ElmoMC SimplIQ Software Manual User Manual
Page 216
SimplIQ
Software Manual
13BFilters
MAN-SIMSW (Ver. 1.4)
14-7
The discrete equivalent form is:
2
1
2
2
1
2
0
a
z
a
z
b
z
b
z
b
+
+
+
+
where:
q
c
p
b
1
1
1
0
+
+
=
,
q
p
b
)
1
(
2
1
1
−
=
,
q
c
p
b
1
1
1
2
+
−
=
,
q
c
p
a
1
2
2
2
+
−
=
q
p
a
b
b
b
a
)
1
(
2
1
2
2
2
1
0
1
−
=
−
−
+
+
=
assuming:
⎟
⎠
⎞
⎜
⎝
⎛
=
2
tan
2
T
d
c
k
k
k
ω
,
2
2
tan
1
⎟
⎠
⎞
⎜
⎝
⎛
=
T
p
k
k
ω
, (
2
,
1
=
k
)
1
2
2
+
+
=
c
p
q
14.2.3 Double-lead Element
(Represented by Second-order Block)
The basic continuous-time double lead-lag element is:
2
⎟
⎠
⎞
⎜
⎝
⎛
+
+
⋅
b
s
a
s
a
b
The frequency a / (2
π
) [Hz] is the lead corner frequency. The frequency b / (2
π
) [Hz] is the lag
corner frequency.
The discrete equivalent form is:
2
-
z
)
-
z(1
G)
-
(1
G
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
+
β
β
Order Parameter
1
k
1
= (1 - β)
2
2
k
2
= Gβ · (Gβ + 2 · (1 - β))
3
k
3
= - (Gβ)
2
4
k
4
= β
2
The DC gain of this block is unity.
β is selected as β = e
-bt
.
G is selected by
a
b
G
=
, with 0 < β < 1 and 1 < G < 3.