JP3077000B2 - Tuning method of fuzzy controller - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a tuning method for a PI (proportional + integral) type fuzzy controller.

[0002]

2. Description of the Related Art In general, a membership function M (x) used in a fuzzy inference method basically has one input variable x as a horizontal axis and a fitness (or membership) t as a vertical axis. When the number of input variables is two or more, the two-dimensional membership function is defined for each input variable. Then, the value of each input variable is determined by the fuzzy inference method using the membership function of the antecedent part of the fuzzy control rule in the form of “If ~, then ...”, and a predetermined operation (usually min operation) is performed. Find the fitness that evaluated all input variables. Further, when there are a plurality of control rules, an operation for obtaining the above-mentioned degree of conformity is performed for each control rule, and the result is integrated by a predetermined operation method to obtain one conclusion.

In the control using the fuzzy inference method, for example, the following expression is used to express the deviation and the rate of change of the deviation that constitute the antecedent of the control rule and the operation amount that constitutes the consequent. Seven kinds of fuzzy labels are used,
A fuzzy set corresponding to each variable, that is, the deviation, the rate of change of the deviation, and the manipulated variable, is divided into regions represented by these labels.

PB (Positive Big): Large on the positive side PM (Positive Medium): Medium on the positive side PS (Positive Small): Small on the positive side ZO (Zero): Almost zero NS (Negative Small): On the negative side Small NM (Negative Medium): Medium on the negative side NB (Negative Big): Large on the negative side When seven types of fuzzy labels are used in this way, seven membership functions are used for the deviation and the rate of change of the deviation. Defined, and 7 × 7 = 49 control rules are required. Note that there are cases where five kinds of fuzzy labels are used by omitting the medium (PM and NM) among the above labels. In this case, five membership functions are defined for each variable, and 5 × 5 = 25 control rules are required.

[0005]

[0007] However, the fuzzy controller tuning, the fuzzy controller based on the operator and experts of experience gay
The parameters are tuned such as tuning and integration constants . This tuning is performed a number of times by thinking and error until the desired performance is achieved. However, the number of parameters is enormous even in the simplest fuzzy controller. For example, when a triangular membership function having seven fuzzy labels is used in a two-input one-output fuzzy controller, 3 (left and right width and vertex) × 7 (the number of labels) × 3
(The number of inputs and outputs) + 7 (the number of labels) x 7 (the number of labels) = 11
Two parameters must be adjusted. Therefore,
Since the tuning of the fuzzy controller requires a great deal of work and time, it is important to determine which parameters are important, in what order, and how.

SUMMARY OF THE INVENTION It is therefore an object of the present invention to provide a fuzzy controller tuning method that can reduce the number of steps and time required to find the optimal value of a fuzzy controller parameter.

[0007]

According to the present invention, in a tuning method of a proportional-integral (PI) type fuzzy controller, a scale factor of a membership function is determined based on a gain and an integration constant of the fuzzy controller.
The top value of the membership function for which the scale factor is determined is the first zone in which the control deviation is small and the control deviation is small, and the control deviation is large on the negative side and the control deviation is small. The second zone is a region in which the control deviation can be from 0 to a large value on the positive side, and the third zone is a region in which the control deviation is large on the positive side and the variation of the control deviation can be from 0 to a large value on the negative side. Determined based on the zone
Fuzzy control rules are based on scale factors and vertex
The value is determined based on the determined membership function .

In the present invention , the fuzzy control rules are:
The first zone, which is a specific area of the fuzzy label,
Can be determined for each of the second zone and the third zone
You .

[0009]

According to the present invention, first, the scale factor of the membership function, by determined <br/> constant from the gain Kp and the integration constant Ti, may define all of the fuzzy labels of membership functions. For this reason, the conventional PI control
Operators have membership based on their experience
Determine the scale factor of the function. Then the members
The vertex values of the membership functions, first, second, by <br/> determined from the third zone, it can be determined here only definition of the fuzzy label. Where the first zone is the deviation and
Since both deviation changes are small and close to the target value, the control system
Related to stability. In the second zone, the deviation is negative.
Is large on the positive side and the variation of the control deviation is large from 0 to the positive side
Corresponding to rules that can take values, the third zone is the deviation
Is large on the positive side and the change in the control deviation is large from 0 to the negative side.
Controls both zones according to rules that can take up to threshold
Related to the responsiveness of the system. Finally , scale factors and peaks
A fuzzy control rule is determined based on the membership function for which the point value has been determined . According to an embodiment of the present invention,
The determination of the fuzzy control rules above depends on the characteristics of the fuzzy labels.
The first zone, the second zone and the third zone
This can be done on a per-session basis.

[0010]

In FIG. 1, if the operator has experience in controlling a PI type fuzzy controller, an initial value of a scale factor is determined based on the experience (steps S1 and S2). Equation (4) described below
According to (5) and (5), the initial value of the scale factor is set to the gain Kp
And the integration constant Ti (steps S1 and S1).
3). Here, seven types of fuzzy labels PB, PM, PS, ZO, as shown in FIGS. 2A and 2B, respectively.
When a standard membership function of NS, NM, NB and a triangle is set, this function has the following conditions.

[0011] is a triangle continuous function of symmetrical. Each adjacent fuzzy label PB, PM, PS, ZO, NS, N
The peaks of the membership functions of M and NB are equally spaced.

Each fuzzy label PB, PM, PS, Z
The half value of the O, NS, NM, NB membership functions is equal to the distance between the peaks of each adjacent membership function.

The peak of the fuzzy label ZO is "0".

By specifying the scale factor in accordance with the above conditions, the membership functions of all fuzzy labels can be determined. In this embodiment, the peak value of the membership function of the fuzzy label PB is defined as the scale factor. Then, when using two conditions and one conclusion, the following three scale factors can be specified.

Se: Scale factor of membership function of control deviation e Sd: Scale factor of membership function of change Δe of control deviation e Su: Scale factor of membership function of change Δu of operation amount Standard speed In the type fuzzy controller, input (deviation e and deviation change Δe) and output (operation amount change Δu)
Can be approximately expressed by the following equation (1). By integrating equation (1), equation (2) is obtained.

Δu (t) / Su = Δe (t) / Sd + e (t) / Se (1) where −Se <e (t) <Se, −Sd <Δe (t) <Sdu (t) ) = Su {e (t) / Sd + ∫e (t) dt / Se} = (Su / Sd) {e (t) + (Sd / Se) ∫e (t) dt} ... (2) For example, In FIG. 2, fuzzy label PB = 3, PM
= 2, PS = 1, ZO = 0, NS = 1, NM = 2, NB
= 3 and scale factor (PB membership function
Is assumed to be 3. First, fix the deviation e
When only the variation Δe of the deviation is changed,
The change Δu changes proportionally and continuously in accordance with Δe.
You. For example, when Δe changes to 3, 2, and 1, Δu also becomes
It changes to 3,2,1. In addition, the variation Δe of the deviation is fixed.
When only the deviation e is changed, the change amount Δu of the operation amount is obtained.
Varies proportionally and continuously with e. And
Both the deviation e and the variation Δe of the deviation are the variation Δu of the manipulated variable.
Equation (1) approximately holds. Fuzzilla
The bell and scale factor are defined for each of the input and output variables.
It is related to each other and adopts the control rule of FIG.
As long as equation (1) can be approximately established as in the above example.

Meanwhile, in PI control, Ru control law is used as shown in the following equation (3). That is, Equation (3) is
Represents the input / output relationship of your controller. u (t) = Kp {e (t) + (1 / Ti)} e (t) dt} (3) When this equation (3) is compared with the above equation (2), Kp = Su / Sd ... ( 4) Sd / Se = 1 / Ti, therefore Ti = Se / Sd here
Where the unit of Se is the process value and the unit of Sd is (process
Value / sampling cycle), the unit of Ti is
The unit time is given by the following equation. Ti = (Se / Sd) × (sampling cycle) (5) In standard fuzzy control, scale factors Su and S
The relationship between d and the gain Kp can be expressed by the above equation (4). Further, since the unit of the variation Δe of the deviation in the equation (4) is [PV / sampling timing], the relationship between the scale factors Se and Sd and the integration constant Ti is expressed by the above equation (5).
Can be represented by As described above, equations (2) and (3)
From the integration effect by the integration constant Ti and the gain Kp
Figure 2 shows the relationship between the increase and decrease of the scale factor.
Is done. In other words, tuning the scale factor (Figure
The first step S4) is, for example, from the response waveform at the time of adjustment.
The integration constant Ti or gain Kp should be increased or decreased.
Judgment and decision to increase or decrease the scale factor
become. The initial value of the scale factor is based on control experience.
Alternatively, it is determined by the above equations (4) and (5). Further, the control deviation e and the variation Δe of the deviation are respectively -Se <e (t)
If the output changes within the range of <Se, -Sd <Δe (t) <Sd, the output (change Δu of the operation amount) can change in response to the change of the input, but exceeds this range. And cannot be increased or decreased any further,
When specifying the magnitude of the scale factor, the range of the control deviation e of the control target and the variation Δe of the deviation must be considered.

Therefore, considering the above, step S3
Can be represented as shown in FIG. 3 (step S4). In FIG. 3, when the scale factor Se of the deviation e increases, the change range of the deviation e becomes
As a result , the integration constant Ti increases . When the scale factor Sd of the variation Δe of the deviation e increases, the variation Δ
When the change range of e increases , the integration constant Ti decreases , the gain Kp decreases, and the scale factor Su of the change amount Δu of the operation amount increases, the change amount Δu increases.

Next, the relationship between the scale factor and the control performance will be described. The transfer function of a standard fuzzy controller can be expressed by the following equations (6) to (8) according to the equation (2).

Gc (s) = U (s) / E (s) = (Su / Sd) ｛E (s) + (Sd / Se) (E (s) / s)｝ / E (s) = K (S + z) / s (6) where K = Su / Sd (7) z = Sd / Se (8) According to this, the standard fuzzy controller has one pole and coordinates at the origin of the s plane. One zero is added to (−z, 0). Further, K shown in the equation (7) is proportional to the gain of the open loop. Therefore, the position of the zero point and the gain of the open loop determine the position of the characteristic root of the closed loop, and further influence the control performance of the control system.

Next, the tuning of the scale factor of the first-order lag control target will be described. When standard fuzzy control is performed on a first-order lag control target of a transfer function represented by the following equation (9), the influence of the position of the zero point on the shape of the root locus can be shown in FIG.

Gp (s) = C / (s + p) (z>p> 0, C: constant) (9) FIG. 5 shows the relationship between the position of the characteristic root and the step response in this case. The smaller the part, the faster the attenuation, and the larger the imaginary part of the characteristic root, the higher the frequency. In addition, the step response of a higher-order system often results in these various linear combinations. On the other hand, since the scale factor Su of the change amount Δu of the operation amount is proportional to the gain of the open loop according to the equation (7), the position of the root due to the magnitude of the change amount Δu of the operation amount and the control performance are further reduced. Is understood from FIG. Since the relationship between the control deviation e and the scale factor of the variation e of the deviation e and the root position can be shown in FIGS. 6 and 7, respectively, the scale factor and the control performance of the fuzzy controller to be controlled by the first-order lag system are shown. Relationship can be easily known.

Next, the tuning of the scale factor of the control target of the second-order lag system will be described. When standard fuzzy control is performed on a second-order lag system controlled by a transfer function as shown in the following equation (10), the influence of the position of the zero point on the shape of the root locus can be shown in FIG. The magnitude of the change Δu in the operation amount affects the control performance.

Gp (s) = C / (s + p1) (s + p2) (10) where z>p1>p2> 0 and the relationship between the control factor e and the scale factor of the change Δe of the error e and the root position. Can be shown in FIGS. 9 and 10, respectively, so that the relationship between the scale factor and the control performance of the fuzzy controller to be controlled by the secondary delay system can be easily known.

Returning to FIG. 1, once the scale factor is determined, the width value of the membership function of the output variable is determined in step S5. Here, the “width value” is the membership
Line and base extending vertically from the vertex of the triangle to the base
It means the length from the intersection with the side to the side point (end) of the base.
For example, in the input / output relationship shown in FIGS. 11A and 11B, both have two rules.

Rule 1: If input = a1, then output = b1 Rule 2: If input = a2, then output = b2 However, the width value shown in FIG. The width value shown in FIG.
It is narrower than the width value shown in FIG. That is, FIG.
11 changes continuously according to the change of the input value, and the output value shown in FIG. 11B changes stepwise according to the change of the input value. Because they are similar, there is no point in using fuzzy logic. here
"Output value" is the value of the output variable (change amount of operation amount Δu)
Say. As shown in FIG. 11A, the membership function
In the region where
, The output value fluctuates.
As shown in (b), the region where the membership functions overlap is
In a few cases, the membership function of one input variable
Only the input area where only
The fitness of a particular output membership function changes,
Since only the product changes, the
The output value is almost constant. Therefore, it is desirable to use the interval between the corresponding vertices as the width value of the membership function of the input variable.

Next, the width value of the membership function of the output variable
Will be described with reference to FIG. FIG. 12 (a)
Indicates the corresponding output value if the fitness is "1" using the membership function of the asymmetric output variable. That is, the output variable is asymmetric and its output value does not match the vertex value, which is irrational. FIG.
(B) shows an output value when the conformity of the two rules is both “0.5” and their widths are not equal. That is, the output value is not in the middle of the two vertices, but rather close to a wide fuzzy label, which is undesirable. Therefore, the output variables, membership functions of equal width symmetrical desirable. In the embodiment, as described above, the scale
After determining the factor, determine the width value of the membership function
However, in the present invention, determination of the width value is not an indispensable condition.
It is only necessary that the vertex value can be determined as follows.

In FIG. 1, the stability and responsiveness of the control system are improved by tuning the vertex value of the membership function (step S6). When the fuzzy control system starts up, the fired rule draws a route that moves to a stable point where both the deviation e and the variation Δe of the deviation become zero, as shown in FIG. Therefore, when the rules are zoned as shown in FIG. 14, the rule of the zone “0” in the center of the figure shows that the deviation e and the variation Δe of the deviation e are small and close to the target value. It is related to stability such as time. An area having a small control deviation and a small change in the control deviation, such as the zone “0”, is defined as a first area.
Zone.

The rules for zones "1" and "3" shown at the upper right and lower left in FIG. 14 correspond to rules having a large deviation e and are used at the time of rising. These relate to the responsiveness of the control system. As in the zone “1”, the control deviation e is large on the negative side and the change amount of the control deviation △
A region where e can take a value from 0 to a large value on the positive side is defined as a second zone, and as in zone “3”, the control variable e is large on the positive side and the variation Δe of the control deviation is from 0 to the negative side. A region that can take a large value is set as a third zone. Here,
Tuning the vertex value of the membership function
By changing the vertex position (vertex value) of the baship function
is there. For example, FIG. 12A shows the membership function
The vertex value is tuned to a position closer to the left from the center
ing. In other words, the tuner of the vertex value of the membership function
In FIG. 2B, the membership function of PM
The vertex value of PB closer to the PB side and closer to the PS side.
Or so that the value of the membership function is 1.0 or less
This is achieved by lowering the vertex value to FIG.
Zones "2", shown at the lower right and upper left, respectively,
Since the rule of "4" is hardly used, tuning has little practical meaning.

Therefore, in step S7 shown in FIG. 1, the control rule for each fuzzy label is changed to a specific area (zone).
Tuning to improve the stability and responsiveness of the control system. Here, the tuning of rules for each fuzzy label
NB, NB defined in the table of FIG.
This is realized by changing the label such as M. This place
In this case, as described above, 3 (left and right width and vertex) × 7 (label
Number) x 3 (number of input / output) + 7 (number of labels) x 7 (label
Number) = the latter half of this formula out of the adjustment of 112 parameters
7 (the number of labels) x 7 (the number of labels) = 49
Adjusting the data can change such labels.
And For example, "Ife = NB and △
e = NB, Then NB corresponding to “u = NB”
The fuzzy label is expressed as “Ife = NBand Δe = N
B, The fuzzy of NM corresponding to Δu = NM ”
It is to change to a label. In addition, control system stability and
In order to improve the responsiveness, the first zone, the second zone
Change the fuzzy label for each zone and third zone
No. Among the membership functions of the deviation e, for example, PS, N
When the vertex value of the fuzzy label corresponding to a small deviation as in S is changed, the change is made in zones “0”,
Affects the rules for "2" and "4", but for zones "2" and
Since the rule of "4" has little meaning in practical use, it actually affects only the rule of zone "0", and thus affects the stability of the system. Also, for example, the vertex value of a fuzzy label corresponding to a large deviation such as PB and NB is
When you make changes, the changes will be "1", "2", "3",
Affects the rule of “4”, but of zones “2” and “4”
The rules are not very meaningful in practice, so in practice zones
Affects only "1" and "3" and therefore the speed of the system
Affects responsiveness. Therefore, by determining the peak value of the deviation e, the responsiveness and stability of the system can be independently adjusted. That is, if the control rule of the zone that affects the stability is changed, only the stability is affected. If the control rule of the zone that affects the responsiveness is changed, only the responsiveness is affected. However, in FIG. 14, the vertex values of the membership functions of the variation Δe of the deviation e and the variation Δu of the manipulated variable are the zone “0” as the first zone and the zone “1” as the second zone. Or the third zone, zone "3", at the same time, so that the stability and the responsiveness cannot be adjusted independently, ie separately. By changing the control rules as described above, the responsiveness and stability of the system can be improved.

According to the above embodiment, when the scale factor of the membership function is changed as shown by the black and white reversal in FIG. 15, all the fuzzy labels PB and PB of the membership function are changed as shown in FIG. PM, PS,
Since the definitions of ZO, NS, NM, and NB always change and affect the antecedent and consequent parts of the fuzzy rule, first determine the scale factor of the membership function.

When the vertex value of the membership function is changed, only the definition of the fuzzy label changes, and only the rules related to the fuzzy label are affected. Therefore, the vertex value of the membership function is determined next. In addition,
One vertex value of the input membership function is shown in FIG.
As shown in (b), the rule of one row or one column is affected, and one vertex value of the membership function of the output is calculated as shown in FIG.
As shown in (c), it affects the corresponding rule in the rule table.

Since the width value of the membership function affects the interpolation performance of the corresponding vertex value, it is determined before the vertex value, and the fuzzy control rule is set as shown in FIG. It only affects the final decision.

[0034]

As described above, according to the present invention, when obtaining the optimum value of the parameter of the fuzzy controller,
Since the scale factor, the vertex value, and the fuzzy control rule of the membership function are determined in order from the one having the largest influence to the one having the smallest influence, the manpower and time can be reduced. The present invention also considers the stability and quick response of the control system.
Membership relationship based on three zones
It decides the vertex value of numbers and the control rules
In the output characteristic with respect to input fluctuation,
Small hunting, excellent stability,
Fast parameters can be determined, and it has excellent responsiveness
Has the effect. The above stability and responsiveness are especially important for processes
This is a very important characteristic in the control system.
Since the present invention is indispensable for driving efficiently,
Very effective control when applied to access control systems.
Can be achieved.

[Brief description of the drawings]

FIG. 1 is a flowchart for explaining an embodiment of a fuzzy controller tuning method according to the present invention.

FIG. 2 is a diagram showing fuzzy labels and their membership functions.

FIG. 3 is a diagram showing an operation of determining a scale factor of a membership function.

FIG. 4 is a diagram showing the influence of the position of a zero point on the shape of a root locus when standard fuzzy control is performed on a first-order lag system control target.

FIG. 5 is a diagram showing a relationship between a position of a characteristic root and a step response in the case of FIG. 4;

FIG. 6 is a diagram showing a relationship between a control deviation and a position of a characteristic root in the case of FIG. 4;

FIG. 7 is a diagram showing a relationship between a change amount of a control deviation and a position of a characteristic root in the case of FIG. 4;

FIG. 8 is a diagram showing the influence of the position of a zero point on the shape of a root locus when performing standard fuzzy control on a second-order delay system control target.

FIG. 9 is a diagram showing a relationship between a control deviation and a position of a characteristic root in the case of FIG. 8;

FIG. 10 is a diagram showing a relationship between a change amount of a control deviation and a position of a characteristic root in the case of FIG. 8;

FIG. 11 is a diagram showing vertex values of a membership function.

FIG. 12 is a diagram showing width values of membership functions of output variables.

FIG. 13 is a diagram showing a route when a fuzzy label is stabilized.

FIG. 14 is a diagram showing a fuzzy label that is zoned.

FIG. 15 is a diagram showing the degree of influence of each parameter of a membership function.

Continuation of the front page (56) References JP-A-3-242730 (JP, A) JP-A-2-91701 (JP, A) JP-A-3-78003 (JP, A) JP-A-2-138603 (JP) , A) Maeda Mikio and one other, "Self-adjustment fuzzy controller", Transactions of the Society of Instrument and Control Engineers, Transactions of the Society of Instrument and Control Engineers, February 1988, Vol. 24, No. 2, p. 191- 197 (58) Field surveyed (Int. Cl. ⁷ , DB name) G05B 13/02 G06F 9/44

Claims (2)

(57) [Claims] 1. A method for tuning a fuzzy controller of a proportional or integral type , wherein a scale factor of a membership function is determined based on a gain and an integral constant of the fuzzy controller.
Is the vertex values of the membership functions scale factor is determined, first zone control deviation is also small area variation of the small and the control deviation, variation of the large and the control deviation control deviation is negative side The second zone is a region in which the control deviation can be from 0 to a large value on the positive side, and the third zone is a region in which the control deviation is large on the positive side and the variation of the control deviation can be from 0 to a large value on the negative side. Determined based on the zone , the fuzzy control rules are based on the scale factor and the
Vertex values are determined based on the determined membership function.
Is, fuzzy controller tuning method, characterized in that. 2. The fuzzy control rule according to claim 1, wherein the fuzzy control rule is determined for each of the first zone, the second zone, and the third zone, which are specific areas of a fuzzy label . How to tune a fuzzy controller.