Information Technology Reference
In-Depth Information
⎧
if
Y
,
then
X
and
X
and...and
X
or
X
and
X
and...and
X
~
1
11
21
n
1
12
21
n
1
A
2
1
:
;
⎪
⎪
or...or
X
and
X
and...and
X
11
21
n
2
⎪
⎪
if
Y
,
then
X
and
X
and...and
X
или
X
and
X
and...and
X
~
2
12
22
n
2
12
21
n
2
~
A
2
2
:
;
A
2
=
⎨
or...or
X
and
X
and...and
X
13
22
n
1
⎪
..........
..........
..........
..........
..........
..........
..........
..
⎪
if
Y
,
then
X
and
X
and...and
X
or
X
and
X
and...and
X
~
⎪
m
1
m
2
m
nm
1
m
−
1
2
m
nm
2
A
:
.
1
2
n
1
2
n
m
⎪
or...or
X
and
X
and...and
X
⎩
Let us consider the block diagram of the fuzzy linguistic governor presented in
Fig. 1.8.
The numerical information from an object under control comes to fuzzificator.
It transforms the information to a linguistic form. Further, linguistic values come
to fuzzy conclusion rule system based on fuzzy expert judgments. As a result,
membership function comes to “defuzzificator” where it will be transformed to the
numerical information used to control an object.
1
m
2
m
nm
−
1
1
2
n
Numerical
Signal
Signal
Numerical
information
Control
Object under
Sensor
information
Control
Defuzzificator
Fuzzificator
Membership function Linguistic value
Fuzzy conclusion
rules system
Fig. 1.8
The block diagram of the fuzzy governor
Example 1.9.
The fuzzy governor. Let us consider a microcontroller operating as
a governor. Its input analogue signal
e
is limited by a range [-1. 1] and is
converted to a digital signal by an analog-to-digital converter with resolution 0.25;
the output signal х is formed by the digital-to-analogue converter and has five
levels:-1, -0.5, 0, 0.5, 1 [82]. Let us denote with
e
Δ
the first error signal
difference at the current discrete point of time.
Let us consider semantic space of an analogue signal with terms:
A
— "high
positive”,
A
— “low positive”,
A
— "zero",
A
— “low negative”,
A
—
“high negative” and semantic space “the first error signal difference at the current
discrete point of time” with terms:
B
— "high positive”,
B
— “low positive”,
B
— "zero",
B
— “low negative”,
B
— “high negative”. Membership
functions of terms of thos
e
two spaces are assumed identical, values of
membership functions
A
i
=
1
are presented in Table 1.2.
,
