JP2845077B2 - Sheet shape control method for sheet rolling - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a sheet shape control method in the field of sheet rolling, and more particularly to an improvement of an automatic shape control method based on a shape detector output of a rolling equipment having a plurality of shape control mechanisms.

[0002]

2. Description of the Related Art Conventionally, as automatic control of a sheet shape in sheet rolling, a feedback control method for performing an arithmetic process based on an output from a shape detector arranged on an output side of a rolling mill and operating a shape control mechanism is known. It is. In recent years, the requirements for the sheet rolling shape have become more severe, and as a result, a rolling mill having a plurality of shape control mechanisms has been developed, and an automatic shape control arithmetic processing logic for operating the plurality of shape control mechanisms has been proposed. As the shape control arithmetic processing logic, for example, the output of the shape detector is approximated to a fourth-order power series, or approximated to a fourth-order orthogonal function, and the coefficients of the approximate expression (two each for a symmetric component and an asymmetric component) ) Or
A logic for calculating the optimal operation amount of a control device having the same number as the number of variables using shape evaluation variables (two each for a symmetric component and an asymmetric component) calculated from the coefficients is disclosed in, for example, Japanese Patent Application Laid-Open No. 54-150066. Gazette, JP-A-55-194
No. 01 and JP-A-55-42144.

[0003] However, the plate shape control method disclosed in these publications has the following problem (1). Problem (1): There is a limitation in approximation of the actual shape, and even if the degree of approximation is improved, only a few points in the plate width direction are noticed and the shape at other points becomes unknown. Limited recognition. Further, when a certain shape control device has reached the operation limit, it is necessary to set another control amount calculation formula, and all the control devices cannot be used effectively. As a means for solving the above problem (1), the present applicant is not limited to approximation of the actual shape, and even if the control device reaches the operation limit, the common operation logic of the remaining operable control devices is shared. The shape control logic used is disclosed in Japanese Patent Application Laid-Open No. 59-218206.

However, the control method disclosed in the above publication is not always satisfactory, and has the following problem (2). Problem (2): Unless the number n of operation terminals that can be controlled simultaneously is equal to or less than the number m of shape variables to be controlled, an optimum solution of the operation terminals cannot be obtained. That is, m <n
When, the solution is not obtained. Therefore, when m <n, all the control mechanisms of the rolling mill cannot be effectively used simultaneously.
Therefore, in order to solve the above problem (2), Japanese Patent Laid-Open Publication No. HEI 9-214400 discloses a method of adding a logic for selecting the same number of devices as control variables from among a plurality of control devices as control logic of a rolling mill having a large number of control devices. In 2-142607,
Further, when a previously selected shape control mechanism reaches an operation limit, a method of adding another logic for calculating an optimal operation amount of the remaining control mechanism is disclosed in Japanese Patent Application Laid-Open Nos. No. 63-177910, respectively.

[0005]

However, the conventional plate shape control method for solving the above problems (1) and (2) also has the following problems (3) to (5). Problem (3): It is necessary to sequentially select the control capabilities of the individual shape control devices depending on the shape failure state, and complicated logic is required to select the optimum shape control device. As a result, a great deal of time is required for the calculation, and the response is restricted. In addition, there is a risk of selecting a combination having a small effect.
Therefore, it is not an effective solution to the conventional problems. Problem (4): All of the above control logics are logics for giving the optimum operation amount of each operation end to make the controlled shape coincide with the target shape, and the actual operation amount for each control step is the calculated optimal amount. The value obtained by multiplying the operation gain in the solution is used. Therefore, it is necessary to independently set the logic for setting the gain, and the calculation becomes very complicated. Problem (5): Generally, when the operation end position of the shape control device reaches the limit, the degree of freedom of the control device of the rolling mill decreases, so that the shape correction ability is reduced and the shape defect is sufficiently controlled. I can't. It is extreme when a shape control device having a high shape correction capability reaches the operation limit. Therefore, it is desirable that each shape control device of the rolling mill be used in the movable range of the operation end that does not reach the operation limit. However, the above logic is a response logic after the shape control device reaches the operation limit, and in order to maintain appropriate control ability, it is predicted that the operation limit will be reached, and it is avoided before reaching the limit. Logic is needed.

The present invention has been made in view of the above circumstances, and has been made to solve the above problems (3) to (5). The number of control variables (degree of function approximation) and the number of shape control devices are different. There is no restriction at all, and all the shape control mechanisms of the rolling mill can be operated effectively at the same time, and even if a certain shape control device reaches the operation limit, the actual optimum value for each control step is It is an object of the present invention to provide a general-purpose sheet shape control method for sheet rolling in which a control operation amount can be obtained. Another object of the present invention is to quantitatively evaluate the possibility of the operation end position of a certain shape control device before reaching the limit, and evaluate the quantitative evaluation value and the operation limit of another shape control device. A general-purpose method that determines the weighting factor of the operation amount of each shape control device of the rolling mill according to the similarity to the mutual shape control effect and the control device operation amount that is less likely to reach the operation limit It is an object of the present invention to provide a method for controlling a shape of a thin sheet rolling.

[0007]

According to a first aspect of the present invention, there is provided a sheet shape control method for a thin plate rolling, comprising: a shape detector capable of detecting a shape at a plurality of positions in a rolled sheet width direction; In a sheet shape control system for sheet rolling having an arithmetic processing unit, an output distribution of the shape detector, a target shape distribution, and an output change of the shape detector with respect to a unit operation amount of the plurality of shape control mechanisms, Position x in plate width direction
A step represented by a first function, a second function, and a third function as a function of the first function, and a second function and a third function from the first function.
The step of creating a first evaluation function by integrating the square value of the value obtained by subtracting the above function at the position x in the plate width direction, and the operation amount of each of the plurality of shape control mechanisms for each control step. It is expressed by the sum of squares of the manipulated variable with the coefficient, which is obtained by multiplying each of the coefficients in consideration of the degree of the shape change by the control mechanism and each of the weight coefficients set so that the sum of the respective weight coefficients becomes 1. Creating a second evaluation function, and setting a first weighting factor and a second weighting factor for determining an arbitrary ratio between the first evaluation function and the second evaluation function, respectively, Creating a shape evaluation function that is a sum of a product obtained by multiplying the first evaluation function and the first weighting coefficient and a product obtained by multiplying the second evaluation function and the second weighting coefficient;
Calculating an operation amount of each of the plurality of shape control mechanisms so as to minimize the shape evaluation function of the sum of products.

According to a second aspect of the present invention, there is provided a method for controlling the shape of a thin-rolled sheet according to the first aspect of the present invention, wherein a root-mean-square value of a deviation from a target shape is calculated.
Based on the magnitude relationship between the calculated value and the first reference value and the magnitude relationship between the amount of change in the control value for each control step and the second reference value, the first weighting factor, the second weighting factor, Is variably set.

According to a third aspect of the present invention, there is provided a method for controlling the shape of a thin plate according to the first or second aspect of the present invention. The possibility of reaching the position limit is individually calculated, and the calculated degree of possibility of the operation limit of each shape control mechanism, the degree of possibility of the operation amount limit of other shape control mechanisms, and mutual shape control are calculated. Considering the similarity to the effect,
The method further includes a step of setting a weight coefficient of an operation amount of each of the plurality of shape control mechanisms constituting the second evaluation function.

[0010]

According to the first aspect of the present invention, there is provided a sheet rolling control system for a thin plate rolling comprising a shape detector capable of detecting a shape at a plurality of positions in a rolled sheet width direction, a plurality of shape control mechanisms, and an arithmetic processing unit. In (1) an output distribution of the shape detector, a target shape distribution,
The output change of the shape detector with respect to the unit operation amount of the plurality of shape control mechanisms is represented by a first function, a second function, and a third function, respectively, as a function of the position x in the plate width direction,
A first evaluation function Φ ₁ is created by integrating a square value of a value obtained by subtracting the second function and the third function from the first function at the position x in the plate width direction. The [Phi ₁ is a function for evaluating the plate-shaped deviation across the strip width. (2) Next, the operation amount of each of the plurality of shape control mechanisms for each control step is set such that the sum of the coefficients in consideration of the degree of shape change by each control mechanism and the respective weighting coefficients becomes 1. each weighting factor obtained by multiplying respectively, to create a second evaluation function [Phi ₂ represented by the sum of squares of the coefficients with operation amount. This Φ ₂ is a function representing the operation amounts of the plurality of shape control mechanisms by the shape change amount, and is an evaluation function defined by the magnitude of each operation amount for each control step. (3) Finally, a first weighting factor that determines the first evaluation function [Phi ₁ and the second in any proportion of the cost function [Phi ₂ g ₁ and the second
Set weighting factors g ₂ and, respectively, a product obtained by multiplying the first evaluation function [Phi ₁ and the first weight coefficient g _1, the second evaluation function [Phi ₂ and the second weighting factor g ₂ An optimal operation amount is obtained by creating a shape evaluation function that is a sum of a product obtained by multiplying the product and the operation amount of each of the plurality of shape control mechanisms so as to minimize the shape evaluation function of the product sum. Things.

According to a second aspect of the present invention, in the first aspect of the present invention, a root mean square value of a deviation from a target shape is calculated, and a magnitude relationship between the calculated value and a first reference value is calculated. The ratio between the first weighting factor and the second weighting factor is variably set based on the magnitude relationship between the amount of change in the calculated value for each control step and the second reference value. As a result, the weights of the first evaluation function for evaluating the shape deviation and the second evaluation function for evaluating the operation amount can be freely changed.

In the invention according to claim 3, in the invention according to claim 1 or 2, the possibility of reaching the limit of the operation end positions of the plurality of shape control mechanisms is individually calculated by fuzzy inference, In consideration of the calculated degree of possibility of the operation amount limit of each shape control mechanism, the degree of possibility of the operation limit of other shape control mechanisms, and the similarity to the mutual shape control effect, A weight coefficient of the operation amount of each of the plurality of shape control mechanisms constituting the evaluation function of No. 2 is set. As a result, it is possible to calculate an optimal operation amount such that each shape control mechanism does not reach the operation limit.

[0013]

DESCRIPTION OF THE PREFERRED EMBODIMENTS The logic of the plate shape control method according to the present invention will be described. A. First, as a method for solving the problems (1) and (2), a shape evaluation function Φ ₁ disclosed by the present applicant in Japanese Patent Application Laid-Open No. Sho 59-218206 is used. First explaining the introduction of the evaluation function [Phi _1. This Φ ₁ represents the output distribution of the shape detector, the target shape distribution, and the output change of the shape detector with respect to the unit operation amount of the shape control mechanism as a function of the position in the plate width direction, and from these functions, the entire plate width is obtained. This is an evaluation function for evaluating a crossing plate shape, and will be described in detail below. Now, the output of the shape detector for detecting the shape at a plurality of positions in the width direction of the rolled sheet is Y, and the output distribution is Y (x).
(Where x is a position in the plate width direction) and the target shape distribution is Y ^* (x), Y (x) and Y ^* (x) can be series transformed by an orthogonal polynomial. (1),
It is represented by (2).

[0014]

(Equation 1)

[0015]

(Equation 2)

Here, a _i and a _i ^* are expansion coefficients of the function approximation by the orthogonal function φ _i (x), and m is the highest order of the function approximation. The control characteristics of the shape control device,
That is, the output change ΔY _j (x) of the shape detector with respect to the unit operation amount of each shape control device j is measured in advance, and when this is converted into a function, it is expressed by the following equation (3).

[0017]

(Equation 3)

Here, b _ij is a function approximation expansion coefficient of a value obtained by partially differentiating Y (x) with δ _j by the orthogonal function φ _i (x),
That is, the rate of change for the [delta] _j of a _i (shape influence coefficient), the operation amount of [delta] _j is an arbitrary shape control apparatus, j is an arbitrary shape control unit (j = 1 to n), m is the best function approximation Degree,
n is the number of shape control devices.

Next, a function expressed by the following equation (4) is defined as a function for evaluating the shape.

[0020]

(Equation 4)

Here, w is a plate width dimension. Evaluation function [Phi ₁ defined by Equation (4) corresponds to the square of the deviation between the actual shape and a target shape after operating the certain shape control device, to make the [Phi ₁ minimizes, the target actual shape It will approach the shape. Moreover, the [Phi ₁ is a function to evaluate all output in the plate width direction of the shape detector, the evaluation function of the shape deviation which does not give any restriction to the real shape recognition.

B. Next, as a method for solving the above problems (3) and (4), in the present invention, as a new evaluation function, a coefficient in consideration of the degree of shape change is added to the operation amount for each control step of each control mechanism. In addition, an operation amount evaluation function Φ ₂ represented by a sum of squares of values weighted by the respective weight coefficients set so that the sum of the respective weight coefficients becomes 1 is introduced. The above evaluation function Φ ₂ is shown in the following equation (5).

[0023]

(Equation 5)

Here, w _j is a weight coefficient of the shape control device j, and the sum of _n weight coefficients (w ₁ , w ₂ ... W _n ) is 1
It is. In this equation, the square root of the sum of squares of the shape change coefficient with respect to the unit operation amount is used as a coefficient in consideration of the degree of the shape change. The function Φ ₂ shown in (5) is
This is a function in which the operation amounts δ _j of the plurality of shape control devices j are represented by the shape change amounts, and is an operation amount evaluation function defined for each control step by the magnitude of the operation amount of each control device. It is possible to control the operation amount of the control devices by the [Phi _2. Also, if you want to actively changing the ratio of the operation amount of the shape control device becomes easy to cope with only by changing the value of the weight coefficient w _j.

C. In the present invention, as a means for solving the problem (5), the operation end position of the shape control device and the operation increment per unit control step are used as an evaluation index,
A step of quantitatively evaluating the possibility that each shape control device reaches the operation limit, and the quantitative evaluation index, and rolling based on the state of reaching the operation limit of other shape control devices and the similarity to the mutual shape control effect, Setting a weight coefficient of the operation amount of each shape control device of the machine, and deriving a shape evaluation function for calculating an optimal control amount based on the ratio, so that each shape control device does not reach the operation limit. Calculating an optimal operation amount. Hereinafter, this will be described in detail.

In the present invention, as a method for solving the problem (5), the operation amount of the shape control device j in the operation amount evaluation function Φ ₂ presented as a means for solving the problems (3) and (4) is used. the weighting factors w _j, by setting in consideration of the possibility of reaching the operating limits, without shape control device reaches easily operating limits, it is possible to maintain adequate control capability. The logic of the plate shape control method will be described below. C (1). In the present invention, the operation end position and the operation amount increment per unit control step are expressed as fuzzy amounts as evaluation indexes, fuzzy inference is executed, and the possibility that the operation amount of each shape control device of the rolling mill reaches the limit is determined. evaluate. The steps will be described below. As described above, the degree of the possibility of reaching the limit of the operation amount of the shape control device j depends on the operation end position U _j of the shape control device _j and the operation increment d per unit control step.
It is determined from the two evaluation indices of U _j by fuzzy inference.

The following (1) to (3) show a part of the fuzzy inference rules. (1) close to the upper limit value of the operation end position U _j is large operation amount, if the operation increments dU _j is large negative per unit step, the possibility of operation terminal position U _j reaches the operation limit in the medium is there. (2) close to the upper limit value of the operation end position U _j is a bit operation amount, if the operation increments dU _j slightly negative per unit step, it is unlikely that the operation end position U _j reaches the operation limit. (3) close to the lower limit value of the operation end position U _j is a bit operation amount, if the operation increments dU _j is large negative per unit step, it is highly likely that the operation end position U _j reaches the operation limit.

Using such a fuzzy inference, evaluation indexes required to determine the possibility _Sj of reaching the operation limit of the shape control device j are defined using membership functions, respectively. FIG. 4 is a diagram illustrating an example of a membership function of a fuzzy variable relating to an operation amount of the shape control device. FIG. 9A shows the operation end position U _j of the shape control device _j.
Shows the membership function of the fuzzy variables of “LB”, “LS”, “MD”, “HS”, “HB” in the figure, where L is low.
That is, MD represents the lower limit of the operation end position, MD represents middle, that is, the middle position of the operation end position, H represents high, that is, the upper limit of the operation end position, and B and S represent big and s, respectively.
represents the degree of magnitude compared to the upper and lower limit values of the operation end position. FIG. 9B shows the membership function of the fuzzy variable of the operation increment dU _j per unit control step, and [NB, NS, ZR, PS, PB] in the figure.
Among them, N represents negative in negative, P represents positive in positive, and ZR is zero.
The meanings of B and S are the same as those in FIG.

Further, a quantitative value _Sj indicating the degree of possibility of reaching the operation limit of the shape control device j is defined by a membership function, and FIG. 9C shows an example of this. In this figure, B is big, M is middle,
S represents small. Using the above parameters,
As a general expression of an inference rule, for example, the above-described inference rule (1) can be expressed as follows. “IF U _{jis
HB and dU j is NB, then} S j
is middle. Table 1 shows an example of the inference rule.

[0030]

[Table 1]

[0031] Based on the fuzzy inference rule performs fuzzy inference operation, determining the likelihood S _j to reach the limit of the operation end position U _j shape control device j. In the fuzzy inference operation, a quantitative value _Sj is calculated by applying a centroid method to an inference result obtained by simultaneously applying a plurality of inference rules.

Although the above-mentioned solution uses fuzzy inference, it is also possible to define and determine another function that relates the operation end position U _j and the operation increment dU _j per unit control step to S _j. . That is, the quantitative evaluation index indicating the possibility that the shape control device j reaches the operation limit is generally represented by the following equation (6).

[0033]

(Equation 6)

In equation (6), S _j is the shape control device j
Is a quantitative evaluation index representing the possibility of reaching the manipulated variable limit of U, U _j represents the operation end position of the shape control device j, and dU
_j represents an operation increment per unit control step of the shape control device j. f (U _j , dU _j ) represents a function relating the operation end position U _j and the operation increment dU _j per unit control step to S _j .

C (2). Next, a weight coefficient of the operation amount of each shape control device of the rolling mill is determined. Here, the quantitative evaluation index _Sj indicating the possibility that the shape control device j reaches the limit of the operation amount, and the situation of achieving the operation limit of the other shape control devices and the similarity to the mutual shape control effect. An index indicating the degree of suppressing δ _j is set. The index is determined by the following equation (7).

[0036]

(Equation 7)

Here, I _j represents the degree of suppressing the operation amount of the shape control device j (operation amount suppression index), j represents an arbitrary shape control device (j = 1 to n), and k is , Any shape control device except for the shape control device j (k = 1 to n, k ≠
j), q represents a constant for adjusting the influence of _wj on the state of reaching the operation limit of any shape control device except the shape control device _j, and _ekj represents the shape control device k (k = 1 ~ N, k
An index representing the correlation (or similarity) between the control effect on the shape by the operation amount of の j) and the control effect on the shape by the operation amount of the shape control device j, and is determined by the following equation (8). You.

[0038]

(Equation 8)

Equation (8) indicates the shape influence coefficient of the shape control device j on the shape influence coefficient vector [b _ok ,..., B _mk ] ^T of the shape control device k (where T is a transposed vector). The magnitude of the direction cosine of the coefficient vector [b _oj ,..., B _mj ] ^T is given, and this is given as an index representing the correlation of the control effect on the shape by the operation amount. Next, equation (5)
In the weighting coefficient of each shape control device in function .PHI ₂ to evaluate the operation amount set, sets the operation amount suppression index I _j is normalized. That is, the weight coefficient w _j is set by the following equation (9).

[0040]

(Equation 9)

The weight coefficient w _j of the manipulated variable of the shape control device j determined by the above method is likely to reach the limit of the operation end position of the shape control device j when determining the manipulated variable. Another shape control device k (k = 1 to n, k ≠)
When the operation end position of j) is unlikely to reach the limit and the control amount on the shape by the operation amount of the shape control device j and the operation amount of the shape control device k is relatively close, the shape control device j Reduce the amount of operation. Then, the operation amount of the shape control device k is increased, and the reduction of the operation amount of the shape control device j is complemented. (2) The possibility of reaching the limit of the operation end position of the shape control device j is low, and another shape control device k (k = 1 to n, k ≠)
If the operation end position of j) is likely to reach the limit and the operation amount of the shape control device j and the control effect on the shape by the operation amount of the shape control device k are relatively close, the shape control device j Is increased, and the reduction of the operation amount of the shape control device k is complemented.

Next, the above-mentioned two evaluation functions Φ ₁ and Φ ₂ are combined, and a shape evaluation function Φ for calculating an optimum control amount for automatic shape control is expressed by the following equation (10).

[0043]

(Equation 10)

Here, g ₁ and g ₂ are Φ with respect to Φ, respectively.
A first and a second weighting factor that determines the effect ratio of ₁ and [Phi _2, and set to any value, it is possible to further the value is variable. Minimizing Φ shown in Expression (10) is to minimize the deviation between the actual shape and the target shape of the rolled plate with the minimum amount of operation of each shape control device, and to minimize Φ The combination of the operation amounts of the respective shape control devices is the optimum control amount.

The function Φ for evaluating the shape deviation is
₁ and the coefficients g ₁ and g ₂ that determine the influence ratio of the function Φ ₂ for evaluating the operation amount are set using the following shape deviation index and the amount of change per unit step as the evaluation index. The shape deviation index is represented by the following equation (11).

[0046]

[Equation 11]

Here, Φ ^* is an index (shape deviation index) representing the shape deviation. The method of setting the coefficients g ₁ and g ₂ is as follows: (1) The shape deviation index Φ ^* and the first predetermined value
And compare the magnitude relation with the threshold value. When Φ ^* exceeds the first threshold and the shape defect is large, the shape correction speed is emphasized, the ratio of g ₁ is set higher than g ₂ , and Φ ^* is set to the first threshold. When the shape defect is reduced below, emphasis is placed on outputting a stable operation amount.
The ₂ ratio is set higher than g _1. (2) Compare the magnitude relationship between the variation ΔΦ ^{* of the} shape deviation index Φ ^* for each control step and a preset second threshold value. When ΔΦ ^* is larger than the second threshold value and the shape changes sharply, the shape correction speed is emphasized and the ratio of g ₁ is set higher than g ₂ , and ΔΦ
^* Is if you are stable shape is obtained less than a second threshold, emphasizes that output a stable operation amount, the ratio of g ₂ is set higher than g _1. Based on the comparison result of the magnitude of the (1) and (2) shows an example of how to set by changing said g ₁ and g ₂ in Figure 10 below.

FIG. 10 shows an evaluation function Φ with respect to the evaluation function Φ.
Is a diagram illustrating a setting example of a ratio g _{1 1.} Now, when the coefficient g ₁ ′ is set by the shape evaluation index Φ ^* shown in FIG. 10A and the coefficient g ₁ ″ is set by the function of ΔΦ ^* shown in FIG. 10B, g ₁ and g _{2 become} , The following equation (2
6), and are set to values calculated by equation (27). g ₁ = (g ₁ ′ + g ₁ ″) / 2 (26) g ₂ = 1−g ₁ (27)

An optimum control operation expression for the control device that minimizes Φ in Expression (10) is calculated. First, the least squares method is applied to Φ. Therefore, Φ is partially differentiated by the manipulated variable δ _j of each shape control device, and the following equation (12) where the value is set to 0 is an equation that gives the minimum value of Φ.

[0050]

(Equation 12)

Here, Φ ₁ and Φ ₂ in the equation (12) can be replaced by the following equations (13) and (14), respectively.

[0052]

(Equation 13)

[0053]

[Equation 14]

Therefore, the first term of the equation (12) becomes the equation (15).

[0055]

(Equation 15)

From the property of the orthogonal function, the following equation (16)
(17) is established.

[0057]

(Equation 16)

[0058]

[Equation 17]

Using equations (16) and (17), equation (12)
Equation (15), which is the first term, can be expressed by equation (18), and the partial differential term of the second term in equation (12) can be expressed by equation (19).

[0060]

(Equation 18)

[0061]

[Equation 19]

By substituting equations (18) and (19) into equation (12), equation (20) is obtained.

[0063]

(Equation 20)

According to the equation (20), the equation for calculating the optimal manipulated variable that minimizes Φ is the following n-element simultaneous equation (21).

[0065]

(Equation 21)

When the simultaneous equations of the equation (21) are displayed in a matrix, the following equation (22) is obtained.

[0067]

(Equation 22)

B _jk in equation (22) is expressed by equation (23) when j = k, by equation (24) when j ≠ k, and A _j is expressed by equation (25). .

[0069]

(Equation 23)

[0070]

(Equation 24)

[0071]

(Equation 25)

The formulas (21) and (22) for obtaining the optimum manipulated variable according to the present invention are not limited by the number m of control variables, but are independently determined only by the number n of control devices of the rolling mill. It is a simultaneous equation given, and is a general-purpose arithmetic expression that can uniquely determine the optimal operation amounts of a plurality of shape control devices. Here, apparently, a similar expression can be obtained assuming that Φ = Φ _{1. In} this case, however, the number of independent expressions is m, the number of control variables, and there is a limited method that can be used only when n ≦ m. Was. However, in the present invention, Φ ₂
Has been improved so that independent equations can be obtained by the number n of shape control devices. Furthermore, this Φ
_2, not only to mathematically independent simultaneous equations, and simultaneously controls all of the shape control device possessed by the rolling mill, with a physical meaning to reduce the [Phi ₁ with minimum operation amount. Therefore, according to the logic of the present invention, with minimum operation amount for each control step, to reduce the shape deviation function [Phi ₁ efficiently, so that the combination of the optimum operation amount is obtained.

Note that g ₁ and g ₂ are Φ with respect to Φ, respectively.
Since the weight factor for determining the effect ratio of ₁ and [Phi _2, by determining how the coefficient values, Which is intended to be selected whether to what extent the priority. Further, the operation logic of the optimal operation amount according to the present invention is similar to the control response and is suitable for controlling a rolling mill having a plurality of shape control devices, regardless of a cold rolling mill or a hot rolling mill. Applicable.

FIG. 1 is a diagram showing an embodiment of a plate shape control method according to the present invention. In the figure, 1 is a rolling mill,
In this example, a pair of upper and lower work rolls 3, an intermediate roll 4,
This is a 12-high cluster rolling mill having a structure in which a backup roll 5 and a small-diameter backup roll 6 are arranged in a cluster. 2 is a rolled plate, and 7 is a shape detector for detecting the shape of the rolled plate 2 at a plurality of positions in the width direction. The physical quantities detected by the shape detector 7 include, for example, tension and elongation strain. Reference numeral 8 denotes a functioning operation device that performs an operation for converting the output distribution of the shape detector 7 into a function, 9 denotes a target shape setting circuit that sets a target shape distribution of the rolled plate 2, and 10 denotes an optimal operation amount according to the present invention described above. The shape control logic to be operated is programmed, for example, and stored in a memory (ROM), and a built-in microprocessor (CPU) is obtained from input signals of the functioning operation device 8 and the target shape setting circuit 9.
Is an optimum operation amount calculating device for calculating an optimum operation amount using the stored shape control logic. The result of calculation by the optimum operation amount calculation device 10 is used as an operation command signal as a roll bending mechanism 1 as a shape control mechanism.
1. It is supplied to the backup roll crown adjusting mechanism 12 and the pressure leveling mechanism 13. Each of the mechanisms 11 to 1
3 individually controls the rolling mills 1 based on operation command signals supplied from the optimum operation amount calculation device 10.

FIG. 2 is a diagram showing a roll portion and a shape control mechanism of a rolling mill. In the figure, reference numerals 2 to 5 are the same as those in FIG. 1, and reference numerals 14, 15, and 16 denote backup roll crown adjusting mechanisms (a), (b), and (c), respectively.
7 is an intermediate roll vendor. In FIG. 2, the backup roll is divided into seven parts, and the other divided rolls are independently eccentric in the direction of the intermediate roll with respect to the fixed center part, so that an arbitrary crown pattern can be set. The intermediate roll bender 17 and the backup roll crown adjusting mechanisms (a), (b), and (c) are used as symmetrical shape control means, and a reduction leveling mechanism 13 is used as asymmetrical shape control means. have. In the following description, the backup roll crown adjusting mechanisms (a), (b) and (c) are simply referred to as shape control means (1), (2) and (3), and the intermediate roll bender 17 is referred to as shape control means. Called (4).

Table 2 below shows the number of control variables and the number of control means according to the present invention in comparison with the conventional example.

[0077]

[Table 2]

Table 2 shows that the shape control means (1) to (1) of the rolling mill 1 are based on the embodiment of FIGS.
(4) in the case of the present invention in which the number of shape control means is controlled to be equal to the number of control variables (that is, Φ
₁ only) and the control method.

FIG. 3 is a diagram showing a control result based on the comparative example of Table 1. The horizontal axis in the figure indicates the position in the sheet width direction from the center of the rolled sheet width, and the vertical axis indicates the elongation-strain difference Δε. Here, the elongation-strain difference refers to the difference between the elongation-strain at a certain reference position (for example, the zero position on the horizontal axis or the position where the elongation-strain is minimum) and the measurement position, and I-Unit is 1 (I -Unit) is 1/10 ⁵ . In FIG. 3, white circles indicate the elongation strain difference distribution before control, and black circles indicate the same distribution after control according to the present invention. When the distribution of the black circles is compared with the same distribution after control according to Conventional Examples 1 to 3, the shape control is insufficient in the conventional example, whereas the distribution of Δε is extremely small in the present invention, and the shape defect is almost zero. It can be seen that it is completely corrected and a good control result is obtained.

FIG. 4 is a diagram showing the operation amounts of the shape control means used in the example of the present invention shown in Table 2 as shape control vectors.
Similarly, FIGS. 5, 6 and 7 respectively show conventional 1 and 2 shown in Table 2.
FIG. 8 is a diagram showing the operation amounts of the shape control means used in 2 and 3 as shape control vectors. FIGS 7 a ₄ and a ₂ of the vertical axis of abscissa in indicates expression of the coefficients a _i of the polynomial in the case of the (21) 4-order polynomial i = 4 and i = 2, respectively, These two coefficients a ₄ and a ₂ are the two control variables in Table 2. The respective figures, the control characteristics in the case where a ₄ = a ₂ = 20 gives (I-Unit) as shape detecting an initial value, and controls this so that the shape target value ^{_{a 4 * = a 2 * =}} 0 The broken line vector in each figure indicates the operation amount of each shape control unit as a vector. The solid line vector in each drawing indicates a change vector of the actual shape as a vector sum of the broken line vector.

The numbers (1) to (4) given to the broken line vectors in FIGS. 4 to 7 correspond to the shape control means (1) to (4) in Table 2.
(4) is shown respectively. Conventional example 1 of FIGS.
In (3), since the number of shape control means that can be controlled simultaneously is limited to two, the same number as the number of control variables, a very large operation amount is required to control to the target shape, and the shape control means (4) Indicates that the intermediate roll bender 17 easily reaches the mechanical operation limit, the shape correction indicated by the solid line vector also reaches the limit, and the target shape cannot be achieved.

On the other hand, in the embodiment of the present invention shown in FIG. 4, all the four shape control means are simultaneously operated effectively.
Since it is not biased toward a specific shape operation means, the optimum control can be achieved without the intermediate roll bender 17 reaching the operation limit. In the example of FIG. 4, the target shape value a ₄ ^* = a ₂ ^* = 0 is achieved by _four control steps.

The shape control logic of the present invention is stored in advance as a program in a memory (ROM) in the optimum manipulated variable operation device 10 in FIG. 1, and the CPU uses the stored shape control logic in real time. Since the optimum operation amount for each control step is calculated and this calculation result is sequentially output to each shape control means as an operation command signal, a desired target shape can be easily obtained without using a complicated control device unlike the related art. Can be achieved.

FIG. 8 is a diagram showing the results of shape control before and after the implementation of the present invention. The black circle in the figure indicates the data after the implementation of this invention, are concentrated in the vicinity of said shape target value _{^{a 4 * = a 2 * =}} 0. This is because a plurality of shape control means of the rolling mill are simultaneously operated effectively, so that a target shape can be achieved in response to any shape defects. In contrast, the crosses in FIG. 5 indicate data in the conventional example before the present invention is implemented, and indicate that there is a considerable variation with respect to the shape target value and the target shape cannot be achieved.

FIG. 11 is a diagram showing the frequency of reaching the operation limit of the shape control device before and after the implementation of the present invention. According to FIG. 11, it can be seen that the frequency at which the shape control device reaches the operation limit is reduced by implementing the present invention. That is, according to the present invention, it is possible to reduce the shape defect that occurs when the operation end position of the shape control device reaches the limit, as compared with the related art. This is because, according to the present invention, considering the possibility of reaching the operation limit of the shape control device for the shape defect, the weight coefficient of the operation amount of the shape control device of the rolling mill is optimally set, and each shape control device of the rolling mill is set. It is possible to easily determine the operation amount so as not to reach the operation limit, and as a result, the shape control device can reduce the shape defect caused by reaching the operation limit as compared with the conventional method. It has become.

[0086]

As described above, according to the present invention, a sheet rolling plate having a shape detector capable of detecting the shape at a plurality of positions in the width direction of the rolled sheet, a plurality of shape control mechanisms, and an arithmetic processing unit. In the shape control system, an output distribution of the shape detector, a target shape distribution, and an output change of the shape detector with respect to a unit operation amount of the plurality of shape control mechanisms are respectively represented as functions of a position x in a plate width direction. , to create a first evaluation function [Phi ₁ to evaluate the shape of a flat plate across the plate width of these functions, also with the amount of operation of each control step of the plurality of the shape control mechanism, taking into account the degree of shape change A second evaluation function represented by the sum of squares of the weighted values and the values weighted by the individual weighting factors, and further, the first evaluation function Φ ₁ and the second evaluation function Φ
_A first weighting factor g ₁ and a second weighting factor g ₂ for determining an arbitrary ratio of ₂ are set, and the first evaluation function Φ
_A shape evaluation function, which is a sum of a product obtained by multiplying ₁ and a first weighting factor g ₁ and a product obtained by multiplying the second evaluation function Φ ₂ and the second weighting factor g ₂ , is created. Since the operation amount of each of the plurality of shape control mechanisms is calculated so as to minimize the shape evaluation function of the sum of products, the control of sheet rolling is limited by the number of shape variables and the number of shape control devices, or complicated. This eliminates problems such as adding a selection function of a plurality of control devices and requiring complicated gain setting logic for determining a control amount for each control step. By applying the optimal control logic of the present invention, it is expected that the shape quality of the product will be further improved.

Further, according to the present invention, the root mean square value of the deviation from the target shape is calculated, the magnitude relationship between the calculated value and the first reference value, the amount of change in the control value for each control step, and the second value. The first weighting coefficient g ₁ based on the magnitude relationship with the reference value
And control the ratio of an emphasis on the second set high to shape correction rate than the weighting factor g ₂ of the stable said second ratio of the weight coefficient g ₂ first set higher than the weighting factor g ₁ It is possible to freely change the control that emphasizes the output of the manipulated variable and perform the optimal control according to the shape deviation situation.

According to the present invention, the optimum operation amount weight coefficient of each shape control device is determined so that the plurality of shape control devices do not reach the operation limit, and the operation amount is calculated based on the weight coefficient. By performing the control, it is possible to reduce the occurrence of shape defects due to reaching the operation limit. Further, since it becomes possible to optimally determine the ratio of the operation amount according to the shape defect, the control ability is increased, and further reduction in the shape defect can be expected.

[Brief description of the drawings]

FIG. 1 is a diagram showing one embodiment of a plate shape control method according to the present invention.

FIG. 2 is a diagram showing a roll portion and a shape control mechanism of a rolling mill.

FIG. 3 is a diagram showing a control result based on a comparative example of Table 1.

FIG. 4 is a diagram in which an operation amount of a shape control unit used in the example of the present invention shown in Table 1 is displayed by a shape control vector.

FIG. 5 is a diagram showing an operation amount of a shape control means used in Conventional Example 1 of Table 1 as a shape control vector.

FIG. 6 is a diagram showing an operation amount of a shape control means used in Conventional Example 2 of Table 1 as a shape control vector.

FIG. 7 is a diagram showing an operation amount of a shape control unit used in Conventional Example 3 of Table 1 as a shape control vector.

FIG. 8 is a diagram showing a shape control result before and after implementation of the present invention.

FIG. 9 is a diagram illustrating an example of a membership function of a fuzzy variable relating to an operation amount of the shape control device.

FIG. 10 shows a ratio g ₁ of the evaluation function Φ ₁ to the evaluation function Φ.
It is a figure showing the example of setting of.

FIG. 11 is a diagram showing the frequency of reaching the operation limit of the shape control device before and after the implementation of the present invention.

[Explanation of symbols]

 DESCRIPTION OF SYMBOLS 1 Rolling machine 2 Rolled plate 3 Work roll 4 Intermediate roll 5 Split backup roll 6 Small diameter backup roll 7 Shape detector 8 Functional calculation processing device 9 Target shape setting circuit 10 Optimal operation amount calculation device 11 Roll bending mechanism 12 Backup roll crown adjustment Mechanism 13 Roll-down leveling mechanism 14 Backup roll crown adjustment mechanism (a) 15 Backup roll crown adjustment mechanism (b) 16 Backup roll crown adjustment mechanism (c) 17 Intermediate roll bender

──────────────────────────────────────────────────続 き Continuing on the front page (72) Inventor Hirohisa Haji 1-2-1, Marunouchi, Chiyoda-ku, Tokyo Inside Nippon Kokan Co., Ltd. (72) Inventor Noriyuki Suzuki 1-1-2, Marunouchi, Chiyoda-ku, Tokyo Japan Inside Kokan Co., Ltd. (72) Inventor Nobuo Nishiura 1-2-1, Marunouchi, Chiyoda-ku, Tokyo Japan Kokan Co., Ltd. (56) References JP-A-3-133509 (JP, A) JP-A-4-100609 ( JP, A) JP-A-4-127908 (JP, A) JP-A-4-135007 (JP, A) (58) Fields investigated (Int. Cl. ⁶ , DB name) B21B 37/28

Claims (3)

(57) [Claims] 1. A thin-plate rolling plate shape control system comprising: a shape detector capable of detecting shapes at a plurality of positions in a rolled sheet width direction; a plurality of shape control mechanisms; and an arithmetic processing unit. A first function, a second function, and a second function each of which are a distribution, a target shape distribution, and an output change of the shape detector with respect to a unit operation amount of the plurality of shape control mechanisms as a function of a position x in a plate width direction. The first evaluation function is created by integrating the square value of the value obtained by subtracting the second function and the third function from the first function at the position x in the plate width direction, The operation amount of each of the plurality of shape control mechanisms for each control step is multiplied by a coefficient in consideration of the degree of shape change by each control mechanism and each weight coefficient set so that the sum of the respective weight coefficients becomes 1. With the coefficient obtained by Creating a second evaluation function represented by a sum of squares of the manipulated variables, and calculating a first weighting factor and a second weighting factor for determining an arbitrary ratio between the first evaluation function and the second evaluation function. Each of them is set, and a shape evaluation function that is a sum of a product obtained by multiplying the first evaluation function and the first weighting coefficient and a product obtained by multiplying the second evaluation function and the second weighting coefficient is created. A method for controlling the shape of a thin-rolled sheet, wherein the operation amounts of the plurality of shape control mechanisms are calculated so as to minimize the shape evaluation function of the sum of products. 2. A method of calculating a mean square value of a deviation from a target shape, and calculating a magnitude relationship between the calculated value and a first reference value and a change amount of the calculated value for each control step and a second reference value. 2. The method according to claim 1, wherein a ratio between the first weighting factor and the second weighting factor is variably set based on the magnitude relation. 3. The possibility of reaching the operation limit of a plurality of shape control mechanisms is individually calculated by fuzzy inference. A weighting factor of an operation amount of each of the plurality of shape control mechanisms constituting the second evaluation function is set in consideration of the degree of possibility of the operation limit and the similarity to the shape control effect. 3. The method for controlling the shape of a thin plate according to claim 1 or 2.