JPH06332505A - Nonlinear controller - Google Patents

Abstract

PURPOSE:To identify the input/output with high precision and with no deterioration of the model approximation precision by calculating an approximation error of the function which approximates the characteristic analysis and performing comparison of approximation errors between the characteristic distribution approximation function acquired by a 2-group analysis algorithm and the characteristic distribution function acquired by a 3-group analysis algorithm, respectively. CONSTITUTION:By excuting a 2-group algorithm which analyzes by using the normalized data and its dummy data, and a 3-group algorithm which analyzes with addition of the dummy data of another group, the approximation error of a characteristic distribution function which is caused by the distribution influence of the analysis data can be reduced. Furthermore, by controlling the membership function of a fuzzy group consisting of the 3rd dummy data in the 3-group analysis algorithm, the characteristic of the analysis result can be controlled. Thus, it is possible to attain the input/output identification with high precision and to improve the reliability of the nonlinear control carried out based on the model identification by means of a fuzzy quantization II class.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a control device for performing non-linear control in a situation where a control model is unknown, and more specifically, it analyzes input / output data to create an input / output model, and based on the input / output model. The present invention relates to a non-linear control device that outputs a control signal corresponding to an input signal. In particular, the present invention relates to a technique for identifying a process or the like for which a mathematical model cannot be obtained, and identifying an input / output relationship based on the input / output data.

[0002]

2. Description of the Related Art Conventionally, fuzzy modeling for creating a control model based on fuzzy theory and non-linear information processing technology using a neural network have been proposed as techniques for performing non-linear control in a situation where a control model is unknown.

However, when a non-linear controller is constructed by using the conventional fuzzy modeling or neural network, the following problems occur.

First, in the case of using fuzzy modeling, a modeling algorithm is generally complicated, and since a model is created by using fuzzy rules and membership functions, a large memory is required. Further, the control based on fuzzy modeling requires a long calculation time.

On the other hand, when a neural network is used, it is difficult to perform all model creation automatically because the appropriate structure of the neural network changes depending on the input / output data given. In addition, since iterative learning is performed, it takes time to create a model based on input / output data. Furthermore, since the created model becomes a black box, it is difficult to make fine adjustments with the knowledge of the operator.

Therefore, the present inventor has proposed a non-linear control device which adopts the method of "fuzzy quantification type II" in the modeling algorithm (Japanese Patent Application No. 3-340700). The fuzzy quantification type II used for this is a kind of fuzzy multivariate analysis method.

Fuzzy multivariate analysis is an extension of ordinary multivariate analysis to handle fuzzy numbers or fuzzy groups. The main fuzzy multivariate analysis techniques proposed so far are as follows. It is as follows.

Fuzzy regression analysis A method of obtaining a possibility linear regression model by treating the coefficients of regression analysis as fuzzy numbers.

Fuzzy time series analysis A method of analyzing fuzzy number data given to a time series and reflecting the possibility distribution in the time series model.

Fuzzy Quantification Class I A method for obtaining the relationship between an objective function taking a real value and a qualitative explanatory variable represented by a value within the range of [0, 1] in a given fuzzy group of samples. .

Fuzzy quantification II class From the data of qualitative objective variables represented by values in the range [0,1] and qualitative explanatory variables represented by values in the range of [0,1], fuzzy A method for finding a linear (first-order) expression that expresses a group.

Fuzzy Quantification III Based on qualitative data represented by values in the class [0,1], each sample and category are quantitatively classified in consideration of the membership function value of the fuzzy group. Technique.

Fuzzy Quantification Class IV A method of giving a numerical value such that the distance between individuals and the degree of familiarity are monotonous, considering the membership function values of individuals belonging to the fuzzy group.

Of these, the fuzzy quantification type I is a method for explaining a quantitatively given external criterion (objective variable) based on a qualitative factor (explaining variable).

On the other hand, the fuzzy quantification type II is a method for explaining a qualitatively given external criterion (fuzzy group) based on a qualitative factor (explaining variable). The difference from the fuzzy quantification type I is that the external criterion is the fuzzy group B1,
It is given by B2, ..., BM. The purpose of this fuzzy quantification II class is, where K is the number of categories,
Data μi of each category Ai (i = 1, 2, ..., K)
For (j), the line form of the category weight ai

[0016]

[Equation 1] (However, j is the data number, j = 1, 2, ..., N)
To best represent the structure of the external reference on the real axis, in other words, the fuzzy group B1 of the external reference on the real axis,
.., to determine the category weights ai such that BM is best separated.

When the category weight ai is determined in this way, the sample value (sample score) of each data is obtained by the equation (1). Then, by plotting the membership value of the external criterion for each sample value, a graph showing the result of data analysis by the fuzzy quantification class II is obtained.

The previously proposed non-linear control device includes a data collecting means for collecting data indicating the input / output relationship of the controlled object, the data is normalized, and the normalized data is fuzzy quantified as described above. Analyze with the method of class II,
A modeling algorithm storage unit that stores an algorithm that approximates the characteristic distribution obtained as a result of the analysis with a function, an approximation function calculation processing unit that executes the modeling algorithm and generates a function that approximates the characteristic distribution, and the control target And a signal output unit for outputting the result of the calculation as a control signal.

According to this, a non-linear system whose control model is unknown uses an algorithm that can create a simple model with high utility as a control law in a short time, does not require a large capacity memory to store it. Can be controlled.

This apparatus uses input / output data of processes to be identified as fuzzy quantification II as analysis data.
The analysis by the fuzzy quantification II is performed according to an analysis algorithm using the normalized output data and the dummy data based on the output data (that is, discriminating two groups of data).

[0021]

However, according to the above non-linear control device, when the normalized values of the output data of the analysis data are unevenly distributed as follows, it is possible to discriminate the portion where the data distribution density is high. Accuracy is emphasized, the characteristic distribution unnaturally varies, and as a result, the approximation accuracy of the model formula deteriorates.

A large amount of data has a value close to 1, and a small amount of data has a value close to 0.

A large amount of data has a value close to 0, and a small amount has a value close to 1.

Many values are close to 0 or 1, and few values are close to 0.5.

That is, there is a problem that the approximation accuracy of the model finally obtained may deteriorate depending on the distribution of the analysis data.

Therefore, an object of the present invention is to fuzzy quantification.
A non-linear controller according to class II, which is capable of identifying an input / output with high accuracy without degrading the approximation accuracy of a model even when the distribution of analysis data is biased.

[0027]

The non-linear control device of the present invention uses a data collection means for collecting data indicating an input / output relationship of a controlled object and a method of fuzzy quantification II by normalizing the data. Analyzing, a modeling algorithm storage unit that stores an algorithm for approximating a characteristic distribution obtained as a result of the analysis with a function, an approximation function calculation processing unit that executes the modeling algorithm and generates a function that approximates the characteristic distribution, A signal input unit that takes in an input signal from the controlled object, a control algorithm storage unit that stores a control algorithm that calculates an output for the input signal using a function generated by the approximate function calculation processing unit, and a control algorithm according to the control algorithm. A control calculation unit that calculates an output value for the input signal, and a calculation result by the control calculation unit. And a signal output unit for outputting as a control signal, wherein the modeling algorithm analyzes a normalized data and its dummy data using a two-group analysis algorithm, and the other two groups of data with another group of dummy data. In addition, a three-group analysis algorithm for analysis is included.

According to a preferred embodiment of the present invention, the approximation error of the function approximating the characteristic distribution is calculated, and the approximation error of the characteristic distribution approximating function obtained by the two-group analysis algorithm and 3
When the latter approximation error is smaller than the former approximation error, the characteristic distribution approximation function obtained by the two-group analysis algorithm is compared with the three-group analysis algorithm by comparing the approximation error of the characteristic distribution approximation function obtained by the group analysis algorithm. An approximation error calculation and comparison evaluation processing unit that updates the characteristic distribution approximation function obtained by

[0029]

According to the present invention, first, the data collecting means collects the data indicating the input / output relationship for the controlled object.
The data are analyzed by the method of fuzzy quantification II after being normalized according to a modeling algorithm. A modeling algorithm is executed that approximates the characteristic distribution obtained as a result of this analysis with a function. that time,
By executing a two-group analysis algorithm that analyzes using normalized data and its dummy data, and a three-group analysis algorithm that adds another group of dummy data to this and analyze it, the analysis data distribution It is possible to reduce the approximation error of the characteristic distribution approximation function due to the influence. Further, in the three-group analysis algorithm, the characteristic distribution of the analysis result can be adjusted by adjusting the membership function of the fuzzy group formed by the dummy data of the third group.

When the characteristic distribution approximation function is obtained by executing the above modeling algorithm, the control calculation unit
An output value for an actual input is calculated using this approximation function.

[0031]

DESCRIPTION OF THE PREFERRED EMBODIMENTS FIG. 1 shows the configuration of a non-linear control device according to an embodiment. The control device includes CPUs 10a to 10c as processing means for executing a modeling algorithm and a control algorithm.
10d and 10e, and storage units 11 to 15 as means for storing these algorithms.

The modeling algorithm describes the nonlinear input / output relationship obtained by the fuzzy quantification II class for the controlled object. It approximates the normalization algorithm for normalizing the data representing input and output, the analysis algorithm for analyzing the normalized data by fuzzy quantification II, and the characteristic distribution obtained as a result of the analysis. An approximation function calculation algorithm for determining a function and an algorithm for calculating an approximation error and performing comparative evaluation as described later are included, and the analysis algorithm includes normalized data and dummy data thereof (similar to the conventional one). Two groups of data) are used for analysis, and another group of dummy data is added to the above two groups of data for analysis.

The respective algorithms constituting the modeling algorithm correspond to the corresponding normalization algorithm storage unit 11, group analysis algorithm storage unit 12a, group 3 analysis algorithm storage unit 12b, approximate function calculation algorithm storage unit 13, approximation error calculation It is stored in the comparative evaluation algorithm storage unit 14.

The CPUs 10a to 10d operate according to the algorithms stored in the corresponding storage units 11, 12a and 12b, 13, 14 respectively. Here, CPU1
0a and the storage unit 11 are a data normalization calculation unit and a CPU 10b.
The storage units 12a and 12b constitute a fuzzy quantification type II analysis operation unit, the CPU 10c and the storage unit 13 constitute a characteristic distribution approximation function calculation processing unit, and the CPU 10d and the storage unit 14 constitute an approximation error calculation / comparison evaluation processing unit. There is. CPU1
The approximate function (model formula) calculated at 0c is the CPU1
After being sent to 0d to undergo approximation error calculation and comparison evaluation with the characteristic distribution (data), it is stored in the model mathematical expression storage unit 16. The approximation error calculated by the CPU 10d is stored in the approximation error storage unit 17.

On the other hand, the control algorithm includes an algorithm for calculating an output (control signal) with respect to an input (state detection signal) from the controlled object based on the model formula (approximation function) stored in the model formula storage unit 16. The output value calculation algorithm is stored in the corresponding storage unit 15.

The CPU 10e performs an operation of generating an output signal for an input signal according to the output value calculation algorithm stored in the storage unit 15. The CPU 10e and the storage unit 15 form a non-linear control calculation unit.

In the above configuration, the arithmetic processing of each unit is performed by each of the CPUs 10a to 10d and 10e. However, the CPUs may collectively perform the above-described modeling algorithm and control algorithm. You may comprise.

Further, the control device of FIG. 1 serves as a data collecting means for collecting data indicating the input / output relationship, and is not a man-machine interface 18 composed of a terminal device, or a man-machine interface from outside via a communication line. A communication device 19 for receiving the data to be transmitted,
The data storage unit 20 that stores the data collected by these data collection units, the signal input unit 21 that receives the input signal representing the state quantity of the controlled object and supplies it to the CPU 10e of the nonlinear control calculation unit, and the CPU 10e calculate. And a signal output unit 22 for outputting a control signal indicating the controlled variable.

In the above configuration, the man-machine interface 18 is used for inputting data, operating instructions to the apparatus (variable adjustment input for normalization in the case of this embodiment), fine adjustment of the created model, etc. It is provided in. The approximation function stored in the model formula storage unit 16 is the CPU 10
In addition to being automatically determined by d, it is also determined by a manual operation on the man-machine interface 18.

In the above embodiment, the man-machine interface 18 and the communication device 19 which are the data collecting means, the data storing section 20, the CPUs 10a to 10d which are the modeling algorithm storing and executing means and the storing sections 11 to 1 are used.
4, model formula storage unit 16, and approximation error storage unit 17
Can be operated as an off-line processing unit by making it independent of the other units, that is, the control unit for online processing.

FIG. 2 shows an execution procedure of the modeling algorithm of the embodiment.

First, the input data X1, X2, ..., Xn and the output data Y1, Y2, ..., Ym are read from the man-machine interface 18 or the communication device 19 (steps ST1 and ST2) and stored in the data storage unit 20. It These data are collected, for example, as showing the operation of a skilled operator with respect to the controlled object.

Next, the CPU 10a calculates the standard deviation σ of each data according to the above normalization algorithm (S
T3), and the range [a, b] that is three times that, that is, 3σ, is normalized to [0, 1] (ST4). The normalized output data is represented as Y1 ', Y2', ..., Ym '.

The CPU 10b creates dummy data (Y1 "= 1-Y1 ', ..., Ym" = 1-Ym') for analysis of the output data Y1 ', Y2', ..., Ym 'according to the two-group analysis algorithm. Then, the characteristic distribution of these two groups of data is calculated by the fuzzy quantification type II (ST6).

Next, the CPU 10c executes a function approximation algorithm to approximate the above characteristic distribution with a high-order nonlinear function obtained by the least square method or a straight line obtained by area division (ST7). Here, the higher-order function approximation by the least squares method is automatically performed, and the linear approximation by region division is manually (operated by the operator).

When the approximate function is obtained in this way, the CPU 1
At 0d, the difference (approximation error) between the approximate function and each data is calculated (ST8), and whether or not the third group discrimination is completed, that is, 3
It is checked whether or not the data analysis by the group analysis algorithm is performed (ST9). When the third group discrimination is not completed, the approximation function is written in the model formula storage unit 16 (ST10), and the approximation error is written in the storage unit 17 (ST11).

Next, in the CPU 10b, the analysis dummy data (Y1 "= 1-Y1 ', ..., Ym" = 1-Y of the output data Y1', Y2 ', ..., Ym' is calculated in accordance with the three-group analysis algorithm.
m ') and another dummy data (Y1 "', ..., Y
m "') is created (ST12), and the characteristic distribution of these three group data is calculated by the fuzzy quantification II class (S).
T6). An example of the third group data and calculation of its characteristic distribution will be described later.

Here, the function approximation is executed by the CPU 10c (ST7). That is, the characteristic distribution of the third group data is approximated by a high-order nonlinear function obtained by the least squares method or a straight line obtained by region division. And CP
The difference (approximation error) between the approximate function and each data is calculated by U10d (ST8).

Next, it is determined whether the above-mentioned third group discrimination is completed (S
T9) Since the third group discrimination has been completed at this stage, the approximation errors are compared (ST14) and it is determined whether the approximation error in the case of the third group data is smaller than the approximation error in the case of the second group data. (ST15). As a result, in the case of "YES", the model formula is updated (ST16), and in the case of "YES", the modeling ends (ST17).

FIG. 3 shows an execution procedure of the control algorithm performed based on the model formula obtained by the above modeling algorithm. That is, when a signal indicating the state quantity of the controlled object is input from the signal input unit 21 (step ST
21), an output value (control amount) is calculated by a model formula (ST22), and the calculated value is output as a control signal (ST2).
3).

An example will be described below.

First, the input of the process to be identified is A,
Let B be the output. In this case, multi-input nonlinear modeling is a mathematical relationship C between a plurality of inputs A and B and an output C.
= F (A, B) is identified (approximately obtained).

It is assumed that the input / output data (input A, B and output C) shown in Table 1 are obtained as the analysis data by the following equation.

[0054]

[Equation 2]

[0055]

[Table 1] ABC 0.0 0.0 0.070 0.3 0.0 0.086 0.7 0.0 0.126 1.0 0.0 0.187 0.0 0.3 0.113 0.3 0.3 0.161 0.7 0.3 0.328 1.0 0.3 0.593 0.0 0.7 0.407 0.3 0.7 0.672 0.7 0.7 0.839 1.0 0.7 0.887 0.0 1.0 0.813 0.3 1.0 0.874 0.7 1.0 0.914 1.0 1.0 0.930 The above data is normalized by a normalization algorithm automatically or by manually inputting a normalization conversion formula by the man-machine interface 18. In this example, since the input data A and B have the minimum value 0 and the maximum value 1, the normalized values A ′ and B ′ are used as they are, and the output data C is the minimum value and the maximum value range [0.07
By substituting [0, 0.930] with [0, 1], a normalized value C ′ is obtained.

Next, in order to analyze the data A ', B', C'normalized as described above by fuzzy quantification II, the normalized output data C '(first fuzzy group)
The dummy data C ″ (second fuzzy group) of is created by the following equation as in the conventional case.

C ″ = 1−C ′ (3) This corresponds to the use of the two fuzzy groups represented by the membership function shown in FIG. 4 in the fuzzy quantification class II.

When the sample score SCR calculated by the analysis of the above two-group data is plotted on the abscissa and the value of C'is plotted on the ordinate, the analysis data is plotted to obtain the characteristic distribution shown in FIG. That is, FIG. 5 shows the result of the analysis algorithm of the two-group discriminant type, and the sample score is SCR = 0.226 A ′ + 0.616 B ′ (4). The model formula (approximation function) that approximates the characteristic distribution is C ′ = − 5.88 SCR3 + 7.43 SCR2−0.95 SCR + 0.02 (5).

The approximation accuracy at this time is evaluated by the error between the curve showing the approximation function of FIG. 5 and the plotted data. If the average error is E2, then E2 = 0.0413.

In this example, since the normalized output data C'in the analysis data of Table 1 has a feature that "there are many values close to 0 or 1 and few values close to 0.5".
As shown in FIG. 5, the characteristic distribution is "the approximation error is large near 0.5 due to the influence of data near 0 or 1."

The model formula obtained by the above-mentioned two-group discrimination is stored in the model formula storage unit 16 of FIG. 1, and the average error is stored in the approximate error storage unit 17.

Next, in order to discriminate the third group, the dummy data C ″ of the above-mentioned normalized output data C ′ is created in the same manner as described above, and another dummy data C ″ ′ (third fuzzy group). Is created by the following formula.

C ″ = 1−2 · | C′−0.5 | (6) This corresponds to the use of the three fuzzy groups represented by the membership function shown in FIG. 6 in the fuzzy quantification class II. .

When the sample score SCR calculated by the analysis on the above-mentioned three groups of data is plotted on the horizontal axis and the value of C'is plotted on the vertical axis, the analysis data is plotted to obtain the characteristic distribution shown in FIG. That is, FIG. 7 shows the result of the analysis algorithm of the three-group discriminant type, and the sample score is SCR = 0.246 A ′ + 0.584 B ′ (7). Further, the model formula (approximation function) that approximates the characteristic distribution is C ′ = − 6.76 SCR3 + 8.42 SCR2−1.18 SCR + 0.03 (8).

The approximation accuracy at this time is evaluated by the error between the curve showing the approximation function of FIG. 7 and the plotted data. If the average error is E3, E3 = 0.0363, which is more accurate than the analysis result of the two-group discriminant type. This gives the third fuzzy group C ′ =
By setting so that the goodness of fit is maximized at 0.5,
It is shown that the data near C ′ = 0.5 is emphasized as the discrimination target and the characteristic distribution in the vicinity is improved.

Next, the average error E2 by the 2-group discriminant analysis of FIG. 5 and the average error E3 by the 3-group discriminant analysis of FIG.
Compare with. As a result, since the latter average error E3 is smaller, the model formula stored in the model formula storage unit 16 of FIG. 1 is updated to the model formula obtained by the three-group discriminant analysis algorithm.

As described above, by using the 3-group discriminant type analysis algorithm in addition to the conventional 2-group discriminant type analysis algorithm, adjustment according to the data distribution becomes possible.
It is possible to prevent the deterioration of the approximation accuracy that may occur due to the bias of the characteristic distribution.

The third fuzzy group used for data analysis in the present invention is not limited to the membership function shown in FIG. 6, and adjustment such as shifting the positions of vertices left and right as shown in FIG. 8 is also possible. Yes, there is no constraint on the shape of the membership function that defines the third fuzzy group.

Further, regarding the first and second fuzzy groups of the related art, the membership function usable in the present invention is not limited to that shown in FIG. 6, but may be replaced with a non-linear membership function shown in FIG. 9, for example. Good.

In short, all the membership functions of the first to third fuzzy groups can be set according to the request of the user of the device of the present invention, and this variable setting almost eliminates the influence of the above-mentioned data distribution. can do.

[0071]

As described above, according to the present invention, the approximation error due to the influence of the distribution of the analysis data is reduced in the non-linear controller using the model obtained by performing the data analysis by the fuzzy quantification type II. be able to. Further, the characteristic distribution of the analysis result can be adjusted in consideration of the influence of the data distribution. Thus, highly accurate input / output identification is possible, the reliability of nonlinear control based on model identification using fuzzy quantification II is further improved, and the application is expanded.

[Brief description of drawings]

FIG. 1 is a diagram showing a configuration of an exemplary embodiment of the present invention.

FIG. 2 is a flowchart showing an execution procedure of a modeling algorithm used in the embodiment.

FIG. 3 is a flowchart showing an execution procedure of a control algorithm performed based on a model formula obtained by the modeling algorithm.

FIG. 4 is a diagram showing a membership function used for 2-group discriminant-type data analysis.

FIG. 5 is a diagram showing an analysis result by a 2-group discrimination type data analysis algorithm.

FIG. 6 is a diagram showing a membership function used for 3-group discriminant-type data analysis.

FIG. 7 is a diagram showing an analysis result by a 3-group discrimination type data analysis algorithm.

8 is a diagram showing a case where the membership function of the third group is adjusted in FIG.

FIG. 9 is a diagram showing an example of a non-linear membership function used for 3-group discriminant data analysis.

[Explanation of symbols]

10a to 10e ... CPU, 11, 12a, 12b, 1
3, 14 and 15 ... Algorithm storage unit, 16 ... Model formula storage unit, 17 ... Approximation error storage unit, 18 ... Man-machine interface, 19 ... Communication device, 20 ... Data storage unit,
21 ... Signal input unit, 22 ... Signal output unit.

[Procedure amendment]

[Submission date] November 19, 1993

[Procedure Amendment 1]

[Document name to be amended] Statement

[Name of item to be corrected] 0015

[Correction method] Change

[Correction content]

On the other hand, the fuzzy quantification type II is a method for explaining a qualitatively given external criterion (fuzzy group) based on a qualitative factor (explaining variable). The difference from the fuzzy quantification type I is that the external criterion is fuzzy group B ₁ ,
B _2, ‥‥, is that given by B _M. The purpose of this fuzzy quantification II class is, where K is the number of categories,
Data μ of each category A _i (i = 1, 2, ..., K)
Linear form of category weight a _i for _i (j)

[Procedure Amendment 2]

[Document name to be amended] Statement

[Correction target item name] 0016

[Correction method] Change

[Correction content]

[0016]

[Equation 1] (However, j is the data number, j = 1, 2, ..., N)
To best represent the structure of the external reference on the real axis, in other words, the fuzzy group B ₁ of the external reference on the real axis ,
.., to determine the category weights a _i such that B _M is best separated.

[Procedure 3]

[Document name to be amended] Statement

[Correction target item name] 0017

[Correction method] Change

[Correction content]

When the category weights a _i are determined in this way, the sample value (sample score) of each data is obtained by the equation (1). Then, by plotting the membership value of the external criterion for each sample value, a graph showing the result of data analysis by the fuzzy quantification class II is obtained.

[Procedure amendment 4]

[Document name to be amended] Statement

[Correction target item name] 0042

[Correction method] Change

[Correction content]

First, the input data X ₁ , X ₂ , ..., X _n and the output data Y ₁ , Y ₂ , ..., Y _m are read from the man-machine interface 18 or the communication device 19 (steps ST1 and ST2), and the data are read. It is stored in the storage unit 20. These data are collected, for example, as showing the operation of a skilled operator with respect to the controlled object.

[Procedure Amendment 5]

[Document name to be amended] Statement

[Correction target item name] 0043

[Correction method] Change

[Correction content]

Next, the CPU 10a calculates the standard deviation σ of each data according to the above normalization algorithm (S
T3), and the range [a, b] that is three times that, that is, 3σ, is normalized to [0, 1] (ST4). Here the normalized output data of the _{Y 1 ', Y 2',} ..., represented as Y _m '.

[Procedure correction 6]

[Document name to be amended] Statement

[Correction target item name] 0044

[Correction method] Change

[Correction content]

In the CPU 10b, the dummy data ( Y ₁ "= 1-Y ₁ ', ..., Y _m " = 1 for analysis of the output data Y ₁ ', Y ₂ ', ..., Y _m ' is used in accordance with the two-group analysis algorithm. -Y _m ' ) is created (ST5), and the characteristic distribution of these two group data is calculated by the fuzzy quantification II class (ST6).

[Procedure Amendment 7]

[Document name to be amended] Statement

[Correction target item name] 0047

[Correction method] Change

[Correction content]

Next, the CPU 10b, in accordance with three groups analysis algorithm, the output data _{Y 1 ', Y 2',} ..., ' dummy data for analysis of the _{(Y 1 "= 1-Y} 1' Y m, ..., Y m "= 1-Y
_m ' ) and another dummy data ( Y ₁ "',…,
Y _m "' ) is created (ST12), and the characteristic distribution of these 3 group data is calculated by the fuzzy quantification II class (ST 6). An example of the 3 group data and its characteristic distribution calculation will be described later. To do.

[Procedure Amendment 8]

[Document name to be amended] Statement

[Name of item to be corrected] 0058

[Correction method] Change

[Correction content]

When the sample score SCR calculated by the analysis of the above two-group data is plotted on the abscissa and the value of C'is plotted on the ordinate, the analysis data is plotted to obtain the characteristic distribution shown in FIG. That is, FIG. 5 shows the result of the analysis algorithm of the two-group discriminant type, and the sample score is SCR = 0.226 A ′ + 0.616 B ′ (4). The model formula (approximation function) that approximates the characteristic distribution is C ′ = − 5.88 SCR ³ +7.43 SCR ² −0.95 SCR + 0.02 (5).

[Procedure Amendment 9]

[Document name to be amended] Statement

[Correction target item name] 0059

[Correction method] Change

[Correction content]

The approximation accuracy at this time is evaluated by the error between the curve showing the approximation function of FIG. 5 and the plotted data. If the average error is E ₂ , then E ₂ = 0.0413.

[Procedure Amendment 10]

[Document name to be amended] Statement

[Correction target item name] 0064

[Correction method] Change

[Correction content]

When the sample score SCR calculated by the analysis on the above-mentioned three groups of data is plotted on the horizontal axis and the value of C'is plotted on the vertical axis, the analysis data is plotted to obtain the characteristic distribution shown in FIG. That is, FIG. 7 shows the result of the analysis algorithm of the three-group discriminant type, and the sample score is SCR = 0.246 A ′ + 0.584 B ′ (7). Further, the model formula (approximation function) that approximates the characteristic distribution is C ′ = − 6.76 SCR ³ ＋8.42 SCR ² −1.18 SCR + 0.03 (8).

[Procedure Amendment 11]

[Document name to be amended] Statement

[Correction target item name] 0065

[Correction method] Change

[Correction content]

The approximation accuracy at this time is evaluated by the error between the curve showing the approximation function of FIG. 7 and the plotted data. If the average error is E ₃ , then E ₃ = 0.0363, which is more accurate than the analysis result of the two-group discriminant type. This gives the third fuzzy group C ′ =
By setting so that the goodness of fit is maximized at 0.5,
It is shown that the data near C ′ = 0.5 is emphasized as the discrimination target and the characteristic distribution in the vicinity is improved.

[Procedure Amendment 12]

[Document name to be amended] Statement

[Correction target item name] 0066

[Correction method] Change

[Correction content]

Next, the average error E ₂ by the two-group discriminant type analysis of FIG. 5 and the average error E ₃ by the three-group discriminant type analysis of FIG.
Compare with. As a result, since the latter average error E ₃ is smaller, the model formula stored in the model formula storage unit 16 of FIG. 1 is updated to the model formula obtained by the three-group discriminant analysis algorithm.

Claims (2)

[Claims] 1. A data collecting means for collecting data indicating an input / output relationship of a controlled object, normalizing the data, analyzing the data by a method of fuzzy quantification II, and analyzing a characteristic distribution obtained as a function. A modeling algorithm storage unit that stores a modeling algorithm to approximate, an approximation function calculation processing unit that executes the modeling algorithm and generates a function that approximates the characteristic distribution, a signal input unit that captures an input signal from the control target, A control algorithm storage unit that stores a control algorithm that calculates an output for the input signal using the function generated by the approximate function calculation processing unit; and a control calculation unit that calculates an output value for the input signal according to the control algorithm. A signal output unit for outputting the result of the calculation by the control calculation unit as a control signal. The modeling algorithm includes a two-group analysis algorithm for analyzing the normalized data and the dummy data thereof and a three-group analysis algorithm for analyzing the two groups of data by adding another group of dummy data. A non-linear control device comprising: 2. An approximation error of a function approximating the characteristic distribution is calculated, and an approximation error of the characteristic distribution approximating function obtained by the two-group analysis algorithm and a characteristic distribution approximating function obtained by the three-group analysis algorithm are calculated. When the latter approximation error is smaller than the former approximation error, the characteristic distribution approximation function obtained by the two-group analysis algorithm is updated to the characteristic distribution approximation function obtained by the three-group analysis algorithm. The non-linear control device according to claim 1, further comprising: an approximation error calculation and comparison evaluation processing unit that performs the above.