JPH0542014B2 - - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION [Field of Industrial Application] The present invention relates to an improvement of a fuzzy inference calculation method in fuzzy adjustment performed by applying so-called "fuzzy logic".

[Conventional technology]

In such fuzzy inference operations, when fuzzy inference is performed using fuzzy variables expressed by membership functions in the antecedent and consequent propositions of a control rule, the composition rule of inference is generally often used. That is, when a plurality of control rules are given, the ambiguous relationship R is determined in advance, and the membership function for the output is determined using the input value expressed by the membership function.

FIG. 4 is an explanatory diagram showing a method for simplifying such conventional fuzzy inference calculations. Hereinafter, a conventional example of the fuzzy inference calculation method will be explained with reference to FIG.

Suppose that there is a control rule expressed by the following equation.

IF x01=A11, x02=A21, x03=A31,...
x0k=Ak1 THEN u=B (If x01=A11, x02=A21, x03=A31,...
...If x0k=Ak1, the manipulated variable u is B) The block surrounded by the broken line in FIG. 4 is the part that performs the antecedent part calculation of the above control rule. In the figure, A11, A21, A31, ...Ak1 are the membership functions of the antecedent part, B1, ...BN are the membership functions of the consequent part, respectively,
x01, x02, x03, . . . x0k are each measured values (in this case, determined values).

1a, 1b, . . . 1k are arithmetic circuits (indicated by the symbol F) that calculate the membership functions, 2 is a minimum value arithmetic circuit (indicated by the symbol Λ) which takes the minimum value from multiple inputs and outputs it, and 3 is the input 4 is a circuit (indicated by *) that multiplies the membership function B1 by a constant (multiply the output of minimum value calculation circuit 2) and outputs the result, and 4 is a maximum value calculation circuit (symbol (denoted by V).

Next, the control operation will be explained. In the arithmetic circuit 1a,
The membership function value is determined from the membership function A11 of the antecedent part and the measured value x01 and output. The same applies to the other arithmetic circuits 1b, . . . 1k. The minimum value calculation circuit 2 receives each output from the calculation circuits 1a, 1b, . . . 1k, selects the minimum value from among them, and outputs it as the effectiveness α1. The antecedent part calculation ends when this validity α1 is determined.

Next, we move on to the consequent operation. The constant multiplier circuit 3 multiplies the consequent membership function B1 by the validity α1, outputs the result as B1', and sends it to the maximum arithmetic circuit 4. The maximum value calculation circuit 4 receives the results obtained by similarly calculating other control rules as B2'...Bn'. In the maximum value calculation circuit 4, those inputs
The maximum value is always selected from among the waveforms of B1'...Bn' and output as the membership function B. To actually obtain the manipulated output value from membership function B, draw a straight line parallel to the vertical axis that bisects the area formed by the function waveform of membership function B and the horizontal axis. A commonly used method is to take the value at the intersection of the two and use it as the manipulated output value.

Of course, there are many other methods of inference calculation. For example, in the above example, the constant multiplier circuit 3 multiplies the consequent membership function B1 by the validity level α1 and outputs the result. There is also a method that selects and outputs the smaller value. There is also a method in which the minimum value circuit 2 does not take the minimum value of the input quantities as in the above example, but instead outputs a value obtained by multiplying the input quantities mutually.

Furthermore, when the measured values x01, x02, x03, ... Another method is to select values and finally select and output the maximum value from among the selected smaller values.

[Problem that the invention seeks to solve]

Conventional fuzzy inference operations as explained above perform a series of operations consisting of antecedent part operations and consequent part operations for each given control rule, so when there are a large number of control rules, However, there were problems in that the time required for calculation was long and prompt control could not be achieved.

Therefore, in the fuzzy inference calculation, the present invention
Even if the number of control rules is large, the time required for calculation is shortened so that control can quickly respond.
are the problems to be solved.

[Means for solving problems]

In order to solve the above problem, in the present invention, when the number M of types of consequent part fuzzy variables is less than the number n of given control rules, each control rule corresponds to which consequent part fuzzy variable. A first table for storing in advance whether there is a fuzzy variable in the consequent part, and at least M storage areas for storing the effectiveness obtained as a result of the antecedent part calculation of each rule, corresponding to the types of fuzzy variables in the consequent part. A second table was prepared.

Now, there are a finite number of fuzzy variables in the consequent part of the control rule (B1, ...BN in Figure 4), and B1 is NB
(negative and large), B2 is NM (negative and medium), B3
is NS (negative and small), B4 is ZE (as is),
B5 is PS (positive and small), B6 is PM (positive and medium)
and B7 represent PB (positive and large), respectively, and the fuzzy variable in the consequent part is based on these seven stages (M
=7).

However, the number of control rules is not limited to seven, and there may be many. However, even in that case, the fuzzy variables with negative consequents of each control rule are the seven mentioned above, namely NB (large negative), NM (medium negative), NS (small negative), ZE (as is),
It always belongs to one of PS (positive and small), PM (positive and medium), and PB (positive and large).

Therefore, the first table was created by determining in advance which control rule corresponds to which consequent fuzzy variable, and storing it in correspondence so that it could be indexed. From now on, it may also be called a rule index storage device.

Please refer again to Figure 4. In FIG. 4, the maximum value calculation circuit 4 always selects and outputs the maximum value from among the waveforms of a finite number of input fuzzy variables (B1'...Bn'). This means that for a certain fuzzy variable B1', if there are multiple control rules corresponding to B1', perform the consequent operation for each control rule to find the value of the fuzzy variable B1', and then calculate the maximum value. Even if it is sent to the circuit 4, the maximum value calculation circuit 4 only uses the maximum value among the values belonging to the fuzzy variable B1', and values smaller than that are discarded.

If this is the case, even if various values are given as the effective number α to be calculated with the fuzzy variable B1 from multiple control rules, the value α other than the highest value will be the same as the fuzzy variable B1. In the end, it is wasteful to perform calculations between the two.

Therefore, for fuzzy variable B1, among the various values of α given from multiple control rules for B1, only the maximum value α is memorized, and only that α is finally calculated between it and fuzzy variable B1. It will be a good thing if you do. Other fuzzy variables
The same applies to B2 and beyond. That is, among the effective numbers α obtained by performing the antecedent part calculation in each control rule, α belonging to the same fuzzy variable is
It is necessary to select and memorize the maximum value with the highest grade among them.

For this purpose, we have created a second table that stores the maximum value of α (value with the highest grade) for each type of consequent fuzzy variable (7 types in this case). The second table may hereinafter be referred to as the consequent fuzzy variable grade store.

[Effect]

When performing an operation on a certain control rule, refer to the first table to find out which consequent fuzzy variable among the M consequent fuzzy variables the rule corresponds to. By knowing the number of the storage area in the second table in which the validity α obtained as a result of the antecedent part calculation of the rule is to be stored, and by actually performing the antecedent part calculation of the rule, When writing the validity α to the storage area of that number, read and compare the validity previously written to the storage area of that number (initially set to 0), and if the former is greater than the latter. , rewrite the latter by the former, leave it as is if it is not large, and repeat the above to complete the antecedent computation for all of the given control rules.At that point, the consequent fuzzy variables are added to the second table. Using the effectiveness stored for each type, the total M
The consequent part calculation is performed for the second time, and then the consequent part calculation is completed.

Conventionally, when there were n control rules (n>M), n consequent operations were performed, but with the present invention, only M operations are required, which reduces the amount of time required for the operation. That's how much time it takes.

〔Example〕

Next, embodiments of the present invention will be described with reference to the drawings.
FIG. 1 is a block diagram showing one embodiment of the present invention.

In the figure, 11 is a measured value input device, 12 is an antecedent part membership function storage device, 13a is an effectiveness calculation device that performs the antecedent part calculation of control rule 1 and outputs the effectiveness degree α1, and 13b is a similarly controlled Rule 2
13n is the control rule N
14 is a consequent proposition calculation command device which instructs the start of the consequent part calculation and outputs the validity degree αn by calculating the antecedent part of the control rules 1 to N. After detecting the completion of the calculation for α, it instructs to start the consequent calculation. 1
5 is a rule index storage device, 16a, 16
b,...16n are effectiveness comparison storage devices, 1
7 is a grade 0 setting device, 18 is a consequent fuzzy variable grade storage device, 19 is a consequent membership function storage device, 20 is a consequent proposition calculation device,
21 is a manipulated value calculation device, and 22 is an output device.

FIG. 2 is a conceptual diagram of the rule index storage device 15 in FIG. 1.

In Figure 2, there are seven fuzzy variables in the consequent part of the control rule, and B1 represents NB (negative and large);
B2 is MN (negative and medium), B3 is NS (negative and small)
, B4 represents ZE (as is), B5 represents PS (positive and small), B6 represents PM (positive and medium), and B7 represents PB (positive and small). Then, control rules 1 and 2 belong to fuzzy variable B1, control rules 3, 4, and 6 belong to B2,
Control rules 5 and 7 belong to B3, and in the following, control rules 13 and 14 belong to B7 in the same manner.

FIG. 3 is a conceptual diagram of the consequent part fuzzy variable grade storage device 18 in FIG.

In FIG. 3, in the α storage area (number storage area) corresponding to the fuzzy variable B1, the antecedent part calculation is performed for each of control rules 1 and 2 to obtain and compare the effectiveness degrees α1 and α2, and the results are as follows. Since α2>α1, this shows that α2 was finally memorized.

Similarly, the α storage area (number storage area) corresponding to fuzzy variable B2 contains control rules 3, 4,
As a result of calculating the antecedent part for each of 6 and comparing the effectiveness degrees α3, α4, and α6, α4 was the largest among them, indicating that α4 was finally memorized. . The same applies hereafter.

Next, the fuzzy inference calculation method according to the present invention will be explained with reference to FIGS. 1 to 3.

First, using the grade 0 setting device 17, the α storage area (or) of the consequent fuzzy variable grade storage device 18 is set to all zeros. Next, the validity calculating device 13a of the control rule 1 calculates the predetermined value of the control rule 1 using a certain membership function given from the antecedent membership function storage device 12 and the measured value given from the measured value input device 11. Performs the subject part calculation, calculates the effectiveness α1, and outputs it.
As already mentioned, which consequent fuzzy variable the control rule 1 belongs to can be determined by referring to the rule index storage device 15.

In this example, it is assumed that it belongs to the fuzzy variable B1, so when this fact is known by referring to the rule index storage device 15, the validity comparison storage device 16a stores the fuzzy variable B1 in the consequent part fuzzy variable grade storage device 18. The corresponding α storage area is read out. Initially, 0 is set here, so
The effectiveness comparison storage device 16a compares α1 with 0, and as a result, α1>0, so α1 is written into the α storage area corresponding to B1.

Similarly, the effectiveness calculation device 13b for control rule 2 uses a certain membership function given from the antecedent membership function storage device 12 and the measured value given from the measured value input device 11 to calculate the validity of control rule 2. The antecedent part is calculated, and the validity α2 is calculated and output. The consequent fuzzy variable to which the control rule 2 belongs can be determined by referring to the rule index storage device 15.

In this case, control rule 2 is still a fuzzy variable
Since it belongs to B1, when this is known by referring to the rule index storage device 15, the validity comparison storage device 16b stores the α storage area corresponding to B1 in the consequent part fuzzy variable grade storage device 18. Read it out in the same way as before.
Then, this time α1 is stored here, so
The effectiveness comparison storage device 16a compares α2 with α1, and if α2>α1 as a result, writes α2 in place of α1 in the α storage area corresponding to B1.
The control rules belonging to fuzzy variable B1 are rules 1 and 2.
In this example, the contents of the α storage area corresponding to B1 of the consequent part fuzzy variable grade storage device 18 are as shown in FIG.
Confirm α2.

Thereafter, in the same way, the effectiveness calculation device 13n of the control rule N calculates the effectiveness of the last control rule 16 αn (however, n
= 16) and output it to the effectiveness comparison storage device 16.
n refers to the rule index storage device 15 and learns the fuzzy variable B5 to which the control rule N belongs,
B5 of consequent part fuzzy variable grade storage device 18
When the content of the α storage area corresponding to is finally determined, the contents of the consequent fuzzy variable grade storage device 18 are all determined.

The consequent proposition calculation commanding device 14 learns that all the contents of the consequent fuzzy variable grade storage device 18 have been determined by the command from the validity calculation device 13n of the control rule N, and then instructs the consequent proposition calculation device 20. Instructs to perform the consequent operation on .

The consequent proposition calculation device 20 receives the required consequent membership function from the storage device 19, and
The validity α is sequentially read from the consequent part fuzzy variable grade storage device 18, the consequent part calculation is performed, and the result is output to the operation value calculation device 21.
The operation value calculated by the device 21 is output to the output device 22.

In the above embodiment, the control rule effectiveness calculation device and effectiveness comparison storage device are prepared for each control rule, but only one set of these devices is prepared, and each control rule sequentially for
It goes without saying that it may also be calculated.

〔Effect of the invention〕

According to the present invention, in the fuzzy inference operation,
Since the number of consequent calculations of a control rule can be reduced from the same number as the number of control rules to a number equal to the type of consequent fuzzy variables, the time required for inference calculations can be reduced accordingly, which in turn improves the control response in fuzzy adjustment. It has the advantage of increasing sex.

Also, in the storage device that stores the consequent membership functions, it is not necessary to store the consequent membership functions as many as the number of control rules; it is sufficient to store only the number equal to the types of consequent fuzzy variables. Another advantage is that the storage capacity can be reduced accordingly.

[Brief explanation of drawings]

FIG. 1 is a block diagram showing one embodiment of the present invention;
Figure 2 is a conceptual diagram of the rule index storage device.
FIG. 3 is a conceptual diagram of a consequent part fuzzy variable grade storage device, and FIG. 4 is an explanatory diagram showing a conventional fuzzy inference calculation method. Explanation of symbols, 11... Measured value input device, 12...
...Antecedent membership function storage device, 13a,
13b, 13n...Efficacy calculation device that calculates the antecedent part of the control rule and outputs the effectiveness α, 14...
Consequent part proposition calculation command device, 15... Rule index storage device, 16a, 16b, 16n... Validity comparison storage device, 17... Grade 0 setting device, 18... Consequent part fuzzy variable grade storage device, 19...Consequent part membership function storage device, 20...Consequent part proposition calculation device, 21...Operation value calculation device, 22...Output device.

Claims (1)

[Claims] 1. Divide the control rule into an antecedent part and a consequent part, and first calculate the antecedent part using the measured value obtained from the controlled object to find the effectiveness, and then calculate the effectiveness. The consequent membership function is obtained by performing the consequent part operation using In a fuzzy inference calculation method for creating an operation output for a controlled object, when the number M of types of consequent fuzzy variables is less than the number n of the given control rules, each control rule is associated with which consequent fuzzy variable. A first table for storing in advance whether or not they correspond, and a storage area for storing the effectiveness obtained as a result of the antecedent part calculation of each rule are made to correspond to the type of consequent part fuzzy variable. When performing an operation on a certain control rule, the first table is used to determine which consequent fuzzy variable the rule corresponds to. By referring to it, we can know the number of the storage area in the second table in which the effectiveness obtained as a result of the antecedent part calculation of the rule is to be stored, and we can actually calculate the antecedent part of the rule and obtain the result. When writing the validity level to the storage area of that number, read and compare the validity level previously written to the storage area of that number, and if the former is larger than the latter, the latter is rewritten by the former and the If there is no fuzzy variable, leave it as is, and repeat the above to complete the antecedent part calculation for all of the given control rules. At that point, the effectiveness degree stored for each type of consequent part fuzzy variable is stored in the second table. A total of M consequent operations are performed using
A fuzzy inference calculation method characterized in that the consequent part calculation is then terminated.