FLCU – Fuzzy logic controller unit

Block SymbolLicensing group: ADVANCED

Function Description
The FLCU block implements a simple fuzzy logic controller with two inputs and one output. Introduction to fuzzy logic problems can be found in [3].

The output is defined by trapezoidal membership functions of linguistic terms of the u and v inputs, impulse membership functions of linguistic terms of the y output and inference rules in the form

If (u is $U_{i}$ ) AND (v is $V_{j}$ ), then (y is $Y_{k}$ ),

where $U_{i}, i = 1, \dots, nu$ are the linguistic terms of the u input; $V_{j}, j = 1, \dots, nv$ are the linguistic terms of the v input and $Y_{k}, k = 1, \dots, ny$ are the linguistic terms of the y output. Trapezoidal (triangular) membership functions of the u and v inputs are defined by four numbers as depicted below.

Not all numbers $x_{1}, \dots, x_{4}$ are mutually different in triangular functions. The matrices of membership functions of the u and v input are composed of rows $[x_{1}, x_{2}, x_{3}, x_{4}]$ . The dimensions of matrices mfu and mfv are ( $nu \times 4$ ) and ( $nv \times 4$ ) respectively.

The impulse 1st order membership functions of the y output are defined by the triplet

y k, a k, b k, <math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mrow><msub><mrow> <mstyle class="mbox"><mtext class="texttt" mathvariant="monospace">y</mtext></mstyle></mrow><mrow><mi>k</mi></mrow></msub><mo class="MathClass-punc">,</mo><mspace width="1em" class="nbsp"></mspace><msub><mrow><mi>a</mi></mrow><mrow><mi>k</mi></mrow></msub><mo class="MathClass-punc">,</mo><mspace width="1em" class="nbsp"></mspace><msub><mrow><mi>b</mi></mrow><mrow><mi>k</mi></mrow></msub><mo class="MathClass-punc">,</mo> </mrow></math>

where $y_{k}$ is the value assigned to the linguistic term $Y_{k}, k = 1, \dots, ny$ in the case of $a_{k} = b_{k} = 0$ . If $a_{k} \neq 0$ and $b_{k} \neq 0$ , then the term $Y_{k}$ is assigned the value of $y_{k} + a_{k} u + b_{k} v$ . The output membership function matrix sty has a dimension of ( $ny \times 3$ ) and contains the rows $[y_{k}, a_{k}, b_{k}], k = 1, \dots, ny$ .

The set of inference rules is also a matrix whose rows are $[i_{l}, j_{l}, k_{l}, w_{l}], l = 1, \dots, nr$ , where $i_{l}, j_{l}$ and $k_{l}$ defines a particular linguistic term of the $u$ and $v$ inputs and $y$ output respectively. The number $w_{l}$ defines the weight of the rule in percents $w_{l} \in {0, 1, \dots, 100}$ . It is possible to suppress or emphasize a particular inference rule if necessary.

Inputs

u	First analog input of the block	Double (F64)
v	Second analog input of the block	Double (F64)

Outputs

y	Analog output of the block	Double (F64)
ir	Dominant rule	Long (I32)
wr	Degree of truth of the dominant rule	Double (F64)

Parameters

umax	Upper limit of the u input $⊙$ 1.0	Double (F64)
umin	Lower limit of the u input $⊙$ -1.0	Double (F64)
nu	Number of membership functions of the input u $↓$ 1 $↑$ 25 $⊙$ 3	Long (I32)
vmax	Upper limit of the v input $⊙$ 1.0	Double (F64)
vmin	Lower limit of the v input $⊙$ -1.0	Double (F64)
nv	Number of membership functions of the input v $↓$ 1 $↑$ 25 $⊙$ 3	Long (I32)
ny	Number of membership functions of the output y $↓$ 1 $↑$ 100 $⊙$ 3	Long (I32)
nr	Number of inference rules $↓$ 1 $↑$ 25 $⊙$ 3	Long (I32)
mfu	Matrix of membership functions of the input u $⊙$ [-1 -1 -1 0; -1 0 0 1; 0 1 1 1]	Double (F64)
mfv	Matrix of membership functions of the input v $⊙$ [-1 -1 -1 0; -1 0 0 1; 0 1 1 1]	Double (F64)
sty	Matrix of membership functions of the output y $⊙$ [-1 0 0; 0 0 0; 1 0 0]	Double (F64)
rls	Matrix of inference rules $⊙$ [1 2 3 100; 1 1 1 100; 1 0 3 100]	Byte (U8)

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