JPH0527981A - Method and device for fuzzy inference - Google Patents

Abstract

PURPOSE:To fix rules required for offline and to shorten time for calculation by omitting the calculation of unwanted rules in the case of online execution by using an area division executing method in an offline processing. CONSTITUTION:A membership function or a representative output value exists in a file 39, and the table of an operating area is prepared in a file 41 through an area division and operating rule extraction processing 40 based on the data. Further, the table of inference discrete functions is prepared from the data of the file 41 through an inference discrete function calculation processing 42 to a file 43. In the online processing, the required data are stored in a memory 45, the input to the inference system is calculated by a process 44 according to the sampling data of a discrete controlled variable inputted from a sensor 2 and an operating area, where the input exists, is judged at the same time. The required data are called by a process 45, the inference is executed, and the manipulated variable is calculated and outputted to a manipulation part 6.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method for executing fuzzy inference at high speed. For example, in a built-in fuzzy controller, a general-purpose micro-controller suitable for designing an application-specific IC for realizing it. The present invention relates to a fuzzy inference method which has a processor and a high calculation performance with a smaller storage capacity than before.

[0002]

[Prior art]

(1) Fuzzy inference method (determined output calculation formula) The most commonly used fuzzy inference method in fuzzy control is Mamdani's method. Therefore, here we focus on the Mamdani method, which is considered suitable for control.
A simple explanation of the addition / centroid method or the simplification method (Sugano: Fuzzy control: Nikkan Kogyo Shimbun, Mizumoto: Fuzzy inference method for fuzzy control: Measurement and control, Vol.28, N
o.11, pp.959-963, (1989), Maeda and Murakami: Fuzzy control and its application: System / Control / Information, Vol.34, No.5, pp2
82-287, (1990)).

In the multi-fuzzy inference format (fuzzy inference system having a plurality of inputs) which is often used in fuzzy control and the like, the control law is expressed by the equation (1).

[0004]

[Equation 1]

Fuzzy inference used for control or the like is a calculation method for obtaining a definite output w ₀ for definite inputs u ₀ , v ₀ .. to the control system. Hereinafter, an example of 2-input 1-output fuzzy inference will be mainly described, but the same applies to the case of 3 inputs or more (in the description dealing with the case of 3 inputs or more, the input variable is generalized to xi ₀ ).

When data (determined input) obtained by sampling or the like is input to the fuzzy inference system, first, the suitability of the rule (conformity of the antecedent part) to the confirmed input is calculated for each rule. This antecedent part fitness means the weight to which each rule is applied when the output is calculated.
Then, ωi is

[0007]

[Equation 2]

It is evaluated as

Next, fuzzy implication calculation (calculation for inferring fuzzy output according to antecedent part conformity) is executed in order to calculate a fuzzy output corresponding to the antecedent part conformance for each rule. If the fuzzy output for each rule is μi (w),
By the method of Mamdani, μi (w) is

[0010]

[Equation 3]

[0011]

Finally, the fuzzy outputs for each rule are integrated (inference integration). The fuzzy output of the entire system is μ
If (w), μ (w) is

[0013]

[Equation 4]

[0014]

Finally, the output is determined from this fuzzy output. In the Mamdani method, the value of the output axis coordinate of the center of gravity of fuzzy output is represented (the center of gravity method). That is,
The final (defuzzified) output (determined output) is

[0016]

[Equation 5]

From this, the reasoning formula by the Mamdani method is

[0018]

[Equation 6]

Is given.

In addition to the Mamdani method, several methods have been proposed for giving operations. In general, fuzzy entailment calculation can be performed by fuzzy logical product, and inference can be integrated by fuzzy logical sum or arithmetic addition. The operation corresponding to fuzzy logical product is generally called t-norm, and is an operation that satisfies monotonicity, associativity, commutativity, and boundary conditions. The s-norm is an operation that satisfies a dual relationship with the t-norm. Fuzzy reasoning formulas can give various kinds of reasoning formulas in addition to Mamdani's method (Mizumoto: Fuzzy logic and Fuzzy reasoning: Mathematical science, N
o.284, FEBRUARY 1987). For example, in the algebraic product-addition-centroid method which is considered to be suitable for control, a method of applying an algebraic product to fuzzy implications and performing inference integration by addition,

[0021]

[Equation 7]

[Mizumoto: Fuzzy inference method for fuzzy control: measurement and control, Vol.28, No.11, p
p.959-963, (1989)).

(2) Execution method of fuzzy inference (execution method of calculation) There are many execution methods of fuzzy inference, but it is assumed to be a device for embedded equipment in which only the input fluctuates and the inference system is fixed. Then, a method of delegating a part of the calculation to the array reference in some form is general. In this method, the inference values calculated in advance are defined as a table (represented by an array), and the array is referred to when the inference is executed.

That is, the calculation required for fuzzy inference is not performed each time it is executed, but a process that frequently appears in the calculation process is calculated in advance and the calculation result is referred to at the time of execution, so that the inference necessary for the inference is performed. By reducing the amount of calculation, it is an execution method that enables real-time processing even with a device that incorporates a microprocessor that does not have high computing performance.

A table reference method is generally used as a method for accelerating such fuzzy inference. An address reference method (Arita and Hirota: Transactions of the Society of Instrument and Control Engineers, Vol.28, No.2, pp.180-187, 1990) has been proposed as one of these formats. This method is basically a method of "calculating outputs for all input patterns in advance, defining this as a table (array), and referencing at the time of execution". In the address reference method, in order to efficiently execute this, the upper bits of the input are regarded as a virtual page, and the input is directly input to the address bus, whereby the inferred value is obtained at high speed.

As another method for speeding up fuzzy inference,
Some handle fuzzy inference expressions in the simplest form possible. This includes, for example, the simplification method (Maeda and Murakami: Fuzzy control and its application: System / Control / Information, Vol.34, N.
o.5, pp282-287, (1990)) and the algebraic product-addition-center of gravity method (Mizumoto: Fuzzy inference method for fuzzy control:
Measurement and control, Vol.28, No.11, pp.959-963, (1989)).

In this method, in the above-mentioned equation 7,
Since the suitability of the antecedent part does not depend on the output variable,

[0028]

[Equation 8]

The integral terms can be summarized as follows. Then, calculate this integral term offline in advance,
By defining it as array data, it is possible to execute fuzzy inference by the barycentric method without online integration calculation.

Further, if Ai is constant regardless of i,
If we set wi = Mi / Ai,

[0031]

[Equation 9]

It becomes as follows.

This is equivalent to the simplification method in which the consequent part of the fuzzy rule is expressed in advance by a constant, and is the same fuzzy inference formula as the simplification method. These methods do not require integral calculation in defuzzification calculation and can execute inference at high speed.

[0034]

The above-mentioned conventional method has the following problems.

The table reference method shown as the first implementation method is certainly excellent in terms of calculation speed. However, in an inference system with a plurality of inputs, the number of required array elements is a power of the number of inputs, so it is difficult to implement the method in a system with memory constraints.

In the method shown as the second implementation method, since the required array is one-dimensional, even if it is necessary for each input or rule, the memory amount can be suppressed appropriately in a normal system. However, since a calculation proportional to the number of rules is required, the calculation speed is inevitably reduced as the number of rules increases.
Moreover, since an array corresponding to integration is required for each rule, the memory amount becomes considerably large in an inference system with a large number of rules.

As described above, in a system involving a plurality of inputs and a large number of rules, it has been difficult to satisfy the contradictory requirements of improving the operation speed and reducing the memory used by the conventional method. Therefore, in a fuzzy control device in which the capacity of the built-in microcomputer or the amount of memory that can be used is limited, it has been unavoidable to suppress the number of inputs or the resolution.

An object of the present invention is to provide a more efficient fuzzy inference realization method for a fuzzy control system with a large number of rules, to use a microcomputer with low computing capacity and to reduce the amount of memory and to achieve high performance. It is to provide a fuzzy control device.

[0039]

In order to achieve the above-mentioned object, one means used in the present invention is to judge the condition for each rule (decision as to whether or not the matching degree is 0), which is conventionally performed at each inference. ) Is not performed, and incompatible rules are extracted in advance according to the input, and excluded from the inference target. Specifically, by mapping the inputs and the rules that are compatible with the inputs, the combination of rules that are compatible with a certain input is obtained, and the inputs that have the same combination are grouped together. , The entire input space is divided into some partial areas corresponding to it (hereinafter referred to as area division execution method), and this is used as an operation area. To create a "list of rules necessary for calculation" for each operation area.

Therefore, it will be briefly described that fuzzy inference can be executed at high speed by using such a list. The suitability of the antecedent part is given for each rule (for example, in the Mamdani's method) by the number 2, but if this is zero, the fuzzy output of the rule by the number 3 is also zero. Therefore, the number 4
If the fuzzy outputs are integrated in (as in addition and other s-norms), then the rule has no effect on the inferred value.

In the above area division execution method, the suitability of rules in a given fuzzy inference system is spatially evaluated. In other words, consider a vector space (input space) in which each input is an element of the input vector, consider each subspace in the input space in which each rule has a positive antecedent fitness in this vector space, and The application area. When a certain operation area does not overlap the application area of the rule, the rule can be omitted in the operation area and the inference system is fixed, that is, the membership function dynamically changes in real time. In the case of a system that does not do so, it is possible to omit rules that do not affect the inferred value by dividing the appropriate operation area in advance and defining a rule corresponding to each operation area.

Specifically, the operation area and operation rule are defined as follows.

[0043]

[Equation 10]

By dividing in this way, the input always belongs to one certain operation area. Then, for inputs that belong to the same operation area, an inference value can be obtained simply by executing inference for a common operation rule.

At this time, for example, the algebraic product-addition-center of gravity fuzzy inference formula of Equation 7 can be expressed as a fuzzy inference formula for each operation area as follows.

[0046]

[Equation 11]

Similarly, the area division execution method is not limited to the algebraic product-addition-center of gravity method, and can be similarly applied to all fuzzy inference methods.

Explaining with a concrete example, an inference system as shown in FIG. 1 will be exemplified by a system of two inputs and two rules. If the input space is divided as shown in FIG.
The rules that are applied are limited to each region, such as only the rule 2 in the region 2 (in this example, the rule 1 is applied in the region 3).
2 and 2 are applied, and the applicable rule does not exist in the area 4, but an error occurs when the applicable rule does not exist in the actual control system, so the control law is defined so that some rule applies in all areas).

Another means used in the present invention divides the entire input space into grid-like regions by the upper bits of input numerical data in order to efficiently determine the operation region.
By associating the operation area with this grid-like area, the operation area including the input is determined at high speed. Therefore, a list of operation areas (numbers) corresponding to the upper bits of the input numerical data is held, and this is linked with a list defining necessary rules for each area.

Still another means used in the present invention is to apply the limiting product, which is a form of fuzzy logical product, to the calculation of the antecedent fitness in the algebraic product-addition-centroid method or the simplification method, and further Apply the divisional execution method. Then, the inference expression for each operation area is converted into a simple calculation expression that can be expressed only by one variable function and a constant and does not require complicated calculation (addition for each rule). Execution method), a table of one-variable functions (hereinafter, inference separation functions) used in the inference formula for each operation area is defined as a one-dimensional array and used.

Therefore, it will be briefly described that the mathematical formula can be modified in this way. In the algebraic product-addition-center of gravity method, the marginal product is applied to the calculation of the antecedent fitness, and processing is performed according to the area segmentation execution method. Here, the limiting product is a form of fuzzy logical product, and the limiting product of a and b is defined by max {0, a + b-1}. Thus, the algebraic product-addition-centroid method expressing the goodness of fit of the rule is

[0052]

[Equation 12]

It can be expressed as

The limit product condition judgment is, after all, a judgment as to whether or not the input exists in the rule application area. Therefore, when the application areas of each rule are overlapped and each element area of the minimum unit constituted by the boundary is set as the operation area, the following inference formula can be expressed for each operation area.

[0055]

[Equation 13]

This inference formula can be further modified as follows.

[0057]

[Equation 14]

Each Σ term in the equation 14 is a function or a constant of each input variable and can be modified as follows.

[0059]

[Equation 15]

If the values of the terms included in the numerator and the denominator of Expression 15 are calculated in advance, various values required for calculating the inferred value can be defined as a one-dimensional array or constants.

If the fuzzy inference method of the present invention is used, the reference table defining the numerical values required for calculation holds the table defining the function of each input variable as a one-dimensional array for each operation area. Fuzzy reasoning can be performed.

In this case, if the operation area determination means using the upper bits of the input data shown above is used, for example, 2
In the case of input, the operation area needs to be a rectangle defined on a two-dimensional input space. However, the shape of the application area of the rule based on the antecedent conformity evaluated by the marginal product is not always rectangular. For example, in FIG.
An example of the actual fuzzy control law given by
In the control rule of the form (1), the meshing function that indicates the condition of the antecedent part is defined from PB to NB, and the membership function that indicates the condition of the consequent part is defined from P4 to N4. Taking the example of the fuzzy control system of rule number 25), the shape becomes irregular as shown in FIG.

Therefore, the suitability of the antecedent part is evaluated as follows.

[0064]

[Equation 16]

This is hereinafter referred to as an expansion limit product.

Further, Di is a rule application area. This Di is

[0067]

[Equation 17]

An arbitrary area is set within the range that satisfies the above condition. For example, taking the fuzzy control law of FIG. 3 as an example, an example of designation of the application area of the rule 13 of FIG. 3 is shown as, for example, FIG. FIG. 13A shows an applicable area when ψ = 1, and the square indicated by the dotted line in the center is the number 1
This is an area that satisfies 7. Therefore, for example, as shown by the hatched portion in FIG. 13A, the application area of Rule 13 must be defined in a smaller range. Also in FIG.
(b) shows the applicable area when ψ = 0,
The shaded area in the center of the figure is the area that satisfies the expression (17). Similarly, the applicable area is arbitrarily designated in a range smaller than this.

However, since the area satisfying the expression 17 is the application area in the original sense, it is desirable to specify the application area as large as possible. The parameter ψ coincides with the marginal product when ψ = 1, and the difference from the marginal product increases as the parameter decreases, so it is desirable to specify the value of ψ as large as possible under the specified conditions.

Thus, the inference formula can be expressed as follows.

[0071]

[Equation 18]

As in the above-mentioned method, it is possible to carry out mathematical processing.

[0073]

[Formula 19]

[0074]

[Equation 20]

After all,

[0076]

[Equation 21]

As shown in the equation (15), it can be transformed into a format having the same structure as the equation (15). Then, as in the case of evaluating the antecedent conformity with the marginal product, as a reference table that defines the numerical values required for calculation, a table that defines the value of the function for each input variable as a one-dimensional array is used. Fuzzy inference can be performed by holding each.

[0078]

In the present invention, by defining the rules to be applied in advance as an array, it is possible to omit unnecessary operations related to incompatible rules, that is, rules that do not affect the operation result. It is possible to shorten the calculation time. The shortened calculation time is given by the difference between the time required for calculation of unnecessary rules and the time required for area determination.

Further, in the present invention, the operation area can be determined at high speed by directly determining the operation area by the upper bits of the input numerical data.

Furthermore, the array defined in the present invention is only a one-dimensional array, and without performing calculation for each rule,
Fuzzy reasoning can be performed. Therefore, even in a fuzzy inference system involving many inputs, the fuzzy inference system can be configured with a relatively small memory, and processing can be performed in a calculation time close to that of the table reference method.

[0081]

EXAMPLES Examples of the present invention will be described in detail below. The present invention is not limited to this.

Here, it is considered to execute the speed type fuzzy PI control as shown in FIG. This is generally represented by a table as shown in (a) and (b) of FIG. Here, for example, in Rule 1, if the input deviation e ₀ is NB (defined in FIG. 3 (c)) and the deviation change Δe ₀ is NB, the output Δm ₀ is N4 (defined in FIG. 3 (d)). It means that there is. Here, an embodiment of the present invention will be described by taking the fuzzy control law defined in FIG. 3 as an example.

The inference process is realized as a control device as shown in FIG. In this fuzzy control system, the controlled variable in the controlled object 1 is sampled by the sensor 2. With respect to the sampled control amount, a deviation (difference between the set value and the control amount) and its change (difference between the deviation one step before) are calculated by the input unit 3, and are input to the fuzzy inference unit 4. In the case of the speed type, this output is given by the difference of the manipulated variables, and therefore the output unit 5 adds the output one step before to determine the manipulated variable. The control of the controlled object is executed by the operation unit 6 based on this operation amount, and the same procedure is repeated thereafter.

In the following embodiments, an example is given in which the fuzzy inference of such a 2-input 1-output system is taken as an example, but the present invention can also handle an object having 3 or more inputs in the same manner. Further, in the following, the embodiment of the fuzzy inference apparatus or method will be described in which e ₀ and Δe ₀ are input as definite inputs to the fuzzy inference unit from the input unit and Δm ₀ is output to the output unit as the inference value for this. When referring to a function assuming three or more inputs, or when explaining the contents common to each input, the input is generalized and displayed as x.

The present invention can be realized by a one-chip microcomputer as shown in FIG. 5, for example, at a high speed and with a small memory. Assuming a general 8-bit microcomputer,
The input from the sensor 2 is discretized through the input port 12 and the A / D converter 10. However. It is assumed that the input data is discretized corresponding to integer values from -127 to 127. However, 0.5 is made to correspond to 64 in the range of -1.0 <x <1.0. The array data corresponding to this input is called from ROM8 or RAM9, and CP
The U core 7 calculates an inference value and an output value (when the inference value is given by the difference between the outputs, a process of calculating the output value from the inference value is necessary), and the result is D / A converter 11
And through the output port 13 to the device of the operation unit 6,
The operation unit operates the control target.

An embodiment for implementing the present invention in a computer system such as the one-chip microcomputer described above will be described below. However, the microcomputer is a general 8-bit microcomputer (internal operation 16 bits).

The first embodiment is an embodiment relating to the area division execution method. In the execution of fuzzy inference by the domain segmentation execution method, prior to execution, it is necessary to "calculate a combination of matching rules corresponding to each input, and to group input comrades whose rule combinations are the same, and correspondingly input space. Is to be divided into several operation areas. Therefore, first, a method of dividing into such operation areas will be described.

FIG. 6 shows the application area of each fuzzy control rule defined in FIG. 3, that is, the area where the antecedent part conformity is positive, by evaluating the antecedent part adaptability with a general function min. An example of the case where it is decided is shown. In FIG. 6, each area is indicated by a shaded area. Here, the areas other than the shaded areas have zero suitability to the antecedent part. That is, the input existing in the applicable area means that the rule is necessary for executing the fuzzy inference, and conversely, the input existing outside the applicable area means that the rule is not necessary for executing the fuzzy inference.

Now, if all of these application areas are overlapped and the input space is divided while paying attention to the boundaries, the input space can be divided as shown in FIG. In this area, for example, the area 1 is an area in which the areas to which the rules 1, rules 2, 6, and 7 are applied are overlapped. Therefore, the input existing in the area 1 is rule 1, rule 2, and rule 6. And rule 7
Since the antecedent part conformity is positive only for, the inference should be performed only for these. Similarly, in region 2, it can be seen that it is sufficient to infer only rules 2, 3, 3, and 8.

Therefore, if each of the areas in FIG. 7 is used as an operation area and the rules in which the antecedent part conformity is positive are used as the operation rules, a table as shown in FIG. 8 can be created.

In the case of this embodiment, these operation areas correspond to the upper 2 bits of each input variable, and a table showing the correspondence as shown in FIG. 9 can be created.

These operations are executed off-line, and the tables defined in FIGS. 8 and 9 are stored as an array in the memory, that is, 8 to 9 in the apparatus of FIG. Then, at the time of execution, first, the upper bit of the input is extracted, then the corresponding operation area is referred to based on FIG. 9, and the operation rule is called based on FIG. After that, normal fuzzy inference should be executed only for the operation rule that was called.

A concrete example of this will be described. FIG. 10 is an example of a flowchart of a program executed by the computer system shown in FIG. 5 according to the present invention. In the data input 16, the set value set in advance as the control target and the sensor 2 and A shown in FIG.
The difference and the difference between the deviations are obtained by taking the difference between the control amounts digitized through the / D conversion 10. Then, the high-order bits of the input data are extracted 17 to extract those high-order bits (high-order 2 bits in this embodiment). This can be done by AND or bit shift. When the high-order bit is extracted, in the area 18 to which the input element belongs, the operation area is determined by referring to the table defined in FIG. When the operation area is determined, the operation rule is called according to the table of FIG. 8 by calling a rule group corresponding to the area.

Execution of inference 20 is similar to normal inference. Taking the simplification method as an example, the conventional fuzzy inference formula for the fuzzy control law of FIG.

[0095]

[Equation 22]

It becomes

Here, w _i is the value of the representative point of the membership function (the value of w that maximizes μ (w)).

If this is converted into the inference formula for each operation area shown in FIG. 7,

[0099]

[Equation 23]

It becomes

As described above, in the embodiment of the control law of FIG.
Fuzzy inference can be performed by executing operations for four rules for each operation area. To execute this in the system of FIG. 5, the membership function and w _i defined in Equation 8 are defined as an array as shown in FIG. Then, Equation 22 may be executed.

Since the obtained inference value is the output difference,
The data output 21 is added to the value one step before to determine the operation amount, and the controlled object is controlled through the D / A conversion 11 and the operation unit 6 shown in FIG.

FIG. 11 shows the sequence data required in the inference execution 20 of FIG. In FIG. 11A, the membership function is represented by an 8-bit integer value from -127 to 128. However, -127 to -1 are not actually used. Also, 1.0 is made to correspond to 64. FIG. 11B shows that w _i defined by Equation 9 is held as data. This w _i is represented by an 8-bit integer value from -127 to 128 here. Also, 1.0 is made to correspond to 64. In the first embodiment, inference, which conventionally required calculation of 25 rules or evaluation of the antecedent conformity of 25 rules, was performed simply by extracting upper bits. Inference can be performed with a reference to an array of operating regions and a calculation of four rules.

The second embodiment is an embodiment relating to the variable separation execution method. This execution method basically evaluates the suitability of the antecedent part by the limiting product, and the application area of each rule is overlapped by the same method as that shown in the first embodiment for each operation area. Transform the inference formula. Then, the addition for each rule is not required as shown in Expression 15, and the calculation is converted into a simple calculation formula of a one-variable function and a constant.

Here again, the configuration of the operation area will be described in order, as in the first embodiment. The application area of the rule obtained by evaluating the antecedent part conformance with the marginal product as in the first embodiment is as shown in FIG. If this is directly overlapped, the operation area can be divided as in the first embodiment, but it is difficult for the shape of the area to correspond to the upper bits of the input.

Therefore, it is considered to evaluate the suitability of the antecedent part by Expression 16. The evaluation of the suitability of the antecedent part in Expression 16 differs depending on how the parameter ψ is given. For example, if ψ = 1 as shown in (a) of FIG.
If ψ = 0 as shown in (b), it must be set smaller than the shaded area. However, it is possible to form the rule application area within the range, that is, the shape corresponding to the boundary by the upper bits. Now, considering the case of ψ = 0, the application area of the rule can be specified exactly as in FIG.
Therefore, the operation area is the same as in FIG.

The operation rules for each operation area are also
Similar to the first embodiment, it is shown in FIG. The operation area corresponds to the upper 2 bits and is shown in FIG. 9 as in the first embodiment. For the operation rule shown in FIG.
Compute the inference separation function according to and hold it as a table. Specifically, in the control law of FIG. 3, the inference formula of the simplification method in which the antecedent conformity is evaluated as in Formula 16 is
From 9, set w _i = M _i / A _i

[0108]

[Equation 24]

It becomes: Transform this,

[0110]

[Equation 25]

It becomes: In this way, the inference separation function is calculated according to the control rule of FIG. 3, whereby the inference value can be easily calculated.

To execute this in the system of FIG. 5, S (x) (inference separation function) of equation 25 is calculated according to the definition of equation 25. This inference separation function is stored as 16-bit data (in the simplification method, the inference separation function necessary for calculating the denominator of Expression 26 is 8 bits). Since array data uses data only in the range of the operation area, if only the range of possible values of e ₀ and Δe ₀ in the operation area k, for example, -127 to -64 in the operation area 1, is defined, Even if the table is not defined, the table configuration as shown in FIG. 11 is sufficient and the amount of memory can be saved.

Then, the online calculation is executed according to the flow chart of the program of FIG. In the data input 22, the set value set in advance as the control target, the sensor 2 and the A / D converter 10 shown in FIG.
The difference and the difference between the deviations are obtained by taking the difference between the digitalized control amounts. Then, the high-order bits of the input data are extracted 23 to extract the high-order bits (high-order 2 bits in this embodiment). This can be done by AND or bit shift. When the upper bit is extracted, the operation area is determined by referring to the table defined in FIG. 9 in the area determination 24 of the input element. When the operation area is determined, the inference separation function corresponding to the input is called in the array call 25 corresponding to the area. Then, in the inference execution 26, the calculation of the equation 25 is executed. This can be done by calculating the numerator and denominator of Equation 25 (simply add an inference separation function and a constant) and calculating an inference value by dividing this.

As in the first embodiment, since the obtained inference value is the output difference, it is added to the value one step before by the data output 27 to determine the operation amount. The control target is controlled through the A conversion 11 and the operation unit 6.

In the second embodiment, since the calculation for each rule is executed off-line and is defined as array data in the form of the inference separation function, online processing simply refers to array data, performs addition and once. It can be executed only by dividing by.

The third embodiment is an embodiment of the device according to the present invention. FIG. 16 is a block diagram of this device. The configuration of the input unit 3 of FIG. 16 is shown in FIG. The subtractor 34 in FIG. 17 calculates the deviation (difference e ₀ between the set value and the controlled variable). This is stored in the memory 35. Since the deviation one step before is stored in the memory 35, the subtracter 36 takes the difference between the deviation one step before and the current deviation, and calculates the difference (Δ
Calculate e ₀ ).

The input high-order bit extraction device 28 of FIG.
Reference numeral 29 has a device configuration as shown in FIG. 18A and takes out the wiring of the upper bit to be extracted. The operation area determination device 30 of FIG. 16 can be realized by arranging the extracted wirings in parallel as shown in FIG. The inference separation function reference devices 31 and 32 of FIG. 16 are arranged, for example, as shown in FIG. 19, in which the output from the high-order bit extraction device and the data line of each input value are arranged in parallel and are directly connected to the address bus of the memory, and the corresponding array Call the data. Note that this method of directly inputting data to the address bus is one of the address reference methods by Arita et al .: Transactions of the Society of Instrument and Control Engineers, Vol.28,
No. 2, pp.180-187, 1990. In this way, a device that can directly call the data of the inference separation function through the conversion of the input to the wiring is possible. The inferred value of the called data is calculated by the output determination device 33 of FIG. The structure of the output determination device 33 is shown in FIG. Constant storage unit 37,
At 38, constants necessary for calculation are stored. Since the value to be stored is fixed, the same pattern may be constantly output using, for example, a ROM. Adders 39, 40, 41 and 42
Adds the data of the inference separation function called. Then, the inferred value is determined by the divider 43. The apparatus shown in FIG. 20 is based on the equation (25) and realizes the method of the second embodiment as an apparatus. With this device, the inference separation function can be called from the input data without calculating the address, and the inference value can be determined with a relatively simple device.

FIG. 21 is a diagram showing this series of processing. The realization of the present invention can be roughly divided into a process of performing calculation and creation of necessary data in advance using WS or the like (offline process) and a process performed by an actual control device (online process) using the result. .

In the off-line processing, the basic data of the fuzzy control law, that is, the membership function and the representative output value are
It exists in the file 39. For example, in the control rule of FIG. 3, the data is the data in the table shown in FIG. Based on this data, through an area division (operation area generation) and operation rule extraction processing 40, an operation area (exemplified in FIG. 9 in the correspondence table with the higher order bits of the input) in the file 41 and its operation A table of rules (operation rules) to be used for inference with respect to the input existing in the area is created (corresponding to the control rule of FIG. 3, illustrated in FIGS. 7 and 8). This processing is as described in the first embodiment. Although not required in the first embodiment (example of the area division execution method), in the second embodiment (example of the variable separation execution method), the data of the file 41 is further processed through the inference separation function calculation process 42 to obtain the file. A table of inference separation functions is created in 43.

In the online processing, necessary data is stored in the memory 45, and the input to the inference system (the deviation and its difference in the embodiment) is performed in the processing 44 from the sampling data of the discretized control amount input from the sensor 2. ) Is calculated, and at the same time, the operation area in which the input exists is determined. Then, in process 45, necessary data is called and inference is executed. Then, the operation amount is calculated and output to the operation unit 6.

The series of processes 44 and 45 corresponds to FIG. 10 in the first embodiment. That is, the processing 44 corresponds to 16, 17, and 18 in FIG.
The processing 45 corresponds to 19, 20, and 21 in FIG.
Is. The second embodiment corresponds to FIG. 15, the process 44 corresponds to 22, 23 and 24 in FIG. 15, and the process 45 corresponds to 25, 26 and 27 in FIG.

The data to be stored in the memory 45 is required for the operation rule table shown in FIG. 8, the operation area table shown in FIG. A membership function (in the simplification method, the output membership function is represented by a representative value as shown in FIG. 11) is required. In addition, the variable separation execution method of the second embodiment requires the operation area table shown in FIG. 9 and the inference separation function table shown in FIG.

[0123]

According to the fuzzy inference method using the domain segmentation execution method of the present invention, the necessary rule can be determined offline, so that unnecessary calculation of the rule (condition judgment) can be omitted when executing online. The calculation time can be shortened as compared with the conventional simplification method.

According to the operation area determination method of the present invention, the operation area can be efficiently determined from the upper bits of the input, so that the calculation time can be shortened.

By the fuzzy inference method using the variable separation execution method of the present invention, the calculation for each rule can also be executed off-line, and at the time of online execution, the inference value can be obtained by referring to the array and adding several times and dividing once. Therefore, the calculation time can be greatly shortened as compared with the conventional simplification method.

The time required for the calculation of the inference value is at most about several times that of the table lookup method, but since the required array is one-dimensional, even in the case of a multi-input system, it is necessary to use the power of the conventional inputs. Compared with the table lookup method, the amount of data is simply proportional to the number of inputs, and especially when there are many entries, the memory used can be significantly reduced compared to the table lookup method. For example, in the example of the control system of FIG. 3, the number of array elements required by the conventional table lookup method is 256 HP256 in an 8-bit microcomputer, but in the present invention, 256 HP4 array elements + 2 constants are sufficient.

When executing the fuzzy inference based on the variable separation execution method by the fuzzy inference apparatus of the present invention, from the upper bit of the input to the area determination and further to the array reference,
This can be realized by combining a device having a simple structure equivalent to a normal data calling device, and high-speed inference processing can be performed.

[Brief description of drawings]

FIG. 1 Example of description of velocity-type fuzzy PI control law

FIG. 2 is an example of an application area of the fuzzy control law of FIG.

FIG. 3 is a control law in the form of FIG.

FIG. 4 is an example of a fuzzy control device using a fuzzy inference device.

[Fig. 5] Example of fuzzy inference device composed of one-chip microcomputer

6 is an example of an application area of the control law of FIG. 3 (evaluation at min)

7 is an example of an operation area of the control law of FIG.

FIG. 8 is an example of an operation rule corresponding to an operation area.

FIG. 9 is an example of an operation rule corresponding to upper bits of an input.

FIG. 10 is an online execution procedure of the first embodiment.

FIG. 11: Sequence data required for online execution of the first embodiment

FIG. 12 is an example of an applicable area in which the antecedent conformity is evaluated by a marginal product.

FIG. 13 is an example of an applicable area in which the antecedent conformity is evaluated by the extended limit product.

FIG. 14: Sequence data required for on-line execution of the second embodiment

FIG. 15 is an online execution procedure of the second embodiment.

FIG. 16 is a device configuration diagram of a third embodiment.

FIG. 17 is an input device according to a third embodiment.

FIG. 18 is an operation area determination device according to the third embodiment.

FIG. 19 is an inference separation function reference device according to the third embodiment.

FIG. 20 is a device configuration of an output determining unit according to a third embodiment.

FIG. 21 is a process flow of the entire process according to the present invention.

[Explanation of symbols]

1 ... Control object, 3 ... Input unit (device or process for calculating definite input such as deviation from control amount), 5 ... Output unit (device or process for calculating definite output such as change in manipulated variable),
7 to 13 ... Each processing device on one-chip microcomputer, 16
To 21 ... Each processing step required for the processing of the first embodiment, 2
2 to 27 ... Each processing step required for the processing of the second embodiment,
28, 29 and 30 ... Components of the operation area determination part,
31, 32 and 33 ... Components of fuzzy inference execution part, 39, 41 and 43 ... Data on computer for offline processing, 45 ... Data on control device for online processing.

   ─────────────────────────────────────────────────── ─── Continued front page    (72) Inventor Yusuke Sakoda             1099 Ozenji, Aso-ku, Kawasaki City, Kanagawa Prefecture             Ceremony company Hitachi Systems Development Laboratory

Claims (3)

[Claims] 1. An input consisting of a plurality of types is applied to a plurality of control rules which are in the if antecedent part then consequent part format and represent the conditions contained in the antecedent part and the consequent part in a fuzzy set. In the method of inferring an output, first information indicating a correspondence relationship between the plurality of inputs and the control rule to which the plurality of inputs match is generated, and the applied control rule is the same based on the first information. The input area consisting of the plurality of types of inputs is divided for each set of inputs, and the degree of conformity for each of the control rules obtained by applying each of the divided areas and the control rule that matches the divided area Second information indicating a correspondence relationship with is generated, and when the external input is input, the divided area including the external input is determined, and the divided information corresponds to the determined area from the second information. Extraction of goodness of fit for each control rule , Fuzzy inference method characterized by calculating the output for the external input from the goodness of fit. 2. The inference method according to claim 1, wherein the input area is composed of a set of input elements each having a plurality of upper bits of a variable corresponding to each input, and the divided area and the input element. And determining the divided area by generating third information indicating a correspondence relation with and searching the third information using a plurality of high-order bits of a variable corresponding to each input. Fuzzy reasoning method. 3. If an input consisting of a plurality of types is applied to a plurality of control rules that are in the antecedent part then the consequent part format and represent the conditions contained in the antecedent part and the consequent part with a fuzzy set. In a device for inferring an output, first storage means for storing a correspondence relationship between the plurality of inputs and the control rule to which the plurality of inputs match, and the control rule applied based on information in the first storage means. For each of the control rules obtained by dividing the input area consisting of the plurality of types of input for each set of the inputs that are the same, and applying the control rules that match the respective divided areas Second storage means for storing a correspondence relationship with the goodness of fit, means for determining the divided area including the external input when an external input is input, and the information from the second storage means Each corresponding to the determined area Extract the fitness of each serial control rules, fuzzy inference apparatus characterized by having an inference execution means for calculating an output to the external input from the goodness of fit.