GB2211324A

GB2211324A - Fuzzy inference apparatus

Info

Publication number: GB2211324A
Application number: GB8819360A
Authority: GB
Inventors: Kohei Nomoto; Michimasa Kondo
Original assignee: Mitsubishi Electric Corp
Current assignee: Mitsubishi Electric Corp
Priority date: 1987-10-16
Filing date: 1988-08-15
Publication date: 1989-06-28
Anticipated expiration: 2008-08-15
Also published as: GB8819360D0; GB2211324B; CA1288168C; DE3832789A1

Description

2211324 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 Automation", November, 1986 (by Kiyoji Asai). In Fig. 1, reference numerals 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 Ae 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 function of the latter half of the rule 2. Further, numeral 11 designates 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 Au from the fuzzy inference apparatus.

Fig. 2 is a block diagram showing one example of a conventional 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 characteristic 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 function 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 characteristic variable 4 (the rate of change Ae of the control error) is slightly deviated positively, then make the inference value 12 (manipulated variable Au) slightly deviated posi- tively". A portion of "If....." is called the aforementioned first half, and a later portion is called the aforementioned 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 e. and the actual value of the rate of change of the control error as the characteristic variable 4 is Aeo, 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 Ae. is "the rate of change of the control error slightly deviated positively" is evaluated as "M" 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 is 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 e. of the control error of the inputted characteristic variable 3 and the actual value Aeo of 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 matching. 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. Furthermore, 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 Auo 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 of 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 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 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 or merely changed slowly, a convergent inference value can be 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 membership 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.

other objects and advantages of the present invention will be apparent from the ensuing detailed description of the embodiments made while referring to the accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS

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.; 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; is Fig. 11 is an explanatory view showing the operating principle of the same; Fig. 12 is a flow chart showing a flow of the operation of the same; Fig. 13 is 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.

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 invention; 6 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 is 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 7 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 8 variation evaluation means for evaluating the degree of variation 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 characteristic variation 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 following 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 large, the present control gain Kc can be judged 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, 9 - 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 "0.411 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 >- Kco above the present control gain Kco is said to be "excessively large" in the degree of the degree of matching "O. C of at least the first half. Then, weighting corresponding to the degree of matching "O.C 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 @gold.

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 - 10 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 membership 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 control gain KclI, 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 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). blore specifically, a control gain wherein the value of the synthesized membership function 34 is the smallest may be selected. Next, judgement for discontinuing the operation is effected (Step ST 7).

When 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 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 12 variables 22 to 25 inputted into the weighting means 45 are Sao, Sbo, Sco and Sdo, whether or not the value Sa. is large and whether the value Sbo 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 "O.C' and "1.0", and among these two evaluated values, the lower value "O.C 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 "O.C 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 of 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 iteration portion to obtain a membership function 32 (Step ST 11). Separately from the former, the characteristic variables 22 to 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). The weighting means 45 prepares the member- ship functions 28 and 31 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 13). The characteristic variation evaluation means 49 evaluates the degree of variation in characteristic 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 membership function 34 (Step ST 15). For this synthesizing operation, 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 14 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 showing 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 fuzzy inference 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 dissatisfaction previously synthesized, 133 a synthesized membership function produced by applying a weighting to the previous synthesized 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 inferencq 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 (4) 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 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 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 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". Where the actual values of the characteristic variables 122 to 125 is 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 tive evaluated values are "O.C and "1.0", and among these two evaluated values, the lower value "O.C 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 gain Kc 2 Kco above the present control gain Kco is said to be "excessively larg-e" in the degree of the degree of matching 11O.C of at least the first half. Then, a weighting corresponding - 18 to the degree of matching "O.C 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 ofthe 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 "0". Therefore, in the multiplying 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 synthesized 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 is 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 Kc, 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 - 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.". Where 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 "O.C and "1.0", and among these evaluated values, the lower value, "O.C, 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 "O.C 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 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 11011 (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 11011. 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 Usatisfying control gain Kcl' so far learned. The thus produced synthesized membership function 134 is inputted into the inference 23 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 obtaining 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 - 24 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=0 and only when a specific phenomenon should occur, it is 0 < Si:g- 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.

Claims

WHAT IS CLAIMED IS:

1. A fuzzy inference apparatus comprising a weighting means having a plurality of rules formed with the first half and the second half using a membership function of a value between "0" and "1", evaluating a degree of matching of said first half from characteristic variables of a process inputted into said rules and weighting the membership function of said second half according to the degree of matching; a synthesizing means for synthesizing a previous synthesized membership function obtained by its own synthesizing operation and the membership functions weighted by said weighting means to obtain a new synthesized membership function; and an inference value deciding means for deciding an inference value from said synthesized membership function obtained by said synthesizing means.

2. A fuzzy inference apparatus according to claim 1, wherein the previous synthesized membership function to be fed back to said synthesizing means is weighted according to the degree of a variation in process characteristic of said process.

3. A fuzzy inference apparatus according to claim 2, wherein each of said rules having said weighting means judges that an inference value to be outputted is "excessively large" and "excessively small", and said synthesizing means synthesizes membership functions representative of a dissatisfaction 26 in a sense of "excessively large" or "excessively small".

4. A fuzzy inference apparatus comprising a weighting means having a plurality of rules formed with the first half and the second half using a membership function of a value between "0" and "P', each rule being described about a degree of satisfaction of each inference value, evaluating a degree of matching of said first half from characteristic variables of a process inputted and weighting the membership function of said second half according to the degree of matching; a synthesizing means for feeding back and inputting a previous synthesized membership function obtained by its own synthesizing operation and synthesizing the first-mentioned membership function and each membership function weighted as described above inputted by said weighting means to obtain a new synthesized membership function; an evaluating and weighting means for weighting said previous synthesized membership function fed back to said synthesizing means according to the degree of a variation in process characteristic of said process; and an inference value deciding means for deciding and outputting an inference value from said synthesized membership function obtained by said synthesizing means.

5. A fuzzy inference apparatus comprising a weighting means having a plurality of rules formed with the first half and the second half using a membership function of a value between "0" and "1", evaluating a degree of matching of said 27 - first half from characteristic variables of a process inputted into said rules and weighting the membership function of said second half according to the degree of matching; a synthesizing means for synthesizing a previous synthesized membership function obtained by its own synthesizing operation and the membership functions weighted by said weighting means to obtain a new synthesized membership function; a detection and weighting means for weighting, as required, the previous synthesized membership function fed back to said synthesizing means when either said membership functions of said second half of each of said rules takes a value larger than "0"; and an inference value deciding means for deciding and outputting an inference value from said synthesized membership function obtained by said synthesizing means.

6. A fuzzy inference apparatus according to claim 5, wherein each of said rules having said weighting means judges that the inference value to be outputted is "excessively large" and "excessively small", and said synthesizing means synthesizes membership functions representative of a dissatisfaction in a sense of "excessively large" or "excessively small".

7. A fuzzy inference apparatus comprising a weighting means having a plurality of rules formed with the first half and the second half using a membership function of a value between "0" and "P', each rule being described about a degree - 28 of satisfaction of each inference value, evaluating a degree of matching of said first half from characteristic variables of a process inputted and weighting the membership function of said second half according to the degree of matching; a synthesizing means for synthesizing a previous synthesized membership function obtained by its own synthesizing operation and membership functions weighted by said weighting means to obtain a new synthesized membership function; a detection means for weighting, as required, the previous synthesized membership function fed back to said synthesizing means; and an inference value deciding means for deciding and outputting an inference value from said synthesized membership function obtained by said synthesizing means.

29 Published 1989 atThe PatentOffice, State House, 66171 Holborn, London W01B 4TP. Furthercopies maybe obtainedfrom The Patent Orace. Wee Branch, St Mary Gray, Orpington, Rent BR5 3P.D. Printed by Multiplex techniques ltd, St Mary Cray, Kent, Con. 1187