Computational Intelligence Techniques - Computational Intelligence in Biomedical Engineering - page 122

Error

Control

Fuzzy rules

∑

Inference

Change in error

Encoding Decoding Feedback

FIGURE 3.25
A basic fuzzy controller structure.

and over time as the derivative of the error. The goal is to design a control
signal u ( t ) such that this error diminishes or the error derivative vanishes.
A fuzzy controller is simply a nonconventional approach to feedback control.
It is an example of a commonly used knowledge-based and model-free control
paradigm. In this type of controller, a system of rules is applied to control the
signal. For example, if the change in error is zero and the error is zero then
we would wish to keep the control signal constant. This is aptly denoted by
the following rule:

if error is ZERO and change in error is ZERO, then change in
control is ZERO

The application of rules should take into account external knowledge such as
“common sense” knowledge or knowledge acquired from prior simulation of
the control model. An example of a fuzzy controller is depicted in Figure 3.25
comprising an input interface, a processing module, and an output module.
The rules and inference form the processing module whereas the encoding and
decoding are the interfaces. In this application, the general rule set template
has the following form:

if error is a and change in error is b , then change in control is c

The detailed computations of the control signals can be performed using
t-norms or s-norms but will not be discussed here. Scaling coecients are used
to ensure that the same linguistic protocol is applied throughout the system,
especially in cases when the inputs and output variables have different ranges.
The scaling method has to be further adapted (using moving averages and nor-
malization) because it must be predetermined prior to the start of the system.
This collection of fuzzy rule-based systems can be further employed to con-
struct a fuzzy expert system that uses fuzzy logic instead of Boolean logic.
In summary, a fuzzy expert system is a collection of membership functions
and rules that are used to interpret data. Unlike conventional expert systems,
which are mainly symbolic reasoning engines, fuzzy expert systems are ori-
ented toward numerical processing.