Fuzzy Controller Types in Java

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Fuzzy Controller Types
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While there exists a number of different types of fuzzy controllers, they all have the same components and involve the same design steps. The differences between types of fuzzy controllers are mainly in the implementation of the inference engine and the defuzzifier.
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Inputs System
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Action Interface
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Fuzzy Rule Base
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Condition Interface
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Fuzzy Controller
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Figure 20.1: A fuzzy controller
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The design of a fuzzy controller involves the following aspects: A universe of discourse needs to be defined, and the fuzzy sets and membership functions for both the input and output spaces have to be designed. With the help of a human expert, the linguistic rules that describe the dynamic behavior need to be defined. The designer has to decide on how the fuzzifier, inference engine and defuzzifier have to be implemented, after considering all the different options (refer to chapter 19). Other issues that need to be considered include the preprocessing of the raw measurements as obtained from measuring equipment. Preprocessing involves the removal of noise, discretization of continuous values, scaling and transforming values into a linguistic form. In the next sections, three controller types are discussed, namely table-based, Mamdani and Takagi-Sugeno.
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Table-Based Controller
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Table-based controllers are used for discrete universes, where it is feasible to calculate all combinations of inputs. The relation between all input combinations and their corresponding outputs are then arranged in a table. In cases where there are only two inputs and one output, the controller operates on a two-dimensional look-up table. The two dimensions correspond to the inputs, while the entries in the table correspond to the outputs. Finding a corresponding output involves a simple and fast look-up in the table. Table-based controllers become inefficient for situations with a large number of input and output values.
Mamdani Fuzzy Controller
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Mamdani and Assilian produced the first fuzzy controller [Mamdani et al. 1975]. Mamdani-type controllers follow the following simple steps: 1. Identify and name input linguistic variables and define their numerical ranges. 2. Identify and name output linguistic variables and define their numerical ranges. 3. Define a set of fuzzy membership functions for each of the input variables, as well as the output variables. 4. Construct the rule base that represents the control strategy. 5. Perform fuzzification of input values. 6. Perform inferencing to determine firing strengths of activated rules. 7. Defuzzify, using centroid of gravity, to determine the corresponding action to be executed.
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Takagi-Sugeno Controller
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For the table-based and Mamdani controllers, the output sets are singletons (i.e. a single set), or combinations of singletons where the combinations are achieved through application of the fuzzy set operators. Output sets can, however, also be linear combinations of the inputs. Takagi and Sugeno suggested an approach to allow for such complex output sets, referred to as Takagi-Sugeno fuzzy controllers [Jantzen 1998, Takagi and Sugeno 1985]. In general, the rule structure for TakagiSugeno fuzzy controllers is if f 1 ( A 1 is a1,A2 is 0 2 , . . . A n is a n ) then C = f 2 ( a 1 , a 2 , . . . , a n ) where f1 is a logical function, and f2 is some mathematical function of the inputs; C is the consequent, or output variable being inferred, ai is an antecedent, or input variable, and Ai is a fuzzy set represented by the membership function ^Ai- The complete rule base is defined by K rules. The firing strength of each rule is computed using the min-operator, i.e. ak = min {A i (a i )}
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Vi\ai Ak
where Ak is the set of antecedents of rule k. Alternatively, the product can be used to calculate rule firing strengths:
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The output of the controller is then determined as
= F7
The main advantage of Takagi-Sugeno controllers is that it breaks the closed-loop approach of the Mamdani controllers. For the Mamdani controllers the system is statically described by rules. For the Takagi-Sugeno controllers, the fact that the consequent of rules is a mathematical function, provides for a more dynamic control.