Chapter 4
FUZZY CONTROL
Fuzzy logic controllers serve the same function as the more conventional con-
trollers, but they manage complex control problems through heuristics and
mathematical models provided by fuzzy logic, rather than via mathematical
models provided by differential equations. This is particularly useful for con-
trolling systems whose mathematical models are nonlinear or for which standard
mathematical models are simply not available.
The implementations of fuzzy control are, in some sense, imitations of the
control laws that humans use. Creating machines to emulate human expertise
in control gives us a new way to design controllers for complex plants whose
mathematical models are not easy to specify. The new design techniques are
based on more general types of knowledge than differential equations describing
the dynamics of the plants.
4.1 Afuzzycontrollerforaninvertedpendulum............
In Chapter 2, we presented examples of controlling an inverted pendulum by
means of standard control. It is interesting to note that, with practice, humans
can solve the inverted pendulum problem based solely on naive physics and
common sense rather than on complicated mathematical models.^1 Balancing
a broom upright in your hand, as in Figure 1.13 for example, involves more
degrees of freedom and is inherently much more complicated than the inverted
pendulum on a cart depicted in Figure 2.3. However, when you balance the
broom, you are clearly not relying on a mathematical model that depends on
accurate measurements of angles and velocity. For the inverted pendulum prob-
lem, it is possible to design a successfulcontroller without knowing or using the
plant dynamics. The implication is that, in a case where plant dynamics are
not available, we can use this new technique to construct control laws.
(^1) For a striking example, see the skilled performer Brad Byers balancing a 100 pound barbell
on his chin, at http://www.bradbyers.com/balancer.html.