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

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Chapter 2 / Target Modelling<br />

_ _<br />

E<br />

TV<br />

A<br />

2.2.6 Target Model 3<br />

: =<br />

⎛<br />

⎜<br />

⎝<br />

π<br />

,<br />

− tan<br />

2-8<br />

−1<br />

⎛ P&<br />

⎜<br />

⎝ P&<br />

ZA<br />

t<br />

hA<br />

t<br />

⎞<br />

⎟<br />

⎠<br />

,<br />

tan<br />

−1<br />

⎛ P&<br />

⎜<br />

⎝ P&<br />

YA<br />

t<br />

XA<br />

t<br />

⎞ ⎞<br />

⎟ ⎟<br />

⎟ ⎟<br />

⎠ ⎠<br />

Equation 2.2-8<br />

The demanded acceleration represents the amplitude of a sinusoidal weave<br />

expressed in the Target Velocity frame,<br />

TAGACC<br />

2.2.7 Target Model 4<br />

A<br />

t<br />

A<br />

TV<br />

D1L<br />

TV ( A ⋅ cos ( ω t)<br />

, t )<br />

= 3 ⇒ P&<br />

& : = T ⋅ ϕ<br />

⋅<br />

D<br />

w<br />

ta<br />

Equation 2.2-9<br />

The demanded acceleration represents the amplitude of a "square" wave<br />

weave expressed in the Target Velocity frame.<br />

TAGACC<br />

2.2.8 Target Model 5<br />

A<br />

t<br />

A<br />

TV<br />

D1L<br />

TV<br />

( sign ( A , cos(<br />

ω t)<br />

) , t )<br />

= 4 ⇒ &P<br />

& : = T ⋅ ϕ<br />

⋅<br />

D<br />

w<br />

ta<br />

Equation 2.2-10<br />

The demanded acceleration in the Target Velocity frame is derived using a<br />

PN guidance law with the missile launcher as the intercept point.<br />

TAGACC<br />

⎛ ⎛ XTV<br />

⎞<br />

⎜<br />

A ⎞<br />

⎜ D ⎟ ⎟<br />

⎜ ⎜<br />

⎟ ⎟<br />

A<br />

A ⎜ ⎜ XT ZT ⎟ ⎟<br />

= 5 ⇒ &P<br />

&<br />

t : = TTV<br />

⋅ ϕD1L<br />

⎜ ⎜ λt<br />

⋅ P&<br />

t ⋅ ωA,<br />

T ⎟<br />

, t ta ⎟<br />

⎜ ⎜<br />

⎟ ⎟<br />

⎜<br />

⎟<br />

⎜ ⎜ XT YT ⎟<br />

⎟<br />

⎝ ⎝ λt<br />

⋅ P&<br />

t ⋅ ωA,<br />

T ⎠ ⎠<br />

Equation 2.2-11<br />

The longitudinal acceleration remains the same as for Target Model 2,<br />

providing the facility to model accelerating attacks on the launcher.<br />

2.2.9 Target Model 6<br />

The demanded acceleration is a combination of Target Models 4 and 5. The<br />

result is an accelerating PN track with a superimposed sinusoidal weave.

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