JP6786848B2 - Support methods, equipment and programs for molten steel temperature control in the steelmaking process - Google Patents

Description

INDUSTRIAL APPLICABILITY The present invention relates to a method, an apparatus, and a method, an apparatus for supporting molten steel temperature control in a steelmaking process in which molten steel is dispensed into a ladle after primary refining in a primary refining furnace, secondary refining, and continuous casting. Regarding the program.

In the steelmaking process at a steelmaking factory, after the smelting is completed from a primary smelting furnace such as an electric furnace or a converter, molten steel is discharged into a ladle, and the RH degassing device or ladle smelting is performed while the ladle is filled with molten steel. The refining process is performed by a secondary refining facility such as an apparatus (LF), and the pieces are transported to a continuous casting machine to produce slabs.
In the steelmaking process, the target temperature is the molten steel temperature at the start of continuous casting, using the operation schedule set in advance before the start of converter smelting, the alloy input for the manufacturing material (steel type), and the condition setting values for secondary refining. As described above, the target temperature indication value at the time of completion of steelmaking to the ladle and the target temperature indication value at the start of secondary refining until the molten steel discharged to the ladle is cast by continuous casting, and the secondary The target temperature indication value at the end of refining is determined before the converter blown.
The target temperature indicated value can be determined based on a detailed condition table for each steel type and operating method, and the ladle transfer time and secondary refining between treatments and changes in the molten steel temperature during treatment. There is a method of expressing by a model expressed by a regression equation from the operating condition actual data during processing and determining by an optimization means such as a mathematical programming method based on the model.

Normally, for a series of processes (hereinafter referred to as charge for each ladle), the upper and lower limits of the molten steel temperature at the completion of steel delivery to the ladle are restricted for each steel type, and the upper and lower limits of the molten steel temperature at the start of secondary refining are applied. The upper and lower limit constraints of the molten steel temperature at the end of the secondary refining are set, and each target temperature indication value must be determined so as to comply with these temperature constraints.
However, if the schedule for the start of secondary refining and the start of continuous casting set before the converter blowing is not appropriate, it may not be possible to determine the target temperature indication value that keeps the above temperature constraints. Therefore, it may be necessary to perform a temperature adjustment process such as a temperature raising process or a cold material input in the secondary refining after the steel is discharged into the ladle. Alternatively, if the operation is performed according to the target temperature indicated value, the molten steel temperature during continuous casting becomes excessively high, and the casting speed must be lowered from the originally planned speed, or the casting speed becomes excessively low. Changes may occur during the operation, such as the casting being forced to be terminated early.

Conventionally, such problems have been solved by optimizing the molten steel temperature and the operation schedule at the same time.
Patent Document 1 is a method for creating an operation schedule in a steelmaking process using at least one converter, at least one secondary refining facility, and at least one continuous casting machine. A schedule information reading process that reads operation schedule information of a plurality of charges in a period, and processing of a charge that has already started processing when there is a charge that has already started processing in each facility among the plurality of charges. Based on the performance information reading process that reads the operation performance information related to the start actual time or the processing end actual time, and the operation schedule information and the operation performance information, as a constraint condition, at least the processing start time in each facility that performs the processing. And the condition of the processing end time, and the condition of the molten steel temperature at the start and end of each facility, the constraint condition generation process, and the objective function including the index calculated by the molten steel temperature in the continuous casting machine are generated. Disclosed is an operation schedule creation method including an objective function generation step and an optimum schedule determination step for determining a schedule for maximizing or minimizing the objective function under the constraint condition. ..
However, it can be said that the method of Patent Document 1 changes the operation schedule in order to satisfy the constraint of the molten steel temperature. If the operation schedule after the secondary refining is determined before the start of the converter blowing, the secondary refining start time and the continuous casting start time cannot be changed as in Patent Document 1.
Therefore, it is required to relax the temperature constraints within the allowable range for operation and quality and to formulate a target temperature path that can be operated, and it is important to present the next best solution even if the constraints are not completely satisfied. is there.

Further, in Patent Document 2, each belt furnace of the heating furnace is individually controlled under some heating constraints by using the LP solution obtained by the calculation by the LP method (linear programming method), and the fuel consumption is controlled. In the heating furnace slab temperature control device that heats each slab charged in the heating furnace to the target extraction temperature while keeping the minimum, the heating constraint condition storage unit that stores the heating constraint conditions with priority. , Even if the calculation by the LP method is performed, if the optimum LP solution satisfying all the heating constraint conditions cannot be found, the heating constraint condition having a lower priority is selected from the heating constraint conditions stored in the heating constraint condition storage unit. Except for this, a heating furnace slab temperature control device including a calculation unit for performing a calculation by the LP method again to find an optimum LP solution and a heating furnace slab temperature control device are disclosed.
However, in the method of Patent Document 2, the shortest order for removing the constraint condition until the LP solution is obtained cannot be known in advance, and there is a possibility that the constraint condition is unnecessarily removed by the time the LP solution is obtained. is there.

JP-A-2014-366974 Japanese Unexamined Patent Publication No. 2000-256734

The present invention has been made in view of the above points, and is a target temperature indicated value at the time of completion of steel delivery to the ladle without changing the operation schedule and appropriately relaxing the temperature constraint. The purpose is to be able to present the target temperature indicated value at the start of the secondary refining, the target temperature indicated value at the end of the secondary refining, and the predicted value of the molten steel temperature at the start of continuous casting.

The gist of the present invention for solving the above problems is as follows.
[1] A method for supporting the temperature control of molten steel in a steelmaking process in which molten steel is put out in a ladle after primary refining in a primary refining furnace and then secondary refining and continuous casting are performed.
The target temperature indication value at the completion of steel delivery to the pan, the target temperature indication value at the start of secondary refining, the target temperature indication value at the end of secondary refining, and the predicted value of the molten steel temperature at the start of continuous casting. , The variable representing the absolute value (called the constraint violation amount) of the amount of deviation from the upper and lower limit constraints of each target temperature indicated value is used as a determination variable, and the predicted value and target of the molten steel temperature at the start of continuous casting. As a linear planning problem whose objective function is a function including the absolute value of the difference from temperature and the sum of the values obtained by multiplying the variable representing the constraint violation amount by a weighting coefficient that takes a non-negative value.
A model that estimates the amount of decrease in molten steel temperature from the completion of steel delivery to the ladle to the start of secondary refining, a model that estimates the amount of decrease in molten steel temperature from the start of secondary refining to the end of secondary refining, and a model that estimates the amount of decrease in molten steel temperature from the start of secondary refining to the end of secondary refining. An equation constraint condition that is determined based on a model that estimates the amount of decrease in molten steel temperature from the end to the start of continuous casting, and is expressed including the respective target temperature indication values and the predicted value of the molten steel temperature at the start of continuous casting. When,
An inequality indicating that the target temperature indication value at the completion of steel delivery to the pan is included within the range in which the upper and lower limit constraints of the target temperature indication value at the completion of steel delivery to the pan are relaxed by the above constraint violation amount. The inequality indicating that the target temperature indicated value at the start of the secondary refining is included within the range in which the upper and lower limit constraints of the target temperature indicated value at the start of the secondary refining are relaxed by the constraint violation amount, and the end of the secondary refining. Based on the inequality constraint condition expressed by the inequality indicating that the target temperature indicated value at the end of the secondary refining is included in the range in which the upper and lower limit constraints of the target temperature indicated value at the time are relaxed by the constraint violation amount. hand,
An optimal solution calculation step for calculating an optimal solution that minimizes the objective function for a plurality of combinations of the weighting coefficients, and
In the optimum solution calculation step, the target temperature indication value at the time of completion of steelmaking to the ladle and the target temperature instruction at the start of the secondary refining in the optimum solution calculated corresponding to each of the plurality of combinations of the weight coefficients. The molten steel temperature control in the steelmaking process is characterized by having a presentation step of presenting a plurality of combinations of a value, a target temperature indicated value at the end of secondary refining, and a predicted value of the molten steel temperature at the start of continuous casting. Support method.
[2] The plurality of combinations of the weighting coefficients are a combination in which the weighting coefficients are all set to 0, and the weighting coefficient of one target temperature indicated value for each targeting temperature indicated value is used as the other targeting temperature indicated value. The method for supporting molten steel temperature control in the steelmaking process according to [1], which includes a combination that is sufficiently larger than the weighting coefficient.
[3] The magnitude of the weighting coefficient is set to 1 or more for the target temperature indicated value that emphasizes falling within the upper and lower limit constraints, and the target temperature indicated value that neglects entering the upper and lower limit constraints. On the other hand, the method for supporting the temperature control of molten steel in the steelmaking process according to [2], wherein the temperature is 0.01 or less.
[4] In the presentation step, the target temperature indicated value at the time of completion of steelmaking to the ladle in the optimum solution calculated in the optimum solution calculation step, the target temperature indicated value at the start of the secondary refining, and the secondary refining A graph in which a plurality of combinations of the target temperature indicated value at the end and the predicted value of the molten steel temperature at the start of continuous casting are plotted against the passage of time is drawn together with the upper and lower limit constraints and the target temperature. The method for supporting molten steel temperature control in a steelmaking process according to any one of [1] to [3], which comprises displaying on a screen on a display device.
[5] A support device for temperature control of molten steel in a steelmaking process in which molten steel is dispensed into a ladle after primary refining in a primary refining furnace and then secondary refining and continuous casting are performed.
The target temperature indication value at the completion of steel delivery to the pan, the target temperature indication value at the start of secondary refining, the target temperature indication value at the end of secondary refining, and the predicted value of the molten steel temperature at the start of continuous casting. , The variable representing the absolute value (called the constraint violation amount) of the amount of deviation from the upper and lower limit constraints of each target temperature indicated value is used as a determination variable, and the predicted value and target of the molten steel temperature at the start of continuous casting. As a linear planning problem whose objective function is a function including the absolute value of the difference from temperature and the sum of the values obtained by multiplying the variable representing the constraint violation amount by a weighting coefficient that takes a non-negative value.
A model that estimates the amount of decrease in molten steel temperature from the completion of steel delivery to the ladle to the start of secondary refining, a model that estimates the amount of decrease in molten steel temperature from the start of secondary refining to the end of secondary refining, and a model that estimates the amount of decrease in molten steel temperature from the start of secondary refining to the end of secondary refining. An equation constraint condition that is determined based on a model that estimates the amount of decrease in molten steel temperature from the end to the start of continuous casting, and is expressed including the respective target temperature indication values and the predicted value of the molten steel temperature at the start of continuous casting. When,
An inequality indicating that the target temperature indication value at the completion of steel delivery to the pan is included within the range in which the upper and lower limit constraints of the target temperature indication value at the completion of steel delivery to the pan are relaxed by the above constraint violation amount. The inequality indicating that the target temperature indicated value at the start of the secondary refining is included within the range in which the upper and lower limit constraints of the target temperature indicated value at the start of the secondary refining are relaxed by the constraint violation amount, and the end of the secondary refining. Based on the inequality constraint condition expressed by the inequality indicating that the target temperature indicated value at the end of the secondary refining is included in the range in which the upper and lower limit constraints of the target temperature indicated value at the time are relaxed by the constraint violation amount. hand,
An optimal solution calculation means for calculating an optimal solution that minimizes the objective function for a plurality of combinations of the weighting coefficients.
The target temperature indication value at the time of completion of steelmaking to the ladle and the target temperature instruction at the start of the secondary refining in the optimum solution calculated corresponding to each of the plurality of combinations of the weight coefficients by the optimum solution calculation means. Steelmaking temperature control in a steelmaking process, which comprises a presenting means for presenting a plurality of combinations of a value, a target temperature indicated value at the end of secondary refining, and a predicted value of the molten steel temperature at the start of continuous casting. Support device.
[6] A program to support the temperature control of molten steel in the steelmaking process of primary refining in the primary refining furnace, secondary refining after the molten steel is put out in the ladle after the primary refining, and continuous casting. There,
The target temperature indication value at the completion of steel delivery to the pan, the target temperature indication value at the start of secondary refining, the target temperature indication value at the end of secondary refining, and the predicted value of the molten steel temperature at the start of continuous casting. , The variable representing the absolute value (called the constraint violation amount) of the amount of deviation from the upper and lower limit constraints of each target temperature indicated value is used as a determination variable, and the predicted value and target of the molten steel temperature at the start of continuous casting. As a linear planning problem whose objective function is a function including the absolute value of the difference from temperature and the sum of the values obtained by multiplying the variable representing the constraint violation amount by a weighting coefficient that takes a non-negative value.
A model that estimates the amount of decrease in molten steel temperature from the completion of steel delivery to the ladle to the start of secondary refining, a model that estimates the amount of decrease in molten steel temperature from the start of secondary refining to the end of secondary refining, and a model that estimates the amount of decrease in molten steel temperature from the start of secondary refining to the end of secondary refining. An equation constraint condition that is determined based on a model that estimates the amount of decrease in molten steel temperature from the end to the start of continuous casting, and is expressed including the respective target temperature indication values and the predicted value of the molten steel temperature at the start of continuous casting. When,
An inequality indicating that the target temperature indication value at the completion of steel delivery to the pan is included within the range in which the upper and lower limit constraints of the target temperature indication value at the completion of steel delivery to the pan are relaxed by the above constraint violation amount. The inequality indicating that the target temperature indicated value at the start of the secondary refining is included within the range in which the upper and lower limit constraints of the target temperature indicated value at the start of the secondary refining are relaxed by the constraint violation amount, and the end of the secondary refining. Based on the inequality constraint condition expressed by the inequality indicating that the target temperature indicated value at the end of the secondary refining is included in the range in which the upper and lower limit constraints of the target temperature indicated value at the time are relaxed by the constraint violation amount. hand,
Optimal solution calculation processing for calculating the optimal solution that minimizes the objective function for a plurality of combinations of the weighting coefficients, and
In the optimum solution calculation process, the target temperature instruction value at the time of completion of steel delivery to the ladle and the target temperature instruction at the start of the secondary refining in the optimum solution calculated corresponding to each of the plurality of combinations of the weight coefficients. A program for causing a computer to execute a presentation process that presents a plurality of combinations of a value, a target temperature indicated value at the end of secondary refining, and a predicted value of a molten steel temperature at the start of continuous casting.

According to the present invention, the target temperature indicated value at the time of completion of steel delivery to the ladle and the target temperature indicated value at the start of secondary refining without changing the operation schedule and appropriately relaxing the temperature constraint. It is possible to present a plurality of combinations of the target temperature indicated value at the end of the secondary refining and the predicted value of the molten steel temperature at the start of continuous casting. This makes it possible to select a combination of each target temperature indicated value suitable for the operation and a predicted value of the molten steel temperature at the start of continuous casting from a plurality of combinations based on the knowledge of the operator.

It is a figure which shows the functional structure of the support device of molten steel temperature control which concerns on embodiment. Multiple target temperature indication values at the completion of steel delivery to the ladle, target temperature indication values at the start of secondary refining, and predicted values of molten steel temperature at the start of continuous casting. It is a figure which shows the example of the screen display which presents a combination. It is a flowchart which shows the support method of the molten steel temperature control by the support device of the molten steel temperature control which concerns on embodiment.

Hereinafter, preferred embodiments of the present invention will be described with reference to the accompanying drawings. In the present embodiment, a steelmaking process in which a converter is used as the primary refining furnace and an RH degassing device is used as the secondary refining device is assumed, but the present invention is also applicable when an electric furnace, LF, or the like is used.

FIG. 1 shows the functional configuration of the molten steel temperature control support device 100 according to the embodiment.
Reference numeral 101 denotes an input unit, and the calculation unit 102 formulates a linear programming problem and inputs information necessary for solving the problem.
The input unit 101 inputs, for the target charge, the operation schedule determined before the start of the converter blowing, the alloy input regarding the manufacturing material (steel grade), and the condition setting values for the secondary refining. These information may be input by the operator using the input device 104, or may be received from an external device such as a process computer.
The input unit 101, the upper limit T _RHSU and lower T max T _LDU and lower T _LDL, 2 primary refining starting mark temperatures indicated value T _RHS of mark temperatures indicated value T _LD during tapping the completion of the ladle _{Enter RHSL} , the upper limit T _RHEU and lower limit T _RHEL of the target temperature indication value T _RHE at the end of secondary refining, and the target temperature T _CCS ^* of the molten steel temperature at the start of continuous casting. This information may be input by the operator each time using the input device 104, for example, or a value preset for each steel type and stored in the storage device may be selected and used. May be good.

Reference numeral 102 denotes a calculation unit that functions as an optimum solution calculation means, and details will be described later. However, a linear planning problem is formulated based on the information input by the input unit 101, and the problem is solved to complete the steel delivery to the ladle. Obtain the target temperature indicated value T _LD at the time, the target temperature indicated value T _RHS at the start of the secondary refining, the target temperature indicated value T _RHE at the end of the secondary refining, and the predicted value T _CCS of the molten steel temperature at the start of continuous casting.
Wherein each mark temperatures indicated value T _LD, T _RHS, T _RHE lower limit restriction on each _{(T LDU, T LDL),} (T RHSU, T RHSL), when deviating from the (T _RHEU, T _RHEL) , The absolute value of the amount of deviation from the upper limit when the upper limit is exceeded, and the absolute value of the amount of deviation from the lower limit when the lower limit is exceeded are called the constraint violation amount.
The calculation unit 102 sets the upper and lower limits of each target temperature instruction value T _LD , T _RHS , T _{R HE} , the predicted value T _CCS of the molten steel temperature at the start of continuous casting, and each target temperature instruction value T _LD , T _RHS , T _{R HE.} about (T _LDU, T _LDL), and _{(T RHSU, T RHSL),} (T RHEU, T RHEL) decision variables the variable m _i representing a constraint violation amount for, also, as in equation (1), the continuous casting adding the absolute value of the difference between the predicted value T _CCS at the start of the molten steel temperature and the target temperature T _CCS ^*, a sum of values obtained by multiplying the weight coefficient W _i taking non-negative value to a variable m _i representing a constraint violation amount We formulate the combined function as a linear planning problem with the objective function z. Incidentally, i is an identification number, upper T _LDU, lower T _LDL, the upper limit T _RHSU, lower T _RHSL, upper T _RHEU, i = 1 in the order of lower limit T _RHEL, · · ·, 6 is provided.
^{_{z = | T CCS * -T CCS}} | + Σ i W i m i ··· (1)
At this time, the amount of decrease in molten steel temperature from the completion of steel delivery to the ladle to the start of secondary refining, the amount of decrease in molten steel temperature from the start of secondary refining to the end of secondary refining, and the amount of decrease in molten steel from the end of secondary refining to the start of continuous casting. and equality constraints based on a model for estimating the amount of drop in the molten steel temperature, the aimed temperature indicator value T _LD, T _RHS, T _RHE lower limit restriction on each _{(T LDU, T LDL),} (T RHSU, T _Optimal to minimize the objective function z for multiple combinations of weighting coefficients _{Wi i} based on the inequality constraint that indicates that _RHSL ), (T _RHEU , T _RHEL ) are included within the range relaxed by the constraint violation amount. Calculate the solution.

103 is an output unit that functions as a presentation unit, the mark temperatures indicated value T _LD of the optimal solution calculated by the calculating unit 102, T _RHS, T _RHE, and continuous casting start of the molten steel temperature predictions T _CCS Output multiple combinations.
The output unit 103 includes, as shown in FIG. 2, each mark temperatures indicated value T _LD of the optimal solution calculated by the calculating unit 102, T _RHS, T _RHE, and continuous casting start of the molten steel temperature predictions T _CCS graph plotting a plurality of combinations against time, i.e. the graph representing a plurality of target temperatures path, each of the upper and lower constraints _{(T LDU, T LDL),} (T RHSU, T RHSL), (T RHEU, T _RHEL ) and the target temperature T _CCS ^{* are} drawn and displayed on the screen on the display device 105.

Operating person is displayed on the screen of the display device 105, suitable for operation from a plurality of combinations of mark temperatures indicated value _{T LD, T RHS, T RHE} , and the predicted value T _CCS continuous casting starting temperature of molten steel The combination considered to be can be selected by using the input device 104.
The output unit 103 transmits each target temperature indicated value T _LD , T _RHS , and T _{R HE} selected by the operator to a computer for converter control (not shown) or a computer for controlling the RH degassing device. Control the molten steel temperature in the steelmaking process.

Reference numeral 104 is an input device such as a pointing device, a keyboard, and a touch panel, and 105 is a display device.

Here, the details of the linear programming problem in this embodiment will be described.
Entering the operating conditions in advance, as shown in equations (2) to (4), the amount of decrease in the molten steel temperature from the completion of steel delivery to the ladle to the start of secondary refining, during secondary refining (start of secondary refining). Create a model of linear regression equation that estimates the amount of decrease in molten steel temperature from the end of secondary refining to the end of continuous casting) and the amount of decrease in molten steel temperature from the end of secondary refining to the start of continuous casting. The model of the linear regression equation can be created from statistical processing such as linear multiple regression analysis of actual data or physical consideration.

Model of the amount of decrease in molten steel temperature from the completion of steel delivery to the ladle to the start of secondary refining T _{LD −} T _RHS = a ₀ + a ₁ T _LD + Σ _k ≧ ₂ a _k x _k・ ・ ・ (2)

Model of the amount of decrease in molten steel temperature from the start of secondary refining to the end of secondary refining _TRHS −T _RHE = b ₀ + b ₁ T _LD + b _{2 TRHS} + Σ _k ≧ ₃ b _k x _k・ ・ ・ (3)

Model of the amount of decrease in molten steel temperature from the end of secondary refining to the start of continuous casting T _RHE −T _CCS = c ₀ + c ₁ T _LD + c ₂ T _RHS + c ₃ T _RHE + Σ _k ≧ ₄ c _k x _k ··· (4 )

Below,
a ₀ + Σ _k ≧ ₂ a _k x _k = R _a
b ₀ + Σ _k ≧ ₃ b _k x _k = R _b
c ₀ + Σ _k ≧ ₄ c _k x _k = R _c
Notated as.
x _k is the operating condition such as transport time and processing time, which is used as an explanatory variable in the model of the amount of decrease in molten steel temperature, and a _k , b _k , and _kk are the intercepts and coefficients in the model of the amount of decrease in molten steel temperature. (K = 0, 1, 2, ...). These values are input and set from the input unit 101.
Each aim temperature indication value T _LD to be determined before the start of converter blowing, T _RHS, T _RHE, and the predicted value T _CCS of continuous casting at the start of molten steel temperature, the planned operating conditions and operating schedule of the charge of interest It is assumed that the models of the based equations (2) to (4) are satisfied.

First, before explaining the linear programming problem in this embodiment, the linear programming problem-1 will be described for comparison.
In linear programming problem -1, each mark temperatures indicated value _{T LD, T RHS, T RHE} , and the predicted value T _CCS continuous casting starting temperature of molten steel and decision variable, also, as in equation (5), continuous The optimum solution that minimizes the objective function z ₁ is calculated as a linear programming problem in which the absolute value of the difference between the predicted value T _CCS of the molten steel temperature at the start of casting and the target temperature T _CCS ^* is the objective function z ₁ .
[Objective function]
z ₁ = | T _CCS ^* -T _CCS | ... (5)
[Coefficient of determination (all non-negative values)]
T _LD , T _RHS , T _RHE , T _CCS ... (6)

Further, when solving the linear programming problem, the equation constraint conditions are defined as equations (7) to (9) based on the models of equations (2) to (4), and the inequality constraint condition is defined as equation (2). 10) ~ Formula (15).
[Equality constraint]
(1-a ₁ ) T _LD −T _RHS = _Ra・ ・ ・ (7)
−B ₁ T _LD + (1-b ₂ ) T _RHS −T _RHE = R _b・ ・ ・ (8)
−c ₁ T _LD −c ₂ T _RHS + (1-c ₃ ) T _RHE −T _CCS = R _c・ ・ ・ (9)
[Inequality constraint]
−T _LD ≧ −T _LDU・ ・ ・ (10)
T _LD ≧ T _LDL・ ・ ・ (11)
−T _RHS ≧ −T _RHSU・ ・ ・ (12)
T _RHS ≧ T _RHSL・ ・ ・ (13)
−T _RHE ≧ −T _RHEU・ ・ ・ (14)
T _RHE ≧ T _RHEL・ ・ ・ (15)

If feasible solution is obtained by linear programming problem -1, aim tapping at completion of mark temperatures indicated value T _LD, 2 primary refining starting mark temperatures indicated value T _RHS, 2 secondary refining at the end of the ladle temperature readings T _RHE, each of the upper and lower constraints _{(T LDU, T LDL),} (T RHSU, T RHSL), (T RHEU, T RHEL) meet, and the optimal solution according model drop of molten steel temperature Is obtained.
However, in linear programming problem-1, it is possible that all inequality constraints cannot be satisfied and it becomes infeasible.

Therefore, the arithmetic unit 102 of the support apparatus 100 of the molten steel temperature control, with respect to the linear programming problem -1, add the variable m _i representing a constraint violation amount as a decision variable, also the objective function, as in formula (1) to the sum of the value obtained by multiplying the weighting factor W _i to take non-negative value to a variable m _i representing a constraint violation amount added, the addition of the variable m _i, further representing a constraint violation amounts to each left side of the inequality constraints, these Formulate a linear planning problem that relaxes the inequality constraint of (hereinafter referred to as linear planning problem-2).

[Objective function]
^{_{z = | T CCS * -T CCS}} | + Σ i W i m i ··· (1)
[Coefficient of determination (all non-negative values)]
_{T LD, T RHS, T RHE} , T CCS, m i (i = 1, ···, 6)
[Equality constraint]
Same as Linear Programming Problem-1 (Equations (7) to (9))
[Inequality constraint]
−T _LD + m ₁ ≧ −T _LDU・ ・ ・ (16)
T _LD + m ₂ ≧ T _LDL・ ・ ・ (17)
−T _RHS + m ₃ ≧ −T _RHSU・ ・ ・ (18)
T _RHS + m ₄ ≧ T _RHSL・ ・ ・ (19)
−T _RHE + m ₅ ≧ −T _RHEU・ ・ ・ (20)
T _RHE + m ₆ ≧ T _RHEL・ ・ ・ (21)

If the optimal solution can be obtained by linear programming problem -1, even linear programming problem -2, each mark temperatures indicated value _{T LD, T RHS, T RHE} , and the predicted value T _CCS continuous casting starting temperature of molten steel is linear programming An optimum solution with the same value as the optimum solution in Problem-1 and m ₁ = ... = m ₆ = 0 can be obtained.
Then, even if the linear programming problem feasible solution run at -1 is not obtained, the linear programming problem -2 constraint violation amount m _i contained in the inequality constraint becomes positive, the equality equality constraints satisfied The solution to be obtained is obtained. However, m _2j and m _2j-1 (in this example, j = 1, 2, 3) do not become positive values at the same time. At that time, each target temperature indication T _LD , T _RHS , T _{R HE} , and the predicted value T _CCS of the molten steel temperature at the start of continuous casting follow the model of the amount of decrease in the molten steel temperature, but the inequality constraint of the linear programming problem-1 It means that the condition is not completely satisfied.

When solving a linear programming problem by the simplex method, the optimal solution has the property of being selected as one of the solutions (single vertices) that satisfy the equal sign of the inequality constraint in the set of executable solutions. Therefore, the value of the variable m _i representing a constraint violation amount in optimal solutions Changing the value of the weighting factor W _i of the objective function changes discontinuously, it can be the optimum solution for any value of the weighting factor W _i constraints the combination of variable m _i representing the violation amount is limited to a finite number. Each mark temperatures indicated value T _LD, T _RHS, T _RHE lower limit restriction on each _{(T LDU, T LDL),} (T RHSU, T RHSL), (T RHEU, T RHEL) for formula (1) of if the corresponding weight coefficient W _i is greater in the objective function, likely to be selected as the optimal solution is the apex of a single variable m _i representing a constraint violation amount is zero.

Utilizing these properties, the combination to the weight coefficient W ₁ to _W-6 all zeros variables m _i representing a constraint violation amount in the objective function z, each mark temperatures indicated value T _LD, T _RHS, each T _RHE Prepare a combination in which the weighting coefficient W _i of one target temperature indicated value is sufficiently larger than the weighting coefficient W _i of the other target temperature indicated value, and even if a feasible solution cannot be obtained in the linear planning problem-1, the weight is weighted. Calculate the next best solution for each target temperature indication value obtained by optimizing the objective function corresponding to each combination of coefficients Wi _i and the predicted value of the molten steel temperature at the start of continuous casting, and make an appropriate decision by the operator. Present so that you can choose one. Here, the weighting coefficient constraint violations of mark temperatures readings should protect the upper and lower constraints by increasing "sufficient", for example, when the aimed temperature indication value T _LD is assumed to satisfy the upper and lower limit constraints, etc. for any combination of mark temperatures indicated value satisfies the equation constraint and mark temperatures indicated value T _LD does not satisfy the upper limit restriction, terms, other aims on the constraint violation of mark temperatures indicated value T _LD of the objective function z It means that it is a combination of weighting coefficients that is surely larger than the sum of the terms related to the amount of constraint violation related to the temperature indicated values _TRHS and _TRHE . For example, using the operation record data of the ladle transfer time between the rotary furnaces RH, the RH processing time, and the ladle transfer time between RH continuous castings, the equation constraint condition is set when the predicted temperature at the start of casting matches the target value. mark temperatures indicated value T _LD, calculates a constraint violation of T _RHS and T _RHE, the lower limit of the distribution when constraints violations weight section about mark temperatures indicated value T _LD of the objective function z is a positive value that satisfies (e.g. distribution 1% point) is larger than the upper limit of the distribution of the sum when any of the constraint violation quantity terms related to the other target indicated temperature is positive (for example, 99% point of the distribution). Can be determined as a combination of. Although a specific value is not determined by this method, the value of the ratio of the weighting coefficient to the constraint violation amount for the target temperature indicated value _TLD and other target temperature indicated values can be determined. As a result of investigation by the inventors, it was found that this ratio should be about 100 times.
Instead of mark temperatures indicated value T _LD above, mark temperatures indicated value T _RHS or T _RHE are the same meaning even in the case of a should satisfy the upper and lower constraints.

In this case, the magnitude of the weighting coefficient W _i is set to 1 or more for, for example, the target temperature instruction value that emphasizes entering the upper / lower limit constraint, and the target temperature instruction that neglects entering the upper / lower limit constraint. The value shall be 0.01 or less as a value sufficiently smaller than 1.
By the upper limit restriction aim temperature readings to be met to evaluate weighted variable m _i representing a constraint violation amount, the variable m _i representing a constraint violation amount for mark temperatures readings should meet the upper and lower limit constraints Make it sufficiently larger than the weighting coefficient Wi _{i of} other target temperature indication values so that the optimum solution that becomes a positive value is difficult to select. Since the difference between the predicted value T _CCS of the molten steel temperature at the start of continuous casting and the target temperature T _CCS ^* is usually about the same as or smaller than the constraint violation amount of the target temperature indicated value, the above equation (1) of the objective function z is used. Compared to the absolute value of the deviation between the predicted value T _CCS and the target temperature T _CCS ^* , it is neglected to fall within the upper and lower limit constraints. Up and down so that the size of the term related to the constraint violation amount of the target temperature indicated value becomes sufficiently small. The weighting coefficient Wi _i for the target temperature indicated value that should satisfy the limit constraint is set to 1, which is about the same as the coefficient for the difference between the predicted value T _CCS of the molten steel temperature at the start of continuous casting and the target temperature T _CCS ^*, and conversely, the upper and lower limits are used. The coefficient of the weighting coefficient Wi with respect to the target temperature indicated value, which disregards entering the vicinity, may be 0.01, which is sufficiently small.

Thus, when tapping the completion of the ladle, during secondary refining start, and at three points of the secondary refining at the end, it determines the variable m _i representing the constraint violations amount is limited to a finite number in the linear programming problem since calculating the optimal solution as a variable, the mark temperatures indicated value _{T LD, T RHS, T RHE} , and can present a plurality of typical combinations of predictive value T _CCS continuous casting starting temperature of molten steel, From among them, it is possible to select a combination suitable for the operation based on the knowledge of the operator.

FIG. 3 is a flowchart showing a method of supporting the molten steel temperature control by the molten steel temperature control support device 100 according to the embodiment.
In step S1, the input unit 101 formulates the linear programming problem in step S2, and inputs the information necessary for solving the linear programming problem.
Specifically, as described above, for the target charge, the operation schedule determined before the start of converter blowing, the alloy input related to the manufacturing material (steel type), and the condition setting values for the secondary refining are input.
The upper limit T _RHSU and lower T _RHSL upper T _LDU and lower T _LDL, secondary refining at the start of mark temperatures indicated value T _RHS of mark temperatures indicated value T _LD during tapping the completion of the ladle, a secondary refining the upper limit T _Rheu and lower T _RHEL aim temperature readings T _RHE at the end, and inputs the target temperature T _CCS of the molten steel temperature at the start of continuous casting ^*.
In addition, the explanatory variables x _k , intercept and coefficients a _k , b _k , and c _k in the model of the amount of decrease in molten steel temperature are input.
Further, the weighting factor of the combination to 0 every combination of (weight coefficient W _i weighting factor W _i, each mark temperatures indicated value T _LD, T _RHS, other mark temperatures indicated value a weighting factor W _i for each T _RHE Enter a combination that is larger than Wi _i ).

In step S2, the calculation unit 102 uses the information input in step S1 to form a linear program represented by equations (1), equations (7) to (9), and equations (16) to (21). Formulate Problem-2. In the formulation, the information given in step S1 is incorporated into the equations (1), (7) to (9), and equations (16) to (21) given in advance as a framework. Say that.

In step S3, the operation section 102, for each combination of weight functions W _i given in step S1, by solving the linear programming problem -2 is formulated in step S2, that is, the optimal solution that minimizes the objective function z Calculated, the target temperature indicated value T _LD at the completion of steel delivery to the ladle, the target temperature indicated value _TRHS at the start of secondary refining, the target temperature indicated value _TRHE at the end of secondary refining, and the start of continuous casting. Obtain the predicted value T _CCS of the molten steel temperature at that time.

In step S4, the output unit 103, as shown in FIG. 2, each mark temperatures indicated value T _LD of the optimal solution calculated in step S3, T _RHS, T _RHE, and continuous casting starting estimated value of the molten steel temperature the plot of the plurality of combinations of T _CCS versus the time course, each of the upper and lower constraints _{(T LDU, T LDL),} (T RHSU, T RHSL), (T RHEU, T RHEL), and the target temperature T _{It is} drawn together with _CCS ^* and displayed on the screen on the display device 105.
Specifically, the horizontal axis the time elapsed after tapping the completion of the ladle, the upper limit restriction _{(T LDU, T LDL),} (T RHSU, T RHSL), (T RHEU, T RHEL) rectangular It is indicated by 201 to 203, and the target temperature T _CCS ^* of the molten steel temperature at the start of continuous casting is displayed at the position of the corresponding elapsed time based on the operation schedule. Thereon, to overplot the line graph linking the aimed temperature readings T _LD obtained for each combination of the weighting factors _{W i, T RHS, T RHE} , and the predicted value T _CCS continuous casting starting temperature of molten steel ..
Operating person is displayed on the screen of the display device 105, suitable for operation from a plurality of combinations of mark temperatures indicated value _{T LD, T RHS, T RHE} , and the predicted value T _CCS continuous casting starting temperature of molten steel The combination considered to be can be selected by using the input device 104.

In step S5, the output unit 103 transmits the aimed temperature readings T _LD is selected by operating person, T _RHS, the T _RHE, the computer or the RH degassing device control computer for converter control (not shown) By doing so, the molten steel temperature in the steelmaking process is controlled.

Hereinafter, the procedure and effect of determining the target temperature indicated value to which the present invention is applied will be described based on the simulation results.
The coefficients used in the models in equations (2) to (4) were determined as follows by multiple regression analysis of actual data at the steel factory to be implemented.
a ₁ = 0.083296
b ₁ = -0.160679, b ₂ = 0.716868
c ₁ = -0.002927, c ₂ = 0.124891, c ₃ = 0.1926405

The upper limit T _RHSU and lower T _RHSL upper T _LDU and lower T _LDL, secondary refining at the start of mark temperatures indicated value T _RHS of mark temperatures indicated value T _LD during tapping the completion of the ladle, a secondary refining the upper limit T _Rheu and lower T _RHEL aim temperature readings T _RHE at the end, and the continuous casting starting temperature of molten steel to the target temperature T _CCS ^* was determined as follows.
T _LDL = 1590 ° C, T _LDU = 1640 ° C
T _RHSL = 1574.9 ° C, T _RHSU = 1618 ° C
T _RHEL = 1558 ° C, T _RHEU = 1570 ° C
T _CCS ^* = 1538 ° C

According to the operation schedule set before the start of converter smelting, the time from the completion of steel delivery to the ladle to the start of secondary smelting is 37 minutes, and the secondary smelting time (time from the start of secondary smelting to the end of secondary smelting). Is 17 minutes, and the time from the end of secondary refining to the start of continuous casting is 23 minutes.

In Linear programming problem-1 (Equation (5) to (15)), there is no feasible solution in the linear programming problem formulated using the above parameters and constraints, so the upper and lower limit constraints of the target temperature indication value are set. The optimum solution to be satisfied cannot be obtained.

In Linear Programming Problem-2 (Equations (1), Eqs. (7) to (9), Eqs. (16) to (21)), the above parameters and constraints are used, and the weighting factors W _{1 to} W ₆ are used. Are prepared for the four cases (a) to (d) in Table 1. Figure 2, for four cases of (a) ~ (d), the aimed temperature indicator value _{T LD, T RHS, T RHE} , and presented a plurality of combinations of predictive value T _CCS continuous casting starting temperature of molten steel It is a thing.
(A) is a weighting factor W _i are all 0, since it is possible to take any value all constraint violations amount m _i is not negative, inequality constraints of formula (16) to (21) must It is filled. That is, it means that all the inequality conditions of the equations (10) to (15) in the linear programming problem-1 are removed.
Further, (b), (c) , (d) is a combination of larger than the weighting factor W _i of the other mark temperatures indicated value a weighting factor W _i for each mark temperatures indicated value, to enter the upper and lower limit constraint 1 is set for the target temperature indicated value that emphasizes, and 0.01 is set for the target temperature indicated value that neglects to fall within the upper and lower limit constraints.

Table 1 shows the optimum solution of the linear programming problem-2 in each of the cases (a) to (d), and in the numerical solution of each target temperature indicated value shown for each combination of weighting factors, ○ is shown on the right side. Those with x indicate those that satisfy the upper and lower limit constraints, and those with x indicate those that do not satisfy the upper and lower limit constraints.
In (a), the upper and lower limit constraints are not satisfied by any of the target temperature indicated values, but the predicted value T _CCS of the molten steel temperature at the start of continuous casting is a solution that matches the target temperature T _CCS ^* . In (b), (c), and (d), an optimum solution satisfying the upper and lower limit constraints with the weighting coefficient Wi _i as 1 can be obtained.
In this way, the target temperature indicated value T _LD at the completion of steel delivery to the ladle, the target temperature indicated value T _RHS at the start of secondary refining, and the target temperature indicated value T _RHE at the end of secondary refining are subject to upper and lower limit constraints. Although it does not completely satisfy, each target temperature indication value that satisfies the upper and lower limit constraints that should be emphasized and the predicted value of the molten steel temperature at the start of continuous casting is close to the target temperature, and the combination of each weighting coefficient for the linear planning problem-2 Can be obtained by solving about once.

As described above, the target temperature indicated value T _LD at the completion of steel delivery to the ladle, the targeted temperature indicated value T _RHS at the start of secondary refining, and the targeted temperature indicated value TR _HE at the end of secondary refining If the upper and lower limit constraints of each are satisfied and the predicted value T _CCS of the molten steel temperature at the start of continuous casting matches the target temperature T _CCS ^* , those temperatures can be adopted. Moreover, mark temperatures indicated value T _LD, T _RHS, none of the T _RHE will meet each upper and lower limit constraint, the solutions predicted value T _CCS of the molten steel temperature at the start of continuous casting is equal to the target temperature T _CCS ^* even if not obtained, without changing the operation schedule, and, while appropriately mitigate the temperature constraint, the next best mark temperatures indicated value _{T LD, T RHS, T RHE} , and continuous casting starting temperature of molten steel Multiple combinations of predicted values T _CCS of are presented and can be selected from them.

Although the present invention has been described above with various embodiments, the present invention is not limited to these embodiments, and changes and the like can be made within the scope of the present invention. For example, in the above embodiment, with respect to the target temperature indicated value T _LD at the completion of steel delivery to the ladle, the targeted temperature indicated value _TRHS at the start of secondary refining, and the targeted temperature indicated value _TRHE at the end of secondary refining. The upper limit and the lower limit are set respectively, but it is also possible to set only one of the upper limit and the lower limit. That is, the upper / lower limit constraint referred to in the present application is a concept that includes not only an upper limit and a lower limit but also a constraint having only one of the upper limit and the lower limit.
The molten steel temperature control support device to which the present invention is applied is realized by, for example, a computer device equipped with a CPU, ROM, RAM, and the like.
The present invention also comprises supplying software (program) that realizes the functions of the present invention to a system or device via a network or various storage media, and the computer of the system or device reads and executes the program. It is feasible.

100: Support device for molten steel temperature control, 101: Input unit, 102: Calculation unit, 103: Output unit, 104: Input device, 105: Display device

Claims (6)

It is a support method for temperature control of molten steel in the steelmaking process in which molten steel is dispensed into a ladle after primary refining in a primary refining furnace and then secondary refining and continuous casting are performed.
The target temperature indication value at the completion of steel delivery to the pan, the target temperature indication value at the start of secondary refining, the target temperature indication value at the end of secondary refining, and the predicted value of the molten steel temperature at the start of continuous casting. , The variable representing the absolute value (called the constraint violation amount) of the amount of deviation from the upper and lower limit constraints of each target temperature indicated value is used as a determination variable, and the predicted value and target of the molten steel temperature at the start of continuous casting. As a linear planning problem whose objective function is a function including the absolute value of the difference from temperature and the sum of the values obtained by multiplying the variable representing the constraint violation amount by a weighting coefficient that takes a non-negative value.
A model that estimates the amount of decrease in molten steel temperature from the completion of steel delivery to the ladle to the start of secondary refining, a model that estimates the amount of decrease in molten steel temperature from the start of secondary refining to the end of secondary refining, and a model that estimates the amount of decrease in molten steel temperature from the start of secondary refining to the end of secondary refining. An equation constraint condition that is determined based on a model that estimates the amount of decrease in molten steel temperature from the end to the start of continuous casting, and is expressed including the respective target temperature indication values and the predicted value of the molten steel temperature at the start of continuous casting. When,
An inequality indicating that the target temperature indication value at the completion of steel delivery to the pan is included within the range in which the upper and lower limit constraints of the target temperature indication value at the completion of steel delivery to the pan are relaxed by the above constraint violation amount. The inequality indicating that the target temperature indicated value at the start of the secondary refining is included within the range in which the upper and lower limit constraints of the target temperature indicated value at the start of the secondary refining are relaxed by the constraint violation amount, and the end of the secondary refining. Based on the inequality constraint condition expressed by the inequality indicating that the target temperature indicated value at the end of the secondary refining is included in the range in which the upper and lower limit constraints of the target temperature indicated value at the time are relaxed by the constraint violation amount. hand,
An optimal solution calculation step for calculating an optimal solution that minimizes the objective function for a plurality of combinations of the weighting coefficients.
In the optimum solution calculation step, the target temperature indication value at the time of completion of steelmaking to the ladle and the target temperature instruction at the start of the secondary refining in the optimum solution calculated corresponding to each of the plurality of combinations of the weight coefficients. The molten steel temperature control in the steelmaking process is characterized by having a presentation step of presenting a plurality of combinations of a value, a target temperature indicated value at the end of secondary refining, and a predicted value of the molten steel temperature at the start of continuous casting. Support method. The plurality of combinations of the weighting coefficients are a combination in which the weighting coefficients are all set to 0, and the weighting coefficient of one target temperature indicating value for each targeting temperature indicating value is obtained from the weighting coefficient of another targeting temperature indicating value. The method for supporting molten steel temperature control in a steelmaking process according to claim 1, further comprising a combination that is sufficiently large. The magnitude of the weighting coefficient is set to 1 or more for the target temperature indicated value that emphasizes falling within the upper and lower limit constraints, and is set to 1 or more for the target temperature indicated value that disregards entering the upper and lower limit constraints. The method for supporting molten steel temperature control in the steelmaking process according to claim 2, wherein the temperature is 0.01 or less. The presentation step includes a target temperature indicated value at the completion of steelmaking to the ladle in the optimum solution calculated in the optimum solution calculation step, a target temperature indicated value at the start of the secondary refining, and a target temperature indicated value at the end of the secondary refining. A graph in which a plurality of combinations of the target temperature indicated value and the predicted value of the molten steel temperature at the start of continuous casting are plotted against the passage of time is drawn together with the upper and lower limit constraints and the target temperature on the display device. The method for supporting molten steel temperature control in the steelmaking process according to any one of claims 1 to 3, wherein the screen is displayed. It is a support device for temperature control of molten steel in the steelmaking process in which molten steel is dispensed into a ladle after primary refining in a primary refining furnace and then secondary refining and continuous casting are performed.
The target temperature indication value at the completion of steel delivery to the pan, the target temperature indication value at the start of secondary refining, the target temperature indication value at the end of secondary refining, and the predicted value of the molten steel temperature at the start of continuous casting. , The variable representing the absolute value (called the constraint violation amount) of the amount of deviation from the upper and lower limit constraints of each target temperature indicated value is used as a determination variable, and the predicted value and target of the molten steel temperature at the start of continuous casting. As a linear planning problem whose objective function is a function including the absolute value of the difference from temperature and the sum of the values obtained by multiplying the variable representing the constraint violation amount by a weighting coefficient that takes a non-negative value.
A model that estimates the amount of decrease in molten steel temperature from the completion of steel delivery to the ladle to the start of secondary refining, a model that estimates the amount of decrease in molten steel temperature from the start of secondary refining to the end of secondary refining, and a model that estimates the amount of decrease in molten steel temperature from the start of secondary refining to the end of secondary refining. An equation constraint condition that is determined based on a model that estimates the amount of decrease in molten steel temperature from the end to the start of continuous casting, and is expressed including the respective target temperature indication values and the predicted value of the molten steel temperature at the start of continuous casting. When,
An inequality indicating that the target temperature indication value at the completion of steel delivery to the pan is included within the range in which the upper and lower limit constraints of the target temperature indication value at the completion of steel delivery to the pan are relaxed by the above constraint violation amount. The inequality indicating that the target temperature indicated value at the start of the secondary refining is included within the range in which the upper and lower limit constraints of the target temperature indicated value at the start of the secondary refining are relaxed by the constraint violation amount, and the end of the secondary refining. Based on the inequality constraint condition expressed by the inequality indicating that the target temperature indicated value at the end of the secondary refining is included in the range in which the upper and lower limit constraints of the target temperature indicated value at the time are relaxed by the constraint violation amount. hand,
An optimal solution calculation means for calculating an optimal solution that minimizes the objective function for a plurality of combinations of the weighting coefficients.
The target temperature indication value at the time of completion of steelmaking to the ladle and the target temperature instruction at the start of the secondary refining in the optimum solution calculated corresponding to each of the plurality of combinations of the weight coefficients by the optimum solution calculation means. Steelmaking temperature control in a steelmaking process, which comprises a presenting means for presenting a plurality of combinations of a value, a target temperature indicated value at the end of secondary refining, and a predicted value of the molten steel temperature at the start of continuous casting. Support device. It is a program to support the temperature control of molten steel in the steelmaking process of primary refining in the primary refining furnace, secondary refining after the molten steel is put out in the ladle after the primary refining, and continuous casting.
The target temperature indication value at the completion of steel delivery to the pan, the target temperature indication value at the start of secondary refining, the target temperature indication value at the end of secondary refining, and the predicted value of the molten steel temperature at the start of continuous casting. , The variable representing the absolute value (called the constraint violation amount) of the amount of deviation from the upper and lower limit constraints of each target temperature indicated value is used as a determination variable, and the predicted value and target of the molten steel temperature at the start of continuous casting. As a linear planning problem whose objective function is a function including the absolute value of the difference from temperature and the sum of the values obtained by multiplying the variable representing the constraint violation amount by a weighting coefficient that takes a non-negative value.
A model that estimates the amount of decrease in molten steel temperature from the completion of steel delivery to the ladle to the start of secondary refining, a model that estimates the amount of decrease in molten steel temperature from the start of secondary refining to the end of secondary refining, and a model that estimates the amount of decrease in molten steel temperature from the start of secondary refining to the end of secondary refining. An equation constraint condition that is determined based on a model that estimates the amount of decrease in molten steel temperature from the end to the start of continuous casting, and is expressed including the respective target temperature indication values and the predicted value of the molten steel temperature at the start of continuous casting. When,
An inequality indicating that the target temperature indication value at the completion of steel delivery to the pan is included within the range in which the upper and lower limit constraints of the target temperature indication value at the completion of steel delivery to the pan are relaxed by the above constraint violation amount. The inequality indicating that the target temperature indicated value at the start of the secondary refining is included within the range in which the upper and lower limit constraints of the target temperature indicated value at the start of the secondary refining are relaxed by the constraint violation amount, and the end of the secondary refining. Based on the inequality constraint condition expressed by the inequality indicating that the target temperature indicated value at the end of the secondary refining is included in the range in which the upper and lower limit constraints of the target temperature indicated value at the time are relaxed by the constraint violation amount. hand,
Optimal solution calculation processing for calculating the optimal solution that minimizes the objective function for a plurality of combinations of the weighting coefficients, and
In the optimum solution calculation process, the target temperature instruction value at the time of completion of steel delivery to the ladle and the target temperature instruction at the start of the secondary refining in the optimum solution calculated corresponding to each of the plurality of combinations of the weight coefficients. A program for causing a computer to execute a presentation process that presents a plurality of combinations of a value, a target temperature indicated value at the end of secondary refining, and a predicted value of a molten steel temperature at the start of continuous casting.

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