JP7234755B2 - Apparatus, method and program for estimating flow characteristics in continuous casting process of multi-layered slab, and control method for continuous casting process of multi-layered slab - Google Patents

Description

TECHNICAL FIELD The present invention relates to an apparatus, method, and program for estimating flow rate characteristics in a continuous casting process for a multi-layered slab, and a control method for the continuous casting process for a multi-layered slab.

Conventionally, a multi-layer cast slab has been produced in which the composition of the surface layer and the composition of the inner layer are different. For example, Patent Literature 1 discloses a configuration in which molten metals having different compositions are separated in a mold by magnetic means, and molten metals having different compositions are supplied above and below the boundary. More specifically, a static magnetic field zone is formed between a relatively upper molten metal supply position and a relatively lower molten metal supply position in the mold such that magnetic lines of force extend in a direction perpendicular to the casting direction. This prevents mixing of molten metals with different compositions.
In the continuous casting process of multi-layer cast slabs, the position of the boundary separating the upper and lower molten metal (molten steel) in the surface layer and the molten steel in the inner layer (hereinafter referred to as the boundary layer level) is kept in the static magnetic field zone. It is necessary to appropriately control the molten steel supply flow rate by the submerged nozzle for the inner layer and the molten steel supply flow rate by the submerged nozzle for the inner layer.

In response to this problem, for example, Patent Document 2 discloses that the level of molten steel in the surface layer (hereinafter simply referred to as the "level") is controlled by manipulating the injection amount of the surface layer while maintaining the injection amount of the inner layer at a set value. A scheme is disclosed. In Patent Document 2, the weight of molten steel in the tundish is measured from the output of a load cell attached to the tundish, and the weight of molten steel in the tundish is used to calculate the flow rate of molten steel injected from the nozzle.

Further, in Patent Document 3, the surface layer injection amount measured by an electromagnetic flow meter attached to the surface layer injection nozzle on the surface layer tundish side and the surface layer injection amount obtained by calculating the set value from the surface layer shell thickness and the casting speed The set value is compared and the stopper of the injection nozzle for the surface layer is opened and closed to adjust the injection amount of the surface layer so that the two match. A method is disclosed in which the inner layer injection amount is adjusted by opening and closing the stopper of the inner layer injection nozzle so that the melt surface level set value obtained by calculating the set value from the speed is compared with the set value so that both match.

JP-A-63-108947 JP-A-3-243262 JP-A-5-104223

Ironmaking & Steelmaking 1997 Vol.24 No.3 "Novel continuous casting process for clad steel slabs with level dc magnetic field" "Pattern Recognition and Machine Learning", Chapter 3 of CM Bishop, Maruzen Publishing, p. 152 W. Dinkelbach “On Nonlinear Fractional Programming” Management Science 1967

In the continuous casting process of a multi-layered slab, in order to produce a good quality multi-layered slab, it is required to accurately know the flow rate from each nozzle and appropriately control it.
If there is a flow meter as in Patent Document 3, it is relatively easy to know the flow rate. There is
When the flow rate at each nozzle is not known accurately, the flow rate can be obtained from the opening value if the flow rate characteristic, which is the relationship between the opening degree and the flow rate at each nozzle, can be accurately known.
However, the flow rate characteristics of each nozzle vary with each casting due to differences in the composition of the molten steel, etc., and also change during casting due to clogging of the nozzles, such as adhesion of bare metal. It is necessary to seek the relationship of
Further, Patent Document 2 discloses that the flow rate of molten steel injected from a nozzle is calculated using the measurement result of the weight of molten steel in the tundish. This is based on the premise that a tundish for the inner layer is provided as a separate facility, which limits applicable continuous casting facilities.

The present invention has been made in view of the above-mentioned points, and is a relationship between the opening degree of a flow control mechanism such as a stopper and a sliding nozzle and the flow rate in each of the surface layer nozzle and the inner layer nozzle without using a flow meter. It is an object of the present invention to accurately estimate the flow rate characteristic and accurately estimate the flow rate in each of the surface layer nozzle and the inner layer nozzle, thereby appropriately controlling the flow rate.

The gist of the present invention for solving the above problems is as follows.
[1] Molten metal is injected into the mold from a surface layer nozzle and an inner layer nozzle, each of which has a flow rate control mechanism for controlling the molten metal supply flow rate according to the opening degree change operation, and multiple layers with different compositions of the surface layer and the inner layer are formed. In a continuous casting process for producing a slab, a flow rate characteristic that is the relationship between the opening degree of a flow control mechanism in the surface layer nozzle and the flow rate, and a flow rate characteristic that is the relationship between the opening degree of the flow control mechanism in the inner layer nozzle and the flow rate. A device for estimating flow rate characteristics in a continuous casting process of a multi-layered slab for estimating
feedback control of the opening of a flow rate control mechanism of one of the surface layer nozzle and the inner layer nozzle using a level gauge for measuring the level of the surface of the molten metal in the mold; During the constant opening control that keeps the melt level constant and keeps the opening of the flow rate control mechanism of the other nozzle constant,
opening changing means for setting a constant opening of the flow rate control mechanism of the other nozzle and changing the opening to this constant opening;
a flow rate calculation value calculating means for calculating a flow rate calculation value, which is a calculated value of the total flow rate flowing through the surface layer nozzle and the inner layer nozzle;
The constant opening of the flow rate control mechanism for the other nozzle set by the opening degree changing means, the calculated flow rate calculated by the calculated flow rate calculating means, and the flow rate control of the other nozzle by the opening changing means Using the convergence value data of the opening degree of the flow control mechanism of the one nozzle collected after changing the mechanism to a constant opening degree, the unknown quantity related to the flow rate characteristics of the surface layer nozzle and the flow rate characteristic of the inner layer nozzle balance formula creation means for creating a mass or volume balance formula with unknowns as variables;
By changing the constant opening of the flow rate control mechanism of the other nozzle set by the opening changing means, the calculation of the calculated flow rate by the calculated flow rate calculation means and the creation of the balance formula by the balance formula creation means are performed. a solution-finding means for solving simultaneous equations constructed by repeating a plurality of times to obtain unknown values relating to flow characteristics of the surface layer nozzle and unknown values relating to flow characteristics of the inner layer nozzle. A device for estimating flow characteristics in continuous strip casting processes.
[2] The apparatus for estimating flow rate characteristics in a continuous casting process for a multi-layer cast slab according to [1], wherein the calculated flow rate calculation means calculates the calculated flow rate based on the casting speed.
[3] In [1], the calculated flow rate calculation means calculates the calculated flow rate based on the measured weight of a tundish that supplies the molten metal to the surface layer nozzle and the inner layer nozzle. A device for estimating flow characteristics in the continuous casting process of the described multi-layered slab.
[4] The flow rate characteristic in the continuous casting process of the multi-layer cast slab according to [3], characterized in that time averaging is performed when calculating the flow rate calculation value based on the weight measurement value of the tundish. estimation device.
[5] The constant opening of the flow rate control mechanism of the other nozzle set by the opening change means, the calculation of the calculated flow rate by the calculated flow rate calculation means, and the calculation of the balance formula by the balance formula creation means Any one of [1] to [4], wherein at least one of the number of repetitions when the production is repeated multiple times is set to a variable value, and the value is changed according to a predetermined condition during casting. 3. The device for estimating flow rate characteristics in the continuous casting process of a multi-layered slab according to 1.
[6] The opening degree changing means is configured to change the surface layer at each time of repeated calculation when the calculation of the calculated flow rate by the calculated flow rate calculating means and the creation of the balance formula by the balance formula creating means are repeated a plurality of times. Controlling the flow rate of the other nozzle by setting and solving an optimization problem using an evaluation function that includes a trace of a variance-covariance matrix of unknowns related to the flow rate characteristics of the nozzle and unknowns related to the flow rate characteristics of the inner layer nozzle. The apparatus for estimating flow rate characteristics in a continuous casting process for a multi-layer cast slab according to any one of [1] to [5], characterized by setting a constant opening of the mechanism.
[7] The evaluation function according to [6], wherein the evaluation function includes a penalty term relating to an opening manipulated variable of the flow control mechanism of the one nozzle and an opening manipulated variable of the flow control mechanism of the other nozzle. A system for estimating flow rate characteristics in the continuous casting process of multi-layered slabs.
[8] The continuous multi-layered slab according to [6] or [7], wherein the opening change means sets and solves the optimization problem for the next time in the repeated calculation. A device for estimating flow characteristics in the casting process.
[9] The multi-layer structure according to [6] or [7], wherein the opening degree changing means sets and solves the optimization problem for a plurality of times including the next time in the repeated calculation. A device for estimating flow rate characteristics in the continuous casting process of slabs.
[10] The optimization problem of the multilayer slab according to any one of [6] to [8], wherein the optimization problem includes a flow rate constraint on the total flow rate of the surface layer nozzle and the inner layer nozzle. A device for estimating flow characteristics in continuous casting processes.
[11] The optimization problem is characterized by including upper and lower limit constraints on the opening manipulated variable of the flow rate control mechanism of the one nozzle and the opening manipulated variable of the flow control mechanism of the other nozzle. The device for estimating flow rate characteristics in the continuous casting process of a multi-layer cast slab according to any one of [9].
[12] The opening change means converts the optimization problem into a one-variable optimization problem and solves it. estimation device.
[13] Before the number of repeated calculations when the calculation of the calculated flow rate by the calculated flow rate calculation means and the creation of the balance formula by the balance formula creation means are repeated a plurality of times reaches a predetermined number of times , the apparatus for estimating flow rate characteristics in a continuous casting process for a multi-layer cast slab according to any one of [1] to [12], characterized in that the iterative calculation is stopped when a predetermined condition is satisfied.
[14] Molten metal is injected into the mold from a surface layer nozzle and an inner layer nozzle, each of which has a flow rate control mechanism for controlling the molten metal supply flow rate according to the opening degree change operation, and multiple layers with different compositions of the surface layer and the inner layer are formed. In a continuous casting process for producing a slab, a flow rate characteristic that is the relationship between the opening degree of a flow control mechanism in the surface layer nozzle and the flow rate, and a flow rate characteristic that is the relationship between the opening degree of the flow control mechanism in the inner layer nozzle and the flow rate. A method for estimating flow characteristics in a continuous casting process of a multi-layered slab for estimating
feedback control of the opening of a flow rate control mechanism of one of the surface layer nozzle and the inner layer nozzle using a level gauge for measuring the level of the surface of the molten metal in the mold; During the constant opening control that keeps the melt level constant and keeps the opening of the flow rate control mechanism of the other nozzle constant,
a first step of setting a constant opening of the flow rate control mechanism of the other nozzle and changing it to this constant opening;
a second step of calculating a calculated flow rate, which is a calculated value of the total flow rate flowing through the surface layer nozzle and the inner layer nozzle;
The constant opening degree of the flow control mechanism of the other nozzle set in the first step, the calculated flow rate calculated in the second step, and the flow control mechanism of the other nozzle in the first step Using the convergence value data of the opening degree of the flow rate control mechanism of the one nozzle collected after changing the constant opening degree of , the unknown value related to the flow rate characteristics of the surface layer nozzle and the unknown value related to the flow rate characteristic of the inner layer nozzle a third step of creating a mass or volume balance equation with
Simultaneous equations constructed by repeating the second step and the third step a plurality of times while changing the constant opening of the flow rate control mechanism of the other nozzle set in the first step and a fourth step of obtaining a solution to obtain an unknown quantity related to the flow characteristics of the surface layer nozzle and an unknown quantity related to the flow characteristics of the inner layer nozzle. Method.
[15] Molten metal is injected into the mold from a surface layer nozzle and an inner layer nozzle each having a flow rate control mechanism for controlling the molten metal supply flow rate according to the opening change operation, and the composition of the surface layer and the inner layer are different. In a continuous casting process for producing a slab, a flow rate characteristic that is the relationship between the opening degree of a flow control mechanism in the surface layer nozzle and the flow rate, and a flow rate characteristic that is the relationship between the opening degree of the flow control mechanism in the inner layer nozzle and the flow rate. A program for estimating
feedback control of the opening of a flow rate control mechanism of one of the surface layer nozzle and the inner layer nozzle using a level gauge for measuring the level of the surface of the molten metal in the mold; During the constant opening control that keeps the melt level constant and keeps the opening of the flow control mechanism of the other nozzle constant,
a first process of setting a constant degree of opening of the flow rate control mechanism of the other nozzle and changing the degree of opening to this constant degree of opening;
a second process of calculating a flow rate calculation value that is a calculated value of the total flow rate flowing through the surface layer nozzle and the inner layer nozzle;
The constant opening degree of the flow control mechanism of the other nozzle set in the first process, the calculated flow rate calculated in the second process, and the flow control mechanism of the other nozzle in the first process Using the convergence value data of the opening degree of the flow rate control mechanism of the one nozzle collected after changing the constant opening degree of , the unknown value related to the flow rate characteristics of the surface layer nozzle and the unknown value related to the flow rate characteristic of the inner layer nozzle A third process of creating a mass or volume balance formula with
Simultaneous equations constructed by repeating the second process and the third process a plurality of times while changing the constant opening of the flow rate control mechanism of the other nozzle set in the first process A program for causing a computer to execute a fourth process of solving to obtain unknown values relating to flow characteristics of the surface layer nozzle and unknown values relating to flow characteristics of the inner layer nozzle.
[16] Using the unknown quantity related to the flow characteristics of the other nozzle obtained by the flow characteristics estimation device in the continuous casting process for a multi-layered slab according to any one of [1] to [13], feedback and a method of controlling a continuous casting process for a multilayer cast slab, characterized by correcting the constant opening of the flow rate control mechanism of the other nozzle in the constant opening control.

According to the present invention, without using a flow meter, the flow rate characteristic, which is the relationship between the opening degree of the flow control mechanism and the flow rate in each of the surface layer nozzle and the inner layer nozzle, can be accurately estimated, and the flow rate in each of the surface layer nozzle and the inner layer nozzle can be estimated. Accurate estimation allows the flow rate to be properly controlled.

BRIEF DESCRIPTION OF THE DRAWINGS It is a figure for demonstrating the outline|summary of the continuous casting process of a multilayer slab. It is a figure which shows the functional structure of the controller which concerns on embodiment. 4 is a flow chart showing a method for estimating flow rate characteristics in a continuous casting process for a multi-layered slab and a method for controlling the continuous casting process for a multi-layered slab in an embodiment. FIG. 10 is a characteristic diagram showing simulation results; It is a figure which shows the functional structure of the opening change part of a controller. FIG. 10 is a characteristic diagram showing simulation results;

Preferred embodiments of the present invention will now be described with reference to the accompanying drawings.
[First embodiment]
With reference to FIG. 1, the outline of the continuous casting process for a multi-layer slab will be described. FIG. 1(a) is a diagram showing the overall configuration of a continuous casting facility, and FIG.
Two submerged nozzles (referred to as a surface layer nozzle 1 and an inner layer nozzle 2 in the present application) having different discharge positions in the casting direction are provided. Molten steel is supplied to the surface layer nozzle 1 and the inner layer nozzle 2 from one tundish 3 . More specifically, the tundish 3 is divided into two chambers, from which molten steels with different compositions are injected into the mold 4 through the surface layer nozzle 1 and the inner layer nozzle 2, respectively. A weight scale 5 can measure the weight of the tundish 3 .

Each of the molten steel injected into the mold 4 from the surface layer nozzle 1 and the inner layer nozzle 2 receives a damping force in the static magnetic field zone formed by the magnetic field generator 6, and the surface layer molten steel and the inner layer molten steel are separated in the mold 4. It is separated vertically across the boundary 7 . The molten steel surface 8 in the mold 4 is the position where the molten steel in the surface layer contacts the molten powder, and the boundary 7 is the separation position between the molten steel in the surface layer and the molten steel in the inner layer. Hereinafter, the position of the molten metal surface 8 will be referred to as the molten metal surface level, and the position of the boundary 7 will be referred to as the boundary layer level. Although the boundary 7 is actually formed as a transition layer between the two layers, it is treated as a boundary line. Line 9 also indicates the solidified shell position.
A molten metal level gauge 10, for example, of a vortex type is installed above the molten metal level 8 in the mold 4 to measure the molten metal level.

The flow rate of molten steel supplied by the surface layer nozzle 1 (hereinafter referred to as the surface layer flow rate) is controlled by changing the opening degree of the surface layer stopper 11 . Similarly, the flow rate of molten steel supplied by the inner layer nozzle 2 (hereinafter referred to as the inner layer flow rate) is controlled by changing the opening degree of the inner layer stopper 12 . The opening degree changing operation of these stoppers 11 and 12 is executed under the control of the controller 100 shown in FIG. In this embodiment, a stopper is used as a flow rate control mechanism for controlling the molten steel supply flow rate according to the operation for changing the degree of opening, but a sliding nozzle may be used.

Although it will be described in detail below, in this embodiment, flow rate characteristics, which are the relationship between the stopper opening and the flow rate in each nozzle 1 and 2, without using a flow meter for measuring the surface flow rate and the flow rate for measuring the inner layer flow rate to estimate
The method of estimating the flow characteristics that realizes this is based on the following viewpoints. During the feedback control using the melt level gauge 10 to control the opening degree of the surface layer stopper 11 to keep the melt level constant, if the control operation is performed to keep the opening degree of the inner layer stopper 12 constant, the surface layer nozzle 1 , whatever the flow rate characteristics of the inner layer nozzle 2 are, the opening of the surface layer stopper 11 converges to a constant value in accordance with those flow rate characteristics. Using this property, the set value of the constant opening of the inner layer stopper 12 is changed stepwise (stepwise) multiple times, and the opening of the surface layer stopper 11 converges each time it is changed (hereinafter referred to as "convergence value data"). ) are collected, the unknown parameters (hereinafter referred to as “unknowns Δ ₁ , Δ ₂ ”) included in the relational expressions representing the respective flow characteristics of the surface layer nozzle 1 and the inner layer nozzle 2 are used as variables. Equations can be constructed and each unknown can be calculated backwards.
In this embodiment, the surface layer stopper 11 is used to keep the molten metal level constant, and the opening degree of the inner layer stopper 12 is kept constant. is kept constant and the opening degree of the surface layer stopper 11 is kept constant.

A functional configuration of the controller 100 according to the present embodiment will be described with reference to FIG.
The controller 101 uses the level meter 10 to control the opening degree of the surface layer stopper 11 to keep the molten metal level constant and to keep the opening degree of the inner layer stopper 12 constant.

The opening degree changing unit 102 sets the constant opening degree of the inner layer stopper 12 and changes it stepwise during the feedback and the constant opening control by the control unit 101 .
The flow rate calculation value calculation unit 103 calculates a flow rate calculation value, which is a calculation value of the total flow rate flowing through the surface layer nozzle 1 and the inner layer nozzle 2, based on the casting speed _Vc . For example, the flow rate calculation value can be substituted by finding the billet withdrawal amount _AVc during steady-state control. Here, the cast strip withdrawal amount AV _c is obtained by multiplying the casting speed V _c before and after the opening degree of the inner layer stopper 12 is changed by the opening degree changing unit 102 by the cross-sectional area A of the mold.
The balance formula creation unit 104 creates a volume balance formula in which the total flow rate through the surface layer nozzle 1 and the inner layer nozzle 2 is equal to the cast strip withdrawal amount _AVc . For example, the balance formula creation unit 104 sets the constant opening of the inner layer stopper 12 set by the opening change unit 102, the flow rate calculation value (slab withdrawal amount AV _c ) calculated by the flow calculation value calculation unit 103, and the opening Using the convergence value data of the opening degree of the surface layer stopper 11 collected after changing the inner layer stopper 12 to a constant opening degree in the changing unit 102, the unknown value Δ ₁ related to the flow rate characteristics of the surface layer nozzle 1 and the flow rate of the inner layer nozzle 2 Create an equation with the unknown quantity Δ ₂ related to the characteristics as variables.

The solution finding unit 105 changes the constant opening of the inner layer stopper 12 set by the opening change unit 102, calculates the flow rate calculation value by the flow rate calculation value calculation unit 103, and calculates the volume balance equation (unknown value Δ ₁ and Δ ₂ as variables) are repeated multiple times (at least _twice ) to form a system of equations. An unknown quantity Δ ₂ related to the flow rate characteristics of the nozzle 2 is obtained.

The controller 101 corrects the constant opening of the inner layer stopper 12 in the feedback and constant opening control using the unknown value Δ ₂ related to the flow rate characteristics of the inner layer nozzle 2 thus obtained.

In this embodiment, the controller 100 functions as a device for estimating the flow characteristics in the continuous casting process of the multi-layered slab and as a control device for the continuous casting process of the multi-layered slab. The controller 100 configured as described above is implemented by a computer device including, for example, a CPU, a ROM, a RAM, and the like. Note that the controller 100 does not need to be configured as a single device, and a plurality of computer devices cooperate to function as the controller 100, or a process computer that manages the continuous casting process, for example, functions as the controller 100. may be

Hereinafter, the estimation of the flow rate characteristics of the nozzles 1 and 2 and the control of the continuous casting process in this embodiment will be described in detail.
First, the symbols used for explanation are described.
Q ₁ (t): surface layer flow rate at time t Q ₂ (t): inner layer flow rate at time t u ₁ (t): surface layer stopper opening degree at time t u ₂ (t): inner layer stopper opening degree at time t y ₁ (t): level of mold level at time t y ₂ (t): level of boundary layer at time t y ₁₀ : target value for steady level of mold level y ₂₀ : target value for boundary layer level W: mold width D: mold thickness A : Cross-sectional area of mold _A2 (t): Cross-sectional area of inner layer at time t d(t): Surface layer thickness at time t _d0 : Target value of surface layer thickness _A10 : Target value of cross-sectional area of surface layer _A20 : Target value of cross-sectional area of inner layer Q ₁₀ : Surface layer flow rate target value _Q20 : Inner layer flow rate target value τ : Dead time from melt surface level position to boundary layer level position τ _act : Dead time due to stopper operation response delay and melt drop ρ ₁ : Surface layer molten steel density ρ ₂ : Inner layer molten steel density α _1nominal : Surface layer flow characteristic nominal value α _2nominal : Inner layer flow characteristic nominal value Δ ₁ : Surface layer flow characteristic multiplicative error Δ ₂ : Inner layer flow characteristic multiplicative error TDW (t): Tundish 3 at time t Weight measurement value V _c : Casting speed K _s : Solidification constant

First, to describe the formulation of the continuous casting process for multilayer slabs, a model of the continuous casting process for multilayer slabs is shown in Patent Document 3 and Non-Patent Document 1, and the present embodiment is based on this model. and
In this model, the surface layer level y ₁ and the boundary layer level y ₂ fluctuate according to equations (1) to (5) in accordance with the fluctuations of the surface layer flow rate Q ₁ (t) and the inner layer flow rate Q ₂ (t).

Formula (1) means that the molten metal level y ₁ fluctuates according to the mass balance between the injection amount and the withdrawal amount into the mold.
Equation (2) means that the boundary layer level y ₂ varies according to the inner layer flow rate, inner layer cross-sectional area, and casting speed.
Here, the inner layer cross-sectional area A ₂ (t) varies according to formula (3), and the surface layer thickness d(t) is expressed by formula (4). In the formula (3), the width of the inner layer portion of the multi-layered slab is represented by “W-2d(t)” and the thickness of the inner layer portion is represented by “D-2d(t)”, and by multiplying these, the inner layer cross-sectional area A ₂ means that (t) can be obtained. Equation (4) implies that the surface layer thickness d(t) varies in proportion to τ ^(1/2) (K _s is the solidification constant).
However, τ is the dead time from the melt surface level position to the boundary layer level position, and satisfies equation (5). Equation (5) means that the molten steel at the surface level position at time t−τ reaches the boundary layer level position at time t through the process of being withdrawn.
If the boundary layer level _y2 rises above the steady-state target value, the surface _layer thickness d decreases. If the flow rate _Q.sub.2 is constant, the boundary layer level _y.sub.2 will decrease according to equation (2), and it will be understood that there is a mechanism that cancels out the initial increase. In this way, the surface layer thickness d(t) and the boundary layer level _y2 ( _{t) have the function of "self-repairing" as the melt surface level y1 and the boundary layer level y2 fluctuate} , which is a feature of this process. is.

If the casting speed V _c (t) is constant, the above equation (5) can be transformed into equation (6), and the dead time τ is the arrival time from the melt surface level to the boundary layer level. means to be sought. Furthermore, if the melt surface level y ₁ is maintained at the steady melt surface level target value y ₁₀ , the melt surface level y ₁ (t-τ) does not depend on the dead time τ, so the dead time τ is given by the equation (7) can be approximated as In this embodiment, it is assumed that constant control is being performed to the steady level target value, so approximation can be performed using equation (7).

From the equations (1) to (4) and (7), for a given casting speed V _c , the target steady-state melt level y ₁₀ , and the target boundary layer level y ₂₀ , the melt surface level and the boundary layer level are calculated as follows: In the steady state of constant control of multi-layer casting, the surface layer flow rate and the inner layer flow rate must satisfy equations (11) and (12). Q ₁₀ and Q ₂₀ determined by equations (11) and (12) are the surface layer flow rate target value and inner layer flow rate target value, respectively.

Therefore, in order to maintain the surface layer level _y1 at the steady surface level target value _y10 and the boundary layer level _y2 at the boundary layer level target value _y20 , the surface layer flow rate and the inner layer flow rate must be set at the casting speed V _c , the surface layer flow rate target value Q ₁₀ and the inner layer flow rate target value Q ₂₀ , which are determined according to the surface layer target value y ₁₀ and the boundary layer level target value y ₂₀ .
In order to realize this flow rate control, in the present embodiment, the flow rate characteristics of each nozzle 1 and 2 are estimated during casting without using a flow meter, and the inner layer stopper 12 is arranged so as to realize the flow rate target value based on the flow rate characteristics. By calculating back the constant opening of , the surface layer flow rate and the inner layer flow rate are kept constant at the respective flow rate target values Q ₁₀ and Q ₂₀ .

In estimating the flow rate characteristics of each nozzle 1, 2, the relationship between the stopper opening and the flow rate in each nozzle 1, 2 (that is, the relational expression representing the flow rate characteristic) is as shown in Equations (13) and (14). is assumed to be a linear approximation to For example, it is a reasonable assumption for continuous slab casting at low throughput such as a test continuous caster, and even for high throughput casting, if the throughput during casting is limited to a certain range, the range Linear approximation is effective in Note that the relational expression representing the flow rate characteristic is not limited to linear approximation, and may be approximated by a more complicated function such as a quadratic function. In equations (13) and (14), surface layer flow characteristic multiplicative error Δ ₁ (above-mentioned unknown quantity Δ ₁ ) and inner layer flow characteristic multiplicative error Δ ₂ (the unknown Δ ₂ described above). That is, the surface flow rate Q ₁ (t) is a formula obtained by multiplying the opening degree u ₁ (t−τ _act ) of the surface layer stopper 11 before τ _act time by the surface flow rate characteristic nominal value α _1nominal , and further by multiplying the unknown value Δ ₁ is approximated by The surface layer flow rate Q ₂ (t) is a formula obtained by multiplying the opening degree u ₂ (t−τ _act ) of the inner layer stopper 12 before τ _act time by the nominal value α _2nominal of the inner layer flow rate characteristic, and further by multiplying the unknown value Δ ₂ is approximated by If these unknowns Δ ₁ and Δ ₂ can be obtained appropriately, the surface layer flow characteristic nominal value α _1nominal and the inner layer flow characteristic nominal value α _2nominal can be corrected to true values, and the flow characteristics can be estimated with high accuracy. The surface layer flow rate characteristic nominal value α _1nominal and the inner layer flow rate characteristic nominal value α _2nominal each include values obtained from the geometric relational expression between the opening of the stopper and the area of the nozzle opening or from past casting data. Used. Incidentally, the dead time τ _act due to the stopper operation response delay and hot water drop usually takes a value of about 0.1 to 0.3 sec.

FIG. 3 shows a flow chart of a method for estimating flow rate characteristics in the continuous casting process for a multi-layered slab and a control method for the continuous casting process for a multi-layered slab in this embodiment. In this embodiment, the time t represents a discrete time obtained for each sampling time.
The flowchart of FIG. 3 is executed, for example, at the beginning of casting immediately after the hot water heating control is shifted to the steady state control, or at regular intervals during casting. That is, the flow chart of FIG. It is executed during constant opening control that keeps the opening constant.
In this feedback and constant opening degree control, the constant opening degree of the inner layer stopper 12 is set so as to keep the inner layer flow rate constant at the inner layer flow rate target value _Q20 . The flow rate does not match the inner layer flow rate target value _Q20 , and accordingly the surface layer flow rate does not match the surface layer flow rate target value _Q10 .

In steps S1 and S2, the controller 100 sets the number of times K of repeated calculations and initializes the number of times K. FIG. The number of times K may be, for example, a predetermined fixed value.
In step S3, the controller 100 determines whether or not the current number k of iterative calculations has reached the number K of times. If so (YES), the process proceeds to step S10.

In step S<b>4 , the opening changer 102 of the controller 100 sets the constant opening u _2,set of the inner layer stopper 12 . The constant opening u _2,set may be set, for example, by selecting from a plurality of predetermined fixed values. Alternatively, for the constant opening u _2,set , an initial set value of the constant opening is determined, and starting from the initial set value, the amount of change in the opening, which is a predetermined fixed value, is sequentially calculated in repeated calculations. You may make it set what added or subtracted.
In step S5, the opening degree changing unit 102 of the controller 100 changes the opening degree of the inner layer stopper 12 to the constant opening degree u _{2,set set} in step S4 in a stepwise manner. FIG. 4(a) shows an example of a time series of opening degrees of the stoppers 11 and 12. As shown in FIG. In the example of FIG. 4A, the constant opening u _2,set of the inner layer stopper 12 is set and changed stepwise at timings T ₁ , T ₂ , T ₃ and T ₄ . As shown in FIG. 4(a), when the constant opening of the inner layer stopper 12 increases, the opening of the surface layer stopper 11 decreases in order to keep the melt level constant, and the constant opening of the inner layer stopper 12 decreases. Then, the opening degree of the surface layer stopper 11 is increased in order to keep the melt level constant. Then, as shown in FIGS. 4(c) and 4(d), the surface layer flow rate and the inner layer flow rate change according to changes in the opening degrees of the stoppers 11 and 12. FIG.

In step S<b>6 , the controller 100 collects convergence value data of the opening degree of the surface layer stopper 11 . Equations (13) and (14) always hold at each time, and the data of the opening degree of the surface layer stopper 11 after changing the constant opening degree of the inner layer stopper 12 is collected over a predetermined period (time t = 1, 2, ..., T). However, since the process response is not stable immediately after the constant opening of the inner layer stopper 12 is changed, the data in the period (time t=T _start , T _start +1, . Using it as data, the relationships of equations (15) and (16) are obtained. The times T _start and T may be predetermined fixed values, for example. It should be noted that the dead time τ _act due to the stopper operation response delay and the molten metal drop does not affect the steady-state value, so it can be ignored here.

In step S7, the calculated flow rate calculator 103 of the controller 100 calculates a calculated flow rate, which is a calculated value of the total flow rate flowing through the surface layer nozzle 1 and the inner layer nozzle 2, based on the actual casting speed _Vc . During steady-state control, the molten steel level can be considered to be substantially constant, and the mass balance between the amount of molten steel injected into the mold 4 and the amount of molten steel withdrawn from the mold 4 can be regarded as substantially the same. Therefore, the cast strip withdrawal amount _AVc obtained by multiplying the casting speed _Vc by the mold cross-sectional area A can be treated as the molten steel injection amount into the mold 4, that is, the total flow rate of the surface layer nozzle 1 and the inner layer nozzle 2. The casting speed _Vc may be basically constant, but when the casting speed changes, the changing value may be used.

In step S8, the balance formula creation unit 104 of the controller 100 generates the constant opening u 2, _set of the inner layer stopper 12 set in step S4, the convergence value data of the opening of the surface layer stopper 11 collected in step S6, and the Using the flow rate calculation value (slab withdrawal amount AV _c ) calculated in S7, a volume balance equation is created as shown in Equation (17). More specifically, from the equations (15) and (16), the surface layer flow rate characteristic multiplication error Δ ₁ which is an unknown quantity related to the flow rate characteristic of the surface layer nozzle 1 and the inner layer flow rate characteristic multiplication error Δ 1 which is an unknown quantity related to the flow rate characteristic of the inner layer nozzle 2 The error Δ ₂ , the surface layer flow characteristic nominal value α _1nominal and the inner layer flow characteristic nominal value α _2nominal , the time average value u ₁ of the opening degree of the surface layer stopper 11, and the constant opening degree u _2,set of the inner layer stopper 12, A volumetric balance equation (17) representing the relationship with the calculated flow value _AVc is created. The time-averaged value u ₁ of the opening degree of the stopper 11 is the time-averaged value in the period (time t=T _start , T _start +1, . is represented as mean(·) represents an average operation. It should be noted that the notation of u ₁ is assumed to be above u ₁ , and the same applies to other characters. Here, an example of calculating and using the time average value u ₁ of the opening degree of the surface layer stopper 11 from the convergence value data of the opening degree of the surface layer stopper 11 has been described. Any value (eg, final value) may be used.
It should be noted that, each time k, the processes of steps S4 to S8 are executed for a certain period of time, for example. Below, the k-th interval may be described as “interval k”.

In step S9, the controller 100 increments the number of times k and returns the process to step S3.
As a result, the constant opening degree u _2, set of the inner layer stopper 12 set in step S4 is changed, and steps S5 to S8 are repeated K times. In the example of FIG. 4A, K=4 times, and the constant opening degree u _2,set of the inner layer stopper 12 is changed four times.

In step S10, the solving unit 105 of the controller 100 constructs simultaneous equations using the surface layer flow rate characteristic multiplicative error _Δ1 and the inner layer flow rate characteristic multiplicative error _Δ2 as variables by repeating calculations K times, as shown in equation (19). , and find Δ ₁ and Δ ₂ by using the method of least squares or the like. Note that u _2,set ^(k) means the constant opening degree of the inner layer stopper 12 at each time k, and u ₁ ^(k) means the time average value of the opening degree of the surface layer stopper 11 at each time k. do.

In step S11, the controller 101 multiplies the constant opening of the inner layer stopper 12 by 1/ _Δ2 to correct the constant opening of the inner layer stopper 12 in the feedback and constant opening control. By this correction, the constant opening of the inner layer stopper 12 can be set to the opening that keeps the inner layer flow rate constant at the inner layer flow rate target value _Q20 , and accordingly, the surface layer flow rate is kept constant at the surface layer flow rate target value _Q10 . can do.

When calculating the flow rate value based on the casting speed _Vc , noise is less than when using the weight measurement value of the tundish 3 described in the second embodiment. , then K=2 and formula (19)' can be constructed. In that case, the surface layer flow rate characteristic multiplicative error Δ ₁ and the inner layer flow rate characteristic multiplicative error Δ ₂ can be obtained from equation (20).

As described above, the opening degree operation for changing the constant opening degree of the inner layer stopper 12 in a stepwise manner is performed a plurality of times (K times) to collect the data of the opening degree of the surface layer stopper 11 . Then, under the assumption of the flow rate characteristics of the equations (13) and (14), the simultaneous equations of the equation (19) consisting of the volume balance equations are constructed. By solving these simultaneous equations, the surface layer flow characteristic multiplicative error _Δ1 and the inner _layer flow characteristic multiplicative error _Δ2 are obtained. Correct the degree.
This method performs additional opening operation for process identification during feedback control and obtains unknown characteristics. If the process characteristics are obtained by using the above method, the accuracy of the estimation results will be poor. However, in this embodiment, steady-state data is used, so the accuracy of the estimation results can be ensured.
In addition, in this embodiment, the flow rate characteristics of each nozzle 1 and 2 can be estimated without using a flow meter. no costs associated with In addition, in a continuous casting facility in which a flow meter is set, the method may be switched to the method of the present invention when the flow meter malfunctions. In addition, there is no limitation such as premised on having a tundish for the surface layer and a tundish for the inner layer, and it is widely applicable.

[Second embodiment]
In the first embodiment, the example in which the flow rate calculation value is calculated based on the casting speed _Vc has been described. On the other hand, in the second embodiment, an example in which the calculated flow rate is calculated based on the weight measurement value TDW(t) of the tundish 3 will be described. In addition, below, it demonstrates centering around difference with 1st Embodiment, and abbreviate|omits the detailed description about the common point with 1st Embodiment.

A method for estimating the flow rate characteristics in the continuous casting process for a multi-layered slab and a method for controlling the continuous casting process for a multi-layered slab in the second embodiment will be described with reference to the flowchart of FIG. The description of the same processing as in the first embodiment will be omitted, and the processing that differs from the first embodiment will be described.
In step S7, the calculated flow rate calculation unit 103 of the controller 100 calculates the calculated flow rate, which is the total flow rate of the surface layer nozzle 1 and the inner layer nozzle 2, based on the weight measurement value TDW(t) of the tundish 3. Calculate. The amount of time change in the weight measurement value TDW(t) of the tundish 3 can be regarded as substantially matching the total flow rate flowing through the nozzles 1 and 2 per unit time.

Here, since the SN ratio of the measured weight of the tundish 3 is generally not good, ΔTDW ( When t) is the calculated flow rate, this calculated flow rate contains noise amplified by the differential operation. FIG. 4B shows an example of the relationship between time and the total flow rate of the surface layer nozzle 1 and the inner layer nozzle 2 . As shown in FIG. 4(b), ΔTDW(t) based on the measured weight of the tundish 3 behaves similarly to the actual total flow rate, but contains noise.
Therefore, as shown in equation (21), in the period (time t=T _start , T _start +1, . . . , T) in which a stable steady response is obtained, Operate as a calculated value.

In step S8, the balance formula creation unit 104 of the controller 100 creates a mass balance formula that the total flow rate flowing through the surface layer nozzle 1 and the inner layer nozzle 2 is equal to the flow rate calculation value ΔTDW. For example, the balance formula creation unit 104 uses the constant opening u _2,set of the inner layer stopper 12 set in step S4, the convergence value data of the opening of the surface layer stopper 11 collected in step S6, and the flow rate calculated in step S7. Using the calculated value ΔTDW, create an equation with the unknown quantity _Δ1 related to the flow characteristics of the surface layer nozzle 1 and the unknown quantity _Δ2 related to the flow characteristics of the inner layer nozzle 2 as variables, as shown in Equation (22). . More specifically, by introducing the molten steel densities ρ ₁ and ρ ₂ , the surface layer flow rate characteristic multiplicative error Δ ₁ and the inner layer nozzle 2 The inner layer flow rate characteristic multiplicative error Δ ₂ , which is an unknown value related to the flow rate characteristic, the surface layer flow rate characteristic nominal value α _1nominal and the inner layer flow rate characteristic nominal value α _2nominal , the time average value u ₁ of the opening degree of the surface layer stopper 11, and the inner layer A mass balance equation (22) representing the relationship between the constant opening u _2,set of the stopper 12 and the calculated flow rate ΔTDW is prepared.

In step S10, the solving unit 105 of the controller 100 composes simultaneous equations by repeating calculations K times as shown in Equation (23), solves them by the least squares method, and calculates the surface layer flow rate characteristic multiplicative error Δ ₁ and the inner layer flow rate Determine the characteristic multiplicative error _Δ2 . In addition, ΔTDW ^(k) ~ means the flow rate calculation value (time average value of ΔTDW(t)) at each time k.
In this embodiment, since the calculated flow rate is calculated based on the measured value (the measured weight TDW(t) of the tundish 3), the calculated flow rate more reflects the actual state of the continuous casting process. can be calculated.

[Modification]
Modifications will be described below.
Changes in flow characteristics may be monitored during casting. For example, during casting, the error error(k) between the flow rate actual value and the flow rate calculated value is calculated for each interval k of a certain period of time using equation (24). Δ ₁ ^(old) is the surface layer flow characteristic multiplicative error up to the previous section, and Δ ₂ ^(old) is the inner layer flow characteristic multiplicative error up to the previous section.
If error(k) in equation (24) deviates from a predetermined threshold value during casting, it is assumed that the flow characteristics have changed, and estimation of the flow characteristics can be performed as in the above-described embodiment. Here, the formulation for calculating the flow rate calculation value based on the weight measurement value of the tundish is shown, but the same applies to the calculation of the flow rate calculation value based on the casting speed.

Further, in the embodiment, an example was described in which fixed values were used as the number of repetition calculations K and the constant opening degree u _2,set of the inner layer stopper 12. However, as variable values, You may make it change.

Further, for example, when the number of times K is set as a fixed value, if error(k) in equation (24) falls below a predetermined threshold value before reaching the number of times K, the constant opening degree u _2,set of the inner layer stopper 12 may be terminated in the middle, that is, the repetitive calculation may be terminated.
In this way, the number of iterations K and the constant opening u _2,set of the inner layer stopper 12 are set as variable values, and by changing the values according to the predetermined conditions during casting, the number of repetitions K and the constant opening u _2, set You can change _{the set} efficiently.

[Example 1]
FIG. 4 shows the estimation of the flow rate characteristics in the continuous casting process to which the present invention is applied and the simulation results of the control of the continuous casting process. FIG. 4(c) shows an example of the relationship between time and surface flow rate (actual, target value). Further, FIG. 4D shows an example of the relationship between time and inner layer flow rate (actual result, target value).
In the simulation, a small-throughput continuous slab caster such as a test continuous caster was targeted, and the mold width W=800 mm, the mold thickness D=100 mm, and the casting speed V _c =0.7 m/m.
Further, as described in the second embodiment, the flow rate calculation value is calculated based on the weight measurement value of the tundish 3 .
In the simulation, the surface layer flow characteristic multiplicative error Δ ₁ =0.8 and the inner layer flow characteristic multiplicative error Δ ₂ =0.7.
The flow characteristics were estimated with K=4 times, and the constant opening of the inner layer stopper 12 in feedback and constant opening control was corrected.

As shown in FIGS. 4(c) and 4(d), at the initial set value (0-T ₁ (=6 sec)) of the constant opening of the inner layer stopper 12, the surface layer flow rate and the inner layer flow rate are the same as the respective flow rate target values. not.

As shown in FIG. 4(a), the constant opening degree of the inner layer stopper 12 is changed in steps of 10 sec four times (T ₁ (=6 sec), T ₂ (=16 sec), T ₃ (=26 sec), T ₄ (=36 sec)), the surface layer flow characteristic multiplicative error Δ ₁ and the inner layer flow characteristic multiplicative error Δ ₂ were identified. As shown in FIG. 4A, by changing the constant opening degree of the inner layer stopper 12, the opening degree of the surface layer stopper 11 changes, and as shown in FIGS. The surface layer flow rate and the inner layer flow rate change according to the change in temperature.

Then, by correcting the constant opening of the inner layer stopper ₁₂ in the feedback and constant opening control using the inner layer flow characteristic multiplicative error Δ2 (T5 (= 46 sec)), Fig. 4 (c), (d) As shown, the surface layer flow rate and inner layer flow rate were maintained near their target flow rates.
By solving equation (23) at K=2 times, 3 times, and 4 times, Δ ₁ =0.7703, Δ ₂ =0.7489, Δ ₁ =0.784, Δ ₂ =0. 732, Δ ₁ =0.782 and Δ ₂ =0.713 were obtained sequentially. As the number of changes was increased in this way, the accuracy of estimating the error in the flow characteristic improved, and a sufficient effect was obtained by repeating the calculation about four times.

[Third Embodiment]
As mentioned in the modified examples of the first and second embodiments, the number of repetition calculations K and the constant opening u _2,set of the inner layer stopper 12 are variable values, and the values are changed according to the state during casting. You may do so.
In the third embodiment, an example will be described in which the constant opening degree u _2,set of the inner layer stopper 12 is set to a variable value in order to solve the simultaneous equations of equations (19) and (23) with high accuracy.
Note that the basic functional configuration and processing operation of the controller 100 are the same as those of the first and second embodiments. The description will focus on differences from the embodiment.

As shown in FIG. 5, the opening change unit 102 of the controller 100 includes an optimization problem setting unit 102a and an optimization problem solving unit 102b. Then, in step S4 of FIG. 3, the opening degree changing unit 102 of the controller 100 obtains the constant opening degree u _2,set of the inner layer stopper 12 by solving the optimization problem described in detail below, set.

In the third embodiment, an example will be described in which an optimization problem is set and solved for the next iterative calculation. That is, the calculation up to the k-th time (section k) is completed, and the opening operation of the inner layer stopper 12 in the next section k+1 is optimized.
(1) Evaluation function In the present embodiment, a constant opening u _2,set ^{(k+1) that} minimizes the evaluation function J of Equation (25) is obtained. The evaluation function J is the estimated unknown value Δ ₁ ^(k+1) ^ related to the flow rate characteristics of the surface layer nozzle 1 and the estimated unknown value Δ ₂ ^(k+ 1) ^ related to the flow rate characteristics of the inner layer nozzle 2 in the interval k+1. is the trace (the summation of the diagonal elements of the matrix) of the variance-covariance matrix P(u _2,set ^(k+1) ) of . The trace of the variance-covariance matrix P(u _2,set ^(k+1) ) represents the sum of the variances of the errors from the true values of the unknowns Δ ₁ and Δ ₂ , and by minimizing it, each time It is possible to reduce the distance from the true values of the unknowns Δ ₁ and Δ ₂ at . Note that the notation of Δ ₁ ^(k+1) ̂ is assumed to be Δ ₁ ^(k+1) with ̂ attached, and the same applies to other characters.

In addition, in order to consider the continuity of the opening degree operation, in ^the evaluation function J _, the opening degree operation A penalty term relating to the amount and amount of manipulation of the degree of opening of the inner layer stopper 12 may be added. For example, as in Equation (26), the trace of the variance-covariance matrix P (u _2,set ^(k+1) ) and the opening degree manipulated variable u ₁ ^(k+1) of the surface layer stopper 11 −u ₁ ^{(k )} and the sum of squares of the opening manipulated variable u _2,set ^(k+1) -u _2,set ^(k) of the inner layer stopper 12, and the weighted sum considering the unit conversion to configure the evaluation function J, and this evaluation A constant opening u _2,set ^(k+1) that minimizes the function J is found.

The optimization problem setting unit 102a sets an optimization problem using equation (25) or equation (26) as an evaluation function, and the optimization problem solving unit 102b solves the optimization problem to obtain a constant Set the opening u _2,set ^(k+1) .
It should be noted that the number of times K may be a fixed value that is repeatedly calculated for that number of times. (k) may be calculated, and if error(k) falls below a predetermined threshold before the number K is reached, the iterative calculation may be terminated.

(2) Formulation of Optimization Problem The formulation and minimization of the evaluation function trace(P(u _{2 , set} ^(k+1) )) of the expression (25) will be specifically described. In the following, P(u _2,set ^(k+1) ) is written as Sk ₊₁ .
The variance-covariance matrix of the parameter (regression coefficient) estimated values of the linear regression model such as Equations (19) and (23) can be evaluated by the calculation formula described in Non-Patent Document 2, for example.
When obtaining the parameter (regression coefficient) estimated value of the linear regression model from the opening degree data obtained up to the interval k, the variance-covariance matrix S _k of the parameter estimated value is expressed as in Equation (27) . Here, Φ _k is a design matrix composed of data on the degree of opening obtained up to interval k, α is the precision parameter of the prior distribution of the regression coefficients, and β is the precision parameter of the prior distribution of the observed values.

In the next interval k+1, when u ₁ ^(k+1) ∼ and u _2,set ^(k+1) are obtained respectively, the design matrix Φ _k+1 in interval k+1 is given by equation (28). expressed. Here, φ _k+1 ^T represents a row vector obtained by extracting the k+1 row of the design matrix φ _k+1 .

The variance-covariance matrix S _k+1 of the parameter (regression coefficient) estimated values of the linear regression model is represented by Equation (29). S _k+1 in this equation (29) corresponds to P(u _2,set ^(k+1) ) in equation (25).

The variance-covariance matrix S _k+1 is given by Equation (30), and if the inverse matrix lemma is used, it is expressed by Equation (31) using S _k and φ _k+1 .

trace(S _k+1 ) can be expressed as in Equation (32).

Here, trace(S _k ) is a constant, and the only term dependent on φ _k+1 is the second term in equation (32). That is, φ _k+1 that minimizes trace(S _k+1 ) is the same as φ _k+1 that maximizes equation (33).

(3) Constraints u ₁ ^(k+1) _and u _2,set ^(k+1) , which are elements of φ k+1, cannot be selected independently. 1 and the total flow through the inner layer nozzle 2 must be met. The total flow rate _Qnominal may be given as the bill withdrawal amount _AVc .

Actually, u ₁ ^(k+1) cannot be known unless u _2,set ^(k+1) is set, but u ₁ ^(k+1 ) is An estimated value may be substituted, and there is no practical problem with this. Δ ₁ ^(k) ̂ and Δ ₂ ^(k) ̂ are estimates of unknowns obtained up to interval k. Equation (35)' is used when calculating the second opening degree set value at the end of k=1. Substituting an estimated value for u ₁ ^(k+1) − makes it impossible to evaluate S _k+1 strictly, but practically there is no problem in approximating it with equation (35).

Further, both the surface layer stopper 11 and the inner layer stopper 12 must satisfy the upper and lower limits of the opening manipulated variable, which are set according to the operational constraints or facility constraints that are normally assumed.

In summary, the optimization problem setting unit 102a sets the optimization problem represented by the equation (36) in consideration of the flow rate constraint of the equation (35) and the upper and lower limits of the opening manipulated variable. .

(4) Solving Optimization Problem The optimization problem solving unit 102b solves the optimization problem represented by Equation (36).
(a) Use of non-linear optimization algorithms The optimization problem expressed in Equation (36) can be solved with standard solvers for optimization. Also, the optimization problem expressed by Equation (36) is a fractional programming problem with positive convex functions in the numerator and denominator under linear constraints. See Patent Document 3).

(b) One-variable optimization Due to the flow constraint of Equation (35) on u ₁ ^(k+1) and u _2,set ^(k+1) , u ₁ ^(k+1) becomes can be expressed only by u _2,set ^(k+1) as follows.

By using this and eliminating u ₁ ^(k+1) ~ from equation (36), the optimization problem represented by equation (36) can be expressed as u _2,set ^{(k +1)} can be transformed into a one-variable optimization problem. To solve a single-variable optimization problem within the search range using an exploratory method (linear search, Brent's method, etc.), or an optimization algorithm such as a method that uses the gradient of a function, such as the steepest descent method or Newton's method. can be done. In this case, if an exhaustive search method such as a linear search is used, the optimal solution can be reliably obtained without falling into a local solution.
In this embodiment, the simultaneous equations of equations (19) and (23) can be solved with high accuracy by obtaining the constant opening degree u _2,set of the inner layer stopper 12 by optimization calculation.

[Modification]
Modifications will be described below.
Up to this point, we have assumed that the flow rate characteristics of each nozzle 1 and 2 can be linearly approximated. be able to.
In the following, a description will be given of formulation when a quadratic function is assumed as the flow rate characteristics of the nozzles 1 and 2, as in Equation (39), but a polynomial function of cubic or higher order can also be formulated in the same way. can be done.

In this case, assuming that the total flow rate flowing through the surface layer nozzle 1 and the inner layer nozzle 2 is equal to the flow rate _Qnominal injected into the mold 4, the simultaneous opening of the equation (40) is Equations can be constructed. Although _Qnominal is set to the same value for each repeated operation, it may be set to a different value for each repeated operation.

The simultaneous equations of equation (40) can be rewritten as equation (41). There are four unknowns, Δ ₁ ⁽¹⁾ , Δ ₁ ⁽²⁾ , Δ ₂ ⁽¹⁾ and Δ ₂ ⁽²⁾ , and at least four opening operations are required to solve the simultaneous equations.

Further, when performing the k+1th opening operation, u _2,set ^(k+1) is set, and u ₁ ^(k+1) is obtained as the convergence value of the opening of the surface layer stopper 11. However, since the actual value of u ₁ ^(k+1) has not been obtained for the k+1-th time, the estimated value u ₁ ^(k+1) ̂ is substituted as in equation (42).

Furthermore, as before, φ _k+1 ^T can be obtained by mathematical optimization by rearranging as in Equation (43). However, in this case, since it is assumed to be a quadratic expression in which the opening of the stopper is 0 and the flow rate is 0, the four components of the equation (44) are not independent variables, but the relationship of the equation (45) must be satisfied.

Furthermore, in addition to this constraint formula, the flow rate characteristic error estimated value obtained at the end of the k-th cycle may be applied to add a flow rate constraint formula as in Equation (46). Until the end of k=3, the flow rate constraint equation may be constructed as shown in Equation (47).

Further, regarding both the surface layer stopper 11 and the inner layer stopper 12, considering the upper and lower limits of the opening manipulated variable, the optimization problem represented by the equation (48) is set and solved.

[Fourth embodiment]
In the fourth embodiment, as in the third embodiment, an example in which the constant opening degree u _2,set of the inner layer stopper 12 is variable will be described.
In the following, description of common points with the third embodiment will be omitted, and differences from the third embodiment will be mainly described.
In the third embodiment, only the next time in the repeated calculation is targeted, whereas in the fourth embodiment, in order to reflect the relevance of multiple times in the repeated calculation, multiple times including the next time are targeted, Set up and solve an optimization problem.

When optimizing the opening degree operation of the inner layer stopper 12 not only for the next section k+1 but also for a plurality of sections after the next section k+2, the optimization calculation described in the third embodiment are sequentially repeated to determine the opening manipulated variable. When the optimization calculation is performed more effectively, it is possible to simultaneously optimize not only the opening manipulated variable of section k+1 but also the opening manipulated variable of all sections including section k+2 and subsequent sections. Although two sections will be described below, a similar formulation can be applied to generalized n sections such as k+1, k+2, . . . , k+n.

(1) Evaluation function In this embodiment, the constant openings u _2,set ^(k+1) and u _2,set ^{(k+2) that} minimize the evaluation function J of Equation (49) are obtained. The evaluation function J is estimated values Δ ₁ ^(k+1) ̂ and Δ ₁ ^(k+2) ̂ of the unknowns related to the flow rate characteristics of the surface layer nozzle 1 , and the unknown values related to the flow rate characteristics of the inner layer nozzle 2 in intervals k+1 and k+2. Estimates of Δ ₂ ^(k+1) ^, Δ ₂ ^(k+2) ^'s variance-covariance matrix P(u _2,set ^(k+1) , u _2,set ^(k+2) ) are traced by Minimize.

In addition, in order to consider the continuity of the opening degree operation, in ^the evaluation function J _, the opening degree operation A penalty term relating to the amount and amount of manipulation of the degree of opening of the inner layer stopper 12 may be added. In this case, taking into consideration the continuity of the three opening degree operations over the k, k+1, and k+2 times, for example, the regularization term of the equation (50) may be added to the equation (49).

(2) Formulation of optimization problem u ₁ ^(k+1) ~, u 2, _set (k+1) , u ₁ (k ^{+ 2)} ~, u _2,set ^{( k+2)} are obtained, Φ _k+2 , Φ _k+1 ^T , and Φ _k+2 ^T are expressed as in equation (51). Here, Φ _k+2 is a design matrix composed of the opening data obtained up to section k+2, and Φ _k+1 ^T and Φ _k+2 ^T are the k+1 row of the design matrix Φ _k+2. A row vector obtained by fetching and a row vector obtained by fetching the k+2th row are respectively represented.

The variance-covariance matrix S k+2 of the estimated values of the parameters (regression coefficients) of the linear regression model obtained from the opening degree data obtained up to section _k+2 is represented by Equation (52).

The variance-covariance matrix S _k+2 is given by Equation (53), and if the inverse matrix lemma is used, it is expressed by Equation (54) using S _k and Ψ ₂ . Here, Ψ ₂ represents a matrix defined as a transposed matrix of a matrix constructed by taking out the elements of the k+1 and k+2 rows of Φ _k+2 .

trace(S _k+2 ) can be expressed as in Equation (55).

where trace(S _k ) is a constant and the only term that depends on ψ ₂ is the second term in equation (55). That is, Ψ ₂ that minimizes trace(S _k+2 ) is the same as Ψ ₂ that maximizes (56).

As in the third embodiment, the optimization problem represented by Equation (57) is set in consideration of the flow rate constraint and the upper and lower limits of the opening manipulated variable.

In the fourth embodiment, by solving the optimization problem represented by Equation (57), u _2,set ^{(k+1) and u 2,set (k+)} for the k+1-th time and the ^k+ ₂ -th time. ²⁾ is obtained, but u _2,set ^(k+2) obtained here is not actually used. At the end of the k+1th cycle, u _2,set ^(k+2) and u _2,set ^(k+3) are obtained again by resolving the optimization problem represented by Equation (57). Use u _2,set ^(k+2) obtained when

The optimization problem represented by equation (57) is not necessarily a convex optimization problem, like the optimization problem represented by equation (36) in the third embodiment, but is a nonlinear optimization problem such as an interior point method. It is easy to find the extrema by algorithm. In order to improve _the convergence performance, the _gradient of the objective function may be given to these optimization algorithms. Just do it.
In the present embodiment, the constant opening degree u _2,set of the inner layer stopper 12 can be obtained by optimization calculation, reflecting the relevance of multiple repetition calculations.

[Example 2]
Table 1 and FIG. 6 show the results of identifying the surface layer flow rate characteristic multiplicative error _Δ1 and the inner layer flow rate characteristic multiplicative error _Δ2 . FIG. 6 shows variations in the multiplicative error of the flow characteristics (error σ from the true value) in the comparative method and the proposed methods 1 and 2. FIG.
In the simulation, a small-throughput continuous slab caster such as a test continuous caster was targeted, and the mold width W=800 mm, the mold thickness D=100 mm, and the casting speed V _c =0.7 m/m.
In the simulation, the surface layer flow characteristic multiplicative error Δ ₁ =0.75 and the inner layer flow characteristic multiplicative error Δ ₂ =1.25.
A noise of about 5% was superimposed on the true flow rate in the calculated flow rate.
A case where the constant opening of the inner layer stopper 12 was changed stepwise to 2 mm, 7 mm, and 12 mm (comparative method), and after the first constant opening was 2 mm, the second and third constant openings were changed. The results were compared between the case of determination by proposed method 1 according to the third embodiment and the case of determination by proposed method 2 according to the fourth embodiment.
Monte Carlo simulation was performed 1000 times to evaluate the average value and variation of the multiplicative error of the flow characteristics.

As shown in Table 1 and FIG. 6, in the comparative method, Δ ₁ and Δ ₂ vary greatly at the end of the second run, but relatively accurate solutions are obtained at the end of the third run.
On the other hand, in both proposed methods 1 and 2, the dispersion of Δ ₁ and Δ ₂ is small at the end of the second run, and high-accuracy solutions are obtained. It is
Compared to proposed method 1, proposed method 2, which simultaneously optimizes multiple intervals, provides solutions with even smaller variations.

As described above, the present invention has been described together with the embodiments, but the above-described embodiments merely show specific examples for carrying out the present invention, and the technical scope of the present invention is not construed in a limited manner. It should not be. That is, the present invention can be embodied in various forms without departing from its technical concept or main features.
In addition, the present invention can also be implemented by supplying software (program) that realizes the functions of the present invention to a system or device via a network or various storage media, and reading and executing the program by the computer of this system or device. It is feasible.

1: surface layer nozzle, 2: inner layer nozzle, 3: tundish, 4: mold, 7: boundary, 8: melt surface, 10: melt surface level gauge, 11 surface layer stopper, 12: inner layer stopper, 100: controller, 101: Control unit 102: Opening change unit 102a: Optimization problem setting unit 102b: Optimization problem solving unit 103: Calculated flow rate calculating unit 104: Balance formula creating unit 105: Solving unit

Claims (16)

Molten metal is injected into the mold from the surface layer nozzle and the inner layer nozzle, each of which has a flow rate control mechanism for controlling the molten metal supply flow rate according to the operation to change the opening, to produce a multi-layered slab with different composition of the surface layer and the inner layer. In the continuous casting process to be manufactured, a flow rate characteristic, which is the relationship between the opening degree of the flow control mechanism in the surface layer nozzle and the flow rate, and the flow rate characteristic, which is the relationship between the opening degree of the flow control mechanism in the inner layer nozzle and the flow rate, are estimated. A device for estimating flow rate characteristics in a continuous casting process of a multi-layered slab,
feedback control of the opening of a flow rate control mechanism of one of the surface layer nozzle and the inner layer nozzle using a level gauge for measuring the level of the surface of the molten metal in the mold; During the constant opening control that keeps the melt level constant and keeps the opening of the flow rate control mechanism of the other nozzle constant,
opening changing means for setting a constant opening of the flow rate control mechanism of the other nozzle and changing the opening to this constant opening;
a flow rate calculation value calculating means for calculating a flow rate calculation value, which is a calculated value of the total flow rate flowing through the surface layer nozzle and the inner layer nozzle;
The constant opening of the flow rate control mechanism for the other nozzle set by the opening degree changing means, the calculated flow rate calculated by the calculated flow rate calculating means, and the flow rate control of the other nozzle by the opening changing means Using the convergence value data of the opening degree of the flow control mechanism of the one nozzle collected after changing the mechanism to a constant opening degree, the unknown quantity related to the flow rate characteristics of the surface layer nozzle and the flow rate characteristic of the inner layer nozzle balance formula creation means for creating a mass or volume balance formula with unknowns as variables;
By changing the constant opening of the flow rate control mechanism of the other nozzle set by the opening changing means, the calculation of the calculated flow rate by the calculated flow rate calculation means and the creation of the balance formula by the balance formula creation means are performed. and a solution-finding means for solving simultaneous equations constructed by repeating a plurality of times to obtain unknown values relating to flow characteristics of the surface layer nozzle and unknown values relating to flow characteristics of the inner layer nozzle. A device for estimating flow characteristics in continuous strip casting processes. 2. The apparatus for estimating flow rate characteristics in a continuous casting process for a multi-layer cast slab according to claim 1, wherein said calculated flow rate calculation means calculates said calculated flow rate based on a casting speed. 2. The multiplexer according to claim 1, wherein said calculated flow rate calculation means calculates said calculated flow rate based on weight measurement values of a tundish that supplies molten metal to said surface layer nozzle and said inner layer nozzle. A device for estimating flow characteristics in the continuous casting process of layered slabs. 4. The device for estimating flow rate characteristics in a continuous casting process for a multi-layer cast slab according to claim 3, wherein time averaging is performed when calculating said flow rate calculation value based on said weight measurement value of said tundish. The constant opening of the flow rate control mechanism of the other nozzle set by the opening change means, the calculation of the calculated flow rate by the calculated flow rate calculation means, and the creation of the balance formula by the balance formula creation means 5. The composite according to any one of claims 1 to 4, wherein at least one of the number of repetitions when the casting is repeated is set to a variable value, and the value is changed according to a predetermined condition during casting. A device for estimating flow characteristics in the continuous casting process of layered slabs. The degree-of-opening change means changes the flow rate of the surface layer nozzle each time the calculation of the calculated flow rate by the calculated flow rate calculation means and the creation of the balance formula by the balance formula creation means are repeated a plurality of times. By setting and solving an optimization problem using an evaluation function including a trace of a variance-covariance matrix of unknowns related to characteristics and unknowns related to the flow characteristics of the inner layer nozzle, the flow rate control mechanism of the other nozzle is fixed. 6. The device for estimating flow rate characteristics in a continuous casting process for a multi-layer cast slab according to any one of claims 1 to 5, wherein the opening is set. 7. The multi-layer structure according to claim 6, wherein the evaluation function includes a penalty term relating to an opening manipulated variable of the flow control mechanism for the one nozzle and an opening manipulated variable of the flow control mechanism for the other nozzle. A device for estimating flow rate characteristics in the continuous casting process of slabs. 8. The flow rate characteristics in the continuous casting process for a multi-layer cast slab according to claim 6, wherein the opening changing means sets and solves the optimization problem for the next time in the iterative calculation. estimation device. 8. The continuous casting of a multilayer slab according to claim 6 or 7, wherein the opening changing means sets and solves the optimization problem for a plurality of times including the next time in the repeated calculation. A device for estimating flow characteristics in a process. The flow rate in the continuous casting process for a multi-layer slab according to any one of claims 6 to 8, wherein the optimization problem includes a flow rate constraint on the total flow rate through the surface layer nozzle and the inner layer nozzle. Property estimator. 10. The method according to any one of claims 6 to 9, wherein the optimization problem includes upper and lower limits on the manipulated opening amount of the flow control mechanism for the one nozzle and the manipulated opening amount of the flow control mechanism for the other nozzle. The device for estimating flow rate characteristics in the continuous casting process for a multi-layered slab according to any one of the above items. 9. The apparatus for estimating flow rate characteristics in a continuous casting process for a multi-layer cast slab according to claim 8, wherein said opening change means solves said optimization problem by converting it into a one-variable optimization problem. Before the number of repeated calculations reaches a predetermined number when the calculation of the calculated flow rate by the calculated flow rate calculation means and the creation of the balance formula by the balance formula creation means are repeated a plurality of times, a predetermined 13. The apparatus for estimating flow rate characteristics in a continuous casting process for a multi-layer cast slab according to any one of claims 1 to 12, wherein the iterative calculation is terminated when a condition is satisfied. Molten metal is injected into the mold from the surface layer nozzle and the inner layer nozzle, each of which has a flow rate control mechanism for controlling the molten metal supply flow rate according to the operation to change the opening, to produce a multi-layered slab with different composition of the surface layer and the inner layer. In the continuous casting process to be manufactured, a flow rate characteristic, which is the relationship between the opening degree of the flow control mechanism in the surface layer nozzle and the flow rate, and the flow rate characteristic, which is the relationship between the opening degree of the flow control mechanism in the inner layer nozzle and the flow rate, are estimated. A method for estimating flow rate characteristics in a continuous casting process of a multi-layered slab, comprising:
feedback control of the opening of a flow rate control mechanism of one of the surface layer nozzle and the inner layer nozzle using a level gauge for measuring the level of the surface of the molten metal in the mold; During the constant opening control that keeps the melt level constant and keeps the opening of the flow rate control mechanism of the other nozzle constant,
a first step of setting a constant opening of the flow rate control mechanism of the other nozzle and changing it to this constant opening;
a second step of calculating a calculated flow rate, which is a calculated value of the total flow rate flowing through the surface layer nozzle and the inner layer nozzle;
The constant opening degree of the flow control mechanism of the other nozzle set in the first step, the calculated flow rate calculated in the second step, and the flow control mechanism of the other nozzle in the first step Using the convergence value data of the opening degree of the flow rate control mechanism of the one nozzle collected after changing the constant opening degree of , the unknown value related to the flow rate characteristics of the surface layer nozzle and the unknown value related to the flow rate characteristic of the inner layer nozzle a third step of creating a mass or volume balance equation with
Simultaneous equations constructed by repeating the second step and the third step a plurality of times while changing the constant opening of the flow rate control mechanism of the other nozzle set in the first step and a fourth step of obtaining a solution to obtain an unknown quantity related to the flow characteristics of the surface layer nozzle and an unknown quantity related to the flow characteristics of the inner layer nozzle. Method. Molten metal is injected into the mold from the surface layer nozzle and the inner layer nozzle, each of which has a flow rate control mechanism for controlling the molten metal supply flow rate according to the operation to change the opening, to produce a multi-layered slab with different composition of the surface layer and the inner layer. In the continuous casting process to be manufactured, a flow rate characteristic, which is the relationship between the opening degree of the flow control mechanism in the surface layer nozzle and the flow rate, and the flow rate characteristic, which is the relationship between the opening degree of the flow control mechanism in the inner layer nozzle and the flow rate, are estimated. A program for
feedback control of the opening of a flow rate control mechanism of one of the surface layer nozzle and the inner layer nozzle using a level gauge for measuring the level of the surface of the molten metal in the mold; During the constant opening control that keeps the melt level constant and keeps the opening of the flow control mechanism of the other nozzle constant,
a first process of setting a constant degree of opening of the flow rate control mechanism of the other nozzle and changing the degree of opening to this constant degree of opening;
a second process of calculating a flow rate calculation value that is a calculated value of the total flow rate flowing through the surface layer nozzle and the inner layer nozzle;
The constant opening degree of the flow control mechanism of the other nozzle set in the first process, the calculated flow rate calculated in the second process, and the flow control mechanism of the other nozzle in the first process Using the convergence value data of the opening degree of the flow rate control mechanism of the one nozzle collected after changing the constant opening degree of , the unknown value related to the flow rate characteristics of the surface layer nozzle and the unknown value related to the flow rate characteristic of the inner layer nozzle A third process of creating a mass or volume balance formula with
Simultaneous equations constructed by repeating the second process and the third process a plurality of times while changing the constant opening of the flow rate control mechanism of the other nozzle set in the first process A program for causing a computer to execute a fourth process of solving to obtain unknown values relating to flow characteristics of the surface layer nozzle and unknown values relating to flow characteristics of the inner layer nozzle. Feedback and constant opening degree control using the unknown quantity related to the flow rate characteristics of the other nozzle obtained by the flow rate characteristic estimation device in the continuous casting process for a multi-layered slab according to any one of claims 1 to 13. A method of controlling a continuous casting process for a multilayer cast slab, characterized by correcting the constant opening of the flow rate control mechanism of the other nozzle in the above.

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