#  What is fuzzy control?

```Date: 17-MAR-95

The purpose of control is to influence the behavior of a system by
changing an input or inputs to that system according to a rule or
set of rules that model how the system operates. The system being
controlled may be mechanical, electrical, chemical or any combination
of these.

Classic control theory uses a mathematical model to define a relationship
that transforms the desired state (requested) and observed state (measured)
of the system into an input or inputs that will alter the future state of
that system.

reference----->0------->( SYSTEM ) -------+----------> output
^                          |
|                          |
+--------( MODEL )<--------+feedback

The most common example of a control model is the PID (proportional-integral-
derivative) controller. This takes the output of the system and compares
it with the desired state of the system. It adjusts the input value based
on the difference between the two values according to the following
equation.

output =  A.e + B.INT(e)dt + C.de/dt

Where, A, B and C are constants, e is the error term, INT(e)dt is the
integral of the error over time and de/dt is the change in the error term.

The major drawback of this system is that it usually assumes that the system
being modelled in linear or at least behaves in some fashion that is a
monotonic function. As the complexity of the system increases it becomes
more difficult to formulate that mathematical model.

Fuzzy control replaces, in the picture above, the role of the mathematical
model and replaces it with another that is build from a number of smaller
rules that in general only describe a small section of the whole system. The
process of inference binding them together to produce the desired outputs.

That is, a fuzzy model has replaced the mathematical one. The inputs and
outputs of the system have remained unchanged.

The Sendai subway is the prototypical example application of fuzzy control.

References:

Yager, R.R., and Zadeh, L. A., "An Introduction to Fuzzy Logic
Applications in Intelligent Systems", Kluwer Academic Publishers, 1991.

Dimiter Driankov, Hans Hellendoorn, and Michael Reinfrank,
"An Introduction to Fuzzy Control", Springer-Verlag, New York, 1993.
316 pages, ISBN 0-387-56362-8. [Discusses fuzzy control from a
theoretical point of view as a form of nonlinear control.]

C.J. Harris, C.G. Moore, M. Brown, "Intelligent Control, Aspects of
Fuzzy Logic and Neural Nets", World Scientific. ISBN 981-02-1042-6.

T. Terano, K. Asai, M. Sugeno, editors, "Applied Fuzzy Systems",
translated by C. Ascchmann, AP Professional. ISBN 0-12-685242-1.

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