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Chapter 7
I/O Characteristics of Fuzzy Controllers
To use a single-input fuzzy controller to reproduce the given characteristic,
use five linguistic terms each for the input and output quantities, naming
them x1, x2, …, x5 and y1, y2, …, y5, respectively. To obtain the stepped
linear sections between the base points, you always must have exactly
two available active rules. To implement this situation, entirely overlap the
triangular membership functions for the input variable, giving each a
typical value that corresponds to a certain base point component, xi.
To obtain characteristic sections that are exactly linear, you must model the
output variable with singleton membership functions, each of which has a
typical value that corresponds to a certain base point component, yi. The
rule base is then a linguistic enumeration of the five base points.
In principle, these conclusions about I/O characteristics are valid for fuzzy
controllers with two or more inputs as well. However, using the AND
(Minimum) antecedent connective to combine the different input
conditions raises an additional nonlinear effect. With the AND (Minimum)
antecedent connective, the fuzzy controller considers the antecedent of the
rule with the lowest degree of truth. Refer to Figure 7-10 for an example.
Figure 7-11 shows the I/O characteristic field for a dual-input fuzzy
controller.
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PID and Fuzzy Logic Toolkit User Manual