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Chapter 6 / Missile Guidance
_ _
the basic PN demand is optimal and no further control effort is required
once a collision course is established. The difference between normalised
and traditional PN is in the velocity scaling. Normalised PN is scaled using
the closing speed whilst traditional PN is scaled by missile speed. The
acceleration demand is applied normal to the missile-target LOS for True
PN, and normal to the missile velocity vector for PPN. The four variants in
the basic PN demand are therefore,
Normalised - True PN
PN
S
SL
Traditional - True PN
PN
m
6-16
XS
m,
t
( ) T
ZS
YS
ω , −
α : = λ ⋅ P&
⋅
ω
S
SL
Normalised - Pure PN
PN
m
XMV
o,
m
A,
S
A,
S
( ) T
ZS YS
− ω ,
α : = λ ⋅ P&
⋅
ω
MV
SL
Traditional - Pure PN
PN
m
XS
m,
t
A,
S
A,
S
( ) T
ZS
YS
ω , −
α : = λ ⋅ P&
⋅
ω
MV
SL
m
XMV
o,
m
A,
S
A,
S
( ) T
ZS YS
− ω ,
α : = λ ⋅ P&
⋅
ω
A,
S
A,
S
Equation 6.5-14
Equation 6.5-15
Equation 6.5-16
Equation 6.5-17
Although the speed advantage required for Traditional PN can be relaxed
for Normalised PN, the later is prone to acceleration limiting and incidence
drag induced speed loss. Although Shukla [S.1] showed that PPN is superior
to TPN, PPN is rarely used as it requires missile incidence as well as seeker
data. In its basic form TPN requires only seeker data, and ideally a
measurement of closing speed. The closing speed and LOS rate are
obtained directly from the missile observer states,
P
2
m,
t
⋅ T
B
S
P
m,
t
⋅ ω
S
A,
S
⋅ P&
: = − P • P&
XS
t
: =
A
m,
t
A
m,
t
B A
B A
( TA
⋅ Pm,
t ) × ( TA
⋅ P&
m,
t )
Equation 6.5-18
Equation 6.5-19
Expanding the Normalised TPN demand in terms of polar dynamics,