# Fuzzy Control

Fuzzy controllers are the most important applications of fuzzy theory.
They work rather different than conventional controllers; expert knowledge
is used instead of differential equations to describe a system.
This knowledge can be expressed in a very natural way using
*linguistic variables*,
which are described by
fuzzy sets.

## Example: Inverted pendulum

The problem is to balance a pole on a mobile platform that can move in only
two directions, to the left or to the right.

First of all, we have to define (subjectively) what *high* speed,
*low* speed etc. of the platform is; this is done by specifying the
membership functions for the fuzzy_sets

- negative high (cyan)
- negative low (green)
- zero (red)
- positive low (blue)
- positive high (magenta)

The same is done for the angle between the platform and the pendulum
and the angular velocity of this angle:

Please notice that, to make it easier, we assume that in the beginning the pole
is in a *nearly upright* position so that an angle greater than, say,
45 degrees in any direction can - by definition - never occur.

On the next page we will set up some *rules* that we wish to apply
in certain situations.

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