Hardware Implementation of Embedded Fuzzy Controllers on FPGAs and ASICs - Fuzzy Modeling and Control: Theory and Applications - page 229

(µ i )

degrees from rule antecedents are combined within the Connective-operator

circuit to calculate the activation degree of the rule

(

h i )

, while the combination of
antecedent labels addresses the Rule-memory location containing the parameters
that define the corresponding consequent

. In the output stage, a crisp value is
obtained by processing the rule consequents with its different activation degrees,
according to the selected defuzzification method. In addition, a control block in
charge of controling the operation of the rest of blocks must be also included in the
diagram.

( p i )

i h i

· c i · w i

Y M =

i h i

(13.1)

· w i

i h i

· ( x 1 · a i + x 2 · b i + c i )

Y TS 1 =

i h i . (13.2)

Different circuit realizations may be considered for each of the blocks in Fig. 13.2 ,
thus making this architecture highly configurable (Sánchez-Solano et al. 2007 ;Brox
et al. 2013 ). MFCs can be implemented using either memory- or arithmetic-based
approaches. The former allows usingmembership functions with unrestricted shapes,
while the latter provides efficient low-cost solutions to generate several families of
membership functions with triangular shapes included in the standardXFL3 package.
The operator used to implement the “and” connective that appears in rule antecedents
can be chosen by the user between “product” and “minimum”. Finally, the architec-
ture supports most of the simplified defuzzification methods available in the Xfuzzy
environment. For Fuzzy Mean (where w i = 1) and first-order Takagi-Sugeno meth-

ods, the division that appears in ( 13.1 ) and ( 13.2 ) can be avoided when i h i = 1.

Fig. 13.2 Active-rule based architecture for efficient implementation of digital fuzzy controllers.
The number and meaning of the parameters stored in the rule memory, p i , depend on the defuzzifi-
cation method that is being employed ( c i , w i , for Mamdani's systems, and a i , b i , c i , for first-order
Takagi-Sugeno's systems). For Mamdani's systems, inputs are not taken into account by the defuzzi-
fier block