A First Course in FUZZY and NEURAL CONTROL

152 CHAPTER 4. FUZZY CONTROL

(c) Motor voltage

Figure 4.9. Prototype fuzzy membershipfunctions for DC servomotor control

This knowledge of the system behavior allows us to formulate a set of general
rules as, for example,

1. If position error is positive and velocity is negative, then apply positive
   voltage.


2. If position error is negative and velocity is positive, then apply negative
   voltage.


3. If position error is zero and velocity is zero, then apply zero voltage.

Using theMatlabfuzzy toolbox, we can set up prototype Gaussian fuzzy
sets for the fuzzy variables, namely, position error, velocity, and motor voltage.
This is illustrated in Figure 4.9.
With the fuzzy sets defined, it is now possible to associate the fuzzy sets in
the form of fuzzy rules. When there are two inputs and one output, it is easy
to visualize the associations in the form of a matrix. For this system, we can
obtain the matrix shown in Figure 4.10.

Figure 4.10. Fuzzy associative matrix for DC servomotor control

The matrix in Figure 4.10 summarizes the following set of nine rules: