Rockwell Automation RSLogix 5000 Fuzzy Designer User Manual
Page 43
Publication LOGIX-UM004A-EN-P - March 2007
FuzzyDesigner Component Library 43
The consequent functions f
i
are typically chosen as instances of a
suitable parameterized function, whose structure remains equal in all
the rules and only the parameters vary. Most often, these functions are
linear combinations of antecedent variables. In control engineering,
each rule usually represents local dynamics in different state space
regions and the consequent is given in the form of a state-space or an
ARX model. The overall model of the system is achieved by fuzzy
blending of these linear models.
FuzzyDesigner supports Takagi-Sugeno fuzzy systems with linear
functions in the rule consequents written in the following form.
or
The Takagi-Sugeno fuzzy system with the constant value in the rule
consequents can be also considered as a fuzzy system with singleton
membership functions in the rule consequents. If the Centroid
Average or Maximum Centroid Average defuzzification and Fuzzy
Arithmetic Inference method is chosen, than the behavior of both
fuzzy systems is the same.
The fuzzy system Output Takagi-Sugeno Variable component stores
parameters of reference linear or constant consequent functions. The
component has two input links – a logical input link (degrees of
fulfillment of all reference functions) that can be multiple, meaning
that the component can be connected to several rule blocks, and a
value input link (connectable to components that produce crisp
values), which can be multiple too. The number of links depends on
the number of consequent variables.
The component has two output links:
• Value link
• Logical link
The output logical link enables the connection of the component
directly to other rule blocks. If the component input link is connected
to one rule block, the output degrees of fulfillment are the same as the
input degrees of fulfillment. If the component is connected to several
rule blocks, the output degrees of fulfillment of reference membership
functions are computed as a maximum of the corresponding input
degrees of fulfillment.
n
in
i
i
in
n
i
i
x
a
x
a
a
y
A
x
A
x
R
+
+
+
=
K
L
1
1
0
1
1
THEN
is
and
and
is
IF
:
0
1
1
THEN
is
and
and
is
IF
:
i
in
n
i
i
a
y
A
x
A
x
R
=
L