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US005245698A
United States Patent [19]
[11] Patent Number:
Matsunaga
[45]
5,245,698
Date of Patent:
Sep. 14, 1993
[54] APPARATUS FOR AND METHOD OF
[57]
CORRECTING MEMBERSHIP FUNCTIONS
[75] Inventor: Nobutomo Mataunaga, Hirakata,
An apparatus for and a method of creating membership
functions for use with fuzzy inference rules in a control~
Japan
-
ler. A control error, which is a difference between a
:
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[73] Asslgnee 0mm“
PM’ Kyoto apan
[21] APPL N05 745,433
[22] Fikd;
All‘ 14’ 1991
5
[52] Us‘ Cl‘ """" "
58] F, M fswch
‘e
controlled variable obtained from a control object and a
target value, is received as an input to the controller and
then a fuzzy reasoning operation is executed in confor
mity with a predetermined fuzzy reasoning rule such
that a manipulated variable resulting from the reasoning
[51] Int. Cl. .......................................
[
ABSTRACT
o
(20?!’ 15/“?
operation is supplied ‘0 the con‘rol object. Thereby
5/59$’3369://156l§
395/61 3’ 51 900
achieving a fuzzy control on the control object. Basic
membership functions are loaded in a memory. In re
""""""""""" "
’ ’ 364/163:
sponse to input data which represents a desired charac
teristic for a predetermined range of a control error in a
[56]
References Cited
U_S_ PATENT DOCUMENTS
response characteristic of the control object, the appa
ratus adjusts the width, height, and/or position of the
basic membership functions associated with the prede
termined range to produce new membership functions
Egggawa """""""""""""
5:049:796 9/1991 Seraji
............................ . 395/34
Primary Examiner—-Allen R. MacDonald
Attorney, Agent, or Firm-Dickstein, Shapiro & Morin
‘
START
which d‘W210!’ the desired chmmhshc
10 Claims, 14 Drawing Sheets
’
é 8
NM
NS
ZR
Ps
PM
PM
ZR
NM
NB
NB
NB
PS
PM
ZR
NM
NB
NB
ZR
PB
PM
ZR
NM
N8
N8
PB
PB
PM
ZR
NM
NM
P8
PB
PB
PM
ZR
READ PRESET DATA
1
READ DATA OF BASIC
MB‘BERSHIP FUI‘CTICNS
~32
I
ACHIEVE COMPUTATION
~33
34
CHANGE-OVER
SWITCH?
CHANGE HEIGHT
CHANGE WIDTH
I
CORRECT AND OUTPUT
MDBERS-IIP FUbCTIClB
END
US. Patent
Sep. 14, 1993
Sheet 1 of 14
5,245,698
Fig.1
y/r
4
I00%
/
TARGET VALUE 1'
w
80%
1
cl
0%
\
7 TIME t
Fig.2
TARGET VALUE
(e=0, i=0)
as
INITIAL VALUE
US. Patent
Sep. 14, 1993
Sheet 2 of 14
Fig.3
Fig.4u
NM
NS
ZR
PS
PM
NS
ZR
PS
PM
Fig.4b
NM
5,245,698
US. Patent
Sep.14, 1993
Sheet 4 of 14
Fig.6
9
NM
NS
ZR
PS
PM
PM
ZR
NM
NB
NB
NB
PS
PM
ZR
NM
NB
NB
ZR
PB
PM
ZR
NM
NB
NS
PB
PB
PM
ZR
NM
NM
PB
PB
PB
PM
ZR
0
8
Fig.7o
50%
I007
PM
PB
50%
D024
W3 , Wy
Fig.7b
NB
NM
-IOO%
—50%
ZR
5,245,698
US. Patent
Sep. 14, 1993
Sheet 5 of 14
5,245,698
US. Patent
Sep. 14, 1993
Sheet 6 of 14
5,245,698
Fig.9
Del
13
wynew
" wxnew
W xnew
'wynew
US. Patent
Sep.14,1993
Sheet 8 of 14
5,245,698
Fig.l'l
‘
START
’
READ PRESET DATA
r“3|
i
l
READ DATA OF BASIC
~ 32
MEmERsHIP PUNcTIoNs
ACHIEVE COMPUTATION
CHANGE-OVER
SW I TCH ?
HEIGHT
35
K“,
CHANGE HEIGHT ]
_
L CHANGE WIDTH
I
CORRECT AND OUTPUT
MEMBERSHIP FUNCTIONS
m
END
37
J
U.S. Patent
Sep. 14, 1993
Fig.l2o
Sheet 9 of 14
5,245,698
Fig.l2c
Mx/4
3Mx/4
o \Mi/Z/a
I00
-IOO
Fig.l2b
-|OO
Fig.l2d
I
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US. Patent
Sep. 14, 1993
Sheet 10 of 14
Fig.13o
5,245,698
Fig.l3c
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US. Patent
Sep. 14, 1993
Sheet 11 of 14
Fig.14c
5,245,698
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US. Patent
Sep.14, 1993
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Sheet 12 of 14
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5,245,698
US. Patent
Sep. 14, 1993
Fig.l6a
Sheet 13 of 14
5,245,698
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US. Patent
Sep. 14, 1993
Sheet 14 of 14
Fig. I70
@
Fig. l7b
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Fig.l7c
a
5,245,698
e
1
5,245,698
2
locus of a point is drawn from the initial point to follow
APPARATUS FOR AND METHOD OF
a straight line of u=0 so as to reach the target point.
As described above and as can been seen from the
CORRECTING MEMBERSHIP FUNCTIONS
I graph of FIG. 1, the quickness in the starting phase and
BACKGROUND OF THE INVENTION
1. Field of the Invention
5 of the convergence in a linear lag system are determined
depending on the values K and a. In addition, as shown
The present invention relates to an apparatus and a
method of generating membership functions for use in a
fuzzy control operation employing predetermined
fuzzy inference rules related to the membership func
tions, wherein a difference between a controlled vari
able attained from a control object and a target value,
in FIG. 2, according to the conventional PD control
system, since the control operation is accomplished in
the overall region of the phase plane based on the ex
pression (1) and K; and Kare constant, the behavior of
the control object is uniquely decided by the values K
and a in the overall region, which disadvantageously
leads to a problem of a
degree of freedom in
the control operation.
duct a fuzzy inference operation based on a predeter
mined fuzzy inference rule associated with the member 15 When different control operations are desired to be
achieved for respective regions according to the con
ship functions, and a manipulated variable resultantly
ventional PD control method, a plurality of PD control
obtained is supplied to the control object, thereby ac
apparatuses are required to be disposed such that a
complishing a fuzzy control on the control object.
change-over operation is appropriately conducted be
2. Description of Related Art
i.e. a control difference, is received as an input to con
In a common practice, a PD (proportion and differen
tiation) control method has been used in this ?eld. Ac
cording to the PD control method, a manipulated vari
able u to be fed to a control object is de?ned as follows.
a=Kp-e+Kv~é
where,
KP: Position gain
Ky: Velocity gain
example, depending on membership functions and fuzzy
e: Velocity error
Let us assume here that the control object is repre
sented as a linear lag (?rst-order lag) system and the
target value to be supplied thereto is expressed as r. In
this situation, the controlled value outputted as y (re
sponse characteristic) from the control object is repre
sented by
(2)
where, 5 indicates a Laplace’s operator or Laplacian.
In a region of time, Expression (2) is reduced to
N)=(i K/T)-[¢XP(—'/7)]~'(I)
ture of the control apparatuses and hence increases the
cost thereof.
On the other hand, a fuzzy control apparatus which
(1) 25 has been recently highlighted and which has been in
creasingly put to practical uses is relatively simple in the
con?guration thereof and has an advantageous feature
of developing arbitrary control characteristics. For
e: Position error
J($)=[K/(1+ TS)]'P(S)
tween these apparatuses depending on a state of the
control object. This resultantly complicates the struc
(3)
inference rules, a discontinuous control and a nonlinear
control can be accomplished.
The fuzzy inference or reasoning rules represent
knowledge, experiences, and know-how of experts of an
objective control ?eld and hence can be determined in
35 a relatively easy manner.
However, in many cases, the contours and positions
of the membership functions utilized in association with
the fuzzy inference rules cannot be extracted from the
knowledge of the experts. Moreover, there has not been
de?ntely established a method of determining the mem
bership functions. Heretofore, consequently, these func
tions are required to be obtained through a trial-and~
error procedure.
FIG. 3 shows a membership function having a quite
45 simple form i.e. a triangular shape. Also for a member
herebelow).
ship function having such a simple contour, it is neces
sary to determine a width (WL and WR and WL+WR),
a height (H), and a center position (distance L from the
The position error e and the velocity error e is ex
pressed as
origin 0). A membership function needs be de?ned for
each of the input/output variables and for each linguis
where, K stands for a gain constant and T denotes a
time constant (to be utilized in the form of l/T=a
(4)
tic information or label (to be simply referred to as a
label herebelow) related to each of the variables. In
consequence, the total number of the membership func
tions is represented by a value which is attained by
55 multiplying the number of the kinds of input and output
The expressions (4) and (5) indicate that the position
variables by the number of the kinds of labels. For ex
error e and the velocity error e, namely, the response
ample, let us assume that the number of the labels and
characteristic of the control object can be uniquely
the number of the kinds of input variables are five and
determined by the value of the gain constant K and the
two, respectively. Under this condition, for the input
(5)
value of a.
In this connection, FIG. 1 shows a response charac
variables (the antecedents of rules), ten (5 X2) kinds of
membership functions are required to be established.
teristic of a linear lag system. In the control operation,
FIG. 4a shows an example of typical membership
a gradient a (quickness) in the starting phase and an
functions. Each function is drawn in the form of an
inclination m (quickness of convergence) at a position
isosceles triangle of which a vertex has a grade of one.
where the output y takes a value in the vicinity (eg 65 In this graph, adjacent triangles intersect each other at
80%) of the target value r serve primary roles.
positions where the grade value is 0.5.
FIG. 2 shows a graph of a phase plane in the PD
This graph includes ?ve kinds of labels (or linguistic
control. The control operation is carried out such that a
information) as follows.
3
5,245,698
PM: Positive Medium.
PS: Positive Small.
ZR: Almost Zero.
According to the present invention, there is also pro
vided a method of generating membership functions for
use with fuzzy inference rules in a fuzzy inference sys
NS: Negative Small.
NM: Negative Medium.
In addition to the labels above, for example, the fol
lowing labels may also be employed in relation to the
membership functions, which will be described later.
PB: Positive Big.
NB: Negative Big.
4
selected membership functions so as to develop the
desired characteristic.
tem wherein a value related to a controlled variable
attained from a control object is received as an input
thereto and then a fuzzy inference operation is executed
in conformity with a preset fuzzy inference rule such
10 that a manipulated variable resultant from the inference
FIG. 4b shows another example of membership func
tions each having a triangular shape.
operation is fed to the control object, thereby achieving
a fuzzy control on the control object.
Let us assume in this speci?cation that for a triangle
The membership function generating method com
constituted with three points and three edges or sides
therebetween, a point having a grade other than zero is
prises the steps of setting basic membership functions,
receiving an input of data which represents a desired
called a vertex and each of two other points having a
characteristic for a predetermined range of a value
related to a controlled variable in a response character
istic of a control object, and accessing in response to
grade equal to zero is called an end point. Moreover, an
edge between the vertex and an end point and an edge
between the end points are to be called a hypotenuse or
input data the basic membership functions to select
an oblique side and a base, respectively.
20 those associated with the predetermined range and cor
In the graph of FIG. 4b, all membership functions
recting the selected membership function so as to de
excepting one associated with the label ZR, namely,
four membership functions respectively denoted with
the labels PM, PS, NS, and NM each have an end point
located at a center position.
velop the desired characteristic.
The value related to the controlled variable is, for
example, a control error. For example, a position error
25 and a velocity error may be used as control errors.
In the cases respectively utilizing the membership
In a mode of carrying out the present invention, rela
functions of FIGS. 40 and 4b, even when the fuzzy
control is accomplished depending on the same fuzzy
tionships between a position gain and a velocity gain in
> a PD control, and a width of a membership function
rules, the behavior resulting from the control operation
varies between the control objects respectively associ
related to a position error and a width of a membership
30 function related to a velocity error are employed to
ated with the cases. Namely, the kinds and the contours
correct a width of the selected basic membership func
tion.
and/0r modi?ed in various manners; moreover, the
In another mode of carrying out the present inven
response characteristic of the control object alters de
tion, the height or the position is corrected for particu
pending on the kinds and the shapes of the membership 35 lar ones of the basic membership functions.
functions. In consequence, it takes a considerably large
The data representing the basic membership func
amount of labor and a long period of time for the user to
tions will be stored, for example, in a memory.
set and/or to adjust the membership functions in order
In accordance with the present invention, there are
of the membership functions may be arbitrarily changed
to establish a desired control.
automatically prepared membership functions which
enable a desired response characteristic to be obtained
SUMMARY OF THE INVENTION
in a desired region of the response characteristic of the
It is therefore an object of the present invention to
control object. In consequence, using a fuzzy control
provide an apparatus for and a method of automatically
unit, there can be developed a control operation to
generating membership function which enables a de
attain a desired characteristic in a desired region of a
sired response characteristic of a control object to be 45 control error (a position error and/or a velocity error).
attained in a desired region of the response characteris
This accordingly makes unnecessary the change-over
tic.
operation which has been required between a-plurality
There is provided, according to the present inven
of control units in the prior art. Thereby simplifying the
tion, an apparatus for creating membership functions for
con?guration of the control unit. Moreover, an appro
use with fuzzy inference rules in a fuzzy inference sys 50 priate control operation can be accomplished depend
tem wherein a value related to a controlled variable
ing on a characteristic of the control object.
obtained from a control object is received as an input
The foregoing and other objects, advantages, manner
and then a fuzzy inference operation is executed in
of operation, and novel features of the present invention
conformity with a predetermined fuzzy inference rule
will be understood from the following detailed descrip
such that a manipulated variable resulting from the 55 tion when read in connection with the accompanying
inference operation is supplied to the control object.
drawings.
Thereby achieving a fuzzy control on the control ob
ject.
BRIEF DESCRIPTION OF THE DRAWINGS
The membership function generating apparatus in
FIG. 1 is a graph illustratively‘showing a response
cludes membership function preset means for setting 60 characteristic of a control object;
therein basic membership functions, data input means
FIG. 2 is a diagram schematically showing a phase
for inputting therefrom data representing a desired
plane;
characteristic for a predetermined range of a value
related to a controlled variable in a response character
istic of a control object, and membership function cor 65
ship functions;
recting means responsive to input data for accessing the
groups of membership functions, respectively;
basic membership functions to select those associated
with the predetermined range and for correcting the
con?guration of a control system;
FIG. 3 is a diagram showing an example of member
FIGS. 40 and 4b are diagrams showing examples of
FIG. 5 is a block diagram schematically showing the
5
5,245,698
FIG. 6 is a table useful to explain fuzzy inference
6
Spectively compute a difference (a position error) a
between an angle 0 (corresponds to the controlled
variabel y above) measured in the servomotor 26 and
the target value r thereof and a discrepancy (a velocity
error) e between an angular velocity 0 also obtained
rules;
FIGS. 7a and 7b are diagrams showing examples of
membership functions related to antecedents and conse
quents of fuzzy rules, respectively;
FIG. 8 is a graph illustratively showing a phase plane
and membership functions preset for a subdivision of
from the servomotor 26 and a target value i' thereof.
These errors e and e are respectively normalized by
normalizer circuits 21 and 22 so as to take values respec
the phase plane;
FIG. 9 is a graph showing another case of the subdi
tively within the overall value range of the input vari
ables to be processed in the fuzzy inference unit 20.
Receiving the normalized position and velocity errors e
and e as inputs thereto, the fuzzy inference unit 20
achieves a reasoning operation based on fuzzy inference
FIG. 11 is a ?owchart showing an operation proce
rules, which will be described later, thereby ?nally
dure of a membership function generation;
15 producing a manipulated (voltage or current) variable u
FIGS. 12a and 12b are graphs showing an example of
in a defuzzi?ed form. The resultant variable u is ampli
response characteristics associated position and velocity
?ed by an amplifier 25 so as to be used to drive the
errors, respectively;
servomotor 26.
FIG. 120 is a graph showing a phase plane related to
The fuzzy reasoning unit 20 may be implemented as
FIGS. 12a and 12b;
20 an apparatus having an architecture (of an analog type
FIG. 12d is a graph showing membership functions
or a digital type) dedicated to the fuzzy reasoning oper
vision of the phase plane in which the subdivision is
effected in a region different from that of FIG. 8;
FIG. 10 is a block diagram showing the constitution
of a membership function generating unit;
related to FIGS. 12a and 12b;
FIGS. 13a and 13b are graphs showing another exam
ation or by use of a binary computer programmed to
execute the fuzzy reasoning operation.
ple of response characteristics associated with position
FIG. 6 is a table showing an example of fuzzy infer
and velocity errors, respectively;
25 ence rules to be processed by the fuzzy inference unit
FIG. 13c is a graph showing a phase plane related to
20. The upper-most row includes labels assigned to
FIGS. 13a and 13b;
membership functions related to the position error e,
FIG. 13d is a graph showing membership functions
whereas the left-most column denotes labels for mem
related to FIGS. 13a and 13b;
bership functions associated with the velocity error e.
FIGS. 14a and 14b are graphs showing still another
These labels are employed in antecedents of fuzzy rules.
example of response characteristics associated with
A matrix constituted with five rows and ?ve columns in
position and velocity errors, respectively;
the remaining portion of the table of FIG. 6 includes
FIG. 14c is a graph showing a phase plane related to
symbols designating labels of membership functions for
FIGS. 14a and 14b;
the manipulated variable u, which are used to express
FIG. 14d is a graph showing membership functions 35 consequents of fuzzy rules. In consequence, this table
related to FIGS. 14a and 14b;
comprises 25 fuzzy inference rules. For example, for
FIG. 15a is a diagram schematically showing an ex
labels e=NM and é=PM, there is attained a fuzzy rule
ample of a preset control position of a volume control;
as follows.
FIG. 15b is a graph showing a phase plane related to
FIG. 15a;
FIG. 150 is a graph showing membership functions
associated with FIG. 150;
FIG. 16a is a diagram schematically showing another
If e=NM and E=PM, then u=ZR
FIG. 7a shows membership functions commonly
adopted for the position and velocity errors e and e in
example of a preset control position of a volume con
trol;
the fuzzy rule above. In this graph, each of the member
45 ship functions is drawn in the form of a triangle.
FIG. 16b is a graph showing a phase plane related to
FIG. 160;
FIG. 160 is a graph showing membership functions
associated with FIG. 164;
FIG. 17a is a diagram schematically showing further
another example of a preset control position of a vol
Let us assume here that the membership functions
respectively associated with the position and velocity
errors e and e have widths Wx and Wy, respectively.
The width of a membership function having a triangular
shape is denoted by a length which is half that of a base
of the triangle. In general, the width of a membership
function is represented by a length equal to half that
ume control;
FIG. 17b is a graph showing a phase plane related to
FIG. 17a; and
associated with a domain represented by a support or a
universe of discourse of the membership function.
The graph of FIG. 7b shows membership functions of
associated with FIG. 170.
the manipulated variable u to be used in the fuzzy rule
above. Each of the membership functions for the conse
DESCRIPTION OF THE PREFERRED
quents is expressed here in the form of a singleton.
EMBODIMENTS
Subsequently, the fuzzy control system of FIG. 5 will
FIG. 5 shows a control system of a servomotor in 60 be compared with the PD control system described
cluding a fuzzy control unit. Although a servomotor is
above.
a control object of a quadratic (second order) lag sys
FIG. 8 shows a graph including a phase plane identi
tem, the behavior thereof is substantially associated
cal to that of the PD control system of FIG. 2. Member
FIG. 170 is a graph showing membership functions
55
with the linear lag system; consequently, the description
ship functions related to the position error e and the
above also applies to this case.
65 velocity error e are respectively established along an
First, a target value r of an angle and a target value i'
axis of the phase error e and an axis of the velocity error
of an angular velocity are supplied to the control sys
e on the phase plane. As a result, the phase plane is
tem. Subtractors 23 and 24 disposed in the system re
subdivided according to regions of these membership
5,245,698
7
functions. In this example, the adjacent membership
functions intersect each other at a point where the grade
takes a value of 0.5.
(7)
_
The controlled variables (0 and 0) respectively con
verge onto the target values (r and i) within a range 5
From expressions (6) and (7), it can be seen that the
denoted by a dotted-line circle A and in the proximity
following condition is satis?ed between the gains KP
thereof. In consequence, the range denoted by the dot
and K, in the PD control and the widths W, and Wy of
the membership functions in the fuzzy control.
ted-line circle A and the proximity thereof are areas
contributing to the convergence of the control variables
onto the respective target values. In these domains, for
the position and velocity errors e and e, the membership
function assigned with the label ZR develops a domi
K
(8)
"r? = “W:
nant in?uence.
More strictly, expression (8) holds on a straight line
u=0 and in ranges —Wx<e<W,, and Wy<e<Wy.
As shown in FIG. 9', let us assume that the width W,
of the membership function ZR related to the velocity
However, also in the vicinity thereof, expression (8) is
substantially satis?ed, namely, equal signs (=) need
only ‘be replaced with nearly equal signs (i-—-.). More
error e is increased to a new width Wyngw. In accor
dance with the change in the width of the membership
function ZR, the other membership functions PM, PS,
over, also on a polygonal line u=0 as shown in FIG. 9,
NS, and NM are also varied in the widths thereof under 20 expression (8) may possibly be considered to hold.
Let us assume that the basic membership functions of
_ a condition that the adjacent membership functions
FIG. 8 are beforehand established and expression (8) is
intersect each other at a position where the grate takes
to be represented as follows.
a value of 0.5. Namely, when the width of the member
ship function ZR related to the velocity error e is in
creased in the neighborhood of the target value, the 25
convergence velocity onto the target value becomes
greater.
In FIG. 9, although the membership function for the
A1 = M1
(9)
In a case where the basic membership functions are
adopted to produce new membership functions, expres
sion (8) is modi?ed to
position error e is not subjected to the change in the
width, the similar operation may also be executed to
vary the width of the membership function related to
Wynew
the position error e.
(10)
Conversely, when the widths of the membership
functions in the periphery of the phase plane, such as
Based on expressions (9) and (10), the following ex
these designated by labels PM, NM and so on, are ex
pression is attained.
panded, the rising or starting characteristic becomes
steeper or improved.
As above, under the condition that the adjacent mem
bership functions intersect each other at a point where
the grade is 0.5, when either one of the membership
functions is changed in the width thereof, the widths of
the other membership functions are determined in a
unique manner. It may also be possible to remove the
condition above such that the widths of the respective
membership functions are altered independently of each
other.
In the PD control, as described above, the response
characteristic in the overall region of the phase plane is
decided depending on the expressions (1), (4), and (5)
WWW
A2
M1
WXIIEW
M2
Al
(11)
In general, the membership functions are adjusted to
obtain Kp/Kv=wy/wx. Consequently, assuming M1 to
be equal to M2, expression (1 l) is reduced to
45
Wynew _ A2
A1
-—
50
(12)
.
Wx
For example, for A1 = 50 and A2=25, expression (12)
is transformed as follows.
and hence can be uniquely determined by the values of
K and a.
As contrast thereto, in the fuzzy control, the width of
each membership function can be changed with respect 55
That is, expression (12) or (13) decides a ratio Wy.
to each region thereof, which enables the rising and
new/WM” between the widths of new membership
converging characteristics to be separately established.
functions to be generated.
This is a quite advantageous feature of the fuzzy con
Based on expression (12) or (13), the user can specify
trol.
the parameter A2 (and the parameter A1 if necessary) to
Expression (1) is reduced as follows through a substi
prepare a membership function developing a desired
tuted of u=0.
e' = — égL e
response characteristic. In place of the parameter A2,
the parameter KP, Ky, wynew, or Wxnew may be desig
(6)
nated for the purpose above. Moreover, the system may
65 be con?gured so that the gain K and the height of a
On the other hand, in the graph of FIG. 8, the following
relationship holds.
membership function are speci?ed as parameters.
The description above has been given of an operation
in which a membership function is generated (or modi
9
5,245,698
tied) in a domain where the membership function ZR is
dominant, namely, for the membership function con
cerning the convergence to the target values. In a simi
lar manner, for other membership functions having a
considerable influence on the rising phase of the re
sponse characteristic such as the membership functions
PM and NM, the shapes thereof may be determined to
attain desired characteristics, respectively. In this case,
employing the condition that the adjacent membership
functions intersect each other at a position where the u
grade is 0.5, when the membership functions PM, NM,
etc. are thus decided, the other membership functions
ZR and the like exisiting in the proximity of the center
are determined in an automatic fashion. If the condition
above is removed, the membership function ZR con
tributing to the convergence characteristic and the
membership functions contributing to the rising charac
teristic can be determined independently of each other.
FIG. 10 shows a con?guration example of a member
ship function generator unit operating as described
above.
The generator includes two volume controls 14 and
15 and a change-over switch 16 employed as input
10
ing a vertex and end points) necessary for specifying a
triangle. This is also the case of membership functions
each having another shape (e.g. a form of a normal
distribution).
The operation unit 13 is used to receive data from the
volume controls 14 and 15 so as to convert the data into
signals (of data denoting the widths Wyn“ and wxnew or
the height, for example) necessary for the correction of
the basic membership functions. For example, when
angles a and w are received, the arithmetic unit 13
achieves a computation to obtain the gains K, and K,
and then produces widths of the membership functions
based on the relationship represented by expression (8).
On the other hand, on receiving data designating de
grees respectively of the rising and converging charac
teristics, the operating unit 13 executes a computation to
create widths or a height associated therewith. More
over, in a case where the ratio A2 or the widths Wyn“,
and wmare directly supplied to the system, the oper
ation unit 13 may possibly be omitted. The controls 14
and 15 may deliver data representing a height of a mem
bership function to the apparatus. In this situation, the
operation unit 13 need not be disposed or the con?gura
means. Each of the controls 14 and 15 is constituted
tion thereof will be modi?ed to achieve a simple compu
with a variable resistor and a rotary regulator knob to 25 tation.
be rotated for a regulation of a voltage, which is devel
The membership function correcting unit 12 is em
oped in association with a position indicated by the
ployed to receive data from the operation unit 13 or
rotary regulator knob. The controls 14 and 15 produce
directly from the controls 14 and 15 so as to modify data
output voltages to be converted respectively by con
representing basic membership functions stored in the
verters 17 and 18 into signals suitable for an operation of 30 basic membership function preset unit 11 based on the
an operation unit 13 for a membership function correct
ing or modifying unit 12). The resultant signals are fed
to the operation unit 13 (or directly to the membership
function modifying unit 12).
The membership function generating unit is imple
mented, for example, by a computer. In such as case, the
operation unit 13 and the membership function correct
ing unit 12 are realized as portion of the computer ap
propriately programmed. Moreover, analog-to-digital
received data. With the change-over switch 16 set to a
position for selecting a width or a height, the member
ship function correcting unit 12 modi?es the width or
the height of the basic membership functions, respec
tively.
FIG. 11 shows an overall processing procedure
adopted in the membership function generating unit.
First, data prepared by the controls 14 and 15 and a
selection signal of the change-over switch 16 are fed to
converters are adopted for the converters 17 and 18. 40 the operation unit 13 (step 31). Subsequently, data of the
The volume controls 14 and 15 may be used to input,
basic membership functions loaded in the preset unit 11
for example, a rising inclination angle a related to the
are delivered to the membership function correcting
rising characteristic and a convergence angle a) (FIG.
unit 12 (step 32). Concurrently, the operation unit 13
1) associated with the convergence characteristic. Fur
achieves operations required to create data representing
thermore, the ratio A2 and the widths Wyn“. and WM", 45 the new widths Wyn“. and Wm,“ or the height (step 33).
may be supplied from the controls 14 and 15 directly to
With the change-over switch 16 set to a position
the system. In addition, the user may input from the
requesting a correction of the height or the width, the
controls 14 and 15 data (information) denoting a degree
system accomplishes a modi?cation of the height or the
indicating a steep or a flat rising gradient or a rapid or
width of the basic membership function, respectively
slow convergence. In either cases, the controls 14 and 50 (steps 34, 35, and 36). The data representing the modi
15 are utilized to input data related to the rising charac
?ed basic membership functions are then supplied to the
teristic and data associated with the convergence char
acteristic, respectively.
The change-over switch 16 is disposed to modify a
fuzzy reasoning unit 20 (step 37).
FIGS. 12a to 120. 13a to 13d. and 14a to 14d respec
tively show membership functions undergone with the
width or a height of a basic membership function, and a 55 width modi?cation and response characteristics devel
selection signal therefrom is delivered to the member
oped as a result of fuzzy control operations executed
ship function correcting unit 12.
A basic membership function preset unit 11 is dis
depending on the membership functions.
In the graphs of FIGS. 12a to 12d, as representatively
posed to store therein such basic membership functions
shown in FIG. 124'. the positions of the membership
PM, PS, ZR, NS, and NM as shown in the graph of 60 functions (each in the form of a singleton) associated
FIG. 8. These membership functions may be commonly
with the manipulated variable u of the consequent are
utilized for the position and velocity errors e and e. The
shift toward the center point (u=0). However, the
basic membership function preset unit 11 may be con?g
membership functions respectively related to the posi
ured, for example, with a memory. When the basic
tion error e and the velocity error e are not modi?ed,
membership functions each have a triangle contour, all 65 namely, the contours of the basic membership functions
data items need not be established to represent the con
are kept unchanged.
tours thereof. Namely, the unit 11 need only be loaded
FIG. 120 shows a phase plane including control con
with the minimum data (e.g. data of coordinates denot
tour lines representing u=0u=Mx/4, u=MX/2, and