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Appendix I / Utilities / Digital Filters
_ _
X
i
− X
i−1
>
X&
L
⋅ ∆t
⇒
⎧
⎪
⎨
⎪
⎩
y
22.8-14
: =
X
i
+ X&
Each rate limiting function is identified by (N).
22.8.21 Digital State Space Update
L
LIMIT
⋅ ∆t
⋅ sign
: =
( X − X )
1
i
i−1
⎫
⎪
⎬
⎪
⎭
Equation 22.8-99
D_STATESPACE takes in state-space matrices A(N,N), B(N,I), C(O,I) and
D(O,I), and input and state vectors U(I) and X(N) at time (tk), where (N), (I)
and (O) represent the number of states, inputs and outputs. It returns the
updated state vector at time (tk+1), and the output vector Y(O) at time (tk).
D_STATESPA CE
22.8.22 Parameter Range Check
( [ A ] , [ B ] , [ C ] , [ D ] , X , U , Y , N , I , O )
X : = A ⋅ X + B ⋅ U
k + 1
k + 1
k
Y : = C ⋅ X + D ⋅ U
k
k
k
k
k
k
k
Equation 22.8-100
Equation 22.8-101
Equation 22.8-102
RANGE_CHECK takes input (X), and returns a flag indicating if the
parameter is in the range specified by the upper and lower limits [ L , U ].
22.8.23 Digital Butterworth Filters
y : = RANGE_CHECK
( X , L , U )
[ L , U ] ⇒ y : 0
X ∈
=
] L , U [ ⇒ y : 1
X ∈
=
Equation 22.8-103
Equation 22.8-104
Equation 22.8-105
D_BUTTER propagates up to 50 digital low pass Butterworth filters of order
(M), with a -3dB break frequency of (ωB) over time interval (∆t), and time
varying characteristics.