural netw orks are performing successfully in a wide v ariety of problems including interpretation, prediction, diagnosis, planing, monitoring, deb ugging, repair instruction, and control. Basically most applications of neural netw orks f all into the follo wing v e cate gories: prediction, classication, data association, data conceptualization, and data ltering.

PAGE 46

CHAPTER 4 F A UL T DETECTION AND ISOLA TION The purpose of this chapter is to de v elop an articial neural netw ork that can be used in f ault detection and isolation (FDI) of x ed-position actuator f ailures. The f ailure class is briey re vie wed and dened mathematically then the procedure to de v elop an articial neural netw ork is outlined. 4.1 F ailure P arameterization A ight control system is w orking properly if all the control ef fectors, i.e., leading edge aps, trailing edge aps, ailerons, stabilators, and rudders maintain the state v ariables in the neighborhood of their desired v alues. A f ault occurs when a certain le v el of deterioration tak es place in one or more state v ariable because of permanent physical change, i.e., jammed or hard-o v er control surf aces. System f ailure occurs when a f ault or combination of f aults lead to complete system deterioration and a sudden termination of ight control. F aults may produce only poor or reduced performance, b ut may also lead to catastrophic f ailure including loss of aircraft and cre w This w ork focuses on the case when a control surf aces freezes in a x ed-position and does not respond to subsequent commands. This is an especially dif cult type of f ailure to o v ercome since the remaining actuators should be recongured not only to achie v e the control objecti v e, b ut also to compensate for a disturbance due to the f ailure. W e assume that the f ailure is unkno wn b ut can be determined from the feature history of state v ariables and position commands to the actuators. The f ailure introduces a constant disturbances into the o v erall closed-loop system so that the solution to the ne w control problem is f ar from tri vial. 35

PAGE 47

36 KJ Feedforw ard Controller LJ Actuators Plant M Feedback Controller / /+ + u c u p Figure 4–1: The structure of a full-state feedback control system The hope is that a positi v e identication of the f ailed control surf ace and x edposition will f acilitate the de v elopment of a re vised control la w to stabilize the f ailed aircraft and reinstate optimal maneuv ering performance. Referring to Figure ( 4–1 ), let u c describes the signal generated by the controller and u p the signal that enters the actual plant through the control surf aces. The reason for making a distinction between u c and u p is that control surf ace jamming is manifested by u p assuming a constant v alue e v en while u c v aries with time. F or simplicity assume that in the case with no f ailures u ctNu pt. A x ed-position actuator f ailure is dene as u ptN O P P Q P P Ru ctif tt f w if tSt f where t f denotes the f ailure instant of the control surf ace and w is the v alue at which the control surf ace has frozen. The proposed neural netw ork will monitor a signal consisting of state measurements and control surf ace position commands, u c to determine if the aircraft is operating properly u ctTu pt, or has suf fered a control surf ace f ailure, u ctVU u pt. When a control surf ace has f ailed the neural netw ork will hopefully identify which control surf ace has f ailed and at what position the f ailure has occurred, w

PAGE 48

37 4.2 FDI via Articial Neural Netw orks 4.2.1 Articial Neural Netw ork FDI F ormulation T raditional methods for FDI tend to emplo y mathematical state-space models of the monitored system such as state observ ers and Kalman lters, which continually estimate predicted state measurements. F ault detection is achie v ed in these methods by comparing predicted to actual state measurements. The pi v otal assumption with these techniques is that the state-space model of the system is kno wn positi v ely In reality state-space models are good assumptions at best. Being based on a mathematical model, the y can be v ery sensiti v e to modeling errors, parameter v ariations, noise, disturbances, etc. F or e xample, modeling errors can be interpreted as a f ault, thus producing f alse alarms, or hinder actual system de gradation from being detected in the rst place. A mathematical model is simply a description of system beha vior and accurate modeling for a comple x nonlinear system is v ery dif cult to achie v e in practice e v en when the analytical equations of motion are kno wn. F or this reason, f ault detection and isolation by these methods is an imprecise science and has sho wn to be quite dif cult o v er the past 20 years. Hence, the de v elopment of a rob ust and less model dependent method for f ault detection and diagnosis for comple x nonlinear system is w arranted. Articial neural netw orks are an ideal solution to this problem since the y demonstrate se v eral desired adv antages: po werful nonlinear mapping properties, noise tolerance, self-learning and parallel processing capabilities. Articial neutral netw orks ha v e been proposed as solutions for a wide v ariety of tasks. Among the most promising applications is that of pattern classication. P attern classication implies observing input data with the intend of recognizing specic traits. This classication process f acilitates the initiation of certain actions based on the input data. The inputs representing a pattern are called the measurement or feature v ector In f ault diagnosis, the dif ferent types of f aults occurring in the system may be vie wed as decision classes. The function preformed by a pattern recognizing neural netw ork is

PAGE 49

38 the mapping of the input feature v ector into one of the v arious decision classes. F ault detection and diagnosis can, therefore, be considered a pattern classication acti vity and, thus, the potential e xists for f ault detection and diagnosis using an articial neural netw ork. 4.2.2 Articial Neural Netw ork De v elopment Neural netw orks are e xcellent mathematical tools for dealing with nonlinear problems, as the y are designed to learn patterns of acti vities. A nonlinear system can be approximated by a neural netw ork gi v en suitable weighting f actors and an architecture consisting of at least one hidden layer The system model can be e xtracted from historical training data using a learning algorithm that often requires little or no a priori kno wledge about the system. Learning is just determining the proper connection strengths to allo w the outputs nodes to achie v e the correct tar get output for a gi v en feature v ector This adapti v e nature of neural netw orks pro vides great e xibility for modeling nonlinear systems by allo wing the weights to be learned by e xperience, thus producing a self-learning system. The def ault performance function for man y feedforw ard neural netw orks is the mean squared error which is the a v erage squared error between the netw ork outputs and the tar get outputs. A backpropagation training algorithm is used to train the netw ork. Learning proceeds by updating the netw ork weights in the direction in which the performance function decreases most rapidly the ne gati v e of the gradient. One iteration of the backpropagation algorithm can be written x kW1x ka k g k where x k is a v ector of current weights, g k is the current gradient, and a k is the learning rate. Learning be gins by initializing all the connection strengths to small randomly selected v alues. Then a training pattern of feature v ectors composed of simulated ight data is introduced into the input nodes of the netw ork.

PAGE 50

39 0 1 2 3 4 5 6 7 8 9 10 -100 -50 0 50 100 150 200 250 300 Time, (sec)Roll Angle, (deg)w=1.72 w=2.13 w=3.96 w=7.35 w=5.45 no failure Figure 4–2: Roll feature v ectors for dif ferent f ailure position w The training data consists of roll angle, pitch angle, ya w angle, roll rate, pitch rate, ya w rate, angle of attack, sideslip, and position commands to the control surf aces for the unf ailed case and a characteristic set of simulated f ailures for a gi v en pilot command. Figure ( 4–2 ) sho ws the roll angle feature history for v e dif ferent f ailures during a pitch doublet, the roll angle is zero for the unf ailed case. The f ailures occurred on the left leading-edge ap at postions denoted by w As can be easily seen by Figure ( 4–2 ) small changes in the f ailure position produce drastic changes in the e v olution of the roll angle of the aircraft. These results constitute historically rich ight data to design a neural netw ork for FDI. Once all these feature v ectors are gathered the input v ectors are then propagated in a feed-forw ard f ashion through the netw ork to produce output v alues. The outputs were compared to the desired tar get outputs to produced a mean squared error signal. The connection strengths are then systematically

PAGE 51

40 adjusted by the learning algorithm to reduced the mean squared error to a desired v alue. After each training c ycle, the neural netw ork will kno w more about the system dynamic beha vior Once the connection strength is properly determined to undershoot the desired mean squared error training is stopped and the neural netw ork is ready for f ault detection and isolation. The output v ector consists of tw o v ariables, namely a surf ace identier and a position indicator i.e., the output v ector#0; 0$corresponds to the absence of an y particular f ault and#n ; w$corresponds to the n t h control surf ace jammed at w Figure 4–3: F/A-18 ight control surf ace numbering scheme The proposed neural netw ork has the ability to detect a specic f ault, control surf ace and x ed-position, using pattern recognition techniques that acti v ate an alarm in the form of the output v ector It therefore acts as a pattern recognizer for the detection of specic f aults and classies the f aults accordingly Figure ( 4–3 ) sho ws the numbering scheme for the control surf aces of an F/A-18 aircraft and T able ( 4–1 ) lists the position limits for each control surf ace, the maximum and minimum v alues are the hardo v er position. After the netw ork is trained, f ault detection and diagnosis is simply a matter of presenting a ne w historically rich feature v ector to the input nodes and reading the output v ector from the output nodes. The neural netw ork can be tested by simulating ne w ight data to produce a ne w input v ector not in the original training pattern.

PAGE 52

41 T able 4–1: F/A-18 Control Surf ace Position Limits # Ef fector Position Limits 1,2 Leading Edge Flaps (lef) 3d l e f33 3,4 T railing Edge Flaps (tef) 8d t e f45 5,6 Ailerons (ail) 25d ail45 7,8 Stabilators (stb) 24d hz t10"5 9,10 Rudders (rud) 30d r ud30 On-line f ault detection and diagnosis can be achie v ed by using a system of delays to produce the historical data necessary for the neural netw ork to perform its calculation properly

PAGE 53

CHAPTER 5 THE ST ABILIZA TION PR OBLEM This chapter presents the formulation of the stabilization solution which is one of the most time-critical components of a reconguration scheme. A x ed-position actuator f ailure can create a constant force and moment disturbance on the aircraft. This constant force and moment can lead to a signicant de viation from the desired trim condition and lea v e the remaining control surf aces incapable of re gaining control of the aircraft. There are se v eral suitable methods for returning an aircraft to a trim condition follo wing a f ailure which include the use of a re gulator system with inte gral control or if the disturbance can be measured, in a linear trim subsystem through the use of feedforw ard control. This w ork will focus on the de v elopment of the latter approach which has the distinct adv antage of rapid response to disturbances while not adv ersely af fecting the stability of the system. Its disadv antage is that an y errors between the approximated disturbance recei v ed through f ault detection and isolation and true disturbance will directly appear in the output. The follo wing sections present a formal description of the stabilization problem and describe a decomposition of the problem which allo ws the use of a f ast and ef cient Matlab algorithm in the solution [ 124 125 ]. 5.1 The Nonlinear T rim Problem During normal ight, the motion of an aircraft with respect to the Earth-axis system can, in general, be described by the nonlinear autonomous dif ferential equations xtXf oxtYut(Zz ytNh oxtYut((5.1) 42

PAGE 54

43 where f o : R n[p\ ]R n and h o : R n[p\ ]R q are nonlinear mappings, xt &R n is the state v ariables v ector ut &R p is the input v ector ztis a v ector of unmeasurable disturbances, and yt &R q is the output v ector The orientation of the aircraft is trimmed at the nominal v aluesx nu nwhen f ox nu nN0 h ox nu nN0 (5.2) During straight and le v el ight the nominal control settings u n are established which maintain steady state ight x0with wings le v el at constant altitude, airspeed, and heading. F ollo wing a x ed-position actuator f ailure, the aircraft dynamics are assumed to satisfy xtXf oxtYut(Zzt!d ytXh oxtYut((5.3) where d is a constant or slo wly v arying measurable disturbance v ector F or our f ailure class, d respresents the constant disturbance that results from the nonzero deection of the f ailed control surf ace. F ollo wing a x ed-position actuator f ailure, a trim condition results when f ox nu n6d0 h ox nu nT0 (5.4) The problem then becomes ho w to determine a solutionx nu nwhich satises Equation ( 5.4 ). The solution can be determined by using the Matlab trimming routine t r im on a nonlinear model of the aircraft' s equations of motion at a desired ight condition. It is only necessary to de v elop the proper constraints on the magnitudes of the control surf aces and states to produce a feasible solution for implementation.

PAGE 55

44 5.2 The Linear T rim Problem Let the open-loop linearized dynamics of the healthy aircraft be described as xtNAxt6But(5.5) where xt &R n is the state v ariables v ector ut &R p is the control v ector A&R n[n is the plant matrix, and B&R n[p is the control matrix. Let the measurements be gi v en by ytNC xt6Dut(5.6) where yt &R q is the output v ector C&R q[n is the output matrix, and D&R q[p is the null matrix. Assume that a postf ailure model of an aircraft at a chosen ight condition is gi v en by xtNAxt6B r u rt6d (5.7) where xtis the state v ector of the linear aircraft dynamics and u rtis the v ector of a v ailable (i.e., f ailed surf ace is deleted) control surf aces deections, and d is a v ector of constant disturbances that can be used to represent forces and moments generated by a f ailed surf ace. F or the general problem, the disturbance v ector d may be measured (e.g., by the use of an FDI algorithm) or unmeasurable. Let the k e y quantities that are to be re gulated in denoted by ytNC xt!Du rt(5.8) Elements of ytmight represent quantities such as altitude, bank angle, ight path angle, and rotational rate perturbation. The objecti v e of our problem will be to automatically select u rtto guarantee that ytachie v es some desired v alue in steady state, y dt. More precisely the linear trim objecti v e can be e xpressed as nding the solutionx nu nthat guarantees ytNy dt(5.9)

PAGE 56

45 and 0Ax nBu nd (5.10) F or this w ork, we will assume that the disturbance d is caused by a x ed-position actuator f ailure which can be measured through FDI. W e will further assume that the disturbance tak es the form db w w (5.11) where w is the dif ference between the jammed position of the f ailed control surf ace and its nominal v alue, and b w is the column remo v ed from the B matrix corresponding to the f ailed control surf ace. No w dene the model of an aircraft with a x ed-position actuator f ailure as xtXAxt!B r u rt!b w w (5.12) where xt &R n is the state v ector u rt &R p1 is the v ector of remaining control surf aces (i.e., f ailed surf ace is deleted), b w w is the input to the aircraft caused by the jammed surf ace w and b w is the column in B corresponding to the jammed surf ace. As with the nonlinear trim formulation, it is necessary to impose some constraints on the allo w able magnitudes of the states and control surf aces,xu, for which a solution should be feasible. These constraints can be described as upper and lo wer limits on the allo w able perturbation, x Lxx U u Luu U (5.13) Equation ( 5.9 ) through ( 5.13 ) describe the main objecti v es of the linear trim problem. That is, produce a control system that achie v es stable ight at constant altitude with certain specied states set to zero, while the de viation of all other states is minimized from their desired v alues. V arious norms and weighting matrices can be used to determine the solution to this problem, the Matlab routine t r im is demonstrated in the nal chapter

PAGE 57

CHAPTER 6 F A UL T -T OLERANT CONTR OL DESIGN METHODS The objecti v e of this w ork is to de v elop a reconguration scheme that is reliable and of fers a de gree of assured success for the tar geted types of f ailures. The reconguration scheme is e xpected to stabilized the aircraft in the e v ent of a control surf ace f ailure and pro vide reasonable command-tracking performance. T o accomplish these goals, tw o approaches are in v estigated and e v aluated in this chapter One is based on linear -quadratic re gulator (LQR) methodology In this approach the ef fect of the jammed surf ace is treated as a measurable constant disturbance to the system. An LQR controller is designed to stabilize the aircraft (stabilization), balance the jammed surf ace (disturbance rejection), and pro vide command tracking. The second method is de v eloped by the author of this w ork, which is based on an H approach. Here the ef fect of the jammed surf ace is treated as a constant disturbance which is bounded by a lo w-pass lter A reference nominal controller is designed for the healthy aircraft with all control surf aces operable. This nominal controller is used as a tar get model in H synthesis to design a rob ust controller which is capable of canceling the inuence of the jammed surf aces and reproduce as closely as possible the desired outputs of the healthy aircraft. The problem formulation for the tar geted type of f ailure is presented before each f ault-tolerant control method is de v eloped in the follo wing sections. Let the open-loop linearized dynamics of the healthy aircraft be described in state v ariable form as xtNAxt6But(6.1) 46

PAGE 58

47 where xt &R n is the v ector of aircraft states and ut &R p is the v ector of control surf aces. Let the measurements be gi v en by ytNC xt6Dut(6.2) where yt &R q is the output v ariables a v ailable for feedback control. It is assumed that a baseline control la w has been designed based on ( 6.1 ) that pro vides satisf actory stabilization and command-tracking performance of the aircraft. Suppose no w that one of the control surf ace actuators f ails suddenly and jams at a position w Let us re write the entire postf ailure system in state space form as xtXAxt!B r u rt!b w w (6.3) where xt &R n is the state v ector u rt &R p1 is the v ector of remaining control surf aces (i.e., f ailed surf ace is deleted), b w w is the input to the aircraft caused by the jammed surf ace w and b w is the column in B corresponding to the jammed surf ace. 6.1 F ault-T olerant Control Design Using LQR Theory LQR design methodology can be applied directly to Equation ( 6.3 ) assuming that b w w is a constant disturbance that can be eliminated by using inte gral control. While that assumption is completely accurate and can produce desired results it is not the approach tak en here. The approach tak en here is based upon a systematic procedure in which the f ailure is identied through FDI, Chapter ( 4 ), and directly canceled by nding a ne w trim condition, Chapter ( 5 ). The result is a ne w linear system which directly considers the ef fects of the constant disturbance. This ne w linear system is achie v ed by considering the results of our automatic trim algorithm 0Ax nB r u nb w w (6.4) where x n&R n is the v ector of nominal aircraft states and u n&R p1 is the v ector of nominal control surf ace deections such that the state deri v ati v es are identically zero.

PAGE 59

48 Note that the trim conditionx nu nis only a v ailable for calculation when w is kno wn through some FDI procedure. By simply rearranging Equation ( 6.4 ) we can achie v e an e xpression for the constant disturbance in terms of the state matrices and trim condition b w w Ax nB r u n(6.5) By substituting this result into Equation ( 6.3 ) we nd our ne w linear system is gi v en by xtNAxtx n6B ru rtu n(6.6) The f ault-tolerant control problem can no w be stated as follo ws using LQR methodology Find the control u rt%u n that minimizes J_^ 0` xx nT Qxx n6 u ru nT Ru ru nbad t (6.7) The optimal control that minimizes ( 6.7 ) is gi v en by u rt%u ncR1 B T Pxt%x nNdKxt%x n(6.8) where P solv es the algebraic Riccati equation 0A T PP AQPBR1 B T P (6.9) Assuming that the linearized model is v alid the feedback la w ( 6.7 ) quarantees that the linearized closed loop system will be stable, and that the important states ( 6.2 ) will approach their desired trajectories re gardless of the constant disturbance. Inte gral control can be added to the design process to minimize errors and impro v e tracking performance. Thus the primary goals of stabilizing the aircraft (stabilization), balancing the jammed surf ace (disturbance rejection), and pro viding command tracking will be met by this LQR f ault-tolerant design.

PAGE 60

49 6.2 F ault-T olerant Control Design Using H Theory This section de v elops the theory for aircraft tracking control for a class of aircraft f ailures using H control design methodology The author uses a tw o-step process of rst designing the feedforw ard part of the controller to achie v e perfect trajectory follo wing and then designing the feedback part of the controller using H re gulator theory The objecti v e of the tracking problem is to get a plant output to track a desired model signal. The design procedure will attempt to e xploit the H -optimality criterion for judging tracking performance while minimizing the w orst case tracking error norm o v er an admissible ball of disturbances. The resulting controller design is an inno v ati v e technique for f ault-tolerant controls in which H methodology is applied directly to the tar geted f ailure class. The desired model signal to be track ed is gi v en by a reference LQR controller design for the healthy aircraft (see Appendix B for controller design) sho wn in Figure ( 6–1 ) eJ I k l qr fJ P M K l qr / /+ + Figure 6–1: Reference closed-loop system where P is the linearized F/A-18 model (see Appendix A), K l qr is the feedback gains, k l qr is the feedforw ard gains, and I is an inte grator The reference controller as sho wn in Figure ( 6–1 ) presents some dif culties in our design process, since, in general, H design frame w orks do not consider inte gral 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 s0 and such a pole in the reference closed-loop

PAGE 61

50 system is not stabilizable. Ho we v er this obstacle can be o v ercome by implementing a tw o-step design approach. First, the feedforw ard and feedback gains are designed using LQR methodology to achie v e desired trajectory follo wing and disturbance rejection criteria for the healthy aircraft. Then the plant model and feedback gains are remo v ed from the reference controller and used as a tar get model for H synthesis. The tar get model, T is gi v en by Figure ( 6–2 ). eg P M K l qr /+ y d Figure 6–2: T ar get Model The goal is to design an H controller that not only achie v es the same tracking performance of the baseline controller b ut one that is capable of rejecting a disturbance caused by a jammed control surf ace. The problem can be set up as follo ws, let the postf ailure state-space form be gi v en as xtNAxt6B r u rt6d (6.10) where u r is the remaining control surf aces (i.e., f ailed surf ace is deleted), and d is a disturbance force. The measurements ytare corrupted by noise such that y nthyt6w n n (6.11) Our objecti v e is to design a control la w so that the ef fect of the disturbance force d on the state measurements of the aircraft is reduced o v er an e xtremely small frequenc y range, 0w0"01, such that the resulting disturbance is modeled as a constant force

PAGE 62

51 upon the system. A lo w-pass lter gi v en by w w0"01 w s0"01 (6.12) is used to limit the disturbance force and achie v e this goal. The result is a constant disturbance upon the system which is magnitude bounded by the position v alue of the jammed surf ace w The synthesis model for H design is sho wn in Figure ( 6–3 ) M w p M J M T M M J P M w n M M w w M w k + + e p y n n u r w e k u c u c y p y d Figure 6–3: H synthesis model where w k is the control weight and w p is the performance weight on the error signal of desired measurements to actual measurements ey dy (6.13) The synthesis model sho wn in Figure ( 6–3 ) along with weighting functions w d w k w n and w p can be used to determine the sub-optimal H controller K H that minimizes the w orst case tracking error norm o v er a magnitude bounded disturbance force. Thus, the primary goal of designing a controller that not only achie v es the same tracking performance of the baseline controller b ut one that is capable of rejecting a disturbance

PAGE 63

52 caused by a jammed control surf ace will be met by this H f ault-tolerant design. The implementation of the H controller is sho wn in the analysis model in Figure ( 6–4 ). KJ I k l qr k H P / + Figure 6–4: H analysis model

PAGE 64

CHAPTER 7 APPLICA TION T O AN F/A-18 In this nal chapter the reconguration scheme proposed throughout this w ork is demonstrated on a high-delity nonlinear F/A-18 simulation. The simulation is based on the 6 de gree-of-freedom equations of motion for a rigid body dri v en by aerodynamic, propulsi v e, and gra vitational forces. The aerodynamic model is nonlinear and full independent control authority is a v ailable with realistic actuator models including rate and position limits. A nonlinear controller is included with this simulation that pro vides e xcellent performance and stability characteristics for a wide v ariety of high-performance maneuv ers o v er the entire F/A-18 ight en v elope. This controller is appropriate for the healthy aircraft and should not be altered; therefore, f ault-tolerance will be achie v ed by switching to a predetermined controller for reco v ery and subsequent command follo wing. The f ailure scenario handled throughout this chapter in v olv es a 2-inch longitudinal stick motion that commands a pitch doublet during which the left trailing-edge ap becomes stuck from a x ed-position actuator f ailure. It is assumed the f ailure is unkno wn b ut can be o v ercome by combining the f ault detection and isolation procedure, Chapter ( 4 ), the stabilization procedure, Chapter ( 5 ), and either of the tw o formulated f ault-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 re vie wed for the unf ailed case so that the reader can properly appreciate the e v olution from the unf ailed baseline controller to the f ault-tolerant controllers. The maneuv er 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 positi v e 2 inches from 53

PAGE 65

54 3-6 seconds, pushes and holds the stick at a ne gati v e 2 inches from 6-9 seconds, then returns and holds the stick to its neural point from 9-20 seconds. 0 5 10 15 20 780 800 820 840 860 880 Total True Airspeed, (fps) 0 5 10 15 20 -4 -2 0 2 4 6 Angle of Attack, (deg) 0 5 10 15 20 -5 0 5 10 15 20 25 30 Pitch Angle, (deg)Time, (sec) 0 5 10 15 20 -0.5 0 0.5 Pitch Rate, (rps)Time, (sec) Figure 7–1: Longitudinal responses: healthy aircraft Figure ( 7–1 ) sho ws the longitudinal responses to the 2-inch longitudinal stick doublet in the unf ailed case. The maneuv er causes the aircraft to pitch upw ards at 0"15 radians/second from 3-6 seconds, then pitch do wn-w ards at0"15 radians/seconds from 6-9 seconds. The aircraft pitches to a maximum 25 de grees then returns back to wings le v el. Figure ( 7–2 ) sho ws the lateral responses to the 2-inch longitudinal stick doublet in the unf ailed case. The maneuv er is essentially decoupled causing no response in the lateral states. This is characteristic of the F/A-18 which is kno wn to ha v e e xcellent maneuv erability

PAGE 66

55 0 5 10 15 20 -4 -2 0 2 4 6 Sideslip Angle, (deg) 0 5 10 15 20 -10 0 10 20 30 Roll Angle, (deg) 0 5 10 15 20 -0.5 0 0.5 Roll Rate, (rps)Time, (sec) 0 5 10 15 20 -0.5 0 0.5 Yaw Rate, (rps)Time, (sec) Figure 7–2: Lateral-directional responses: healthy aircraft Figure ( 7–3 ) sho ws the control surf ace deections commanded by the 2-inch longitudinal stick doublet in the unf ailed case. The leading-edge aps, trailing-edge aps, and stabilators are used collecti v ely 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 unf ailed case.

PAGE 67

56 0 2 4 6 8 10 12 14 16 18 20 -10 0 10 LEF 0 2 4 6 8 10 12 14 16 18 20 -10 0 10 TEF 0 2 4 6 8 10 12 14 16 18 20 -5 0 5 AIL 0 2 4 6 8 10 12 14 16 18 20 -5 0 5 STB 0 2 4 6 8 10 12 14 16 18 20 -5 0 5 RUDTime (sec) Figure 7–3: Control surf ace deections: healthy aircraft

PAGE 68

57 7.2 F ailed F/A-18 In this section we sho w the ef fects of the left trailing-edge ap f ailure on the baseline controller The maneuv er is identical to the pre vious section with no attempt by the pilot to correct for the se v ere de viations from the desired trajectory While this is not an ideal assumption, it is made in this case to simplify the f ault detection and isolation process and to guarantee full control authority is passed to the f ault-tolerant controller The f ailure occurs at 4 seconds with the left trailing-edge ap becoming stuck at approximately 3"96 de grees. While this f ailure may not sound se v ere the ef fects upon performance and stability are de v astating. 0 5 10 15 20 780 800 820 840 860 880 Total True Airspeed, (fps) 0 5 10 15 20 -6 -4 -2 0 2 4 6 Angle of Attack, (deg) 0 5 10 15 20 -20 -10 0 10 20 30 Pitch Angle, (deg)Time, (sec) 0 5 10 15 20 -0.5 0 0.5 Pitch Rate, (rps)Time, (sec) Figure 7–4: Longitudinal responses: f ailed aircraft Figure ( 7–4 ) sho ws the longitudinal responses to the 2-inch longitudinal stick doublet with a left trailing-edge ap f ailure at 4 seconds. The aircraft retains reasonable responses for pitch angle and pitch rate during the maneuv er Once the aircraft is

PAGE 69

58 commanded back to wings le v el it be gins to pitch do wnw ard violently At 20 seconds the aircraft is pitched do wnw ard at a ne gati v e 16 de grees with increasing pitch rate and total true airspeed. 0 5 10 15 20 -0.5 0 0.5 1 Sideslip Angle, (deg) 0 5 10 15 20 -40 -20 0 20 40 60 80 100 Roll Angle, (deg) 0 5 10 15 20 -0.5 0 0.5 Roll Rate, (rps)Time, (sec) 0 5 10 15 20 -0.04 -0.02 0 0.02 0.04 Yaw Rate, (rps)Time, (sec) Figure 7–5: Lateral-directional responses: f ailed aircraft Figure ( 7–5 ) sho ws the lateral responses to the 2-inch longitudinal stick doublet with a left trailing-edge ap f ailure at 4 seconds. As pre viously sho wn, for the unf ailed aircraft' s the lateral states are not e xcited by a pitch doublet. This decoupling is not the case for a pitch doublet in which the leading-edge ap has f ailed. At 20 seconds the aircraft has rolled completely on its side with a constant roll rate and a minimal side-slip and ya w rate. The aircraft continues to roll and pitch until it is nose do wn. Finally the aircraft impacts the ground in approximately 37 seconds (time of f ailure plus 34 seconds) tra v eling just o v er Mach 1.

PAGE 70

59 0 2 4 6 8 10 12 14 16 18 20 -10 0 10 LEF 0 2 4 6 8 10 12 14 16 18 20 0 5 10 TEF 0 2 4 6 8 10 12 14 16 18 20 -1 0 1 AIL 0 2 4 6 8 10 12 14 16 18 20 -5 0 5 STB 0 2 4 6 8 10 12 14 16 18 20 -2 0 2 RUDTime (sec) Figure 7–6: Control surf ace deections: f ailed aircraft Figure ( 7–6 ) sho ws the control surf ace deections for a 2-inch longitudinal stick doublet with a left trailing-edge ap f ailure at 4 seconds. First, it is essential to notice the ef fects of the f ailure on the left trailing-edge ap. This is sho wn by the red dashed line in the second response. The position of the control surf ace remains constant after the f ailure instant. Also notable is the e xcitation of the ailerons and rudders by the feedback elements of the baseline controller attempting to counter the roll and ya w moments generated by the f ailure. This is also apparent in the dif ferential stabilator deection. Functioning with only nine operational control surf aces, the baseline controller pro v es ill-equipped to handle the f ailure.

PAGE 71

60 7.3 Articial Neural Netw ork FDI The articial neural netw ork (ANN) proposed in Chapter ( 4 ) for f ault detection and isolation (FDI) of a x ed-position actuator f ailure is de v eloped and e v aluated in this section for the proposed scenario. The netw ork w as designed in Matlab and accepts as inputs v e seconds of ight data sampled at 5 Hz. The measurements used for creating the input feature v ector are Euler angles, Euler rates, angle-of-attack, sideslip, and position commands to the trailing-edge aps, ailerons, stabilators, and rudders. It w as determined that the position commands to the leading-edge aps, which are primarily used for trimming the aircraft, were not producing a “rich” feature history; therefore, the y were not used for training the netw ork or performing the FDI operation. The remo v al of the leading-edge aps position commands from the netw ork design and operation is without incident, since there e xists ample measurements with “rich” feature histories to generate desired results. As pre viously stated, the netw ork is designed to accept as input a v ector composed of position commands and aircraft measurements generated by the baseline controller; and output a v ector identifying the f ailed control surf ace and f ailed postion in the e v ent a f ailure occurs. The netw ork used for the scenario presented throughout this chapter w as designed to monitor ight maneuv ers including pitch and roll doublets and wind-up turns. The specications of the netw ork include: four layers with 312 neurons in the input layer; 156 neuron in the rst hidden layer; 78 neurons in the second hidden layer; and 2 neurons in the output layer The acti v ation functions are constant throughout each layer and are l o gsig l o gsig l o gsig and pur el ine respecti v ely The learning algorithm selected w as t r ainscg which is a backpropagation technique where the netw ork training function updates weight and bias v alues according to the scaled conjugate gradient method. The algorithm is capable of training an y netw ork as long as its weights, net inputs, and acti v ation functions ha v e deri v ati v es, which are satised by the design. The netw ork w as designed and trained of f-line with a x ed architecture. Once the desired

PAGE 72

61 mean-squared error w as achie v ed with the training algorithm the netw ork weights and bias were not changed during FDI operation. F or the proposed scenario, v e seconds of ight data starting from the f ailure instant were input into the nalized netw ork to produce FDI results. The actual f ailure occurs on the left trailing-edge ap (control surf ace #3) at a x ed-position of 3.96 de grees. The netw ork results are gi v en by ANN output O P P Q P P R3"01 f ailed surf ace 3"99 f ailed position (7.1) These results demonstrate the capability of an articial neural netw ork to perform f ault detection and isolation of x ed-position actuator f ailures. The rst result, 3"01, represents the identier for the f ailed control surf ace and correctly identies the left-trailing edge ap (control surf ace #3) as the f ailed surf ace. The second result, 3"99, represents the identier for the control surf ace position in de grees. This result achie v es the desired accurac y and positi v ely identies a left trailing-edge ap f ailure with precision suitable to continue with trimming and f ault-tolerant control. Acceptable results for this simulation w ould ha v e included a f ailed surf ace identier ofi0"25 the actual inte ger v alue or a f ailed position identier ofi0"5 de grees the actual position v alue. While these ranges were reached through the process of trial and error the y ha v e been determined to consistently f acilitate desired results throughout the entire reconguration scheme. 7.4 Stabilization The stabilization solution from Chapter ( 5 ) w as implemented on the scenario presented throughout this chapter using the f ault detection and isolation (FDI) results, Equation ( 7.1 ), from Section ( 7.3 ). The constraints placed upon the Matlab function t r im included returning the aircraft with the f ailed control surf ace back to wings le v el ight at constant altitude, airspeed, and heading. This orientation can be e xpressed as

PAGE 73

62 nding the nominal control surf ace position u n such that 0B r u nb r w (7.2) while the nominal state v ector x n is gi v en by 0x n (7.3) Also, the allo w able deection of each control surf ace w as constrained by the position limits dened by the nonlinear simulation, which can be found in T able ( 4–1 ). The results for a left trailing-edge ap f ailure at 3.99 de grees are gi v en as T able 7–1: Stabilization Results Surf ace Results d l e f l 1.74 d l e f r 1.74 d t e f l 3.99 d t e f r -2.47 d ail l -9.25 d ail r 3.47 d s t b l 1.18 d s t b r -0.85 d r ud l 0.07 d r ud r 0.07 These results can be easily v eried by solving the equation representing the aircraft with a control surf ace f ailure, Equation ( 5.12 ), using the appropriate x n u n and w such that 0Ax nB r u nb w w (7.4) 7.5 F ault-T olerant Control Nonlinear Simulations The results included in this section sho w the implementation of the de v eloped reconguration techniques on a nonlinear F/A-18 simulation. The only alteration to the nonlinear simulation, inaddition to the ne w f ault-tolerant controllers, in v olv ed permitting each control surf ace independent deection rather than the traditional

PAGE 74

63 collecti v e or dif ferential deection of the baseline controller The f ailure scenario continues from the pre vious sections. While performing a pitch doublet the left trailing-edge ap f ails at 3.96 de grees at 4 second, resulting in an undesired roll, pitch, and ya w motion. The task of the reconguration scheme de v eloped throughout this w ork is to positi v ely identify that f ailure has occurred, determine the se v erity of the f ailure, and then switch control from the baseline controller to a f ault-tolerant controller to re gain stability and restore performance. The FDI procedure w as performed of f-line using v e seconds of ight data from 4-9 seconds with acceptable results to proceed with control authority switching from the baseline controller to the f ault-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 f ault-tolerant controller on the nonlinear equations of motion. The goal here w as to pitch the aircraft without e xciting an y lateral states of the aircraft, just as in the unf ailed case. The follo wing gures sho w the results for each control methodology Figures ( 7–7 )-( 7–9 ) sho w the control surf ace deection and state responses using the LQR f ault-tolerant controller and Figures ( 7–10 )-( 7–12 ) sho w the control surf ace deection and state responses using the H f ault-tolerant controller F or the state responses, the red dashed line is the desired performance of a healthy F/A-18 performing tw o consecuti v e pitch doublets while the black solid line is the results achie v ed with each f ault-tolerant controller In each case, the pitch moment is primarily generated by the deection of the stabilators about a ne w trim point. Similar results are achie v ed by each f ault-tolerant controller The rise time during the commanded maneuv er is slightly slo wer than the desired healthy F/A-18. The maneuv er is performed with zero steadystate error and without producing an y measurable roll angle or roll rate during the pitch maneuv er e v en though the left trailing-edge ap has f ailed. The desired results are achie v ed, stability is restored, and command-tracking is performed.

PAGE 75

64 0 10 20 30 40 -0.5 0 0.5 Sideslip Angle, (deg) 0 10 20 30 40 -30 -20 -10 0 10 20 30 Bank Angle, (deg) 0 10 20 30 40 -0.5 0 0.5 1 Roll Rate, (rps)Time, (sec) 0 10 20 30 40 -0.04 -0.02 0 0.02 0.04 0.06 Yaw Rate, (rps)Time, (sec) Figure 7–7: Lateral responses : LQR FTC

PAGE 76

65 0 10 20 30 40 760 780 800 820 840 860 880 Total True Airspeed, (fps) 0 10 20 30 40 -6 -4 -2 0 2 4 6 8 Angle of Attack, (deg) 0 10 20 30 40 -0.5 0 0.5 Pitch Rate, (rps)Time, (sec) 0 10 20 30 40 -10 0 10 20 30 Pitch Angle, (deg)Time, (sec) Figure 7–8: Longitudinal responses : LQR FTC

PAGE 77

66 0 5 10 15 20 25 30 35 40 -10 0 10 LEF 0 5 10 15 20 25 30 35 40 -10 0 10 TEF 0 5 10 15 20 25 30 35 40 -2 0 2 AIL 0 5 10 15 20 25 30 35 40 -10 0 10 STB 0 5 10 15 20 25 30 35 40 -5 0 5 RUDTime (sec) Figure 7–9: Control surf ace deections : LQR FTC

PAGE 78

67 0 10 20 30 40 -0.5 0 0.5 1 Sideslip Angle, (deg) 0 10 20 30 40 -30 -20 -10 0 10 20 Bank Angle, (deg) 0 10 20 30 40 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 Roll Rate, (rps)Time, (sec) 0 10 20 30 40 -0.04 -0.03 -0.02 -0.01 0 0.01 0.02 0.03 Yaw Rate, (rps)Time, (sec) Figure 7–10: Lateral responses : H FTC

PAGE 79

68 0 10 20 30 40 760 780 800 820 840 860 880 Total True Airspeed, (fps) 0 10 20 30 40 -6 -4 -2 0 2 4 6 8 Angle of Attack, (deg) 0 10 20 30 40 -0.5 0 0.5 Pitch Rate, (rps)Time, (sec) 0 10 20 30 40 -10 0 10 20 30 Pitch Angle, (deg)Time, (sec) Figure 7–11: Longitudinal responses : H FTC

PAGE 80

69 0 5 10 15 20 25 30 35 40 -10 0 10 LEF 0 5 10 15 20 25 30 35 40 0 5 10 TEF 0 5 10 15 20 25 30 35 40 -10 0 10 AIL 0 5 10 15 20 25 30 35 40 -5 0 5 STB 0 5 10 15 20 25 30 35 40 -2 0 2 RUDTime (sec) Figure 7–12: Control surf ace deections : H FTC

PAGE 81

CHAPTER 8 CONCLUSIONS A reconguration scheme for ight control adaptation to x ed-position actuator f ailures is e xpected to accomplish three tasks. First, the scheme must ha v e a f ast and ef cient method for identifying that a f ailure has occurred and the resulting ef fects upon stability and performance. Second, the scheme must adjust the trim v alues for command input so that le v el ight can be achie v ed. Third, the closed-loop system must ensure command-tracking, despite the detrimental ef fects of the f ailure and reduction in control ef fecti v eness. The f ailure class analyzed throughout this w ork is a x edposition or jammed actuator f ailure, which results in a ight control surf ace becoming inoperable. This w ork has introduced, de v eloped, and demonstrated the necessary concepts to satisf actorily achie v e all three goals for the tar geted f ailure class. The reconguration scheme de v eloped through this w ork is a systematic procedure that attempts to maximize the tracking performance of the f ailed aircraft while satisfying the stability requirements. As a result, the proposed scheme relied on three interdependent processes: 1) f ault detection and isolation, 2) stabilization, and 3) command-tracking. The use of articial neural netw orks pro v ed to be an e xcellent tool for identifying x ed-position actuator f ailures. These highly or ganized and v ersatile architectures were readily suited to perform the f ault detection and isolation (FDI) task which maps state measurements into v arious f ailure classes. The results from the FDI procedure f acilitated the de v elopment of a feedforw ard trim solution to reco v er system stability and tw o f ault-tolerant control strate gies to restore system performance. The tw o f ault-tolerant methodologies e xplored, LQR and H assumed that the ef fects of the f ailed surf aces w ould introduce a constant disturbance into the dynamical equations go v erning the motion of the aircraft. The resulting theoretical de v elopment relied 70

PAGE 82

71 on e xploiting the rob ustness of each technique to directly address and o v ercome the ef fects of the f ailure by as nearly as possible reconstructing the forces and moments of the unf ailed aircraft. The complete reconguration scheme w as demonstrated on a nonlinear simulation of an F/A-18 to sho w the potential of the tw o methods in recongurable controls. The LQR and H methods achie v ed virtually the same results for the tar geted f ailure class with both re gaining stability and restoring performance in all instances. The author of this w ork recognizes that se v eral assumptions made throughout this w ork limit its application into ight systems. F or e xample, the solutions presented throughout this w ork were de v eloped using a single ight condition for a v ery specic f ailure class. No consideration w as gi v en to e xpanding the results o v er the entire ight en v elope or into other f ailure scenarios. Furthermore, the standards used for judging the f ault-tolerant controllers design were e xceptionally high. Success w as only dened by the the complete restoration of pref ailure performance. In some situations in which an aircraft has suf fered a signicant system f ailure, it may not be necessary or e v en desirable to restore the performance to that of the healthy aircraft. Therefore, a method for determing ho w much performance is desired after a specic f ailure must be de v eloped in conjunction with the pilots who y the aircraft. Additionally the incorporation of a reconguration scheme into an aircraft will most lik ely not be accomplished successfully post-production; rather the tools for reconguration must be inte grated into the initial design concepts of the aircraft. The initial design inte gration of reconguration technology may lead to design conicts between normal operation and the rare occurrence of man y of the f ailures currently under in v estigation in recongurable ight controls. Finally a reconguration scheme will ha v e to be ight tested to pro v e its usefullness in real-w orld situations. Such testing on full-size piloted aircraft is the essential step in demonstrating the promised benets of the reconguration technology

PAGE 83

72 In summary the results achie v ed in this w ork demonstrate the ability of articial neural netw orks with linear control techniques to accommodate a v ery specic f ailure class while restoring stability and command-tracking to an aircraft which has e xperienced a signicant control system f ailure. The methods de v eloped here appear to be v ery ef fecti v e in achie ving the major objecti v e to de v elop a reconguration scheme to accommodate x ed-position actuator f ailures.

PAGE 84

APPENDIX A LINEARIZED MODEL OF THE F/A-18 The follo wing is a linearized model of an F/A-18 generated from a high delity six de gree-of-freedom nonlinear simulator Since the aircraft potentially has ten independent control surf aces, it is an ideal candidate for control restructuring and is used throughout this w ork for control synthesis. The ight conditions for the linearized model are Mach0"8, height10000 ft, a trim1"23, q trim1"23, f trimb trim0, and weight30777 lbm. Let u d l e f l d l e f r d t e f l d t e f r d ail l d ail r d s t b l d s t b r d r ud l d r ud r T be the input v ector of control surf aces perturbations from the trim v alues, where d l e f l d l e f r are the left and right leading-edge aps, d t e f l d t e f r the left and right trailing-edge aps, d ail l d ail r the left and right ailerons, d s t b l d s t b r the left and right stabilators, and d r ud l d r ud r the left and right rudders. All of the control surf ace surf ace deections are in de grees. The sign con v ention is positi v e leading-edge ap deection is up, positi v e trailing-edge ap deection is do wn, positi v e aileron deection is do wn, positi v e stabilator deection is do wn, and positi v e rudder deection is left looking forw ard. The surf ace trim v alues are 1"72for the trailing-edge aps, 1"12for the stabilators, and 0for the trailing-edge aps, ailerons, and rudders. Let the state v ector for perturbations from the trim conditions be x u w q f v p r fT where the components are, in order of appearance in x forw ard v elocity v ertical v elocity pitch rate, pitch angle, side v elocity roll rate, ya w rate, and roll angle. The units are in radians/second for angular rates, radians for angles, and feet/seconds for v elocities. The linearized dynamics of the F/A-18 at the preceding 73

PAGE 85

74 ight conditions are gi v en by xtNAxt6But(1) where xtis the state v ector and utis the v ector of a v ailable control surf aces. The dynamics of the A matrix are decoupled in the longitudinal and lateral directors, while the B matrix is not. The rst four states represent the longitudinal dynamics and the second four represent the lateral dynamics such that A A l on 0 0 A l a tn r(2) and BkjB 1 B 2l(3) with A l on 0"0209 0"048218"338732"13610"03771"8386 853"19090"6901 0"00020"02060"9431 0 0 0 1"000 0n r(4) A l a t 0"3196 18"3106860"7181 32"13610"03466"9243 0"7349 0 0"0098 0"00440"3233 0 0 1"0000 0"0215 0n r(5)

PAGE 86

75 B 1 0"0259 0"0259 0"0097 0"0097 0"0111 0"3174 0"31742"53672"53670"56990"03020"0302 0"0262 0"02620"0252 0 0 0 0 00"00000"0000 0 00"0381 0"0000 0"0000 0"53170"5317 0"3497 0"0000 0"00000"0066 0"00660"0028 0 0 0 0 0n r(6) B 2 0"01110"13040"1304 0 00"56992"03192"0319 0 00"02520"25600"25600"00050"0005 0 0 0 0 0 0"03810"2425 0"2425 0"5106 0"51060"3497 0"51340"5134 0"0765 0"0765 0"0028 0"00340"00340"04650"0465 0 0 0 0 0n r(7) The open-loop eigen v alues of the aircraft are LongitudinalO P P Q P P RShort Period:1"3921i4"0273 j Phugoid:0"0076i0"0799 j LateralO P P P P P P Q P P P P P P RDutch Roll:0"3535i2"9485 j Spiral:0"0014 Roll:6"8587

PAGE 87

APPENDIX B NOMIN AL CONTR OLLER DESIGN The design process follo wed to arri v e at the reference state-feedback controller used for the tar get model in the H design uses LQR methodology Since the longitudinal and lateral dynamics are decoupled for the unf ailed aircraft, we can design controllers for them separately See Appendix A for the linearized aircraft model for the form xtNAxt6But(8) T o decouple the inputs, we need to mix them to obtain dif ferential and collecti v e inputs. W e do this as follo ws. Let B mixd 1 1 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 11 0 0 0 0 0 0 0 0 0 0 11 0 0 0 0 0 0 0 0 0 0 11 0 0 0 0 0 0 0 0 0 0 11 0 0 0 0 0 0 0 0 0 0 11n r(9) so u ne wB mix'u where u ne wmd l e f c d t e f c d s t b c d l e f d d t e f d d ail d d s t b d d r ud c T where the components are, in order of appearance in u ne w collecti v e leading-edge aps, collecti v e trailing-edge aps, collecti v e stabilators, dif ferential leading-edge aps, dif ferential trailing-edge aps, dif ferential ailerons, dif ferential stabilators, and collecti v e rudders. The rst three 76

PAGE 88

77 mix ed inputs represent the longitudinal control while the the last v e mix ed inputs represent the lateral control. W e can no w scale the inputs to ease our controller design such that 1 unit in each input is approximately equi v alent in terms of importance. W e pick the scaling for the ne w inputs as follo ws u pS1 1 u ne w (10) where S 1ddiag#334510"533454510"530$(11) W e then let B 1BB mix 1 S 1 (12) be our ne w B matrix, which is mix ed and scaled. W e can follo w the same reasoning for the state v ariables such that x pT 1'x (13) where T 1diag#0"010"01110"01111$(14) then our ne w system matrices are A pT 1'A a'T1 1 B pT 1'B 1 (15) and the linear aircraft model becomes x pA p x pB p u p (16) W e can no w split the aircraft into longitudinal and lateral models and design controllers for each indi vidually

PAGE 89

78 Longitudinal Design The longitudinal model is gi v en by A l on 0"0209 0"04820"18340"32140"03771"8386 8"53190"0069 0"02222"05620"9431 0"0 0"0 0"0 1"0 0"0n rB l on 0"0086 0"00440"0137 0"10471"14150"21340"9978 1"17892"6884 0 0 0n r(17) The states are the scaled v ersions of the longitudinal states, x u w q qT and the scaled inputs are u d l e f c d t e f c d s t b c T W e w ould lik e to control the pitch angle in the longitudinal axis. This is done by augmenting the system with an inte grator on pitch angle. Let C l on j0 0 0 1l(18) so that yqC l on x (19) Then our ne w longitudinal system becomes x x In r z A l on 0 C l on 0n r x x In r B l on 0n ru (20) or z Az Bz (21)

PAGE 90

79 W e then proceed to design an LQR controller for this augmented model. W e used Q l ondiag#0"00"31"25"036"0$R l ondiag#1"01"00"6$(22) The result is K l on 0"0009 0"029313"219054"436453"1336 0"00330"1085 24"7311 133"9899 116"72050"0010 0"030318"238269"043170"0172n r(23) Figure (B-1) sho ws the state responses to a pitch doublet, the black line represents the nominal controller designed here while the red dashed line represents the nonlinear baseline controller 0 5 10 15 20 -0.2 0 0.2 Pitch Rate, (rps) 0 5 10 15 20 0 10 20 30 Pitch Angle, (deg) 0 5 10 15 20 0 10 20 30 Roll Angle, (deg)Time, (sec) 0 5 10 15 20 -0.2 0 0.2 Roll Rate, (rps)Time, (sec) Figure B-1: Nominal Longitudinal Responses

PAGE 91

80 Lateral Design The lateral model is gi v en by A l a t 0"3196 0"18318"6072 0"32143"45596"9243 0"7349 0"0 0"9842 0"00440"3233 0"0 0"0 1"0 0"0215 0"0n rB l a t 0"000 0"00"01720"0255 0"1532 0"000 23"9279 15"7358 5"3908 2"29560"00000"29590"1255 0"03601"3954 0 0 0 0 0n r(24) The states are the scaled v ersions of the lateral states, x v p r fT and the scaled inputs are u d l e f d d t e f d d ail d d s t b d d r ud c T The goal we w ould lik e to achie v e with lateral design is automatically coordinated ight. One w ay to achie v e this is by controlling side v elocity and roll angle so that a nonzero commanded roll angle with zero-commanded side v elocity will produce a steady turn. This is done by augmenting the system with an inte grator on side-v elocity and roll angle. Let C l a t 1 0 0 0 0 0 0 1n r(25) so that y v fn r C l a t x (26) Then our ne w lateral system becomes x x In r z A l a t 0 C l a t 0n r x x In r B l a t 0n ru (27)

PAGE 92

81 or z Az Bz (28) W e then proceed to design an LQR controller for this augmented model. W e used Q l a tdiag#0"010"00150"00"0110"01"0$R l a tdiag#1"05"01"00"251"0$(29) The result is K l a t 0"0000 0"00000"0000 0"0000 0"0000 0"0000 0"0819 1"272314"2166 8"9759 0"1520 8"5733 0"2299 4"165329"2495 30"0738 0"4254 29"3576 0"0315 1"3124 9"3172 10"2124 0"0568 10"6313 0"4417 0"4901230"87034"1777 0"872711"0881n r(30) Figure (B-2) sho ws the state responses to a roll doublet, the black line represents the nominal controller designed here while the red dashed line represents the nonlinear baseline controller

PAGE 93

82 0 5 10 15 20 -2 0 2 Pitch Rate, (rps) 0 5 10 15 20 0 100 200 300 400 Pitch Angle, (deg) 0 5 10 15 20 0 100 200 300 400 Roll Angle, (deg)Time, (sec) 0 5 10 15 20 -2 0 2 Roll Rate, (rps)Time, (sec) Figure B-2: Nominal Lateral Responses

PAGE 94

REFERENCES [1] Burk en, J. J., Lu, P ., W u, Z., and Bahm, C., “T w o Recongurable Flight-Control Design Methods: Rob ust Serv omechanism and Control Allocation” J ournal of Guidance Contr ol, and Dynamics V ol. 24, No. 3, 2001, pp. 482-493. [2] Stengel, R. F ., “Intelligent F ailure-T olerant Control, ” Pr oceedings of the 5th IEEE International Symposium on Intellig ent Contr ol V ol. 1, Philadelphia, P A, 1990, pp. 548-557. [3] American Airlines A300-600, “ An Airb us A300 of American Airlines on nal approach to London Heathro w Airport, ” http://home.w anadoo.nl/airruud/a300aa.htm (visited July 10, 2003). [4] American Airlines Flight 587 Belle Harbor Ne w Y ork, “In v estigation Information, ” March 2003, http://www .ntsb .go v/e v ents/2 001/A A587/d ef ault.htm (visited July 10, 2003). [5] American Airlines Flight 587 Belle Harbor Ne w Y ork, “ Amer ican Airlines Flight 587 crashes in NYC, ” No v ember 2002, http://www .cnn.com/2001/US/11/12/AA587.f acts/ (visited July 10, 2003). [6] American Airlines Flight 587 Belle Harbor Ne w Y ork, “Flight 587 Crashes, ” October 2002, www .september11ne ws.com/ No v12Flight587AerialFire.jpg (visited July 10, 2003). [7] American Airlines Flight 587 Belle Harbor Ne w Y ork, “Feds rule out sabotage in N.Y crash, ” October 2002, www .cnn.com/2002/US/South/10/29/ight.587/ (visited July 10, 2003). [8] Eslinger R. A., and Chandler P R., “Self-Repairing Control System Program Ov ervie w ” Pr oceedings of the IEEE National Aer ospace and Electr onics Confer ence V ol. 2, Dayton, OH, 1988, pp. 504-511. [9] P atton, R. J., “F ault-T olerant Control: The 1997 Situation, ” Pr oceedings of IF A C Symposium on F ault Detection, Supervision and Safety for T ec hnical Pr ocesses : SAFEPR OCESS'97 Uni v ersity of Hull, UK, 1998, pp. 1033-1055. [10] Bajpai, G., and Chang, B. C., “Decoupling of F ailed Actuators in Flight Control Systems, ” Pr oceedings of American Contr ol Confer ence Arlington, V A, 2001, pp. 1836-1840. 83

PAGE 95

84 [11] Bajpai, G., Chang, B. C., and Lau, A., “Reconguration of Flight Control Systems for Actuator f ailures, ” IEEE Aer ospace and Electr onics Systems Ma gazine V ol. 16, No. 9, 2001, pp. 29-33. [12] Owen, D. H., F eedbac k and Multivariable Systems Peter Pere grinus, Ste v enage, England, 1978. [13] V eilltette, R. J., Medanic, J. B., and Perkins, W R., “Design of Reliable Control Systems, ” IEEE T r ansactions on A utomatic Contr ol V ol. 37, No. 3, 1992, pp. 290-304. [14] Birdwell, J. D., Castanon, D. A., and Athans, M., “On Reliable Control System Designs, ” IEEE T r ansactions on Systems, Man, and Cybernetics V ol. SMC-16, No. 5, 1986, pp. 703-711. [15] Blank e, M., Izadi-Zamanabadi, R., Bogh, S. A., and Lunau, C. P ., “F ault T olerant Control Systems : A Holistic V ie w ” Department of Contr ol Engineering R-1997-4175, Aalbor g Uni v ersity Denmark, March 1997. [16] W illsk y A. S., “ A Surv e y of Design Methods for F ailure Detection in Dynamic Systems, ” A utomatica V ol. 12, No. 6, 1976, pp. 601-611. [17] Mirono vski, L. A., “Functional Diagnosis of Dynamic Systems : A Surv e y ” A utomation and Remote Contr ol V ol. 41, 1980, pp. 1122-1143. [18] Isermann, R., “Process F ault Detection Based on Modeling and Estimation Methods : A Surv e y ” A utomatica V ol. 20, No.4, 1984, pp. 387-304. [19] Milne, R., “Strate gies for Diagnosis, ” IEEE T r ansactions on Systems, Man, and Cybernetics V ol. SMC-17, No. 3, 1987, pp. 333-339. [20] Gertler J., “Surv e y of Model-Based F ailure Detection and Isolation in Comple x Plants, ” IEEE Contr ol Systems Ma gazine December 1998, pp. 3-11. [21] Frank, P M., “F ault Diagnosis in Dynamic System Using Analytical and Kno wledge Based Redundanc y ” A utomatica V ol. 26, No. 3, 1990, pp. 459-474. [22] P atton, R. J. and Chen, J., “Rob ust F ault Detection Using Eigenstructure Assignment : A T utorial Consideration and Some Ne w Results, ” Pr oceedings of the 30th IEEE Confer ence on Decision and Contr ol Brighton, UK, 1991, pp. 2242-2247. [23] Leitch, R. R., and Quek, H. C., “ An Architecture for Inte grated Process Supervision, ” IEEE Pr oceedings Contr ol Theory and Applications V ol. 139, No. 3, 1992, pp. 317-327. [24] P atton, R. J., “F ault Detection and Diagnosis in Aerospace Systems Using Analytical Redundanc y ” Computing and Contr ol Engineering J ournal V ol. 2, No. 3, 1991, pp. 127-136.

PAGE 96

85 [25] De Persis, C., and Isidori, A., “ A Geometric Approach to Nonlinear F ault Detection and Isolation, ” IEEE T r ansactions on A utomatic Contr ol V ol. 46, No. 6, 2001, pp. 853-865. [26] Frank, P M., “On-line F ault Detection in Uncertain Nonlinear Systems Using Diagnostic Observ ers : A Surv e y ” International J ournal of Systems Science V ol. 25, No. 12, 1994, pp. 2129-2154. [27] P atton, R. J., Frank, P M., and Clark, R. N., F ault Dia gnosis in Dynamic Systems, Theory and Applications Prentice Hall, Ne w Y ork, NY 1989. [28] Frank, P M., “ Application of Fuzzy Logic to Process Supervision and F ault Diagnosis, ” Pr oceedings of the IF A C/IMA CS Symposium on F ault Detection, Supervision and Safety for T ec hnical Pr ocesses : SAFEPR OCESS'94 Helsinki, Finland, June 13-16, 1994, pp. 531-538. [29] Isermann, R., “Inte gration of F ault Detection and Diagnosis Methods, ” Pr oceedings of the IF A C/IMA CS Symposium on F ault Detection, Supervision and Safety for T ec hnical Pr ocesses : SAFEPR OCESS'94 Helsinki, Finland, June 13-16, 1994, pp. 597-612. [30] Krishnasaami, V ., and Rizzoni, G., “Nonlinear P arity Equation Residual Generation for F ault Detection and Isolation, ” Pr oceedings of the IF A C/IMA CS Symposium on F ault Detection, Supervision and Safety for T ec hnical Pr ocesses : SAFEPR OCESS'94 Helsinki, Finland, June 13-16, 1994, pp. 305-310. [31] P atton, R. J., Chen, J., and Nielsen, S. B., “Model-Based Methods for F ault Diagnosis : Some Guide-Lines, ” T r ansactions of The Institute of Measur ement and Contr ol V ol. 17, No. 2, 1995, pp. 73-83. [32] Isermann, R., and Balle, P ., “T rends in the Application of Model Based F ault Detection and Diagnosis of T echnical Processes, ” Pr oceedings of the 13th IF A C W orld Congr ess V ol. N, San Francisco, USA, June 30 July 5, 1996, pp. 1-12. [33] Basse ville, M., and Ben v eniste, A., “Detection of Abrupt Changes in Signals and Dynamical Systems, ” Lectur e Notes in Contr ol and Information Sciences V ol. 77, Springer -V erlag, Ne w Y ork, NY December 1985. [34] Barron, R. L., Cellucci, R. L., Jordan, P R., and Beam, N. E., “ Application of Polynominal Neural Netw orks to FDIE and Recongurable Flight Control, ” Pr oceedings of the IEEE National Aer ospace and Electr onics Confer ence V ol. 2, Dayton, OH, May 1990, pp. 507-519. [35] Le gg, J. M., “Computerized Approach for Matrix-F orm FMEA, ” IEEE T r ansactions on Reliability V ol. R-27, No. 1, October 1978, pp. 154-157. [36] Herrin, S. A., “Maintainability Applications Using the Matrix FMEA T echnique, ” IEEE T r ansactions on Reliability V ol. 30, No. 3, 1981, pp. 212-217.

PAGE 97

86 [37] Bell, A. R., “Managing Murphy' s La w: Engineering a Minimum-Risk System, ” IEEE Spectrum June 1989, pp. 24-26. [38] Hunt, J. E., Pugh, D. R., and Price, C. J., “F ailure Mode Ef fects Analysis: A Practical Application of Functional Modeling, ” Applied Articial Intellig ence V ol. 9, No. 1, 1995, pp. 33-44. [39] Sa v ono v M. G., Stability and Rob ustness of Multivariable F eedbac k Systems MIT Press, Cambridge, MA, 1980. [40] Morari M., and Zarou, E., Rob ust Pr ocess Contr ol Prentice Hall, Engle w ood Clif fs, NJ, 1989. [41] Maciejo wski, J. M., Multivariable F eedbac k Design Addison W esle y Reading, MA, 1989. [42] Zhou, K., Do yle, J., and Glo v er K., Rob ust and Optimal Contr ol Prentice Hall, Upper Saddle Ri v er NJ, 1996. [43] Eterno, J. S., W eiss, J. L., Looze, D. P ., and W illsk y A., “Design Issues for F ault T olerant-Restructurable Aircraft Control, ” Pr oceedings of the IEEE 24th Confer ence on Decision & Contr ol V ol. 2, F ort Lauderdale, FL, 1985, pp. 900-905. [44] Stengel, R. F ., “Intelligent F ailure-T olerant Control, ” IEEE Contr ol System Ma gazine V ol. 11, No. 4, 1991, pp. 14-23. [45] Lane, S. H., and Stengel, R. F ., “Flight Control Design Using Non-Linear In v erse Dynamics, ” A utomatica V ol. 24, No. 4, 1988, pp. 471-483. [46] Ochi, Y ., and Kanai, K., “Design of Restructurable Flight Control Systems Using Feedback Linearization, ” J ounrnal of Guidance Contr ol, and Dynamics V ol. 14, No. 5, 1991, pp. 903-911. [47] Gao, Z., and Antsaklis, P J., “Stability of the Pseudo-In v erse Method for Recongurable Control Systems, ” International J ournal of Contr ol V ol. 53, No. 3, 1991, pp. 717-729. [48] Calise, A. J., Lee, S., and Sharma, M., “Direct Adapti v e Recongurable Control of a T ailless Fighter Aircraft, ” Guidance Navigation and Contr ol Confer ence Boston, MA, August 1998, pp. 88-97. [49] Idan, M., Johnson, M., and Calise, A. J., “ A Hierarchical Approach to Adapti v e Control for Impro v ed Flight Safte y ” J ournal on Guidance Contr ol and Dynamics July 2001, pp. 1012-1023. [50] Johnson, E. N., and Calise, A. J., “Neural Netw ork Adapti v e Control of Systems with Input Saturation, ” Pr oceedings of the American Contr ol Confer ence V ol. 5, Arlington, V A, June 2001, pp. 3527-3532.

PAGE 98

87 [51] Huang, C. Y ., and Stengel, R. F “Restructurable Control Using ProportionalInte gral Implicit Model F ollo wing, ” J orunal of Guidance Contr ol, and Dynamics V ol. 13, No. 2, 1990, pp. 303-309. [52] Morse, W E., and Ossman, K. A., “Model F ollo wing Recongurable Flight Control System for the AFTI/F-16, ” J ournal of Guidance Contr ol, and Dynamics V ol. 13, No. 6, 1990, pp. 969-976 [53] Jiang, J., “Design of Recongurable Control Systems Using Eigenstructure Assignments, ” Internation J ournal of Contr ol V ol. 59, No. 2, 1994, pp. 395-410. [54] W u, N. E., “Rob ust Feedback Design with Optimized Diagnostic Performance, ” IEEE T r ansactions on A utomatic Contr ol V ol. 42, No. 9, 1997, pp. 1264-1268. [55] Nett, C. N., Jacobson, C. A., and Miller A. T ., “ An Inte grated Approach to Controls and Diagnostics : The 4-P arameter Controller ” Pr oceedings of the 1988 American Contr ol Confer ence Atlanta, USA, 1988, pp. 824-835. [56] T yler M. L., and Morari, M., “Optimal and Rob ust Design of Inte grated Control and Diagnostic Modules, ” Pr oceedings of the 1994 American Contr ol Confer ence Baltimore, MD, June 1994, pp. 2060-2064. [57] Murad, G. A., Postlethw aite, I., and Gu, D. W ., “ A Rob ust Design Approach to Inte grated Controls and Diagnostics, ” Pr oceedings of the 13th IF A C W orld Congr ess V ol. N, San Francisco, CA, USA, 1996, pp. 199-204. [58] Ak esson, M., “Inte grated Control and F ault-Detection for a Mechanical Serv o Process, ” Pr oceedings of the IF A C Symposium on F ault Detection, Supervision and Safety for T ec hnical Pr ocesses SAFEPR OCESS'97 Hull, England, August 1997, pp. 1252-1257. [59] Eich, J., and Sattler B., “F ault T olerant Control System Design Using Rob ust Control T echniques, ” IF A C Safepr ocess Uni v ersity of Hull, UK, 1997, pp. 1246-1251. [60] Chiang, C. Y ., and Y oussef, H. M., “Neural Netw ork and Fuzzy Logic Approach to Aircraft Recongurable Control Design, ” Pr oceedings of the American Contr ol Confer ence V ol. 5, Seattle, W A, June 1995, pp. 3505-3509. [61] P atton, R. J., and Chen, J., “Rob ust F ault Detection and Isolation (FDI) Systems, ” Contr ol and Dynamic Systems V ol. 74, 1996, pp. 171-224. [62] Mariton, M., “Detection Delays, F alse Alarm Rates and Reconguration of Control Systems, ” International J ournal of Contr ol V ol. 49, 1989, pp. 981-992. [63] Srichander R., and W alk er B. K., “Stochastic Stability Analysis for Continuous T ime F ault T olerant Control Systems, ” International J ournal of Contr ol V ol. 57, No. 2, 1993, pp. 433-452.

PAGE 99

88 [64] Rauch, H., “ Autonomous Control Reconguration, ” IEEE Contr ol Systems Ma gazine V ol. 15, No. 6, 1995, pp.37-48. [65] Buckle y A. P ., “Hubble Space T elescope Pointing Control System Design Impro v ement Study Results, ” IEEE Contr ol Systems Ma gazine V ol. 15, No. 2, 1995, pp. 34-42. [66] Eryurek, E., and Upadhyaya, B. R., “F ault-T olerant Control and Diagnostic for Lar ge-Scale Systems, ” IEEE Contr ol Systems Ma gzaine V ol. 15, No. 5, 1995, pp. 34-42. [67] Polycarpou, M. M., and V emuri, A. T ., “Learning Methodology for F ailure Detection and Accomodation, ” Contr ol Systems Ma gazine Special Issue on Intellig ent Learning Contr ol V ol. 15, 1995, pp. 16-24. [68] Kw ong, W A., P assino, K. M., Lauk onen, E .G., Y urk o vich, S., “Expert Supervision of Fuzzy Learning Systems with Applications to Recongurable Control for Aircraft, ” Pr oceedings of the 33r d IEEE Confer ence on Decision and Contr ol V ol. 4, Lak e Buena V ista, FL, December 1994, pp. 4116-4121. [69] Kw ong, W A., P assino, K. M., Lauk onen, E. G., Y urk o vich, S., “Expert Supervision of Fuzzy Learning Systems for F ault-T olerant Aircraft Control, ” Pr oceedings of the IEEE V ol. 83, No. 3, March 1995, pp. 466-483. [70] Fierro, R., Le wis, F L., “ A frame w ork for hybrid control design, ” T r ansactions on Systems, Man and Cybernetics V ol. 27, No. 6, No v ember 1997, pp. 765-773. [71] Horo witz, I., Arnold, P B., and Houpis, C. H., “Flight Control System Reconguration Design Using Quantitati v e Feedback Theory ” Pr oceedings of the National Aer ospace & Electr onics Confer ence Dayton, OH, May 1985, pp. 578-585. [72] K eating, M. S., P achter M., and Houpis, C. H., “QFT Applied to F aultT olerant Flight Control System Design, ” Pr oceedings of the American Contr ols Confer ence Seattle, W A, June 1995, pp. 184-188. [73] McF arlane, D. C., and Glo v er K., “Rob ust Controller Design using Normalised Coprime F actor Plant Descriptions, ” Lectur e Notes in Contr ol and Information Sciences V ol. 138, Springer V erlag, Berlin, German y 1989. [74] W illiams, S., and Hyde, R. A., “ A Comparision of Characteristic Locus and H Design Methods for VST OL Flight Control System Design, ” Pr oceedings of American Contr ols Conder ence San Die go, CA, May 1990, pp. 2508-2513. [75] P assino, K. M., and Antsaklis, P J., “On In v erse Stable Sampled Lo w P ass Systems, ” International J ournal of Contr ol V ol. 47, No. 6, June 1988, pp. 1905-1913.

PAGE 100

89 [76] Bosk o vic, J. D., and Mehra, R. K., “ A Multiple Model-Based Recongurable Flight Control System Design, ” Pr oceedings on the 37th IEEE Confer ence on Decision & Contr ol V ol. 4, T ampa, FL, December 1998, pp. 4503-4508. [77] Gopinathan, M., Bosk o vic, J. D., Mehra, R. K., and Rago, C., “ A Multiple Model Predicti v e Scheme for F ault-T olerant Flight Control Design, ” Pr oceedings of the 37th IEEE Confer ence on Decision & Contr ol V ol. 2, T ampa, FL, December 1998, pp. 1376-1381. [78] Bosk o vic, J. D., and Mehra, R. K., “Stable Multiple Model Adapti v e Flight Control for Accommodation of a Lar ge Class of Control Ef fector F ailures, ” Pr oceedings of the American Contr ol Confer ence V ol. 3, San Die go, CA, June 1999, pp. 1920-1924. [79] Bosk o vic, J. D., Li, S. M., and Mehra, R. K., “Recongurable Flight Control Design Using Multiple Switching Controllers and On-Line Estimation of Damage Related P arameters, ” Pr oceedings of the 2000 IEEE International Confer ence on Contr ol Applications Anchorage, AK, September 2000, pp. 479-484. [80] Bosk o vic, J.D., Li, S. M., and Mehra, R. K., “Study of an Adapti v e Recongurable Control Scheme for T ailless Adv anced Fighter Aircraft (T AF A) in the Presence of W ing Damage, ” Pr oceedings of the P osition, Location, and Navigation Symposium San Die go, CA, March 2000, pp. 341-348. [81] Bosk o vic, J.D., Li, S. M., and Mehra, R. K., “Rob ust Supervisory F ault-T olerant Flight Control System, ” Pr oceedings of the American Contr ol Confer ence V ol. 3, Arlington, V A, June 2001, pp. 1815-1820. [82] Bosk o vic, J. D., and Mehra, R. K., “ A decentralized scheme for accommodation of multiple simultaneous actuator f ailures, ” Pr oceedings of the American Contr ol Confer ence V ol. 6, May 2002, pp. 5098-5103. [83] Bosk o vic, J. D., and Mehra, R. K., “Multiple model-based adapti v e recongurable formation ight control design, ” Pr oceedings of the 41st IEEE Confer ence on Decision and Contr ol V ol. 2, December 2002, pp. 1263-1268. [84] Bosk o vic, J. D., and Mehra, R. K., “F ault accommodation using model predicti v e methods, ” Pr oceedings of the American Contr ol Confer ence V ol. 6, May 2002, pp. 5104-5109. [85] Kane v S., and V erhae gen, M., “ A Bank of Recongurable LQG Controllers for Linear Systems Subjected to F ailures, ” Pr oceedings of the 39th IEEE Confer ence on Decision and Contr ol V ol. 4, Sydne y NSW Australia, December 2000, pp. 3684-3689. [86] Kane v S., and V erhae gen, M., “Controller Reconguration for Non-Linear Systems, ” Contr ol Engineering Pr actice V ol. 8, October 2000, pp. 1223-1235.

PAGE 101

90 [87] Kane v S., V erhae gen, M., and Nijsse, G., “ A Method for the Design of F aultT olerant Systems in Case of Sensor and Actuator F aults, ” Submitted to the Eur opean Contr ol Confer ence Houf f alize, Belgium, September 2001. [88] Demetriou, M. A., “ Adapti v e Reor ganization of Switched Systems with F aulty Actuators, ” Pr oceedings of the 40th IEEE Confer ence on Decision and Contr ol V ol. 2, Orlando, FL, December 2001, pp. 1874-1884. [89] Zhang, Y ., and Jiang, J., “ An Interacting Multiple-Model Based F ault Detection, Diagnosis and F ault-T olerant Control Approach, ” Pr oceedings of the 38th Confer ence on Decision & Contr ol V ol. 4, Phoenix, AZ, December 1999, pp. 3593-3598. [90] Maybeck, P S., “Multiple Model Adapti v e Algorithms for Detecting and Compensating Sensor and Actuator/Surf ace F ailures in Aircraft Flight Control Systems, ” International J ournal of Rob ust and Nonlinear Contr ol V ol. 9, 1999, pp. 1051-1070. [91] Zhang Y ., Rong Li, X., “Detection and Diagnosis of Sensor and Actuator F ailures Using Interacting Multiple-Model Estimator ” Pr oceedings of the 36th IEEE Confer ence on Decision and Contr ol V ol. 5, San Die go, CA, December 1997, pp. 4475-4480. [92] Munir A., Atherton, D. P ., “Maneuvring T ar get T racking Using Dif ferent T urn Rate Models in the Interacting Multiple Model Algorithm, ” Pr oceedings of the 34th IEEE Confer ence on Decision and Contr ol V ol. 3, Ne w Orleans, LA, December 1995, pp. 2747-2751. [93] Burk en, J. J, and Burcham, F W ., “Flight-T est Results of Propulsion-Only Emer genc y Control System on MD-11 Airplane, ” J ournal of Guidance Contr ol and Dynamics V ol. 20, No. 5, October 1997, pp. 980-987. [94] Burcham, F W ., Burk en, J. J., Maine, T A., and Bull, J., “Emer genc y Flight Control Using Only Engine Thrust and Lateral Center -Of-Gra vity Of fset: A First Look, ” T ec hnical r eport N ASA, 1997. [95] Burcham, F W ., Burk en, J. J., Maine, T A., and Fullerton, C. G., “De v elopment and Flight T est of an Emer genc y Flight Control System Using Only Engine Thrust on an MD-11 T ransport Airplane, ” T ec hnical r eport N ASA, October 1997. [96] Bordignon, K. A, and Durham, W C., “Closed-F orm Solutions to Constrained Control Allocation Problem, ” J ournal of Guidance Contr ol and Dynamics V ol. 18, No. 5, September 1995, pp. 717-725. [97] Durham, W C., and Bordignon, K. A., “Multiple Control Ef fector Rate Limiting, ” J ournal of Guidance Contr ol and Dynamics V ol. 19, No. 1, February 1996, pp. 30-37.

PAGE 102

91 [98] Da vidson, J. B., Lallman, F J., and Bundick, W T ., “Inte grated Recongurable Control Allocation, ” Submitted to the AIAA Guidance Navigation, and Contr ol Confer ence and Exhibit Montreal, Canada, August 6-9 2001. [99] Zhen yu, Y ., Huazhang, S., and Zongji, C., “The Frequenc y-Domain Heterogeneous Control Mix er Module for Control Reconguration, ” Pr oceedings of the 1999 IEEE International Confer ence on Contr ol Applications V ol. 2, K ohala Coast, HI, August 1999, pp. 1223-1228. [100] Idan, M., Johnson, M., Calise, A. J., and Kaneshige, J., “Intelligent Aerodynamic/Propulsion Flight Control for Flight Safety: A Nonlinear Adapti v e Approach, ” American Contr ol Confer ence V ol. 4, Arlington, V A, June 2001, pp. 2918-2923. [101] Calise, A. J., Ho v akimyan, N., and Idan, M., “ Adapti v e Output Feedback Control of Nonlinear Systems Using Neural Netw orks, ” A utomatica V ol. 37, No. 8, March 2001, pp. 1201-1211. [102] Calise, A. J., Lee, S., and Sharma, M., “De v elopment of a Recongurable Flight Control La w for the X-36 T ailless Fighter Aircraft, ” Guidance Navigation, and Contr ol Confer ence Den v er CO, August 2000, pp. 896-902. [103] W ise, K. A.,Brink er J. S., Calise, A. J, Enns, D. F ., Elgersma, M. R., and V oulgaris, P ., “Direct Adapti v e Recongurable Flight Control for a T ailless Adv anced Fighter Aircraft, ” International J ournal of Rob ust and Nonlinear Contr ol V ol. 9, No. 14, December 1999, pp. 999-1010. [104] Brink er J. S., and W ise, K. A., “Flight T esting of Recongurable Control La w on the X-36 T ailless Aircraft, ” J ournal of Guidance Contr ol and Dynamics V ol. 24, No. 5, September 2001, pp. 903-909. [105] Shtessel, Y B., and Buf ngton, J., “Multiple T ime Scale Flight Control Using Recongurable Sliding Modes, ” J ournal on Guidance Contr ol and Dynamics V ol. 22, No. 6, 1999, pp. 873-883. [106] Shtessel, Y ., Buf ngton, J., Banda, S., “T ailless Aircraft Flight Control Using Multiple T ime Scale Recongurable Sliding Modes, ” IEEE T r ansactions on Contr ol Systems T ec hnolo gy V ol. 10, No. 2, March 2002, pp. 288-296. [107] Shtessel, Y B., T ournes, C. C., “Inte grated Flight Control Problem on Decentralized Sliding Modes, ” Pr oceedings of the T wenty-Se venth Southeastern Symposium on System Theory Starkville, MS, March 1995, pp. 487-491. [108] Shk olnik o v I. A., and Shtessel, Y B., “T racking MIMO Nonlinear Nonminimum Phase Systems Using Dynamic Sliding Manifolds, ” J ournal of Guidance Contr ol and Dynamics V ol. 24, No. 3, June 2001, pp. 826-836.

PAGE 103

92 [109] Andry A. N., Shapiro, E. Y ., and Chung, J. C., “Eigenstructure Assignment for Linear Systems, ” IEEE T r ansactions on Aer ospace Electr onic Systems V ol. 19, No. 5, September 1983, pp. 711-728. [110] Da vidson, J. B., and Andrisani, D., “Lateral-Directional Eigen v ector Flying Qualities Guidelines for High Performance Aircraft, ” T ec hnical r eport N ASA, December 1996. [111] K onstantopoulos, I. K., and Antsaklis, P J., “Eigenstructure Assignment in Recongurable Control Systems, ” T ec hnical r eport : Inter disciplinary Studies of Intellig ent Systems January 1996. [112] Belkharraz, A. I., and Sobel, K., “F ault-T olerant Flight Control for a Class of Control Surf ace F ailures, ” Pr oceedings of the American Contr ol Confer ence V ol. 6, Chicago, IL, June 2000, pp. 4209-4213. [113] Zhang, Y ., and Jiang, J., “Inte grated Design of Recongurable F ault-T olerant Control Systems, ” J ournal of Guidance V ol. 24, No. 1, July 2000, pp. 133-136. [114] Bodson, M., and Groszkie wicz, J. E., “Multi v ariable Adapti v e Algorithms for Recongurable Flight Control, ” IEEE T r ansactions on Contr ol Systems T ec hnolo gy V ol. 5, No. 2, 1997, pp. 217-229. [115] Groszkie wicz, J. E., and Bodson, M., “Flight Control Reconguration Using Adapti v e Methods, ” Pr oceedings of the 34th Confer ence on Decision & Contr ol V ol. 2, Ne w Orleans, LA, December 1995, pp. 1159-1164. [116] Maciejo wski, J. M., “The Implicit Daisy-Chaining Property of Constrained Predicti v e Control, ” Applied Math and Computer Science V ol. 8, No. 4, 1998, pp. 695-711. [117] Huzmezan, M., and Maciejo wski, J. M., “Recongurable Flight Control of a High Incidence Research Model Using Predicti v e Control, ” UKA CC International Confr ence on Contr ol V ol. 2, Sw ansea, UK, September 1998, pp. 1169-1174. [118] Huzmezan, M., and Maciejo wski, J. M., “Reconguration and Scheduling in Flight Using Quasi-LPV High-Fidelity Models and MBPC Control, ” Pr oceedings of the American Contr ol Confer ence V ol. 6, Philadelphia, P A, June 1998, pp. 3649-3653. [119] Nelson, R. C., Flight Stability and A utomatic Contr ol McGra w Hill, Boston, MA, 1998. [120] Y echout, T R., Morris, S. L., Bossert, D. E., and Hallgren, W F ., Intr oduction to Air cr aft Flight Mec hanics American Institute of Aeronautics and Astronautics, Herndon, V A 2003.

PAGE 104

93 [121] Hagan, M. T ., Demuth, H. B., and Beale, M., Neur al Network Design PWS Publishing, Boston, MA, 1996. [122] Haykin, S., Neur al Networks: A Compr ehensive F oundation Prentice Hall, Ne w Y ork, NY 1999. [123] Cook, M. V ., Flight Dynamics Principles John W ile y & Sons Inc., Ne w Y ork, NY 1997. [124] Looze, D. P ., Krole wski, S., W eiss, J. L., Barrett, N. M., and Eterno, J. S., “ Automatic Control Design Procedures for Restructurable Aircraft Control” N ASA Contr actor Report January 1985. [125] W eiss, J. L.,Looze, D. P ., Eterno, J. S., and Grunber g, D. B., “Initial Design and Ev aluation of Automatic Restructurable Flight Control System Concepts” N ASA Contr actor Report June 1986.

PAGE 105

BIOGRAPHICAL SKETCH Robert Eick w as born in Long Beach, California. He attended Stanton Colle ge Preparatory High School in Jackson ville, Florida, where he recei v ed an International Baccalaureate diploma with a concentration in Renaissance art in May of 1998. Starting colle ge at the Uni v ersity of Florida the follo wing f all he recei v ed a Bachelor of Science in Aerospace Engineering with high honors in May of 2002. F ollo wing graduation he interned with John Burk en at N ASA Dryden Flight Research Center o v er the summer of 2002. He then started graduate school at the Uni v ersity of Florida under the supervision of Dr Rick Lind joining a dynamics, systems, and controls laboratory He is the recipient of the Brightfutures Scholarship (1998), the N ASA Under graduates Student Research Scholarship (2002), the Aerospace Engineering, Mechanics, and Engineering Science Best P aper A w ard (2002), the Uni v ersity of Florida Graduate Alumni Fello wship (2002), and the Mechanical and Aerospace Engineering Best Presentation A w ard (2003). He is a member of the AIAA. 94


Permanent Link: http://ufdc.ufl.edu/UFE0001265/00001

Material Information

Title: A Reconfiguration Scheme for Flight Control Adaptation to Fixed-Position Actuator Failures
Physical Description: Mixed Material
Copyright Date: 2008

Record Information

Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
System ID: UFE0001265:00001

Permanent Link: http://ufdc.ufl.edu/UFE0001265/00001

Material Information

Title: A Reconfiguration Scheme for Flight Control Adaptation to Fixed-Position Actuator Failures
Physical Description: Mixed Material
Copyright Date: 2008

Record Information

Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
System ID: UFE0001265:00001


This item has the following downloads:


Full Text











A RECONFIGURATION SCHEME FOR FLIGHT CONTROL ADAPTATION TO
FIXED-POSITION ACTUATOR FAILURES















By

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


2003

































Copyright 2003

by

Robert S. Eick















I dedicate this work to my family.















ACKNOWLEDGMENTS

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 . . . . . . . . . .

CHAPTER

1 INTRODUCTION ...............


Motivating Example.
Overview ......


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 . .


page

iv


. . . . . .









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

APPENDIX

A LINEARIZED MODEL OF THE F/A-18 . . . . 73

B NOMINAL CONTROLLER DESIGN . . . . . 76

REFEREN CE S . . . . . . . . . 83

BIOGRAPHICAL SKETCH ............................. ..94















LIST OF TABLES
Table page

4-1 F/A-18 Control Surface Position Limits . . . . 41

7-1 Stabilization Results . . . . . . . 62















LIST OF FIGURES
Figure

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 .. .............


page

S 3

S 4

S 5

S 9


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

By
Robert S. Eick

August 2003

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.















CHAPTER 1
INTRODUCTION

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

significant attention.

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

failure.

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 [1]. 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) [2]. 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) [3], 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) [6]. 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) [7], 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.

1.2 Overview

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







6

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.















CHAPTER 2
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 [8]. 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.

2.1 Introduction

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 [9].









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 [12] 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. [13] and Birdwell et al. [14] 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. [15]. 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

reconfiguration strategy.



















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. [34], 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 [35], Herrin [36], Bell [37], Hunt et al. [38], and Blanke

et al. [15] 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. [43] and Stengel [44] 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. [14] and Veilltette et al. [13], 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

[45] and Ochi and Kanai [46] pursued the use of feedback linearization and Gao

and Antsaklis [47] described the use of pseudo-inverse methods. Adaptive control

approaches using artificial neural networks are consider by Calise et al. [48], Idan et









al. [49], Johnson and Calise [50], and many others. While Huang and Stengel [51],

Morse and Ossman [52] and Jiang [53] 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 [54] 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 [53] 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 [56] 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

[62]. The combination of the FDI system and control reconfiguration is a complex

issue and one study by Srichander and Walker [63] 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.

2.2.7 Supervision

Different forms of selection logic and system management have been introduced

into fault-tolerant systems by various investigators including Rauch [64], Buckely [65],

Eryurek and Upadhyaya [66], and Polycarpou and Vemuri [67]. 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 [70] 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. [15] 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

design.

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
Control
Multiple I Feedback Predictive
Allocation
Models Linearization I I Control
U- L---_______-J L-_______ -- L_-_---- J

Propulsion
Controlled
Aircraft
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 [43].

Among those who have extend their work on robust control to deal with passive

fault-tolerance are Horowitz et al. [71] and Keating et al. [72] who used quantitative

feedback theory, and McFarlane and Glover [73] and Williams and Hyde [74] who

employed the frequency domain approach based on Ho-norm optimization. Nett et

al. [55], Tyler and Morari [56], and Murad et al. [57] 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

reconfiguration interval.

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 [51]. The latter involves

the calculation of new controller parameters in response to a control impairment, Gao

and Antsaklis [47] 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 [75]. Stengel [2] 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.

2.4.2.1 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 [88], Zhang and Jiang [89], and Maybeck [90]. In MMST Boskovic et al.

[76] 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 [91] and Munir and

Atherton [92] 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 [93] 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

control.

2.4.2.2 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 [96] and Durham and Bordignon [97] addressed the

problem of control allocation with magnitude and rate limits on the actuators, Davidson

et al. [98] develops a control allocation technique for the extremely over-actuated









Innovative Control Effector (ICE) aircraft and Zhenyu et al. [99] looks at restoring as

much of the performance of the original system as possible after a actuator failure.

2.4.2.3 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 [104] and Wise et al. [103] 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. [103] 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.

2.4.2.4 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.

2.4.2.5 Eigenstructure assignment (EA)

The concept of Eigenstructure Assignment (EA) was formally introduced by

Andry et al. [109]. 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 [110] 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 [111], Belkharraz and Sobel [112], and Zhang and

Jiang [113].

2.4.2.6 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 [114] and Groszkiewicz and Bodson

[115] 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.









2.4.2.7 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 [116] 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 [86], a multi-model

switching scheme as done by Boskovic and Mehra [76], 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.















CHAPTER 3
PRELIMINARIES

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) [123]. 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

vector.

3.1.1.1 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















b2V Vb3


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.

3.1.1.2 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.

3.1.1.3 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

u

VB v (3.1)

w

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 ,

etc.)

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

1w
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

0
-900 <0 < 900 (3.6)

-1800 < < 1800

The angular rotation rates are defined relative to the body axis system as,


P
OB = q (3.7)

r

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









transformations,

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

P
q (3.9)

r

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)
dt J

and the moment equation as

d (om)
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

X
F= y (3.12)

Z

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.

3.1.2.1 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

moment equations

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

equations

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


x=Ax+Bu (3.18)


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

xi (t)

X2(t)
x = state vector (n x 1) (3.20)


Xn (t)



























The matrices A, B, C




A=


ui(t)

u= input vector (p x 1)


Up (t)

yli(t)

y2(t)
y = output vector (q x 1)


yq(t)
are constant matrices and defined as follows


a12 .. aln





an2 nn


plant matrix (n x n)


bll bi2 bip

b21



bnl bn2 1.. bnp

C\\ C12 *...* Cln

C21


control matrix (n x p)


(3.24)


output matrix (q x n)


(3.25)


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.


(3.21)


(3.22)









(3.23)










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.

3.2.1.1 The Biological Neuron





Dendrites: Accept inputs


Soma: Process the inputs

Axon: Turn the processed inputs
into outputs

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

final result.

3.2.1.2 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.

3.2.2 Design

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.

3.2.2.1 Layers

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

generalization.









3.2.2.2 Learning

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

work.

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 [121]. 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.















CHAPTER 4
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

crew.

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 S if t > tf

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

occurred, w.









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

network.

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 -
lo
7:'$3 w=3.96'

o) 100


S50 -

no failure
Sw=1.72

50


-100
0 1 2 3 4 5 6 7 8 9 10
Time, (sec)

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

hardover position.

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

properly.














CHAPTER 5
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)) +
(5.1)
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
(5.2)
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

to satisfy

x(t) = fo (x(t),u(t)) + (t) +d
(5.3)
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

results when

fo (xn,n) +d = 0
(5.4)
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


y(t) =yd(t)


(5.9)









and

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

allowable perturbation,

XL (5.13)
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

final chapter.














CHAPTER 6
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

(6-1)







Klqr




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).


P Yd





Klqr


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


0.01w
Ww = --
s+0.01


(6.12)


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


(6.13)


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







52

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















CHAPTER 7
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.


, 880
c/i

860

S840

0 820

800
0
780
0 5 10 15 20



30
,25

-z 20

S15
10
5

0
5
0 5 10 15 20
Time, (sec)


Figure 7-1: Longitudinal


0 5 10
Time, (sec)


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

level.

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

maneuverability.


15 20














on
C)
-3




CS)
h





3-







0.


ci
&



a;


4


2


0


2

A


0.5








0.5



0.5


5 10 15 20 0
Time, (sec)


Figure 7-2: Lateral-directional responses:


5 10
Time, (sec)


healthy aircraft


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


unfailed case.


3 5 10 15 2(


0 5 10 15 20


5






0


15 20


.5






























'U

S0

-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

Time (sec)











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.

S880 6

860


0





S780 6
0 5 10 15 20 0 5 10 15 20


30 0.5

^ 20 :

S10
0 0

0 -
-10

20 0.5
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.


1



0.5



S 0
mS


5 10 15 20


100
80
S60
5 40
20

20


-40
0 5 10 15 20


0.5





0


5 10 15 20 0 5 10
Time, (sec) Time, (sec)


Figure 7-5: Lateral-directional responses: failed aircraft


15 20


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.















-10
-10 ----------------------------------------
0 2 4 6 8 10 12 14 16 18 20
10


-5 7 ^ -- --- ---- --- -- -
0 1 16 18 20
0
0 2 4 6 8 10 12 14 16 18 20
1







0
-5'

0 2 4 6 8 10 12 14 16 18 20




-0
0 2 4 6 8 10 12 14 16 18 20


10
Time (sec)


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

reconfiguration scheme.

7.4 Stabilization

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

Surface Results
681e, 1.740
81ef, 1.740
8tefi 3.990
8tefr -2.47
5aill -9.25
5ailr 3.470
8 tbi 1.18
8 tbr -0.850
8rudj 0.070
6rudr 0.070


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.









64



















0.5 30

20

S10
0 0


~, 10

S-20

0.5 -30
0 10 20 30 40 0 10 20 30 40



1 0.06

0.04

S0.5 -
0.02

^I 0
00
-0.02

-0.5 -0.04
0 10 20 30 40 0 10 20 30 40
Time, (sec) Time, (sec)


Figure 7-7: Lateral responses : LQR FTC





























S880

-860

S840

* 820

800

c 780

760
0 10 20 30 40



30


) 20


10 /


0


-10
0 10 20 30 40
Time, (sec)


0 10 20 30 40
Time, (sec)


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(


2
100 5 10 15 20 25 30 35 4(

10

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-- -


-5
0 5 10 15 20 25 30 35 4(
Time (sec)


Figure 7-9: Control surface deflections : LQR FTC


10

M 0

-10
10


0
H4


-U
,0
30


e

























































0 10 20
Time, (sec)


30 40


0 10 20
Time, (sec)


Figure 7-10: Lateral responses : Ho FTC


30 40




























880 8
0 6
S860
4
840 -
c 2
820
< \< o
800 0
-2
780 _4

760 6
0 10 20 30 40 0 10 20



30 0.5


o 20


o I !
t 10 0 I -

\ I
+ 0


10 0.5
0 10 20 30 40 0 10 20
Time, (sec) Time, (sec)


Figure 7-11: Longitudinal responses : Hc FTC


30 40


30 40
























10

t 0
-10
100 5

0 5


100 5
10


10--
0 5

0-
5 -----
m ,


Figure 7-12: Control surface deflections : Hc FTC


-2 1 I I I
0 5 10 15 20 25 30 35 40
Time (sec)















CHAPTER 8
CONCLUSIONS

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

all instances.

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

reconfiguration technology.







72

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.














APPENDIX A
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

right rudders.

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)
0 Alat

and

B= [B B2] (3)

with
-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
Alat= (5)
0.0098 0.0044 -0.3233 0

0 1.0000 0.0215 0











0.0259

0.3174

-0.0302

0

-0.0000

0.0000

0.0000

0


0.0259

0.3174

-0.0302

0

-0.0000

0.0000

0.0000

0


0.0111 -0.1304

-0.5699 -2.0319

-0.0252 -0.2560

0 0
B2=
0.0381 -0.2425

-0.3497 0.5134

0.0028 0.0034

0 0

The open-loop eigenvalues of the aircraft


Short Period:
Longitudinal
Phugoid:


Dutch Roll:

Spiral:

Roll:


-1.3921 4.0273j

-0.0076 0.0799j



0.3535 2.9485j

0.0014


6.8587


0.0097

-2.5367

0.0262

0

0

0.5317

-0.0066

0

-0.1304

-2.0319

-0.2560

0

0.2425

-0.5134

-0.0034

0


0.0097

-2.5367

0.0262

0

0

-0.5317

0.0066

0

0

0

-0.0005

0

0.5106

0.0765

-0.0465

0


0.0111

-0.5699

-0.0252

0

-0.0381

0.3497

-0.0028

0

0

0

-0.0005

0

0.5106

0.0765

-0.0465

0


are


Lateral















APPENDIX B
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

the form

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
1100000

0011000

0000001
0 0 1 0 0 0
0 0 0 0 0 0 1

1 -1 0 0 0 0 0
B "
Bmix
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
0000001

0000000


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)


where

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)

where

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
(15)
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.









Longitudinal Design


The longitudinal model is given by


-0.0209

-0.0377

0.0222

0.0

0.0086

0.1047

-0.9978

0


0.0482

-1.8386

-2.0562

0.0

0.0044

-1.1415

1.1789

0


-0.1834

8.5319

-0.9431

1.0

-0.0137

-0.2134

-2.6884

0


-0.3214

-0.0069

0.0

0.0


(17)


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

angle. Let


(18)


on =[ 0 0 0 1


so that


(19)


y = 0 = Clon

Then our new longitudinal system becomes


x A,,o 0 x Bion
=z= + u
xI Clon O xi 0


(20)


= Az+Bz


Aion







Blon


(21)










We then proceed to design an LQR controller for this augmented model. We used


Qlon

Rion


diag [0.0, 0.3,1.2,5.0,36.0]

diag[1.0, 1.0,0.6]


(22)


The result is


-0.0009

0.0033

-0.0010


0.0293

-0.1085

0.0303


-13.2190

24.7311

-18.2382


-54.4364

133.9899

-69.0431


-53.1336

116.7205

-70.0172


(23)


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

baseline controller.


5 10 15 20


0 5 10 15 20


7:$20


10


0

10 15 20 0 5 10
Time, (sec) Time, (sec)
Figure B-1: Nominal Longitudinal Responses


15 20


-0.2
0



0.2-



0-


-0.2
0


Klon -










Lateral Design


The lateral model is




Alat =







Blat =


given by

-0.3196

-3.4559

0.9842

0.0

0.000

0.000

-0.0000

0


0.1831

-6.9243

0.0044

1.0

0.0

23.9279

-0.2959

0


-8.6072

0.7349

-0.3233

0.0215

-0.0172

15.7358

-0.1255

0


0.3214

0.0

0.0

0.0

-0.0255

5.3908

0.0360

0


0.1532

2.2956

-1.3954

0


(24)


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


so that
v
y= CiatX


Then our new lateral system becomes


S Alat 0 x Blat
=z= + u
I Clat 0 X 0


(26)


(27)









or

S=Az+Bz (28)

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]
(29)
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

baseline controller.


























400
on
3300

-5200

o 100
-<-
'


0 5 10 15 20


0 5 10
Time, (sec)


0 5 10 15 20
0 5 10 15 20


S300

t200

100

0


15 20


0 5 10
Time, (sec)


15 20


Figure B-2: Nominal Lateral Responses















REFERENCES


[1] Burken, J. J., Lu, P., Wu, Z., and Bahm, C., "Two Reconfigurable Flight-Control
Design Methods: Robust Servomechanism and Control Allocation" Journal of
Guidance, Control, and Dynamics, Vol. 24, No. 3, 2001, pp. 482-493.

[2] Stengel, R. F., "Intelligent Failure-Tolerant Control," Proceedings of the 5th
IEEE International Symposium on Intelligent Control, Vol. 1, Philadelphia, PA,
1990, pp. 548-557.

[3] American Airlines A300-600, "An Airbus A300 of Ameri-
can Airlines on final approach to London Heathrow Airport,"
http://home.wanadoo.nl/airruud/a300aa.htm (visited July 10, 2003).

[4] American Airlines Flight 587 Belle Harbor, New York, "Investigation Informa-
tion," March 2003, http://www.ntsb.gov/events/2001/AA587/default.htm (visited
July 10, 2003).

[5] American Airlines Flight 587 Belle Harbor, New York, "Amer-
ican Airlines Flight 587 crashes in NYC," November 2002,
http://www.cnn.com/2001/US/ 1/12/AA587.facts/ (visited July 10, 2003).

[6] American Airlines Flight 587 Belle Harbor, New York, "Flight 587 Crashes,"
October 2002, www.september11 news.com/ Nov 2Flight587AerialFire.jpg
(visited July 10, 2003).

[7] American Airlines Flight 587 Belle Harbor, New York, "Feds rule out sabotage
in N.Y crash," October 2002, www.cnn.com/2002/US/South/10/29/flight.587/
(visited July 10, 2003).

[8] Eslinger, R. A., and Chandler, P. R., "Self-Repairing Control System Program
Overview," Proceedings of the IEEE National Aerospace and Electronics
Conference, Vol. 2, Dayton, OH, 1988, pp. 504-511.

[9] Patton, R. J., "Fault-Tolerant Control: The 1997 Situation," Proceedings ofIFAC
Symposium on Fault Detection, Supervision and Safety for Technical Processes :
SAFEPROCESS'97, University of Hull, UK, 1998, pp. 1033-1055.

[10] Bajpai, G., and Chang, B. C., "Decoupling of Failed Actuators in Flight Control
Systems," Proceedings of American Control Conference, Arlington, VA, 2001,
pp. 1836-1840.









[11] Bajpai, G., Chang, B. C., and Lau, A., "Reconfiguration of Flight Control
Systems for Actuator failures," IEEE Aerospace and Electronics Systems
Magazine, Vol. 16, No. 9, 2001, pp. 29-33.

[12] Owen, D. H., Feedback and Multivariable Systems, Peter Peregrinus, Stevenage,
England, 1978.

[13] Veilltette, R. J., Medanic, J. B., and Perkins, W. R., "Design of Reliable Control
Systems," IEEE Transactions on Automatic Control, Vol. 37, No. 3, 1992, pp.
290-304.

[14] Birdwell, J. D., Castanon, D. A., and Athans, M., "On Reliable Control System
Designs," IEEE Transactions on Systems, Man, and Cybernetics, Vol. SMC-16,
No. 5, 1986, pp. 703-711.

[15] Blanke, M., Izadi-Zamanabadi, R., Bogh, S. A., and Lunau, C. P., "Fault Tol-
erant Control Systems : A Holistic View," Department of Control Engineering,
R-1997-4175, Aalborg University, Denmark, March 1997.

[16] Willsky, A. S., "A Survey of Design Methods for Failure Detection in Dynamic
Systems," Automatica, Vol. 12, No. 6, 1976, pp. 601-611.

[17] Mironovski, L. A., "Functional Diagnosis of Dynamic Systems : A Survey,"
Automation and Remote Control, Vol. 41, 1980, pp. 1122-1143.

[18] Isermann, R., "Process Fault Detection Based on Modeling and Estimation
Methods : A Survey," Automatica, Vol. 20, No.4, 1984, pp. 387-304.

[19] Milne, R., "Strategies for Diagnosis," IEEE Transactions on Systems, Man, and
Cybernetics, Vol. SMC-17, No. 3, 1987, pp. 333-339.

[20] Gertler, J., "Survey of Model-Based Failure Detection and Isolation in Complex
Plants," IEEE Control Systems Magazine, December 1998, pp. 3-11.

[21] Frank, P. M., "Fault Diagnosis in Dynamic System Using Analytical and
Knowledge Based Redundancy," Automatica, Vol. 26, No. 3, 1990, pp. 459-474.

[22] Patton, R. J. and Chen, J., "Robust Fault Detection Using Eigenstructure
Assignment : A Tutorial Consideration and Some New Results," Proceedings
of the 30th IEEE Conference on Decision and Control, Brighton, UK, 1991, pp.
2242-2247.

[23] Leitch, R. R., and Quek, H. C., "An Architecture for Integrated Process
Supervision," IEEE Proceedings Control Theory and Applications, Vol. 139, No.
3, 1992, pp. 317-327.

[24] Patton, R. J., "Fault Detection and Diagnosis in Aerospace Systems Using
Analytical Redundancy," Computing and Control Engineering Journal, Vol. 2,
No. 3, 1991, pp. 127-136.









[25] De Persis, C., and Isidori, A., "A Geometric Approach to Nonlinear Fault
Detection and Isolation," IEEE Transactions on Automatic Control, Vol. 46, No.
6, 2001, pp. 853-865.

[26] Frank, P. M., "On-line Fault Detection in Uncertain Nonlinear Systems Using
Diagnostic Observers : A Survey," International Journal of Systems Science,
Vol. 25, No. 12, 1994, pp. 2129-2154.

[27] Patton, R. J., Frank, P. M., and Clark, R. N., Fault Diagnosis in Dynamic
Systems, Theory and Applications, Prentice Hall, New York, NY, 1989.

[28] Frank, P. M., "Application of Fuzzy Logic to Process Supervision and Fault
Diagnosis," Proceedings of the IFAC/IMACS Symposium on Fault Detection,
Supervision and Safety for Technical Processes : SAFEPROCESS'94, Helsinki,
Finland, June 13-16, 1994, pp. 531-538.

[29] Isermann, R., "Integration of Fault Detection and Diagnosis Methods," Proceed-
ings of the IFAC/IMACS Symposium on Fault Detection, Supervision and Safety
for Technical Processes : SAFEPROCESS'94, Helsinki, Finland, June 13-16,
1994, pp. 597-612.

[30] Krishnasaami, V, and Rizzoni, G., "Nonlinear Parity Equation Residual
Generation for Fault Detection and Isolation," Proceedings of the IFAC/IMACS
Symposium on Fault Detection, Supervision and Safety for Technical Processes :
SAFEPROCESS'94, Helsinki, Finland, June 13-16, 1994, pp. 305-310.

[31] Patton, R. J., Chen, J., and Nielsen, S. B., "Model-Based Methods for Fault
Diagnosis : Some Guide-Lines," Transactions of The Institute of Measurement
and Control, Vol. 17, No. 2, 1995, pp. 73-83.

[32] Isermann, R., and Balle, P., "Trends in the Application of Model Based Fault
Detection and Diagnosis of Technical Processes," Proceedings of the 13th IFAC
World Congress, Vol. N, San Francisco, USA, June 30 July 5, 1996, pp. 1-12.

[33] Basseville, M., and Benveniste, A., "Detection of Abrupt Changes in Signals and
Dynamical Systems," Lecture Notes in Control and Information Sciences, Vol.
77, Springer-Verlag, New York, NY, December 1985.

[34] Barron, R. L., Cellucci, R. L., Jordan, P. R., and Beam, N. E., "Application
of Polynominal Neural Networks to FDIE and Reconfigurable Flight Control,"
Proceedings of the IEEE National Aerospace and Electronics Conference, Vol. 2,
Dayton, OH, May 1990, pp. 507-519.

[35] Legg, J. M., "Computerized Approach for Matrix-Form FMEA," IEEE
Transactions on Reliability, Vol. R-27, No. 1, October 1978, pp. 154-157.

[36] Herrin, S. A., "Maintainability Applications Using the Matrix FMEA Tech-
nique," IEEE Transactions on Reliability, Vol. 30, No. 3, 1981, pp. 212-217.









[37] Bell, A. R., "Managing Murphy's Law: Engineering a Minimum-Risk System,"
IEEE Spectrum, June 1989, pp. 24-26.

[38] Hunt, J. E., Pugh, D. R., and Price, C. J., "Failure Mode Effects Analysis: A
Practical Application of Functional Modeling," Applied Artificial Intelligence,
Vol. 9, No. 1, 1995, pp. 33-44.

[39] Savonov, M. G., Stability and Robustness of Multivariable Feedback Systems,
MIT Press, Cambridge, MA, 1980.

[40] Morari M., and Zafirou, E., Robust Process Control, Prentice Hall, Englewood
Cliffs, NJ, 1989.

[41] Maciejowski, J. M., Multivariable Feedback Design, Addison Wesley, Reading,
MA, 1989.

[42] Zhou, K., Doyle, J., and Glover, K., Robust and Optimal Control, Prentice Hall,
Upper Saddle River, NJ, 1996.

[43] Eterno, J. S., Weiss, J. L., Looze, D. P., and Willsky, A., "Design Issues for
Fault Tolerant-Restructurable Aircraft Control," Proceedings of the IEEE 24th
Conference on Decision & Control, Vol. 2, Fort Lauderdale, FL, 1985, pp.
900-905.

[44] Stengel, R. F., "Intelligent Failure-Tolerant Control," IEEE Control System
Magazine, Vol. 11, No. 4, 1991, pp. 14-23.

[45] Lane, S. H., and Stengel, R. F., "Flight Control Design Using Non-Linear
Inverse Dynamics," Automatica, Vol. 24, No. 4, 1988, pp. 471-483.

[46] Ochi, Y, and Kanai, K., "Design of Restructurable Flight Control Systems Using
Feedback Linearization," Jounrnal of Guidance, Control, and Dynamics, Vol. 14,
No. 5, 1991, pp. 903-911.

[47] Gao, Z., and Antsaklis, P. J., "Stability of the Pseudo-Inverse Method for
Reconfigurable Control Systems," International Journal of Control, Vol. 53, No.
3, 1991, pp. 717-729.

[48] Calise, A. J., Lee, S., and Sharma, M., "Direct Adaptive Reconfigurable Control
of a Tailless Fighter Aircraft," Guidance, Navigation and Control Conference,
Boston, MA, August 1998, pp. 88-97.

[49] Idan, M., Johnson, M., and Calise, A. J., "A Hierarchical Approach to Adaptive
Control for Improved Flight Saftey," Journal on Guidance, Control and
Dynamics, July 2001, pp. 1012-1023.

[50] Johnson, E. N., and Calise, A. J., "Neural Network Adaptive Control of Systems
with Input Saturation," Proceedings of the American Control Conference, Vol. 5,
Arlington, VA, June 2001, pp. 3527-3532.









[51] Huang, C. Y, and Stengel, R. F, "Restructurable Control Using Proportional-
Integral Implicit Model Following," Jorunal of Guidance, Control, and Dynam-
ics, Vol. 13, No. 2, 1990, pp. 303-309.

[52] Morse, W. E., and Ossman, K. A., "Model Following Reconfigurable Flight
Control System for the AFTI/F-16," Journal of Guidance, Control, and
Dynamics, Vol. 13, No. 6, 1990, pp. 969-976

[53] Jiang, J., "Design of Reconfigurable Control Systems Using Eigenstructure
Assignments," Internation Journal of Control, Vol. 59, No. 2, 1994, pp. 395-410.

[54] Wu, N. E., "Robust Feedback Design with Optimized Diagnostic Performance,"
IEEE Transactions on Automatic Control, Vol. 42, No. 9, 1997, pp. 1264-1268.

[55] Nett, C. N., Jacobson, C. A., and Miller, A. T., "An Integrated Approach to
Controls and Diagnostics : The 4-Parameter Controller," Proceedings of the
1988 American Control Conference, Atlanta, USA, 1988, pp. 824-835.

[56] Tyler, M. L., and Morari, M., "Optimal and Robust Design of Integrated
Control and Diagnostic Modules," Proceedings of the 1994 American Control
Conference, Baltimore, MD, June 1994, pp. 2060-2064.

[57] Murad, G. A., Postlethwaite, I., and Gu, D. W., "A Robust Design Approach
to Integrated Controls and Diagnostics," Proceedings of the 13th IFAC World
Congress, Vol. N, San Francisco, CA, USA, 1996, pp. 199-204.

[58] Akesson, M., "Integrated Control and Fault-Detection for a Mechanical Servo
Process," Proceedings of the IFAC Symposium on Fault Detection, Supervision
and Safety for Technical Processes SAFEPROCESS'97, Hull, England, August
1997, pp. 1252-1257.

[59] Eich, J., and Sattler, B., "Fault Tolerant Control System Design Using Robust
Control Techniques," IFAC Safeprocess, University of Hull, UK, 1997, pp.
1246-1251.

[60] Chiang, C. Y, and Youssef, H. M., "Neural Network and Fuzzy Logic Approach
to Aircraft Reconfigurable Control Design," Proceedings of the American
Control Conference, Vol. 5, Seattle, WA, June 1995, pp. 3505-3509.

[61] Patton, R. J., and Chen, J., "Robust Fault Detection and Isolation (FDI)
Systems," Control and Dynamic Systems, Vol. 74, 1996, pp. 171-224.

[62] Mariton, M., "Detection Delays, False Alarm Rates and Reconfiguration of
Control Systems," International Journal of Control, Vol. 49, 1989, pp. 981-992.

[63] Srichander, R., and Walker, B. K., "Stochastic Stability Analysis for Continuous
Time Fault Tolerant Control Systems," International Journal of Control, Vol. 57,
No. 2, 1993, pp. 433-452.









[64] Rauch, H., "Autonomous Control Reconfiguration," IEEE Control Systems
Magazine, Vol. 15, No. 6, 1995, pp.37-48.

[65] Buckley, A. P., "Hubble Space Telescope Pointing Control System Design
Improvement Study Results," IEEE Control Systems Magazine, Vol. 15, No. 2,
1995, pp. 34-42.

[66] Eryurek, E., and Upadhyaya, B. R., "Fault-Tolerant Control and Diagnostic for
Large-Scale Systems," IEEE Control Systems Magzaine, Vol. 15, No. 5, 1995,
pp. 34-42.

[67] Polycarpou, M. M., and Vemuri, A. T., "Learning Methodology for Failure
Detection and Accomodation," Control Systems Magazine, Special Issue on
Intelligent Learning Control, Vol. 15, 1995, pp. 16-24.

[68] Kwong, W. A., Passino, K. M., Laukonen, E .G., Yurkovich, S., "Expert
Supervision of Fuzzy Learning Systems with Applications to Reconfigurable
Control for Aircraft," Proceedings of the 33rd IEEE Conference on Decision and
Control, Vol. 4, Lake Buena Vista, FL, December 1994, pp. 4116-4121.

[69] Kwong, W. A., Passino, K. M., Laukonen, E. G., Yurkovich, S., "Expert
Supervision of Fuzzy Learning Systems for Fault-Tolerant Aircraft Control,"
Proceedings of the IEEE, Vol. 83, No. 3, March 1995, pp. 466-483.

[70] Fierro, R., Lewis, F. L., "A framework for hybrid control design," Transactions
on Systems, Man and Cybernetics, Vol. 27, No. 6, November 1997, pp. 765-773.

[71] Horowitz, I., Arnold, P. B., and Houpis, C. H., "Flight Control System Recon-
figuration Design Using Quantitative Feedback Theory," Proceedings of the
National Aerospace & Electronics Conference, Dayton, OH, May 1985, pp.
578-585.

[72] Keating, M. S., Pachter, M., and Houpis, C. H., "QFT Applied to Fault-
Tolerant Flight Control System Design," Proceedings of the American Controls
Conference, Seattle, WA, June 1995, pp. 184-188.

[73] McFarlane, D. C., and Glover, K., "Robust Controller Design using Normalised
Coprime Factor Plant Descriptions," Lecture Notes in Control and Information
Sciences, Vol. 138, Springer Verlag, Berlin, Germany, 1989.

[74] Williams, S., and Hyde, R. A., "A Comparision of Characteristic Locus and H,
Design Methods for VSTOL Flight Control System Design," Proceedings of
American Controls Conderence, San Diego, CA, May 1990, pp. 2508-2513.

[75] Passino, K. M., and Antsaklis, P. J., "On Inverse Stable Sampled Low Pass
Systems," International Journal of Control, Vol. 47, No. 6, June 1988, pp.
1905-1913.









[76] Boskovic, J. D., and Mehra, R. K., "A Multiple Model-Based Reconfigurable
Flight Control System Design," Proceedings on the 37th IEEE Conference on
Decision & Control, Vol. 4, Tampa, FL, December 1998, pp. 4503-4508.

[77] Gopinathan, M., Boskovic, J. D., Mehra, R. K., and Rago, C., "A Multiple
Model Predictive Scheme for Fault-Tolerant Flight Control Design," Proceedings
of the 37th IEEE Conference on Decision & Control, Vol. 2, Tampa, FL,
December 1998, pp. 1376-1381.

[78] Boskovic, J. D., and Mehra, R. K., "Stable Multiple Model Adaptive Flight
Control for Accommodation of a Large Class of Control Effector Failures,"
Proceedings of the American Control Conference, Vol. 3, San Diego, CA, June
1999, pp. 1920-1924.

[79] Boskovic, J. D., Li, S. M., and Mehra, R. K., "Reconfigurable Flight Control
Design Using Multiple Switching Controllers and On-Line Estimation of
Damage Related Parameters," Proceedings of the 2000 IEEE International
Conference on Control Applications, Anchorage, AK, September 2000, pp.
479-484.

[80] Boskovic, J.D., Li, S. M., and Mehra, R. K., "Study of an Adaptive Recon-
figurable Control Scheme for Tailless Advanced Fighter Aircraft (TAFA) in
the Presence of Wing Damage," Proceedings of the Position, Location, and
Navigation Symposium, San Diego, CA, March 2000, pp. 341-348.

[81] Boskovic, J.D., Li, S. M., and Mehra, R. K., "Robust Supervisory Fault-Tolerant
Flight Control System," Proceedings of the American Control Conference, Vol.
3, Arlington, VA, June 2001, pp. 1815-1820.

[82] Boskovic, J. D., and Mehra, R. K., "A decentralized scheme for accommodation
of multiple simultaneous actuator failures," Proceedings of the American Control
Conference, Vol. 6, May 2002, pp. 5098-5103.

[83] Boskovic, J. D., and Mehra, R. K., "Multiple model-based adaptive reconfig-
urable formation flight control design," Proceedings of the 41st IEEE Conference
on Decision and Control, Vol. 2, December 2002, pp. 1263-1268.

[84] Boskovic, J. D., and Mehra, R. K., "Fault accommodation using model
predictive methods," Proceedings of the American Control Conference, Vol. 6,
May 2002, pp. 5104-5109.

[85] Kanev, S., and Verhaegen, M., "A Bank of Reconfigurable LQG Controllers for
Linear Systems Subjected to Failures," Proceedings of the 39th IEEE Conference
on Decision and Control, Vol. 4, Sydney, NSW, Australia, December 2000, pp.
3684-3689.

[86] Kanev, S., and Verhaegen, M., "Controller Reconfiguration for Non-Linear
Systems," Control Engineering Practice, Vol. 8, October 2000, pp. 1223-1235.