G. Leng, MDTS, NUS
MDTS 5705 : ControlLecture 1 : Missile control configurations
G. Leng, MDTS, NUS
References
• G. M.. Siouris, “Missile Guidance and Control Systems”,
Springer-Verlag, 2004
• B. Stevens. "Aircraft Control & Simulation", J. Wiley,
1992.
• D. McRuer, I. Askenas & D. Graham, "Aircraft Dynamics
and Automatic Control“, Princeton University Press, 1973
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Training Programme
1 : Missile control configurations
or making sense of the aerodynamics for flight control
2 : Missile dynamics and control models
or when to simplify, when to stop and how to simulate
3: Designing the flight control system
or defining the control limits of the missile
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1.1.1 : A first step is to define a convenient axis system or
reference frame fixed to the missile.
Question : Why fixed to the missile ?
1.1 : Axes System
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x
z
1.1.2 : Body axes
yy
The convention for flight dynamics is :
I) The positive x axis points towards the nose
II) The positive y axis points to the right
III) The positive z axis points downwards.
Note that this is a right handed
coordinate system.
Question : Where should the
origin be placed ?
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1.1.3. The set of axes as defined in 1.1.2 is called the body axes. It is fixed to the missile and translates and rotates with it.
Question : Implications for equations of motion ?
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1.1.4 : Aerodynamics axes
Question : Why do the axes point
this way ?
x
z
y
y
Typically, aerodynamicists and structural engineers use different
conventions for their axis systems creating unnecessary
confusion
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1.1.5. Using the body axes, the missile's velocity V is written
as V = {u, v, w} where
u, v, w
are the velocity components in the X,Y,and Z axes direction.
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x
z
Figure 1.1.1 : Velocity components
y
v
w
u
V
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1.1.6. Similarly we denote the missile's rotation with an
angular velocity vector = {p, q, r } where p, q, r, are the
roll (wings up/down)
pitch (nose up/down)
yaw (nose right/left)
rotational rates.
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x
z
Figure 1.1.2 : Angular velocity components
yp roll rate
r yaw rate
q pitch rate
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1.2 : Aerodynamic Forces and Moments
1.2.1. Aerodynamic forces and moments on the missile depend
on the orientation of the missile with respect to the flight
trajectory
1.2.2. This orientation is specified by the two important angles
: angle of attack
: sideslip angle
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v
u
w
Figure 1.2.1 : AOA & sideslip angle definition 1
V
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v
u
w
Figure 1.2.1 : AOA & sideslip angle – definition 2
V
s
Question : Can you spot the difference ?
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Example : Aerodynamic database
How does the aerodynamics vary for a real missile ?
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Example – CZ variation
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Example - Cm variation
Question : Why must Cm vary this way with AOA ?
AOA
Cm
e
trim pt
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How does one “control” a missile ?
Maverick
Sidewinder
Control
surfaces
Control
surfaces
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Missile aerodynamic control surfaces
servo motor
control
surface
hinge
line
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• Deflection of control surfaces changes aerodynamic forces acting on the surface
• Changes in forces generate moments about the cg which roll, pitch and yaw the missile
• How well does this work ?
• Can you estimate the aerodynamic control forces on a missile ?
Basic aerodynamic control technique
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Ex : Control force estimation
• AIM 9 @ Mach 2.5
• Triangular fin
• Area = ½ x 0.3 x 0.3
= 0.045 m2
Force =
=
=
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Examples of missile control surfaces
• Foldable fins
• Tube launched weapons
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Examples of missile control surfaces
• Lattice control surface
• AA-12 Adder
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Performance implications 1
Tail control missile
Lw
W Lt
So what’s the problem ?
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Non–minimum phase response
time
commanded
latax
actual latax
Initial response heads off in the wrong direction
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Performance implications 2
Canard control missile
Lw
W
Lc
Comments ?
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Ex : Comment on the control configuration of this missile
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Multi-control surfaces - Rafael Python 4
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1.3 Missile control methods - examples
ailerons
rudder
elevator
Where are the control surfaces ?
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1.3.1 Cartesian control for homing
• Separate sets of control surfaces
for pitch (up/down) and yaw
(left/right)
• Guidance generates required
latax for pitch and yaw planes
• Pitch and yaw controls can act
simultaneouslytarget
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Missile control methods - example
Moving wings serve as both
ailerons and elevators
Fixed tail surfaces
Question : What can of control
method was employed ?
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1.3.2 Polar control for homing
• Guidance generates
roll command and
required pitch latax
(twist & steer)
• Needs roll angle
reference
• How fast is the
missile response ?
target
target
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1.3.3 Skid to turn for mid-course
• Turn executed by
“skidding” the missile
• Hence missile is not
aligned with velocity
vector during turn
• Typically used for fast
turn response
• May lead to large AOA &
sideslip – problems ?
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1.3.4 Bank to turn for mid course
• Missile rolls to vector lift
• Missile is aligned with velocity vector during turn
• Small AOA & sideslip
• Why bank to turn ?