Fuzzy Control Systems

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CHAPTER I

1. Fuzzy control
Fuzzy control is a practical alternative for a variety of challenging control applicationssince it provides a convenient method for constructing nonlinear controllersvia the use of heuristic information. In a sense fuzzy systems can be “trained” and can “learn” how to perform throughout a control task and are considered as intelligent control system. Fuzzy control system design is based on empirical methods, basically a methodical approach to trail-and-error. The general process is as follows: * Document the system’s operational specifications and inputs and outputs * Document the fuzzy sets for inputs

* Document the rule set
* Determine the defuzzification method
* Run through test suite to validate systems, adjust details as required * Complete document and release to production
Fuzzy identification and control methods are used in many engineering systems. Aircraft flight control and navigation systems, which have traditionally used gain scheduling, are now increasingly employing methods of fuzzy control. Some automobile manufacturers use fuzzy logic to control automatic braking systems, transmissions, and suspension systems. In process control systems, fuzzy logic is used to control distillation columns and desalinization processes. In the field of robotics, fuzzy control is used to control end - effector position and path. At least one appliance manufacturer employs a fuzzy system to control turbidity in washing machine water, and at least one camera manufacturer ironically uses fuzzy logic in their autofocus system. 2. Fuzzy logic

Fuzzy logic provides a formal framework for constructing system exhibiting both good numeric performance (precision) and linguistic representation (interpretability). Fuzzy modeling—meaning the construction of fuzzy systems—is an arduous task, demanding the identification of many parameters. Fuzzy logic deals with uncertainty in engineering by attaching degrees of certainty to the answer to a logical question which is commercial and practical. 2.1 Fuzzy Logic as A three-step process:

(1) Classification, (2) Fuzzy decision blocks, and (3) Defuzzification. 2.1.1 Classification.
The first step is to convert the signal into a set of fuzzy variables. This is called fuzzy classification or fuzzification. It is done by giving values to each of a set of membership functions. The values for each membership function are labeled and determined by the original measure signal and the shapes of the membership functions. A common fuzzy classifier splits the signal x into five fuzzy levels: a) LP: x is large positive.

b) MP: x is medium positive.
c) S: x is small
d) MN: x is medium negative.
e) LN: x is large negative

Fig.1.Measuring membership levels
2.1.2 Fuzzy decision blocks.
Fuzzy control uses fuzzy equivalents of logical AND, OR and NOT operations to build up fuzzy logic rules. The operations are similar to their usual meanings. AND rule applies if UA is the membership of class A for a measured variable UB and is the membership of class B for another measure variable, then fuzzy AND is obtained as the minimum of the two membership values. OR rule applies if UA is the membership of class A for a measured variable UB and is the membership of class B for another measure variable, then fuzzy AND is obtained as the maximum of the two membership values. NOT rule applies for membership UA as 1 – UA.

2.1.3 Defuzzification.
The last step in building fuzzy logic system is turning the fuzzy variables generated by the fuzzy logic rules into a real signal again. The fuzzy logic process which does this is called defuzzification because it combines the fuzzy variables to give a corresponding real signal which can then be used to perform some action. A five level defuzzifier block will have five outputs corresponding to five actions: a) LP: Output signal large (positive).

b) MP: Output signal medium (positive).
c) S: Output signal small....
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