# Fuzzy Systems (PID and Fuzzy Logic Toolkit)

LabVIEW 2012 PID and Fuzzy Logic Toolkit Help

Edition Date: June 2012

Part Number: 370401J-01

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A fuzzy system is a system of variables that are associated using fuzzy logic. A fuzzy controller uses defined rules to control a fuzzy system based on the current values of input variables. You can use the Fuzzy System Designer and the Fuzzy Logic VIs to design and control fuzzy systems.

Fuzzy systems consist of three main parts: linguistic variables, membership functions, and rules.

## Linguistic Variables

Linguistic variables represent, in words, the input variables and output variables of the system you want to control. For a heater, you might have two input linguistic variables, current temperature and desired temperature, and one output linguistic variable, heater setting. Each linguistic variable has a range of expected values. For example, the range of current temperature might be 0 to 100 degrees. The range of desired temperature might be 50 to 80 degrees.

A fuzzy controller requires at least one input linguistic variable and one output linguistic variable.

## Linguistic Terms and Membership Functions

Linguistic terms represent, in words, categories for the values of a linguistic variable. The linguistic variables current temperature and desired temperature each might include the linguistic terms cold, moderate, and hot. The linguistic variable heater setting might include the linguistic terms off, low, and high.

Membership functions are numerical functions corresponding to linguistic terms. A membership function represents the degree of membership of linguistic variables within their linguistic terms. The degree of membership is continuous between 0 and 1, where 0 is equal to 0% membership and 1 is equal to 100% membership. For example, the linguistic variable current temperature might have full membership (1) within the linguistic term hot at 100 degrees, no membership (0) within that term at 70 degrees or less, and partial membership at all temperatures between 70 and 100 degrees.

## Rules

Rules describe, in words, the relationships between input and output linguistic variables based on their linguistic terms. For example, you might define the following rule:

 IF current temperature is cold AND desired temperature is moderate, THEN heater setting is low.

The clauses "current temperature is cold" and "desired temperature is moderate" are the antecedents of this rule. The AND connective specifies how the fuzzy logic controller relates the two antecedents to determine the truth value for the aggregated rule antecedent. The clause "heater setting is low" is the consequent of this rule.

A rule base is the set of rules for a fuzzy system. The rule base is equivalent to the control strategy of the controller.