Documentation

# Fuzzy Logic Controller

Evaluate fuzzy inference system

• Library:
• Fuzzy Logic Toolbox ## Description

The Fuzzy Logic Controller block implements a fuzzy inference system (FIS) in Simulink®. You specify the FIS to evaluate using the FIS name parameter.

For more information on fuzzy inference, see Fuzzy Inference Process.

To display the fuzzy inference process in the Rule Viewer during simulation, use the Fuzzy Logic Controller with Ruleviewer block.

## Ports

### Input

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For a single-input fuzzy inference system, the input is a scalar signal. For a multi-input fuzzy system, combine the inputs into a vector signal using blocks such as:

### Output

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For a single-output FIS, the output is a scalar signal. For a multi-output FIS, the output is a vector signal. To split system outputs into scalar signals, use the Demux block.

Fuzzified input values, obtained by evaluating the input membership functions of each rule at the current input values.

For a type-1 FIS, `fi` is an NR-by-NU matrix signal, where NR is the number of FIS rules. Element (i,j) of `fi` is the value of the input membership function for the jth input in the ith rule.

For a type-2 FIS, `fi` is an NR-by-(2*NU) matrix signal. The first NU columns contain the fuzzified values of the upper membership function for each rule, and the last NU columns contain the fuzzified values from the lower membership functions.

For more information on fuzzifying input values, see Fuzzify Inputs.

#### Dependencies

To enable this port, select the Fuzzified inputs (fi) parameter.

Rule firing strengths, obtained by evaluating the antecedent of each rule; that is, applying the fuzzy operator to the values of the fuzzified inputs.

For a type-1 FIS, `rfs` is a column vector signal of length NR, where NR is the number of rules, and element i is the firing strength of the ith rule.

For a type-2 FIS, `rfs` is an NR-by-2 matrix signal. The first column contains the rule firing strengths generated using upper membership functions, and the second column contains the rule firing strengths generated using lower membership functions.

For more information on applying fuzzy operators, see Apply Fuzzy Operator.

#### Dependencies

To enable this port, select the Rule firing strengths (rfs) parameter.

Rule outputs, obtained by applying the rule firing strengths to the output membership functions using the implication method specified in the FIS.

For a type-1 Mamdani FIS, `ro` is an NS-by-(NRNY) matrix signal, where NR is the number of rules, NY is the number of outputs, and NS is the number of sample points used for evaluating output variable ranges. Each column of `ro` contains the output fuzzy set for one rule. The first NR columns contain the rule outputs for the first output variable, the next NR columns correspond to the second output variable, and so on.

For a type-2 Mamdani FIS, `ro` is an NS-by-(2*NR*NY) matrix signal. The first NR*NY columns contain the rule outputs generated using upper membership functions, and the last NR*NY columns contain the rule outputs generated using lower membership functions.

For a type-1 Sugeno system, each rule output is a scalar value. In this case, `ro` is an NR-by-NY matrix signal. Element (j,k) of `ro` is the value of the kth output variable for the jth rule.

For a type-2 Sugeno system, `ro` is an NR-by-(3*NY) array. The first NY columns contain the rule output levels. The next NY columns contain the corresponding rule firing strengths generated using upper membership functions. The last NY columns contain the rule firing strengths generated using lower membership functions. For example, in a three-output system, columns 4 and 7 contain the firing strengths for the output levels in column 1.

For more information on fuzzy implication, see Apply Implication Method.

#### Dependencies

• To enable this port, select the Rule outputs (ro) parameter.

• To specify NS, use the Number of samples for output discretization parameter.

Aggregate output for each output variable, obtained by combining the corresponding outputs from all the rules using the aggregation method specified in the FIS.

For a type-1 Mamdani fuzzy inference system, the aggregate result for each output variable is a fuzzy set. In this case, `ao` is as an NS-by-NY matrix signal, where NY is the number of outputs and NS is the number of sample points used for evaluating output variable ranges. Each column of `ao` contains the aggregate fuzzy set for one output variable.

For a type-2 Mamdani FIS, the aggregate result for each output variable is a fuzzy set. In this case, `ao` is as an NS-by-(2*NY) matrix signal. The first NY columns contain the aggregated outputs generated using upper membership functions, and the last NY columns contain the aggregated outputs generated using lower membership functions.

For a type-1 Sugeno system, the aggregate result for each output variable is a scalar value. In this case, `ao` is a row vector of length NY, where element k is the sum of the rule outputs for the kth output variable.

For a type-2 Sugeno system, `ao` is an NR-by-(3*NY) array. `aggregatedOut` contains the same data as `ro` with the columns sorted based on the output levels. For example, in a three-output system, when the output levels in column 1 are sorted, the corresponding firing strengths in columns 4 and 7 are adjusted accordingly.

For more information on fuzzy aggregation, see Aggregate All Outputs.

#### Dependencies

• To enable this port, select the Aggregated outputs (ao) parameter.

• To specify NS, use the Number of samples for output discretization parameter.

## Parameters

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### General

Fuzzy inference system to evaluate, specified as one of the following:

• `mamfis` or `sugfis` object — Specify the name of a type-1 FIS object in the MATLAB® workspace.

• `mamfistype2` or `sugfistype2` object — Specify the name of a type-2 FIS object in the MATLAB workspace.

• File name — Specify the name of a `.fis` file in the current working folder or on the MATLAB path. Including the file extension in the file name is optional.

To save a type-1 fuzzy inference system to a `.fis` file:

• In Fuzzy Logic Designer or Neuro-Fuzzy Designer, select File > Export > To File.

• At the command line, use `writeFIS`.

To save a type-2 fuzzy inference system to a `.fis` file, use `wrtieFIS`.

Number of samples for discretizing the range of output variables, specified as an integer greater than `1`. This value corresponds to the number of points in the output fuzzy set for each rule.

To reduce memory usage while evaluating a Mamdani FIS, specify a lower number of samples. Doing so sacrifices the accuracy of the defuzzified output value. Specifying a low number of samples can make the output area for defuzzification zero. In this case, the defuzzified output value is the midpoint of the output variable range.

### Note

The block ignores this parameter when evaluating a Sugeno FIS.

Signal data type, specified as one of the following:

• `double` — Double-precision signals

• `single` — Single-precision signals

• `fixdt(1,16,0)` — Fixed-point signals with binary point scaling

• `fixdt(1,16,2^0,0)` — Fixed-point signals with slope and bias scaling

• Expression — Expression that evaluates to one of these data types

For fixed-point data types, you can configure the signedness, word length, and scaling parameters using the Data Type Assistant. For more information, see Specifying a Fixed-Point Data Type (Simulink).

Enable output port for accessing intermediate fuzzified input data.

Enable output port for accessing intermediate rule firing strength data.

Enable output port for accessing intermediate rule output data.

Enable output port for accessing intermediate aggregate output data.

Simulation mode, specified as one of the following:

• `Interpreted execution` — Simulate fuzzy systems using precompiled MEX files for `single` and `double` data types. Using this option reduces the initial compilation time of the model.

• `Code generation` — Simulate fuzzy system without precompiled MEX files. Use this option when simulating fuzzy systems for code generation applications.

For fixed-point data types, the Fuzzy Logic Controller block always simulates using `Code generation` mode.

### Diagnostics

Diagnostic message behavior when an input is out of range, specified as one of the following:

• `warning` — Report the diagnostic message as a warning.

• `error` — Report the diagnostic message as an error.

• `none` — Do not report the diagnostic message.

When an input value is out of range, corresponding rules in the fuzzy system can have unexpected firing strengths.

#### Dependencies

• Diagnostic messages are provided only when the Simulate using parameter is `Interpreted execution`.

Diagnostic message behavior when no rules fire for a given output variable, specified as one of the following:

• `warning` — Report the diagnostic message as a warning.

• `error` — Report the diagnostic message as an error.

• `none` — Do not report the diagnostic message.

When No rule fired is `warning` or `none` and no rules fire for a given output, the defuzzified output value is set to its mean range value.

#### Dependencies

• Diagnostic messages are provided only when the Simulate using parameter is `Interpreted execution`.

Diagnostic message behavior when an output fuzzy set is empty, specified as one of the following:

• `warning` — Report the diagnostic message as a warning.

• `error` — Report the diagnostic message as an error.

• `none` — Do not report the diagnostic message.

When Empty output fuzzy set is `warning` or `none` and an output fuzzy set is empty, the defuzzified value for the corresponding output is set to its mean range value.

#### Dependencies

• This diagnostic message applies to Mamdani systems only.

• Diagnostic messages are provided only when the Simulate using parameter is `Interpreted execution`.

## Compatibility Considerations

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Warns starting in R2019b