PLCs and Fuzzy Logic (10)

Input/Output Determination
Once the fuzzy system configuration has been established, the next step is to determine which inputs and outputs will be used in the fuzzy logic controller. The input conditions, or fuzzy input variables, must be able to be expressed by IF…THEN statements.

That is, the input conditions to the fuzzy controller must be able to trigger conditional rules, meaning that they specify one or more output conditions. Inputs should be selected according to the process situations they describe. These variables should relate to similar process elements. If two inputs have little to do with each other, they will generate an outcome that is less effective than the outcome generated by two inputs that deal with the same element. For example, in a temperature-regulating batching operation, the batch temperature and tank jacket temperature both relate to the regulation of the steam valve output. By analyzing these two inputs together, a fuzzy controller can make a precise decision about how much to adjust the steam valve. An analysis of two unrelated inputs, such as batch temperature and liquid level, would not provide such an informed decision.

Fuzzy Inference Engine
The selection of the fuzzy inference engine encompasses the determination of how the fuzzification process will take place (e.g., the number and form of membership function, etc.), how the rules determine an outcome, and how the fuzzy controller implements defuzzification.
The fuzzification process, which utilizes the membership functions defined by the user, assigns a grade to each fuzzy input received. This grade determines the level of outcome that will be triggered. Therefore, the shape of a fuzzy set’s membership functions is important, since this shape determines the input signals’ grades, which are mapped to the output membership function.
Some fuzzy controllers allow the user to choose the shape of the membership functions by trial and error, while others have predefined membership function shapes. When using trial and error to determine the function shapes in a closed-loop fuzzy control system, the input membership functions should begin with overlapped L-shaped labels (see Figure 12). This ensures smoother control for the first trial due to the coverage provided by the L shape and the overlapping at the minimum and maximum points, which creates a balance (i.e., when one label grade is 1, the other is 0). The number of labels, or membership functions, that will form the fuzzy set is also an important part of the system design. For example, if a fuzzy set has five labels covering the same input data range as a three-label fuzzy set, the one with five labels will provide more fine-tuned control, especially if the output membership function also has five labels.

Although membership functions do not have to be symmetrical, asymmetrical fuzzy sets should be carefully designed to ensure that they describe the fuzzy variable input properly. In Figure 13a, the inner membership functions provide more sensitivity near the zero label (from NS to PS) than at the NL and PL labels (from NL to NS and from PS to PL). Asymmetrical membership functions are typically used in open-loop system applications.

Sometimes, a membership function in a fuzzy set may not provide any sensitivity between two labels. As illustrated in Figure 13b, the flat sections of the membership functions do not influence
neighboring functions or the output. Therefore, the output will not change if the input variable falls in these regions.

to be continued…………….

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