JPH0353301A - Fuzzy controller - Google Patents

Abstract

PURPOSE:To obtain a fuzzy controller which can perform the fuzzy control and also minimizes the number of rules to attain the linear control by using the algebraic product of the grade of a fuzzy variable of an antecedent part corresponding to the input value as the grade of a fuzzy variable of a consequent part. CONSTITUTION:A CPU 11 performs the total control of a device while using the storage area of a RAM 12b based on a control program stored in a ROM 12a. Then the grade of a fuzzy variable is obtained to the degrees of plural types of input value inputted based on a set control rule and a member ship function. At the same time, the algebraic product is operated for the grades of plural types of input value. In this case, the algebraic product of the grade of the input value is used as the grade of a fuzzy variable of a consequent part of the control rule with which the input value is satisfied. Thus it is possible to obtain a fuzzy controller which is capable of the fuzzy control and also suited to the linear control.

Description

[Detailed Description of the Invention] [Industrial Application Field] The present invention provides a method for manually generating multiple types of information indicating the state of a controlled system, and generating multiple types of information indicating the relationship between the amount of operation for operating the controlled system and the human input. The present invention relates to a fuzzy controller that controls a controlled system based on fuzzy control rules.

[Conventional technology]

FIG. 2 is a diagram showing an example of a fuzzy feedback control system using this type of fuzzy controller, and shows a case where there is one control loop.

In the figure, 10 is a fuzzy controller composed of a microcomputer, etc., 20 is various controlled systems, and the fuzzy controller 10 uses, for example, a control deviation e (controlled variable y and the target value r) and the difference Δe thereof, the manipulated variable m is determined so that the controlled variable y becomes a predetermined target value r, and is output to the controlled system 20.

Hereinafter, an example of fuzzy control will be explained in which a manipulated variable m is output for the control deviation e and the human power of the difference Δe.

In this type of fuzzy control, it is determined how much the control deviation e is and how much the difference Δe is, and the manipulated variable m is determined according to a combination of these degrees.

Therefore, for each domain of the control deviation e, the difference Δe, and the manipulated variable m, a fuzzy variable whose grade is determined by a membership function as shown in FIG. The degree of the difference Δe and the manipulated variable m is expressed. For explanatory purposes, the figure represents the control deviation e, the difference Δe, and the manipulated variable m by a variable X, and shows the membership number μ(×). ,ZO,PS,PM,
PB is a fuzzy variable. Note that the variable names of fuzzy variables have the following meanings.

NB: Large in the negative direction NM: To some extent in the negative direction NS: A little in the negative direction ZO: Almost zero PS: A little in the positive direction PM: To some extent in the positive direction PB: Large in the positive direction These fuzzy variables (NB, NM, NS, ZO,
PS, PM, PB) are variables that represent the degree of deviation between the variable X and a preset value (“0” in this example) overlapping predetermined intervals; has the attribute of a fuzzy variable corresponding to the interval to which this variable X belongs. The degree of the attribute (grade μ1) is represented by a value from O to 1 using the membership function μ(x). Note that in the support part (slanted part) of the membership function, two fuzzy variables and two grades are determined for one variable X, and the sum of these two grades is l.

For example, if the variable X is a control deviation e and its value is ex as shown in FIG. 17, then control? Difference e. The fuzzy variables of are PS and PM, and this fuzzy variable (PS ,
Each grade of PM) is μ■, μAffi(μ■
+μAz=1). Note that in the vertex and core part (horizontal part) of the membership function, one grade is 1 and the other is O.

On the other hand, as shown in the following equation (1), the fuzzy controller 10 has an IF and
...THEN... A plurality of control rules are set.

IP(e is A+) and(Δe is Bj
) THEN m is [i・1~l, j・1~n] A i v Bj s Cij : Fuzzy variable The antecedent part (the part between "IF" and "THIliN") of the above equation (1) is, The control variable e and the difference Δe are associated with fuzzy variables Ai, B, respectively, and the preconditions are AND-combined, and the consequent part (the part after "THI!N") is as follows.
A conclusion is shown in which the manipulated variable m and the fuzzy variables C i j are associated with each other. Then, according to this control rule, "the control deviation e is A, degree, and the difference Δe is B, degree C ij
...(1)? In this case, the manipulated variable m is approximately C ij. ” rules are stipulated.

The fuzzy controller 10 calculates the input control deviation e and the difference Δ
According to e, a fuzzy variable of the manipulated variable m of the consequent is determined by driving a control rule that satisfies the antecedent part, and from the grade of the control deviation e and the difference Δe, and the grade of the fuzzy variable of each manipulated variable m. , fuzzy set C of output value m0 of manipulated variable m
Estimate O, defuzzify this fuzzy set, and determine the output value.

Next, a conventional fuzzy control method up to determining the output value m0 as described above will be explained.

(Conventional Fuzzy Control Method) The fuzzy controller 10 refers to a preset membership function and calculates the fuzzy variables A, gA2 and grade μ■ of the control deviation e from the input control deviation e and the difference Δe. μA2, fuzzy variable B of difference Δe, ,B. and the grades μ■, μ3■, respectively, and the four combinations of fuzzy variables Az, Az, B l+82 (
A l and B,,A, and B2? Az and B+, Az and 82
) to generate four fuzzy variables C, , c, for the manipulated variable m.
2,c,. , ctt.

Also, grade μa+ s μazs #lIt e
Regarding llmz, an operation called min operation (mini operation) is performed in correspondence with the and combination of the antecedent part of the control rule, and for the above four control rules, the fuzzy variable A. and the fuzzy variable B of the difference Δe. Each grade μ. ．． , μlj, the smaller of the four values μ
■7,. Find each j. In addition, these four values μl
Iill+ij indicates the degree of adaptation of each of the four control rules.

Next, 4 for the manipulated variable m estimated as above.
two fuzzy variablesC. , (C++, C+■, C21, C
2) In order to obtain the output value m0 of the manipulated variable m, the following calculation called max-min combination is performed.

In other words, the four values μ+ obtained by the min operation of the antecedent part
min+ij and the four corresponding fuzzy variables C
mi0 with each membership function μe+ij of i j
From the calculation (μ淘・n*ij8μc,t=)&, the manipulated variable m is set as a variable corresponding to each fuzzy variable C i j 4
The following equation (2) is obtained by calculating the four functions and using the sum of these four functions.
The membership function μ-'(m) of the fuzzy set C0 in operation 31m is determined as follows.

?゜゜(″′) ふ１：：：会■c；H；] Sj, E
:::father:::'. z:] ． ．． ．． (2) (However,
ω-th=μ・i−▲J) Then, the output value m0 is obtained from the center of gravity of the fuzzy set CO as shown in the following equation (3).

By the way, if we set a three-dimensional space (hereinafter referred to as control space) defined by the variables of the control deviation e, the difference Δe, and the manipulated variable m, one relationship between input and output due to fuzzy control is shown in Figure 20. It can be expressed as a point in the control space as follows. In the figure, points P, Q, R, and S are defined by the following four control rules (b) j ((1)?
(r) and (S) indicate the point where both fuzzy variables in the antecedent part have a grade of 1, and are points representing each control rule (hereinafter referred to as representative points).

1F (e is Z O) and (Δe is Z
O) THEN m i's IF( e is Z O
) and (Δe is NS) THEN m is I
F(e is N S) and (Δe is N
S) THEN is IF (e is N S)
and (Δe is ZO) THEN is now the above four control rules (p), (Q), (r
), (S), the fuzzy variable of the control deviation e, the fuzzy variable of the difference Δe, and the membership function of the manipulated variable m are set as shown in Figures 18 (a) to (C), respectively, and the manually controlled control deviation and the difference are el tΔe as shown
．． Assuming that, for the control deviation e1, the grade μ of the fuzzy variable ZO is 0.8, the grade μ of the fuzzy variable NS is 0.2 (Fig. 18(a)), and the deviation Δe
．． For, the grade μ of the fuzzy variable ZO is 0.6 and the grade μ of the fuzzy variable NS is 0.4 (0 in the same figure).
))).

As shown in FIG. 19(a) to (d), by performing the min operation on the grades obtained in this way, the four control rules (p), (q), (r) + (s
) for each antecedent part ZO...ω) PS...(q) PM...(r) PS...(S) For each pair of control deviation and difference, the smaller grade μ The value μmin+ij is 0.6, 0.4, 0 in this order.
．． 2,0.2 is obtained.

Furthermore, due to the max-min combination, the control rule (p) 9 (q) 9 (r)
9 A trapezoidal function is obtained from the membership functions of the fuzzy variables ZO, PS, PM of the manipulated variable m corresponding to each consequent of (S), and by the sum of this function, The membership function μc'(m) of the fuzzy set C0 is obtained. And the fuzzy set C0
The center of gravity of is determined as the output value m0 using the above equation (3). Note that if the relationship among the control deviation e1, the difference Δe, and the output value m0 is shown in the control space, it becomes, for example, point T in FIG. 20.

In this way, the output value mO obtained by the fuzzy controller
(manipulated amount m) is controlled by control rules and membership functions, so by setting control rules appropriately, there is no need to consider parameters that indicate the characteristics of the controlled system, regardless of whether it is linear or nonlinear. Fuzzy control can be performed on any control target.

[Problem to be solved by the invention]

However, in the conventional fuzzy controller as described above, a min operation is performed to find the smaller value of each membership function value (grade) in response to the AND combination of the antecedent part of the control rule. Therefore, the following problems arise.

FIG. 14 is a diagram showing the calculated value of the min calculation in the direct product of each membership function corresponding to the two fuzzy variables of the antecedent part in one control rule, in correspondence with the above min calculation. The calculated value (height of the diagram) indicates the degree to which the rule is driven.

In addition, if the input values of the control deviation e and the difference Δe deviate from the representative points P, Q, R, and S, as at point T shown in FIG. 20, the control driven by the support part of the membership function There are four rules, but the overall driving degree by each rule is shown by adding up the calculated values in Figure 14.
It will look like surface F in the figure.

As can be seen from the figure, the height is maximum at the center of the support part, and the center point of the rectangle surrounded by representative points P, Q, R, and S,
In other words, the most ambiguous parts will be emphasized. Therefore, the surface (control surface) that the control deviation e, the difference Δe, and the output value m0 constitute in the control space is as shown in FIG. 16, for example, and is a rectangle surrounded by the representative points P, Q, R, and S. The output value within includes a nonlinear element with respect to the control variable e and the deviation Δe.

By the way, the greatest advantage of fuzzy control is that the control rules can be freely configured, and this makes it possible to construct a fuzzy controller for any controlled object, regardless of whether it is linear or nonlinear. However, on the other hand, even for an expert with specialized knowledge, it is too complicated to create many control rules, and the degree of freedom of the fuzzy controller actually becomes troublesome. In addition, in the actual process, PI
Linear control based on D operation is often required, and it is effective to minimize the number of control rules so that they can be heard, such as when using a fuzzy controller as a linear controller.

However, when linear control is performed using the conventional fuzzy controller described above, it is necessary to narrow the interval between the representative points until the nonlinear elements mentioned above fall within an allowable range. In order to configure this, it is necessary to increase the number of control rules.

An object of the present invention is to provide a fuzzy controller that is capable of fuzzy control and is also suitable for linear control.

[Means to solve the problem]

The fuzzy controller of the present invention, which has been made to solve the above problems, has an antecedent part consisting of a plurality of conditions expressing the degree of the input quantity with fuzzy variables for a plurality of types of input quantities indicating the state of the controlled system. A plurality of control rules are set, each having a consequent part that indicates the degree of operation amount of the controlled system with respect to this antecedent part using a fuzzy variable, and a membership function of the fuzzy variable of the antecedent part is set, In a fuzzy controller that determines the manipulated variable to be output to the controlled system from the fuzzy variable and grade of the consequent based on a control rule that satisfies multiple types of input quantities,
Based on the set control rule and membership function, the grade of the fuzzy variable corresponding to the degree of the input amount of the plurality of types is determined, and the algebraic product of the grades of the input amount of the plurality of types is calculated. The present invention is characterized in that it comprises a calculation means, and the algebraic product of the grade of the input quantity is made the grade of the fuzzy variable in the consequent part of the control rule that the input quantity satisfies.

[Operation] In the fuzzy controller of the present invention, the manipulated variable to be output to the controlled system is determined from the algebraic product of the fuzzy variable of the consequent part of the control rule that satisfies multiple types of input quantities and the grade of the input quantity. Ru.

Figure 4 shows the calculation of the algebraic product of the above grade,
It is a diagram showing the calculated value of the algebraic product in the direct product of each membership function corresponding to two fuzzy variables of the antecedent part,
This calculated value (height of the figure) indicates the degree to which the rule is driven.

In addition, if there are, for example, four control rules driven by the support part of the membership function, the sum of the above calculated values is the fifth one.
It will look like plane F' in the figure.

In this way, the overall driving degree becomes uniform, and the center of the support part, that is, the most ambiguous part, is not emphasized. For example, as shown in FIG. 6, the representative points P, Q,
The output values within the rectangle surrounded by R and S no longer include nonlinear elements with respect to the control variable e and the difference Δe.

[Example] Hereinafter, an example of the present invention will be described for a case where a control deviation e and a difference Δe thereof are input as input quantities and an output value m0 is output.

First, the fuzzy control method in the fuzzy controller of the present invention will be explained.

(Fuzzy control method) Membership functions of control deviation e, difference Δe, and manipulated variable m are stored in advance in correspondence with fuzzy variables, and
The control rule is stored as shown in the following equation (1) as described above.

IP (e is A!) and (Δe i
s BJ) THEN is CHJ-(1)
[i=1−j! tj=1~n]A,,BJ
, C, , : Fuzzy variable A. of the input control deviation e from the preset membership function. The fuzzy variable 81 and grade μlj with grade μ,i and difference Δe are respectively determined, and a control rule having an antecedent part corresponding to each combination of fuzzy variables A, ,B, is determined from a plurality of set control rules. The fuzzy variable C1 for the manipulated variable m is determined by the consequent part of the driven control rule.

Also, the grade μ of the fuzzy variables A,,B,. ,,μ,
For J, and of the antecedent part of the driven control rule.
The algebraic product is calculated for each combination corresponding to the connection, and the product of grades (hereinafter referred to as grade product), ω11′−μ4,・μ,1 (4), is determined for each driven control rule. Next, for each driven control rule, the grade product ωij
′ and the fuzzy variable C i of the consequent corresponding to this product
The member simplification function μ of j. ．． The algebraic product of , ω,
/ ·μC+ij (5) is determined, and from the sum of these and the sum of the grade product ωij', the output value m0 is determined by the following equation (6).

In the above description, the subscript 1tJ was used to explain -C, but as an example, a case will be described in which the control rules are set as shown in Table 1 in correspondence with linear control.

Table 1 The control aspects that are admonished by the control rules in Table 1 above are
For example, the four control rules for the representative points P, Q, R, and S in the figure correspond to the combinations of fuzzy variables underlined in Table 1 above, and the following four control rules are applied as shown above. Corresponds to rules (P), (Q), (r), and (S). 1F (e is Z O) and (Δe is
ZO) THEIII is IF( e is Z
O) and (Δe is NS)TI{EN m
isIF(e is N S) and(Δe i
s N S)TIIEN m isIF( e is
N S) and (Δe is Z○) THEN m
is Each of the above control rules is structured as follows for simplicity.

In other words, the membership function of the fuzzy variable is a triangular membership function as shown in Figure 8, and the grade is 1.
By setting the values at equal intervals left and right,
The fuzzy variables are arranged at equal intervals. In addition, as can be seen from Table 1 above, regularity is given to the structure of the control rules, and the control aspect by each control rule (Figure 7)
are configured to form a plane. Note that this condition is
Representative zO...(p) PS...(QI PM...('') PS...(SJ) This is when the point (et, Δet, mt) satisfies the following equation (4).

a-et+b・Δet+c-m, 10d=o・・-<'
t) [a, b, c, d are constants. Also, in this case, the number of rules driven in response to the input of control deviation e and difference Δe is is one, if it is on the network connecting the representative points there are two, and in other cases there are four.

FIG. 9 is a diagram showing a part of the membership function of the manipulated variable m when the control rule is set as described above.
In this case, the grade product ω. Substituting the previous equation (5) for calculating the algebraic product of / and the membership function μ,, 1j by the following equation ωij'・mc+ij...(5)', the output value m'' is obtained by the following equation (6)'. can be found.

For example, the fuzzy variable of the input control deviation e? AI
,A2, its grade is μ■, μAl, and the fuzzy variable of the manually generated difference Δe is B,,B2, its grade is μ
■, μ3■, then the fuzzy variables AI,
A! , Bl, B2 (AI and B
+ , A+ and Bz, At and B, , A2 and 82) by driving four control rules with antecedent parts corresponding to
Four fuzzy variables for operation lmC. ,CI■,C
Find zl, C2■.

Next, for each combination of the antecedents of the four driven control rules, the algebraic product of grades is ω■ 0μAI' μB+9 ωI2 = μ
Al'μ82? ω21 = μAt'μ
Ills ω2! = μAl1'μ! lt
seek.

Then, from the stored membership functions, four fuzzy variables C. ．． ,C. ■The value of the manipulated variable m that makes the grade of s set+ s Cz■ 1 me, z * mc
＋＋■、me、! I! me. Read z■,
This value mc, I. , me, . ■, mc. 2■m
．． ．． ■ and the grade product ω. ', ω, 2', ω2I', ω2
(2) From ', the output value m0 is determined as shown in the following equation (7).

FIG. 1 is a block diagram showing a fuzzy controller according to an embodiment of the present invention. used. In addition, the input amount is controlled iy, and is limited to a certain period of time? I
Take in and memorize the quantity y, and then calculate the i-th control III quantity Y.
For the input of i, the target value r and the stored i-1th controlled variable y. -1 and control deviation e. -, the current control deviation e! is calculated internally by the following equation (8). and the difference Δe. is required.

e5=rYieΔei=ei ei-t...(8
) The CPU t controls the RAM 1 based on the control program stored in the ROM 12a, as will be explained later.
2. The entire device is controlled while using the storage area of 2b.

The fuzzy controller of this embodiment is capable of fuzzy control of a plurality of controlled devices, and the control 4i1ffiy from each controller is input via an MPX (multiplexer) 2, and each The control amount y is ADC (
The data is converted into digital data by the A/D converter (A/D converter) 13a, and sequentially sampled and read by the CPU II. In addition, the type of controlled device is specified for the DAC (D/A converter) 13b, and the data of the determined output value m0 is sent to the DAC (D/A converter) 13b as an analog manipulated variable m.
is converted into and output to the controlled device. In addition, ADC13
a has a FIFO as a buffer memory for values converted into digital data, and the data held in this FIFO is read by the CPU II via the system bus 14.

The control rules and membership functions are input from the keyboard l5 via the keyboard interface 15a,
The input control rules and membership functions are stored in the RAM 12b in a predetermined format.

In addition, the setting contents when inputting control rules and membership functions, operation instruction information, or control amount y during control,
Data such as control deviation e, difference Δe, output value m0, etc. are 31
0 (serial 10) 16a, it is output to the CRT display 16.

In addition, the arithmetic unit 17 performs processing such as four arithmetic operations on data set from the CPUI 1.
The load on II is reduced.

The ROM 12a contains the above-mentioned equations (4), (5)', and (6).
)′ equation, equation (8), and a linear equation representing the support part of the membership function are programmed and stored in the form of a general equation, and the CPU 1 inputs the input data (
Regulation? Alternatively, each calculation is performed using the calculation result as an argument, and the calculation result is stored in a preset variable.

Next, an example of a storage format of control rules and membership functions and an example of a rule driving method will be described.

(Example of format) For a manually created control rule, for example, the condition (eisAt)t(ΔeisB1) in the antecedent part and the conclusion (
m *s Cij), control deviation e, difference Δe,
Manipulated amount m, multiple fuzzy variables A. * Bj t C
A predetermined character expression or code is associated with ij, and the condition of the antecedent part and the conclusion of the consequent part are associated and stored in the RAM 12b for each rule.

Also, the membership function has each change between the point where the grade becomes 1 and the point where the grade becomes 0 (feature point)! (control deviation e
, difference Δe, and manipulated variable m) are associated with fuzzy variables, and a plurality of fuzzy variables are associated with each variable type and stored in the RAM 12b.

Furthermore, each value of the control deviation e and the difference Δe obtained by the calculation is determined based on a predetermined control deviation e, similar to the control rule.
The control deviation e and the difference Δe are stored in correspondence with a character expression or a code indicating the difference Δe, so that the correspondence between the control deviation e and the difference Δe and the above code can be referred to.

Then, fuzzy variables and grades corresponding to the values of the control deviation e and the difference Δe are determined as follows.

By comparing the respective values of the control deviation e and the difference Δe obtained by the calculation with the values of the feature points of the menharship function, the interval to which the control deviation e and the difference Δe belong,
That is, each fuzzy variable corresponding to the value of the feature point is determined. In addition, each grade is obtained by substituting the data of the feature point for which this fuzzy variable has been determined and the value of the control deviation e or difference Δe into the general equation of the straight line, and the grade and fuzzy Remember variables.

(An example of a rule driving method) When the grades and fuzzy variables are stored for the control deviation e and the difference Δe as described above, the variable type (control deviation e or difference Δe) and the type of fuzzy variable are matched with the antecedent part of the control rule, and the fuzzy variables of the consequent part of the matched control rule are determined. On the other hand, for the grade of each antecedent part, an algebraic product is calculated, and this algebraic product and the determined fuzzy variable of the consequent part are stored in correspondence.

Then, the output value m' is obtained from the above-mentioned equations (5)' and (6)'.

FIG. 3 is a flowchart showing the CPU II control program.

When the control program is started, it prompts whether or not to perform input settings for control rules and membership functions (step S), and determines whether or not input settings are made using predetermined keys manually (step SZ). If not, specify the analog output channel, set parameters for converting human data (voltage values) to internal data (engineering values), set upper and lower limits of engineering values, set scales for graphically displaying output results, Perform manual operations for various initial settings such as setting the target value r, initializing the manipulated variable and the controlled variable (step S,), and clear the FIFO (step 34).
.

When input settings are to be made, a control rule or membership function setting operation is performed and stored in the format described above (step Ss), an initial setting operation similar to the above is performed (step S3), and the FIFO is cleared. do(
Step S4).

After clearing the FIFO as described above, array variables are set to store the name of the controlled device, fuzzy variables, grade, analog output data, etc. (step S6).

When the above step is completed, human power data is sampled from the FIFO and stored in a predetermined variable to check the human power voltage, and the human power voltage data is converted to engineering value data (step S7).

Next, the control deviation e and the difference Δe are calculated based on the above-mentioned equation (8) (step S8), and the control deviation e is calculated as described above.
and the difference Δe are converted into fuzzy variables and grades (step S.).

Furthermore, based on the control rule, the grade of the consequent part by the algebraic product of (4) 2 above is calculated for all combinations of fuzzy variables in the antecedent part (step Sho), and the rules are driven to obtain individual conclusions. (Step S11). That is, the product of the grade of the fuzzy variable of the consequent part and the member symp function value is calculated using equation (5)'.

Then, calculate the center of gravity of the multiple conclusions, that is, the output value m', using (6)'2 above (step S, 2), and add the output value m0 to the currently output set value of the manipulated variable m to create a new one. At the same time, the upper and lower limits of the set value are checked (step S13), and if there is no abnormality, the set value is converted to output voltage data, a predetermined controlled device is specified, and the DAC is
13b (step S14).

After outputting each manipulated variable to the plurality of controlled devices as described above, the process returns to step S7 and repeats the same cycle.

As described above, in the fuzzy controller of the present invention, the algebraic product of the fuzzy variables in the antecedent part of the control rule is taken.

Now, the control deviation e of the antecedent part is determined by two fuzzy variables A. Suppose that we take a value between .

At this time, the control rule is driven by the combination of fuzzy variables as shown in Table 2 below, but the sum of the consequent grades, a b + a (1- b) + b (1- a) +
It is easy to see that (1 - a) (1 - b) always equals 1.

Table 2 Therefore, the value defuzzified by the above equation (6) coincides with the center of gravity of the individual inference results of the four driven control rules.

In the above case, the antecedent part is two-dimensional (control deviation e and difference Δe)
However, it can be easily seen by mathematical induction, for example, that even if one S has n dimensions (the number of driven control rules is 2''), the sum of the grades is 1.

As described above, if an algebraic product is defined for the AND combination of the antecedents of a control rule, it can be seen that the overall inference result coincides with the center of gravity of the individual inference results.

In addition, in the above embodiment, the case where the control rules are set as shown in Table 1 is explained, but even if the control rules are set as shown in Table 1, the number of rules increases significantly as the number of control loops increases. This may result in longer calculation time. Therefore, in the case of fuzzy control that performs control in real time,
In order to shorten the control period, it is necessary to contract the control rules.

However, for example, the surface surrounded by the representative points P, Q, R, and S (Fig. 7) is a plane as explained in relation to Fig. 6, so even if the interval between the representative points is increased, the control surface will not be linear. The control rules can be reduced by reducing the number of representative points. Note that the number of control rules can be reduced to the minimum number that allows defining a plane in the control space using representative points, that is, to three.

FIG. 10 is a diagram showing a method of contracting control rules,
37 rules other than those marked with “()” in the previous table 1.
6 control rules (representative points ■～■)
Alternatively, it shows that it can be replaced with three control rules (plane inclusion A-C).

Figure 11 shows how the membership function changes as the control rule is reduced, and as the control rule is reduced, the number of fuzzy variables is reduced and the membership function becomes continuous. The interval of the variable is widened in order to

In addition, when the control rules are configured so that the representative points are in a grid shape as shown in Figure 7, the control rules that are driven by human power are four around the human power point (one on the representative point).
(1, 2 in the edition).

Therefore, in addition to the minimum three control rules required to represent a plane, one rule (exception rule) is required to define a case where none of the three rules apply.

This exception rule can be derived based on the operation output when the human power of the controller is O, taking into account the balanced state of the control system, and its representative point is as shown in Figure 12 (a). Point O
It forms a rectangular area together with the other three representative points.

Furthermore, even when reduced to six control rules, there are three fuzzy variables for each of the control deviation e and the difference Δe, as shown in Figure 12(b). can take nine control rules using the same member synoptic function, but by placing the exception rule in the center when it does not apply to six rules, we can create a structure consisting of two rectangular areas and a triangular area by seven rules. Grid-like representative points can be set in a hexagonal area.

Figure 13 shows the case where the and combination of the antecedent corresponds to the algebraic product of grades and the conventional m! FIG. 4 is a diagram showing an example of a simulation result of a step response in the case of corresponding to n-time calculation, and it can be seen that the transient response is improved by controlling by algebraic product.

[Effects of the Invention] As explained above, the present invention expresses multiple types of input amounts indicating the state of the system and the degree of operation amount of the controlled system using fuzzy variables, respectively. control rules and
A fuzzy controller in which the membership and function of fuzzy variables are set, and the manipulated variable to be output to the controlled system is determined from the fuzzy variable and its grade in the consequent part of a control rule that satisfies the antecedent part. In , the algebraic product of the grades of the fuzzy variables in the antecedent part corresponding to the input quantity is used as the grade of the fuzzy variable in the consequent part, so that the control surface surrounded by the representative points in the control space according to the control rule Nonlinear elements are no longer included, the interval between representative points can be increased while maintaining the linearity of the control surface, and the control rules can be reduced to a minimum. Further, since control rules can be set as necessary, fuzzy control can be performed.

Therefore, it is possible to obtain a fuzzy controller that is capable of fuzzy control and that can perform linear control by minimizing the number of control rules.

[Brief explanation of drawings]

Fig. 1 is a block diagram showing a fuzzy control system according to an embodiment of the present invention; Fig. 2 is a diagram showing an example of a fuzzy feed control system according to the present invention; Fig. 3 is a flowchart relating to the embodiment; The figure shows the calculation result of the algebraic product of grades in the fuzzy control of the present invention. Figure 5 shows the overall drive degree of the control rule in the fuzzy control of the present invention. Figure 6 shows the fuzzy control of the present invention. FIG. 7 is a diagram showing an example of the control surface according to the control rules in the embodiment. FIG. 8 is a diagram showing the triangular membership function in the embodiment. Figure 10 is a diagram showing a part of the menharship function in operation 1, Figure 10 is a diagram showing a method for contracting the control rule 9 in the example, and Figure 11 is a diagram showing the membership function associated with the reduction of the control rule in the example. FIG. 12 is a diagram showing an example of representative points of an exception rule for control rule reduction in the embodiment; FIG. 13 is an example of simulation results of fuzzy control according to the present invention and conventional fuzzy control. Figure 14 is a diagram showing the calculation results of the min calculation corresponding to conventional fuzzy control, Figure 15 is a diagram showing the overall driving degree of the control rule corresponding to conventional fuzzy control, and Figure 16 is a diagram showing the calculation result of the min calculation corresponding to conventional fuzzy control. Fig. 17 is a diagram showing an example of membership functions related to fuzzy control; Fig. 18 is a diagram showing an example of conventional fuzzy control; Fig. 19 is a diagram showing members in conventional fuzzy control. FIG. 20 is a diagram showing an example of the ship function. FIG. 20 is a diagram showing the relationship between control space and input/output. Figure 1 Figure 2 Figure 7 Figure e Figure 8 △e (a) 6 rules of 4@- (b) 3 rules of winding 11 Figure ○ 3 rules of 1 and the moon time Figure 13 Bi Figure 16 O ex Exit 17 Figure 18 Zo 20 ZO zO NS PS e1 Δe1 m e1 ▲e1 m e1 Δe1 m ZO PS PM Figure 19

Claims (1)

[Scope of Claims] An antecedent part consisting of a plurality of conditions expressing the degrees of input quantities of a plurality of types indicating the state of the controlled system using fuzzy variables, and an operation amount of the controlled system with respect to this antecedent part. A plurality of control rules are set, each having a consequent part that indicates the extent of the condition by a fuzzy variable, and a membership function of the fuzzy variable of the antecedent part is set, thereby providing control that satisfies multiple types of input amounts. In a fuzzy controller that determines the manipulated variable to be output to the controlled system based on the fuzzy variable and grade of its consequent based on the rule, The grade of the fuzzy variable corresponding to the degree of multiple types of input quantities is calculated, and the algebraic product of the grades of the input quantities is calculated by calculating the algebraic product of the grades of the input quantities. A fuzzy controller characterized in that the grade of a fuzzy variable in the consequent part of a control rule is satisfied.