JPH06274207A - Non-linear control device - Google Patents

Abstract

PURPOSE:To identify input/output (I/O) by a highly precise and simplified approx imate function by approximating characteristic distribution obtained by a fuzzy quantification 2nd group by a function after converting data relating to I/O into extended data and then normalizing, the converted data. CONSTITUTION:A CPU 10a adds the inverse of data relating to the I/O of a controlled system inputted from a man/machine interface 17 or a communication equipment 18 based upon modeling algorithm or variation to the data to generate extended data. A CPU 10b normalizes the data similarly to the operation of the CPU 10a and a CPU 10c analyzes the normalized data by the fuzzy quantification 2nd group method. A CPU 10d approximates characteristic distribution obtained by the analyzed result by means of a function. A signal input part 20 enters an input signal from a controlled object and a signal extending processing part 21 generates an extended input by adding the inverse of the input signal or variation to the signal. A CPU 10e executes algorithm for computing an output corresponding to the extended input by using the function generated by the CPU 10d.

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 data handled by this fuzzy quantification type II are shown in FIG. The difference from the fuzzy quantification class I is that the external criterion is fuzzy group B1.
, B2, ..., BM. The purpose of this fuzzy quantification type II is that each category Ai (i = 1,
2, ..., K) Category weight ai linear format

[0016]

[Equation 1] 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 a i is determined in this way, the value (sample score) of each sample ω is calculated by the equation (1).
Is required. 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 the input / output data of the process or the like to be identified as the analysis data as it is, and performs the analysis by the fuzzy quantification type II only with this. In, the output variable is represented by an integer quadratic function of 0 or more of the input variable.

[0021]

However, according to the above-mentioned non-linear control device, when the output value is determined by the reciprocal of the input value or the variation amount in the input / output relationship of the process to be identified, etc. , Fuzzy quantification II analysis cannot detect those effects. Therefore, the analyzed result does not correspond to the actual input-output relationship,
The accuracy of the approximation function that identifies the input / output relationship becomes poor.

For example, in the case of identifying the collision risk felt by a person against an obstacle, the closer the moving obstacle is (ie, the smaller the relative distance is), the higher the danger is.
The collision risk cannot be properly identified only by measuring the relative distance and using the value, and it is necessary to use the reciprocal of the relative distance. Further, since it is felt that the higher the moving obstacle is, the higher the risk is, it is necessary to use the measured change amount of the relative distance. In this way, when a human is making a comprehensive judgment using a lot of information, it is necessary to incorporate the reciprocal of the measured value and the amount of change in order to identify it from the data.

If the reciprocal of the input value or the amount of change influences the determination of the output value as described above, the analysis results will also vary, so the correspondence relationship between the input and output values of the data used in the analysis can be expressed by a function. There is a problem in that if an attempt is made to make an accurate fit, a function approximation with a higher degree than necessary will be obtained, and finally the identification result will be a complicated description.

Therefore, an object of the present invention is to fuzzy quantification.
(EN) A non-linear controller according to class II, which is capable of identifying an input and an output with a simplified approximation function with higher accuracy than that proposed previously.

[0025]

A non-linear control device of the present invention includes a data collecting means for collecting data indicating an input / output relationship of a controlled object, and a reciprocal number, a change amount, and other necessary quantity added to the data. By inputting the extended data, normalizing the extended data, analyzing the normalized data by the method of fuzzy quantification II, and storing the algorithm for approximating the characteristic distribution obtained as a result of the analysis with a function. A modeling algorithm storage unit, 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, and an inverse number of the input signal, and the like. A signal expansion processing unit that generates an expansion input to which a change amount and other necessary quantities are added, and a function generated by the approximate function calculation processing unit are used. A control algorithm storage unit that stores a control algorithm that calculates an output for the expanded input, a control calculation unit that calculates an output value for the expanded input according to the control algorithm, and outputs the result of the calculation by the control calculation unit as a control signal. And a signal output unit that operates.

According to the embodiment of the present invention, the data collecting unit, the modeling algorithm storage unit and the approximate function calculation processing unit are independent offline processing units.

[0027]

According to the present invention, first, the data collecting means collects the data indicating the input / output relationship for the controlled object.
According to the modeling algorithm, these data are converted into extended data by adding the reciprocal number, the amount of change, and other necessary quantities, normalized, and then fuzzy quantification.
It is analyzed by the method of class II. A modeling algorithm is executed that approximates the characteristic distribution obtained as a result of this analysis with a function. Further, a control algorithm that calculates an output value for an actual input using the function is executed by the control calculation unit.

As described above, by introducing the technique of creating an algorithm for describing the nonlinear input / output relationship obtained by the fuzzy quantification II class, the nonlinear control algorithm can be easily created, and the memory capacity for storing it is small. In addition to the above, the approximation function is simplified and the approximation accuracy is improved by using the extended algorithm.

[0029]

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.
110d and 10e, and storage units 11, 12, 13, 14 and 15 as means for storing these algorithms.

The modeling algorithm describes the non-linear input / output relation obtained by the fuzzy quantification II class for the controlled object. This is a data expansion algorithm for performing data expansion processing described later, a normalization algorithm for normalizing data representing input / output,
Includes an analysis algorithm for analyzing normalized data by fuzzy quantification II and an approximation function calculation algorithm for determining a function approximating the characteristic distribution obtained as a result of the analysis. It is stored in the storage units 11, 12, 13, and 14.

The CPUs 10a to 10d operate according to the algorithms stored in the corresponding storage units 11, 12, 13, and 14, respectively. Here, the CPU 10a and the storage unit 11 are the data expansion processing unit, the CPU 10b and the storage unit 12 are the normalization calculation unit, the CPU 10c and the storage unit 13 are the analysis calculation unit by the fuzzy quantification II class, and the CPU 10d and the storage unit 14.
Respectively constitute a characteristic distribution approximation function calculation processing section. The approximate function calculated by this is stored in the model formula storage unit 16.

The control algorithm is the model formula storage unit 1
An output value calculation algorithm includes an algorithm for calculating an output (control signal) with respect to an input (state detection signal) from a controlled object based on the mathematical formula (approximation function) stored in 6 and a signal expansion process described later. It is stored in the storage unit 15.

The CPU 10e performs an operation of generating an output signal for an input signal according to an 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, it is possible to collectively execute the modeling algorithm and the control algorithm by one CPU. You may comprise.

Further, the control device shown in FIG. 1 serves as a data collecting means for collecting data indicating the input / output relationship, from the man-machine interface 17 consisting of a terminal device, or from the outside not via the man-machine interface but via a communication line. A communication device 18 for receiving the data to be transmitted,
A data storage unit 19 for storing the data collected by these data collecting units, a signal input unit 20 for taking in an input signal representing the state quantity of the controlled object, and a signal expansion process included in the control algorithm for the input signal. A signal expansion processing unit 21 that performs the above-mentioned operation and supplies the CPU 10e of the non-linear control calculation unit, and a signal output unit 22 that outputs a control signal representing the control amount calculated by the CPU 10e.

In the above-mentioned configuration, the man-machine interface 17 is prepared in addition to the data input, the operation instruction to the apparatus (in the case of the embodiment, the data expansion processing instruction described later and the variable adjustment input for normalization). It is provided for fine adjustment of the model. The approximation function stored in the model formula storage unit 16 is automatically determined by the CPU 10d and also manually determined by the man-machine interface 17. Further, the signal extension processing included in the control algorithm is an operation of adding the reciprocal number or the variation amount to the signal from the signal input unit 21, and converts the input signal into these extension signals.

The data expansion processing unit in this embodiment is
Not only the input data but also its reciprocal and its variation are expanded and processed. Therefore, as shown in FIG. 2, the data expansion algorithm storage unit 11 includes a reciprocal availability determination algorithm storage unit 111, a reciprocal calculation / registration algorithm storage unit 112, and a change amount calculation / registration algorithm storage unit 113.

In this case, the CPU 10a uses the extended processing instruction signal input unit 1 included in the man-machine interface 17.
In accordance with the instruction signal from 01, each storage unit 111, 11
The operation based on the algorithm stored in 2, 113 is performed. The CPU 10a and the storage unit 111 are the reciprocal number extension propriety determination unit, the CPU 10a and the storage unit 112 are the reciprocal number input extension unit,
The CPU 10a and the storage unit 113 respectively form a change amount input expansion unit.

Here, the reciprocal extension propriety determination unit determines the validity of using the reciprocal of the input variables (A, B, C) included in the analysis data (for example, A, B, C, D) as the input variable. judge. The reciprocal extension feasibility determination algorithm therefor is as follows. That is, when the data of a certain input variable (for example, B) included in the analysis data are all positive values or all negative values, B is regarded as a non-zero quantity, and it is determined that “reciprocal expansion is possible”. To do. In cases other than the above, B is determined as "quantity that can take 0" as "reciprocal expansion not possible".

The reciprocal input expansion unit calculates the reciprocal of the analysis data corresponding to the corresponding input variable when the result of the judgment by the reciprocal expansion feasibility judging unit is "reciprocal expansion is possible", and this is newly input. Register as data corresponding to the variable.

The change amount expansion unit registers the change amount of the input variable included in the analysis data as the data corresponding to the new input variable when the analysis data is time series data.

The extension processing instruction signal input unit 101 inputs a signal for instructing execution of the above data extension processing.

The input extension data calculated by the data extension processing section configured as described above is sent to the normalization arithmetic processing by the CPU 10b.

In the above embodiment, the man-machine interface 17 and the communication device 18, which are the data collection means, the data storage section 19, the CPUs 10a to 110d, which are the modeling algorithm storage and execution means, and the storage sections 11 to 1.
4, and the model expression storage unit 16 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. 3 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 17 or the communication device 18 (steps ST1 and ST2) and stored in the data storage section 19. It These data are collected, for example, as showing the operation of a skilled operator with respect to the controlled object.

Next, in the CPU 10a, the reciprocals 1 / X1, 1 / X2, and 1 / X2 of the input data stored in the data storage unit 19 are calculated according to the data expansion algorithm.
, 1 / Xn and change amounts dX1, dX2, ..., dXn are calculated (ST3 and ST4).

In the CPU 10b, from the input / output data expanded by adding the reciprocal number and the amount of change to the input data,
The standard deviation σ of each data is calculated according to the normalization algorithm (ST5), and the standard deviation σ is tripled, that is, the range of 3σ [a,
b] is normalized to [0, 1] (ST6). The normalized output data is represented as Y1 ', Y2', ..., Ym '.

The CPU 10c creates analysis dummy data (Y1 "= 1-Y1 ', ..., Ym" = 1-Ym') of the output data Y1 ', Y2', ..., Ym 'according to the analysis algorithm ( ST7), data analysis by fuzzy quantification type II,
That is, the characteristic distribution based on the sample score is calculated (S
T8).

The CPU 10d approximates the above-mentioned characteristic distribution by a high-order nonlinear function obtained by the least square method or a straight line obtained by area division according to a function approximation algorithm (ST9). 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). The approximate expression thus obtained is written in the model expression storage unit 16 (S
T10).

FIG. 4 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 20 (step ST
11), and the signal processing extension unit 21 performs extension processing (ST1
2), an output value (control amount) is calculated by a model formula (ST13), and it is output as a control signal (ST1).
4).

An example will be described below.

First, the input of the process to be identified is A,
B and C, and output is D. In this case, multi-input non-linear modeling is to identify (approximately) a mathematical relationship D = f (A, B, C) between a plurality of inputs A, B, C and an output D.

As analysis data, input / output data (inputs A, B, C and output D) actually obtained from the process to be identified are input to the apparatus of the embodiment.

The data expansion is performed by reciprocal data (1 / A, 1 / B, 1 / C) of each of the input variables (input variables for the identification object) A, B, C in the analysis data and the amount of change. Extended data (A, B, C, 1 / A, 1 / B, 1 / C, dA, dB, added with data (dA, dB, dC)
This is an operation for converting to dC).

In the following example, among the extended data, the input data A, B and C, the reciprocal 1 / B and the variation dC are important.

The above approximation function of the input / output relationship D = f (A, B, C) is approximated by the following equation according to the algorithm used in the previously proposed nonlinear control device.

D '= Rn (WAA' + WBB '+ WCC') n + Rn-1 (WAA '+ WBB' + WCC ') n-1 + ... + R1 (WAA' + WBB '+ WCC') + R0 ... (2 ) However, A ′, B ′, C ′, D ′ are for analysis [0, 1]
Input / output variables normalized to, WA, WB, WC are category weights, Rn, Rn-1, ..., R1, R0 are coefficients of higher-order function approximation, and the value in () WA A '+ WBB '+ WCC' =
S is a sample score.

On the other hand, the extended algorithm used in the control device of the present invention is approximated by the following equation.

D '= Rn {WAA' + WBB '+ WCC' + W1 / B (1 / B) '+ WdC (dC)'} n + Rn-1 {WAA '+ WBB' + WCC '+ W1 / B (1 / B)' + WdC (dC) '} n-1 + ..... + R1 {WAA' + WBB '+ WCC' + W1 / B (1 / B) '+ WdC (dC)'} + R0 ... (3) However, A ', B' , C ', (1 / B)', (dC) ',
D'is an input / output variable normalized to [0,1] for analysis, WA, WB, WC, W1 / B, WdC are category weights, R
n, Rn-1, ..., R1 and R0 are coefficients of the higher-order function approximation, values in {} WAA '+ WBB' + WCC '+ W1 / B (1 /
B) '+ WdC (dC)' = S is a sample score.

Therefore, when the original input / output relationship of the identification target is D = 3A + 2 / B + dC (4), it is difficult to perform accurate approximation with the nonlinear controller proposed previously.

In the case of the above example, the following input / output data is actually obtained from the process to be identified. However,
1 / B and dC are extended data and are not used in the previously proposed algorithm.

A B C 1 / B dC D 1 1 10 1.0 − 15 2 2 18 0.5 8 15 3 5 24 0.2 6 15.4 4 2 29 0.5 5 18 5 1 33 1.0 4 21 6 2 36 0.5 3 22 7 5 40 0.2 4 25.4 8 2 45 0.5 5 30 9 1 51 1.0 6 35 10 2 59 0.5 8 39 The above data can be normalized by the normalization algorithm or manually by the man-machine interface 17. It is done by entering an expression. Here, in order to make the data easier to see, the following conversion formula is manually input to normalize [0, 1].

A '= A / 10 B' = B / 5 C '= (C-10) / 50 (1 / B)' = 1 / B (dC) '= (dC-3) / 5 D' = (D-15) / 25 The following results are obtained from the above conversion formula.

A'B 'C' (1 / B) '(dC)'D'0.1 0.2 0.00 1.0 − 0.000 0.2 0.4 0.16 0.5 1.0 0.000 0.3 1.0 0.28 0.2 0.6 0.016 0.4 0.4 0.38 0.5 0.4 0.120 0.5 0.2 0.46 1.0 0.2 0.240 0.6 0.4 0.52 0.5 0.0 0.280 0.7 1.0 0.60 0.2 0.2 0.416 0.8 0.4 0.70 0.5 0.4 0.600 0.9 0.2 0.82 1.0 0.6 0.800 1.0 0.4 0.98 0.5 1.0 0.960 By analyzing the above normalized data with fuzzy quantification II, The category weight is obtained. The horizontal axis represents the sample score S calculated using these category weights, and the vertical axis represents the value of D ′.
When the data for analysis is plotted, it is shown in FIG. 5 and FIG. 6, respectively.
The result of is obtained.

FIG. 5 shows the result obtained by the previously proposed algorithm. The sample score is S = 1.022 A'-0.152 B '+ 0.064 C'Category weight is WA = 1.022, WB = -0.152, wC
= 0.064.

FIG. 6 shows the result of the extended algorithm of the embodiment of the present invention. S = 1.240 A '+ 0.083 (1 / B)' + 0.207 (dC) 'The category weight is WA = 1.240, W1 / B = 0.083, Wd
C = 0.207.

Next, when the results of FIGS. 5 and 6 are approximated by a higher-order function by the method of least squares, the following results are obtained.

In the previously proposed algorithm, D "=-0.348645S3 + 1.391022S2-0.130135S-0.
[003355] Average approximation error (D "-D ') = 0.017941 In the extended algorithm of the embodiment, D" = 0.96774S-0.480058 Average approximation error (D "-D') = 0.000158 As is clear from the above results, the extended algorithm Using, the approximation function becomes simpler and the approximation accuracy improves.

[0070]

As described above, according to the present invention, since the input / output can be identified with a higher approximation accuracy and a simplified approximation function than the modeling in the previously proposed nonlinear controller, fuzzy quantification is possible. The effects of improving reliability of multi-input non-linear control and expanding applications by class II are obtained.

[Brief description of drawings]

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

FIG. 2 is a diagram showing a configuration of a data expansion processing unit in the embodiment.

FIG. 3 is a flowchart showing an execution procedure of a modeling algorithm used in the embodiment.

FIG. 4 is a flowchart showing an execution procedure of a control algorithm performed based on a model formula obtained by the modeling algorithm.

FIG. 5 is a diagram showing an analysis result based on the previously proposed algorithm.

FIG. 6 is a diagram showing an analysis result by the extended algorithm of the embodiment of the present invention.

FIG. 7 is a diagram showing a structure of data handled in the fuzzy quantification type II.

[Explanation of symbols]

10a to 10e ... CPU, 11, 12, 13, 14, 1
5 ... Algorithm storage unit 3, 16 ... Model formula storage unit,
17 ... Man-machine interface, 18 ... Communication device, 1
9 ... Data storage unit, 20 ... Signal input unit, 21 ... Signal expansion processing 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 data handled by this fuzzy quantification type II are shown in FIG. The difference from the fuzzy quantification type I is that the external criterion is fuzzy group B.
It is given by ₁ , B ₂ , ..., B _M. The purpose of this fuzzy quantification class II is that each category A _i (i = 1,
2, ..., K) Line weight of category weight a _i

[Procedure Amendment 2]

[Document name to be amended] Statement

[Correction target item name] 0016

[Correction method] Change

[Correction content]

[0016]

[Equation 1] 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 value (sample score) of each sample ω is calculated by the equation (1).
Is required. 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] 0046

[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 17 or the communication device 18 (steps ST 1 and ST 2), and the data are read. It is stored in the storage unit 19. 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] 0047

[Correction method] Change

[Correction content]

Next, in the CPU 10a, the reciprocals 1 / X ₁ , 1 / X _{2 of} the input data stored in the data storage unit 19 are calculated according to the data expansion algorithm .
, 1 / X _n and change amounts dX ₁ , dX ₂ , ..., dX _n are calculated (ST3 and ST4).

[Procedure correction 6]

[Document name to be amended] Statement

[Correction target item name] 0048

[Correction method] Change

[Correction content]

In the CPU 10b, from the input / output data expanded by adding the reciprocal number and the amount of change to the input data,
The standard deviation σ of each data is calculated according to the normalization algorithm (ST5), and the standard deviation σ is tripled, that is, the range of 3σ [a,
b] is normalized to [0, 1] (ST6). Here the normalized output data of the _{Y 1 ', Y 2',} ..., represented as Y _m '.

[Procedure Amendment 7]

[Document name to be amended] Statement

[Correction target item name] 0049

[Correction method] Change

[Correction content]

In the CPU 10c, the dummy data for analysis ( Y ₁ "= 1-Y ₁ ', ..., Y _m " = 1-Y of the output data Y ₁ ', Y ₂ ', ..., Y _m ' is used in accordance with the analysis algorithm. _m ' ) (ST7), data analysis by fuzzy quantification type II,
That is, the characteristic distribution based on the sample score is calculated (S
T8).

[Procedure Amendment 8]

[Document name to be amended] Statement

[Name of item to be corrected] 0058

[Correction method] Change

[Correction content]

D '= R _n (W _A A' + W _B B '+ W _C C') ⁿ + R _n-1 (W _A A '+ W _B B' + W _C C ') ^n-1 + + R ₁ (W _A A '+ W _B B' + W _C C ') + R ₀ (2) However, A', B ', C', D'are [0, 1] for analysis.
Input / output variables normalized to, W _A , W _B , W _C are categorical weights, R _n , R _n-1 , ..., R ₁ , R ₀ are coefficients of higher-order function approximation, () Value within W _A A '＋ W _B B' ＋ W _C C ' ＝
S is a sample score.

[Procedure Amendment 9]

[Document name to be amended] Statement

[Correction target item name] 0060

[Correction method] Change

[Correction content]

D '= R _n {W _A A' + W _B B '+ W _C C' + W _{1 / B} (1 / B) '+ W _dC (dC)'} ⁿ + R _n-1 {W _A A '+ W _B B '+ W _C C' + W _{1 / B} (1 / B) '+ W _dC (dC)'} ^n-1 + ・ ・ ・ ・ ・ ・ ＋ R ₁ {W _A A '＋ W _B B' + W _C C '+ W _{1 / B} (1 / B) '+ W _dC (dC)'} + R ₀ (3) where A ', B', C ', (1 / B)', (dC) ',
D'is an input / output variable normalized to [0, 1] for analysis, W _A , W _B , W _C , W _{1 / B,} W _dC are category weights, R
_n , R _n-1 , ..., R ₁ and R ₀ are coefficients of the higher-order function approximation, and the value in {} W _A A '+ W _B B' + W _C C '+ W _{1 / B} (1 / B) '＋ W _dC (dC)'
= S is a sample score.

[Procedure Amendment 10]

[Document name to be amended] Statement

[Correction target item name] 0066

[Correction method] Change

[Correction content]

FIG. 5 shows the results obtained by the previously proposed algorithm. The sample score is S = 1.022 A'-0.152 B '+ 0.064 C'Category weight is W _A = 1.022, W _B = -0.152, W _C
= 0.064 .

[Procedure Amendment 11]

[Document name to be amended] Statement

[Correction target item name] 0067

[Correction method] Change

[Correction content]

FIG. 6 shows the result of the extended algorithm of the embodiment of the present invention. S = 1.240 A '+ 0.083 (1 / B)' + 0.207 (dC) 'The category weight is W _A = 1.240, W _{1 / B} = 0.083, W
_dC = 0.207 .

[Procedure Amendment 12]

[Document name to be amended] Statement

[Correction target item name] 0069

[Correction method] Change

[Correction content]

[0069] In the algorithm of the destination in the ^{proposal, D "= -0.348645 S 3 +1.391022} S 2 -0.130135S-0.
[003355] Average approximation error (D "-D ') = 0.017941 In the extended algorithm of the embodiment, D" = 0.96774S-0.480058 Average approximation error (D "-D') = 0.000158 As is clear from the above results, the extended algorithm Using, the approximation function becomes simpler and the approximation accuracy improves.

Claims (2)

[Claims] 1. A data collection means for collecting data indicating an input / output relationship for a controlled object, and inputting extension data by adding a reciprocal number, a variation amount, and other necessary quantity to the data, and the extension data. And a normalized algorithm is analyzed by the method of fuzzy quantification II, and a modeling algorithm storage unit that stores a modeling algorithm that approximates the characteristic distribution obtained as a result of the analysis with a function, and executes the modeling algorithm. Then, an approximate function calculation processing unit that generates a function that approximates the characteristic distribution, a signal input unit that takes in an input signal from the control target, and an extended input that adds the reciprocal number, change amount, and other necessary amount to the input signal. And an output for the extended input using a function generated by the approximation function calculation processing unit. A control algorithm storage unit that stores a control algorithm to be output, a control calculation unit that calculates an output value for the extended input according to the control algorithm, and a signal output unit that outputs the result of the calculation by the control calculation unit as a control signal. Equipped with a non-linear control device. 2. The non-linear control device according to claim 1, wherein the data collecting means, the modeling algorithm storage section, and the approximate function calculation processing section are independent offline processing sections.