Thesis - Leigh Moody.pdf - Bad Request - Cranfield University

Chapter 3 / Inertial Navigation
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3.3.1.3 IMU-2 Kinematics
Extending the dynamic analysis of the Master IMU to the angular rate of the
Missile Body frame (M) in a flexible missile attached to a pylon on the wing
of an aircraft,
ω
M
C,
M
M
P
P P W W B
M
( ω + T ⋅ ( ω + T ⋅ ω ) ) +
: = T ⋅
ω
W,
P
3.3-8
W
B,
W
B
C,
B
P,
M
Equation 3.3-30
Wing motion with respect to the fuselage comprises wing bending and low
frequency wing flexure in the frequency range < 1 Hz and 5-15 Hz; these
are complex functions of fuel and armament load, aircraft speed, turn rate,
buffet and vortex shedding. Pylon motion with respect to the wing has a
spectral content of typically 30-50 Hz. Missile vibration is constrained by
its supports, stiffness, and the mode of vibration, a function of the number
of supports and the distance between them. The effect of these static and
dynamic components is twofold. Low frequency motion effects target
designation performance and the ability of the weapon system to keep the
target in the seeker field-of-view. High frequency motion causes the energy
falling on the seeker detector to be smeared when using IR staring arrays
reducing the acquisition range and accuracy. When studying the effect of
this motion on the seeker smear it must be modelled, not at the highest
modal frequency within the seeker bandwidth (70-100 Hz), but at a
frequency commensurate with the internal gimbal dynamics and the detector
stare time, typically > 2 kHz.
These models are derived from instrumented wing, pylon and missile data
and it is extremely difficult to isolate the individual noise components
comprising the overall spectra and the cross coupling between axes. Data
reduction invariably results in separate, none co-ordinated roll-pitch-yaw
spectra that are a function of the operating conditions. Flexure models are
thus partitioned into a static elements associated with the wing, pylon
attachment, missile supports and missile body misalignment. Thus the
orientation of the Missile Body frame with respect to the Launcher Body
frame comprises a nominal orientation, onto which is superimposed small
angle transforms representing the quasi-static and flexure components
denoted by “N”, “S” and “F” respectively,
M
B
M
DTB
M
STB
M P W
( T ⋅ T T )
T : = ⋅ ⋅
⋅
N
P
N
W
N
B
Equation 3.3-31
The various static misalignments, such as the residual harmonisation angle
of the pylon and missile, are modelled as initial zero mean, Gaussian errors.
Wing bending is treated as a quasi-static misalignment that is a function of
say speed and turn rate. When designating targets it is this component of
structural motion that some aircraft attempt to compensate for, not the
higher frequency pylon noise that invariably requires a small scan pattern.