Fuzzy logic provides programmable logic controllers (PLCs) with the ability to make “reasoned” decisions about a process, thereby allowing them to make autonomous output calculations based on system inputs. Fuzzy logic systems use a three-step process—fuzzification, fuzzy processing, and defuzzification—to evaluate system parameters. In fuzzification, the system translates inputs into sets of data defined by membership functions and labels. During fuzzy processing, the system analyzes the input sets by comparing them against a set of predetermined rules. During defuzzification, the system translates the fuzzy processing data into a control system output. Thus, by using this three-step process, a PLC with fuzzy logic capabilities can judiciously determine the proper control response to system inputs based on predefined criteria.

**INTRODUCTION TO FUZZY LOGIC**

Fuzzy logic is the branch of artificial intelligence that deals with the reasoning algorithms used to emulate human thinking and decision making in machines. These algorithms are used in applications where process data cannot be represented in binary form. For example, the statements “the air feels cool” and “he is young” are not discrete statements. They do not provide concrete data about the air temperature or the person’s age (i.e., the air is at 65°F or the boy is 12 years old). Fuzzy logic interprets vague statements like these so that they make logical sense. In the case of the cool air, a PLC with fuzzy logic capabilities would interpret both the level of coolness and its relationship to warmth to ascertain that “cool” means somewhere between hot and cold. In straight binary logic, hot would be one discrete value (e.g., logic 1) and cold would be the other (e.g., logic 0), leaving no value to represent a cool temperature.

In contrast to binary logic, fuzzy logic can be thought of as gray logic, which creates a way to express in-between data values. Fuzzy logic associates a grade, or level, with a data range, giving

it a value of 1 at its maximum and 0 at its minimum. For example, Figure 1a illustrates a fuzzy logic representation of a cool air temperature range, where 70°F indicates perfectly cool air (i.e., a grade value of 1). Any temperature over 80°F is considered hot, and any temperature below 60°F is considered cold. Thus, temperatures above 80°F and below 60°F have values of 0 cool, meaning they are not cool at all. Figure 1b shows another representation of the cool temperature range, where the dotted line shows that hot and cold temperatures are not cool. At 65°F, the fuzzy logic algorithm considers the temperature to be 50% cool and 50% cold, indicating a level of coolness. Below 60°F, the fuzzy logic algorithm considers the temperature to be cold.

Fuzzy logic requires knowledge in order to reason. This knowledge, which is provided by an expert who knows the process or machine, is stored in the fuzzy system. For example, an expert may specify that a steam valve should be turned clockwise a “little bit” if the temperature rises in a batching operation. The fuzzy system might interpret this expression as a 10-degree clockwise rotation that closes the output valve opening by 5%. As the name implies, a description like a “little bit” is a fuzzy description, meaning that it does not have a definite value. A fuzzy logic system takes this vague description and translates it into a decisive output.

*to be continued………*

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