ElmoMC SimplIQ Software Manual - Manual (Page 217)

SimplIQ Software Manual 13BFilters
MAN-SIMSW (Ver. 1.4)
14-8
14.2.4 First-order Element
(Represented by Second-order Block)
The basic continuous-time single lead-lag element is:
b s
a s
a
b
+
+
⋅
The discrete equivalent form is:
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
−
−
⋅ ⎟
⎠
⎞
⎜
⎝
⎛
−
−
β
α
α
β
z
z
1
1
Order Parameter
1
k
1
= 1 - β
2
α
α
β
⎟
⎠
⎞
⎜
⎝
⎛
−
−
=
1
1
2
k
3 k
3
= 0
4 k
4
= 0
For a single pole,
p s
s
+
⋅
parameters are pT e
− = = β α
, 0 .
Example:
A filter consist of one second-order block and one first-order block. The second-order block
is a notch filter with a 300-Hz notch frequency and a damping of 0.14. The sample time is
360 microseconds. The discrete equivalent of the filter is parameterized by:
k1 = 0.3372, k2 = 0.4573, k3 = -0.7277 and k4 = 0.5222.
The second block is a simple pole with a 400-Hz frequency. It may be represented by:
k1 = 0.1341, k2 = 0, k3 = 0 and k4 = 0.
The KV parameter vector should be programmed as follows:
Parameter Value Description
KV[0] 100
KV[1] 12 Last index used
KV[2] 16 First block, non-scheduled
KV[3] Float2Par(0.3372) Parameter 1 (k1)
KV[4] Float2Par(0.4573) Parameter 2 (k2)
KV[5] Float2Par (-0.7277) Parameter 3 (k3)
KV[6] Float2Par(0.5222) Parameter 4 (k4)
KV[7] 16 Second block, non-scheduled
KV[8] Float2Par(0.1341) Parameter 1 (k1)
KV[9] 0 Parameter 2 (k2)
KV[10] 0 Parameter 3 (k3)
KV[11] 0 Parameter 4 (k4)