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

Appendix I / Utilities / Digital Filters
_ _
χ
k
: =
χ
k − 1
χ
0
⎛ X
+
⎜
⎝
22.8-3
I
− 1
( k −1
)
− 2 ⋅ χ
∆t
+ 2 ⋅ t
−1
D
: = χ : = 2 ⋅ X
( t t ) ⋅ X ( k −1
) − ( t t )
k −1
I
⎞
⎟ ⋅ ∆t
⎠
Equation 22.8-13
Equation 22.8-14
( −1
) ⋅ ( χ + χ )
yk : = N D I
N D
k k −1
Equation 22.8-15
If (I := 1), and on first use, the filter is re-initialised without integration
using input (XI). Each filter is identified by a unique number (N).
22.8.4 Digital Integration Filters
D_INTEG propagates up to 50 digital integrators over time interval (∆t),
with a time varying gain, starting from an initial state (X0).
( X , X , ∆t
, t , N , I ) ≡ ( X , t )
y : = D_INTEG
ϕ
O
I
C
DI
I
C
Equation 22.8-16
These filters are the discrete equivalent to the continuous transfer function:
y
⎛ X
⎜
⎝ s ⋅ t
( ) ⎟ = + ⎜ I
s : X
χ : = χ −
k
k
1
χ0 = χ−
1
0
C
( k −1
)
⎛ XI
+
⎜
⎝ 2 ⋅ t
C
: : = 0.
5 ⋅ X
yk : = χk
+ χk
−1
⎞
⎠
⎞
⎟ ⋅ ∆t
⎠
I
Equation 22.8-17
Equation 22.8-18
Equation 22.8-19
Equation 22.8-20
If (I := 1), and on first use, the filter is re-initialised without integration
using input (XI). Each filter is identified by a unique number (N).