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

Appendix H / Steady State Tracking Filters
_ _
χ
3
χ
2
( + 1 ) : = χ ( k ) + χ ( k ) ⋅ ∆t
k 2
3
( + 1 ) : = χ ( k ) − ( ϕ − X ( k ) ) ⋅ ∆t
k 3
2 I
21-9
Equation 21.5-6
Equation 21.5-7
3
2
2 2
( ω + ω ⋅ ω ) ⋅ χ ( k ) + ( 2 ⋅ ω + ω ) ⋅ χ ( k ) + 2 ⋅ ω ⋅ χ ( k )
E
E
W
2
1
2
ϕ
2
E
: =
W
2
E
Equation 21.5-8
3
2
( k + 1 ) + ( ω − ω ⋅ ω ) ⋅ χ ( k + 1 )
Xk + 1 : = − 2 ⋅ ωE
⋅ ωW
⋅ χ2
E E W 3
Equation 21.5-9
3
2
2
( ω − ω ⋅ ω ) ⋅ χ ( k + 1 ) + 2 ⋅ ω ⋅ χ ( k + 1 )
X& k + 1 : = E E W 2
E 3
X&
&
Equation 21.5-10
3
2
( ω + ω ⋅ ω ) ⋅ χ ( k + 1 ) + 2 ⋅ ω ⋅ ( ω ⋅ χ ( k + 1 ) + χ ( k + 1 ) )
E
χ
2
χ
E
W
1
k + 1
E
: =
E
2
3
Equation 21.5-11
3
2
2
( ) ( ωE
− ωE
⋅ ωW
) ⋅ X&
I ( k ) − 2 ⋅ ωE
⋅ X&
&
I ( k )
k : =
3
2 2 4 2
( ω − ω ⋅ ω ) − 4 ⋅ ω ⋅ ω
1
χ
( k )
3
( k )
: =
X
: =
I
E
X&
&
I
E
W
2 2
( k ) + 2 ⋅ ω ⋅ ω ⋅ χ ( k )
ω
3
E
E
− ω
E
⋅ ω
W
2
W
2 ( k ) − 2 ⋅ ω ⋅ χ ( k ) − 2 ⋅ ω ⋅ χ ( k )
E
3
E
ω
2
+ ω
E
⋅ ω
2
W
2
E
E
W
Equation 21.5-12
Equation 21.5-13
3
Equation 21.5-14
3