DEVELOPMENT OF A NEUROFUZZY CONTROL SYSTEM FOR THE GUIDANCE OF AIR TO AIR MISSILES (Master Thesis)

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DEVELOPMENT OF A NEUROFUZZY CONTROL SYSTEM FOR
THE GUIDANCE OF AIR TO AIR MISSILES
By
Eng. Ahmed Momtaz Ahmed
A Thesis submitted to
The Faculty of Engineering, Cairo University
In partial fulfillment of the degree of
MASTER OF SCIENCE
in
Mechanical Design and Production
Under the Supervision of
Prof. Galal A. Hassaan
Professor of System Dynamics
Dr. Yasser F. Zeyada
Assistant Professor of System Dynamics
Department of Mechanical Design and Production
Faculty of Engineering, Cairo University
Giza, Egypt
2004

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ACKNOWLEDGEMENT
The author would like to acknowledge with great thanks Prof. Galal A. Hassaan,
Department of Mechanical Design and Production, Cairo University, for his supervision,
sincere help and valuable advice.
The author would like also to thank Dr. Yasser F. Zeyada, for the great efforts he
offered to prepare this thesis.
Thanks also to the staff members of the Department of Mechanical Design and Production,
Cairo University who offered their help and support.

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SUMMARY
Recently, neurofuzzy modeling techniques have been successfully applied to modeling
complex systems, where traditional approaches hardly can reach satisfactory results due
to lack of sufficient domain knowledge. Much research has been done on applications of
neural networks (NNs) for identification and control of dynamic systems. According to
their structures, the NNs can be mainly classified as feedforward neural networks and
recurrent neural networks. It is well known that a feedforward neural network is
capable of approximating any continuous functions closely. However, the feedforward
neural network is a static mapping. Without the aid of tapped delays the feedforward
neural network is unable to represent a dynamic mapping. Although much research has
used the feedfoward neural network with tapped delays to deal with dynamical problem,
the feedforward neural network requires a large number of neurons to represent a
dynamic response in the time domain. Moreover, the weight updates of the feedforward
neural network do not utilize the internal information of the neural network and the
function approximation is sensitive to the training data. On the other hand, recurrent
neural networks (RNNs) have superior capabilities than the feedforward neural
networks, such as dynamic and ability to store information for later use. Since recurrent
neuron has an internal feedback loop, the RNN is a dynamic mapping and demonstrates
good control performance in the presence of uncertainties, which is usually composed of
unpredictable plant parameter variations, external force disturbance, unmodeled and
nonlinear dynamics, in practical application of air-to-air missile.
In recent years, the concept of incorporating fuzzy logic into a neural network has been
grown into a popular research topic. In contrast to the pure neural network or fuzzy
system, the fuzzy neural network (FNN) possesses both their advantages. It combines the
capability of fuzzy reasoning in handling uncertain information and the capability of
artificial neural networks in learning from processes. In missiles controlling branch it is
needed to minimize the output performance errors until fulfilling the required
specifications such as the minimum locking time and the maximum fuse distance.
Nowadays we have different types of missiles using different types of control strategy

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some of them uses reference frame unit as they controlled by a remote base or an
aircraft. Consequently controlling such missiles by reference angles  ,, with respect
to fixed frame, other type of control strategy doesn’t use reference frame unit (fire and
forget types) such as all heatseeking, active radar missiles. In this paper, both types of
control strategy are discussed. A technique for the preliminary design of a control
system is presented using neurofuzzy systems for a diverse data range of a highly
nonlinear MIMO 5 DOF model (multi-input multi-output 5 degree of freedom AIM 9R
air to air missile). This system is composed of 3-body axes velocities and rotating in both
pitch and yaw direction only as the rolling motion is prevented due to gyroscopic
stabilizers (anti roll system) attached at the rear fins. The model has cross coupling
effects between the longitudinal and lateral motions due to the coupled equations of
motion. MIMO model was divided into two separated SISO models (single-input single-
output) taking into consideration the nonlinear cross coupling effects, then generating
the neural network controller for each separated SISO model (single-input single-output
model), blending the output performance using a 25 rule base Mamdani type fuzzy logic
controller. A Mamdani fuzzy logic controller can deal with the system uncertainty due
to cross coupling effect and affecting gust in the whole system when instantaneously
applying both inputs to the model. The main goal is to fulfill certain specifications within
its limited ranges such as proximity fuse distance and the target locking time during the
whole mission of the missile consequently keeping the error between actual and desired
performance according these tolerances. The first obvious error is due to the AOA
(angle of attack of the missile) and SSA (side slipping angle), resulting in error in the
desired trajectory itself as the (camera) detector is attached to the body frontal area of
the missile that is inclined to the actual body velocity vector. A second error is due to the
error between the desired and actual trajectory of the missile and this is actually due to
the whole system performance (AIM_9R dynamic model and controllers). To minimize
the second error over different regimes of flight, a hierarchical design of multi NN
controllers using a TSK(Takagi Suguno Kang) fuzzy fusion system classifier is
recommended which compute the weight of each controller according to the flight
regime parameters such as (altitude, velocity, required track rate [target-seeker
distance]). Fortunately both types of performance errors are damping each other to
some extent, this will lead to minimize the net output error of the actual performance.

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The model was established and simulated through (MATLAB-SIMULINK), and the
final performance was examined using FLC fuzzy logic controllers with and without
NNC neural network controllers.

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LIST OF CONTENTS
ACKNOWLEDGMENT i
SUMMARY ii
LIST OF CONTENTS vi
ABBREVIATIONS viii
NOMENCLATURE ix
LIST OF FIGURES xi
LIST OF TABLES xv
Chapter 1 GENERAL BACKGROUND ON AIR TO AIR
MISSILES
1.1 Historical Background 1
1.2 Overview 8
1.3 AIM Missiles 13
Chapter 2 LITERATURE REVIEW
2.1 Introduction 32
2.2 Conventional Guidance and Control Design 34
2.3 Neural Net-based Guidance and Control Design 37
2.4 Fuzzy Logic-Based Guidance and Control Design 43
2.5 Gain-Scheduling Guidance and Control Design 49
2.6 Guidance Laws 53
2.7 Advantages over conventional designs 55
2.8 Problem Formulation 56
2.9 Previous Work 56
2.10 Thesis Layout 56

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Chapter 3 MODELING OF AIR TO AIR MISSILE
3.1 Introduction 58
3.2 The Rigid –Body Equations 58
3.3 Evaluation of the Angular Momentum 61
3.4 Euler’s Equations of Motion 62
3.5 Orientation and Position of the Missile 63
3.6 The Flight Path Determination 65
3.7 The Orientation of the Missile 66
3.8 The Applied Forces 68
3.9 AIM 9R Model Characteristics 73
3.9.1 Model verification 73
3.9.2 Cross effect representation 74
3.9.3 Gust effect 75
3.10 Summary 76
Chapter 4 NEURAL NETWORK FOR MISSILE GUIDANCE
4.1 Introduction 77
4.2 Theory and Examples 80
4.2.1 Single-input neuron 80
4.2.2 Multiple-input neuron 80
4.2.3 A layer of neurons 81
4.2.4 Multiple layer of neurons 82
4.3 Neural Network Controllers 83

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4.3.1 Control with inverse models 83
4.3.2 Control by feedfoward models 86
4.3.3 Control by feedback linearization 87
4.4 Summary 91
Chapter 5 MISSILE GUIDANCE USING FUZZY LOGIC
CONTROL
5.1 Introduction 92
5.2 Applying Fuzzy Inference System for Control 92
5.2.1 Designing membership functions (Fuzzification process) 93
5.2.2 Rule derivation 95
4.2.3 Fu 5.2.3 Fuzzy rule-based inference 97
5.2.4 Response pattern of a simple generic fuzzy control system 100
5.3 Fuzzy Logic Control Application 102
5.4 Comparison between Different Fuzzy Logic Controllers and PD Controller 103
5.5 Low pass Filter 104
5.6 The Effect of Using Neural Network in the First Time Period 106
5.7 Fuzzy Logic Controller Output Signal 107
5.8 Neurofuzzy Structure 107
5.9 The Effect of Flight Regimes on Neurofuzzy Controller Performance 108
5.10 Composite Fuzzy Guidance Law 108
5.11 Summary 120
Chapter 6 A HYBRID NEUROFUZZY CONTROL SYSTEM FOR
MISSILE GUIDANCE

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6.1 Introduction 121
6.2 Methodology 122
Chapter 7 DISCUSSIONS AND CONCLUSIONS
7.1 Discussions 128
7.2 Conclusions 130
7.3 Recommendation for Future Work 131
References 132
Appendix A Simulink models

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ABBREVIATIONS
AAM Air to Air Missile
AFD Arm/Fire Device
AGM Air to Ground Missile
AIM Air Intercept Missile
AOA Angle of Attack
ASM Air to Surface Missile
CLOS Command to Line of Sight
DOF Degree Of Freedom
DSMAC Digital Scene Matching Area Correlation
F.O.R Frame Of Reference (at earth)
FLC Fuzzy Logic Controller
FNN Fuzzy Neural Network
GBU Ground Bomb Unit
GPS Global Positioning System
IR Infra Red
MIMO Multi Input Multi Output
NNC Neural Network Controller
OOLD Out-Of-Line Device
RF Radio Frequency
RNN Recurrent Neural Network
SISO Single Input Single Output
SSA Side Slipping Angle
TASM Tactical Air to Surface Missile
TDD Target Detection Device
TERCOM Inertial and Terrain Contour Matching
TIVS Thermally Initiated Venting System
TSK Tagaki Suguno Kang
USAF United States Air Force
WGU Wing Ground Unit

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NOMENCLATURE
ac Acceleration vector of missile mass center (m/s2)
(acx, acy, acz) Scalar components of ac in X, Y, Z directions respectively (m/s2)
A, B, C Moments of inertia about (x, y, z) axes respectively (kg/m2)
CL Lift coefficient
CD Drag coefficient
CN Side force coefficient
Cm Pitching moment coefficient
Cn Yawing moment coefficient
D Product of inertia yz (kg/m2)
E Product of inertia xz (kg/m2)
J Product of inertia xy (kg/m2)
ea, ee, er Mass eccentricities of control surfaces (m)
F Resultant external force vector (N)
(Fx,Fy,Fz) Scalar components of F in X, Y, Z directions respectively (N)
(Fa, Fe, Fr) Generalized control forces for aileron, elevator and rudder deflection
respectively (N)
f Generalized force in Lagrange’s equation (N)
G Resultant external moment vector (N.m)
h Angular momentum vector of the missile (kg.m2/s)
h’ Angular momentum vector of spinning rotor inside the missile (kg.m2/s)
hx, hy, hz Scalar components of h in X, Y, Z directions respectively (kg.m2/s)
h'x, h’y, h’z Scalar components of h’ in X, Y, Z directions respectively (kg.m2/s)
Ha, He, Hr Hinge moments on aileron, elevator and rudder respectively (N.m)
Ia, Ie, Ir Effective moments of inertia of control systems (kg/m2)
L, M, N Scalar components of G (N.m)
ma, me, mr Masses of aileron, elevator and rudder respectively (kg)
P, Q, R Scalar components of ω (rad/s)

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Sw Wing surface area (m2)
Vc Absolute velocity of the missile (m/s)
U, V, O Scalar components of Vc in X, Y, Z direction (m/s)
X, Y, Z Missile body axes components in X, Y, Z directions respectively
x’, y’, z’ Fixed frame of reference axes components in X, Y, Z directions respectively
α Angle of attack (rad)
β Side angle (rad)
δa, δe, δr Deflection angles of aileron, elevator and rudder respectively (rad)
ρ Air density (kg/m3)
Ψ, Θ, Φ Euler equation angles (rad)
ω Absolute angular velocity of the missile (rad/s)

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LIST OF FIGURES
Fig. (1.1) Henschel Hs 293 air-to-ship, wireless guided, gliding bomb A 1
Fig. (1.2) Henschel Hs 293 air-to-ship television guided gliding bomb A 2
Fig (1.3) The Ruhrstahl SD 1400 'Fritz X' air-to-ship, wireless guided 6
Fig. (1.4) The Ruhrstahl SD 1400 'Fritz X' air-to-ship, wireless guided 7
Fig. (1.5) Types of ASM missiles 9
Fig. (1.6) Russian AAM 10
Fig. (1.7) TERCOM, DSMAC missiles guidance technique 11
Fig. (1.8) Tomahawk missile 13
Fig. (1.9) Chinese nuclear missiles DONG FENG/JULANG SERIES 13
Fig. (1.10) Missile components 14
Fig. (1.11) Active homing system 15
Fig. (1.12) Semiactive homing system 16
Fig. (1.13) Comparison between AIM 7 and AIM 120 guidance technique 23
Fig. (1.14) AIM 7 air to air missile 26
Fig. (2.1) Supervisory control scheme 38
Fig. (2.2) Hybrid control scheme 39
Fig. (2.3) Model reference control scheme 40
Fig. (2.4) Internal model control scheme 41
Fig. (2.5) Adaptive control scheme 41
Fig. (2.6) Predictive control scheme 42
Fig. (2.7) Model reference control of coupled lateral dynamics 43
Fig. (2.8) Fuzzy PD controller 45
Fig. (2.9) Typical adaptive fuzzy control scheme 46
Fig. (2.10) Fuzzy sliding mode control scheme 46
Fig. (2.11) Fuzzy model-following control scheme 47
Fig. (2.13) A fuzzy terminal guidance system 49
Fig. (2.14) Conventional gain-scheduling control scheme 50
Fig. (2.15) Fuzzy gain-scheduling control scheme 51

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Fig. (2.16) Neural network gain-scheduling PID control scheme 52
Fig. (2.17) Neural-fuzzy gain-scheduling control scheme 53
Fig. (2.18) Integrated control model for the guidance of AIM 9R missile 57
Fig. (3.1) Missile body axes 58
Fig. (3.2) Missile orientation 64
Fig. (3.3) The applied forces 67
Fig. (3.4) Missile model algorithm 71
Fig. (3.5) AIM 9 Nonlinear Model 72
Fig. (3.6) Pitch angle step response for 5 DOF and 3 DOF models 73
Fig. (3.7) Pitch angle dynamic response for 3D, 2D models 73
Fig. (3.8) Cross coupling effect (yawpitch) 74
Fig. (3.9) Mean value of cross coupling effect versus input frequencies 74
Fig. (3.10) Standard deviation of cross coupling effect 75
Fig. (3.11) Gust effect (pitch yaw) 75
Fig. (4.1) Single Input neuron 80
Fig. (4.2) Multiple Input Neuron 81
Fig. (4.3) Layer of (S) Neurons 82
Fig. (4.4) Direct inverse control 84
Fig. (4.5) Direct Inverse Control at steady state flight 84
Fig. (4.6) Direct Inverse Control at climb angle =90 deg 85
Fig. (4.7) Direct Inverse Control at initial velocity =700 m/s 85
Fig. (4.8) Control by Feedforward 86
Fig. (4.9) Control by Feedforward at steady state flight 86
Fig. (4.10) Control by feedback linearization 87
Fig. (4.11) Control by Feedback Linearization at steady state flight 88
Fig. (4.12) Pitch motion using NN controller with combined sine wave input 89
Fig. )4.13) Integrated square error using NN controller with combined sine wave
input
89
Fig. (4.14) Absolute velocity of the missile using NNC with combined sine wave 90

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input
Fig. (4.15) Angle of attack using NNC with combined sine wave input 90
Fig. (4.16) Elevator deflection angle using NNC with combined sine wave input 91
Fig. (5.1) The structure of a Fuzzy Logic Control System 93
Fig. (5.2) Triangular membership function 94
Fig. (5.3) Membership function for input (e) 94
Fig. (5.4) Membership function for input (ce) 94
Fig. (5.5) Membership function for output (u) 95
Fig. (5.6) Fuzzy matching process 97
Fig. (5.7) Fuzzy inference process 97
Fig. (5.8) Fuzzy combination process 98
Fig. (5.9) Defuzzification process 99
Fig. (5.10) Rule base calculations 99
Fig. (5.11) Architecture of the generic fuzzy control system 100
Fig. (5.12) Step response of a simple generic fuzzy controller 101
Fig. (5.13) Fuzzy inference system control action 102
Fig. (5.14) Comparison between fuzzy logic and NN controllers 102
Fig. (5.15) Effect of normalized and denormalized factors 103
Fig. (5.16) Comparison between PD and FL controllers with combined sine wave
input
103
Fig. (5.17) Integral square error for PD and FL controllers 104
Fig. (5.18) Dynamic response of a low pass filter 104
Fig. (5.19) Integrated square error for different fuzzy logic controllers using low
pass filter
105
Fig. (5.20) Error rate using filter 105
Fig. (5.21) Error rate using delay only 106
Fig. (5.22) Effect of using NNC for the first 5 seconds 106
Fig. (5.23) Error, error rate and control signal 107
Fig. (5.24) Neurofuzzy structure 107
Fig. (5.25) Two types of fuzzy logic controllers output performance 108

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Fig. (5.26) Composite guidance law 109
Fig. (5.27) Defuzzification process 109
Fig. (5.28) Fusion Fuzzy system output K1 110
Fig. (5.31) Comparison between FL, PD controllers in pitch motion with combined
sine wave
111
Fig. (5.32) Integrated square error for PD and FL controllers with combined sine
wave
111
Fig. (5.33) Angle of attack using FLC with combined sine wave input 112
Fig. (5.34) Elevator deflection angle using FLC with combined sine wave input 112
Fig. (5.35) Absolute velocity of the missile using FLC with combined sine wave
input
113
Fig. (5.36) Comparison between fuzzy logic controller and PD controller for .3 rad
step input
114
Fig. (5.37) Comparison between FLC and PD controller for a step response 114
Fig. (5.38) Elevator deflection angle for .3 rad step input using FLC 115
Fig. (5.39) Angle of attack for .3 rad step input using FLC 115
Fig. (5.40) Absolute velocity for .3 rad step input using FLC 116
Fig. (5.41) Path angle response using PD, FL controllers with ramp input 117
Fig. (5.42) Comparison between integrated square error for PD, FL controllers with
ramp input
117
Fig. (5.43) Angle of attack using FLC with ramp input 118
Fig. (5.44) Missile velocity using PD, FL controllers with ramp input 118
Fig. (5.45) Elevator deflection angle using PD, FL controllers with ramp input 119
Fig. (6.1) AIM 9 Model with 2 separate controllers 121
Fig. (6.2) Fig. (5.2) NeuroFuzzy structure 122
Fig. (6.3) Target location transformation from fixed frame of reference coordinate
to missile body axes coordinate
123
Fig. (6.4) Actual trajectories for target and missile 124
Fig. (6.5) 3D Plot for missile trajectory in both X, Y axes with respect to time 124
Fig. (6.6) 3D Plot for missile trajectory in both X, Z axes with respect to time 125
Fig. (6.7) Calculation of Maximum fuse distance, and the best triggering point 126

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Fig. (6.8) Error in Z direction due to AOA, control system error 127
Fig. (6.9) Error in Y direction due to SSA, control system error 127
LIST OF TABLES
Table (1.1) Tomahawk specification 12
Table (1.2) Major types (J, L, M, P, R) of AIM 9 missiles 20
Table (1.3) Major types (B, D, E, G, H) of AIM 9 missiles 21
Table (1.4) Data specifications of AIM 7 25
Table (5.1) Control rules for simple generic fuzzy controller 101
Table (7.1) ISE for PD, NN, FL controllers 129
Table (7.2) Comparison between NNC and FLC for the first 5_seconds 129

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ABBRIVIATIONS
A/C Aircraft
AAM Air to Air Missile
AFD Arm/Fire Device
AGM Air to Ground Missile
AIM Air Intercept Missile
AOA Angle of Attack
ASM Air to Surface Missile
C/L Center Line
DOF Degree Of Freedom
DSMAC Digital Scene Matching Area Correlation
F.O.R Frame Of Reference
F.O.R Frame of Reference (at earth)
FLC Fuzzy Logic Controller
FNN Feedforward Neural Network
GBU Ground Bomb Unit
GPS Globe Positioning System
IR Infra Red
MIMO Multi Input Multi Output
NNC Neural Network Controller
OOLD Out-Of-Line Device
RF Radio Frequency
RNN Recurrent Neural Network
SISO Single Input Single Output
SSA Side Slipping Angle
TDD Target Detection Device
TERCOM Inertial and Terrain Contour Matching
TIVS Thermally Initiated Venting System
TSK Tagaki Suguno
WGU Wing Ground Unit

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Chapter (1)
GENERAL BACKGROUND ON AIR TO AIR MISSILE
1.1 Historical Background
During World War 2 there have been many ideas about guided weapons such as
guided bombs instead of direct projectiles or bombs. The beginning ideas that were to
evolve into the HenschelHs 293 [1] appeared in as early as 1939 {Fig. (1.1)}. In 1940, an
experimental model having the shape of a glider was built. The goal was to develop a
remote-controlled air-to-surface missile against ships. Development proceeded even
though no suitable rocket motors were available. The experimental model used a
standard SC 500 bomb with extra wings and tail unit but no rudder. Finally a
propulsion system was developed, and the liquid rocket was fitted under the main
missile body. An 18-channel radio system was used for control.
Fig. (1.1) HenschelHs 293 air-to-ship, wireless guided, gliding bomb, model A
The missile was designed to be carried under a parent bomber. Warm exhaust air from
the aircraft engines was channeled to the missile to prevent it from freezing up at high
altitudes. Once dropped the Hs 293 would fall for some 90m (295ft) before the rocket
achieved maximum thrust. The parent bomber would continue to fly a pre_designated
course parallel with the target. The Aircraft could visually track the missile with the aid
of red guidance flare in the tail, and control the projectile using a small control box with
a joystick. The actual flight path resembled a series of arcs as corrections were received
and followed.

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The main weakness of the Hs 293A was that the parent bomber had to fly a steady, level
path. Evasive moves to avoid anti-aircraft fire were impossible, even though the Hs 293
outranged most ship-borne anti-aircraft guns. An improved Hs 293D with a television
camera installed in the head of the missile as aiming system was planned but the war
concluded before it could be realized. Also, the problem of icing was never resolved and
thus further propulsion units were designed. The war ended before these plans left the
experimental stage.
The Hs 293 was based on a normal 500 kg (1,102 lb) bomb with wings and fins added
and an engine suspended from the main body. The Hs 293V-4 and C-1 were guided by
radio, like the Fritz-X, but after the Germans found that the Allies were capable of
interfering with the control signals to the missile wire guidance was adopted.
The C-3, C-4, and A-0 versions of the Hs293 relied on wire guidance. During the
bomb's fall, two wired coils on the wing tips unwound, so maintaining the link with the
launch plane and allowing the transmission of electrical pulses for guidance.
A model D {Fig. (1.2)} was also built, which transmitted television images of the target to
the controller. Model H was supplied with an acoustic/magnetic detector to attack
bomber formations.
Fig. (1.2) HenschelHs 293 air-to-ship television_guided gliding bomb, model D (3views)

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The guidance operators always sat on the starboard right side of the cabin, and
therefore it was always necessary to attack a target from the port side and in the same
movement direction. Another version from Henschel guided bomb was HenschelHs 294
which used the television guidance from launch plane.
In 1941,Professor Wagner conceived and designed the Schmetterling anti-aircraft
missile and submitted it for appraisal and approval to the RLM
(Reichsluftfahrtministerium, phew!) or the State Ministry of Aviation, which rejected
the design because its defensive purpose was considered weak and still unnecessary.
Official support finally came in 1943, when Allied strategic bombing had accelerated the
war to a higher stage, and the Reich was feeling the pain.
The Henschel company, which was also developing several other types of missiles, was
given the go-ahead and development contract to begin production in February 1945.
Experiments and production were interrupted by Allied bombers and there were only
59 experimental launchings, 34 of them failed for different reasons. Schmetterling was a
bomb-shaped projectile with wings and fins, and two rocket boosters were attached to
the outside for take-off.
The external rockets were powered by solid fuel, while the internal motor was driven by
a fuel composed of hydrocarbon and nitric acid. It could accelerate up to 200 m/s and
had an effective range of approximately 8 km with a ceiling of 1000m. A ground
controller would guide the missile through radio signals and track its course visually.
The warhead contained 20 kg of high explosive and was armed with a proximity fuse
called "Fox."
The lion's share of post-World War II literature concerning German guided missiles has
concentrated on the V-1 "Buzz Bomb" and the V-2 stratospheric rocket. However, the
guidance systems of these weapons were so rudimentary that a successful launch was
one which hit a target as vast as London. German science developed several other, more
sophisticated guidance systems for weapons which were used successfully in combat
before either the V-1 or V-2.

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These first true guided missiles, by current definition, are virtually unknown today.
They were Henschel'sHs 293A and Ruhrstahl's SD1400X, known as "Fritz X." Both
missiles were air-launched from mother bombers and radio-controlled primarily against
maritime targets. It is interesting to note that of the fifteen battleships lost to airpower
(seven in the open sea) one of these, the 41,650-ton Italian flagship, Roma, was sunk by a
Fritz X. Later, the British battleship, Warspite, was hit by a Fritz X and put out of
action for six months. Fritz Xs also sunk the Royal Navy light cruiser, Spartan, heavily
damaged the cruiser USS Savannah, and hit the cruiser USS Philadelphia.
The Henschel program received a great boost when the RLM assigned Prof. Dr. Herbert
A. Wagner to assume control of their missile program. The brilliant Wagner had earlier
been dismissed by Junkers Aircraft as the company found it impossible to reconcile his
intermittent and desultory research methods with its ideas of series production. After
his dismissal, he carried out independent research on an anti-ship ricochet bomb.
In January 1940, Wagner joined Henschel's already distinguished missile research team.
This team of specialists included: ReinhardLahde and Otto Bohlmann (aeronautics),
Wilfried Hell, from Schwarz Propeller Werke (engineering), Josef Schwarzmann
(electronics), and Dr. Hinrici (design study). Theodor Sturm of
StassfurterRundfunkGessellschaft worked closely with the Henschel team in developing
and adapting radio systems.
The first Henschel design, designated Hs 293V-1, was a standard glider bomb bearing
slight resemblance to its Schwarz forerunner. The Hs 293V-1 did not leave the drawing
board.
The second design, the Hs 293V-2 (later FZ21) was built as a model in February 1940
and used in control tests at Karlshagen. It, too, was unarmed and powerless. Note that,
unlike German aircraft prototype 'V' numbers where only one example was built for
each V number, the Henschel missile V numbers referred to design alone and many
examples could have been built.
Further studies led to a new design in July 1940, the Hs 293V-3. The powerless
prototype was test launched from minimum release altitudes of 3,280 feet. Since the

5
RLM was primarily interested in an anti-ship missile, it was found that a pure glide
bomb lacked sufficient speed and weight to penetrate warship hulls.
The first successful test launching occurred two days later against a small barn as a
target. Subsequent tests ended in failure usually for two main reasons. First, the original
white tracking flares were difficult to follow and were replaced with red flares.
Secondly, the electrical system often failed due to design failure particularly with tubes
which were replaced with relays. In 1941, drop tests used a Heinkel He 177A-0 bomber
and later two He 177A-1s were used in the first successful tests.
The A-0 design led to the finalization of the production design, the Hs 293A-1, which
consisted of three pre-production models (V-2, V-3, A-0). One thousand nine hundred
were produced for the test and modification programs which continued into early 1944
(1,700 were A-0s). Early Hs 293 production was carried out at HenschelWerke 111,
Spandau-Hakenfelde but was transferred to Berlin-Schoenfeld in August 1943.
In early tests, bomb-aimers had difficulty following the bomb in flight due to its high
velocity. Also, the electromagnetically activated spoilers tended to jam. Pneumatic
power was tested but was found to develop problems in low temperatures causing the
electromagnetic system to be retained. It was not until early 1942, when a high-speed
wind tunnel had been constructed, that Dr. Kramer's control spoilers were modified and
that a velocity-reducing tail-mounted air brake was perfected.
As issued the Fritz X was the standard SD 100X armor-piercing (AP) bomb with four
centrally-mounted standard cruciform wings giving the bomb aerodynamic pivotal
points for control. The total span across the wings was 4 feet 5 inches. The tail assembly
consisted of four fins similar to those of an orthodox bomb, but were surrounded by the
air brake ring which contained the control spoilers and operating solenoids. The dive
brake was fitted around the tail fins to limit the terminal velocity of the bomb to 600
miles per hour. The dive brake was fabricated of metal but a section was electrically
insulated to serve as a radio antenna. The fuselage and tail measured 10 feet 8* inches
and had a diameter of 1 foot 10 inches.

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The sudden but arranged capitulation of the Italian fleet to the Allies on 9 September
1943 spurred the Germans to take quick actions against their former ally. The battleship
Italia was damaged and Roma sunk as victims of a new type of air-to-surface weapon,
the Ruhrstahl/Kramer X-1 [1] as shown in Fig. (1.3) or Fritz X. It was a free-falling
bomb guided by the parent aircraft. Usually it was dropped at an altitude of about
6,000m (19,685ft); by the time of detonation it would have had gained a velocity close to
that of sound.
The first tests were conducted in Germany in 1942, and were moved to Italy later. In
Italy, pneumatic power was tested to substitute for the electromagnetic actuation of the
spoilers. However, variations in temperature in different parts of the atmosphere posed
obstacles and the idea had to be dropped. The Allied advance to Italy forced the
Germans to press the Fritz X into increased use. The cruiser USS Savannah was
attacked successfully alongside several naval transports. During a night attack two
British cruisers collided in utmost confusion. Seven days later the Germans scored hits
on the battleship HMS Warspite, which had to be towed to Malta.
Fig. (1.3) The Ruhrstahl SD 1400 'Fritz X' air-to-ship, wireless guided, gliding bomb
German wire-guided missiles belong generally to the X-series. The X-4air-to-air missile
shown in Fig. (1.4) was the first of the series to be developed in June 1943. It was a
finned and winged projectile with a wingspan of 6ft 6in, and powered by a rocket using
a combination of two fuels (T and C stoff). The wire, coiled around spools, was stored in
the wing tips and carried guidance signals to control spoiler tabs and ailerons on the

7
wings to alter direction. The warhead composed of 20 kg of explosive and a acoustic
proximity fuse called "Kranich."
Fig. (1.4) Restored Ruhrstahl X-4 Air-to-Air missile
It was certainly natural and reasonable that a ground-to-ground version of the X-4 [1]
was also developed, as an anti-tank weapon, in addition the successful Panzerfaust. This
new cousin missile was called the X-7. The X-7 was navigated and stabilized by a
gyroscope and guided by wire, like the X-4, but it contained a hollow charge warhead
armed with an impact fuse which could penetrate over 200mm of armor within 1000
meters. It was driven by a two-stage, solid-fuel rocket motor and weighed 10 kg.
In early 1943, work began on the X-4 air-to-air wire-guided missile by Dr. Kramer at
Ruhrstahl. The missile received a development order in the summer of 1943 and was
given the number 8-344 by the RLM, and was developed to give fighters a chance to
down the ever increasing number of Allied bombers from outside of their defensive gun
range.
By the early sixties the sidewinder waqs the principal heatseeker in western service it
was used by USAF, USN. Its early combat record was not spectacular, as the seeker
performance limitations were exacerbated by the poor reliability of the tube electronics
and the inexperience of its users. Kill probabilities were in the tens of percent, very
sensitive to how well the launch aircraft was positioned. Designed to intercept lumbering
bombers, the AIM was ill suited to knife-fights with MIG-17s at low level.
Nevertheless, no less than 28 MIGs were killed for 175 launches between 1965 and 1968,
by USAF F-4C/D aircraft, an aggregate (kill probability) of 16 %.

8
In 1973, Ford began production of an enhanced AIM-9J-L, later registered the AIM-
9N. The November model employed a similar configuration to the AIM-9B, but the main
printed circuits were redesigned to improve seeker performance.
In 1982 AIM-9L was produced which is essentially an improved AIM-9L. The Mile
has improved background rejection, counter-countermeasures capability and a low
smoke motor to reduce the visual signature of the inbound weapon.
1.2 Overview
Missiles are classified according to many specifications such as range, warhead
weight, guidance technique and mission type. Many types of missiles will be shown and
discussed briefly in the following pages. But the focus of this thesis will be the air to air
missiles. Air-to-air missiles have many guidance techniques such as active, semi-active
radar, laser and heatseeking missiles. These types of guidance technique are classified
according to the range of each missile. For example, radar homing missiles will have
long range than the other heatseeking ones according to the capability of the detecting
element itself. In this thesis, the air-to-air heatseeking missiles (SIDEWINDER AIM 9R)
will be discussed. This missile has a large number of produced units all over the world
about 21000 piece that from the USAF inventory. Table (1.1) gives the specifications of
this missile for many versions.
1.2.1 Missiles types
There are many common types of missiles such as AAM, ASM, SAM, TASM cruise
and ballistic missiles. The next section will discuss each type briefly. Each type of
missiles is classified in accordance with guidance techniques, target-missile range,
propulsion and type of the missile warhead. The basic type will be discussed in this
research is the AAM or AIM missiles.
1.2.1.1 ASM missiles
Figure (1.5) shows different types of ASM missiles.

9
Fig (1.5) Types of ASM Russian missiles
1.2.1.2 AAM missiles
Figure (1.6) shows different types of AAM missiles.

10
Fig (1.6) Russian AAM
1.2.1.3 Cruise missiles
Tomahawk is an all-weather submarine or ship-launched land-attack cruise missile.
After launch, a solid propellant propels the missile until a small turbofan engine takes
over for the cruise portion of flight. Tomahawk is a highly survivable weapon. Radar
detection is difficult because of the missile's small cross-section and low altitude flight.

11
Similarly, infrared detection is difficult because the turbofan engine emits little heat.
Systems include Global Positioning System (GPS) receiver; an upgrade of the optical
Digital Scene Matching Area Correlation (DSMAC) system; Time of Arrival (TOA)
control, and improved 402 turbo engines.
The Tomahawk land-attack cruise missile has been used to attack a variety of fixed
targets, including air defense and communications sites, often in high-threat
environments. The land attack version of Tomahawk has inertial and terrain contour
matching (TERCOM) radar guidance {Fig. (1.7)}. The TERCOM radar uses a stored
map reference to compare with the actual terrain to determine the missile's position. If
necessary, a course correction is then made to place the missile on course to the target.
Terminal guidance in the target area is provided by the optical Digital Scene Matching
Area Correlation (DSMAC) system, which compares a stored image of target with the
actual target image.
Fig (1.7) TERCOM, DSMAC missiles guidance technique
The Tomahawk missile {Fig. (1.8), Table (1.1)} provides a long-range, highly survivable,
unmanned land attack weapon system capable of pinpoint accuracy. The Surface Navy’s
deep strike capability resides in the Tomahawk missile system – the proven weapon of
choice for contingency missions.

12
Table (1.1) Tomahawk specifications
Specifications
Primary Function
Long-range subsonic cruise missile for attacking land
targets.
Contractor Hughes Missile Systems Co., Tucson, Ariz.
Power Plant
Williams International F107-WR-402 cruise turbo-fan
engine; solid-fuel booster
Length
18 feet 3 inches (5.56 meters); with booster: 20 feet 6
inches (6.25 meters)
Weight
2,650 pounds (1192.5 kg); 3,200 pounds (1440 kg) with
booster
Diameter 20.4 inches (51.81 cm)
Wing Span 8 feet 9 inches (2.67 meters)
Range
Land attack, conventional warhead: 600 nautical miles
(690 statute miles, 1104 km)
Speed Subsonic - about 550 mph (880 km/h)
Guidance System Inertial and TERCOM
Warheads
Conventional: 400 kg Bullpup, or
Conventional submunitions dispenser with combined
effect bomblets, or
WDU-36 warhead w/ PBXN-107 explosive & FMU-148
fuze, or
200 kt. W-80 nuclear device
Date Deployed 1983

13
Fig (1.8) Tomahawk missile
1.2.1.4 Chinese nuclear missiles
Figure (1.9) shows different types of Chinese nuclear missiles.
Fig. (1.9) Chinese nuclear missiles DONG FENG/JULANG SERIES MISSILES
Chinese nuclear missiles are classified according the range an the warhead weight
most of them are guided either by inertial/fiber optic, strap down inertial system or
GPS.
1.3 AIM Missiles
1.3.1 Missile components
Guided missiles are made up of a series of subassemblies as shown in Fig. (1.10). The
various subassemblies form a major section of the overall missile to operate a missile

14
system, such as guidance, control, armament (warhead and fusing), and propulsion. The
major sections are carefully joined and connected to each other. They form the complete
missile assembly. The arrangement of major sections in the missile assembly varies,
depending on the missile type.
The guidance section is the brain of the missile. It directs its maneuvers and causes the
maneuvers to be executed by the control section. The armament section carries the
explosive charge of the missile, and the fusing and firing system by which the charge is
exploded. The propulsion section provides the force that propels the missile.
Fig. (1.10) Missile components
1.3.1.1 Guidance and control section
The complete missile guidance system includes the electronic sensing systems that
initiate the guidance orders and the control system that carries them out. The elements
for missile guidance and missile control can be housed in the same section of the missile,
or they can be in separate sections.

15
There are a number of basic guidance systems used in guided missiles. Homing-type,
air-launched, guided missiles are currently used. They use radar or infrared homing
systems. A homing guidance system is one in which the missile seeks out the target,
guided by some physical indication from the target itself. Radar reflections or thermal
characteristics of targets are possible physical influences on which homing systems are
based. Homing systems are classified as active, semiactive, and passive.
(a)-Active homing system
In the active homing system as shown in Fig. (1.11), target illumination is supplied by a
component carried in the missile, such as a radar transmitter. The radar signals
transmitted from the missile are reflected off the target back to the receiver in the
missile. These reflected signals give the missile information such as the target's distance
and speed. This information lets the guidance section compute the correct angle of
attack to intercept the target. The control section that receives electronic commands
from the guidance section controls the missile’s angle of attack. Mechanically
manipulated wings, fins, or canard control surfaces are mounted externally on the body
of the weapon. They are actuated by hydraulic, electric, or gas generator power, or
combinations of these to alter the missile's course.
Fig. (1.11) Active homing system
(b)-Semiactive homing system
In the semiactive homing system as shown in Fig (1.12), the missile gets its target
illumination from an external source, such as a transmitter carried in the launching

16
aircraft. The receiver in the missile receives the signals reflected off the target, computes
the information, and sends electronic commands to the control section. The control
section functions in the same manner as previously discussed.
Fig. (1.12) Semiactive homing system
(c)-Passive homing system
In the passive homing system, the directing intelligence is received from the target.
Examples of passive homing include homing on a source of infrared rays (such as the
hot exhaust of jet aircraft) or radar signals (such as those transmitted by ground radar
installations). Like active homing, passive homing is completely independent of the
launching aircraft. The missile receiver receives signals generated by the target and then
the missile control section functions in the same manner as previously discussed.
1.3.1.2 Armament Section
The armament system contains the payload (explosives), fusing, Safety and Arming
(S&A) devices, and target-detecting devices (TDDs).
(a)-Payload
The payload is the element or part of the missile that does what a particular missile is
launched to do. The payload is usually considered the explosive charge, and is carried in
the warhead of the missile. High-explosive warheads used in air-to-air guided missiles

17
contain a rather small explosive charge, generally 10 to 18 pounds of H-6, HBX, or PBX
high explosives. The payload contained in high-explosive warheads used in air-to-
surface guided missiles varies widely, even within specific missile types, depending on
the specific mission. Large payloads, ranging up to 450 pounds, are common. Comp B
and H-6 are typical explosives used in a payload. Most exercise warheads used with
guided missiles are pyrotechnic signaling devices. They signal fuse functioning by a
brilliant flash, by smoke, or both. Exercise warheads frequently contain high explosives,
which vary from live fuses and boosters to self-destruct charges that can contain as
much as 5 pounds of high explosive.
(b)-Fusing
The fusing and firing system is normally located in or next to the missile's warhead
section. It includes those devices and arrangements that cause the missile's payload to
function in proper relation to the target. The system consists of a fuse, a Safety and
Arming (S&A) device, a Target-Detecting Device (TDD), or a combination of these
devices. There are two general types of fuses used in guided missiles—proximity fuses
and contact fuses. Acceleration forces upon missile launching arm both fuses. Arming is
usually delayed until the fuse is subjected to a given level of accelerating force for a
specified amount of time. In the contact fuse, the force of impact closes a firing switch
within the fuse to complete the firing circuit, detonating the warhead. Where proximity
fusing is used, the firing action is very similar to the action of proximity fuses used with
bombs and rockets.
(c)-Safety and arming devices
S&A devices are electromechanical, explosive control devices. They maintain the
explosive train of a fusing system in a safe (unaligned) condition until certain
requirements of acceleration are met after the missile is fired.
(d)-Target detecting devices
TDDs are electronic detecting devices similar to the detecting systems in VT fuses. They
detect the presence of a target and determine the moment of firing. When subjected to

18
the proper target influence, both as to magnitude and change rate, the device sends an
electrical pulse to trigger the firing systems. The firing systems then act to fire an
associated S&A device to initiate detonation of the warhead. Air-to-air guided missiles
are normally fused for a proximity burst by using a TDDwith an S&A device. In some
cases, a contact fuse may be used as a backup. Air-to-surface guided missile fusing
consists of influence (proximity) and/or contact fuses. Multifusing is common in these
missiles.
1.3.1.3 Propulsion section
Guided missiles use some form of jet power for propulsion. There are two basic types of
jet propulsion power plants used in missile propulsion systems—the atmospheric (air-
breathing) jet and the thermal jet propulsion systems. The basic difference between the
two systems is that the atmospheric jet engine depends on the atmosphere to supply the
oxygen necessary to start and sustain burning of the fuel. The thermal jet engine
operates independently of the atmosphere by starting and sustaining combustion with its
own supply of oxygen contained within the missile.
There are three types of atmospheric jet propulsion systems—the turbojet, pulsejet, and
ramjet engines. Of these three systems, only the turbojet engine is currently being used
in Navy air-launched missiles. A typical turbojet engine includes an air intake, a
mechanical compressor driven by a turbine, a combustion chamber, and an exhaust
nozzle. The engine does not require boosting and can begin operation at zero
acceleration.
Thermal jets include solid propellant, liquid propellant, and combined propellant
systems. As an AO, you come in contact with all three systems. The solid propellant and
combined propellant systems are currently being used in some air-launched guided
missiles. The majority of air-launched guided missiles used by the Navy use the solid
propellant rocket motor. They include the double base and multibase smokeless powder
propellants as well as the composite mixtures. Grain configurations vary with the
different missiles. Power characteristics and temperature limitations of the individual
rocket motors also vary. In some guided missiles, different thrust requirements exist

19
during the boost phase as compared to those of the sustaining phase. The dual thrust
rocket motor (DTRM) is a combined system that contains both of these elements in one
motor. The DTRM contains a single propellant grain made of two types of solid
propellant—boost and sustaining. The grain is configured so the propellant meeting the
requirements for the boost phase burns at a faster rate than the propellant for the
sustaining phase. After the boost phase propellant burns itself out, the sustaining
propellant sustains the motor in flight over the designed burning time (range of the
missile).
1.3.2 Sidewinder AIM 9 missiles
Tables (1.2) and (1.3) show the characteristics of major types of AIM 9 missiles.

20
Table (1.2) Characteristics of major types of AIM 9 missiles.
Subtype AIM-9J AIM-9L AIM9-M AIM-9P AIM-9R
Service USAF Joint Joint USAF USN
Origin AIM-9E AIM-9H AIM-9L AIM-9J/N AIM-9M
Detector PbS InSb InSb InSb Focal
PlaneArray
Cooling Peltier Argon Argon Argon
Dome MgF2 MgF2 MgF2 MgF2 Glass
Reticle speed
(Hz)
100 125 125 100 Focal Plane
Array
Modulation AM FM FM FM Focal
PlaneArray
Tracking rate
(deg/s)
16.5 classified Classified >16.5 Classified
Electronics Hybrid Solid state Solid state Solid state Solid state
Warhead Blast
/fragmentation
Annular BF Annular BF Annular
BF
Annular BF
Fuse Passive-IR IR/Laser IR/Laser IR/Laser IR/Laser
Manufacturer Hercules
/Aerojet
Hercules
/Bermite
MTI/Hercules Hercules
/Aerojet
MTI/Hercules
Type MK.17 MK36 MOD.7,8 MK.36 MOD.9 SR.116 MK.36MOD.9
launcher AERO-111 Common Common Common Common
Length (m) 3 2.9 3 3 2.9
Span (m) 0.55 0.6 0.6 0.55 0.6
Mass (kg) 70 90 90 90 90
Velocity
(Mach)
<3 <3 <3 <3 <3

21
Table (1.3) Characteristics of AIM-9B, 9D, 9E , 9G, 9H
Subtype AIM-9B AIM-9D AIM-9E AIM-9G AIM-9H
Service Joint USN USAF USN USN
Origin NWC AIM-9B AIM-9B AIM-9D AIM-9G
Detector PbS PbS PbS PbS PbS
Cooling Uncooled Nitrogen Peltier Nitrogen Nitrogen
Dome
window
Glass MgF2 MgF2 MgF2 MgF2
Reticle speed
(Hz)
70 125 100 125 125
Modulation AM AM AM AM AM
Track rate
(deg/s)
11.0 12.0 16.5 12.0 >12.0
Electronics Thermionic Thermionic hybrid Thermionic Solid state
Warhead Blast/frag. Continuous
rod
Blast/frag. Continuous
rod
Continuous
rod
Fuse Passive-IR Passive-
IR/HF
Passive-IR Passive-
IR/HF
Passive-
IR/HF
Manufacturer Thiokol Hercules Thiokol Hercules Hercules
Bermite
Type MK.17 MK.36 MK.17 MK.36 MK.36
launcher Aero-111 LAU-7A Aero-111 LAU-7A LAU-7
Length(m) 3 2.8 2.9 2.8 2.8
Span(m) 0.5 0.6 0.5 0.6 0.6
Mass (kg) 70 90 75 90 89
Velocity
(Mach)
<3 <3 <3 <3 <3

22
1.3.2.1 The imaging Sidewinder-AIM-9R
The AIR-9R is the latest production sidewinder, using an imaging seeker which is a
fundamental departure from the established design. Developed by the naval weapons
center, the AIM-9R uses a modified AIM-9R control actuator, while retaining the fuse,
warhead, motor, wings and canards of its predecessor.
The imaging seeker is built around a focal plane array imaging device, analogous to
the CCDs employed in modern television cameras. A focal plane array has a much
greater instantaneous field of view than a reticle seeker (conventional technique), and
stares at the target and its immediate background, tracking the target by means of
contrast lock similar to that employed by TV guided weapons such as Maverick or
GBU-15. In this fashion, the seeker can account for the background contrast and reject
it, while also providing the potential to discriminate between multiple targets and
countermeasures such as flares.
The WGU-19 seeker uses a three gimbal stabilized platform mounting a visible band
focal plane array device, most likely a 256X256 element InSb array, or a higher
resolution PtSi device on a peltier cooled substrate, to provide coverage down to 4
micron band. The video signal produced by the array is then digested and processed by
a software programmable digital image processor, which tracks the targets and feeds
the autopilot with data so that it can send steering commands to the control actuators.
The AIM-9R is the latest naval sidewinder, using the airframe, fuse and motor of the
AIM-9M with a new digital imaging seeker. The new seeker employs a focal plane array
imaging device effective to visual wavelengths, mounted on a gimbaled stabilized
platform. The use of the imaging seeker has provided a vast improvement in target
detection range, off bore-sight angle, rejection of background and ability to selectively
aim for vulnerable areas of the target. Imaging seekers are immune to jamming
techniques effective against reticle seekers.

23
The AIM-9 provides a major increase in target acquisition range over established
subtypes, with much better tracking performance, and the ability to reject both
background terrain and clouds. The total field of view of the seeker is much greater,
allowing acquisition of off-bore-sight and maneuvering targets, while the software
provides for intelligent selection of an aim point when impacting a target, also the
manufacturer claim effective counter-countermeasures capability against known and
postulated jamming or seduction techniques.
1.3.3 AIM-120 AMRAAM Slammer
The AIM-120 advanced medium-range air-to-air missile (AMRAAM) is a new
generation air-to-air missile. It has an all-weather, beyond-visual-range capability and
is scheduled to be operational beyond 2000. AMRAAM is a supersonic, air launched,
aerial intercept, guided missile employing active radar target tracking, proportional
navigation guidance, and active Radio Frequency (RF) target detection. It employs
active, semi-active, and inertial navigational methods of guidance to provide an
autonomous launch and leave capability against single and multiple targets in all
environments as shown in Fig. (1.13).
Fig. (1.13) Comparison between AIM 7 and AIM 120 guidance technique

24
The AMRAAM weighs 340 pounds and uses an advanced solid-fuel rocket motor to
achieve a speed of Mach 4 and a range in excess of 30 miles. In long-range engagements
AMRAAM heads for the target using inertial guidance and receives updated target
information via data link from the launch aircraft. It switches to a self-guiding terminal
mode when the target is within range of its own monopulse radar set. The AIM-120
also has a "home-on-jam" guidance mode to counter electronic jamming. With its
sophisticated avionics, high closing speed, and excellent end-game maneuverability,
chances of escape from AMRAAM are minimal. Upon intercept an active-radar
proximity fuse detonates the 40-pound high-explosive warhead to destroy the target. At
closer ranges AMRAAM guides itself all the way using its own radar, freeing the launch
aircraft to engage other targets.
AMRAAM is a follow-on to the AIM-7 Sparrow missile series {Fig (1.14)} and
Table (1.4). The missile is faster, smaller and lighter, and has improved capabilities
against low-altitude targets. It incorporates an active-radar with an inertial reference
unit and micro-computer system, which makes the missile less dependent upon the fire-
control system of the aircraft. Once the missile closes on a target, its active radar guides
it to intercept. This enables the pilot to aim and fire several missiles simultaneously at
multiple targets. The pilot may then perform evasive maneuvers while the missiles
guide themselves to their targets.

25
Table (1.4) Specification data of AIM 120 (AMRAAM)
Primary Function Air-to-air tactical missile
Contractor Hughes Aircraft Co. and Raytheon Co.
Power Plant High performance (solid fuel)
Length 143.9 inches (3.66 m)
Launch Weight 335 pounds (150.75 kg)
Diameter 7 inches (177.8 mm)
Wingspan 20.7 inches (525.8 mm)
Range <20 miles (<32 Km)
Speed Supersonic < 4 Mach
Guidance System Active radar terminal/inertial midcourse
Warhead Blast fragmentation
Unit Cost $386,000
Relative costs of
AMRAAM
components
Guidance 68%
Control 9%
Fuse 9%
Warhead 2%
Propulsion 6%
Airframe 6%
Date Deployed September 1991
Aircraft platforms
Navy: F-14D and F/A-18
Air Force: F-15 and F-16
NATO: German F-4, British Tornado and Sea Harrier

26
Fig. (1.14) AIM 7 air to air missile
The AIM-120 grew out of a joint agreement, no longer in effect, among the United
States and several NATO nations to develop air-to-air missiles and to share the
production technology. The AMRAAM program was established as a result of Joint
Service Operational Requirement for an Advanced Air-to-Air Tactical Missile needed
in the post-1985 time frame. The AMRAAM program began with a 1975 study which
recommended that future aerial threats be engaged at 3-40 miles of range.
The AIM-120A is a non-reprogrammable missile (requires a hardware change to
upgrade the missile software). The AIM-120B/C is reprogrammable through the missile
umbilical using Common Field-level Memory Reprogramming Equipment (CFMRE).
The AIM-120C has smaller aero surfaces to enable internal carriage on the Air Force
F-22 aircraft. The USAF All-Up-Round (AUR) container houses an internal cable
which enables up to four missiles to be reprogrammed while in the container. USN
containers are not equipped with the cable and must be opened to reprogram the

27
missile. All three AMRAAM variants are currently approved for use on the F-15C/D/E,
F-16C/D, and F/A-18C/D aircraft.
Four wings, four fins (control surfaces), and the wiring harness cover are mounted
externally, providing additional distinguishing features from other similar missiles,
such as AIM-7 Sparrow. The AIM-120C utilizes ‘’clipped’’ wings and fins in order to
meet the internal carriage requirements of the F-22. AMRAAM consists of the
following major sections: Guidance, Armament, Propulsion, and Control. Other
components include a wiring harness, harness cover, Thermally Initiated Venting
System (TIVS), and wing and fin assemblies.
1.3.3.1 Weapons guidance section
Weapons Guidance Unit. The Weapons Guidance Unit (WGU) consists of the radome,
seeker, servo, transmitter-receiver, electronics unit, Inertial Reference Unit, Target
Detection Device (TDD), the harnesses, and frame structure. All units except the TDD
are contained within a sealed structure composed of the pyroceramicradome, titanium
skin sections, and aluminum aft bulkhead. The TDD, RF and video processor, and the
antennas are attached to the aft skin section as a complete testable assembly.
Electronics group functions include radar signal processing, seeker servo control, and
all of the computations performed in the central data processor. The WGU-16B is used
on AIM-120A missiles, the WGU-41/B is used on AIM-120B missiles, and the WGU-
44/B is used on AIM-120C missiles. Guidance sections on AIM-120B and AIM-120C
missiles contain Electronic Erasable Programmable Read Only Memory which allow
reprogramming of the missile software. Missile software versions are denoted by Tape
and Revision Numbers.
1.3.3.2 Weapons propulsion section
Weapons Propulsion Unit. The Weapons Propulsion Unit (WPU)-6/B consists of an
airframe, integral rocket motor, a blast tube and exit cone, and an Arm/Fire Device
(AFD) with a visible safe-arm indicator. The high performance rocket motor utilizes a
reduced smoke, hydroxyl terminated, polybutadiene propellant in a boost sustain
configuration, an asbestos-free insulated case (an integral part of the airframe), and an

28
integral aft closure, blast tube, and nozzle assembly with a removable exit cone to
facilitate control section installation/removal. Wings are attached in wing sockets at the
forward end of the propulsion section. Provisions are included within this section for
mounting the filter rectifier assembly.
1.3.3.3 Weapons control section
Weapons Control Unit. The Weapons Control Unit (WCU)-11/B consists of four
independently controlled electro-mechanical servo actuators, four lithium-aluminum
batteries connected in parallel, and a steel fuselage section that is bolted to the
propulsion section aft skirt. Each actuator consists of a brushless DC motor ballscrew,
an infinite resolution potentiometer directly coupled to the output shaft, and pulse
width modulated control electronics. The output shaft is engaged directly to a squib
actuated lock so that it does not interfere with the fin (control surface) installation and
removal. The wiring harness cover extends from the aft end of the guidance section to
the forward end of the control section. Its primary purpose is to provide protection for
the wiring harness. The main wiring harness electrically connects the umbilical
connector, guidance section, and control section. The wiring harness cover also houses
the TIVS. The TIVS is designed to vent rocket motor pressure in the event the missile is
exposed to a fuel fire. The TIVS consists of an external thermal cord which, when
ignited, triggers an Out-Of-Line Device (OOLD) that ignites a Linear Shape Charge
that weakens the rocket motor, allowing the rocket motor to vent without exploding.
The OOLD prevents the shaped charge from detonating should the booster in the
OOLD inadvertently detonate due to causes such as high impact. The unit has an
additional safety feature that causes it to “reset” within nine to thirteen units of gravity,
such as the acceleration experienced during missile launching. This feature prevents the
system from functioning during missile free flight so that the associated aerodynamic
pressures do not inadvertently enable the TIVS and thereby degrade the missile
performance. An indicator is on the wiring harness cover showing the condition of the
TIVS, either ‘’ENABLE’’ or ‘’DISABLE’’. Only TIVS equipped missiles are deployed
aboard Aircraft Carriers. The WPU-6/B Propulsion Section (with TIVS) meets the fast
cook-off and sympathetic detonation requirements of the IM program and the policy
delineated in OPNAV Instruction (OPNAVINST) 8010.13B. The other requirements

29
(bullet impact, fragment impact, and slow cook-off) have not been met with the current
configuration. However, the WPU-6/B has been granted the appropriate waivers for
shipboard use.
1.3.3.4 Wing and fin assemblies
Wing and fin assemblies provide flight control of the missile. The four wings are
detachable, stationary flight surfaces with ball fasteners to facilitate quick installation
and removal. The four fins provide the movable control surfaces. The AIM 7 is
interchangeable with AIM-120A and AIM-120B missiles. The AIM-120C utilizes
‘’clipped’’ wings and fins in order to meet the internal carriage requirements on ATD
starting in FY98 that will advance the AMRAAM development to provide a full-up
integration. AMCOM will deliver 2 AMRAAM fire units in 2Q FY99 for Marine Corps
operational suitability and effectiveness testing.
1.3.4 Air to air missiles features and techniques
To understand the benefits of applying the control strategy, many topics in that field
are needed to be discussed. These topics are very important in evaluating any type of
missile. The following subsections present these topics.
1.3.4.1 Target acquisition technique
It is classified into many ways to detect and track a target, these types are classified
according to the range of the missiles and target type, such as TV guided missiles, laser,
radar, and infrared ones (IR). All these different technique follow some guidance laws in
each guidance phases to verify the best trajectory of the missile that it should follow to
keep the target in the required dome origin (shifted) to shorten the duration time until
hitting the target.
1.3.4.2 Aim point when impacting the target
It is the best point in the target at which the missile can cause the greatest damage
after hitting it which is usually the center of the target image on the focal plane array on
the missile dome.

30
1.3.4.3 Proximity fuse distance and locking time
Proximity fuse distance is the maximum distance between the target and the seeker
within which the missile can cause great damage to that target. This is determined by
the type of the missile, the type and quantity of the ammunition, the target geometrical
feature and the control strategy of the missile.
The proximity fuse in AIM-9R functions according to the intensity of the IR rays
coming from the target indicating the target-seeker distance.
Locking time is the time required since the missile enters the proximity fuse envelope
until activating the missile ammunition which could be constant or variable time.
Locking time is very beneficial to secure direct and close impact of the target.
1.3.4.4 Jamming and seduction techniques
All countermeasures that have been established to protect aircraft from missiles such
as Electronic Countermeasures are usually attached to the aircraft at the front part. The
theory of this countermeasures is simply the capability of the instrument to guide the
missile wrongly away from the real position of the target which is done electronically,
but simple jamming and seduction techniques are activated either by dropping flares for
heat seeking missile or chaff for the radar missiles.
1.3.4.5 Reticle seeker (conventional technique)
It is used in most air-to-air missiles as a way to determine the location of the target on
the dome window of the missile in such a way using the wave shift and frequency of the
detector rotating element.
The reticle seeker is the most common optical system design employed in conventional
heat seeking missiles. It was invented by the Germans during the latter phase of World
War 2. It provides a means of using a single detector element to produce an error signal
in rectangular coordinates, for a point target somewhere within the cone which
represents the view of the seeker.
The technique is based on the idea of mechanically chopping the light flux which
impinges on a detector, in such a fashion that the characteristics of the chopped light
pulses vary with position of the light source in the field of view. Because the detector

31
produces an electrical signal directly proportional to the impinging light flux, electronic
hardware can be built to extract a positional error signal in X, Y coordinates, suitable
for driving a missile autopilot with traditional linear controllers.
1.3.4.6 Target seeker distance calculation
Target seeker distance can be easily evaluated from the targets area on the focal plane
array through the missile dome window using the similarity and the target pre-
calculated geometry using the following simple relation.
Target-seeker distance (x) is inversely proportional to the square root of the area of
the target on the focal plane array of the missile detecting screen. Eq. (1.1) is used to
determine target-seeker distance.
Tc
ar
Target-seeker distance=
(1.1)
Where (ar) represents the target area on the frontal screen of the missile (m2), Tc
represents a constant depending on the target geometry and the projection angle of the
target on the frontal screen of the missile (target orientations).
This thesis consists of six chapters and two appendices:
- Chapter 1 includes appropriate background about different types of missiles.
- Chapter 2 includes literature review, problem formulation, objectives and thesis
layout.
- Chapter 3 describes modeling procedure of air-to-air missiles.
- Chapter 4 discusses different types of neural network models used for control.
- Chapter 5 explains the fuzzy logic technique and how to apply it for control.
- Chapter 6 presents the results of the computer simulations of the proposed
system.
- Chapter 7 discusses the final conclusions and future work.
- Appendix A presents the Simulink models for the air-to-air missile, neural
network controller, fuzzy logic controller and the whole integrated control
system.
- Appendix B presents an example of a gust effect as a system disturbance.

32
Chapter 2
LITERATURE REVIEW
2.1 Introduction
The development and application of most present day systems and control theory
were spurred on by the need to resolve aerospace problems. This is roughly the problem
of analyzing and designing guidance law and flight control systems (autopilot) for
tactical missiles or aircraft. Therefore, it is beneficial to review the development of
systems and control theory. The guidance and control laws used in current tactical
missiles are mainly based on classical control design techniques. These control laws were
developed in the 1950s and have evolved into fairly standard design procedures (Locke,
1955). Earlier guidance techniques worked well for targets that were large and traveled
at lower speeds. However, these techniques are no longer effective against the new
generation targets that are small, fast, and highly maneuverable. For example, when a
ballistic missile reenters the atmosphere after having traveled a long distance, its radar
cross section is relatively small, its speed is high and the remaining time to ground
impact is relatively short. Intercepting targets with these characteristics is a challenge
for present-day guidance and control designs. In addition, the missile-target dynamics
are highly nonlinear partly because the equations of motion are best described in an
inertial system while the aerodynamic forces and moments are best represented in a
missile and target body axis system.
Moreover, unmodeled dynamics or parametric perturbations usually exist in the plant
modeling. Because of the complexity of the nonlinear guidance design problem, prior
approximations or simplifications have generally been required before the analytical
guidance gains can be derived in the traditional approaches (Lin, 1991) [2]. Therefore,
one does not know exactly what the true missile model is, and the missile behavior may
change in unpredictable ways. Consequently, one cannot ensure
optimality of the resulting design. In the last three decades, optimality-based guidance
designs have been considered to be the most effective way for a guided missile engaging
the target (Bryson and Ho 1969; Lin, 1991; Zarchan,1994) [3], [2] and [4]. However, it is
also known from the optimal control theory that a straightforward solution to the

33
optimal trajectory shaping problem leads to a two-point boundary value problem
(Bryson and Ho,1969) [3], which is too complex for real-time onboard implementation.
Based on the reasons given above, advanced control theory must be applied to a
missile guidance and control system to improve its performance. The use of intelligent
control systems has infiltrated the modern world. Specific features of intelligent control
include decision making, adaptation to uncertain media, self organization, planning and
scheduling operations. Very often, no preferred mathematical model is presumed in the
problem formulation, and information is presented in a descriptive manner. Therefore,
it may be the most effective way to solve the above problems. Intelligent control is a
control technology that replaces the human mind in making decisions, planning control
strategies, and learning new functions whenever the environment does not allow or does
not justify the presence of a human operator. Artificial neural networks and fuzzy logic
are two potential tools for use in applications in intelligent control engineering. Artificial
neural networks offer the advantage of performance improvement through learning by
means of parallel and distributed processing. Many neural control schemes with back-
propagation training algorithms, which have been proposed to solve the problems of
identification and control of complex nonlinear systems, exploit the nonlinear mapping
abilities of neural networks (Miller et al., 1991 [5]; Narendra and Parthasarthy, 1990
[6]). Recently, adaptive neural network algorithms have also been used to solve highly
nonlinear flight control problems. A fuzzy logic-based design that can resolve the
weaknesses of conventional approaches has been cited above. The use of fuzzy logic
control is motivated by the need to deal with highly nonlinear flight control and
performance robustness problems. It is well known that fuzzy logic is much closer to
human decision making than traditional logical systems. Fuzzy control based on fuzzy
logic provides a new design paradigm such that a controller can be designed for
complex, ill defined processes without knowledge of quantitative data regarding the
input-output relations, which are otherwise required by conventional approaches
(Mamdani and Assilian, 1975 [7]; Lee, 1990 [8] ;Driankovet al., 1993 [9]). An overview
of neural and fuzzy control designs for dynamic systems was presented
by Dash et al. (1997) [10]. Very few papers have addressed the issue of neural or fuzzy-
based neural guidance and control design. The published literature in this field will be
introduced in this paper. The following sections are intended to provide the reader with

34
a basic, and unified view of the concepts of intelligent control. Many potentially
applicable topologies are well studied. It is hoped that the material presented here will
serve as a useful source of information by providing for solutions for current problems
and future designs in the field of guidance and control engineering.
2.2 Conventional Guidance and Control Design
Tactical missiles are normally guided from shortly after launch until target
interception. The guidance and control system supplies steering commands to
aerodynamic control surfaces or to correct elements of the thrust vector subsystem so as
to point the missile towards its target and make it possible for the weapon to intercept a
maneuvering target.
2.2.1 Guidance
From the viewpoint of a control configuration, guidance is a special type of
compensation network (in fact, a computational algorithm) that is placed in series with a
flight control system (also called autopilot) to accomplish an intercept. Its purpose is to
determine appropriate pursuer flight path dynamics such that some pursuer objective
can be achieved efficiently. For most effective counterattack strategies, different
guidance laws may need to be used to accomplish the mission for the entire trajectory.
First, midcourse guidance refers to the process of guiding a missile that cannot detect its
target when launched; it is primarily an energy management and inertial
instrumentation problem. When a radar seeker is locked onto a target and is providing
reliable tracking data, such as the missile-target relative range, line-of-sight (LOS)
angle, LOS angle rate and bore sight error angle, the guidance strategy in this phase is
called terminal guidance. Steering of
the missile during this period of flight has the most direct effect on the final miss
distance. The steering law should be capable of achieving successful intercept in the
presence of target maneuvers and external and internal disturbances.
2.2.2 Flight control system
The flight control system executes commands issued based on the guidance law with
fidelity during flight. Its function is three-fold: it provides the required missile lateral

35
acceleration characteristics, it stabilizes or damps the bare airframe, and it reduces the
missile performance sensitivity to disturbance inputs over the required flight envelope.
2.2.3 Conventional design methods
The principles behind controlling guided missiles are well known to control engineers.
Since the basic principles were extensively covered by Locke (1955) [11], a large number
of control technologies have been developed to improve missile performance and to
accommodate environmental disturbances. These techniques are mainly based on
classical control theory. Many different guidance laws have been exploited based on
various design concepts over the years. Currently, the most popular terminal guidance
laws defined by Locke (1955) [11] involve LOS guidance, LOS rate guidance, command-
to-line-of-sight(CLOS) guidance (Ha and Chong, 1992) [12] and other advanced
guidance strategies, such as proportional navigation guidance (PNG) (Locke, 1955) [11],
augmented proportional navigation guidance (APNG) (Zarchan, 1994) [13] and optimal
guidance law based on linear quadratic regulator theory (Bryson and Ho, 1969 [3];
Nazaroff, 1976 [14]), linear quadratic Gaussian theory (Potter, 1964 [15]; Price and
Warren, 1973 [16]) or linear exponential Gaussian theory (Speyer et al., 1982). Classical
guidance laws different from these guidance laws were discussed by Lin (1991) [2], and
the performance of various guidance laws was extensively compared. Among the current
techniques, guidance commands proportional to the LOS angle rate are generally used
by most high speed missiles today to correct the missile course in the guidance loop. This
approach is referred to as PNG and is quite successful against nonmaneuvering targets.
While PNG exhibits optimal performance with a constant velocity target, it is not
effective in the presence of target maneuvers and often leads to unacceptable miss
distances. Classical and modern guidance designs were compared by Nesline and
Zarchan (1981) [17]. The midcourse guidance law is usually a form of PNG with
appropriate trajectory-shaping modifications for minimizing energy loss. Among the
mid-course guidance laws, the most effective and simplest one is the explicit guidance
law (Cherry, 1964) [18].The guidance algorithm has the ability to guide the missile to a
desired point in space while controlling the approach angle and minimizing a certain
appropriate cost function. The guidance gains of the explicit guidance law are usually
selected so as to shape the trajectory for the desired attributes (Wang, 1988 [19]; Wang

36
et al., 1993 [20]). Other midcourse guidance laws are theoretically optimal control-based
approaches (Glasson and Mealy, 1983 [21]; Cheng and Gupta, 1986 [22]). These
research efforts have produced many numerical algorithms for open-loop solutions to
problems using digital computers. However, the main disadvantage of these algorithms
is that they generally converges slowly and are not suitable for real-time applications.
Unfortunately, only rarely is it feasible to determine the feedback law for nonlinear
systems which are of any practical significance. The flight control system used in almost
all operational homing missiles today is a three loop autopilot, composed of a rate loop,
an accelerometer, and a synthetic stability loop. Generally, the controller is in a form of
proportional-integral-derivative (PID) parameters, and the control gains are deter-
mined by using classical control theory, such as the root locus method, Bode method or
Nyquist stability criterion (Price and Warren, 1973 [16]; Neslineet al.,1981 [17]; Nesline
and Nesline, 1984 [23]). Modern control theory has been used extensively to design the
flight control system, such as in the linear quadratic techniques (Stallard, 1991 [24]; Lin
et al., 1993 [25]), generalized singular linear quadratic technique (Lin and Lee, 1985)
[26], design technique (Lin, 1994) [27] and feedback linearization (Lin, 1994) [27]. Over
the past three decades, a large number of guidance and control designs have been
extensively reported in the literature. For a survey of modern air-to-air missile guidance
and control technology, the reader is referred to Cloutieret al. (1989) [28]. Owing to
space limitations, only representative ones were cited above. For further studies on
various design approaches that have not been introduced in this section, the reader is
referred to Lin (1991) [2] and Zarchan (1994) [13]. Current highly maneuverable
fighters pose a challenge to contemporary missiles employing classical guidance
techniques to intercept these targets. Guidance laws currently in use on existing and
fielded missiles may be inadequate in battlefield environments. Performance criteria will
probably require application of newly developed theories, which in turn will necessitate
a large computation capability compared to the classical guidance strategy. However,
advances in microprocessors and digital signal processors allow increased use of
onboard computers to perform more sophisticated computation using guidance and
control algorithms.

37
2.3 Neural Net-based Guidance and Control Design
The application of neural networks has attracted significant attention in several
disciplines, such as signal processing, identification and control. The success of neural
networks is mainly attributed to their unique features:
(1) Parallel structures with distributed storage and processing of massive amounts of
information.
(2) Learning ability made possible by adjusting the network interconnection weights and
biases based on certain learning algorithms.
The first feature enables neural networks to process large amounts of dimensional
information in real-time (e.g. matrix computations), hundreds of times faster than the
numerically serial computation performed by a computer. The implication of the second
feature is that the nonlinear dynamics of a system can be learned and identified directly
by an artificial neural network. The network can also adapt to changes in the
environment and make decisions despite uncertainty in operating conditions.
2.3.1 Supervisory control
The neural controller in the system is utilized as an inverse system model as shown in
Fig. (2.1). The inverse model is simply cascaded with the controlled system such that the
system produces an identity mapping between the desired response (i.e., the net-work
input r) and controlled system output y. This control scheme is very common in robotics
applications and is appropriate for guidance law and autopilot designs. Success with this
model clearly depends on the fidelity of the inverse model used as the controller
(Napolitano and Kincheloe, 1995 [29]; Guezet al., 1998 [30]). In the terminal guidance
scheme proposed by Lin and Chen (1999) [31], a neural network constructs a specialized
on-line control architecture, which offers a means of synthesizing closed-loop guidance
laws for correcting the guidance command provided by the PNG. The neural network
acts as an inverse controller for the missile airframe. The results show that it can not
only perform very well in terms of tracking performance, but also extend the effective
defensive region. Moreover, based on its feature of adaptively, the neural net-based
guidance scheme has been shown to provide excellent performance robustness. It was
also demonstrated by Cottrell et al. (1996) [32] that using a neuro control scheme of this
type for terminal guidance law synthesis can improve the tracking performance of a

38
kinetic kill vehicle. Hsiao (1998) [33] applied the control scheme to treat the disturbance
rejection problem for the missile seeker. In addition, a fuzzy neural network control
architecture, called the fuzzy cerebellar model articulation controller (fuzzy CMAC),
similar to this scheme, was proposed by Geng and MaCullough (1997) [34] for designing
a missile flight control system. The fuzzy CMAC is able to perform arbitrary function
approximation with high speed learning and excellent approximation accuracy. A
control architecture based on the combination of a neural network and a linear
compensator was presented by Stecket al. (1996) [35] to perform flight control
decoupling. In Zhu and Mickle (1997) [36], a neural network was combined with a linear
time-varying controller to design the missile autopilot.
Fig. (2.1) Supervisory control scheme
2.3.2 Hybrid control
Psaltiset al. (1987) [37] discussed the problems associated with this control structure by
introducing the concepts of generalized and specialized learning of a neural control law.
It was thought that off-line learning of a rough approximation to the desired control law
should be performed first, which is called generalized learning. Then, the neural control
will be capable of driving the plant over the operating range and without instability. A
period of on-line specialized learning can then be used to improve the control provided
by the neural network controller. An alternative is shown in Fig. (2.2), it is possible to
utilize a linear, fixed gain controller in parallel with the neural control law. This fixed

39
gain control law is first chosen to stabilize the plant. The plant is then driven over the
operating range with the neural tracking performance of a kinetic kill vehicle. Hsiao
(1998) [33] applied the control scheme to treat the disturbance rejection problem for the
missile seeker. In network tuned online to improve the control. The guidance law (Lin
and Chen, 1999) [31] and flight control system (Stecket al., 1996) possess a similar
control scheme of this type.
Fig. (2.2) Hybrid control scheme
2.3.3 Model reference control
The two control schemes presented above do not consider the tracking performance. In
this scheme, the desired performance of the closed-loop system is specified through a
stable reference model, which is defined by its input-output pair {r(t), yR (t)}. As shown
in Fig. (2.3), the control system attempts to make the plant output y(t) match the
reference model output asymptotically. In this scheme, the error between the plant and
the reference model outputs is used to adjust the weights of the neural controller. In
papers by Light body and Irwin (1994) [38], Psaltiset al. (1987) [37] discussed the
problems the neural net-based direct model reference adaptive control scheme was
applied to design an autopilot for a bank-to-turn missile. A training structure was
suggested in these papers to remove the need for a generalized learning phase.

40
Techniques were discussed for the back propagation of errors through the plant to the
controller. In particular, dynamic plant Jacobian modeling was proposed for use as a
parallel neural forward model to emulate the plant.
Fig. (2.3) Model reference control scheme
2.3.4 Internal model control (IMC)
In this scheme, the role of the system forward and inverse models is emphasized. As
shown in Fig. (2.4), the system forward and inverse models are used directly as elements
within the feedback loop. The network NN1 is first trained off-line to emulate the
controlled plant dynamics directly. During on-line operation, the error between the
model and the measured plant output is used as a feedback signal and passed to the
neuro-controller NN2 . The effect of NN1 is to subtract the effect of the control signal
from the plant output; i.e., the feedback signal is only the influence due to disturbances.
The IMC plays a role as a feedforward controller. However, it can cancel the influence
due to unmeasured disturbances, which cannot be done by a traditional feed-forward
controller. The IMC has been thoroughly examined and shown to yield stability
robustness (Hunt and Sbarbaro-Hofer, 1991) [39]. This approach can be extended
readily to autopilot designs for nonlinear airframes under external disturbances.

41
Fig. (2.4) Internal model control scheme
2.3.5 Adaptive linear or nonlinear control
The connectionist approach can be used not only in nonlinear control, but also as a part
of a controller for linear plants. The tracking error cost is evaluated according to some
performance index. The result is then used as a basis for adjusting the connection
weights of the neural network. It should be noted that the weights are adjusted on-line
using basic back propagation rather than off-line. The control scheme is shown in Fig.
(2.5)
Fig. (2.5) Adaptive control scheme
2.3.6 Predictive control
Within the realm of optimal and predictive control methods, the receding horizon
technique has been introduced as a natural and computationally feasible feedback law.
In this approach, a neural network provides prediction of future plant response over a
specified horizon. The predictions supplied by the network are then passed on to a

42
numerical optimization routine, which attempts to minimize a specified performance
criteria in the calculation of a suitable control signal (Montague et al., 1991 [40]; Saint-
Donat et al., 1994 [41]). Figure (2.6) shows the complete scheme of a predictive
controller.
Fig. (2.6) Predictive control scheme
2.3.9 Example
A hybrid model reference adaptive control scheme is described here, where a neural
network is placed in parallel with a linear fixed-gain independently regulated autopilot
as shown in Fig. (2.7) (McDowell et al., 1997 [42]). The linear autopilot is chosen so as to
stabilize the plant over the operating range and provide approximate control. The
neural controller is used to enhance the performance of the linear autopilot when
tracking is poor by adjusting its weights. A suitable reference model is chosen to define
the desired closed-loop autopilot responses ¨ Zrefand ¨ Yrefacross the flight envelop.
These outputs are then compared with the actual outputs of the lateral autopilot ¨ Z and
¨ Y to produce an error measurement vector [ezey]T , which is then used in conjunction
with an adaptive rule to adjust the weights of the neural network so that the tracking
error will be minimized. A direct effect of this approach is to suppress the influence
resulting from roll rate coupling.

43
Fig. (2.7) Model reference control of coupled lateral dynamics
2.4 Fuzzy Logic Based Guidance and Control Design
The existing applications of fuzzy control range from micro-controller based systems
in home applications to advanced flight control systems. The main advantages of using
fuzzy are as follows:
(1) It is implemented based on human operator’s expertise which does not lend itself to
being easily expressed in conventional proportional-integral- derivative parameters of
differential equations, but rather in situation/action rules.
(2) For an ill-conditioned or complex plant model, fuzzy control offers ways to
implement simple but robust solutions that cover a wide range of system parameters
and, to some extent, can cope with major disturbances.
The sequence of operations in a fuzzy system can be described in three phases called
fuzzification, inference, and defuzzification shown as in Fig. 11. A fuzzification interface
converts input data into suitable linguistic values that may be viewed as labels of fuzzy
sets. An inference mechanism can infer fuzzy control actions employing fuzzy
implication and the rules of the interface in fuzzy logic. A defuzzification interface yields
a nonfuzzy control action from an inferred fuzzy control action. The knowledge base
involves the control policy for the human expertise and necessary information for the
proper functioning of the fuzzification and defuzzification modules. Fuzzy control was
first introduced and applied in the 1970’s in an attempt to design controllers for systems
that were structurally difficult to model. It is now being used in a large number of

44
domains. Fuzzy algorithms can be found in various fields, such as estimation, decision
making and, especially, automatic control.
2.4.1 Fuzzy proportional integral derivative (PID) control
In this case, fuzzy rules and reasoning are utilized on-line to determine the control
action based on the error signal and its first derivative or difference. The conventional
fuzzy two-term control has two different types: one is fuzzy-proportional-derivative
(fuzzy-PD) control, which generates a control output from the error and change rate of
error, and is a position type control; the other is the fuzzy-proportional integral (fuzzy-
PI) control, which generates an incremental control output from the error and change
rate of error, and is a velocity type control (Driankovet al., 1993) [9]. Figure (2.8) shows
a fuzzy-PD controller with normalization and denormalization processes. In Mizumoto
(1992) [43] and Qiao and Mizumoto (1996) [44], a complete fuzzy-PID controller was
realized using a simplified fuzzy reasoning method. Control schemes of these types can
be easily designed and directly applied to guidance and control system design. In fuzzy
logic terminal guidance design, the LOS angle rate and change of LOS angle rate can be
used as input linguistic variables, and the lateral acceleration command can be used as
the output linguistic variable for the fuzzy guidance scheme (Mishra et al., 1994) [45].
The LOS angle rate and target acceleration can also be used as input linguistic variables
to obtain an alternative fuzzy guidance scheme (Mishra et al., 1994 [45]; Lin et al., 1999
[31]). It has been shown that these fuzzy guidance schemes perform better than
traditional proportional navigation or augmented proportional navigation schemes, i.e.,
smaller miss distance and less acceleration command. A terminal guidance law was
proposed by Leng (1996) [46] using inverse kinematics and fuzzy logic with the LOS
angle and LOS angle rate constituting the input linguistic variables. A complete PID
guidance scheme employing heading and flight path angle errors was proposed by
Gonslaves and Caglayan (1995) [47] to form the basis for fuzzy terminal guidance. The
fuzzy-PD control scheme has also been applied to various missile autopilot designs
(Schroeder and Liu, 1994 [48]; Lin et al., 1998 [49]). Input-output stability analysis of a
fuzzy logic-based missile autopilot was presented by Farinewataet al. (1994) [50]. A
fuzzy logic control for general lateral vehicle guidance designs was investigated by
Hessburg (1993) [51]. In the papers by Zhao et al. (1993) [52] and Ling and Edgar (1992)

45
[53], fuzzy rule-based schemes for gain-scheduling of PID controllers were proposed.
These schemes utilize fuzzy rules and reasoning to determine the PID controller’s
parameters. Based on fuzzy rules, human expertise is easily utilized for PID gain
scheduling.
Fig. (2.8) Fuzzy PD controller
2.4.2 Hybrid fuzzy controller
Fuzzy controllers can have inputs generated by a conventional controller. Typically,
the error is first input to a conventional controller. The conventional controller filters
this signal. The filtered error is then input to the fuzzy system. Since the error signal is
purified, one needs fewer fuzzy sets describing the domain of the error signal. Based on
this specific feature, these types of controllers are robust and need a less complicated
rule base.
2.4.3 Fuzzy adaptive controller
The structure is similar to that of fuzzy PID controllers. However, the shapes of the
input/output membership functions are adjustable and can adapt to instantaneous
error. A typical fuzzy adaptive control scheme is shown as in Fig. (2.9) Since the
membership functions are adaptable, the controller is more robust and more insensitive
to plant parameter variations (Dash and Panda, 1996) [54]. In a paper by Lin and Wang
(1998) [49], an adaptive fuzzy autopilot was developed for bank-to-turn missiles. A self-
organizing fuzzy basis function was proposed as a tuning factor for adaptive control. In
Huang et al. (1994) [55], an adaptive fuzzy system was applied to autopilot design of the
X-29 fighter.

46
Fig. (2.9) Typical adaptive fuzzy control scheme
2.4.4 Fuzzy Sliding Mode Controller (SMC)
Although fuzzy control is very successful, specially for control of non-linear systems,
there is a drawback in the designs of such controllers with respect to performance and
stability. The success of fuzzy controlled plants stems from the fact that they are similar
to the SMC, which is an appropriate robust control method for a specific class of non-
linear systems. The fuzzy SMC as shown in Fig. (2.10) can be applied in the presence of
model uncertainties, parameter fluctuations and disturbances, provided that the upper
bounds of their absolute values are known (Driankovet al., 1993 [9]; Ting et al., 1996
[56]; Palm and Driankov, 1997 [57]).
Fig. (2.10) Fuzzy sliding mode control scheme
2.4.5 Fuzzy model following controller
To have the advantages of a fuzzy logic controller with a desired level of performance, a
fuzzy adaptive controller can be used in a model-following control system as shown in

47
Fig. (2.11) In this scheme, the error between the plant output and the reference model
output is used to adjust the membership functions of the fuzzy controller (Kwong and
Passino,1996) [58].
Fig. (2.11) Fuzzy model-following control scheme
2.4.6 Hierarchical fuzzy controller
In a hierarchical fuzzy controller as shown in Fig. (2.12), the structure is divided into
different levels. The hierarchical controller gives an approximate output at the first
level, which is then modified by the second level rule set. This process is repeated in
succeeding hierarchical levels (Kandel and Langholz, 1994 [59]).
Fig. (2.12) Hierarchical fuzzy control system

48
2.4.7 Optimal control
A fuzzy logic system can be utilized to realize an optimal fuzzy guidance law. In this
approach, exact open-loop optimal control data from the computed optimal time
histories of state and control variables are used to generate fuzzy rules for fuzzy logic
guidance. First, data related to the state and control variables of optimal guidance are
generated using several scenarios of interest. The fuzzy logic guidance law possesses a
neurofuzzy structure. Critical parameters of the membership functions of linguistic
variables are presented in the connecting weights of a neural network. The collected
data are then used to train the network’s weights by using the gradient algorithm or
other numerical optimization algorithms. After training has been performed
successfully, missile trajectories and acceleration commands for the optimal solution
and fuzzy logic guidance solution will be close during actual flight using these scenarios.
This approach can effectively resolve the computational difficulty involved in solving the
two-point boundary-value problem. The problem considered by Bouletet al. (1993) [60]
was that of estimating the trajectory of a maneuvering object using fuzzy rules. The
proposed method uses fuzzy logic algorithms to analyze data obtained from different
sources, such as optimal control and kinematical equations, using values sent by sensors.
2.4.8 Example
Figure (2.13) shows a fuzzy logic oriented architecture employed in a fuzzy terminal
guidance system (Gonsalvs and Caglayan, 1995) [47]. The architecture is duplicated for
both the heading and flight path angle channels. Guidance path errors drive in parallel
with a PD and a PI controller. The results produced by the fuzzy PD/PI controllers
(uPDand uPI,respec-tively) are combined via a fuzzy weighting rule-base. The combined
control utotalis then processed via a gain scheduler to account for variations over the
flight envelope. A fuzzy terminal guidance system can readily achieve satisfactory
performance that equals or exceeds that of conventional guidance approaches with
additional advantages, such as intuitive specification of guidance and control logic, the
capability of rapid prototyping via modification of fuzzy rule-bases and robustness to
sensor noise and failure accommodation.

49
Fig. (2.13) A fuzzy terminal guidance system
It should be noted that fuzzy control systems are essentially nonlinear systems.
Therefore, it is difficult to obtain general results from the analysis and design of
guidance and control systems. Furthermore, knowledge of the aerodynamics of missiles
is normally poor. Therefore, the robustness of the resulting
designs must be evaluated to guarantee stability in spite of variations in aerodynamic
coefficients.
2.5 Gain-Scheduling Guidance and Control Design
Gain scheduling is an old control engineering technique which uses process variables
related to dynamics to compensate for the effect caused by working in different
operating regions. It is an effective way to control systems whose dynamics change with
the operating conditions. It is normally used in the control of nonlinear plants in which
the relation-ship between the plant dynamics and operating conditions is known, and for
which a single linear time-invariant model is insufficient (Rugh, 1991 [61]; Hualin and
Rugh, 1997 [62]; Tan et al., 1997 [63]). This specific feature makes it especially suitable
for guidance and control design problems. Gain-scheduling design involves three main
tasks: partitioning of the operating region into several approximately linear regions,
designing a local controller for each linear region, and interpolation of controller
parameters between the linear regions. The main advantage of gain scheduling is that
controller parameters can be adjusted very quickly in response to changes in the plant
dynamics. It is also simpler to implement than automatic tuning or adaptation.

50
2.5.1 Conventional Gain-Scheduling (CGS)
A schematic diagram of a CGS control system is shown in Fig. (2.14). As can be seen,
the controller parameters are changed in an open-loop fashion based on measurements
of the operating conditions of the plant. A gain-scheduled control system can, thus, be
viewed as a feedback control system in which the feedback gains are adjusted using
feedforward compensation (Tan et al., 1997) [63]. Gain scheduled autopilot designs for
tactical missiles have been proposed by Balas and Packard (1992) [64] and Eberhardt
and Wise (1992) [65]. An approach to gain scheduling of linear dynamic controllers has
been considered for a pitch-axis autopilot design problem. In this application, the linear
controllers are designed for distinct operating conditions using H- methods (Nichols et
al., 1993 [66]). A gain scheduling eigenstructure assignment technique has also been
used in autopilot design (Piou and Sobel, 1996) [67].
Fig. (2.14) Conventional gain-scheduling control scheme
2.5.2 Fuzzy Gain-Scheduling (FGS)
The main drawback of CGS is that the parameter change may be rather abrupt across
the boundaries of the region, which may result in unacceptable or even unstable
performance. Another problem is that accurate linear time-invariant models at various
operating points may be difficult, if not impossible, to obtain. As a solution to these
problems, FGS has been proposed, which utilizes a fuzzy reasoning technique to
determine the controller parameters (Takagi and Sugeno, 1985) [68]. For this approach,
human expertise in the linear control design and CGS are represented by means of fuzzy

DEVELOPMENT OF A NEUROFUZZY CONTROL SYSTEM FOR THE GUIDANCE OF AIR TO AIR MISSILES (Master Thesis)

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DEVELOPMENT OF A NEUROFUZZY CONTROL SYSTEM FOR THE GUIDANCE OF AIR TO AIR MISSILES (Master Thesis)