Rockwell Automation RSLogix 5000 Fuzzy Designer - Manual (Page 34)

Publication LOGIX-UM004A-EN-P - March 2007
34 FuzzyDesigner Component Library
Parameters
• Name of the component
• Vector b = [b
0
, b
1
,,b
m
] , coefficients of the filter transfer function
numerator b(d)– optional
• vector a = [a
1
, …,a
n
], coefficients of the filter transfer function
denominator a(d) – optional
Input Linguistic Variable The fuzzy system Input Linguistic Variable component stores
membership functions (fuzzy sets) of terms and is used for
fuzzification (classification) of the component input – a crisp value.
The component output is a vector of degrees of fulfillment of all terms
for the crisp input or degree of overlapping for the input fuzzy set.
An Input Linguistic Variable component consists of linguistic terms.
Each linguistic term is defined by a fuzzy set, that is by the
membership function and the name. There are four supported
membership functions.
• Trapezoidal membership function
• S-shaped membership function
• Inverse trapezoidal membership function
• Inverse S-shaped membership function
Linguistic terms are defined on specified range [x
min
, x
max
] (universe
of discourse).
The component crisp input is fuzzified. The result of fuzzification of
the crisp input value x
*
is a degree of fulfillment (DOF) of the terms,
which is computed for each term given by the membership function
A(x) as follows.
trapezoid trapezoid inverse trapezoid inverse trapezoid inverse s-shape inverse s-shape s-shape s-shape
⎪
⎩
⎪
⎨
⎧
>
<
∈
=
max
*
max
min
*
min
max min
* *
) (
) (
] , [ ) (
) (
x x if x A
x x if x A
x x x if x A
A DOF