Note: Descriptions are shown in the official language in which they were submitted.
~ ~8~
FUZZY INFERENCE APPARATUS
BACKGROUND OF THE INVENTION
Field of the Invention
This invention relates to a recurrent type fuzzy inference
apparatus which monitors various industrial processes to infer
a value of parameter suitable for the industrial process.
Prior Art
Fig. 1 is an explanatory view showing the operating
principle of a conventional fuzzy inference apparatus, for
example, shown in "Fuzzy System Theory and Fuzzy Control"
appearing on pages 61 to 66 of "Labor Saving and A~tomation",
November, 1986 (by Kiyoji Asai). In Fig. 1, reference nume-
rals 1 and 2 designate inference rules, and 3 and 4 designate.
characteristic variables to be inputted in the fuzzy inference
apparatus, which are respectively the control error e and
the rate of change Qe of the control error in the control
system. Reference numerals 5 and 6 are membership functions
of the first half of the rule 1, 7 the membership of the
second half of the rule 1, 8 and 9 the membership functions
of the first half of the rule 2, and 10 the membership func-
tion of the latter half of the rule 2. Further, numeral 11designates the membership function obtained by synthesizing
the membership functions 7 and 10, and 12 the inference
value obtained by taking the center of gravity out of the
membership function 11, and in this example, it is outputted
as a manipulated variable Qu from the fuzzy inference apparatus.
-- 1 -- '~
8~
The background of the invention as explained below makes
reference to Figures 1 and 2 of the accompanying drawings.
For the sake of convenience, all of the drawings will first be
introduced briefly, as follows:
BRIEF DESCRIPTION OF THE DRA~INGS
-
Fig. 1 is an explanatory view showing the operating
principle of a conventional fuzzy inference apparatus;
Fig. 2 is a block diagram showing the apparatus of
Fig. l;
Fig. 3 is a block diagram showing one embodiment of a
recurrent type fuzzy inference apparatus according to one
embodiment of the present invention;
Fig. 4 is a block diagram showing an example in which
a controller for controlling the process is applied to a tuning
of a control gain;
Fig. 5 is an explanatory view showing the operating
principle of the same;
Fig. 6 is a flow chart showing a flow of the operation;
Fig. 7 is an explanatory view showing the operating
principle of another embodiment;
Fig. 8 is a flow chart showing a flow of the operation
of the same;
Fig. 9 is a block diagram showing a recurrent type fuzzy
inference apparatus according to a further embodiment of the
present invention;
Fig. 10 is a block diagram showing an example in which
a controller for controlling the process is applied to a tuning
of a control gain;
iX881~i8
Fig. 11 is an explanatory view showing tile operating
principle of the same;
Fig. 12 is a flow chart showing a flow of the operation
of the same;
Fig. 13 ls an explanatory view showing the operating
principle of another embodiment of the present invention; and
Fig. 14 is a flow chart showing a flow of the operation
of the same.
Fig. 2 is a block diagram showing one example of a con-
ventional fuzzy inference apparatus on the basis of the
operating principle as mentioned above. In Fig, 2, reference
numeral 13 designates the weighting means which evaluates the
degree of matching of the first half from the inputted charac-
teristic variables 3 and 4 with respect to the rules 1 and 2
to weight the membership function of the second half on the
basis of the degree of matching, 14 the synthesizing means
for synthesizing the membership functions weighted by the
weighting means 13, and 15 the inference value deciding means
for deciding an inference value 12 from the membership func-
2~ tion synthesized by the synthesizing means 14 to output the
same.
The operation will be described hereinafter. The rule
1 herein refers to "If the characteristic variable 3 (control
error e) is slightly deviated negatively and the characteris-
tic variable 4 (the rate of change ~e of the control error)
is slightly deviated positively, then make the inference
value 12 (manipulated variable ~u) slightly deviated posi-
tively", A portion of "If . . ,.." is called the aforemen-
tioned first half, and a later portion is called the afore-
-- 3 --
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mentioned second half. Accordingly, the membership function
5 of the first half of the rule 1 defines "aggregation of
the control error slightly deviated negatively", and the
membership function 6 defines "aggregation of the rate of
change of the control error slightly deviated positively".
Assume now that the actual value of the control error
as the characteristic variable 3 inputted into the weighting
means 13 is eO and the actual value of the rate of change of
the control error as the characteristic variable 4 is ~eO,
the degree that the value eO is "the control error slightly
deviated negatively" is evaluated as "0.8" by the membership
function 5, and the degree that the value ~eO is "the rate
of change of the control error slightly deviated positively"
is evaluated as "0.7" by the membership function 6. Out of
these evaluated values, the lower value "0.7" is employed to
constitute the degree of matching of the first half of the
rule 1. The membership function 7 of the second half of the
rule 1 has a meaning that "make the manipulated variable
slightly deviated positively", the membership function 7
being weighted 0.7 times in accordance with the value of the
degree of matching of the first half.
This is totally true for the rule 2. That is, the degree
of matching of the first half is evaluated on the basis of
the actual value eO of the control error of the inputted
characteristic variable 3 and the actual value ~eO f the
rate of change of the control error of the characteristic
variable 4, and the membership function 10 is weighted 0.5
times on the basis of the value "0.5" of the degree of match-
ing. The thus weighted membership functions 7 and 10 are
inputted into and synthesized by the synthesizing means 14
to obtain the synthesized membership function 11. Further-
more, the synthesized membership function 11 is inputted
into the inference value deciding means 15 for calculation
of the center of gravity, as a consequence of which the mani-
pulated variable ~uO is outputted as the inference value 12
from the fuzzy inference apparatus.
As described above, in the fuzzy inference apparatus, a
plurality of rules simultaneously function whereby the weight-
ing of the second half corresponding to the degree of matching
f the first half is effected and the value balanced as a whole
is outputted as the inference value.
Since the conventional fuzzy inference apparatus is
constructed as described above, in the case where the charac-
teristic variable (Si) which is the input of the fuzzy
inference apparatus is normally Si=0 but only when a certain
phenomenon occurs, 0 < Si < 1, the inference is impossible.
And there further involves a problem in that even if the
inference could be made, the inference value would not be
a continuous value and in addition, if a parameter to be
2a inferred is constant or merely changed slowly, it is not
possible to obtain a convergent inference value.
SUMMARY OF THE INVENTION
-
The present invention has been accomplished in order to
overcome these problems as noted above with respect to prior
art. It is an object of the present invention to provide a
fuzzy inference apparatus in which even the characteristic
variable which is normally often "0", the inference can be
made, in which the inference value can be a continuous value,
and in which even when a parameter to be inferred is constant
3~ or merely changed slowly, a convergent inference value can be
12881~:8
obtained.
It is a further object of the present invention to
provide a fuzzy inference apparatus in which in synthesizing
membership functions, not only the membership function of
the second half of each of rules but the previous synthesized
membership function are synthesized at the same time.
It is another object of the present invention to provide
a fuzzy inference apparatus in which in synthesizing member-
ship functions, not only the membership function of the second
half of each of rules but the previous synthesized membership
function being weighted according to the degree of the change
in characteristic of the process are synthesized at the same
time so as to describe a satisfaction of each inference value
on each of the rules.
PREFERRED EMBODIMENTS OF THE INVENTION
In the following, one embodiment of the present invention
will be described with reference to the drawings. Fig. 3 is
a block diagram showing one embodiment of a recurrent type
fuzzy inference apparatus according to the present irvention;
12~381~iB
Fig. 4 is a block diagram in which a controller for controll-
ing the process is applied to a tuning of a control gain; and
Fig. 5 is an explanatory view showing the operating principle
of the same. In these drawings, reference numerals 20 and 21
designate inference rules, 22 to 25 characteristic variables
to be inputted in the recurrent type fuzzy inference apparatus,
26 and 27 membership functions of the first half of the rule
20, 28 a membership function of the second half thereof, 29
and 30 membership functions of the first half of the rule 21,
an 31 a membership function of the second half thereof.
Reference numeral 32 designates a synthesized membership
function indicative of a dissatisfaction of the previously
synthesization, 33 a synthesized membership function with
said previous synthesized membership function 32 indicative
of dissatisfaction weighted according to the characteristic
change of the process, 34 a synthesized membership function
obtained by synthesizing the membership function 28 of the
second half of the rule 20 and the membership function 31 of
the second half of the rule 21 and the weighted previous
membership function 33, which represents the fuzzy aggrega-
tion of "dissatisfied control gain Kc", and 35 an inference
value obtained from the synthesized membership function 34,
which in this example, is outputted as the control gain Kc
from the recurrent type fuzzy inference apparatus.
Further, reference numeral 36 designates a process to
be controlled, 37 a controller, for example, such as a PID
controller, 38 a recurrent type fuzzy inference apparatus in
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accordance with the present invention which supplies the
inference value (control gain Kc) to the controller 37, 39
a characteristic variable extraction unit for supplying
characteristic variables 22 to 25 to the fuzzy inference
apparatus 38, 40 a reference input (r) applied from the
outside of a control system, 41 a controlled variable ~y)
outputted from the process 36, 42 a control error (e), which
is inputted into the controller 37, between the reference
input 40 and the controlled variable 41, 43 a manipulated
variable (x) applied to the process 36, and 44 a process
characteristic variation amount sent from the process 36
to the fuzzy inference apparatus 38.
Furthermore, reference numeral 45 designates a weighting
means which evaluates the degree of matching of the first
half from the characteristic variables 22 to 25 inputted
into the rules 20 and 21 to weight the membership function
of the second half on the basis of the degree of matching,
46 a synthesizing means for synthesizing the membership
functions 28, 31 weighted by the weighting means 45 and the
previous synthesized membership function 33 to obtain a new
synthesized membership function 34 indicative of the degree
of dissatisfaction of the inference value 35, 47 an inference
value deciding means for deciding the inference value 35 from
the previous synthesized membership function 35 synthesized
by the synthesizing means 46 to output the same, 48 a delay
means for delaying a new synthesized membership function 32
synthesized by the synthesizing means 46, 49 a characteristic-
128~
variation evaluation means for evaluating the degree ofvariation in characteristic of the process on the basis of
the process characteristic variation amount 44 inputted from
the process 36, and 50 a multiplying means forming an evalua-
tion and weighting means together with the characteristicvariation evaluation means 49 to multiply the synthesized
membership function 32 delayed by the delay means 48 by the
evaluated value from the characteristic variation evaluation
means 49 to effect weighting to feedback it as the synthesized
membership function 33 to the synthesizing means 46.
The operation will now be described. The object of the
inference in the recurrent type fuzzy inference apparatus is
to monitor the characteristic variables 22 to 25 of the pro-
cess to effect tuning of the control gain Kc. So, first, the
characteristic variables 22 to 25 are specifically shown.
That is, the characteristic variable 22 is the divergent
trend of the error (e) 42, the characteristic variable 23
the magnitude Sb of the error 42, the characteristic variable
24 the followin~J degree of the controlled variable (y) with
respect to the variation of the reference input (r) 40, and
the characteristic variable 25 the magnitude Sd(=Sb) of the
error 42. At this time, the rule 20 has a meaning that "If
the divergent trend of the error (e) 42 is large, and the
absolute value thereof is also 1arge, the present control
gain Kc can be jud~ed to be too large". Where the actual
values of the characteristic variables 22 to 25 inputted
into the weighting means 45 are SaO, Sbo, ScO and Sdo,
1288~68
whether or not the value SaO is "large" and whether or not the
value Sbo is "large", in the rule 20, are respectively evaluated
by the membership functions 26 and 27 of the first half of the
rule 20. In the example shown in Fig. 5, the respective
evaluated values, the lower value "0.4" is employed as the
degree of matching of the first half of the rule 20.
Further, the second half of the rule 20 defines the fuzzy
aggregation of "excessively large control gain Kc", and the
control gain Kc 2 Kco above the present control gain Kco is
said to be "excessively large" in the degree of the degree
of matching "0.4" of at least the first half. Then, weighting
corresponding to the degree of matching "0.4" of the first
half is effected to prepare a membership function 28. This
is totally true for the rule 21, and a membership function
31 of the second half is prepared on the basis of the degree
of matching whereby the actual values ScO and Sdo Of the
inputted characteristic variables 24 and 25 are evaluated by
the membership functions 29 and 30. In this example, the
membership function 31 is the function whose all values are
""-
Fig. 6 is a flow chart showing the flow of the operation.The synthesized membership function 32, which was synthesized
by the synthesizing means 46 in the previous iteration and
sent as an input of the subsequent iteration (Step ST 8), is
given a delay of one iteration portion (Step ST 1). Separately
from this, the characteristic variables are inputted into the
weighting means 45, and the process characteristic variation
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~288168
amount 44 from the process 36 is inputted into the characteris-
tic variation evaluation means 49 (Step ST 2). The weighting
means 45 prepares the membership functions 28 and 31 of the
second half by evaluating the inputted characteristic variables
22 to 25 by the membership functions 26, 27 and 29, 30 of the
first half of the rules 20 and 21 and on the basis of the
obtained degree of matching (Step ST 3). The characteristic
variation evaluation means 49 evaluates the degree of varia-
tion in characteristic of the process from the inputted process
characteristic variation amount 44 and sends its evaluated
value to the multiplying means 50. This evaluated value is
multiplied by the previous synthesized membership function 32
delayed by the delay means 48 for weighting to obtain the
weighted synthesized membership function 33 (Step ST 4).
The membership functions 28 and 31 of the second half of
the rules 20 and 21 and the thus weighted and synthesized
membership function 33 are inputted into and synthesized by
the synthesizing means 46 to produce a new synthesized member-
ship function 34 (Step ST 5~. For this synthesizing operation,
arithmetic operation for the union is used. Accordingly, the
synthesized membership function 34 is the sum aggregation of
the fuzzy aggregation of "excessively large control gain Kc"
and fuzzy aggregation of "excessively small contro.l gain Kc",
and therefore, after all, can be understood to be the fuzzy
aggregation of "dissatisfied control gain Kc". The synthesized
membership function 34 is inputted into the inference value
deciding means 47, which is turn decides a control gain Kco as
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the inference value 35 on the basis thereof and then is out-
putted to the controller 37 from the recurrent type fuzzy
inference apparatus 38 (Step ST 6). ~ore specifically, a
control gain wherein the value of tile synthesized membership
function 34 is the smallest may be selected. Next, judgement
for discontinuing the operation is effected (Step ST 7).
~hen the operation is desired to be continued, the processing
is returned to the Step ST 8 where the synthesized membership
function obtained at the Step ST 5 uses as an input of the
subsequent iteration.
Another embodiment of this invention will be described
hereinafter with reference to Figs. 3, 4, 7 and 8.
Fig. 7 is an explanatory view showing the operating
principle of another embodiment of the present invention,
and Fig. 8 is a flow chart for explaining the operation thereof.
In this embodiment, the aforesaid characteristic variables
22 to 25 are specifically shown. That is, the characteristic
variables 22 is the divergent trend of a error (e) 42, the
characteristic variable 23 is the magnitude Sb of the error
42, the characteristic variable 24 is the following degree Sc
of the controlled variable (y) with respect to variation of
the reference input (r) 40, and the characteristic variable
25 is the magnitude Sd(=Sb) of the error 42. At this time,
the rule 20 has a meaning that "If the divergent trend of the
error (e) 42 is large and the absolute value thereof is also
large, the control gain Kc is preferably smaller than the
present value". Where the actual values of the characteristic
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variables 22 to 25 inputted into the weighting means 45 are
SaO, Sbo, ScO and Sdo, whether or not the value SaO is large
and whether the value Sb~ is large, in the rule 20, are
evaluated by the membership functions 26 and 27, respectively,
of the first half of the rule 20. In the example shown in
Fig. 7, the respective evaluated values are "0.4" and "1.0",
and among these two evaluated values, the lower value "0.4"
is employed as the degree of matching of the first half of
the rule 20. The second half of the rule 20 defines the
fuzzy aggregation of "smaller control gain Kc (=satisfying
control gain Kc)" and prepares a membership function 28 with
a peak wherein weighting corresponding to the degree of
matching "0.4" of the first half is made at a smaller value
than the present control gain Kco~ This is totally true for
the rule 21. The membership function 31 of the second half
is prepared on the basis of the degree of matching wherein
the actual values ScO and Sdo f the inputted characteristic
variables 24 and 25 are evaluated by the membership functions
29 and 30 of the first half. In this example, the membership
function 31 is the function whose all values are "0".
Fig. 8 is a flow chart showing the flow of the operation.
The synthesized membership function 34, which was synthesized
by the synthesizing means 46 in the previous iteration and
sent as an input of the subsequent iteration (Step ST 18),
is sent to the delay means 48 and given a delay for one itera-
tion portion to obtain a membership function 32 (Step ST 11).
Separately from the former, the characteristic variables 22 to
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25 are inputted into the weighting means 45 and the process
characteristic variation amount 44 from the process 36 is
inputted into the characteristic variation evaluation means
49 (Step ST 12). Tlle weighting means 45 prepares the member-
ship functions 28 and 31 by evaluating the inputted charac-
teristic variables 22 to 25 by the membership functions 26,
27 and 29, 30 of the first half of the rules 20 and 21 and
on the basis of the obtained degree of matchins (Step ST 13).
The characteristic variation evaluation means 49 evaluates
the degree of variation in characteri$tic of the process from
the process characteristic variation amount 44 inputted, sends
its evaluated value to the multiplying means 50, and multiplies
the evaluated value by the previous synthesized membership
function 32 delayed by the delay means 48 for weighting to
obtain the weighted synthesized membership function 33 (Step
ST 14).
The membership functions 28 and 31 of the second half
of the rules 20 and 21 and the thus weighted synthesized
membership function 33 are inputted into and synthesized by
the synthesizing means 46 to produce a new synthesized member-
ship function 34 (Step ST 15). For this synthesizing opera-
tion, arithmetic operation of the union is used. Accordingly,
the synthesized membership function 34 defines the fuzzy
aggregation of "satisfying control gain Kc" so far learned
by the rules 20 and 21. The synthesized membership function
34 is inputted into the inference value deciding means 47,
which in turn decides a control gain Kco as the inference
lZ88168
value 35 on the basis thereof to output it to the controller
37 from the recurrent type fuzzing inference apparatus 38
(Step ST 16). Specifically, the center of gravity of the
synthesized membership function 34 is calculated to decide
a representative value Kco of a satisfying control gain.
Next, judgement for discontinuing the operation is effected
(Step ST 17). Where the operation is desired to be continued,
processing is returned to Step ST 18, and the synthesized
membership function obtained by Step ST 15 is used as an input
for the subsequent iteration.
A further embodiment of the present invention will be
described hereinafter with reference to Figs. 9 to 12. Fig.
9 is a block diagram showing one embodiment of a recurrent
fuzzy inference apparatus according to this invention; Fig.
10 is a block diagram showing an example in which a controller
for controlling a process is applied to a tuning of a control
gain; and Fig. 11 is an explanatory view showinq the operating
principle thereof. In these drawings, reference numerals 120
and 121 designate rules for inference, 122 to 125 characteris-
tic variables to be inputted into the recurrent type fuzzyinference apparatus, 126 and 127 membership functions of the
first half of the rule 120, 128 a membership function of the
second half of the rule 121, and 131 a membership function of
the second half. Reference numeral 132 designates a synthe-
sized membership function representative of a dissatisfactionpreviously synthesized, 133 a synthesized membership function
produced by applying a weighting to the previous synthesized
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membership function 132 representative of said dissatisfaction
where either membership functions 128 or 131 takes a value
larger than "0", 134 a synthesized membership function obtained
by synthesizing a membership function 128 of the second half
of the rule 120 and a membership function 131 of the second
half of the rule 121 and a previous synthesized membership
function 133 weighted according to the aforesaid conditions,
the membership function 134 being representative of the fuzzy
aggregation of "dissatisfactory control gain Kc", and 135 an
inference value obtained from the synthesized membership func-
tion 134, which in this example, is outputted as a control
gain Kc from the recurrent type fuzzy inference apparatus.
Further, reference numeral 136 designates a process to
be controlled, 137 a controller, for example, such as a PID
controller for controlling the process 136, 138 a recurrent
type fuzzy inference apparatus according to this invention
for supplying an inference value (control gain Kc) 135 to
the controller 137, 139 a characteristic variable extraction
unit for supplying characteristic variables 122 to 125 to
the fuzzy inference apparatus 138, 140 a reference input (q)
applied by the outside of the control system, 141 a controlled
variable (y) outputted from the process 136, 142 a error (e)
between the reference input 140 and the controlled variable
141 inputted into the controller 137, and 143 a manipulated
variable (x) applied to the process 136 from the controller
137.
Further, reference numeral 144 designates a weighting
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means which evaluates the degree of matching of the first half
from the characteristic variables 122 to 125 inputted into
the rules 120 and 121 to weight the membership functions of
the second half on the basis of the degree of matching, 145
a synthesizing means for synthesizing the membership functions
128, 131 weighted by the weighting means 144 and the previous
synthesized membership function 133 to obtain a new synthe-
sized membership function 134 representative of the degree of
a dissatisfaction of the inference value 135, 146 an inference
value deciding means for deciding the inference value 135 from
the synthesized membership function 134 synthesized by the
synthesizing means 145 to output it, 147 a delay means for
delaying a new synthesized membership function 132 synthesized
by the synthesizing means 145, 148 a detection means for
detecting whether or not either membership function 128 or
131 of the second half of the rules 120, 121 takes a value
larger than "0", and 149 a multiplying means which constitutes
detection and weighting means together with the detection
means 148 and in which where the detection means 148 detects
that either membership functions 128 or 131 takes a value
larger than "0", a previous synthesized membership function
132 delayed by the delay means 147 is subjected to a pre-
determined weighting for use as a synthesized membership
function 133, which is fed back to the synthesizing means
145.
Next, the operation will be described. The object of
the inference in the recurrent type fuzzy inference apparatus
1288168
is to effect a tuning of a control gain Kc by monitoring the
characteristic variables 122 to 125. So, first, the charac-
teristic variables 122 to 125 are specifically illustrated.
That is, the characteristic variable 122 is the divergent
5 trend Sa of the error (e) 142, the characteristic variable
123 the magnitude Sb of the error 142, the characteristic
variable 124 the following degree Sc of the controlled vriable
(y) with respect to a variation of the reference input (r)
140, and the characteristic variable 125 the magnitude Sd (=Sb)
of the error 142. At this time, the rule 120 has a meaning
that "If the divergent trend of the error (e) 142 is large
and the absolute value thereof is also large, the present
control gain Kc can be judged to be too large". ~here the
actual values of the characteristic variables 122 to 125
15 inputted into the weighting means 144 are SaO, Sbo, ScO and
Sdo, whether or not the value SaO is "large" and whether
the value Sbo is large, in the rule 120, are evaluated by
the membership functions 126 and 127 of the first half of
the rule 120. In the example shown in Fig. 11, the respec-
20 tive evaluated values are "0.4" and "1.0", and among thesetwo evaluated values, the lower value "0.4" is employed as the
degree of matching of the first half of the rule 120.
The second half of the rule 120 defines the fuzzy aggre-
gation of "excessively large control gain Kc", and a control
25 gain Kc _ Kco above the present control gain Kco is said to
be "excessively large" in the degree of the degree of matching
"0.4" of at least the first half. Then, a ~eighting corresponding
-- 18 --
~Z88168
to the degree of matching "0.4" of the first half is effected
to prepare a membership function 128. This is totally true
for the rule 121. The membership function 131 of the second
half is prepared on the basis of the degree of matching wherein
the actual values ScO and Sdo of the inputted characteristic
variables 124 and 125 are evaluated by the membership func-
tions 129 and 130 of the first half. In this example, the
membership function 131 is the function in which all the
values are "0".
Fig. 12 is a flow chart showing the flow of the operation.
The synthesized membership function 134, which was synthesized
by the synthesizing means 145 in the previous iteration and
sent as an input of the subsequent iteration (Step ST 30), is
sent to the delay means 147 and given a delay for one iteration
portion to obtain the membership function 132 (Step ST 21).
Separately from the former, the characteristic variables 122
to 125 are inputted into the weighting means 144 (Step ST 22),
which in turn prepares the membership functions 128 and 131 of
the second half by evaluating the inputted characteristic
variables 122 to 125 by the membership functions 126, 127 and
129, 130 of the first half of the rules 120 and 121 and on the
basis of the degree of matching (Step ST 23). The detection
means 148 detects whether or not either membership function
128 or 131 takes a value larger than "0" (Step ST 24), and
requirement of weighting is judged (Step ST 25). In the
illustrated example, the rule 120 is excited, and the member-
ship function 128 of the second half takes a value larger than
-- 19 --
~Z881~;8
"0". Therefore, in the multiplyiny means 149, the previous
synthesized membership function 132 is subjected to weighting,
for example, in 0.9 times, to produce the synthesized member-
ship function 133 (Step ST 26).
The membership functions 128 and 131 of the second half
of the rules 120 and 121 and the synthesized membership func-
tion 133 weighted as needed are inputted into and synthesized
by the synthesizing means 145 to produce a new svnthesized
membership function 134 (Step ST 27). For this synthesizing
operation, the arithmetic operation of the union is used. If
all the membership functions 128 and have only the values of
"0", the previous synthesized membership function 132 is
multiplied by 1.0 by the multiplying means 149 and is inputted
as the synthesized membership function 133 into the synthe-
sizing means 145 without being subjected to weighting. Accord-
ingly, the new synthesized membership function 134 obtained by
the synthesizing operation of the synthesizing means 145 is
the same as the previous membership function 132. As described
above, the synthesized membership function 134 represents the
fuzzy aggregation of "dissatisfied control gain Kc" so far
learned. The thus produced synthesized membership function
134 is inputted into the inference value deciding means 147,
which in turn decides the control gain ~cO as an inference
value 135 on the basis thereof to output it to the controller
137 from the recurrent fuzzy inference apparatus 138 (Step ST
28). Specifically, a control gain, wherein the value of the
synthesized membership function 134 is the smallest, may be
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1~881~;8
selected. Next, judgement for discontinuing the operation
is effected (Step ST 29), and when the operation is desired
to be continued, processing is returned to Step ST 30 and
the synthesized membership function obtained by Step ST 27
is used as an input for the subsequent iteration.
In the following, another embodiment of the present
invention will be described with reference to Figs. 9, 10
and 13.
First, the characteristic variables 122 to 125 are
specifically shown. That is, the characteristic variable
122 is the divergent trend Sa of the error (e) 142, the
characteristic variable 123 the magnitude Sb of the error
142, the characteristic variable 124 the following degree
Sc of the controlled variable (y) with respect to a varia-
tion of the reference input (r) 140, and the characteristic
variable 125 the magnitude Sd(=Sb) of the error 142. At
this time, the rule 120 has a meaning that "If the divergent
trend of the error (e) 142 is large and the absolute value
thereof is also large, the control gain Kc is preferably
smaller than the present value.". ~here the actual values
of the characteristic variables 122 to 125 inputted into
the weighting means 144 are SaO, Sbo, ScO and Sdo, whether
or not the value SaO is large and whether or not the value
Sbo is large, in the rule 120, are respectively evaluated
by the membership functions 126 and 127 of the first half
of the rule 120. In the example shown in Fig. 13, the
respective evaluated values are "0.4" and "1.0", and among
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~Z88168
these evaluated values, the lower value, "0.4", is employed
as the degree of matching of the first half of the rule 120.
The second half of the rule 120 defines the fuzzy aggregation
of "smaller control gain Kc (=satisfying control gain Kc)".
A membership function 128 with a peak wherein weighting
corresponding to the degree of matching "0.4" of the first
half is made at a value smaller than the present control gain
Kco is prepared. This is totally true for the rule 121. The
membership function 131 of the second half is prepared by
evaluating the actual values ScO and Sdo of the inputted
characteristic variables 124 and 125 by the membership func-
tions 129 and 130 of the first half and on the basis of the
degree of matching resulting from such evaluation. In this
example, the membership function 131 is the function whose
all values are "0".
Fig. 14 is a flow chart showing the flow of the operation.
The synthesized membership function 134, which was synthesized
by the synthesizing means 145 in the previous iteration and
sent as an input of the subsequent iteration ~Step ST 40), is
sent to the delay means 147 and given a delay for one iteration
portion to obtain a membership function 132 (Step ST 31).
Separately from the former, the characteristic variables 122
to 125 are inputted into the weighting means 144 (Step ST 32),
and the weighting means 144 prepares the membership functions
128 and 131 of the second half by evaluating the characteristic
variables 122 to 125 inputted by the membership functions 126,
127 and 129, 130 of the first half of the rules 120 and 121 and
~Z88~6~
on the basis of the obtained degree of matching (Step ST 33).
The detection means 148 detects whether or not either member-
ship function 128 or 131 takes a value larger than "0" (Step
ST 34), and requirement of weighting is judged (Step ST 35).
In the illustrated example, the rule 120 is excited and the
membership function 128 of the second half takes a value larger
than "0". Therefore, the previous synthesized membership
function 132 is weighted 0.9 times, for example, in the multi-
plying means 149 to produce a synthesized membership function
133 (Step ST 36).
The membership functions 128 and 131 of the second half
of the rules 120 and 121 and the synthesized membership func-
tion 133 weighted as needed are inputted into and synthesized
by the synthesizing means 145 to produce a new synthesized
membership function 134 (Step ST 37). For this synthesizing
operation, arithmetic operation of the union is used. If the
membership functions 128 and 131 have only the value of "0",
the synthesized membership function 132 is multiplied by 1.0
by the multiplying means 149 and is inputted as the synthesized
membership function 133 into the synthesizing means 145 without
being subjected to weighting. Accordingly, the new membership
function 134 obtained by the synthesizing operation of the
synthesizing means 145 is the same as the previous synthesized
membership function 132. As described above, the synthesized
membership function 134 represents the fuzzy aggregation of
"satisfying control gain Kc" so far learned. The thus produced
synthesized membership function 134 is inputted into the inference
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value deciding means 115, which in turn decides the control
gain Kco as an inference value 135 on the basis thereof to
output it to the controller 137 from the recurrent type fuzzy
inference apparatus 138 (Step ST 38). Specifically, the
center of gravity of the synthesized membership function 134
is calculated to decide a representative value Kco of a
satisfying control gain. Next, a judgement for discontinuing
the operation is effected (Step ST 39), and when the operation
is desired to be continued, processing is returned to Step ST
40 and a synthesized membership function obtained in Step ST
37 is used as an input of the subsequent iteration.
While in the above-described embodiment, an example using
two rules of inference has been illustrated, it is to be noted
that more than three rules may be used. In addition, the
number of inputs and outputs and the number of stages of the
conditions in the first half can be suitably set. Furthermore,
for a method of obtainin~ an inference value from a synthesized
membership function, an area bi-section method or the like can
be used in place of calculation of the center of gravity.
Moreover, while in the above-described embodiment, the
case which is applied to a tuning of a control gain in a
controller for controlling a process has been described, it
is to be noted that it can be applied to an inference of other
parameters to achieve effects similar to those attained by the
above-described embodiment.
As described above, according to the present invention,
a synthesized membership function obtained by a previous
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~Z88168
synthesizing operation is fed back and/or fed back with weight-
ing according to the conditions, which is reused for synthe-
sization of a present membership function. Therefore, even
in the case where the characteristic variable (Si) is normally
Si=O and only when a specific phenomenon should occur, it is
O c Si _ 1, inference is possible. Furthermore, in the case
where not only the inference value takes a continuous value
but a parameter to be inferred is constant or merely varied
slowly, a convergent inference value may be obtained.
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