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

Chapter 5 / Missile State Observer
_ _
⎛
⎜
⎜
⎜
⎜
⎜
⎜
⎝
⎛ 2
⎜ − Po,
t ⋅
⎜
⎜ 2
⎜ Po,
t ⋅ P&
t
⎜
⎜
2
⎝ Po,
t ⋅ P&
t
ϕ
ϕ
ϕ
X
Y
Z
⎞
⎟
⎟
⎟
⎟
⎟
⎟
⎠
rA ( P&
)
XA
XA
t
: =
− 2 ⋅ P
L
YA
⋅ P&
− 2 ⋅ P
t
L
ZA
⋅ P&
− 2 ⋅ P
t
2
⎛
⎜
⎜
⎜
⎜
⎜
⎜
⎝
XA
t
XA
t
XA
t
YA YA ZA ZA XA XA rA
( P ⋅ P&
+ P ⋅ P&
) ⋅ P&
− P ⋅ ( P&
)
t
XA XA ZA ZA YA YA vA
( P ⋅ P&
+ P ⋅ P&
) ⋅ P&
− P ⋅ ( P&
)
t
( ) ( ) ⎟ ⎟⎟⎟⎟⎟⎟
XA XA YA YA ZA ZA hA 2
P ⋅ P&
+ P ⋅ P&
⋅ P&
− P ⋅ P&
⋅ ϕ
⋅ ϕ
⋅ ϕ
X
Y
Z
t
M
M
M
M
M
∂ P&
&
t
t
t
A
t
2
o,
t
P
− P
2
o,
t
P
⋅ P&
2
o,
t
⋅
⋅ P&
∂ P
XA
t
5-22
t
t
t
⋅ P&
vA ( P&
)
YA
t
A
t
t
: =
YA
t
L
ZA
⋅ P&
− 2 ⋅ P
t
L
2
t
t
t
λ ⋅ P
t
− 2 ⋅ P
− 2 ⋅ P
−4
o,
t
YA
t
YA
t
YA
t
⋅ ϕ
⋅ ϕ
⋅ ϕ
X
Y
Z
t
t
L
t
M
M
M
M
M
2
o,
t
P
2
o,
t
P
− P
t
t
t
⋅ P&
⋅ P&
2
o,
t
XA
t
YA
t
⋅
t
t
t
2
2
⎞
⎠
Equation 5.9-10
⋅ P&
− 2 ⋅ P&
L
ZA
⋅ P&
− 2 ⋅ P&
⋅ ϕ
⋅ ϕ
( ) ⎟ ⎟⎟⎟⎟⎟⎟
hA 2 ZA
P&
− 2 ⋅ P&
⋅ ϕ
t
ZA
t
t
L
ZA
t
ZA
t
t
X
Y
Equation 5.9-11
A target kinematic gain of 3 is used thereby avoiding the complication of
estimated this parameter in the observer, contrary to the ethos of pseudomeasurements.
The variability in this parameter should be accounted for in
the measurement uncertainty weighting.
5.9.3 Missile Dynamic Pseudo-Measurements
A simplified set of missile dynamics is often used for the observer process
model, with the system noise accounting for thrust, drag airframe and
aerodynamic uncertainties. Alternatively these dynamics can be introduced
as pseudo-measurements driven by fin measurements, constraining a simple
process model. This method provides greater control over the order and rate
that measurements are processed to smooth out the computational load. The
force and moment balances defined in §6 together with the aerodynamic
derivatives, are simplified by assuming that:
• Roll inertia is small compared with the lateral inertia
• Cross inertia terms are small
• The missile is symmetric with equal pitch and yaw inertia
• Aerodynamic damping force is small,
• Earth rate and tilt over its surface are ignored
• Gravitational variations with height are small and are ignored
• The missile reference point lies on the missile centreline
• The forces and moments are related to the missile reference point (m) that is
displaced from the centre of gravity
Z
⎞
⎠