JP6900866B2 - Rolling schedule creation device, rolling schedule creation method, and program - Google Patents

Description

The present invention relates to a rolling schedule making apparatus, a rolling schedule making method, and a program, and is particularly suitable for use in making a rolling schedule of a material to be rolled to be rolled by a tandem rolling mill.

When rolling a plate material with a tandem rolling mill, the plate crown on the outlet side of the final stage rolling stand (the most downstream rolling stand) is used as the product while keeping the plate shape on the outlet side of each rolling stand within a certain range. It is required to be within the permissible range. If the plate crown ratios on the entry side and the exit side of each rolling stand are significantly different, the plate shape deteriorates due to the difference in the elongation ratio at each position in the plate width direction of the plate material, which hinders stable plate passage.

Therefore, it is necessary to appropriately set the crown and shape control ends of each rolling stand. For example, a roll bender is used as the crown / shape control end of each rolling stand. In the roll vendor, roll bending force is applied to each of the drive side and the work side of the work roll. Thereby, the plate crown and the shape (elongation ratio, etc.) can be controlled.

However, in order to realize the desired plate crown / shape, the control ability of the crown / shape control end of each rolling stand may be insufficient. In such a case, it is possible to change the rolling load of each rolling stand and bring it closer to the desired plate crown / shape by changing the plate thickness schedule (schedule of the protruding side plate thickness of each rolling stand). .. As such a technique, there is a technique described in Patent Document 1. In Patent Document 1, the roll bending force for forming the target plate crown and the target plate shape is obtained, and if it does not satisfy the hardware constraint condition, the plate thickness correction value and the evaluation function for the plate crown and the plate shape are obtained. Is disclosed as a method for obtaining a plate thickness correction amount for approaching the target plate crown and the target plate shape under constraint conditions. Here, in Patent Document 1, the evaluation function φ of the following equation (1) is used.

In equation (1), C ^* is the target plate crown. C _n ⁰ is a plate crown on the exit side of the rolling stand in the final stage. Δh _j is a plate thickness correction value of the rolling stand j. α _hj ⁱ is the influence coefficient of the plate thickness correction value on the plate crown on the exit side of the rolling stand in the final stage. The optimum solution of the plate thickness correction amount Δh _j (the plate thickness correction amount Δh _j that minimizes the evaluation function φ) can be obtained by using a quadratic programming method.

Japanese Patent No. 2888364 JP-A-59-76605

The Iron and Steel Institute of Japan Joint Study Group Rolling Theory Subcommittee, "Theory and Practice of Plate Thickness", The Iron and Steel Institute of Japan, published on September 30, 2010

Here, the evaluation function φ of Eq. (1) can be transformed as shown in Eq. (2) below. That is, the evaluation function φ in Eq. (1) is the square of the difference between the _{plate crown C n} on the exit side of the rolling stand in the final stage and the target crown C ^* , taking into account the change in the plate crown due to the correction of the plate thickness. expressed.

As described above, in the technique described in Patent Document 1, only the deviation between the predicted value and the target value of the plate crown is evaluated. _{Therefore, the optimum solution of the plate thickness correction amount Δh j} obtained by using the evaluation function φ of Eq. (1) may not be the plate thickness correction amount desirable in operation. Furthermore, even under almost the same rolling conditions, it is possible to obtain significantly different plate thickness schedules. _{Therefore, the plate thickness schedule obtained from the plate thickness correction amount Δh j} calculated by using the evaluation function φ in Eq. (1) may be far from the plate thickness schedule based on past experience.

Explaining how this affects the operation, first, when the plate thickness schedule is changed, the rolling load changes because the rolling amount of each rolling stand changes. Further, in order to make the mass flow (product of plate thickness, plate width and plate speed) on the entry side and the exit side of each rolling stand constant, it is necessary to change the rolling speed. Since the amount of heat generated by rolling and the amount of heat removed by cooling change due to such changes in rolling load and rolling speed, the plate temperature also changes. When the plate temperature changes, the rolling load changes due to the change in the plastic properties of the material. Due to these changes in basic rolling conditions, various other rolling conditions will also change. Then, it becomes necessary to correct the setting of each rolling stand according to the change of these rolling conditions, and when the correction amount is large, it becomes a factor that increases the variation in quality. Furthermore, the operator corrects the setting of the rolling stand based on the past experience when rolling the same material as the plate material to be scheduled this time, and secures the stability and quality of rolling. However, if the rolling conditions are significantly different from those in the past rolling, the experience cannot be utilized and it becomes difficult to make appropriate corrections.

The present invention has been made in view of the above problems, and is based on a plate thickness schedule obtained from substantially the same rolling conditions and a plate thickness schedule that is not far from the plate thickness schedule based on past experience. The purpose is to enable proper control of the plate crown and shape.

The rolling schedule creating apparatus of the present invention includes a plate crown control amount, which is the amount of plate crown on the exit side of the rolling stand, which is changed by the operation of the plate crown and shape control ends in a plurality of rolling stands constituting the tandem rolling mill. A first constraint equation that defines a permissible range or target value of a plate crown on the output side of the rolling stand in the final stage, which is a rolling schedule creation device that creates a rolling schedule including the thickness of the output side plate of the rolling stand. A second constraint equation that defines the permissible range of the shape of the material to be rolled on the outlet side of the rolling stand for each of the plurality of rolling stands, and the permissible range of the plate crown control amount of the plurality of rolling stands. The amount of correction from the ideal plate thickness of the constraint formula setting means for setting the constraint formula including the third constraint formula specified for each and the outer plate thickness of the rolling stand excluding the rolling stand of the final stage is reduced. An evaluation function setting means for setting an evaluation function for the purpose of, and a rolling stand excluding the final stage rolling stand when the value of the evaluation function becomes the minimum or maximum within the range satisfying the constraint equation. The optimum calculation means for deriving the correction amount of the output side plate thickness from the ideal plate thickness and the plate crown control amount at the plurality of rolling stands by performing an optimization calculation by a mathematical programming method, and deriving by the optimum calculation means. Based on the amount of correction from the ideal plate thickness of the outer plate thickness of the rolling stand excluding the rolling stand of the final stage and the ideal plate thickness, the outer plate thickness of the rolling stand is used as the plate thickness schedule. It is characterized by having a plate thickness schedule creating means to be created.

The method for creating a rolling schedule of the present invention includes a plate crown control amount, which is the amount of plate crown on the exit side of the rolling stand, which is changed by operating the plate crown and shape control ends in a plurality of rolling stands constituting the tandem rolling mill. A first constraint formula for creating a rolling schedule including the thickness of the output side plate of the rolling stand, which defines an allowable range or a target value of a plate crown on the output side of the rolling stand in the final stage. A second constraint equation that defines the permissible range of the shape of the material to be rolled on the outlet side of the rolling stand for each of the plurality of rolling stands, and the permissible range of the plate crown control amount of the plurality of rolling stands. The amount of correction from the ideal plate thickness of the constraint formula setting step of setting the constraint formula including the third constraint formula specified for each and the outer plate thickness of the rolling stand excluding the rolling stand of the final stage is reduced. The evaluation function setting process for setting the evaluation function for the purpose of, and the rolling stand excluding the final stage rolling stand when the value of the evaluation function becomes the minimum or the maximum within the range satisfying the constraint equation. The optimum calculation process for deriving the correction amount of the output side plate thickness from the ideal plate thickness and the plate crown control amount at the plurality of rolling stands by performing an optimization calculation by a mathematical programming method, and deriving by the optimum calculation process. Based on the amount of correction from the ideal plate thickness of the outer plate thickness of the rolling stand excluding the rolling stand of the final stage and the ideal plate thickness, the outer plate thickness of the rolling stand is set as the plate thickness schedule. It is characterized by having a plate thickness schedule creation process to be created.

The program of the present invention is characterized in that a computer functions as each means of the rolling schedule making apparatus.

According to the present invention, it is possible to control an appropriate plate crown and shape based on a plate thickness schedule obtained from substantially the same rolling conditions and a plate thickness schedule that does not deviate from the plate thickness schedule based on past experience. it can.

It is a figure which showed an example of the schematic structure of the hot rolling equipment. It is a figure which conceptually shows an example of the direction of the rolling load acting on a rolling stand, and the roll bending force applied to a work roll. It is a figure which shows the 1st example of the functional structure of the rolling schedule making apparatus. It is a flowchart explaining the 1st example of the process of the rolling schedule making apparatus. It is a figure explaining an example of a plate crown and a stretch ratio. It is a figure which shows the 2nd example of the functional structure of the rolling schedule making apparatus. It is a flowchart explaining the 2nd example of the process of the rolling schedule making apparatus. It is a figure which shows the steepness and the WR vendor setting value about the comparative example 1. FIG. It is a figure which shows the steepness and the WR vendor setting value about the comparative example 2. It is a figure which shows the steepness and the WR vendor setting value about the invention example. It is a figure which shows the rolling ratio in each rolling stand. It is a figure which shows an example of the plate crown, the steepness, and the WR vendor set value when the constraint condition relaxation amount is evaluated in the first order. It is a figure which shows an example of the plate crown, the steepness, and the WR vendor set value when the constraint condition relaxation amount is evaluated secondarily.

Hereinafter, embodiments of the present invention will be described with reference to the drawings. In each figure, for convenience of notation, a part of the configuration is omitted and simplified. Further, the xyz coordinates shown in each figure indicate a direction, and the origin of the xyz coordinates in each figure is the same (the origin of the xyz coordinates does not exist at the position shown in each figure).

(First Embodiment)
First, the first embodiment will be described.
<Outline configuration of hot rolling equipment>
FIG. 1 is a diagram showing an example of a schematic configuration of a hot rolling equipment.
In FIG. 1, the hot rolling equipment includes a rough rolling mill 10, a finishing rolling mill 20, a runout table 30, and a coil winding device 40.

The rough rolling mill 10 is for rough rolling a slab A heated by a heating furnace (not shown) and supplied to a hot rolling line to form a sheet bar B which is a material to be rolled.
The finish rolling mill 20 is for forming the strip C by continuously finishing and rolling the sheet bar B by a plurality of rolling stands (seven rolling stands F1 to F7 in the example shown in FIG. 1).
Each rolling stand F1 to F7 constituting the tandem rolling mill is provided with load cells 21a to 21g, a hydraulic reduction mechanism 22a to 22g, and roll benders 23a to 23g.
The load cells 21a to 21g measure the rolling load generated when the sheet bar B passes between the upper and lower work rolls of the rolling stands F1 to F7 and is rolled.
The hydraulic reduction mechanisms 22a to 22g adjust the reduction position of the seat bar B when rolled by the rolling stands F1 to F7.

In FIG. 1, a case where the load cells 21a to 21g are arranged on the upper side of the rolling stands F1 to F7 and the hydraulic reduction mechanisms 22a to 22g are arranged on the lower side of the rolling stands F1 to F7 is shown as an example. However, the arrangement of the load cells 21a to 21g and the hydraulic reduction mechanism 22a to 22g is not limited to that shown in FIG. For example, load cells 21a to 21g may be arranged below the rolling stands F1 to F7, and hydraulic reduction mechanisms 22a to 22g may be arranged above the rolling stands F1 to F7. Further, load cells 21a to 21g may be arranged on both the upper side and the lower side of the rolling stands F1 to F7.

The roll benders 23a to 23g apply a roll bending force (also referred to as a bender force or a bender pressure) to a bearing (chock) at the end of the work roll by a hydraulic cylinder to correct the deflection generated in the work roll. .. In this embodiment, roll benders 23a to 23g are examples of crown / shape control ends.
FIG. 2 is a diagram conceptually showing an example of the directions of the rolling load acting on the rolling stands F1 to F7 and the roll bending force applied to the work roll.

The direction indicated by the white arrow line shown in FIG. 2 is the direction of the rolling load acting on the rolling stands F1 to F7. The direction indicated by the black double-headed arrow line is the direction of the roll bending force applied to the work roll. As shown in FIG. 2, the roll bending force is applied to each of both ends of the work roll. As described above, the roll bender is also provided at both ends of the work roll on the side opposite to the end on the side where the roll benders 23a to 23g shown in FIG. 1 are provided.

The roll vendors 23a to 23g include, for example, an increase vendor and a degree vendor. The increase bender applies a roll bending force (bending force) in a direction of increasing the distance between the bearings of the upper and lower work rolls. The decrease vendor applies a roll bending force (bending force) in a direction that narrows the space between the bearings of the upper and lower work rolls.

In addition, load relays are provided on the rolling stands F1 to F7, respectively. The load relay provided on the rolling stands F1 to F7 turns on when the tip of the seat bar B bites into the rolling stands F1 to F7, and turns off when the tail end of the seat bar B comes out of the rolling stands F1 to F7.
Further, a cooling spray (not shown) for cooling the work roll is provided at a position close to the work roll of each rolling stand F1 to F7 of the finishing rolling mill 20.

The run-out table 30 is for cooling the strip C that has been finish-rolled by the finish rolling mill 20.
The coil winding device 40 is generally called a coiler, and is for winding the strip C cooled by the runout table 30.

<Rolling schedule creation device 300>
The rolling schedule creation device 300 of the present embodiment includes the thickness of the exit side plates of the rolling stands F1 to F6 of the material to be rolled (sheet bar B) to be hot-rolled by such a hot rolling facility, and roll benders 23a to 23g. The roll bending force applied in 1 is derived before rolling the material to be rolled.

FIG. 3 is a diagram showing an example of a functional configuration of the rolling schedule creation device 300. The hardware of the rolling schedule creation device 300 is realized by using, for example, an information processing device including a CPU, ROM, RAM, HDD, various interfaces, and dedicated hardware. Further, FIG. 4 is a flowchart illustrating an example of processing of the rolling schedule creation device 300.

[Data storage unit 301]
The data storage unit 301 stores the operation record data and the equipment data in the hot rolling equipment. Here, among various operation record data and equipment data, the operation record data and equipment data used when the ideal plate thickness schedule acquisition unit 303, which will be described later, creates the ideal plate thickness schedule are stored.

The operation performance data includes, for example, the entry side plate thickness, the exit side plate thickness, the rolling load, the plate temperature, and the plate speed (rotational speed of the work roll) for each of the rolling stands F1 to F7. These data are stored in the data storage unit 301 as operation record data for each material category (material of the material to be rolled). In addition, the equipment data includes the roll diameter of the work roll, the crown generated on the work roll and the backup roll for each of the rolling stands F1 to F7.

[Operation Standard Acquisition Unit 302, Step S401]
The operation standard acquisition unit 302 acquires a reference value of the control amount at the crown / shape control end. As described above, in the present embodiment, the crown / shape control ends are roll benders 23a to 23g. Therefore, the operation standard acquisition unit 302 acquires the reference value of the roll bending force in each rolling stand F1 to F7. The reference value of the roll bending force in each rolling stand F1 to F7 is a value for each material category (material of the material to be rolled).

The operation standard acquisition unit 302 uses, for example, a representative value (for example, an average value) of the roll bending force of each rolling stand F1 to F7 obtained from the past operation results as a reference value of the roll bending force of each rolling stand F1 to F7. Can be obtained. In this case, the reference value of the roll bending force at each rolling stand F1 to F7 is a fixed value.

Further, the operation standard acquisition unit 302 may calculate the reference value of the roll bending force in each rolling stand F1 to F7 by using the logic. For example, as described in Patent Document 2, the roll bending force (control amount at the crown / shape control end) at each rolling stand F1 to F7 is calculated in consideration of the plate passing limit value of the plate shape of the material to be rolled. , The calculated value can be used as a reference value of the roll bending force in each rolling stand F1 to F7.
In the following description, the reference value of the roll bending force in each rolling stand F1 to F7 is abbreviated as the reference value of the roll bending force or simply the reference value, if necessary.

[Ideal plate thickness schedule acquisition unit 303, step S402]
The ideal plate thickness schedule acquisition unit 303 uses the operation performance data and equipment data stored in the data storage unit 301 and the reference value of the roll bending force in each rolling stand Fi obtained by the operation standard acquisition unit 302. _{, An ideal plate thickness schedule h0 i} indicating a desired output plate thickness of each rolling stand Fi is derived. The ideal plate thickness schedule h0 _i is derived for each material category (material of the material to be rolled). Here, the subscript i is a variable for identifying the rolling stands, and when the total number of rolling stands is n, it is an integer of 1 to n, and the smaller the value is given to the rolling stands on the upstream side. In the example shown in FIG. 1, since there are seven rolling stands F1 to F7, the total number n of the rolling stands is 7, and 1, 2, ... , 7 are given as the value of the variable i, respectively.

The ideal plate thickness schedule acquisition unit 303, for example, obtains the operation record data and equipment data stored in the data storage unit 301 and the reference value of the roll bending force in each rolling stand Fi obtained by the operation standard acquisition unit 302. The desired rolling load balance at each rolling stand Fi (for example, the desired rolling load value at each rolling stand Fi when the maximum rolling load value is set to "1") is obtained, and the obtained rolling load balance is obtained. The output side plate thickness of each rolling stand F1 to F7 when the rolling load balance is close to (preferably matching) is derived for each material category as _{an ideal plate thickness schedule h0 i.}
The ideal plate thickness schedule acquisition unit 303 may acquire the ideal plate thickness schedule h0 _i derived by an external device without deriving the ideal plate thickness schedule h0 _i . Further, when the ideal plate thickness schedule h0 _i has been obtained in the past, the ideal plate thickness schedule h0 _i may be used.

[Model parameter derivation unit 304, step S403]
The model parameter derivation unit 304 uses the ideal plate thickness schedule h0 _{i obtained by the ideal plate thickness schedule acquisition unit 303 as the output side plate thickness h i} of each rolling stand Fi, and uses a rolling model to obtain a reference rolling load P0 _i . influence coefficient from delivery side thickness h to the rolling load P and (∂P / ∂h) _i, derives the influence coefficient of the rolling load P (∂P / ∂H) _i from the entry side thickness H.

The reference rolling load P0 _i is the rolling load of each rolling stand Fi when rolling with the plate thickness schedule (without changing the plate thickness schedule) currently applied to the hot rolling equipment. Since the rolling model used here can be constructed by using, for example, the technique described in Non-Patent Document 1, detailed description thereof will be omitted here.

Further, the model parameter derivation unit 304 uses the rolling model and the reference value of the roll bending force in each rolling stand F1 to F7 obtained by the operation standard acquisition unit 302 to set the reference plate crown C0 _i and the reference elongation ratio. Derivation of ε0 _i. The reference plate crown C0 _{i is a plate crown C i} when the roll bending force on the rolling stand Fi is a reference value. Further, the reference elongation ratio ε0 _{i is the elongation ratio ε i} when the roll bending force at the rolling stand Fi is a reference value.
Since the rolling model used here can also be constructed by using, for example, the technique described in Non-Patent Document 1, detailed description thereof will be omitted here.

FIG. 5 is a diagram illustrating an example of a plate crown C _i (FIG. 5 (a)) and an elongation ratio ε _i (FIG. 5 (b)).
FIG. 5A shows a cross section of the material to be rolled (sheet bar B) cut along the plate thickness direction.
In FIG. 5 (a), the strip crown C _i from a thickness h _i at the center of the plate width direction is a value obtained by subtracting the thickness d _i of the crown defining point _{501 (= h i -d i)} . Divided by the thickness h _i a sheet crown C _i at the center of the plate width direction (= C _i / h _i) is plate crown ratio. The crown definition point 501 is a position on the plate end side in the plate width direction (x-axis direction) (a position X mm from the end portion in the plate width direction (X is a value of 0 or more)).

In FIG. 5B, the material to be rolled (sheet bar B) is virtually cut out in the longitudinal direction (y-axis direction) of the plate by the reference length L, and cut into small pieces along the y-axis (FIG. 5). (Dotted line in (b)), an image of a plate wave appearing in the z-axis direction stretched on an xy plane is drawn. Since the plate shape of the material to be rolled (sheet bar B) is caused by the plate length being different in the plate width direction, the plate shape is expressed as an elongation difference Δl in the longitudinal direction (y-axis direction) in FIG. 5 (b). The elongation ratio ε _i is a value (= Δl / L) obtained by dividing the elongation difference Δl by the reference length L. As shown in FIG. 5B, when the material to be rolled (seat bar B) is an ear wave, the plate length at the crown definition point 501 is the center position of the material to be rolled (seat bar B) in the plate width direction. It is longer than the plate length in, and the elongation difference Δl is the difference. On the other hand, when the material to be rolled (seat bar B) is medium-stretched, the plate length at the crown definition point 501 is shorter than the plate length at the center position in the plate width direction of the material to be rolled (sheet bar B) and is elongated. The difference Δl is the difference. As shown in FIG. 5B, when the material to be rolled (seat bar B) is an ear wave, the elongation difference Δl shows a positive value. On the other hand, when the material to be rolled (sheet bar B) has medium elongation, the elongation difference Δl shows a negative value. The position in the plate width direction (x-axis direction) for measuring the reference length L is the position where the plate length of the material to be rolled (sheet bar B) is the shortest, but the actual elongation difference Δl is the reference length L. Since it is sufficiently smaller than the above, the position in the width direction in which the reference length L is measured has almost no effect on _{the elongation ratio ε i.}

Returning to the explanation of FIG. 3, the model parameter derivation unit 304 uses the rolling model to obtain the crown ratio inheritance coefficient η _i , the shape change coefficient ξ _i , and the influence coefficient from the rolling load P to the plate crown C (∂C _i / /. ∂P _i ) is derived.
Since the rolling model used here can also be constructed by using, for example, the technique described in Non-Patent Document 1, detailed description thereof will be omitted here.
In the following description, when the parameters derived by the model parameter derivation unit 304 are collectively referred to, they are referred to as model parameters as necessary.

[Constraint expression / evaluation function setting unit 305, step S404]
The constraint expression / evaluation function setting unit 305 sets the constraint expression and the evaluation function using the model parameters and the like derived by the model parameter derivation unit 304. The constraint equation and evaluation function used in this embodiment will be described below.

[[Model expression]]
First, the model formula will be described.
_{The plate crown C i} and the elongation ratio ε _i due to the plate thickness rolling by the rolling mill are expressed by the following model equations (3) to (5).

Here, C _i, C _i-1, respectively rolling stand Fi, a strip crown at the delivery side of the Fi-1. C0 _i and C0 _{i-1 are reference plate crowns C0 i} on the exit side of the rolling stands Fi and Fi-1, respectively. η _i is the crown ratio genetic coefficient in the rolling stand Fi. h _i, h _i-1, respectively rolling stand Fi, a left side thickness at the center of the plate width direction of Fi-1. y _i is a plate crown amount that is changed with respect to the reference plate crown C0 _i by operating the crown / shape control ends (roll benders 23a to 23g). In the following description, this plate crown amount will be referred to as a plate crown control amount, if necessary.

ε _i and ε _i-1 are the elongation ratios on the exit side of the rolling stands Fi and Fi-1, respectively. ε0 _{i-1 is a reference elongation ratio ε0 i-1} on the exit side of the rolling stand Fi-1. ξ _i is the coefficient of variation of the shape of the rolling stand Fi. λ _i is the steepness on the exit side of the rolling stand Fi. The steepness is a value obtained by dividing the height of the wave generated in the material to be rolled due to the elongation difference by the pitch of the wave.

_{When the above model equation is transformed, the plate crown C i} and the elongation ratio ε _i are expressed in a linear form relating to the plate crown control amount y _i , as shown in the following equations (6) to (9). Will be done.

α _{i, j} (α _{i, k} ) is a coefficient of influence of the plate crown control amount y _j (y _k ) on the rolling stand Fj (Fk) on the plate crown on the exit side of the rolling stand Fi. That is, for α _{i, j} (α _{i, k} ), how much the operation of the rolling stand Fj (Fk) on the plate crown / shape control end (roll bender) affects the plate crown on the exit side of the rolling stand Fi. It is a coefficient indicating whether or not.

Further, β _{i, j} (β _{i, k} ) is an influence coefficient of the plate crown control amount y _j (y _k ) on the rolling stand Fj (Fk) on the elongation ratio on the exit side of the rolling stand Fi. That is, for β _{i, j} (β _{i, k} ), how much the operation of the rolling stand Fj (Fk) on the plate crown / shape control end (roll bender) affects the elongation coefficient on the exit side of the rolling stand Fi. It is a coefficient indicating whether to give.

When the rolling stand Fi is on the upstream side of the rolling stand Fj, even if the plate crown / shape control end (roll bender) of the rolling stand Fj is operated, the plate crown / elongation ratio on the exit side of the rolling stand Fi will be changed. Does not affect. Therefore, as shown in Eqs. (8) and (9), when i <j, α _{i, j} and β _{i, j} become 0 (zero). Further, the plate crown control amount y _i on the exit side of the rolling stand Fi is directly applied to the rolling stand Fi. Therefore, as shown in Eq. (8) and (9), when i = j, α _{i, j} becomes 1, and β _{i, j} becomes ξ _i / h _i .

In equation (6), the plate crown C _{i on the outlet side of the rolling stand Fi is caused by the operation of the reference plate crown C0 i} on the outlet side of the rolling stand Fi and the plate crown / shape control end of each rolling stand Fj. It is shown that it is a value obtained by adding the amount of change of the plate crown generated on the outlet side of the rolling stand Fi.
In equation (7), the elongation ratio ε _i on the exit side of the rolling stand Fi is caused by the reference elongation ratio ε0 _i on the outlet side of the rolling stand Fi and the operation of the plate crown / shape control end of each rolling stand Fj. It is shown that the value is the sum of the amount of change in the elongation ratio obtained on the output side of the rolling stand Fi.

_{In order to add the output side plate thickness h i} of each rolling stand Fi to the control amount, the equations (6) to (9) are expanded to the following equations (10) to (15).

Here, Δh _i (Δh _k ) is a correction amount of the outer plate thickness of the rolling stand Fi. P0 _i is a reference rolling load P0 _i on the rolling stand Fi. (∂P / ∂h) _i is a coefficient of influence from the output side plate thickness h to the rolling load P at the rolling stand Fi. (∂P / ∂H) _i is a coefficient of influence from the input side plate thickness H to the rolling load P at the rolling stand Fi. (∂C _i / ∂P _i ) is a coefficient of influence from the rolling load P to the plate crown C at the rolling stand Fi.

In the third term on the right side of the equation (10), the third term on the right side of the equation (11), and the second term on the right side of the equation (12), the integration range is k = 1 to n-1. delivery thickness h _n out of the rolling stand Fn in the final stage, can not change because of a plate thickness of the product, the possible modification, the other roll stand F ₁ ~F _n-1 of the delivery side thickness h ₁ to h _{n Because} it is -1.

φ _{i and k} are influence coefficients indicating the degree of influence on the plate crown on the output side of the rolling stand Fi due to the change in the plate thickness on the output side of the rolling stand Fk. μ _{i and k} are influence coefficients indicating the degree of influence on the elongation ratio of the rolling stand Fi by changing the thickness of the protruding side of the rolling stand Fk.
The third term on the right side of the equation (10) shows the amount of change in the plate crown that occurs on the output side of the rolling stand Fi due to the change in the output side plate thickness of each rolling stand Fk excluding the rolling stand Fn in the final stage.
The third term on the right side of the equation (11) shows the amount of change in the elongation ratio obtained on the output side of the rolling stand Fi due to the change in the output side plate thickness of each rolling stand Fk excluding the rolling stand Fn in the final stage. ..

[[Constraint expression]]
Next, the constraint expression will be described. The constraints due to the hardware of the rolling stand and the constraints required from the operational constraints are expressed as constraint equations (constraints). In this embodiment, the following constraint equation is used.
First, the constraint equation regarding the control ability of the crown / shape control end (roll bender) of the rolling stand Fi is expressed as the following equation (16) as the range of the value of _{the plate crown control amount y i.}

The upper limit values y _{max, i} and the lower limit values y _{min, i} of the plate crown control amount y _{i in} the rolling stand Fi are obtained by a rolling model based on the control ability of the crown / shape control end (roll bender) of the rolling stand Fi. Can be done. Since the rolling model used here can also be constructed by using, for example, the technique described in Non-Patent Document 1, detailed description thereof will be omitted here. If past knowledge or the like is obtained about the upper limit values y _{max, i} and the lower limit values y _{min, i} of the plate crown control amount y _{i in the rolling stand Fi, those values may be used.}

Further, the restrictions on the shape (elongation ratio) required for operation are expressed by the following equation (17).

The upper limit values ε _{max, i} and lower limit values ε _{min, i of the elongation ratio ε i} on the outlet side of the rolling stand Fi are based on past findings by investigating the elongation ratio for each material and size of the material to be rolled. Can be obtained.
_{The elongation ratio ε i} on the exit side of the rolling stand Fi is obtained by Eq. (11).

_{Further, the restrictions on the plate crown C n} on the exit side of the rolling stand Fn in the final stage are expressed as the following equations (18) or (19).

Equation (18) is a constraint equation when the target values C _{aim, n are given to the plate crown C n} on the exit side of the rolling stand Fn in the final stage. Equation (19) is a constraint when the allowable range (upper limit value C _{max, n} and lower limit value C _{min, n} ) is given to the _{plate crown C n} on the exit side of the rolling stand Fn in the final stage. It is an expression.
_{The plate crown C n} on the exit side of the rolling stand Fn in the final stage is obtained by the equation (10).

The constraint equation / evaluation function setting unit 305 sets the upper limit values y _{max, i} and the lower limit values y _{min, i of the plate crown control amount y i} in the rolling stand Fi with respect to the equation (16).
Further, the constraint equation / evaluation function setting unit 305 sets the upper limit values ε _{max, i} and the lower limit values ε _{min, i of the elongation ratio ε i} on the exit side of the rolling stand Fi with respect to the equation (17).

When the target value C _{aim, n is given to the plate crown C n} on the exit side of the rolling stand Fn in the final stage, the constraint expression / evaluation function setting unit 305 sets the target value C _{aim, n} ( 18) Set to equation. On the other hand, when the permissible range (upper limit value C _{max, n} and lower limit value C _{min, n ) is given to the plate crown C n} on the exit side of the rolling stand Fn in the final stage, the constraint equation / evaluation function The setting unit 305 sets the upper limit value C _{max, n} and the lower limit value C _{min, n according} to the equation (19).

In addition, the constraint equation / evaluation function setting unit 305 uses the model parameters derived by the model parameter derivation unit 304 and the total number of rolling stands Fk (7 in the example shown in FIG. 1) in equations (8) and (9). Set to equations (13) to (15). Further, the constraint equation / evaluation function setting unit 305 sets the ideal plate thickness schedule h0 _{k as the output side plate thickness h k} of each rolling stand Fk in the plate thickness schedule in the equations (8) and (9).

[[Evaluation function]]
Next, the evaluation function will be described. Define an evaluation function to express the desired plate thickness schedule for operation. In this embodiment, the evaluation function of the following equation (20) is used.

The evaluation function J of the equation (20) is an evaluation function for the purpose of reducing _{the correction amount Δh k of the output side plate thickness of each rolling stand Fk.} Here, as an example thereof, the correction amount Δh _k of the output side plate thickness of each rolling stand Fk is directly evaluated.
Here, since the plate thickness of the material to be rolled is thicker _{on the upstream side, the correction amount Δh k} of the output side plate thickness of the rolling stand Fk is often larger as the rolling stand Fk is on the upstream side. _{Therefore, in order to evaluate the correction amount Δh k} of the output side plate thickness of each rolling stand Fk in the same manner, in the equation (20), the ideal plate thickness schedule h0 _{k of the correction amount Δh k} of the output side plate thickness of the rolling stand Fk. Use the absolute value of the ratio to. As described above, since the outer plate thickness of the rolling stand Fn in the final stage cannot be changed, the integration range is k = 1 to n-1.

The constraint equation / evaluation function setting unit 305 sets the model parameters derived by the model parameter derivation unit 304, the total number n of rolling stands Fk (7 in the example shown in FIG. 1), and the ideal plate thickness schedule h0 _k into equation (20). Set.

[Optimal calculation unit 306, step S405]
The optimum calculation unit 306 is a constraint equation / evaluation function within a range satisfying the equations (16), (17), (18) or (19) set by the constraint equation / evaluation function setting unit 305. Mathematically, the _{plate crown control amount y k} at the rolling stand Fk and the correction amount Δh _k of the output side plate thickness of the rolling stand Fk when the value of the evaluation function J of equation (20) set by the setting unit 305 is minimized. Derived by performing optimization calculation by the planning method. The constraint expression is expressed by a linear equation or inequality, and the evaluation function is expressed by a linear form. Therefore, the optimization calculation can be performed by the linear programming method in which the plate crown control amount y _{k and the correction amount Δh k} of the exit side plate thickness are set as the determinants. The optimization calculation by the linear programming method can be realized by using a known solver.

[Plate thickness schedule creation unit 307, step S406]
_{The plate thickness schedule creation unit 307 sets the correction amount Δh k} of the output side plate thickness of each rolling stand Fk derived by the optimum calculation unit 306 to the output _{side plate thickness h k of} each rolling stand Fk (k = 1 to n-1). The plate thickness schedule is the sum of the ideal plate thickness schedule h0 _k. Further, the plate thickness schedule creation unit 307 includes the plate thickness of the product in the plate thickness schedule as the output _{side plate thickness h n of the rolling stand Fn in the final stage.}

[Output unit 308, step S407]
The output unit 308 rolls including the plate thickness schedule created by the plate thickness schedule creation unit 307 and the plate crown control amount y _{i at each rolling stand Fi (i = 1 to n) derived by the optimum calculation unit 306.} Create a schedule and output it.
_{Further, the output unit 308 indicates the plate crown control amount y i} in each rolling stand Fi (i = 1 to n) derived by the optimum calculation unit 306 and the degree of influence on the plate crown by changing the roll bending force. The roll bending force at each rolling stand F1 to Fn may be derived based on the influence coefficient, and the roll bending force at each rolling stand F1 to Fn may be included in the rolling schedule and output.
As a form of output of the rolling schedule, for example, a display on a computer display may be performed, and an operator who refers to the display may adjust the rolling reduction device and the roll bending force of each rolling stand, or directly from the rolling schedule creation device 300. , The plate thickness schedule and the roll bending force may be output as the set values of the rolling reduction device and the roll bending force control device of each rolling stand.

<Summary>
As described above, in the present embodiment, the _{constraint equations relating to the plate crown control amount y i} and the elongation ratio ε _i on the exit side of each rolling stand Fi and the constraints relating to the plate crown C n on the outlet side of the final stage rolling stand F _n. In each rolling stand Fi when the value of the evaluation function J, which aims to reduce the deviation amount of the output side plate thickness of the rolling stand Fk _{from the ideal plate thickness schedule h0 k, is minimized within the range satisfying the equation.} The plate crown control amount y _{i and the correction amount Δh k} of the output side plate thickness of each rolling stand Fk excluding the final stage are derived. Therefore, when the control capability of the crown / shape control end (roll bender) of each rolling stand F1 to Fn is insufficient, a plate thickness schedule that minimizes the correction of the protruding side plate thickness of the rolling stands F1 to Fn-1 is set. Can be created. As a result, a relatively close plate thickness schedule can be obtained under almost the same rolling conditions. In addition, it is possible to suppress the creation of a plate thickness schedule that is far from the past plate thickness schedule for the material to be rolled of the same material. Further, since the plate thickness correction amount Δh _k of each rolling stand F1 to Fn-1 can be uniquely determined, a plate thickness schedule that contributes to the operation can be created. _{Therefore, the appropriate plate crown C i} and elongation ratio ε _i are controlled based on the plate thickness schedule obtained from almost the same rolling conditions and the plate thickness schedule that is not far from the plate thickness schedule based on past experience. Will be possible.

<Modification example>
[[Modification 1]]
In order to make it easier to obtain the solution by the optimization calculation described in the present embodiment, the following may be performed.
That is, as a constraint expression, when the target values C _{aim, n are given to the plate crown C n} on the exit side of the rolling stand Fn in the final stage, the following (18) is replaced with the following ( 21) When the allowable range (upper limit value C _{max, n} and lower limit value C _{min, n} ) is given to the _{plate crown C n} on the exit side of the rolling stand Fn in the final stage. (19) may be replaced with the formula (22), and the evaluation function may be the following formula (23) instead of the formula (20).

Δc in the equations (21) to (23) is the amount of relaxation of the constraint condition of the constraint equation with respect to the _{plate crown C n on the exit side of the rolling stand Fn in the final stage.} The constraint condition relaxation amount δc is a variable having 0 or a positive value, and when δc> 0, the upper and lower limits of the constraint equations of Eqs. (18) and (19) are expanded, and Eqs. (16) and (16) and ( It has the effect of expanding the range of solutions that satisfy Eqs. 17) and Eqs. (18) or (19), making it easier to obtain solutions.

In this modification, as shown in Eq. (23), the constraint condition relaxation amount δc is included in the evaluation function J so that the constraint condition relaxation amount δc does not become an unnecessarily large value. _{In order to reduce the correction amount Δh k of the} output side plate thickness of each rolling stand Fk (the amount of deviation of the output side plate thickness of the rolling stand Fk _{from the ideal plate thickness schedule h0 k} ), it is necessary to increase the constraint condition relaxation amount δc. As there are, these are in a trade-off relationship. _{The second term w δc} of the evaluation function J in the equation (23) is a weighting coefficient for adjusting this trade-off, and is a correction amount Δh _k (rolling) of the output side plate thickness of each rolling stand Fk with the constraint condition relaxation amount δc. It represents the balance of the output side plate thickness of the stand Fk with respect to the deviation amount from the _{ideal plate thickness schedule h0 k).} That is, it is prioritized to satisfy the constraint condition rather than reducing _{the correction amount Δh k of the} output side plate thickness of each rolling stand Fk (the amount of deviation of the output side plate thickness of the rolling stand Fk _{from the ideal plate thickness schedule h0 k).} In the case of making it, the value of the _{weighting coefficient w δc is increased.
In this modification, the constraint equation / evaluation function setting unit 305 has a weight coefficient w δc} in addition to the model parameters derived by the model parameter derivation unit 304 and the total number n of rolling stands Fk (7 in the example shown in FIG. 1). To set.

[[Modification 2]]
Further, instead of the constraint condition relaxation amount δc for the plate crown on the outlet side of the final stage rolling stand Fn described in the first modification, the constraint condition relaxation for the elongation ratio (shape) on the outlet side of each rolling stand F1 to Fn is relaxed. The quantity δε may be used. In this case, as the constraint equation, the following equation (24) is adopted instead of the equation (17), and the equation (18) or the equation (19) is used as it is. As the evaluation function, the following equation (25) is adopted instead of equation (20).

[[Modification 3]]
Further, both the constraint condition relaxation amount δc for the plate crown on the exit side of the rolling stand Fn in the final stage and the constraint condition relaxation amount δε for the elongation ratio (shape) on the outlet side of each rolling stand F1 to Fn are used. May be good. In this modification, the equation (24) is adopted as the constraint equation instead of the equation (17), and the target value C _{aim, for the plate crown C n on the exit side of the rolling stand Fn in the final stage. When n} is given, the equation (21) is used instead of the equation (18), and the allowable range (upper limit value C _{max) is used for the plate crown C n on the exit side of the rolling stand Fn in the final stage. , N} and the lower limit C _{min, n} ) are given, the equation (22) is adopted instead of the equation (19). As the evaluation function, the following equation (26) is adopted instead of the equation (20).

[[Modification 4]]
Further, as a constraint condition other than the plate crown and the elongation ratio (shape), it relates to a physical quantity g expressed in a linear form using at least one _{of a plate crown control amount y i} and a correction amount Δh _{k of the protruding side plate thickness.} As the constraint equation, for example, when the following equation (27) or equation (28) is added and the constraint equation of equation (28) is added, for example, instead of equation (20), ( 29) Equation may be adopted. In Eqs. (27) and (28), b is a constraint value for the physical quantity g. In the equations (28) and (29), δg is a constraint condition relaxation amount with respect to the physical quantity g. The physical quantity g, for example, rolling force P _i shown in equation (12).

[[Modification 5]]
In the evaluation functions J of the equations (23), (25), (26), and (29) shown in the modified examples 1 to 4, the value of the evaluation function J is set to the constraint condition relaxation quantities δc, δε, and δg. On the other hand, it changes linearly. As a general property of linear programming, the optimal solution exists on the boundary of the feasible region that satisfies all the constraints. Therefore, in the evaluation function J shown in the variants 1 to 4, the constraint relaxation amount δc, If there is a solution in which δε and δg are 0 (zero), the solution can be easily obtained.

However, when the control capability of the crown / shape control end (roll bender) of the rolling stand Fi (that is, the plate crown control amount y _i in the rolling stand Fi) is close to the upper and lower limit values, the constraint condition relaxation amount Even if there is a solution in which δc, δε, δc, and δg are 0 (zero), it is better to set the constraint condition relaxation quantities δc, δε, and δg to values slightly larger than 0 (zero). In some cases, a desirable solution with a margin in the control capability of the control end can be obtained.

Further, the calculated values of the plate crown C _i and the elongation ratio ε _i include the prediction error of the model equations (for example, equations (10) to (15)). Therefore, the constraint condition relaxation amounts δc, δε, and δg are set to 0 (zero), and the constraint condition relaxation amounts δc, δε, and δg are slightly larger than 0 (zero) to slightly deviate from the original constraint range. In many cases, there is no substantial difference in setting the plate crown C _i and the elongation ratio ε _{i to desirable values.}

From the above viewpoint, in this modification, the constraint condition relaxation amount δc, δε, δg is reduced from 0 (zero) by including the squared term of the constraint condition relaxation amount δc, δε, δg in the evaluation function J. Is also easy to take a slightly larger value (a value less than the prediction error of the above-mentioned model formula (for example, a value less than 1 [μm])). That is, in this modification, instead of the equation (23), the following equation (30) is replaced with the equation (25), and the following equation (31) is replaced with the equation (26). Instead of the formula (29), the following formula (33) is adopted. In this case, the optimization calculation is performed by, for example, a quadratic programming method instead of the linear programming method.

By doing so, for example, by selecting a solution that sets the constraint condition relaxation amount δc to 0 (zero) in the constraint on the _{plate crown C n (Equation (21) or (22)), (24).} ), It is possible to suppress that the elongation ratio ε _i is close to the upper and lower limit values and that _{the difference in the plate crown control amount y i between the rolling stands adjacent to each other becomes large.} Therefore, the balance of the set values with respect to the plate crown C _n , the elongation ratio ε _{i, and the roll vendor can be improved.}

[[Modification 6]]
In the present embodiment, an optimization problem that minimizes the value of the evaluation function J has been described as an example. However, for example, it may be an optimization problem that maximizes the value of the evaluation function J by multiplying each term on the right side of the evaluation function J by (-1).

[[Modification 7]]
_{In the present embodiment, the case where} the absolute value of the correction amount Δh k of the output side plate thickness of each rolling stand Fk is obtained in the evaluation function J has been described as an example. However, this is not always necessary if the evaluation function J is constructed for the purpose of reducing _{the correction amount Δh k} of the output side plate thickness of each rolling stand Fk. For example, the absolute value of the first term of the evaluation function J in Eq. (20) may be replaced with the square (that is, | Δh _k / h0 _k | may be changed to [Δh _k / h0 _k ] ² ). In this case, the optimization calculation is performed by, for example, a quadratic programming method instead of the linear programming method.

[[Modification 8]]
In the present embodiment, the case where the elongation ratio is used as the shape of the material to be rolled has been described as an example. However, the shape of the material to be rolled is not limited to the elongation ratio. For example, the steepness represented by the equation (5) may be used.

[[Modification 9]]
In the present embodiment, the case where the control amount at the crown / shape control end is the roll bending force has been described as an example. However, the amount of control at the crown / shape control end is not limited to the roll bending force. For example, when the rolling stand is a pair cross mill, the angle at which the upper and lower work rolls and the backup roll are crossed in pairs may be the control amount at the crown / shape control end. Further, when the rolling stand is a mill having a work roll shift mechanism, the shift amount of the upper and lower work rolls may be used as the control amount at the crown / shape control end.

(Second Embodiment)
Next, the second embodiment will be described. As shown in the equation (13), the influence of the correction of the protruding side plate thickness of each rolling stand Fk is not linear. Therefore, in the present embodiment, the output side plate thickness of each rolling stand Fk constituting the plate thickness schedule created by the plate thickness schedule creation unit 307 is set as a new output side plate thickness h _k of each rolling stand Fk, and the model parameter is set. The accuracy of the rolling schedule is further improved by repeating the derivation and execution of the optimization calculation, the creation of the plate thickness schedule, and _{the derivation of the plate crown control amount y i until a predetermined convergence condition is satisfied.} As described above, the present embodiment is mainly different from the first embodiment in that the calculation is repeated. Therefore, in the description of the present embodiment, the same parts as those of the first embodiment are designated by the same reference numerals as those shown in FIGS. 1 to 5, and detailed description thereof will be omitted.

FIG. 6 is a diagram showing an example of a functional configuration of the rolling schedule creating device 600 of the present embodiment. Further, FIG. 7 is a flowchart illustrating an example of processing of the rolling schedule creating apparatus 600 of the present embodiment. The rolling schedule creating apparatus 600 of the present embodiment will be described with reference to the flowchart of FIG. 7.

First, in step S701, the operation standard acquisition unit 302 acquires the reference value of the roll bending force in each rolling stand F1 to F7. The process of step S701 is the same as that of step S401 described in the first embodiment.
Next, in step S702, the ideal plate thickness schedule acquisition unit 303 derives the _{ideal plate thickness schedule h0 i.} The process of step S702 is the same as that of step S402 described in the first embodiment.

Next, in step S703, the model parameter derivation unit 601 derives the model parameter. The first process of step S703 is the same as step S403 described in the first embodiment. In the second and subsequent processes, the model parameter derivation unit 601 is not the ideal plate thickness schedule h0 _i , but the (latest) plate thickness schedule created in step S709 described later (the output plate thickness of each rolling stand Fk constituting). With h _{k ) as the output side plate thickness h i} of each rolling stand Fi, using a rolling model, the reference rolling load P0 _i and the coefficient of influence from the output side plate thickness h to the rolling load P (∂P / ∂h) _i , The coefficient of influence (∂P / ∂H) _i on the rolling load P is derived from the entry side plate thickness H.

Next, in step S704, the constraint expression / evaluation function setting unit 602 sets the constraint expression and the evaluation function using the model parameters and the like derived by the model parameter derivation unit 304. In this embodiment, the evaluation function J and the constraint equation described in the first embodiment are used. That is, the evaluation function J of the equation (20) is used as the evaluation function J. Further, the constraint equations of the equation (16), the equation (17), the equation (18) or the equation (19) are used.

Step first process of S704, the constraint expression and evaluation function setting unit 602, the rolling of the ideal thickness schedule h0 _k as delivery side thickness h _k stand Fk (8) below in the sheet thickness schedule, (9) set to with, it sets the correction amount Delta] h _k a (20) from the ideal thickness schedule h0 _k as the correction amount Delta] h _k of thickness at delivery side of the rolling stand Fk in the sheet thickness schedule. In the second and subsequent processes, the constraint equation / evaluation function setting unit 602 was created (latest) in step S709 described later for equations (8) and (9) _{instead of the ideal plate thickness schedule h0 k.} sets the (side thickness h _k out of the rolling stand F1~Fn included therein) thickness schedule, (20) for expression, rather than the correction amount Delta] h _k from the ideal thickness schedule h0 _k, steps described below to set the correction amount Δh _k from the (delivery side thickness h _k of each rolling stand F1~Fn to configure) has been (the latest) thickness schedule created in S709. The other processing of step S704 is the same as that of step S404 described in the first embodiment.

Next, in step S705, the optimum calculation unit 306 in the rolling stand Fi when the value of the evaluation function J also set in step S704 becomes the minimum within the range satisfying the constraint equation set in step S704. The plate crown control amount y _{i and the correction amount Δh k} of the output side plate thickness of the rolling stand Fk are derived by performing an optimization calculation by a mathematical programming method. The process of step S705 is the same as that of step S405 described in the first embodiment.

Next, in step S706, the plate thickness schedule creation unit 603 creates a plate thickness schedule. The first process of step S706 is the same as step S406 described in the first embodiment. That is, the plate thickness schedule creation unit 603 sets the plate thickness schedule by adding _{the correction amount Δh k} of the output side plate thickness of each rolling stand F1 to Fn-1 derived in step S705 to the ideal plate thickness schedule h0 _k. .. In the second and subsequent processes, the plate thickness schedule creation unit 603 sets the correction amount Δh _k of the output side plate thickness of each rolling stand Fk derived in step S705 in step S709 described later instead of the ideal plate thickness schedule h0 _k. The plate thickness schedule is the sum of the created (latest) plate thickness schedule (the output side plate thickness h _{k of each rolling stand Fk constituting the rolling stand Fk).}

Next, in step S707, the convergence determination unit 604 determines whether or not the convergence condition for the optimization calculation by the optimum calculation unit 306 is satisfied. As the convergence condition, a known condition used as the convergence condition for the optimization calculation can be adopted. For example, it is determined that the convergence condition is satisfied when the absolute value of the difference between the current value and the previous value _{of the correction amount Δh k} of the output side plate thickness of each rolling stand Fk is equal to or less than the threshold value. _{Further, even if the absolute value of the difference between the current value and the previous value of the correction amount Δh k} of the output side plate thickness of each rolling stand Fk is not equal to or less than the threshold value, when the number of determinations of the convergence condition reaches a predetermined value. Can be determined to satisfy the convergence condition.

As a result of this determination, if the convergence condition is satisfied, the process proceeds to step S708. In step S708, the output unit 605 rolls including the plate thickness schedule created by the plate thickness schedule creation unit 603 when the convergence condition is satisfied and the plate crown control amount y _{i when the convergence condition is satisfied.} Create a schedule and output it. Then, the process according to the flowchart of FIG. 7 is completed.

On the other hand, if the convergence condition is not satisfied, the process proceeds to step S709. Proceeding to step S709, the convergence test unit 604 creates a plate thickness schedule to be used by the model parameter derivation unit 601, the constraint expression / evaluation function setting unit 602, and the plate thickness schedule creation unit 603 in step S706 (immediately before). Change to the board thickness schedule. Then, the process returns to step S703 described above.

As described above, in the present embodiment, the rolling schedule (plate crown control amount y _i and plate thickness schedule) is updated until the convergence condition is satisfied. Therefore, in addition to the effects described in the first embodiment, the rolling schedule (plate thickness schedule and plate crown control amount y _i ) can be derived more accurately.

Also in this embodiment, various modifications described in the first embodiment can be adopted.

(Third Embodiment)
Next, a third embodiment will be described. In the second embodiment, as an evaluation function J for the purpose of reducing _{the correction amount Δh k of the output side plate thickness of each rolling stand Fk, the correction amount Δh k} itself of the output side plate thickness of each rolling stand Fk is reduced. An example of using an evaluation function for the purpose of this has been described (see equation (20)). However, in order to allow the material to be rolled to pass through the plate stably, it is preferable that the output side plate thickness of each rolling stand Fk is as close as possible _{to the ideal plate thickness schedule h0 k.} Therefore, in the present embodiment, the evaluation function J for the purpose of reducing _{the correction amount Δh k of the output side plate thickness of each rolling stand Fk is not the correction amount Δh k} itself of the output side plate thickness of each rolling stand Fk. An evaluation function is used for the purpose of reducing the amount of deviation of the output side plate thickness (= h _k + Δh _k ) of the rolling stand Fk from the ideal plate thickness schedule h0 _{k (desirable output side plate thickness of the rolling stand Fk).} As described above, the evaluation function J is mainly different between the present embodiment and the second embodiment. Therefore, in the description of the present embodiment, the same parts as those of the first to second embodiments are designated by the same reference numerals as those given in FIGS. 1 to 7, and detailed description thereof will be omitted.

In the present embodiment, in step S704 of the flowchart of FIG. 7 described in the second embodiment, the constraint equation / evaluation function setting unit 602 uses the following equation (34) as the evaluation function J instead of the equation (20). Set the evaluation function of.

The evaluation function J of the equation (34) is an evaluation function for the purpose of reducing _{the correction amount Δh k} of the output side plate thickness of each rolling stand Fk, as in the equation (20). However, the equation (34) is, as an example, an ideal plate thickness schedule of the output side plate thickness (= h _k + Δh _{k ) of each rolling stand Fk, not the correction amount Δh k itself of the output side plate thickness of each rolling stand Fk.} This is an evaluation function for the purpose of reducing the amount of deviation from _{h0 k (desirable output side plate thickness of the rolling stand Fk).}

Here, since the plate thickness of the material to be rolled is thicker _{on the upstream side, the correction amount Δh k} of the output side plate thickness of the rolling stand Fk is often larger as the rolling stand Fk is on the upstream side. _{Therefore, in order to evaluate the correction amount Δh k} of the output side plate thickness of each rolling stand Fk in the same manner, the ideal plate thickness schedule of the output side plate thickness of the rolling stand Fk is also applied to the equation (34) as in the equation (20). The absolute value of the ratio of the amount of deviation from h0 _k to the ideal plate thickness schedule h0 _{k is used.}

In the first processing of step S704, the constraint equation and evaluation function setting unit 602, as a side plate thickness h _k out of each rolling stand Fk in the sheet thickness schedule, in (34) (h _k of the molecule), ideal Set the plate thickness schedule h0 _{k. Further, Δh k} in the equation (34) is a correction amount from the ideal plate thickness schedule h0 _k. Therefore, in the first process, the values of the equations (20) and (34) are the same. On the other hand, in the second and subsequent processes, the constraint equation / evaluation function setting unit 602 was created in step S709 _{as the output side plate thickness h k} of each rolling stand Fk in the plate thickness schedule, instead of the ideal plate thickness schedule h0 _k. The (latest) plate thickness schedule (outside plate thickness h _k of each rolling stand F1 to Fn constituting each) is set to the formula (34) (molecule h _{k). Here, Δh k} in the equation (34) is a correction amount from the (latest) plate thickness schedule created in step S709 described later.

Further, as in the second embodiment, in the first process of step S706, the plate thickness schedule creation unit 603 corrects the output plate thickness of each rolling stand F1 to Fn-1 derived in step S705 Δh _k. Is added to the ideal plate thickness schedule h0 _{k, and the plate thickness schedule is defined as.} On the other hand, in the second and subsequent processes, the plate thickness schedule creation unit 603 sets the correction amount Δh _k of the output side plate thickness of each rolling stand Fk derived in step S705 in step S709 instead of the ideal plate thickness schedule h0 _k. The plate thickness schedule is the sum of the created (latest) plate thickness schedule (the output side plate thickness h _{k of each rolling stand Fk constituting the rolling stand Fk).}

As described above, in the present embodiment, the deviation amount of the output _{side plate thickness (= h k} + Δh _k ) of each rolling stand Fk from the ideal plate thickness schedule h0 _{k is reduced.} Therefore, in addition to the effects described in the first and second embodiments, it is possible to derive a _{rolling schedule (plate thickness schedule and plate crown control amount y i} ) so that the material to be rolled can be passed through the plate more stably. it can.
In this embodiment as well, various modifications described in the first embodiment can be adopted. For example, the evaluation function J of the equation (34) can be modified as in the modification examples 1 to 8.

(Fourth Embodiment)
Next, a fourth embodiment will be described. In the second embodiment, since the correction amount Δh _k of the output side plate thickness of each rolling stand Fk is evaluated in the same manner, the correction amount Δh _k of the output side plate thickness of the rolling stand Fk is relative to the ideal plate thickness schedule h0 _k . The case where the evaluation function J is expressed using the absolute value of the ratio has been described as an example. On the other hand, in the present embodiment, the ideal plate thickness schedule h0 _k is not included in the evaluation function J, and the ratio of _{the correction amount Δh k} of the output side plate thickness of the rolling stand Fk to the _{output side plate thickness h k of the rolling stand Fk.} The evaluation function J is expressed using the absolute value. It is better to use the second embodiment instead of the third embodiment because the ideal plate thickness schedule derived by the ideal plate thickness schedule acquisition unit 303 is not always desirable for stable plate thickness. It can be said that there are cases where it is not important to reduce the amount of deviation from the schedule h0 _k. Therefore, in such cases, even for the denominator of the evaluation function J, instead of the ideal thickness schedule h0 _k used in the second embodiment, because attempts to use delivery thickness h _k out of a rolling stand Fk Is the intention. As described above, a part of the content of the evaluation function J is mainly different between the present embodiment and the second embodiment. Therefore, in the description of the present embodiment, detailed description of the same parts as those of the first and second embodiments will be omitted by adding the same reference numerals as those given in FIGS. 1 to 7 and the like.

In the present embodiment, in step S704 of the flowchart of FIG. 7 described in the second embodiment, the constraint equation / evaluation function setting unit 602 uses the following equation (35) as the evaluation function J instead of the equation (20). Set the evaluation function of.

The evaluation function J of the equation (35) is an evaluation function for the purpose of reducing _{the correction amount Δh k} of the output side plate thickness of each rolling stand Fk, as in the equation (20). However, in the equation (35), since the correction amount Δh _k of the output side plate thickness of each rolling stand Fk is evaluated in the same manner, each rolling stand Fk is based on the _{output side plate thickness h k of each rolling stand Fk in the plate thickness schedule. Divide the correction amount Δh k} of the output side plate thickness of.

In the first processing of step S704, the constraint equation and evaluation function setting unit 602, as a side plate thickness h _k out of each rolling stand Fk in the sheet thickness schedule, in (35) (h _k of the denominator), ideal Set the plate thickness schedule h0 _{k. Further, Δh k} in the equation (35) is a correction amount from the ideal plate thickness schedule h0 _k. Therefore, in the first process, the values of the equations (20) and (35) are the same. In the first process of step S704, the values of the equation (34) described in the third embodiment are the same as those of the equations (20) and (35). On the other hand, in the second and subsequent processes, the constraint equation / evaluation function setting unit 602 sets the output plate thickness h _k of each rolling stand Fk in the plate thickness schedule to the ideal plate in equation (35) (denominator h _k). Instead of the thickness schedule h0 _k , the (latest) plate thickness schedule (latest plate thickness h _{k on} the exit side of each rolling stand F1 to Fn in step S709) is set. _{Here, Δh k} in the equation (35) is a correction amount from the (latest) plate thickness schedule created in step S709 described later.

Further, as in the second embodiment, in the first process of step S706, the plate thickness schedule creation unit 603 corrects the output plate thickness of each rolling stand F1 to Fn-1 derived in step S705 Δh _k. Is added to the ideal plate thickness schedule h0 _{k, and the plate thickness schedule is defined as.} On the other hand, in the second and subsequent processes, the plate thickness schedule creation unit 603 sets the correction amount Δh _k of the output side plate thickness of each rolling stand Fk derived in step S705 in step S709 instead of the ideal plate thickness schedule h0 _k. The plate thickness schedule is the sum of the created (latest) plate thickness schedule (the output side plate thickness h _{k of each rolling stand Fk).}

Even as described above, the same effect as described in the second embodiment can be obtained.
Also in this embodiment, the modified examples described in the first and second embodiments can be adopted. For example, the evaluation function J of the equation (35) can be modified as in the modification examples 1 to 8.

Further, it is preferable to perform the convergence calculation as described in the second, third, and fourth embodiments _{because the accuracy of the rolling schedule (plate thickness schedule and plate crown control amount y i} ) can be further improved. However, the evaluation function J of the formula (34) described in the third embodiment or the evaluation function J of the formula (35) described in the fourth embodiment has been described in the first embodiment (20). It may be used instead of the evaluation function J of the equation, and as described in the first embodiment, the rolling schedule (plate thickness schedule and plate crown control amount y _i ) may be derived without performing the convergence calculation.

(Example)
Next, an embodiment will be described.
<Example 1>
First, in the method described in the third embodiment, assuming that the thickness of the output side plate of each rolling stand Fk is not modified, the steepness of each rolling stand F1 to F7 and the set value for the roll vendor (WR vendor set value). Was derived as Comparative Example 1. However, here, as shown in the following equation (36), on the right side of the equation (34), the second term “W _δc δc” on the right side of the equation (23) shown in the modification 1 of the first embodiment. Is used as the evaluation function J. In this case, since the correction amount Δh _k of the output side plate thickness of each rolling stand Fk is set to 0 (zero), the value of the first term of the evaluation function J in equation (34) becomes 0 (zero) (that is, J). = W _δc δc).

FIG. 8 is a diagram showing the steepness of each rolling stand F1 to F7 and the set value (WR vendor set value) for the roll bender for such Comparative Example 1. The steepness is obtained by the equation (5), and the set value for the roll vendor (WR vendor set value) corresponds to the roll bending force.

In FIG. 8A, the broken lines 801 and 802 indicate the upper limit value and the lower limit value of the steepness, respectively. The solid line 803 indicates the obtained steepness. The dotted line 804 indicates a target value of steepness. That is, the deviation between the target value of the elongation ratio obtained by using the target value of steepness and the relationship of the equation (5) and the obtained elongation ratio is added to the evaluation function of the equation (36). In actual operation, it is common to set a target value for steepness or elongation, and add the deviation between the target value and the set value to the evaluation function. In FIG. 8B, the broken lines 811 and 812 indicate the upper limit value and the lower limit value of the set value (WR vendor set value) for the roll vendor, respectively. The solid line 813 indicates a set value (WR vendor set value) for the obtained roll vendor. In FIGS. 8 (a) and 8 (b), the numerical values shown beside the graph are the steepness (solid line 803) and the set value for the roll vendor (WR vendor set value, solid line 813) (solid line 813), respectively. ● value) is shown.
As shown in FIG. 8A, unless the thickness of the outer side plate of each rolling stand Fk is corrected, the rolling stands F6 and F7 on the downstream side do not satisfy the shape restriction range.

Further, the steepness and roll of each rolling stand F1 to F7 are performed by the technique described in Patent Document 1 (a technique of correcting the output side plate thickness of each rolling stand Fk but _{using an evaluation function that does not include the correction amount Δh k).} The set value for the bender (WR vendor set value) was derived as Comparative Example 2.
FIG. 9 is a diagram showing the steepness of each rolling stand F1 to F7 and the set value (WR vendor set value) for the roll bender for such Comparative Example 2.

In FIG. 9A, the broken lines 901 and 902 indicate the upper limit value and the lower limit value of the steepness, respectively. The solid line 903 indicates the obtained steepness. The dotted line 904 indicates a target value of steepness. In FIG. 9B, the broken lines 911 and 912 indicate the upper limit value and the lower limit value of the set value (WR vendor set value) for the roll vendor, respectively. The solid line 913 shows the set value (WR vendor set value) for the obtained roll vendor. In FIGS. 9 (a) and 9 (b), the numerical values shown beside the graph are the steepness (solid line 903) and the set value for the roll vendor (WR vendor set value, solid line 913), respectively. ● value) is shown.

Further, by the method of the third embodiment, the steepness of each rolling stand F1 to F7 and the set value for the roll vendor (WR vendor set value) are derived as an example of the invention. However, the equation (36) is also used as the evaluation function J here.
FIG. 10 is a diagram showing the steepness of each rolling stand F1 to F7 and the set value (WR vendor set value) for the roll vendor for such an example of the invention.

In FIG. 10A, the broken lines 1001 and 1002 indicate the upper limit value and the lower limit value of the steepness, respectively. The solid line 1003 indicates the obtained steepness. The dotted line 1004 indicates a target value of steepness. In FIG. 10B, the broken lines 1011 and 1012 indicate the upper limit value and the lower limit value of the set value (WR vendor set value) for the roll vendor, respectively. The solid line 1013 indicates a set value (WR vendor set value) for the obtained roll vendor. In addition, in FIG. 10A and FIG. 10B, the numerical values shown beside the graph are the values of the steepness (solid line 1003) and the set values for the roll vendor (WR vendor set value, solid line 1013), respectively. ● value) is shown.

Further, FIG. 11 is a diagram showing the rolling reduction ratios of the rolling stands F1 to F7. The reduction rate is obtained from the inlet side plate thickness and the outlet side plate thickness.
FIG. 11A is a diagram showing an example of the pre-change reduction rate, the post-change reduction rate, and the reduction correction rate as a result obtained by the method of Comparative Example 2. FIG. 11B is a diagram showing an example of the pre-change reduction rate, the post-change reduction rate, and the reduction correction rate as a result obtained by the method of the invention example. The reduction correction rate is the ratio of the value obtained by subtracting the reduction rate before change from the reduction rate after change to the reduction rate before change as a percentage.

In Comparative Example 2, as shown in FIG. 9A, the plate thickness schedule can be created so as to satisfy the constraint range of the shape, but as shown in FIG. 11A, the correction amount of the plate thickness is growing. On the other hand, in the example of the invention, as shown in FIG. 10A, the plate thickness schedule can be created so as to satisfy the constraint range of the shape, and moreover, as shown in FIG. 11B, the plate thickness can be created. The amount of correction of the above can be made smaller than that of Comparative Example 2, and can be suppressed to the minimum necessary.

<Example 2>
In this embodiment, as described in the modified example 5 of the first embodiment, the constraint condition relaxation amounts δc, δε, and δg are compared between the case of primary evaluation and the case of secondary evaluation, and the constraint condition relaxation. The effect of secondary evaluation of the quantities δc, δε, and δg was verified. Here, as an example, the constraint condition relaxation amount δc of the constraint equation for the _{plate crown C n} on the exit side of the rolling stand Fn in the final stage was evaluated. In this example, a simulation was performed in the case of rolling a material to be rolled of a steel type different from that of Example 1.

First, equation (36) is used as the evaluation function J for linearly evaluating the constraint condition relaxation amount δc, and equation (22) is used as the constraint equation for the _{plate crown C n on the exit side of the rolling stand Fn in the final stage.} By the method of the third embodiment, the plate crown C _i on the exit side of each rolling stand F1 to F7, the steepness of each rolling stand F1 to F7, and the set value for the roll vendor (WR vendor set value) were derived. ..

12, the steepness of the constraint condition relaxing amount δc of when evaluated in the primary, the strip crown C _i, each rolling stand F1-F7 on the delivery side of the rolling stands F1-F7, and set values for roll bender (WR It is a figure which shows an example of a bender setting value).

In FIG. 12A, broken lines 1201 and 1202 indicate the upper limit value and the lower limit value _{of the plate crown C 7} on the exit side of the rolling stand F7 in the final stage, respectively. The solid line 1203 indicates the obtained plate crown C _i . _{The plate crown C 7} on the exit side of the final stage rolling stand F 7 was 40.0 [μm] (see point 1204).

In FIG. 12B, the broken lines 1211 and 1212 indicate the upper limit value and the lower limit value of the steepness, respectively. The solid line 1213 indicates the obtained steepness. The dotted line 1214 indicates a target value of steepness. In FIG. 12 (c), the broken lines 1221 and 1222 indicate the upper limit value and the lower limit value of the set value (WR vendor set value) for the roll vendor, respectively. The solid line 1223 indicates a set value (WR vendor set value) for the obtained roll vendor.
In FIGS. 12 (a), 12 (b), and 12 (c), the numerical values shown beside the graph are set for the plate crown (solid line 1203), steepness (solid line 1213), and roll vendor, respectively. The value (value of ●) of the value (WR vendor set value, solid line 1223) is shown.

As shown in FIG. 12 (a), the plate crown C ₇ on the outlet side of the rolling stand F7 in the final stage is exactly the upper limit of 40 [μm], and the plate crown on the outlet side of the rolling stand Fn in the final stage. A _{solution satisfying the constraint condition regarding C n} (that is, a solution in which the constraint condition relaxation amount δc becomes 0 (zero) (δc = 0)) is obtained. However, as shown in FIG. 12B, the difference between the steepness and the target value 1214 becomes large. Further, as shown in FIG. 12 (c), the set value (WR vendor set value) for the roll vendor between the rolling stands F3 and F4 is 94 [t / c] (= | (-118)-(-24). ) |), Etc., the difference in the set value (WR vendor set value) for the roll vendor between the rolling stands adjacent to each other became large. That is, the set value for the roll vendor is a value that is not so desirable from the past operation experience of the production line to be calculated in this embodiment.

Next, the following equation (37) is used as the evaluation function J for quadrically evaluating the constraint condition relaxation amount δc, and the constraint equation (22) is used as the constraint equation for the _{plate crown C n on the exit side of the rolling stand Fn in the final stage.} By the method of the third embodiment, the plate crown C _i on the exit side of each rolling stand F1 to F7, the steepness of each rolling stand F1 to F7, and the set value for the roll vendor (WR bender set value). ) Was derived. _{The evaluation function J of the equation (37) has the second term “W δc} (δc) ² ” on the right side of the equation (30) shown in the modified example 5 of the first embodiment on the right side of the equation (34). It is an addition.

13, in the case of evaluating the constraint condition relaxing amount δc secondary, strip crown C _i at the delivery side of the rolling stand F1-F7, the steepness of each rolling stand F1-F7, and set values for roll bender ( It is a figure which shows an example of WR vendor setting value).

In FIG. 13A, the broken lines 1301 and 1302 indicate the upper limit value and the lower limit value _{of the plate crown C 7} on the exit side of the rolling stand F7 in the final stage, respectively. The upper limit value and the lower limit value are the same as the upper limit value and the lower limit value shown in FIG. 12A, respectively. The solid line 1303 indicates the obtained plate crown C _i . _{The plate crown C 7} on the exit side of the final stage rolling stand F 7 was 40.2 [μm] (see point 1304).

In FIG. 13B, the broken lines 1311 and 1312 indicate the upper limit value and the lower limit value of the steepness, respectively. The solid line 1313 shows the obtained steepness. The dotted line 1314 indicates a target value of steepness. The upper limit value, the lower limit value, and the target value are the same values as the upper limit value, the lower limit value, and the target value shown in FIG. 12B, respectively. In FIG. 13 (c), the broken lines 1321 and 1322 indicate the upper limit value and the lower limit value of the set value (WR vendor set value) for the roll vendor, respectively. The upper limit value and the lower limit value are the same as the upper limit value and the lower limit value shown in FIG. 12 (c), respectively. The solid line 1323 indicates a set value (WR vendor set value) for the obtained roll vendor.
In FIGS. 13 (a), 13 (b), and 13 (c), the numerical values shown beside the graph are set for the plate crown (solid line 1303), steepness (solid line 1313), and roll vendor, respectively. The value of the value (WR vendor set value, solid line 1323) is shown.

In the result shown in FIG. 13A, the constraint condition relaxation amount δc was 0.2 (δc = 0.2). That is, as shown in FIG. 13A, the plate crown C ₇ on the exit side of the rolling stand F7 in the final stage is 40.2 [μm], which exceeds the upper limit of 40 [μm]. However, this value is sufficiently smaller than the prediction accuracy (at least about several μm) of the model formula of the _{plate crown C i.}

Further, as shown in FIG. 13 (b), the steepness is closer to the target value 1314 than the steepness shown in FIG. 12 (b).
Further, as shown in FIG. 13 (c), the difference in the set value (WR vendor set value) between the rolling stands F3 and F4 with respect to the roll bender is 52 [t / c] (= | (-78)-(-). The difference in the set value (WR vendor set value) for the roll vendor between the rolling stands adjacent to each other, such as 26) |), is smaller than that shown in FIG. 12 (c), and the past operation is performed. There is no problem in light of experience.
Therefore, in the result shown in FIG. 13, _{the balance of the set values for the plate crown C n} , the elongation ratio ε _i , and the roll vendor can be improved with respect to the result shown in FIG. 12, and the desired setting can be obtained. I understand.

(Other variants)
The embodiment of the present invention described above can be realized by executing a program by a computer. Further, a computer-readable recording medium on which the program is recorded and a computer program product such as the program can also be applied as an embodiment of the present invention. As the recording medium, for example, a flexible disk, a hard disk, an optical disk, a magneto-optical disk, a CD-ROM, a magnetic tape, a non-volatile memory card, a ROM, or the like can be used.
In addition, the embodiments of the present invention described above are merely examples of embodiment of the present invention, and the technical scope of the present invention should not be construed in a limited manner by these. It is a thing. That is, the present invention can be implemented in various forms without departing from the technical idea or its main features.

(Relationship with claims)
The relationship between the claims and the embodiments is shown below. The present invention is not limited to the following relationship as described in the modified example.
The constraint expression setting means is realized by using, for example, the constraint expression / evaluation function setting units 305 and 602. The first constraint equation is realized by, for example, the equation (18), the equation (19), the equation (21), or the equation (22). The second constraint equation is realized by, for example, the equation (17) or the equation (24). The third constraint equation is realized by, for example, equation (16). The fourth constraint equation is realized by, for example, the equation (27) or the equation (28). It should be noted that the relaxation amount may or may not be specified in the constraint equation as described in the first modification of the first embodiment. Further, the fact that the shape is not limited to the elongation ratio is as described in the modified example 8 of the first embodiment.
The evaluation function setting means is realized by using, for example, the constraint expression / evaluation function setting units 305 and 602.
The optimum calculation means is realized by using, for example, the optimum calculation unit 306.
The plate thickness schedule creation means is realized, for example, by using the plate thickness schedule creation units 307 and 603.
The convergence test means is realized by using, for example, the convergence test unit 604.
Claim 2 corresponds to modifications 1 to 5 of the first embodiment, and claim 3 corresponds to modification 5 of the first embodiment. It is possible to apply the modified examples 1 to 5 of the first embodiment also in the second to fourth embodiments as described in the modified examples after the second to fourth embodiments.
Claim 4 corresponds to the first embodiment, and the evaluation function according to claim 4 corresponds to, for example, the evaluation function J (Equation (20)) of the first embodiment.
Claim 5 corresponds to the second embodiment, and the evaluation function according to claim 5 corresponds to, for example, the evaluation function J (formula (20)) of the second embodiment.
Claim 6 corresponds to the third embodiment, and the evaluation function according to claim 6 corresponds to, for example, the evaluation function J (Equation (34)) of the third embodiment.
Claim 7 corresponds to the fourth embodiment, and the evaluation function according to claim 7 corresponds to, for example, the evaluation function J (Equation (35)) of the fourth embodiment.
It should be noted that the equation (34) or the equation (35) may be used instead of the equation (20) as in the first embodiment (convergence calculation may not be performed) in the fourth embodiment. It is as explained in the modified example after the explanation of.
Claim 9 corresponds to the modified example 4 of the first embodiment, and the fourth constraint equation is realized by, for example, the equation (27). Claim 10 also corresponds to the modified example 4 of the first embodiment, the fourth constraint equation is realized by the equation (28), for example, and the evaluation function is realized by the equation (29), for example. Claim 11 corresponds to a modified example 5 of the first embodiment. The first term according to claim 12 is realized by, for example, the first term on the right side of the equation (10), and the second term is realized by, for example, the second term on the right side of the equation (10). Is realized by, for example, the third term on the right side of the equation (10). The fourth term is realized by, for example, the first term on the right side of the equation (11), the fifth term is realized by, for example, the second term on the right side of the equation (11), and the sixth term is, for example, It is realized by the third term on the right side of the equation (11).

300/600: Rolling schedule creation device, 301: Data storage unit, 302: Operation standard acquisition unit, 303: Ideal plate thickness schedule acquisition unit, 304/601: Model parameter derivation unit, 305/602: Constraint formula / evaluation function setting Unit, 306: Optimal calculation unit, 307/603: Plate thickness schedule creation unit, 308: Output unit, 605: Convergence judgment unit

Claims (14)

The plate crown control amount, which is the amount of plate crown on the outlet side of the rolling stand, which is changed by the operation of the plate crown and shape control ends in a plurality of rolling stands constituting the tandem rolling mill, and the plate crown thickness on the output side of the rolling stand. A rolling schedule creation device that creates a rolling schedule including
The first constraint equation that defines the permissible range or target value of the plate crown on the outlet side of the rolling stand in the final stage and the permissible range of the shape of the material to be rolled on the outlet side of the rolling stand are set for the plurality of rolling stands. A second constraint formula that defines each of them, a constraint formula setting means that sets a constraint formula that includes a third constraint formula that defines the allowable range of the plate crown control amount for each of the plurality of rolling stands, and a constraint formula setting means.
An evaluation function setting means for setting an evaluation function for the purpose of reducing the amount of correction of the outer plate thickness of the rolling stand excluding the final stage rolling stand from the ideal plate thickness.
The amount of correction from the ideal plate thickness of the outer plate thickness of the rolling stand excluding the rolling stand of the final stage when the value of the evaluation function becomes the minimum or maximum within the range satisfying the constraint equation, and the above. Optimal calculation means for deriving the plate crown control amount in a plurality of rolling stands by performing optimization calculation by a mathematical programming method.
Based on the amount of correction from the ideal plate thickness of the output side plate thickness of the rolling stand excluding the final stage rolling stand derived by the optimum calculation means from the ideal plate thickness and the ideal plate thickness, the exit side plate in the rolling stand. A rolling schedule creating apparatus comprising: a plate thickness schedule creating means for creating a thickness as a plate thickness schedule. In at least one of the first constraint expression and the second constraint expression, the relaxation amount for the allowable range specified for the constraint expression is further specified.
The evaluation function is a function including a correction amount from the ideal plate thickness of the outer plate thickness of the rolling stand excluding the rolling stand in the final stage, the relaxation amount, and a weighting coefficient for balancing them. The rolling schedule creating apparatus according to claim 1, wherein the rolling schedule is created. The evaluation function includes a correction amount from the ideal plate thickness of the outer plate thickness of the rolling stand excluding the rolling stand in the final stage, a square term of the relaxation amount, and a weighting coefficient for balancing them. The rolling schedule creating apparatus according to claim 2, wherein the rolling schedule is a function including. The evaluation function is the final stage of the absolute value or the square of the value obtained by dividing the correction amount of the outer plate thickness of the rolling stand from the ideal plate thickness by the ideal plate thickness of the outer side of the rolling stand. The rolling schedule creating apparatus according to any one of claims 1 to 3, further comprising a term for obtaining the sum of the plurality of rolling stands excluding the rolling stands of the above. Further, it has a convergence test means for determining whether or not the result of the optimization calculation has converged.
Until it is determined by the convergence determination means that the result of the optimization calculation has converged, at least by the correction amount of the output side plate thickness of the rolling stand derived by the optimization calculation determined to have not converged. The latest output side plate thickness of the modified rolling stand is reset to the constraint equation and the evaluation function, the optimization calculation is performed using the reset evaluation function, and the optimum It is a schedule creation device that repeats convergence calculation to correct the output side plate thickness of the rolling stand to the latest output side plate thickness by the correction amount of the output side plate thickness of the rolling stand derived by the calculation. ,
In the first calculation of the convergence calculation, the outer plate thickness of the rolling stand is corrected as the correction amount of the outer plate thickness of the rolling stand excluding the rolling stand of the final stage, which is derived by the optimization calculation. , The correction amount from the ideal plate thickness is derived, and the evaluation function divides the correction amount from the ideal plate thickness of the output side plate thickness of the rolling stand by the ideal plate thickness on the exit side of the rolling stand. Includes a term for the absolute value or square of the value obtained by calculating the sum of the plurality of rolling stands excluding the rolling stands in the final stage.
In the second and subsequent calculations of the convergence calculation, the outer plate thickness of the rolling stand is corrected as the correction amount of the outer plate thickness of the rolling stand excluding the rolling stand of the final stage, which is derived by the optimization calculation. The correction amount from the latest output plate thickness of the rolling stand corrected in the previous convergence calculation is derived, and the evaluation function is the correction amount of the outside plate thickness of the rolling stand from the ideal plate thickness. Instead of, the amount of correction of the outer plate thickness of the rolling stand from the latest outer plate thickness of the rolling stand, which was corrected in the previous convergence calculation, is divided by the ideal plate thickness of the outer side of the rolling stand. The rolling schedule creating apparatus according to claim 4, further comprising a term for obtaining the sum of the absolute value or the square of the performed value for the plurality of rolling stands excluding the rolling stand in the final stage. Further, it has a convergence test means for determining whether or not the result of the optimization calculation has converged.
Until it is determined by the convergence determination means that the result of the optimization calculation has converged, at least by the correction amount of the output side plate thickness of the rolling stand derived by the optimization calculation determined to have not converged. The latest output side plate thickness of the modified rolling stand is reset to the constraint equation and the evaluation function, the optimization calculation is performed using the reset evaluation function, and the optimum It is a schedule creation device that repeats convergence calculation to correct the output side plate thickness of the rolling stand to the latest output side plate thickness by the correction amount of the output side plate thickness of the rolling stand derived by the calculation. ,
In the first calculation of the convergence calculation, the rolling stand of the final stage is excluded as the correction amount of the outer plate thickness of the rolling stand excluding the rolling stand of the final stage, which is derived by the optimization calculation. The amount of correction of the outer plate thickness of the rolling stand from the ideal plate thickness is derived, and the evaluation function determines the amount of correction of the outer plate thickness of the rolling stand from the ideal plate thickness of the rolling stand. Includes a term for the absolute value or square of the value obtained by dividing by the ideal plate thickness on the side to obtain the sum of the plurality of rolling stands excluding the final stage rolling stand.
In the second and subsequent calculations of the convergence calculation, the correction amount of the outer plate thickness of the rolling stand excluding the rolling stand of the final stage, which is derived by the optimization calculation, is corrected in the previous convergence calculation. When the correction amount from the latest output side plate thickness of the rolling stand is corrected, the correction amount from the ideal plate thickness of the latest output side plate thickness of the rolling stand corrected in the previous convergence calculation is derived. And, the evaluation function is a correction amount from the latest output side plate thickness of the rolling stand, which was corrected in the previous convergence calculation, instead of the correction amount of the output side plate thickness of the rolling stand from the ideal plate thickness. Dividing the amount of correction from the ideal plate thickness of the latest output plate thickness of the rolling stand corrected in the previous convergence calculation by the ideal plate thickness of the exit side of the rolling stand in the case of correction in The rolling schedule creating apparatus according to claim 4, further comprising a term for obtaining the sum of the absolute value or the square of the performed value for the plurality of rolling stands excluding the rolling stand in the final stage. Further, it has a convergence test means for determining whether or not the result of the optimization calculation has converged.
Until it is determined by the convergence determination means that the result of the optimization calculation has converged, at least by the correction amount of the output side plate thickness of the rolling stand derived by the optimization calculation determined to have not converged. The latest output side plate thickness of the modified rolling stand is reset to the constraint equation and the evaluation function, the optimization calculation is performed using the reset evaluation function, and the optimum It is a schedule creation device that repeats convergence calculation to correct the output side plate thickness of the rolling stand to the latest output side plate thickness by the correction amount of the output side plate thickness of the rolling stand derived by the calculation. ,
In the first calculation of the convergence calculation, the outer plate thickness of the rolling stand is corrected as the correction amount of the outer plate thickness of the rolling stand excluding the rolling stand of the final stage, which is derived by the optimization calculation. , The correction amount from the ideal plate thickness is derived, and the evaluation function divides the correction amount from the ideal plate thickness of the output side plate thickness of the rolling stand by the ideal plate thickness on the exit side of the rolling stand. Includes a term for the absolute value or square of the value obtained by calculating the sum of the plurality of rolling stands excluding the rolling stands in the final stage.
In the second and subsequent calculations of the convergence calculation, the outer plate thickness of the rolling stand is corrected as the correction amount of the outer plate thickness of the rolling stand excluding the rolling stand of the final stage, which is derived by the optimization calculation. The correction amount from the latest output plate thickness of the rolling stand corrected in the previous convergence calculation is derived, and the evaluation function is the correction amount of the outside plate thickness of the rolling stand from the ideal plate thickness. and instead of the division divided by the ideal thickness of the exit side of the rolling stands, wherein the thickness at delivery side of the rolling stand, the correction amount of the latest delivery side thickness or al of the rolling stands that have been modified in the previous convergence calculation Is the absolute value or square of the value obtained by dividing by the latest output plate thickness of the rolling stand, which was corrected in the previous convergence calculation, and is the sum of the plurality of rolling stands excluding the rolling stand in the final stage. The rolling schedule creating apparatus according to claim 4, wherein the rolling schedule is included. The rolling schedule creating apparatus according to any one of claims 1 to 7, wherein the shape has an elongation ratio or a steepness. The constraint equation is a physical quantity different from the plate crown and the shape, and is a physical quantity derived based on at least one of the plate crown control amount and the change amount of the exit side plate thickness of the rolling stand. The rolling schedule creating apparatus according to any one of claims 1 to 8, further comprising a fourth constraint equation that defines an allowable range. The fourth constraint equation further defines the amount of relaxation for the permissible range defined for the fourth constraint equation.
The evaluation function is defined for the amount of correction of the output side plate thickness of the rolling stand excluding the final stage rolling stand among the plurality of rolling stands from the ideal plate thickness and the fourth constraint equation. The rolling schedule creating apparatus according to claim 9, wherein the rolling schedule creator is a function including the relaxation amount and a weighting coefficient for balancing them. The evaluation function is defined for the amount of correction of the output side plate thickness of the rolling stand excluding the final stage rolling stand among the plurality of rolling stands from the ideal plate thickness and the fourth constraint equation. The rolling schedule creating apparatus according to claim 10, wherein the rolling schedule creator is a function including a square term of the relaxation amount and a weighting coefficient for balancing them. The formula for deriving the plate crown on the exit side of the rolling stand includes the first term indicating the reference plate crown in the rolling stand, and the plate crown in the rolling stand and the plurality of rolling stands other than the rolling stand. The second term for obtaining the integrated value for each of the plurality of rolling stands of the plate crown generated on the outlet side of the rolling stand due to the operation of the shape control end, and the above-mentioned other than the rolling stand and the rolling stand. The integrated value of the plate crown generated on the exit side of the rolling stand due to the change in the thickness of the outside plate of the plurality of rolling stands for each of the rolling stands excluding the final stage rolling stand among the plurality of rolling stands. Including the third term to be sought,
The formula for deriving the shape on the outlet side of the rolling stand includes the fourth item indicating the shape of the reference in the rolling stand, and the plate crown / shape in the rolling stand and the plurality of rolling stands other than the rolling stand. The fifth term for obtaining the integrated value for each of the plurality of rolling stands of the shape obtained on the outlet side of the rolling stand due to the operation of the control end, and the above-mentioned other than the rolling stand and the rolling stand. Cumulative value for each of the rolling stands excluding the final stage rolling stand of the plurality of rolling stands of the shape obtained on the protruding side of the rolling stand due to a change in the thickness of the protruding side of the plurality of rolling stands. The rolling schedule making apparatus according to any one of claims 1 to 11, further comprising the sixth item. The plate crown control amount, which is the amount of plate crown on the outlet side of the rolling stand, which is changed by the operation of the plate crown and shape control ends in a plurality of rolling stands constituting the tandem rolling mill, and the plate crown thickness on the output side of the rolling stand. It is a rolling schedule creation method for creating a rolling schedule including
The first constraint equation that defines the permissible range or target value of the plate crown on the outlet side of the rolling stand in the final stage and the permissible range of the shape of the material to be rolled on the outlet side of the rolling stand are set for the plurality of rolling stands. A second constraint formula that defines each of them, a constraint formula setting step that sets a constraint formula that includes a third constraint formula that defines the allowable range of the plate crown control amount for each of the plurality of rolling stands, and a constraint formula setting step.
An evaluation function setting process for setting an evaluation function for the purpose of reducing the amount of correction of the outer plate thickness of the rolling stand excluding the final stage rolling stand from the ideal plate thickness, and
The amount of correction from the ideal plate thickness of the outer plate thickness of the rolling stand excluding the rolling stand of the final stage when the value of the evaluation function becomes the minimum or maximum within the range satisfying the constraint equation, and the above. An optimum calculation process for deriving the control amount of the plate crown in a plurality of rolling stands by performing an optimization calculation by a mathematical programming method, and
Based on the amount of correction from the ideal plate thickness of the outer plate thickness of the rolling stand excluding the rolling stand of the final stage, which was derived by the optimum calculation step , and the ideal plate thickness, the outer plate of the rolling stand. A method for creating a rolling schedule, which comprises a plate thickness schedule creating process for creating a thickness as a plate thickness schedule, and a rolling schedule creating process. A program characterized in that a computer functions as each means of the rolling schedule creating apparatus according to any one of claims 1 to 12.

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