A First Course in FUZZY and NEURAL CONTROL

146 CHAPTER 4. FUZZY CONTROL

Then, in view of the hypothesis and the fact that ifA,B,Paren◊nmatrices
withP positive definite and bothATPA−P< 0 andBTPB−P< 0 ,then

ATPA+BTPB− 2 P< 0

we see that 4 V(x(k))< 0.

4.4 Fuzzycontrollerdesign........................

Let us now investigate the ease with which we can design a fuzzy controller. In
this section, we give three examples of controller design using fuzzy methodology.
Each of these examples can be compared with an example given in Chapter 2
of controller design using standard methodology to solve a similar problem.

4.4.1 Example:automobilecruisecontrol ............

In Section 2.7.1, we discussed the design of an automobile cruise control system
using the standard approach. Here we solve the same problem using the Mam-
dani method, a fuzzy approach (see pages 110 and 140). It should become clear
that this fuzzy approach, which provides a model-free approach to developing a
controller, is simpler.

(a) Velocity error (b) Velocity error (solid), acceleration (dotted)

Figure 4.1. Velocity error and its rate of change

We definevelocity erroras the difference ìdesired velocity minus actual
velocityî where the desired velocity is the set-point. Then the acceleration is
the time-derivative of the velocity error. These are represented in Figure 4.1
where the velocity error varies between positive (the automobile is traveling too
slowly) and negative (the automobile is travelingtoofast)andtherateofchange
of the velocity error varies between negative and positive.
From the dynamics of the system, in this case an automobile, if the actual
velocity is less than the desired velocity, we need to accelerate the vehicle by