Analysis and Synthesis of Fuzzy Control Systems. By Gang Feng. Edition 1st Edition.

## Fuzzy Logic Tech

First Published Imprint CRC Press. Pages pages. Export Citation. A fuzzy control system is a control system based on fuzzy logic —a mathematical system that analyzes analog input values in terms of logical variables that take on continuous values between 0 and 1, in contrast to classical or digital logic, which operates on discrete values of either 1 or 0 true or false, respectively.

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Fuzzy logic is widely used in machine control. The term "fuzzy" refers to the fact that the logic involved can deal with concepts that cannot be expressed as the "true" or "false" but rather as "partially true". Although alternative approaches such as genetic algorithms and neural networks can perform just as well as fuzzy logic in many cases, fuzzy logic has the advantage that the solution to the problem can be cast in terms that human operators can understand, so that their experience can be used in the design of the controller. This makes it easier to mechanize tasks that are already successfully performed by humans.

## Analysis and Synthesis of Fuzzy Control Systems | A Model-Based Approach | Taylor & Francis Group

Fuzzy logic was first proposed by Lotfi A. Zadeh of the University of California at Berkeley in a paper. Work on fuzzy systems is also proceeding in the United State and Europe, although on a less extensive scale than in Japan. Research and development is also continuing on fuzzy applications in software, as opposed to firmware , design, including fuzzy expert systems and integration of fuzzy logic with neural-network and so-called adaptive " genetic " software systems, with the ultimate goal of building "self-learning" fuzzy-control systems.

The input variables in a fuzzy control system are in general mapped by sets of membership functions similar to this, known as "fuzzy sets". The process of converting a crisp input value to a fuzzy value is called "fuzzification". A control system may also have various types of switch , or "ON-OFF", inputs along with its analog inputs, and such switch inputs of course will always have a truth value equal to either 1 or 0, but the scheme can deal with them as simplified fuzzy functions that happen to be either one value or another.

### Why Use Fuzzy Logic in Control Systems

Given " mappings " of input variables into membership functions and truth values , the microcontroller then makes decisions for what action to take, based on a set of "rules", each of the form:. In this example, the two input variables are "brake temperature" and "speed" that have values defined as fuzzy sets. The output variable, "brake pressure" is also defined by a fuzzy set that can have values like "static" or "slightly increased" or "slightly decreased" etc. Fuzzy controllers are very simple conceptually.

They consist of an input stage, a processing stage, and an output stage.

The input stage maps sensor or other inputs, such as switches, thumbwheels, and so on, to the appropriate membership functions and truth values. The processing stage invokes each appropriate rule and generates a result for each, then combines the results of the rules. Finally, the output stage converts the combined result back into a specific control output value. The most common shape of membership functions is triangular, although trapezoidal and bell curves are also used, but the shape is generally less important than the number of curves and their placement.

From three to seven curves are generally appropriate to cover the required range of an input value, or the " universe of discourse " in fuzzy jargon. Typical fuzzy control systems have dozens of rules.

## Modern Fuzzy Control Systems and Its Applications

This rule uses the truth value of the "temperature" input, which is some truth value of "cold", to generate a result in the fuzzy set for the "heater" output, which is some value of "high". This result is used with the results of other rules to finally generate the crisp composite output. Obviously, the greater the truth value of "cold", the higher the truth value of "high", though this does not necessarily mean that the output itself will be set to "high" since this is only one rule among many.

In some cases, the membership functions can be modified by "hedges" that are equivalent to adverbs. Common hedges include "about", "near", "close to", "approximately", "very", "slightly", "too", "extremely", and "somewhat".

These operations may have precise definitions, though the definitions can vary considerably between different implementations. In practice, the fuzzy rule sets usually have several antecedents that are combined using fuzzy operators, such as AND, OR, and NOT, though again the definitions tend to vary: AND, in one popular definition, simply uses the minimum weight of all the antecedents, while OR uses the maximum value.

There is also a NOT operator that subtracts a membership function from 1 to give the "complementary" function. There are several ways to define the result of a rule, but one of the most common and simplest is the "max-min" inference method, in which the output membership function is given the truth value generated by the premise.

Rules can be solved in parallel in hardware, or sequentially in software. The results of all the rules that have fired are "defuzzified" to a crisp value by one of several methods. There are dozens, in theory, each with various advantages or drawbacks. Guide for Reviewers Reviewers Login. AbdelRahman Mohamed A. Tweet Share Share Email. New Issue Alert Join the journal on Facebook! Open Access Policy This journal provides immediate open access to its content on the principle that making research freely available to the public supports a greater global exchange of knowledge.