JP3196346B2 - Subsystem setting device - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a subsystem setting device.

[0002]

2. Description of the Related Art Hitherto, as an invention for approximating a high-order input / output characteristic by a low-order function, for example, Japanese Patent Application Laid-Open No. 3-176783 discloses
As disclosed in Japanese Patent Application Laid-Open No. H10-209, there has been a configuration in which a plurality of regions are divided and each of the divided regions is linearly approximated (linear function) to thereby approximate the entirety to a polygonal line. Further, as an invention approximated by a quadratic function, for example, there is one disclosed in Japanese Utility Model Laid-Open No. 64-46863.

[0003]

However, in the above-described conventional device, a certain region is represented by one function, and there is a limit in approximation at the boundary of the region. Further, in order to perform accurate approximation, it is necessary to divide the region into a large number.

The present invention provides a subsystem setting device capable of setting a subsystem capable of expressing a complicated input / output characteristic function given by a third order by approximating a plurality of simpler quadratic functions. To provide.

[0005]

To achieve the above object SUMMARY OF THE INVENTION The sub-system setting device according to the present invention, the input value
And input / output characteristics represented by a cubic function passing through the target function data, which is four discrete point data constituted by a combination of the output values and the output values , by approximating the input / output characteristics with a lower-order function.
It is assumed that the device can set the subsystem .

Then, the target function data is input to the
One with the smallest input value and one with the second smallest input value
And the data with the third smallest input value
Group the data with the largest input value into another group
And Mel grouping means, the in each group 2
A function generating unit to create a secondary function connecting the pieces of object feature data, and function setting means subsystem <br/> sets the function to the function creating unit creates the subsystem, it said in the respective group 2 A normal distribution creating means for creating a normal distribution by obtaining an average value and a standard deviation in the group from the target function data, and the subsystem having the normal distribution created by the normal distribution creating means as a membership function.
Means for setting the membership function of the subsystem to be set to:
Quadratic function and membership function set in subsystem
Membership set in subsystem by setting means
Integrating means for calculating the product of the function and the product of each of the groups
And an adding means for adding the result of integration by the calculating means .

[0007] Preferably , two of each of said groups
The average of the input values of the target function data of
To obtain the output value by substituting
The purpose of the present invention is to provide a purpose function data conversion means for increasing the number of data.

[0008]

When complex target function data is given, the target function data is divided into groups, and the data of each group is converted into data expressing a simple target function to be given to a subsystem having a simpler structure. That is, conversion is performed to approximate the input / output characteristic equation given by the cubic equation with a plurality of quadratic functions. As a result, a subsystem having a function for obtaining a quadratic function and a membership function unit for setting a membership function for weighting the quadratic function is set. Since the set subsystem is expressed by a simple combination of functional elements as compared with a higher-level system that directly expresses the original target function data, manufacture as an actual device is easily performed.

[0009]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS Preferred embodiments of a subsystem setting apparatus according to the present invention will be described below in detail with reference to the accompanying drawings. This example shows an example in which the present invention is applied to a system for generating an optimal humidity target value y to be set according to a temperature x detected by a temperature sensor in an air conditioner. That is, as shown in FIG. 1, as shown in FIG. 1, when an input x is given, arithmetic processing is performed in accordance with a function F1 which is a certain input / output characteristic, and a target value y is output. ) It is represented by a curve as shown by a solid line. Then, in order to design (set) such a system (function F1), four coordinate points ｛(x
1, y1), (x2, y2), (x3, y3), (x
4, y4)} (provided that x1 <x2 <x3 <x4). Then, the target function data K1 becomes a higher-order target function to be performed by the higher-order system F1. Note that these four coordinate points are important points representing the features in the complicated function (input / output characteristics). In addition, the purpose of input is “ 3 passing through the target function data K1”.
A function that approximates the input / output characteristics expressed by
It becomes a control system to design "and the like.

Since the above-mentioned function F1 is expressed by a higher-order equation (for example, a cubic equation), it is necessary to satisfy a complicated objective function as expressed by such a cubic equation. , The use of complex functional elements, it is not only very difficult to design a system composed of such complex functional elements,
If it is attempted to use it, the process for performing the control is complicated, high-speed processing cannot be performed, and real-time response cannot be performed.
Therefore, the purpose is further simplified by using the device according to the present invention,
That is, lower-order target function data for a subsystem expressed by a function having a lower order is generated, and a desired subsystem corresponding to the purpose is created. The specific configuration for performing such processing is as follows.

[0011] As shown in FIG. 2, the device (subsystem setting device is integrated), the grouping of dividing the object function data K1 which constitutes a part of the subgoals generator A in two pairs An output of the grouping unit 1 is input to a first purpose conversion unit 2 as data conversion means. The grouping unit 1 pays attention to the magnitude relationship of x, which is the input data of the final system, and sets two smaller data (x
1, x1), (x2, y2) and two larger data (x3, y3), (x4, y4). The first purpose conversion unit 2 converts a given target into a simplified lower-order target. Specifically, the first target conversion unit 2 converts a given function into a higher-order function (n
By subtracting 1 from the order of the following equation, the order of the function to be set in the subsystem is determined. In this example, since the function specified by the target function data K1 is a cubic expression, the subsystem is a function represented by a quadratic expression. Then, it is determined whether or not the subsystem can be processed based on each of the grouped data. When the data cannot be processed, the data is converted into data that can be processed. In this example, data of two coordinate points are included in one group. Therefore, since a quadratic function can be set using these two data, no particular data conversion is performed. That is, in this example, the first purpose conversion unit 2 outputs “two types of target function data K21 [(x1,
y1), (x2, y2)], K22 [(x3, y3),
(X4, y4)], and create a function that specifies a section in which each of the quadratic functions expresses the original function F1 ”. Will be output.

On the other hand, the output of the first purpose conversion unit 2 is
The sub-system setting unit B is connected to an (n-1) -order function creating section (quadratic function creating section) 3 and a normal distribution creating section 4 as means for calculating an adaptive range. The data of (xi, yi) is sent to the next-stage quadratic function creating unit 3 for each group, and the data of (xi) is sent to the next-stage normal distribution creating unit 4 for each group.

The quadratic function generator 3 obtains a quadratic curve (function) passing through two coordinates for each group. In this example, in order to simplify the configuration, a = 1 or −1 among y = ax ² + bx + c, which is a general expression of a quadratic function, and the sign of a is a change of each part of the cubic function. , That is, it is desirable to determine based on the magnitude relationship between the four data. In this example,
For convenience, a is set to 1 for a group having a small x, and -1 is set to a for a group having a large x. Therefore, in practice, b and c are obtained. Since the two coordinates are known, b and c can be easily calculated by solving the simultaneous quadratic equations.

The normal distribution creating unit 4 calculates an average value m from two x values of the same group, and further calculates a standard deviation σ. That is, if one group (x1, x2) is described for convenience of explanation, it can be easily obtained by m1 = (x1 + x2) / 2. Further, the standard deviation σ can be calculated by σ1 = (x2−x1) / 2 . Next, a normal distribution G (m1, σ1) having the average value m and σ is obtained.

The above-mentioned quadratic function creating section 3 is transmitted via a system setting section 5 which constitutes a part of the subsystem setting section B.
Is set to the function part of the subsystem, and the output of the normal distribution creation part 4 is set to the membership function part of the subsystem. That is, the subsystem created by the present invention is:
As shown in FIG. 3, a plurality (two) of quadratic function parts (F21, F22) 10a, 1 having lower orders than the system F1.
0b and membership function parts (μ21, μ22) 11a, 11b indicating the applicable range of the original function F1 that can be expressed by the respective quadratic function parts (F21, F22) 10a, 10b. , A paired function and a membership function (F21 and μ21, F22 and μ22) are multiplied (weighted) via multipliers 12a and 12b to obtain an output expression (μ
21 (x) * F21 (x), μ22 (x) * F22 (x) ) through the adder 13.

Next, the processing procedure of the present apparatus will be described. As shown in FIG. 4, first, the target function data K1 is read, divided into two groups, and the target function data element (one of the groups) is formed. x1, y
1), the (x2, y2) based quadratic function (F21 (x passing through the two ^{points) = x 2 + b1 x +} c1) calculated, then object function data elements (x3 constituting the other group, y
3), (x4, y4) 2 linear function passing through the two points based on (F22 (x) = - x 2 + b2 x + c2) obtaining the (S
101-104).

Then, based on the target data element (x1, x2) of one group, the average value m1 and the standard deviation σ
1 and a normal distribution G (m
1, σ1), and calculate it as μ21 (μ21 (x) = G (x;
m1, σ1)). Similarly, an average value m2 and a standard deviation σ2 are obtained based on the target data elements (x3, x4) of the other group, and a normal distribution G (m2, σ2) having both values m2, σ2 is obtained, which is expressed as μ22 μ22 (x) =
G (x; m2, σ2)) (S105, 106).

Then, based on each calculation result obtained in each of the above steps, it is set in each part of the subsystem (S10).
7). That is, in this set subsystem, a function of a cubic expression achieved by a higher-order purpose is configured using simplified simplified functional elements expressed by a function of a quadratic expression using the higher-order purpose. Will be done. Note that the function F
1 is a cubic function, that is, the function part 10 of the subsystem
If it is known that the functions F21 and F22 of a and 10b are quadratic functions, instead of setting the function formula as described above, each coefficient (b1, c1, m1, σ1, b2,
c2, m2, σ2), and the obtained system parameters may be set in each function unit. Also,
If the order is known in this way, the first objective conversion unit 2 is not provided, and the objective function data obtained by grouping is used as it is, as the quadratic function creation unit 3, the normal distribution creation unit 4, and the second objective unit 6 described later. It may be sent to.

On the other hand, the subsystem set as described above is a combination of a quadratic function as compared with a cubic function that directly expresses a higher-order objective, and therefore, although each functional element can be simplified, In this example, as shown in FIG. 2, by providing a predetermined device at a subsequent stage, a secondary subsystem composed of a combination of a more simplified linear function can be created.

First, the outline of the present embodiment will be described. As shown in FIG. 5, a quadratic function (indicated by a two-dot chain line in the figure) converted and created by the above processing is approximated by a straight line, and the straight line ( This is for expressing a quadratic function by a combination of linear functions. That is, the second objective conversion unit 6 is connected to the outputs of the first objective conversion unit 2, the quadratic function creation unit 3 and the normal distribution creation unit 4, and the output of the first objective conversion unit 2 is higher than that of the second objective conversion unit. The target function data, that is, K21 and K22 formed by grouping K1 and the order (second order) set by the upper function unit are given. Also, the latter gives a quadratic function equation set by the function units 10a and 10b of the subsystem.

The second purpose conversion section 6 converts the given function data into given function data required for processing in the lower-order secondary subsystem. That is, first, as preprocessing, 2
The order to be set in the function part of the next subsystem is obtained.
That is, by subtracting 1 from the given order (second order), the function of the secondary subsystem is expressed by a combination of linear expressions. Note that, as in the case of the first objective conversion unit 2 described above, if it is known that the objective function data K1 initially given to the system is of a cubic type, it is inevitable that the secondary In the system, a combination of linear expressions is used, so that the determination processing can be omitted. Next, the number of target function data (two in this example) constituting one group is detected, and it is determined whether or not the data is sufficient when setting the function of the secondary subsystem. Then, in the case of this example, the number is two, and it is not possible to represent a plurality of linear functions (straight lines) that represent a quadratic function using the two data. Converts the target function data.

That is, basically, a process of increasing the number of data is performed based on data of two coordinate points set in each group. That is, as shown in FIG. 6, first, one group K21 [(x1, y1), (x2, y
2) Conversion of target function data corresponding to [1]. That is, the midpoint between x1 and x2 is determined, and the coordinate point is set to x6. Further, a position symmetrical with respect to the calculated x6 (on the x-axis) is calculated with reference to x1, and the coordinate point is defined as x5. Further, a midpoint between x3 and x2, which are coordinate data on adjacent x in the other group, is obtained, and the coordinate point is defined as x
7 is assumed. And x5, x6 obtained in this way
The x7, by substituting the output characteristic equation y = F21 which is an upper sub-system for this group (x), Ru respectively y5, y6, determined <br/> Me a y7.

Next, the given and calculated 5
The two coordinate data are sorted on the basis of the x-coordinate to obtain lower-order target function data K31. That is, the lower purpose function data K31 is

[0024]

## EQU1 ## K31 = [(x5, y5), (x1, y1), (x6, y6), (x2, y2), (x7, y7)], and the target function data K31 is set in the secondary subsystem. The data is sent to the linear function generator 7 and the normal distribution generator 8 of the unit C.

Similarly, the target function data is converted for the other group, and the target function data K32 shown below is obtained and sent to the secondary subsystem setting unit C.

[0026]

K32 = [(x8, y8), (x3, y3), (x9, y9), (x4, y4), (x
10, y10)]. Similarly to the above-described quadratic function generator 3, the primary function generator 7 generates two adjacent coordinate point data (for example, (x5, y5) and (x1, y
1) Find a straight line passing through). At this time, since such a straight line can be represented by the general formula y = ax + c, a and c can be easily obtained by inputting the coordinates of the above 2 into x and y. Then, the calculation results are set as a51 and c51.

The normal distribution creating unit 8 performs the same processing as the normal distribution creating unit 4 in the subsystem setting unit B, and calculates the normal distribution parameters m51 and σ51 for x5 and x1.

By repeating the above processing in order, a linear expression and a normal distribution concerning four straight lines are obtained, and the calculation results are transmitted via the system setting section 9 to the function section of the secondary subsystem shown in FIG. 20d and membership function units 21a to 21d. That is, for example, F31 becomes F31 (x) = a51x + c51,
μ31 becomes μ31 (x) = G (x; m51, σ51).

The secondary subsystem set in this way is, as shown in FIG. 8, a pair of function units 20a.
, And the membership function units 21a are connected via multipliers 22a, the outputs of the multipliers 22a are combined via an adder 23, and the combined result is output.

The other group (the target function data K
32), the same processing as described above is performed, and a specific description thereof will be omitted. Further, since there is no function that is simpler than the linear expression, the breakdown of the purpose and the like is not performed any more. That is, there are no nested sub-systems that go further inside this secondary subsystem. In other words, if the function represented by the target function data given to the entire system first is a quartic function or more,
The above-described nested subsystems, objective function data converters, and subsystem setting units required for designing the subsystems can be provided by appropriately increasing the number of subsystems.

On the other hand, whether or not the subsystem (secondary subsystem) set as described above satisfies the original system depends on whether the subsystem or the like has complicated target function data K1. Input sample data such as xi, and evaluate whether or not the obtained output is yi. If the evaluation result is low, use a function to correct the membership function in the fuzzy inference apparatus, etc.
This can be dealt with by modifying the shape or the like of the membership function stored in the membership function section.

Then, the subsystem setting unit B
The secondary subsystem setting unit C constitutes a subsystem setting device according to the present invention. On the other hand, among the lower purpose generation units A, "the grouping unit 1 and the first purpose conversion unit 2", "the grouping unit 1" Unit 1, the first purpose conversion unit 2 and the second purpose conversion unit 6 "and" the grouping unit 1 and the second purpose conversion unit 6 (the first purpose conversion unit is not provided, and the output of the grouping unit is directly used for the second purpose conversion unit). Connected to the conversion unit) constitute a data conversion device expressing the target function according to the present invention.

The above-described embodiment describes an apparatus for automatically designing a system for achieving a given purpose, and various converters and subsystems constituting each part of the apparatus. As a system mounted on an actual air conditioner, for example, a secondary subsystem including a function part expressed by a plurality of linear functions and a membership function part specifying a characteristic region expressed by the function is used. It is not necessary to provide a higher-order subsystem. If the given target function data expresses a cubic expression in advance, and it is known that the finally obtained function is a combination of linear expressions, for example,
In the block diagram shown in FIG. 2, the first purpose conversion unit 2 and the system setting unit 5 become unnecessary.

[0034]

As in the above, according to the present invention, in the present onset bright, given by the third-order
Complex input / output characteristics functions can be converted to simpler multiple secondary
Subsystems that can be approximated by functions
Can be set. Therefore, in such a subsystem, the system design can be represented by a combination of simple functional elements, and the system can be designed based on simple target function data, so that the system can be automatically generated by a machine.

[Brief description of the drawings]

FIG. 1 is a diagram showing a high-order object and a high-order system to be processed by the present invention.

FIG. 2 is a block diagram showing an embodiment of the apparatus according to the present invention.

FIG. 3 is a diagram showing a subsystem in which the higher-level system shown in FIG. 1 is broken down by one stage.

FIG. 4 is a flowchart illustrating a processing procedure of a subsystem setting unit.

FIG. 5 is a diagram illustrating target function data for a secondary subsystem.

FIG. 6 is a flowchart illustrating a processing procedure of a second purpose conversion unit.

FIG. 7 is a flowchart illustrating a processing procedure of a secondary subsystem setting unit.

FIG. 8 is a diagram showing a secondary subsystem in which the subsystem shown in FIG. 3 is further broken down by one stage.

[Explanation of symbols]

DESCRIPTION OF SYMBOLS 1 Grouping part 2 1st objective conversion part (conversion means) 3 Quadratic function creation part (means for designing a lower system) 4 Normal distribution creation part (means for calculating the adaptive range of an upper system) 6 2nd objective conversion Unit (conversion means) 7 linear function creation unit (means for designing a lower system) 8 normal distribution creation unit (means for calculating the adaptation range of a higher system) 10a to d, 20a to function unit (lower system) 11a to d, 21a-Membership function part (means for specifying the applicable range of the upper system)

──────────────────────────────────────────────────続 き Continued on the front page (72) Inventor Yumi Saito 10th Hanazono Todocho, Ukyo-ku, Kyoto, Kyoto Prefecture Inside of Omron Corporation (72) Inventor Motoki 10th Hanazono Todocho, Ukyo-ku, Kyoto, Kyoto In-company (72) Inventor Tadashi Maeda 10 Okado Dodo-cho, Ukyo-ku, Kyoto-shi, Japan OMRON Corporation (56) References JP-A-53-99843 (JP, A) JP-A-3-176783 (JP, A) JP-A-62-249068 (JP, A) JP-A-4-65719 (JP, A) JP-A-59-38807 (JP, A) JP-A-3-123902 (JP, A) JP-A-2- 93942 (JP, A) Fully open sho 64-6863 (JP, U) (58) Fields investigated (Int. Cl. ⁷ , DB name) G06F 9/44 G06F 17/10 G05B 13/02 G05B 11/36 G06N 7/02

Claims (2)

(57) [Claims] 1. An apparatus comprising a combination of an input value and an output value.
Target function data, which is four discrete point data
The input / output characteristics represented by the passing cubic function are converted to lower order functions.
Can set subsystems to be approximated by
In the subsystem setting device, the target function data is set to the data having the smallest input value.
Combine data with small input values into one group,
Thirdly, the data with the smallest input value and the data with the largest input value
And grouping means to group over data to the other one group, the a function generating unit configured to generate a quadratic function connecting the two object function data in each group, sub-system functions that this function creating unit creates a function setting unit subsystem to be set in, the from the two objective function data in each group and the normal distribution forming means for forming an average value and a normal distribution with the standard deviation in the group, the normal distribution creating means Means for setting the normal distribution created by the sub-system as a membership function in the subsystem; and setting of the sub-system by the function setting means in each group.
Quadratic function and membership function setting procedure set in the stem
Membership function set to subsystem by step
Summing means for calculating the product of
And a subsystem setting device. 2. The two target function data sets of each group.
The average value of the input values of the data is substituted into the quadratic function and the output value
2. The subsystem setting device according to claim 1 , further comprising target function data conversion means for increasing the number of the target function data by obtaining the target function data.