Input port, Filter denominator parameters : a – Rockwell Automation RSLogix 5000 Fuzzy Designer User Manual
Page 32
Publication LOGIX-UM004A-EN-P - March 2007
32 FuzzyDesigner Component Library
Inverse S-shaped Membership Function (cubic spline) with Parameters: (a,b,c,d)
If a = b then A(a) = 1. If c = d then A(c) = 1.
Inverse S-shaped membership functions can be used in an input
linguistic variable component.
Singleton Membership Function with Parameter (position, center) c
Singleton membership functions can be used in an output linguistic
variable component.
Input Port
The fuzzy system Input Port component stores an actual input value
entering the HFS. Optionally, you can preprocess the input values by
using the linear digital filter. This filter is defined by its pulse-transfer
operator H, expressed in terms of the backward-shift operator d, or
equivalently in time-domain as a difference equation, as follows.
Filter numerator parameters : b
0
, b
1
, …b
m
; filter denominator
parameters : a
1
, …a
n
There are two ways for designing the filter:
• user defined filter.
• butterworth low pass filter .
2
3
2
3
1
2
3
(
)
( , ]
(
)
2
( )
0
( , )
2
3
(
)
[ , )
(
)
2
1
if
x a
a b
x b
x
if
x
a b
b a
A x
if
x
b c
d c
x c
x
if
x
c d
c d
if
x d
≤
⎧
⎪
−
⎛
⎞
⎪
−
−
∈
⎜
⎟
⎪ −
⎝
⎠
⎪
=
∈
⎨
⎪
−
⎛
⎞
⎪
−
−
∈
⎜
⎟
−
⎪
⎝
⎠
⎪
≥
⎩
a
b
c
d
0
1
A(x)
x
a
b
c
d
0
1
A(x)
x
a
b
c
d
0
1
A(x)
x
1
( )
0
if x c
A x
otherwise
=
⎧
= ⎨
⎩
c
0
1
A(x)
x
c
0
1
A(x)
x
0
1
1
1
0
1
( )
( )
,
( )
( ) ( )
( )
1
( )
(
1)
(
)
( )
(
1)
(
)
m
m
n
n
n
m
b
b d
b d
b d
H d
y d
H d u d
a d
a d
a d
y t
a y t
a y t
n
b u t
b u t
b u t
m
+
+
+
=
=
=
+
+
+
= −
− −
−
−
+
+
− +
−
L
L
L
L