MISSILE CONTROL Concept

MISSILE CONTROL
A missile control system consists of those components that
control the missile airframe in such a way as to automatically

provide an accurate, fast, and stable response to guidance
commands throughout the flight envelope while rejecting uncertainties
due to changing parameters, unmodeled dynamics,
and outside disturbances. In other words, a missile control
system performs the same functions as a human pilot in a
piloted aircraft; hence, the name autopilot is used to represent
the pilotlike functions of a missile control system. Missile
control and missile guidance are closely tied, and for the purposes
of explanation, a somewhat artificial distinction between
the two roles is now made. It must be remembered,
however, that for a guided missile the boundary between
guidance and control is far from sharp. This is due to the
common equipment and the basic functional and operational
interactions that the two systems share. The purpose of a
missile guidance system is to determine the trajectory, relative
to a reference frame, that the missile should follow. The
control system regulates the dynamic motion of the missile;
that is, the orientation of its velocity vector. In general terms,
the purpose of a guidance system is to detect a target, estimate
missile-target relative motion, and pass appropriate instructions
to the control system in an attempt to drive the
missile toward interception. The control system regulates the
motion of the missile so that the maneuvers produced by the
guidance system are followed, thereby making the missile hit
or come as close as required to the target. The autopilot is the
point at which the aerodynamics and dynamics of the airframe
(or body of the missile) interact with the guidance system.
Instructions received from the guidance system are
translated into appropriate instructions for action by the control
devices (e.g., aerodynamic control surfaces, thrust vec-
J. Webster (ed.), Wiley Encyclopedia of Electrical and Electronics Engineering. Copyright # 1999 John Wiley & Sons, Inc.
MISSILE CONTROL 303
Figure 1. A block diagram describing the
functional relations among the compo-
Guidance
command
+
–
Controller Actuator
Sensor
Aerodynamic
control surface
Missile
dynamics
nents of the missile control system.
toring or lateral thrusters) that regulate the missile’s flight- transmitter radiates a frequency-modulated wave toward
the earth, and the reflected signal is received on path. A block diagram describing these missile control system
operations is depicted in Fig. 1 where the function of each a separate antenna and combined with the signal taken
directly from the transmitter. The frequency difference component is further explained as following.
between the transmitted and the reflected signals indicates
the height of the missile. Radio altimeters can be
COMPONENTS OF MISSILE CONTROL SYSTEMS used to maintain automatically a missile at a preset altitude.
Sensor Units
Controller Units Sensor units measure some aspects of the missile’s motion.
Gyroscopes and accelerometers are the two primary sensor Controller units can be regarded as the ‘‘brain’’ of a missile,
units used in any missile control system. They provide the which tell a missile how to deflect the control surfaces or how
information of rotational and translational motions of a mis- to alter the thrust direction. The controller is in the form of
sile, respectively. preprogrammed logic and/or numerical operations installed
in the on-board computer of a missile. There are two inputs
1. Gyroscope. A gyroscope is a mechanical device con- to the controller units. One is from the sensor units, which
taining an accurately balanced rotor with its spin axis provide the information about the actual motions of a missile,
passing through the center of gravity. When the rotor and the other input is from the guidance system, which prorotates
at a high speed, it assumes the rigidity charac- vides the information about the commanded motions of a misteristics
that resist any force tending to displace the ro- sile. The commanded motion and the actual motions are comtor
from its plane of rotation. The tendency of a gyro- pared and manipulated in the controller units via a series of
scope to maintain its spin direction in the inertial space logic and/or numerical operations in order to output an intelallows
us to measure, with respect to the spin direction, ligent decision, which renders the actual motions of a missile
the angular motion of the missile on which the gyro- to match the commanded motions as closely as possible when
scope is mounted. Some recent gyroscopes, such as fed into the actuator units. The series of operations involved
fiber-optical gyroscopes and ring-laser gyroscopes, do in the controller unit is called control law. The most widely
not use a spinning rotor. They calculate the body rate used control laws include amplification, integration, and difby
use of the Sagnac effect. Fiber-optical gyroscopes ferentiation of the error signal between the commanded mohave
an especially high specification with reasonable tions and the actual motions.
cost.
2. Accelerometer. The basic principle of operation of an ac- 1. Amplification. The amplification of error signal imcelerometer
consists of the measurement of the inertial proves the robustness of the missile control system
reaction force of a mass to an acceleration. The inertial against uncertainties present in missile dynamics.
reaction force of the mass causes a displacement of the 2. Integration. The integration of error signal effectively
mass, which is suspended in an elastic mounting sys- increases the closeness between the commanded motem
within the missile, and the acceleration of the mis- tions and the actual motions.
sile can be read from the displacement of the suspended
3. Differentiation. The differentiation of error signal pro- mass. Velocity and position information can be obtained
vides the trend of error propagation and decreases the by integrating the accelerometer signal. One must avoid
required time for the actual motions to track the com- placing the accelerometer near an antinode of the prinmanded
motions. cipal bending mode of the missile; otherwise, the vibration
pick-up at this point may result in destruction of
With the increasing computation power of on-board com- the missile.
puters, more advanced control laws can be implemented in
3. Altimeter. The altimeter, which is an instrument used the missile control loop to improve the agility of a missile.
to measure altitude, is another sensor unit frequently This point is addressed in more detail later.
employed in cruise missile systems. There are two common
types of altimeters. A pressure altimeter, which is
Actuator Units simply a mechanical aneroid barometer, gives an approximate
altitude from which a more accurate value Actuator units are energy transformation devices. They receive
the command from controller units and transfer it into can be calculated; on the other hand, radio altimeters
give absolute altitude directly. In radio altimeters, a enough power to operate control surfaces in order to direct
304 MISSILE CONTROL
the missile to the right heading. There are three methods of changed by the action of actuators, which exert forces on control
surfaces or on exhaust vanes. Altering missile heading operating control surfaces: (1) by a pneumatic piston, (2) by a
hydraulic piston, or (3) by an electric motor. The selection of by deflecting control surfaces is called aerodynamic control,
whereas altering missile heading by deflecting exhaust vanes actuating power depends on factors such as the speed, size,
altitude, range, and weight of the missile. or by changing the jet direction is called thrust vector control.
A control surface is not effective until the airflow across the
surface has attained sufficient speed to develop a force. When 1. Pneumatic Actuator. In a pneumatic system, air from a
missile speed is not high enough during the beginning of pressure source passes through suitable delivery tubes,
launch, the aerodynamic control is not effective, and its role valves, and pressure regulators to do work upon some
is taken over by thrust vector control. The following two sec- mechanical units such as a piston or a diaphragm,
tions are dedicated to missile aerodynamic control and missile which is connected to the missile control surfaces. Unthrust
vector control. like a hydraulic system, a pneumatic system does not
reuse its transfer medium after it has performed work
on the load. For that reason, the air must be stored at MISSILE AERODYNAMIC CONTROL
a pressure much higher than that necessary for actuating
the load. Therefore, a pneumatic system that de- To control a missile accurately via aerodynamic forces, two
pends on tanks of compressed air is obviously limited in general types of control surfaces (i.e., primary and secondary
range. The performance of a pneumatic system is also controls) are used. Primary control surfaces include ailerons,
limited by the property of air compressibility. Because elevators, rudders, and canards; secondary control surfaces
air is compressible, the movement of a pneumatic actua- include tabs, spoilers, and slots. An understanding of missile
tor is slow because of the time it takes to compress the aerodynamics is needed before a discussion of how these two
air in the actuator to a pressure sufficient to move it. groups of control surfaces work.
2. Hydraulic Actuator. The operation of a hydraulic system
is similar to the pneumatic system. The most prom- Missile Aerodynamics
inent difference between the two systems is that the
Missile aerodynamics, like other flight vehicle aerodynamics, medium of transfer in the pneumatic system is a gas,
is basically an application of Bernoulli’s theorem, which says whereas the medium of the transfer in the hydraulic
that if the velocity of air over a surface is increased, the pres- system is a liquid. Hydraulic fluid is practically incomsure
exerted by the air on the surface must decrease, thus pressible and will produce a faster reaction on an actuakeeping
the total energy constant. The top surface of a missile tor, especially when the actuator must move against
wing section has a greater curvature than the lower surface. large forces. This asset is evidenced by the fact that
The difference in curvature of the upper and lower surfaces large, high-speed missiles are controlled by hydraulic
builds up the lift force. Air flowing over the top surface of the actuators. The main drawback of a hydraulic actuator is
wing must reach the trailing edge of the wing in the same its weight and the maintenance problems. A hydraulic
time as the air flowing under the wing. To do this, air passing system normally weighs more because of the need for a
over the top surface must move at a greater velocity than air pump, a reservoir, filters, and an accumulator. Also a
passing below the wing because of the greater distance the hydraulic system is hard to maintain, requiring filling
air must travel via the top surface. The increased velocity and bleeding operations.
means a corresponding decrease of pressure on the surface
3. Electric Actuators. Generally, motors are used as the according to the Bernoulli’s theorem. Therefore, a pressure
actuators in the electrical energy transfer systems. Di- differential is created between the upper and lower surface of
rect current (dc) motors develop higher stall torque than the wing, forcing the wing upward and giving it lift. Besides
alternating current (ac) motors and, therefore, are used the wing, any other lifting surfaces and control surfaces of a
more often for driving heavy loads encountered in high- missile exhibit exactly the same function.
speed missile control. An ac motor is inherently a con- The three-dimensional motion of a missile can be described
stant-speed device that is not suitable for the require- in the body-axis coordinate system as shown in Fig. 2. The
ments of a servo motor where variation in rotation longitudinal line through the center of the fuselage is called
speed is necessary. This factor also makes the dc motor the roll axis (x axis), the line that is perpendicular to the x
more applicable than the ac motor as an electric actua- axis and parallel to the wings is called the pitch axis (y axis),
tor in missile control. The use of all-electric missile con- and the vertical line is considered as the yaw axis (z axis).
trol would simplify manufacture, assembly, and mainte- The origin of the body-axis coordinate system (x, y, z) locates
nance. Also, it would be easier to transmit information at the center of gravity. The three-dimensional missile motion
or power to all parts of the missile by wires rather than can be resolved into two planar motions: pitch plane motion
by hydraulic or pneumatic tubing. To enforce actuating and yaw plane motion, where pitch plane is normal to the
efficiency, different methods of energy transfer (e.g., pitch axis, and yaw plane is normal to the yaw axis. The
electropneumatic and electrohydraulic actuators) can angle, measured in the pitch plane, between the projected
be combined. missile velocity and the roll axis is called the angle of attack
(AOA) denoted by . The angle, measured in the yaw plane,
between the projected missile velocity and the roll axis is The preceding introduction describes the components and
the operations of a missile control loop. A more detailed and called the angle of sideslip denoted by . The resultant force
on the wing or body can also be resolved into two components: fundamental introduction to the elements of missile control
system can be found in Refs. 1 and 2. A missile’s heading is the component in the pitch plane is called normal force, and
MISSILE CONTROL 305
Roll
rotates on
longitudinal axis Pitch
rotates on
lateral axis
elevator tab
elevator
aileron tab Canard
Relative wind
Wing
?
ß
?
a
Center of Gravity
Yaw
rotates on
vertical axis Rudder
Rudder
tab
aileron
y, Y, V
x, X, U
Iyy, M, q
Ixx, L, p
Izz, N, r
z, Z, W
Figure 2. Schematic demonstration of the nomenclature used in missile dynamics. The locations
of the primary control surfaces (rudder, elevator, aileron, and canard) and the secondary control
surface (tabs) are shown. The definition of the roll, pitch, and yaw motions is also shown.
the component in the yaw plane is called side force. The nor- coefficient CL depends on the wing span and the profile
of the wing. Increasing wing span or using the leading- mal force can be further resolved into two components: the
component perpendicular to the projected missile velocity (in edge slot or trailing-edge flap to increase the camber of
wing profile may effectively increase the lift coefficient. the pitch plane) is called lift and the component along the
projected missile velocity is called drag. In many tactical mis- 2. Drag Force. Drag is the resistance of air to forward mosiles
(e.g., short-range air-to-air missiles), the wing providing tion and is an adverse factor of control effectiveness. It
the lift force is not prepared. They keep a suitable AOA in the is the force that must be overcome by the thrust. The
flight, where the lift force is produced by control fins or stabil- drag force in formula is
ity fins. Some fundamental control-related missile aerodynamics
are surveyed in the following list. Readers who are
interested in advanced missile aerodynamics can refer to D = CD
?
2
AV2 (2)
Refs. 3 and 4 for details.
where CD is the coefficient of drag obtained from charac-
1. Lift Force. Lift force is the force by which aerodynamic teristic curves of airfoils via wind-tunnel tests. For a
control surfaces can change the attitude of a missile. small AOA, CD changes very little with the AOA. As the
Lift force depends on the contour of a wing, AOA, air AOA increases, CD increases. The drag coefficient is
density, area of the wing, and the square of the air- usually quite small when compared with the lift coeffi-
speed. The common equation for lift is given as cient. There are three sources of air drag. The skin friction
of air on the wing is called profile drag; the air
resistance of the parts of a missile that do not contrib- L = CL
?
2
AV2 (1)
ute to lift is called parasite drag; and the part of airfoil
drag that contributes to lift is called induced drag. CL, where L is the lift; CL is the lift coefficient, which de-
CD, and other aerodynamic coefficients can be evaluated pends on the wing contour and the AOA; is the air
from empirical techniques, computational fluid dynam- density; A is the area of the wing; and V is the airspeed.
ics (CFD) modeling, or by the processing of wind tunnel The lift coefficient CL is determined by wind-tunnel
test data. It should be noted that various degrees of un- tests and is plotted versus AOA as a characteristic
certainty are associated with each of these methods, curve for the particular airfoil. As the AOA increases,
with wind tunnel measurements usually being accepted the lift coefficient increases linearly to a certain maxias
the most accurate. mum value, which is the point where the air no longer
flows evenly over the wing surface but tends to break 3. Wingtip Vortex. The asymmetric wingtip vortex, which
has a remarkable effect causing row-yaw instability at away. This breaking away is called the stalling angle.
After the stalling angle is reached, the lifting force is a high AOA, is always a challenge to missile control system
design. As air flows about a wing, the pressure of rapidly lost, as is the airspeed. For a fixed AOA, the lift
306 MISSILE CONTROL
the air immediately above the upper surface is less than This of course is the reason why feathers are placed at
the rear end of an arrow to move the c.p. aft. If a missile the air pressure immediately below the surface. With
the air at a higher pressure below the wing, air will has no autopilot (i.e., no instrument feedback), a sizable
static margin, say 5% or more of the overall length, has spill by the wingtips to the upper surface. This flow of
air from the lower surface combines with the normal to be allowed to ensure stability. However, if the static
margin is excessively positive, the missile is unneces- flow of air, causing a swirl of air at the wingtips. This
swirl is called a wingtip vortex. At each side of the sarily stable, and control moments will be relatively ineffective
in producing a sizable maneuver. On the other wingtip, the action of the vortex is to throw the air inward
and downward. Induced drag is related to the hand, although a missile with negative static margin
is statically unstable, it may exhibit great agility when downflow caused by the wingtip vortices.
autopilot is installed. It is worth noting that the static 4. Downwash. Because of the camber shape of the wing
margin of a missile is not a fixed value, because of the airfoil, air flow over the wing is deflected downward toc.
p. variation for different flight conditions and the c.g. ward the elevator. This angle of deflection is called the
variation caused by propellant usage. A challenging downwash angle. When missile tail control is considmissile
control problem is to ensure the stability of the ered, the downwash effect caused by the wing must be
airframe for all possible c.p. and c.g. locations. seriously taken into account because downwash can sig-
2. Yaw Stabilizer. Missile stability about the vertical nificantly reduce the effective AOA of the tail surface
(yaw) axis is usually provided for by a vertical fin. If a and reduce the elevator ability of pitch control.
missile tends to turn to the left, the pressure on the 5. Shock Wave Effect. Shock wave is a prominent aerodyright
side of the fin is increased. This increased pres- namic phenomenon when missile speed is at the transure
resists the rotation and forces the tail in the oppo- sonic or supersonic ranges. As the speed of a missile
site direction. In some missiles, the fin may be divided increases, there comes a point at which the air can no
and have a movable part called the rudder that is used longer get out of the way fast enough. The air tends to
for directional control. Besides the fin, the vertical sides pile up or compress in front of the missile, setting up
of the fuselage also act as stabilizing surfaces. Another what is known as shock waves. In a shock wave, the
way to increase the yaw stability is via sweepback of pressure of air varies sharply, seriously altering the
wings. forces and pressure distribution on a missile. When
3. Row Stabilizer. Missile stability about the longitudinal shock waves are formed on the wings or control sur-
(row) axis is achieved by a dihedral and by the position- faces, the air flow across the shock waves tends to sepaing
of the wing. A dihedral angle is the angle formed by rate, causing drag to rise suddenly much as in a lowa
reference line through the wing surface and the lat- speed stall. At certain missile speeds, especially near
eral axis of the missile. Dihedral produces stability by the transonic range, the deflection of control surfaces
causing a change of lift on the wing surfaces. As a mis- may deteriorate the shock wave effect, which produces
sile starts to roll, it will sideslip slightly and thus create a peculiar vibration called flutter on control surfaces
a relative wind component. This component increases and can make control surfaces ineffective and even disthe
lift on the lower wing and decreases the lift on the integrated.
higher wing. Hence, an opposite torque is generated to
stop rowing. The positioning of the wings at the time Missile Stability
a missile is constructed is another means of obtaining
A stable missile can recover from the perturbed states sponta- stability about the row axis. A missile has greater row
neously without control. Such stability is made possible by stability if the wings are placed above the center of
devices that stabilize a missile about its three axes. Accord- gravity than if they are placed below the center of
ingly, these devices are called stabilizers. The simplest stabi- gravity.
lizer is the feathered fins at the rear of an arrow because it
provides for a stable line of flight. Three types of stabilizers Primary Control Surfaces
are required to stabilize a missile about its three axes.
Ailerons, rudders, elevators, canards, and their various combinations
are considered primary controls. These control sur- 1. Pitch Stabilizer. Missile stability about the lateral
faces are shown schematically in Fig. 2. As these control sur- (pitch) axis is achieved by a horizontal surface at the
faces are deflected, they present a surface to the existing air tail of the missile. This horizonal surface consists of two
flow at an angle that will cause a force to exist. This force parts: the stationary part as the pitch stabilizer and the
pushing against the control surface moves the wing or tail to movable part as the elevator. The degree of pitch stabilwhich
the control surface is attached in a direction opposite ity can be quantitatively expressed by an index called
to the control surface movement. static margin, which is the distance of the center of
pressure (c.p.) to the center of gravity (c.g.). The c.p. is
1. Ailerons. A conventional aileron is attached to the the point through which the combined aerodynamic
outer trailing edge of the wings to control the missile forces caused by body, wings, and control surfaces are
row motion in a manner that when one aileron is low- acting. If c.p. is behind the c.g. (i.e., the static margin is
ered, the opposite one is raised. positive), the missile is said to be statically stable. In
this case, any perturbation of the body away from the 2. Elevators. Elevators are attached to the pitch stabilizer
on the tail to control pitch motion. They are raised and direction of the velocity vector results in a moment
about the c.g. that tends to decrease this perturbation. lowered together.
MISSILE CONTROL 307
3. Rudders. A rudder is attached to the rear part of the 3. Spoilers. As the name indicates, a spoiler is used to
generate turbulence flow and ‘‘spoil’’ the lift on a wing. vertical stabilizer and is used to maintain directional
(yaw) control. When not used, spoilers are recessed into the upper
camber of the wings and allow the flow of air over the 4. Canards. A canard is basically a forward wing located
wing to be smooth and uninterrupted. If, however, a ahead of the center of gravity of the missile for the purgust
of wind has caused the right wing to drop, the con- poses of stabilization and pitch control. One type of catrol
system instantly calls for the spoiler on the left nard structure consists of a fixed stabilizing plane with
wing to extend. As the spoiler extends, the lift on the a surface control attached to the trailing edge. Another
left wing is spoiled and reduced a considerable amount. type of canard structure uses a pivoted mechanism that
The wings then tend to return to the original position. allows the entire stabilizing plane to rotate up or down.
5. Dual-Purpose Control Surfaces. The preceding control
surfaces can be properly combined to give multipurpose MISSILE THRUST VECTOR CONTROL
control functions. Feasible combinations include elevons,
ailevators, and rudder-vators. As the names indi- A completely different method of steering a missile is to alter
cate, they consist of control surfaces that accomplish the direction of the efflux from the propulsion motor. This
two purposes. For instance, an elevon takes the place of method is known as thrust vector control (TVC). TVC is
an elevator and an aileron, giving control of pitch and clearly not dependent on the dynamic pressure of the atmoroll.
sphere and is generally used in the phase of flight where mis-
6. Variable-Incidence Control Surfaces. This type of con- sile speed is so low that the airfoil sections do not have
trol rotates the position of an entire wing rather than enough aerodynamic stabilizing effect. On the other hand,
just part of it. The variable incidence control can over- TVC is inoperative after propulsion motor burn-out, but at
come the problem of flutter and the need for structural this time aerodynamic forces become large enough to take
strength of control surfaces and yet have a control that over the role of TVC. There are several methods of directing
is sensitive and effective at various speed ranges. The the thrust of a rocket motor, and each has advantages and
variable incidence control can be used on the wing, hori- disadvantages, which may or may not recommend it for a parzonal
stabilizer, or vertical stabilizer. ticular application. References 1 and 5 provide more information
on TVC.
Secondary Control Surfaces
1. Exhaust Vanes. Exhaust vanes are surfaces that are in- Primary control surfaces can be looked upon as the main constalled
directly in the exhaust path of the jet engine. trolling factor of the missile’s path; however, by using second-
When the position of the vane is changed, it deflects the ary control surfaces, a missile can be controlled much more
exhaust and causes the thrust to be directed in opposi- accurately and efficiently. A secondary group of aerodynamic
tion to the exhaust vane. The operation of exhaust control surfaces is composed of tabs, slots, and spoilers, which
vanes is sketched in the middle part of Fig. 3. Because are schematically demonstrated in Fig. 2. For the convenience
of the severe erosion problem caused by the tremendous of compact illustration, all six primary control surfaces and
heat in the exhaust, the life of exhaust vanes is gener- the three secondary control surfaces are put together in one
ally short. Graphite and more recently tungsten and missile, as shown in Fig. 2; however, a missile may not be
molybdenum have been used as the materials of the ex- equipped with all types of primary and secondary control surhaust
vanes. To reduce the complexity of the actuator faces. For example, missiles in general do not have both tail
design, the actuating mechanism of an exhaust vane of- and canard controls, and conventional missiles do not have
ten shares with that of aerodynamic control surfaces; secondary control surfaces, which are almost exclusively used
therefore, when control surfaces move in the ambient in large cruise missiles.
air path, an exhaust vane moves, simultaneously and
with the exact same manner, within the exhaust path 1. Tabs. Tabs are small pieces of movable or fixed metal
of the jet engine. The device ‘‘jetavators’’ is the outcome attached to the trailing edge of the primary control surof
such a design idea, which can control jet and elevator faces. They help to trim the missile or to alleviate the
simultaneously. Perhaps the oldest TVC is the exhaust loading of the primary control surfaces, but they do not
vane used in the German V2 in World War II. Many in themselves determine the direction of missile motion.
surface-to-surface missiles, including the American Per- Tabs can be divided into three types: fixed, trim, and
shing, have used exhaust vanes to control the jet direc- booster. A fixed tab can be bent uniformly in the retion.
quired direction to trim the missile. A trim tab is movable
and controllable, and is used to trim the missile 2. Gimbaled Engine. By mounting the combustion chamwith
varying attitude, speed, or altitude. A booster tab, bers in gimbals and controlling its position by servos,
sometimes known as a servo tab, is used to assist in the direction of thrust can be altered. The operation of
moving primary control surfaces with large area. gimbaled engine is sketched in the lower part of Fig. 3.
Two serious objections to this method are that all the 2. Slots. A slot is a high-lift device located along the leading
edge of the wing. The slot is ineffective in the region various fuel lines must be made flexible, and the servo
system that actuates the jet must be extremely strong. of a normal AOA, but when a missile reaches a high
AOA, the slot can be opened to allow air to spill through However, gimbaled liquid-propellant engines have been
used successfully for many years. For example, the Vik- and hence delay the formation of turbulence flow over
the top surface of the wing. ing research vehicles have been successfully flown many
308 MISSILE CONTROL
deflection of up to 12
 has been obtained by injecting
hot gas bled directly from the combustion chamber.
5. Reaction Control Thruster. An easier system of jet control
is accomplished by placing several small thrusters
at various points about the missile body. Control is accomplished
by using one or another of these jets as desired,
thus giving different directions of thrust. The operation
of reaction control thruster is sketched in the
upper part of Fig. 3. This method eliminates the use of
the outside control surfaces, affording a cleaner missile
surface. When reaction control thrusters are used, there
will be an interaction of the jet plume with the free
stream flow. This jet interaction is very nonlinear with
the AOA and dominates the effective moment produced
by the reaction thrusters. The produced moment may
be larger or smaller than the jet thrust force times its
moment arm, depending on the height by which the jet
penetrates into the free stream. Reference 6 discusses
missile attitude control using reaction control thruster.
6. Jet-Driving Control Surfaces. This method employs jet
or air injection over aerodynamic surfaces for actuating
augmentation.
MISSILE CONTROL CONFIGURATION
According to the aforementioned various missile control
methodologies, we can now give a classification of missile con-
figuration with respect to the location of controls. If the controls
are located well behind the center of gravity of the missile,
the term tail control applies. If the controls are placed
forward of the center of gravity, the term canard control applies.
When the control is mounted on the main lifting surface
Deflection
charges
Auxilary
directional
thrust
Changes
direction of
thrust Gimbaled
engine
Jet vans
Deflects
jet stream
Jet control
near the center of gravity, the term wing control applies. Figure 3. Three thrust vector control methods. The upper part
What type of control surface to be used depends on the type sketches the operation of reaction control thruster; the middle part
of missile configuration in question. Regarding missile con- sketches the operation of exhaust vane; and the lower part sketches
figuration, Refs. 1, 5, and 7 serve as good references. the operation of gimbaled engine.
Wing-Control Configuration
times using this type of control during phases of flight A wing-control configuration consists of a relatively large allwherein
aerodynamic control is inadequate. moving wing located close to the center of gravity of the mis-
3. Moving Nozzles. Instead of moving the entire combus- sile and a set of tail or stabilizing surfaces at the aft end
tion chamber, we can also alter the direction of thrust of missile. This all-moving wing serves as an aforementioned
by changing the orientation of the nozzle. This can be variable-incidence control surface. This type of control is used
accomplished by using a flexible nozzle or a ball-and- mostly in an air-to-air missile because of its extremely fast
socket nozzle. A flexible nozzle is formed by attaching response characteristics. If the right and left moving wings
the nozzle to the motor case by means of a flexible rub- are controlled by separate servos, they can be used as ailerons
ber mounting that is very stiff axially but relatively and elevators; the word elevons as mentioned earlier is apcompliant
in the pitch and yaw planes. Thrust deflec- plied to such a dual-purpose control surface. There are two
tion of 4
 to 5
 is feasible by this method, but a large main advantages in using wing-control configuration:
resistance to movement is encountered when an increasingly
larger deflection angle is required. Another • Air Inlet Consideration. Instantaneous lift can be develway
of attaching the nozzle to the propulsion motor is oped as a result of wing deflection via a pivoted mechavia
a ball-and-socket joint with some form of low-fric- nism with little increase of missile AOA. This low value
tion seal. Although there will be some coulomb friction of AOA is advantageous particularly from the standin
this type of connection, the actuation torque will not points of inlet design for air-breathing power-plant and
increase with the deflection angle. guidance-seeker design. For example, if the propulsion
system is a ram jet, the air inlet is likely to choke if the 4. Injection Method. By injecting a liquid or gas into the
motor venturi, we can obtain a sideways component of body AOA is large, say 15
 or more. The use of wing control
can greatly reduce the chance of inlet choke and resultant thrust. The maximum jet deflection by using
inert liquid as the injection fluid was found to be 4
. Jet maintain the engine efficiency by keeping the body AOA
MISSILE CONTROL 309
to a minimum. This point will be further addressed in Tail Control Configuration
the later sections.
Many missiles employ tail control for its convenient packag-
• Servo Location Consideration. The servos used in wing- ing. Usually it is desirable to have the propulsion system
control configuration are located near the center of the placed centrally in the missile so that the center of gravity
missile body. There are some occasions when the servos movement caused by propellant usage is minimized. It is conare
most conveniently placed near the center of the mis- venient and sometimes essential to have the warhead and
sile. For example, if a medium-range missile has two sep- fuse at the front together with any associated electronics inarate
motors, a boost motor and a sustain motor, the for- cluding the guidance receiver. This leaves the control system
mer may occupy the whole of the rear end of the missile to occupy the rear end with the propulsion blast pipe passing
and the sustainer motor may occupy most of the re- through its center.
maining rear half of the body. In such a case, there is
just no room to install servos at the rear. If the missile Advantages. Advantages of tail control include the folcarries
a homing head, the servos cannot be placed at the lowing:
front either.
• The tail loads and hinge moments can be kept relatively
However, there are some distinct penalties involved in the low as the total AOA on the tail is reduced.
use of wing control. • The wing-tail interference effects are reduced because
the forward main lifting surface is fixed (i.e., no down-
• Pitch control effectiveness from the wings is generally wash caused by wing deflection). Therefore, the aerodyvery
low as a result of short pitching moment arm be- namic characteristics are more linear than those for
cause the lift developed is located close to the center of wing-control design.
gravity of the missile.
• Large aerodynamic hinge moments are required because Disadvantages. Disadvantages include the following:
of the large wing area.
• With this type of control, it is obvious that the tail de- • Relatively large loss will be induced in tail effectiveness
flection must be opposite in direction to the AOA. This as a result of downwash.
feature results in relatively slow response characteristics • Nonlinear aerodynamics is resulted from downwash
because the initial lift is in a direction opposite to the caused by both wing deflection and AOA.
desired one.
• Severe adverse rolling moments is induced on the tail
• Deficiency of tail surfaces to provide the desired lateral surfaces from combined effects of AOA and wing decontrol.
flection.
Wing Arrangements
Canard-Control Configuration
Wing arrangements have a significant influence on the types
A canard-control configuration consists of a set of small con- of missile control to be used. Three types of wing arrangetrol
surfaces called canards located well forward on the body ments are discussed here.
and a set of large surfaces (wing or tail) attached to the middle
or aft section of the missile. Its advantages and disadvan-
1. Cruciform. The most commonly used configuration in tages follow.
missile design is the cruciform, which possesses four
wing surfaces and four tail surfaces. There are several
Advantages. Advantages of canards include the following: major advantages in the use of this type of configuration:
(i) fast response in producing lift in any direction,
• Canards, because of their small size, do not generate a (ii) identical pitch and yaw characteristics, and (iii) simsignificant
amount of downwash to affect the longitudi- pler control system as the result of item (ii). One of the
nal stability adversely. Thus relatively large static-sta- most important aspects associated with a cruciform debility
margins can easily be obtained by simple changes sign is the orientation of the tail surface with respect to
in wing location. the wing planes. The significant conclusion from considerable
experience and experimental data was that an • Canard configuration has the inherent simplicity of packin-
line tail surface (i.e., all the four tail surfaces are in aging because the control system is small.
the same orientations as the four wing surfaces) provides
the best overall aerodynamic characteristics for
Disadvantages. Disadvantages include the following:
most missile applications. The other possible wing-tail
geometrical relation is called interdigitated configura-
• Roll stabilization is difficult when the canard surface is tion where there is a 45
 separation between the wing
used because of their size and downwash effect on the and tail orientation. For a cruciform missile, the most
wings. Usually a separate set of lateral controls such as difficult parameter to determine accurately is the inwing-
tip ailerons is needed for canard configuration. duced rolling moment. The rolling moments arise whenever
the missile simultaneously executes pitch and yaw • Relative high control-surface rates are required to obtain
the desired rate of response because AOA must be gener- maneuvers that are unequal in magnitude. Such maneuvers
result in unequal or asymmetric flow patterns ated before any lift is developed.
310 MISSILE CONTROL
over the aerodynamic lifting surface; consequently, roll- Up to now, the existing missile control strategies in various
mission phases include two major categories: skid-to-turn ing moments are induced on the airframe. Hence, roll
(STT) strategy and bank-to-turn (BTT) strategy. It is interest- stabilization or control is a critical issue for cruciform
ing to note that the progress in control strategy for crewed missiles.
aircraft is from BTT to direct sideslip control (i.e., STT), 2. Monowing. The monowing arrangements are generally
whereas the progress in missile control strategy is from STT used on cruise-type missile (i.e., missiles design to
to BTT. The applications and limitations of STT and BTT will cruise for relatively a long range like crewed aircraft).
be introduced in the following sections. This type of design is generally lighter and has less
drag than the cruciform configuration. The wing area
Skid-to-Turn Strategy and span are, however, somewhat larger. Although the
monowing missile must bank to orient its lift vector in In STT the missile roll angle may be either held constant or
the desired direction during maneuvering flights, the uncontrolled; in either case, the magnitude and orientation of
response time may be sufficiently fast and acceptable the body acceleration vector is achieved by permitting the
from a guidance-accuracy standpoint. The induced-roll missile to develop both an AOA and a sideslip angle. The
presence of the sideslip imparts a ‘‘skidding’’ motion to the problem for the monowing configuration is substantially
missile; hence the name skid-to-turn. The STT missile autopi- less severe than that associated with the cruciform conlot
receives the guidance command interpreted in terms of figuration. A separate set of lateral control surfaces,
the Cartesian system. In the Cartesian system, the missile- such as flaps, spoilers, and wing-tip ailerons, is generguidance
system produces two signals, a left–right signal and ally used in a monowing design. This stems from the
an up–down signal, which are transmitted to the missile-con- fact that the canard or tail surfaces that are usually
trol system by a wire or radio link to rudder servos and eleva- employed for pitch control on monowing design are gentor
servos, respectively. If a cruciform missile adopts STT con- erally inadequate for lateral control.
trol strategy, the two servo channels can be made identical 3. Triform. This type of wing arrangement, which embecause
of the identical pitch and yaw characteristics of a cru- ploys three wings of equal area spaced 120
 apart, is
ciform missile as mentioned earlier. Hence, in STT missiles, seldom used because no noticeable advantage can be reboth
pitch control and yaw control are called lateral control, alized. Results of a brief preliminary analysis indicate
which is different from the definition of aircraft control. that the total wing area of the triform is equal to that
The other control loop of the STT missile is roll control, used on a cruciform arrangement and that consequently
which is used to stabilize the missile roll position. For a per- no noticeable change in drag may be realized. In addifect
performance of the STT missile, it is assumed that the tion, little or no weight saving will be realized, even
missile will remain in the same roll orientation as at launch though one less arrangement or fitting is required beduring
the whole flight. In this ideal case, up–down signals, cause the total load remains the same.
if sent to the elevator servos, should then result in a vertical
maneuver only; and left–right signals, if sent to the rudder
MISSILE CONTROL STRATEGY servos, should result in a horizontal maneuver only. However,
a missile, except for a monowing missile, is not designed like
Because the missile control system (autopilot) is commanded an airplane and there is no tendency to remain in the same
by the missile guidance system, the autopilot command struc- roll orientation. In fact, it will tend to roll for many reasons
ture is dependent on guidance requirements for various mis- such as accidental rigging errors, asymmetrical aerodynamic
sion phases. loadings, and atmospheric disturbances. Two methods ensure
that left–right commands are performed by rudder servos and
• Separation (Launch) Phase. A body rate command sys- up–down commands are performed by elevators. The first
tem is typically used during launch because of its ro- method applies a quick roll servo (with bandwidth larger than
bustness to the uncertain aerodynamics. that of lateral servos) to stabilize the roll dynamics and to
recover the missile to the original roll orientation. The second • Agile Turn. During an agile turn, directional control of
method allows the missile to roll freely but installs a roll gyro the missile’s velocity vector relative to the missile body
and resolver in the missile to ensure that the commands are is desired. This amounts to commanding AOA or sideslip,
mixed in the correct proportions to the elevators and rudders. and regulating roll to zero.
However, roll stabilization (the first method) is generally • Midcourse and Terminal Phases. An acceleration commore
preferred for the following reasons: mand autopilot is commonly employed in these two
phases.
• There are many occasions when roll position control is
• End of Homing Phase. At the end of terminal homing, necessary, for example, to ensure that the warhead or
the missile attitude may be commanded to improve the altimeter always points downward.
lethality of the warhead. • If the missile is free to roll, high roll rates may cause
cross-coupling between the pitch and yaw channels and
Among these four autopilot structures, separation, midcourse, tend to unstabilize the system.
and endgame autopilots are in general well understood and
have been implemented in production missiles. Autopilot de- An STT missile with properly controlled roll motion may
signs for agile turns are significantly less well understood. provide the following advantages:
Reference 8 gives a detailed discussion of the challenges involved
in agile turn, and several solution techniques were • Same degree of vertical and horizontal maneuverability
can be achieved. provided there.
MISSILE CONTROL 311
• With STT control it is possible to resolve three-dimen- 3. BTT Autopilot Design. If a ramjet missile has two fixed
wings and is controlled with four cruciform tails, the sional target and missile motion into two independent
planar motions and to consider the pitch and yaw chan- best solution is to adopt a BTT autopilot, which can ensure
small values of AOA and sideslip angle. nels as an independent two-dimensional problem. Hence,
both guidance law and control system design can be done
Only the technique in item 3 is discussed here. The design via two-dimensional analysis. This simplification makes
of a highly maneuverable BTT autopilot poses a severe chal- it possible to apply the classic control theory, which
lenge to the control designer. High maneuverability means treats single-input single-out (SISO) system to the misnot
only high aerodynamic acceleration but also the ability to sile autopilot design.
change the orientation of the acceleration rapidly. This means
that the roll rate can be expected to be much larger (perhaps Bank-to-Turn Strategy
by an order of magnitude) than they would be in a STT mis-
The concept of BTT stems from the motion of crewed aircrafts, sile. The large roll rates induce substantial cross-coupling bewhich
use ailerons to bank (roll) to the left or right. During a tween the pitch and the yaw axes, whereas in a typical STT
left or right turn, a small amount of rudder is also applied in missile this cross-coupling is negligible. The main advantage
an attempt to make the air flow directly along the longitudi- of BTT strategy is its adaptability to ramjet missile control,
nal axis of the aircraft. Hence, in BTT motion, there is no but there are many difficulties that cannot be conquered by
sideslip and no net side force. From a passenger’s point of the techniques used in STT strategy:
view, this method of maneuvering is the most comfortable because
the total force experienced is always symmetrically • The cross-coupling between the pitch and yaw axes rethrough
the seat. When BTT concept is applied to missile con- quires the designer to consider both axes together as a
trol, the missile is rolled first so that the plane of maximum single multi-input/multi-output (MIMO) system. The
aerodynamic normal force is oriented to the desired direction classic SISO control approach becomes inadequate for
and the magnitude of the normal force is then controlled by BTT application, and modern MIMO control theory
adjusting the pitch attitude (AOA). If we consider the guid- needs to be considered.
ance command for an STT missile as being expressed in the
• The cross-axes couplings are proportional to the roll rate, Cartesian coordinates (x, y) where x is the right–left comwhich
is a dynamic variable. This means that the dynam- mand and y is the up–down command, then the guidance
ics of the pitch and yaw axes are not only cross-coupled command for a BTT missile can be considered as being exbut
also nonlinear. Therefore, a single fixed-coefficient pressed in the polar coordinates (r,     ) where     is the angle to
linear autopilot may be unable to cover the whole flight roll and r is the distance to be steered in the pitch plane.
envelope, and linear autopilot with gain scheduling or Therefore,BTT strategy is sometimes called polar control or
nonlinear autopilot design should be taken into account. ‘‘twist-and-steer’’ control.
• The three-dimensional motion of a BTT missile cannot Although BTT control has been used in crewed aircraft for
be resolved into two planar motions. Hence, the guidance a long time, the interest in BTT missile control only began in
law design for a BTT missile needs detailed three-dimen- the late 1970s. The principle motivation for developing the
sional analysis. BTT missile autopilot stems from the successful application
of ramjet propulsion technology to missile system. Several
In summary, a BTT missile can be considered as a MIMO ramjet missiles were developed in the late 1970s, including
system with nonlinear dynamics and with three-dimensional ramjet interlab air-to-air technology (RIAAT program,
kinematics, whereas a STT missile can be well approximated Hughes), advanced common intercept missile demonstration
as an integration of three SISO systems with linear dynamics (ACIMD program, Naval Weapons Center), advanced strateand
with two-dimensional kinematics. Reference 8 summa- gic air-launched multi-mission missile (ASALM program,
rizes some status and concerns of BTT missiles. How modern McDonnell Douglas and Martin-Marietta). These BTT procontrol
theory can be used to design BTT autopilots is dis- grams are thoroughly surveyed in Ref. 9. All these ramjet
cussed in Ref. 10. missile programs require autopilot to prevent missile maneuvers
from shading the inlet (i.e., the AOA needs to be small
and positive) and to limit sideslip in order to increase en- MISSILE AUTOPILOT DESIGN
gine efficiency and thereby maximize range. The conventional
STT strategy cannot satisfy these limitations on and . The Equations of Motion
applicability of the ramjet missile requires investigation in
The equations of motion of a missile with controls fixed may the following areas:
be derived from the Newton’s second law of motion, which
states that the rate of change of linear momentum of a body
1. Monowing Configuration. Ramjet missiles have two in- is proportional to the summation of forces applied to the body
lets external to the main body and there is room for and that the rate of change of the angular momentum is proonly
one pair of wings (i.e., monowing). portional to the summation of moments applied to the body.
2. Variable-Incidence Wing Control. Because the inlets Mathematically, this law of motion may be written as
could accept only a small AOA as a result of interference
from the body, the use of variable-incidence wing
control, which can provide instantaneous lift without increasing
the AOA of the body, is very suitable for ramjet
engines.
d
dt ?
??
mU
mV
mW
???
= ?
??
X
Y
Z
???
,
d
dt ?
??
Hx
Hy
Hz
???
= ?
??
L
M
N
???
(3)
312 MISSILE CONTROL
where (X, Y, Z) and (L, M, N) are the resultant forces and of inertia about the y axis is generally equal to that about the
z axis (i.e., Iyy Izz). Hence, the resulting equations become moments caused by aerodynamic forces, gravity, and propulsive
forces, along the body axes (x, y, z). (U, V, W) and (Hx,
Hy, Hz) are the components of the velocity and angular momentum
of the missile about the x, y, and z axes, respectively.
The two main reasons for the use of body axes in the dynamic
analysis of the missile are (1) the velocity along these axes
are identical to those measured by instruments mounted in
the missile and (2) the moments of inertia (i.e., Ixx, Ixy, etc.)
are independent of time. Equation (3) and (4) can be expressed
in terms of the moments of inertia and the missile
m( ? U + QW - RV ) = X (6a)
m( ? V + RU - PW) = Y (6b)
m( ? W + PV - QU) = Z (6c)
? PIxx = L (6d)
? QIyy + PR(Ixx - Izz ) = M (6e)
? RIzz + PQ(Iyy - Ixx ) = N (6f)
angular velocity P, Q, and R as follows:
These are the general equations used in the analysis of STT
control strategy, especially for agile STT missiles with substantial
induced roll. When rolling rate P is relatively small
when compared with Q and R, further simplification of Eq.
(6) is possible by dropping the terms relating to P, and the
result is the three decoupled servo channels used in the conventional
STT autopilots.
1. Pitch dynamics:
m( ? W - QU0) = Z, Iyy ? Q = M (7a)
m?
??
? U + QW - RV
? V + RU - PW
? W + PV - QU
???
= ?
??
X
Y
Z
???
(4a)
???
Ixx -Ixy -Ixz
-Ixy Iyy -Iyz
-Ixz -Iyz Izz
???
???
? P
? Q
? R
???
+
???
0 -R Q
R 0 -P
-Q P 0
???
???
Ixx -Ixy -Ixz
-Ixy Iyy -Iyz
-Ixz -Iyz Izz
???
???
P
Q
R
???
= ?
??
L
M
N
???
(4b)
2. Yaw dynamics:
For a missile with monowing configuration, the xz plane is a
plane of symmetry. Consequently, Iyz Ixy 0 from the defi- m( ? V + RU0 ) = Y, Izz ? R = N (7b)
nition of moment of inertia. Hence, Eqs. (4) may be simplified
as follows:
3. Roll dynamics:
Ixx ? P = L (7c)
where the forward speed U is assumed to be a constant U0
because U? is generally small. It can be observed that each
servo channel is decoupled, linear, and SISO (i.e., each channel
has a single input and a single output: the pitch dynamics
with elevator input and AOA [ (t) W(t)/U0] output, the yaw
dynamics with rudder input and sideslip [ (t) V(t)/U0] outm(
? U + QW - RV ) = X (5a)
m( ? V + RU - PW) = Y (5b)
m( ? W + PV - QU) = Z (5c)
? PIxx + QR(Izz - Iyy ) - Ixz ( ? R + PQ) = L (5d)
? QIyy + PR(Ixx - Izz ) + Ixz (P2 - R2) = M (5e)
? RIzz + PQ(Iyy - Ixx ) - Ixz ( ? P - QR) = N (5f)
put, and the roll dynamics with aileron input and roll rate P
output). This formulation is rather simplified, but very prom-
These differential equations govern the motion of a monowing ising results had been recognized in an STT autopilot applimissile
with BTT control. It can be seen that these equations cation.
are nonlinear and cross-coupled; none of the equations can be In general, the resultant forces X, Y, Z, and moments L,
isolated from the others. Taking Eq. (5b) as an example, the M, N in Eq. (6) are nonlinear functions of U, V, W, P, Q, R,
term mPW says that there is a force in the y direction and of the control surface deflections. However, a linear concaused
by the incidence in pitch (i.e., W/U) and the roll trol system is designed under the condition that the missile
motion P. In other words, the pitching motion (W) of the mis- is exercised through small perturbations about some trim consile
is coupled to the yawing motion (Y force) on account of ditions (equilibrium conditions). From the viewpoint of autoroll
rate P. Equation (5a) does not really concern us because, pilot design, a linear Taylor expansion of the resultant forces
in most cases, we are interested in the acceleration normal to and moments about the trim conditions is adequate. We will
the velocity vector as this will result in a change in the veloc- use the symbol with subscript zero (0) to stand for trim condiity
direction. In any case, in order to determine the change in tion and the symbol with a lowercase letter to denote the perthe
forward speed U, we need to know the magnitude of the turbation quantities. For example, V is expressed by V(t)
propulsive and drag force. Nevertheless, except for power V0 v(t) where V0 is the steady-state side speed and v is the
phase, the variation of U is generally very small. perturbed side speed which is a function of time. The other
For a missile with cruciform configuration, further simpli- variables can be expressed in the same way. The deflection
fications can be made because (1) the xy plane (as well as xz) angles of aileron, elevator, and rudder, will be denoted by a,
e, and r, respectively. is also a plane of symmetry (i.e., Ixz 0) and (2) the moment
MISSILE CONTROL 313
Forces and moments can also be expanded in a perturbed follow-up units as a complete missile control system as described
at the beginning of this article. form. For example, assume that the side force Y(V, R, r) is a
function of V, R, and r. It can be expanded as
Classic Control Design
Figure 4 depicts the block diagram of a lateral autopilot performing
side force control, where a rate gyro measuring yaw
Y(V,R, dr) = Y(V0,R0, dr0 ) +
?Y
?v
v +
?Y
?r
r +
?Y
?dr
dr
= Y0 + yvv + yrr + ydr dr
(8)
rate and an accelerometer measuring side acceleration are
used as feedback sensors. The missile’s aerodynamic transfer where Y0 is the steady-state side force; yv ( Y/ v (V0, R0,
function in Fig. 4 are obtained from Eq. (10). The controller r0), yr ( Y/ r) (V0, R0, r0), y r
( Y/ r) (V0, R0, r0) are called
is in the form of proportion and integration (PI). The problem aerodynamic derivatives evaluated at the specified trim conof
autopilot design is to design properly the seven parameters dition. Aerodynamic derivatives with respect to state vari-
KP, KI, Ka, Kg, s, s, and Ks such that the actual missile side ables are also called stability coefficients such as yv, and yr;
force y follows the commanded side force yd as quickly as pos- derivatives with respect to control surface deflection are also
sible. Among the seven parameters, the two controller gains called control coefficients such as y r. Remaining forces and
KP and KI can be further tuned to satisfy different flight condi- moments can be linearized in a similar way as in Eq. (8).
tions. The remaining five parameters have fixed values and Substituting these linearized quantities into Eq. (7) yields the
cannot be tuned on line. The selection of the seven parame- control equations for a STT missile as
ters is aided by such tools as root locus, Bode, Nyquist, or
Nicholls plots that enable visualization of how the system dy- 1. Pitch dynamics:
namics are being modified. The performance specifications of
the side force response may be given in the frequency domain
(e.g., bandwidth and gain/phase margins) or in the time domain
(e.g., overshoot, damping ratio, rise time, and settling ? w
? q = zw U0 + zq
mw mq w
q + zde
mde de (9)
time).
2. Yaw dynamics: The classic control design process of missile autopilot can
be summarized in the following steps. Detailed procedures
and practical design examples can be found in Refs. 5 and
11. How aerodynamic derivatives affect the missile autopilot ? v
?r = yv -U0 + yr
nv nr v
r + ydr
ndr dr (10)
design is discussed in Ref. 12. A useful review of classically
designed autopilot controllers may be found in Ref. 13, where 3. Roll dynamics:
the relative merits of proportional and PI autopilot controllers
are discussed and the novel cubic autopilot design is intro- ? p = lpp + lda da (11)
duced.
The Laplace transfer function from the aileron input a to
the roll rate output can be found from Eq. (11) as 1. Based on the system requirements analysis, the designer
selects a flight control system time constant, a
damping ratio, and an open loop cross-over frequency
that will meet the system requirements for homing acp
da = -lda /lp
Tas + 1
(12)
curacy and stability.
where l a/lp can be regarded as the steady state gain and 2. The autopilot gains are calculated. The gains such as
Ta 1/lp can be regarded as the time constant of the roll KP and KI in Fig. 4 are obtained in a variety of linearchannel.
The Laplace transfer function from the rudder input ized flight conditions and must be scheduled by appro-
r to the body yaw rate r can be obtained from Eq. (10) as priate algorithms to account for the changing environment.
3. A model of the flight control system is developed. Inir
dr =
ndr s - ndr + nvydr
s2 - (yv + nr)s + yvnr +U0nv
(13)
tially the flexible body dynamics are neglected and the
rigid body stability is analyzed to determine if adequate Let and n be the damping ratio and the undamped natural
phase and gain margins have been achieved. If not, the frequency of the yaw channel, respectively, then we have
response characteristics are modified and the design is
iterated. 2??n = -(yn + nr ), ?2n
= ynnr +U0nv (14)
4. When the low-frequency design is complete, the flexible
body dynamics are incorporated into the frequency mod- It can be seen that the characteristics of the open-loop responses
in Eqs. (12) and (14) are determined by the related els, and the stability is reexamined. For typical tactical
homing missiles, the flexible body model should include aerodynamic derivatives. For example, to ensure that the
open-loop yawing motion (i.e., without control) is stable, we the first, second, and third resonant mode dynamics of
the pith and yaw channels and at least the first mode must have yv nr 0. If the open-loop motion is unstable or
is near the margin of instability, then autopilot must be in- of the roll channel. Depending upon the characteristics
of the roll airframe structure, additional modes may stalled to form a closed-loop system that integrates missile
dynamics, sensor units, controller units, actuator units, and have to be modeled.
314 MISSILE CONTROL
+
+
+
+
+
–
Kp + yd
r ?
Kg
Rate gyro
Accelerometer
Lateral acceleration
Side force
response
Missile dynamics Rudder angle
Actuator
Controller Side force
command
y
Yaw rate
r
Is
KI
s ? 2 s + +1
–Ks
s2
? s
2
s
? s
y rs2 – y rnrs – U0
(n r yv – nvy r
) d d d d
s2 – (yv + nr)s + yvnr + U0nv
n rs + nvy – n r yv d d d
y rs2 – y rnrs – U0
(n r yv – nvy r d d d d
K a
Figure 4. An autopilot structure performing side force command tracking. Both missile and
rudder servos are modeled as second-order dynamics; the gyro and accelerometer are modeled as
constant gains; and the controller is in the form of proportion and integration with tuning gains
KP and KI.
5. In cases where the stability margins do not meet the Ref. 16. The technique has been applied to the control of the
extended medium-range air-to-air missile in Ref. 17. design criteria the autopilot design is modified through
adjustment of the autopilot gains and/or the inclusion
of structural filters that adjust the gain or phase in the LQR Autopilot Design. LQR control theory is a well-estabarea
of the natural resonances. lished control system design technique (18). The LQR control
gains are all obtained simultaneously from the minimization
Modern Control Design of a suitable performance index (usually the integral of a quadratic
cost function). The design is synthesized in the time Classic control techniques have dominated missile autopilot
domain as opposed to the complex frequency domain. Refer- design over the past decades. Autopilot design for future misence
14 demonstrates the effectiveness of LQR design tech- sile systems will be dominated by the requirement of ultimate
niques for the missile flight control problem—describing the agility in the entire flight envelope of the missile. Critical isapplication
of various LQR formulations to the design of sin- sues in the next generation autopilot will include (1) fast regle-
plane lateral acceleration autopilot controllers. Reference sponse to the commanded accelerations, (2) high maneuver-
19 further considers the advantages obtainable by combining ability and guaranteed robustness over a wide range of
classical PI and modern LQR methodologies for a multivari- mission profiles at all speeds and altitudes, (3) performance
able airframe model with high frequency structural modes. robustness against uncertainties in the aerodynamic derivatives,
in the thrust profile, in the effectiveness of the control
Robust Autopilot Design. Robust control methods provide surfaces, and in the varying mass and moment of inertia, (4)
the means to design multivariable autopilots that satisfy per- cancellation or attenuation of highly nonlinear and coupled
formance specifications and simultaneously guarantee stabil- missile dynamics as a result of high AOA. The development of
ity when the missile deviates from its nominal flight condition eigenstructure assignment, linear quadratic regulator (LQR)
or is subject to exogenous disturbance. Several investigations control, robust control, nonlinear control, adaptive control,
have been undertaken specifically to research missile autopi- and intelligent control techniques have revolutionized missile
lot robustness. Early work was directed toward specific con- control system design considerably. They provide power tools
figurations and problems (20), with more recent work using to realize the aforementioned critical issues. Reference 14
the robust control system synthesis techniques of quantita- provides an excellent discussion of various applications of
tive feedback theory (QFT) (21), H control (22), -synthesis modern control theory to flight control systems.
(23), normalized coprime factor loop-shaping H control (24),
and linear matrix inequality (LMI) self-scheduling control Eigenstructure-Assignment Autopilot Design. Eigenstructure
(25). Research has also been carried out on a number of re- assignment is the multivariable extension of the root locus
lated ways of assessing the robustness of missile autopilot method. The behavior of a MIMO system is characterized by
controller design (26). A good literature survey in robust au- eigenvalues and eigenvectors. The eigenvalues determine statopilot
design can be found in Ref. 15. The robust control de- bility, and the eigenvectors characterize the shape and cousign
is formulated to minimize the following effects: pling of different modes. The technique is concerned with the
placing of eigenvalues and their associated eigenvectors by
feedback, to satisfy directly closed loop damping, settling • Parameter Variation. Aerodynamic derivatives, moment
of inertia, and the center of gravity may have significant time, and decoupling specifications. A review of eigenstructure
assignment for aerospace applications can be found in variations over the entire missile flight envelope.
MISSILE CONTROL 315
• Coupling Dynamics. The residual error caused by inex- trast, direct adaptive controls such as the self-tuning regulator
(33) and model reference adaptive control (34) update the act cancellation in decoupling pitch and roll–yaw dynamics
for BTT missiles needs to be addressed. autopilot gains directly on the basis of the history of system
inputs and tracking errors. • Unmodeled Dynamics. Most missile autopilot design consider
missile rigid-body dynamics only, and the missile
flexible modes are regarded as unmodeled dynamics. Ro- Intelligent Autopilot Design. Missile autopilot design task
bust control design allows the unmodeled dynamics to be requires tuning parameters to achieve desirable performance.
taken into account to avoid structural vibration or insta- By augmenting a neural network in the tuning process, the
bility. parameter adjustment process can be standardized. This can
• Sensor Noises. Autopilot needs to attenuate the effects be done as follows. First, build the desired flying qualities into
caused by sensor noises, calibration errors, drifts, and the performance model. The autopilot structure is prefixed
parasitic dynamics. with the parameters undetermined. Then by comparing the
actual system performance with the desired flying qualities, • Tracking Error. A successful missile interception dethe
neural network is trained to learn the rules of tuning. pends on the ability of autopilot to track the guidance
Accordingly, the autopilot parameters can be updated to meet commands. The uncertainties and noises in the seeker
the requirements. Application of neural network techniques output and in the prediction of target maneuvers may
to missile autopilot design and to future generation flight con- affect the autopilot tracking performance.
trol system was investigated in Refs. 35 and 36.
Nonlinear Autopilot Design. Nonlinear control techniques
used in missile autopilot design include feedback lineariza-
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CIANN-DONG YANG
CHI-CHING YANG
HSIN-YUAN CHEN
National Cheng Kung University