Page 50 - Algorithm Collections for Digital Signal Processing Applications using MATLAB

38 Chapter 1

Truncate the portions of the Zsmall, Zmedium and Zlarge sections of the
output relationship above the corresponding thresholds obtained from output
fuzzy membership as shown in the figure. Remaining portions are combined
with overlapping of the individual sections. Combined sections can also be
obtained by adding the individual sections instantaneously as illustrated in
the example given in the section 5.4 Obtain the crisp value Zout which
divides the combined sections into two halves as shown in the figure. Thus
crisp value Zout is obtained for the corresponding input crisp value Xinput
and Yinput using Fuzzy logic system.

5.3 Why Fuzzy Logic System?

The Automatic system uses set of rules framed with the input data to
decide the output data. For example the automatic system is designed to
maintain the temperature of the water heater by adjusting the heat knob
based on the water level at that particular instant and temperature at that
particular instant. In this example water level measured using the sensor at
that particular instant and temperature measured using the sensor at that
particular instant are the input to the control system. Control system uses the
set of rules framed as given below for deciding the position of the heat knob
which is the output of the control system

• If T1<=Temperature <=T2 and W1<=Water level<=W2, Adjust the heat
knob position to K1. (Say).
• If T0<=Temperature <=T1 and W0<=Water level<=W1, Adjust the heat
knob position to K2. (Say) etc.

Suppose if the temperature is just less than T1, this rule is not selected.
The small variation ‘ΔT’ makes the automatic control system not to select
this particular rule. To overcome this problem instead of using crisp value
for framing the rule, fuzzy values can be used to frame the rules (i.e) without
using the actual values obtained through input sensors This is called fuzzy
base rule as given below

• If the temperature of the water is small and water level is high, place the
heat knob in the high position. (say)
• If the temperature of the water is medium and water level is less, place
the heat knob in the less position. (say) etc.