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Chapter 6 / Missile Guidance
_ _
6.5.1.6 Stability and Observability
The analytical stability of PN is considered by Rew [R.6] . Song [S.6-7] modified
the PN law by oscillating the target LOS to make the system more
observable and effective for mid-course guidance. Hull [H.4] optimised both
control effort and information content, convergence of the shooting
technique solution requiring a gradual transfer of weight from control effort
to observability.
6.5.2 Conventional PN Guidance Laws
For constant closing speed engagements in which the missile has a speed
and lateral acceleration advantage over the target, PN laws have proven to
be remarkably robust. Enhancement of the basic PN concept is introduced,
reducing the target LOS rate to zero whilst compensating for,
• Short range engagements dominated by the missile boost phase
• Accelerating targets using sophisticated avoidance manoeuvres
• High altitude engagements with increasing missile incident lag
Essentially the PN guidance demands decompose into four terms:
• The basic demand required to reduce the target LOS rate to zero
• Compensate for the uncontrolled missile longitudinal acceleration
• Augmentation to account for quasi-constant target acceleration
• Compensation for gravitational acceleration
Combining these terms, and expressed them in the Missile Body frame so
that the autopilot can be closed around the body referenced accelerometer
output,
PN
α
Β
D
≡
YΒ
ZΒ T
Β Β
Β Β
( α , α ) : = α + α + α + α
PN
D
PN
D
6-14
PN
SL
PN
MA
PN
TA
GA
Equation 6.5-5
Acceleration normal to the LOS is determined in different reference frames
depending on the form of PN. To generate the equivalent acceleration in the
Missile Body frame requires the inverse scaling,
B
o,
m
T
T F
( & YB ZB
F
P&
, &P
& ) : = ( T ) &P
&
&P & ≡
⋅
o,
m
o,
m
B
o,
m
Equation 6.5-6