JP6881170B2 - Secondary cooling control device for continuous casting machine, secondary cooling control method for continuous casting machine, and program - Google Patents

Description

The present invention relates to a secondary cooling control device for a continuous casting machine, a secondary cooling control method for a continuous casting machine, and a program, and particularly controls the amount of cooling water injected into a slab in the secondary cooling zone of the continuous casting machine. It is suitable for use in order to do so.

In continuous casting, the uncoagulated liquid phase in which the solute component is concentrated at the end of solidification of the slab is attracted to the negative pressure part in the solid-phase dendrite structure due to solidification shrinkage, which may cause central segregation in the slab. .. As a technique for preventing the central segregation of the slab, so-called light reduction of the slab is known. This is a technique for preventing central segregation from occurring in a slab by compensating for the pressure on the slab by reducing the slab immediately before cutting.

Under light slab reduction, it is effective to reduce the slab in the thickness direction over several meters in the casting direction and determine the reduction speed in the casting direction by the central solid phase ratio (central solid phase ratio) of the slab. It is shown in Patent Document 1 that central segregation can be prevented.
In Patent Document 1, 1.0 to 2.0 mm in the range from the position where the temperature at the center of the slab is lower than the liquidus temperature, that is, the position where the solid phase ratio starts to exceed 0 (zero) to the flow limit solid phase ratio. In addition to preventing central segregation, V segregation and inverse V segregation are not only prevented by depressing at a depressing rate of / min, and then depressing at a depressing rate of less than 0.3 mm / min until the slab is completely solidified. It has been shown that defects such as can be prevented. As described in Patent Document 1, the V-segregation is a V-shaped segregation, and is V-shaped on both sides of the slab in the thickness direction from the vicinity of the center in the thickness direction of the slab toward the casting direction. It is an elongated form of segregation. Inverse V segregation is V segregation in the direction opposite to the casting direction (the direction of the meniscus).

On the other hand, regarding the control of the amount of cooling water in the secondary cooling zone of the continuous casting machine, Patent Documents 2 and 3 disclose a technique for adjusting the surface temperature of the slab when the casting speed changes. Patent Document 2 discloses a method of suppressing a change in the surface temperature of a slab when the casting speed is changed by predetermining the relationship between the casting speed and the amount of cooling water in order to prevent cracks on the surface of the slab. Has been done. Further, Patent Document 3 discloses a method of controlling the surface temperature of the entire slab to a target value when the casting speed is changed.

In addition, if the casting speed changes during casting, the temperature and solid phase ratio of the center of the slab are cast from the start of the change in casting speed until the entire slab in the strand is cast at the same speed. The distribution of directions changes. Therefore, there are methods disclosed in Patent Documents 4 and 5 as a method of estimating the state amount of a slab during operation and using it for controlling the amount of reduction when the slab is lightly reduced. In Patent Document 4 and Patent Document 5, the future change of the solidification completion position of the slab is predicted by using the response model of the solidification completion position to the change of the casting speed or the molten steel temperature in the tundish, and the predicted value is set as the target value. A method of calculating the matching casting rate and / or the amount of change in the amount of cooling water is disclosed. In Patent Document 4, a database of the response of the change in the solidification completion position of the slab to the amount of cooling water in the secondary cooling zone or the casting speed is calculated in advance. Further, in Patent Document 5, a response model showing the relationship between the solidification completion position of the slab with respect to the change in the casting speed and / or the amount of cooling water is created.

Special Fair 5-30548 Gazette Japanese Patent No. 2932196 Japanese Patent No. 5757296 JP-A-2007-268559 JP-A-2007-268536

Toru Katayama, "New Edition Applied Kalman Filter", Asakura Shoten, 2000, p.84

By the way, in order to prevent not only central segregation but also V segregation or reverse V segregation, the state of the central portion should be appropriately maintained within the range where the central portion is in the solid-liquid coexistence region in the casting direction of the slab. Even if the casting speed is changed, it is necessary to reduce the fluctuation of the position of the slab portion where the solid phase ratio at the center of the slab is equal to or higher than the flow limit. However, V segregation or reverse V segregation may occur only by controlling the solidification completion position of the slab as in Patent Documents 4 and 5.

Further, as in Patent Documents 2 and 3, when the amount of cooling water in the secondary cooling zone is controlled so as to keep the surface temperature of the slab in the casting direction constant, when the casting speed decreases, the slab of the slab The temperature and solid phase ratio of the central part fluctuate greatly. Therefore, when the amount of reduction with respect to the slab when the slab is lightly reduced is kept constant, V segregation or reverse V segregation may occur as described above.

The present invention has been made in view of the above problems, and the slab before and after the change in the casting speed does not cause a large change in the solid phase ratio at the center of the slab even if the casting speed is changed. It is an object of the present invention to make it possible to keep the amount of reduction with respect to the slab at the time of light reduction to be constant.

The secondary cooling control device of the continuous casting machine of the present invention divides the secondary cooling zone for cooling the slabs drawn from the mold of the continuous casting machine into a plurality of cooling zones in the casting direction of the slabs. It is a secondary cooling control device of a continuous casting machine that controls the temperature of the slab by controlling the flow rate of the cooling water injected from the cooling spray included in each cooling zone, and is based on the heat transfer equation. The temperature inside the slab cross section, which is the temperature inside the cross section perpendicular to the casting direction of the slab, the slab cross section surface temperature, which is the temperature of the surface of the slab in the cross section, and the solid phase ratio in the cross section. It is measured during casting of the slab at a predetermined temperature measurement position and a model storage means for storing the heat transfer solidification model, which is a calculation formula for at least calculating the solid phase ratio distribution in the slab cross section, which is the distribution. The slab surface temperature acquisition means for acquiring the measured value of the surface temperature of the slab, the operation data acquisition means for acquiring the operation data including the casting speed of the continuous casting machine and the flow rate of the cooling water, and the above. The temperature evaluation position in the mold, which is the position for evaluating the temperature in the slab cross section, the surface temperature in the slab cross section, and the solid phase ratio distribution in the slab cross section, which is the position in the casting direction of the slab. Temperature evaluation position setting means that sets a predetermined interval from the position of the molten metal to the position of the machine end outlet, and heat transfer on the surface of the slab used in the calculation of the heat transfer solidification model. The coefficient uses the amount of the cooling water included in the operation data, the measured value of the surface temperature of the slab at the temperature measurement position, and the heat transfer coefficient correction parameter for correcting the heat transfer coefficient. The first calculated value including the heat transfer coefficient estimation means calculated by the above, the temperature in the slab cross section at each of the temperature evaluation positions, the slab cross section surface temperature, and the solid phase ratio distribution in the slab cross section. Each time the casting progresses by the interval between the temperature evaluation positions, the temperature solid phase ratio distribution calculation means calculated by using the heat transfer solidification model, the measured value of the surface temperature of the slab at the temperature measurement position, and the measured value. An estimated value of the surface temperature of the slab at the temperature measurement position, which is the temperature of the surface of the slab calculated based on the first calculated value calculated by the temperature solid phase ratio distribution calculation means. The heat transfer coefficient correction means for deriving the heat transfer coefficient correction parameter using the estimated value of, and the slab center target temperature which is the target value of the slab center temperature which is the temperature of the center of the slab. With respect to the slab center target temperature setting means for setting each of the temperature evaluation positions and each of the temperature evaluation positions. The range from the temperature evaluation position to a predetermined position on the downstream side in the casting direction from the temperature evaluation position is set as a future prediction range of the temperature evaluation position, and for each of the temperature evaluation positions, the said. Each of the temperature evaluation positions within the future prediction range with respect to the temperature evaluation position is set as the future prediction position with respect to the temperature evaluation position, and then the casting speed and the amount of the cooling water are set to the current time. The temperature inside the slab cross section at the current time at each of the temperature evaluation positions, the slab cross section surface temperature, and the slab calculated using the heat transfer solidification model, assuming that the values do not change. With the solid phase ratio distribution in the cross section as the initial value, the temperature in the slab cross section at the future predicted position at the time when each of the temperature evaluation positions advances from the current time to each of the future predicted positions, and the slab cross section. From the future prediction means for calculating the surface temperature and the second calculated value including the solid phase ratio distribution in the cross section of the slab using the heat transfer solidification model, and the actual value of the amount of the cooling water at the current time. It is a cooling water amount change amount instruction value which is an instruction value of the change amount of the cooling water amount, and the cooling water amount change amount instruction value for each of the cooling zones is used as a determination variable, and the cooling water amount change amount instruction value is followed. Purpose including a term representing the difference between the slab center temperature at each of the future predicted positions and the slab center target temperature at each of the future predicted positions when the amount of cooling water is changed. The cooling water amount change amount instruction value calculation means for calculating the cooling water amount change amount instruction value and the cooling water amount change by solving the optimization problem for obtaining the cooling water amount change amount instruction value that maximizes or minimizes the value of the function. Based on the cooling water amount change amount indicating value for each of the cooling zones calculated by the amount indicating value calculating means and the actual value of the cooling water amount of each of the cooling waters at the current time, the cooling zone Each has a cooling water amount changing means for changing the amount of the cooling water, and the objective function is calculated based on the second calculated value at each of the future predicted positions with respect to the temperature evaluation position. The predicted value of the slab center temperature at each of the future predicted positions, the slab center target temperature at each of the future predicted positions set by the slab center target temperature setting means, and the cooling. It is expressed using the water amount change amount indicated value, and every time the casting advances by at least the interval between the temperature evaluation positions, the slab surface temperature acquisition means and the operation data acquisition Means, wherein the temperature evaluation position setting means, the heat transfer coefficient estimation means, said temperature solid fraction distribution calculating means, the heat transfer coefficient correcting means, the billet center target temperature setting means, the future prediction unit, the cooling By repeatedly executing the water amount change amount instruction value calculation means and the cooling water amount change means, the slab center temperature at the future predicted position at an arbitrary time during casting can be set to the slab center target temperature. It is characterized by being close to.

In the secondary cooling control method of the continuous casting machine of the present invention, the secondary cooling zone for cooling the slabs drawn from the mold of the continuous casting machine is divided into a plurality of cooling zones in the casting direction of the slabs. It is a secondary cooling control method of a continuous casting machine that controls the temperature of the slab by controlling the flow rate of the cooling water injected from the cooling spray included in each cooling zone, and is based on the heat transfer equation. The temperature inside the slab cross section, which is the temperature inside the cross section perpendicular to the casting direction of the slab, the slab cross section surface temperature, which is the temperature of the surface of the slab in the cross section, and the solid phase ratio in the cross section. It is measured during casting of the slab at a predetermined temperature measurement position and a model storage step of storing a heat transfer solidification model, which is a calculation formula for at least calculating the solid phase ratio distribution in the slab cross section, which is the distribution. The slab surface temperature acquisition step of acquiring the measured value of the surface temperature of the slab, the operation data acquisition step of acquiring the operation data including the casting speed of the continuous casting machine and the flow rate of the cooling water, and the above. The temperature evaluation position in the mold, which is the position for evaluating the temperature in the slab cross section, the surface temperature in the slab cross section, and the solid phase ratio distribution in the slab cross section, which is the position in the casting direction of the slab. A temperature evaluation position setting step that sets a predetermined interval from the position of the molten metal to the position of the machine end outlet, and heat transfer on the surface of the slab used for calculation of the heat transfer solidification model. The coefficient uses the amount of the cooling water included in the operation data, the measured value of the surface temperature of the slab at the temperature measurement position, and the heat transfer coefficient correction parameter for correcting the heat transfer coefficient. The first calculated value including the heat transfer coefficient estimation step calculated by the above, the temperature in the slab cross section at each of the temperature evaluation positions, the slab cross section surface temperature, and the solid phase ratio distribution in the slab cross section. Each time the casting progresses by the interval between the temperature evaluation positions, the temperature solid phase ratio distribution calculation step calculated using the heat transfer solidification model, the measured value of the surface temperature of the slab at the temperature measurement position, and An estimated value of the surface temperature of the slab at the temperature measurement position, which is the temperature of the surface of the slab calculated based on the first calculated value calculated in the temperature solid phase ratio distribution calculation step. The heat transfer coefficient correction step for deriving the heat transfer coefficient correction parameter using the estimated value of, and the slab center target temperature which is the target value of the slab center temperature which is the temperature of the slab center. For each of the slab center target temperature setting steps and the temperature evaluation positions, which are set for each of the temperature evaluation positions. The range from the temperature evaluation position to a predetermined position on the downstream side in the casting direction from the temperature evaluation position is set as a future prediction range of the temperature evaluation position, and for each of the temperature evaluation positions, the said. Each of the temperature evaluation positions within the future prediction range with respect to the temperature evaluation position is set as the future prediction position with respect to the temperature evaluation position, and then the casting speed and the amount of the cooling water are set to the current time. The temperature inside the slab cross section at the current time at each of the temperature evaluation positions, the slab cross section surface temperature, and the slab calculated using the heat transfer solidification model, assuming that the values do not change. With the solid phase ratio distribution in the cross section as the initial value, the temperature in the slab cross section at the future predicted position at the time when each of the temperature evaluation positions advances from the current time to each of the future predicted positions, and the slab cross section. From the future prediction step of calculating the surface temperature and the second calculated value including the solid phase ratio distribution in the cross section of the slab using the heat transfer solidification model, and the actual value of the amount of the cooling water at the current time. It is a cooling water amount change amount instruction value which is an instruction value of the change amount of the cooling water amount, and the cooling water amount change amount instruction value for each of the cooling zones is used as a determination variable, and the cooling water amount change amount instruction value is followed. Purpose including a term representing the difference between the slab center temperature at each of the future predicted positions and the slab center target temperature at each of the future predicted positions when the amount of cooling water is changed. The cooling water amount change amount instruction value calculation step for calculating the cooling water amount change amount instruction value and the cooling water amount change by solving the optimization problem for obtaining the cooling water amount change amount instruction value that maximizes or minimizes the value of the function. Based on the cooling water amount change amount indication value for each of the cooling zones calculated by the amount instruction value calculation step and the actual value of the cooling water amount of each of the cooling waters at the current time, the cooling zone Each has a cooling water amount changing step of changing the water amount of the cooling water, and the objective function is calculated based on the second calculated value at each of the future predicted positions with respect to the temperature evaluation position. The predicted value of the slab center temperature at each of the future predicted positions, the slab center target temperature at each of the future predicted positions set by the slab center target temperature setting step, and the cooling. It is expressed using the water amount change amount indicated value, and every time the casting advances by at least the interval between the temperature evaluation positions, the slab surface temperature acquisition step and the operation data acquisition Step, wherein the temperature evaluation position setting step, the heat transfer coefficient estimating step, said temperature solid fraction distribution calculating step, the heat transfer coefficient correction step, the billet center target temperature setting step, the future prediction step, the cooling By repeatedly executing the water amount change amount instruction value calculation step and the cooling water amount change step, the slab center temperature at the future predicted position at an arbitrary time during casting can be set to the slab center target temperature. It is characterized by being close to.

The program of the present invention is characterized in that the computer functions as each means of the secondary cooling control device of the continuous casting machine.

According to the present invention, even if the casting speed is changed, the solid phase ratio at the center of the slab does not change significantly, and the amount of reduction with respect to the slab during light reduction of the slab before and after the change of the casting speed is constant. Can be held in.

It is a figure which shows an example of the structure of the secondary cooling control device (cooling control device) of a continuous casting machine, and the continuous casting machine which is an application example thereof. It is a figure which shows an example of the cross section to be calculated conceptually. It is a figure which shows an example of the installation position of a thermometer. It is a figure which shows an example of the relationship of the enthalpy, the temperature, and the heat transfer coefficient correction parameter. It is a figure which shows an example of the functional structure of a cooling control device. It is a flowchart explaining an example of the secondary cooling control method of a continuous casting machine. It is a figure which shows the relationship between the temperature of the center part of a slab (center part temperature) in the comparative example, and the distance in the casting direction (distance from a molten metal surface) of molten steel in a mold from the molten metal surface. In the comparative example, the relationship between the deviation between the temperature at the center of the slab and the target value (deviation of the temperature target value at the center) and the distance of the molten steel in the mold in the casting direction from the molten metal surface (distance from the molten metal surface) It is a figure which shows. It is a figure which shows the relationship between the solid phase ratio of the central part of a slab (the solid phase ratio of a central part) of a comparative example, and the distance (distance from the molten metal surface) of the molten steel in a mold in the casting direction from the molten metal surface. It is a figure explaining the problem of the prior art. It is a figure which shows the relationship between the temperature of the center part of a slab (center part temperature) in the invention example, and the distance in the casting direction (distance from a molten metal surface) of molten steel in a mold from the molten metal surface. In the example of the invention, the relationship between the deviation between the temperature at the center of the slab and the target value (deviation of the temperature target value at the center) and the distance of the molten steel in the mold in the casting direction from the molten metal surface (distance from the molten metal surface). It is a figure which shows. It is a figure which shows the relationship between the solid phase ratio of the central part of a slab (solid phase ratio of a central part) in the invention example, and the distance in the casting direction (distance from a molten metal surface) of molten steel in a mold from the molten metal surface.

Hereinafter, an embodiment of the present invention will be described with reference to the drawings.
(Outline configuration of continuous casting machine)
FIG. 1 is a diagram showing an example of a configuration of a secondary cooling control device for the continuous casting machine of the present embodiment and a continuous casting machine as an application example thereof. Since the continuous casting machine itself can be realized by a known technique, only the part necessary for the description of the present embodiment is shown in FIG. 1 in a simplified manner. Further, in the following description, the secondary cooling control device of the continuous casting machine will be referred to as a cooling control device, if necessary.

Molten steel is supplied into the mold 1 from a tundish (not shown) via a dipping nozzle or the like. A molten steel meniscus 4 is formed on the uppermost portion of the molten steel in the mold 1. The molten steel is cooled in the mold 1, and the strands solidified on the outside are sandwiched between a plurality of support rolls (not shown) and supported, and the molten steel is pulled out from the mold 1 at a drawing speed (casting speed). The plurality of support rolls are arranged at positions facing each other so as to sandwich the slab 5 in between, and are arranged at predetermined intervals in the casting direction. Cooling sprays 2a to 2t for injecting cooling water toward the slab 5 are arranged between two support rolls adjacent to each other in the casting direction. The flow rate of the cooling water injected by the cooling sprays 2a to 2t is controlled by the flow rate adjusting valves 3a to 3e installed in the piping. The opening degree of the flow rate adjusting valves 3a to 3e is adjusted based on the water amount indicated value given by the cooling control device 100. In the present embodiment, the cooling control device 100 sprays cooling water onto the long side surface of the slab 5 (the surface of the slab 5 shown in FIG. 1 is the surface on the short side of the slab 5). An example of controlling the flow rate of the cooling sprays 2a to 2t (hereinafter, referred to as the amount of water if necessary) will be described.

The cooling water pipe is installed corresponding to a cooling zone (cooling zone divided by the cooling zone boundary lines 6a to 6f) in which the length of the slab 5 in the casting direction is divided into a plurality of lengths. The distribution of the amount of cooling water in the casting direction in the strand is controlled for each cooling zone. In the following description, the first cooling zone, the second cooling zone, and the like may be referred to in order from the cooling zone immediately below the mold 1. The entire cooling zone is called a secondary cooling zone.
A thermometer 7 for measuring the temperature of the surface of the slab 5 during casting is arranged at a predetermined temperature measurement position of the secondary cooling zone. Further, the number of thermometers 7 may be one or a plurality. In this embodiment, as shown in FIG. 3 described later, a case where a plurality of thermometers 7a to 7f are arranged at a plurality of temperature measurement positions will be described as an example.

A reduction segment roll group 9 for lightly reducing the slab is arranged on the downstream side of the secondary cooling zone in the casting direction for the slab 5 that has been bent and straightened. Further, the casting speed measuring roll 8 and the support roll 10 are arranged on the downstream side in the casting direction from the reduction segment roll group 9. The casting speed measuring roll 8 sequentially measures the casting speed of the slab 5. Here, the machine end outlet is the position of the outlet (in the casting direction) of the most downstream roll in the casting direction (drawing direction) in the continuous casting machine. In the example shown in FIG. 1, the positions of the outlets of the casting speed measuring roll 8 and the support roll 10 are the machine end outlets.

(Heat transfer solidification model)
Next, an example of the heat transfer solidification model used in the cooling control device 100 of the present embodiment will be described. Based on the heat transfer equation, the heat transfer solidification model is based on the temperature inside the slab cross section, which is the temperature inside the cross section perpendicular to the casting direction of the slab 5, and the slab cross section, which is the temperature of the surface of the slab 5 in the cross section. It is a calculation formula for calculating at least the surface temperature and the solid phase ratio distribution in the slab cross section, which is the distribution of the solid phase ratio in the cross section.

The distribution of the temperature and solid phase ratio of the slab 5 in the strand reflects the distribution of the temperature and solid phase ratio in each calculation target cross section of the slab 5 and the cooling conditions at each calculation point in each calculation target cross section. It is calculated by solving the discrete heat conduction equation under the boundary condition of the heat transfer coefficient. Here, the cross section to be calculated is the slab in the direction perpendicular to the casting direction at the calculation position set at regular intervals in the casting direction in the region from the molten metal surface (molten steel meniscus 4) in the mold 1 to the machine end outlet. It is a cross section of a slab 5 when 5 is cut. In the initial condition of the heat conduction equation for each calculation target cross section, the calculation result in the calculation target cross section adjacent to the calculation target cross section on the upstream side is set. For each calculation target cross section, the calculation target until the calculation target cross section moves from the position of the calculation target cross section to the position of the calculation target cross section one downstream side of the calculation target cross section by pulling out the slab 5. The overall temperature and solid phase ratio of the slab 5 is calculated by repeating the calculation of the enthalpy, temperature, and solid phase ratio in the cross section over time.

<Coordinates in cross section to be calculated and state variables>
In the present embodiment, the calculation target cross section of the slab 5 is rectangular. Further, among the surfaces of the slab 5, the surface corresponding to the long side of the cross section to be calculated is referred to as the long side surface of the slab, and the surface corresponding to the short side is referred to as the short side surface of the slab, if necessary. FIG. 2 is a diagram conceptually showing an example of a cross section to be calculated. In each calculation target cross section, the direction along the side corresponding to the long side surface of the slab is referred to as the width direction, and the direction along the side corresponding to the short side surface of the slab is referred to as the thickness direction. The coordinates in the cross section to be calculated are such that one apex of the slab 5 is the origin 0, the axis in the width direction is the x-axis, and the axis in the thickness direction is the y-axis. Let X be the width and Y be the thickness of the slab 5. Further, the drawing direction (that is, the casting direction) of the slab 5 is defined as the z-axis. In FIG. 2, those marked with x in ◯ indicate that the paper is directed from the front side to the back side. Further, in FIG. 2, the long side surface of the slab is the x-z plane, and the short side surface of the slab is the yz plane.

In the heat transfer solidification model, the following are set as state variables at the coordinates (x, y) in the cross section to be calculated at time t. In addition, μ is a number for identifying a solute component in molten steel, and takes a value of _{1, 2, 3, ..., Μ max.} Here, μ _max is the maximum number of solute components considered in the heat transfer solidification model.
Enthalpy: H (x, y, t)
Temperature: T (x, y, t)
Solid phase ratio: f _s (x, y, t)
Solute component concentration on the liquid phase side at the solid-liquid interface: _CL μ (x, y, t)
The physical property parameters in the heat transfer solidification model are as follows.
Thermal conductivity (depending on temperature): λ (x, y, t) = λ (T (x, y, t))
Specific heat of steel (depending on temperature): c (x, y, t) = c (T (x, y, t))
Latent heat of solidification: L _h
Liquidus temperature: T _L
Density: ρ

<Basic equation of model>
Since the enthalpy is the energy at each calculation point in the calculation target cross section including the latent heat of solidification, the time change can be expressed by the following equation (1), which is a heat conduction equation expressing the heat balance at each calculation point.

Here, q _x represents the heat flux in the x-axis direction, and q _y represents the heat flux in the y-axis direction. The following equations (2) and (3) hold at the inner points that are points other than the boundary line in the calculation target cross section.

Here, λ _x represents the thermal conductivity in the x-axis direction, and λ _y represents the thermal conductivity in the y-axis direction. Therefore, from the equations (2) and (3), the equation (1) is expressed as the following equation (4) at the inner point of the cross section to be calculated.

<Boundary condition>
The heat flux is expressed by the following equation (5) at the cross-sectional boundary of the calculation target cross section corresponding to the surface of the slab 5, that is, the _{short side surface of the slab of x = x B} (x _{B = 0 or X).} It is assumed that the heat flux is expressed by the following equation (6) on the long side surface of the slab of y = y _B (y _{B = 0 or Y).}

Here, K _x (x _B , y, t) is the heat transfer coefficient on the short side surface of the slab, and K _y (x, y _B , t) is the heat transfer coefficient on the long side surface of the slab. In the present embodiment, these are expressed using model formulas based on the cooling mode (see formulas (29) to (32) described later). Further, T _a is the ambient atmosphere temperature. ε _x and ε _y are parameter variables that represent the difference between the model formula and the actual value of the heat transfer coefficient when the model calculation is applied. In the following description, this parameter variable will be referred to as a heat transfer coefficient correction parameter, if necessary. The heat transfer coefficient correction variables ε _x and ε _y are based on the model equations based on the above-mentioned cooling mode in the width direction (x-axis direction) and thickness direction (y-axis direction) of the slab 5 in the secondary cooling zone, respectively. It is a variable that represents the deviation between the heat transfer coefficient and the heat transfer coefficient of the actual machine.

In the present embodiment, at each center line side boundary line (broken line in FIG. 2) of the cross section to be calculated, it is assumed that each variable is symmetric with the center line in between, and heat exchange across each center line side boundary line is performed. It is assumed that the following equations (7) and (8) hold. As shown in FIG. 2, in the following formula (7), X / 2 is the center in the width direction of the slab 5, and in the following formula (8), Y / 2 is the center in the thickness direction of the slab 5. Is.

In this embodiment, the symmetry is used as described above, and the so-called quarter cross section from the corner of the slab 5 to the center of the slab 5 (for example, the diagonal line in FIG. 2) is used in the calculation target cross section. The area indicated by) is set as the calculation target area.

<Relationship between enthalpy and temperature and solid phase ratio>
In solidification of alloy steel, when the temperature _{falls below the liquidus temperature TL} determined by the component concentration, solidification starts and the solid phase ratio f _s > 0, and solidification is completed and the solid phase ratio f _s = 1. The temperature drops in the meantime. Considering that the solid phase ratio f _s is 0 ≦ f _s ≦ 1, the relationship between the enthalpy and the temperature is expressed by the following equation (9).

Here, T ₀ is an arbitrary integration constant, and T is the temperature at the calculation point in the calculation target cross section.
<Heat conduction equation with enthalpy as a variable>
Since the following equation (10) is obtained by partially differentiating both sides of the equation (9) with respect to x, the heat flux q _x in the x-axis direction is expressed by the following equation (11). _{Similarly, the heat flux q y} in the y-axis direction is expressed by the following equation (12) by partially differentiating both sides of the equation (9) with respect to y.

By substituting the equations (11) and (12) into the equation (1), the heat conduction equation can be rewritten to the following equation (13) with the enthalpy as a variable at the inner point of the cross section to be calculated. ..

Several models have been proposed so far that represent the relationship between the temperature T and the solid phase ratio f _s. One of them is a model that interpolates the _{solid phase ratio f s between the liquidus temperature TL at} which solidification starts and the solidus temperature at which solidification is completed, as shown in the following equation (14). ..

The interpolation function φ (T (x, y, t)) is generally monotonically increasing, and there are a method of making the temperature T a linear expression and a method of making the temperature T a quadratic expression.

Since equations (9), (13), and (14) are _{closed for the variables H, T, and f s} , the enthalpy H (x, y, t), temperature T (x, y, t), and solid phase ratio f _s (x, y, t) are obtained.
The solid-liquid coexisting region, the temperature is determined by the liquid phase side solute concentration at the interface between the solid phase and the liquid phase, from the state diagram, as another model that represents the relationship between the temperature T and the solid fraction f _s, Like the model of equation (15) using the function θ that expresses the relationship between the solute component concentration and temperature and the equation (16) using the _{function γ L μ that expresses the relationship between the solid phase ratio and the solute concentration on the liquid phase side.} The model represented by may be used. Here, μ _max is the maximum number of solute components considered in the heat transfer solidification model.

Since equations (9), (13), (15), and (16) are _{closed for the variables H, T, f s} , and _CL μ, they can be calculated by solving them simultaneously. The enthalpy H (x, y, t) in the cross section, the temperature T (x, y, t), the solid phase ratio f _s (x, y, t), and the solute concentration on the liquid phase side of the solid-liquid interface C _L μ ( x, y, t) is obtained.
In this embodiment, any of the formula (14) and the formulas (15) and (16) may be used. By using the formulas (15) and (16), the liquid-phase side solute concentration C _L μ (x, y, t) at the solid-liquid interface can be obtained, but the calculation load increases. _{Equations (15) and (16) are used to obtain the liquid-phase solute concentration C L} μ (x, y, t) at the solid-liquid interface even if the calculation load increases. If not, the equations (15) and (16) are used. Equation (14) may be used.

(Time and spatial discretization of heat transfer solidification model)
In this embodiment, a numerical solution is obtained by discretizing the above partial differential equations in space and time. That is, in the present embodiment, the differential equation of the equation (13) is spatially discretized within the calculation target cross section and on the boundary line of the calculation target cross section, and is discretized in a form incorporating the boundary conditions on the surface of the slab 5. A model that is updated at the time t = 0, 1, 2, ... Is used.
It is assumed that the position of the cross section to be calculated for carrying out the calculation of the heat transfer solidification model described above is set at a constant distance interval Δz. The number n of the cross section to be calculated is such that the position of the molten steel surface in the mold 1 (the position of the molten steel meniscus 4) is n = 0, and hereinafter, n = 1, 2, ..., Nmax in the drawing direction (casting direction). In each calculation target cross section, calculation points are commonly set inside and on the boundary of the calculation target cross section. When updating the state variable from the calculation target cross section n to the calculation target cross section n + 1, the time discretization step Δt is expressed by the following equation (17).

Here, v _c is the casting speed.
As described above, in the present embodiment, the so-called quarter cross section from the corner of the slab 5 to the center of the slab 5 is set as the calculation target area in the calculation target cross section. That is, as shown by the shaded area in FIG. 2, the lower left corner of the cross section to be calculated is set as the origin 0, and from the origin 0, the center x = X / 2 in the width direction of the slab 5 and the thickness direction of the slab 5 The range up to the center y = Y / 2 is set as the calculation target area. Calculation points to be calculated sectional coordinates (x _i, y _j) is, i = 0,1,2, ···, I , and, j = 0,1,2, ···, for J, x ₀ Let = 0 and x _I = X / 2, and y ₀ = 0 and y _J = Y / 2. Position the coordinates of the calculation points appropriately so that the minimum spacing of the coordinates of the calculation points in the x-axis direction and the minimum spacing of the coordinates of the calculation points in the y-axis always satisfy the stability condition in the numerical solution of the partial differential equation. Place in. As a condition of stability, a method of analytically deriving from the coefficient of the equation to be solved is known, but in this embodiment, it is confirmed that the solution obtained by the preliminary simulation is numerically stable, and the x-axis. Determine the minimum distance between the coordinates of the calculation points in the direction and the calculation points in the y-axis direction.
In the following, the following equations (18) to (21) are given for i = 0,1,2, ···, I-1, and j = 0,1,2, ···, J-1. It shall hold.

<Discretization of model formula>
In the following description, for variables other than coordinates, the subscript i + 1/2 means a quantity at an intermediate position between the calculation points i and i + 1 in the x-axis direction. In the actual calculation, when it is given as an argument of the function, the average value of the values corresponding to the subscripts i and i + 1 is adopted as the value corresponding to the subscript i + 1/2. In the present embodiment, calculation points (x _i, y _j) discretized model in enthalpy, temperature, solid fraction, and, by using the enthalpy and solid fraction at calculation points adjacent to the calculation point, the following Can be expressed as the equation (22) and the equation (23) of. Here, the calculation points adjacent to the calculation points of the coordinates (i, j) are the coordinates (i + 1, j), the coordinates (i, j + 1), the coordinates (i-1, j), and the coordinates (i, j-1). ) Is the calculation point.

Here, N (i, j) is calculated points (x _i, y _j) represents a set of calculation points adjacent to. Further, a ^t _{i, j} is the discrete approximated by central difference the partial differential equation of Formula (13), a H _{i, j,} coefficient according to _t in the case of organized form of Equation (22). α ^t _{i, j} is also a coefficient related to _{f si, j, t.} The coefficients a ^t _{i, j are coefficients including the thermal conductivity λ x} or λ _y , the specific heat ρ, and the latent heat of solidification L _h appearing in the equation (13), and the α ^t _{i, j} are the coefficients in the equation (13). It is a coefficient including the thermal conductivity λ _x or λ _y , the specific heat c, and the density ρ appearing in. Further, bi _{, j} is always 0 (zero) when the calculation point (x _i , y _j ) is not a point on the boundary of the surface of the slab 5, and the calculation point (x _i , y _i ) is cast. If it is a point on the boundary of the surface of piece 5, it includes the heat transfer coefficient K _x or K _y in equations (5) and (6) after the discrete approximation of equation (2) (T _{a −} Ti _{, j,} It is a coefficient related to _t).

In addition, ω is a variable that takes any value of 1, 0, and 1/2. In the update of enthalpy, the explicit method is used when ω = 1, the implicit method is used when ω = 0, and ω = 1 /. In the case of 2, it means that the semi-positive and semi-implicit method (Crank-Nicholson method) is used. _{Further, p} in T p and H _p in the equation (23) are abbreviated notations representing calculation points (i, j). Further, the range of values that the temperature T can take is divided into a plurality of temperature categories in advance. k (p) is the number k of the temperature division such ^{that T k (p)} ≤ T (p) <T ^{k (p) + 1} including the temperature T (p). Further, I _c (T ^{k (p)} ) is a value obtained by pre-calculating the integral in the equation (9) up to the boundary value T ^{k (p)} _{from the temperature T 0.} c ^* _{k (p) + 1/2} is a representative value of the specific heat c of the molten steel in the temperature category k (p). For example, the average value of the specific heat c of the molten steel in the temperature category k (p) is a representative value c ^*. Used as _{k (p) + 1/2.}

Arrange the right-hand sides of equations (22) and (23) at each calculation point, solve simultaneous equations for Hi _{, j, and t + 1 when ω = 1 or 1/2, and then each at time t.} When the variable values of the calculation points are arranged in a vector in an appropriate order, the enthalpy in the section to be calculated and the temperature at the temperature measurement position of the thermometer 7 are the matrices A _H , A _f , _BT , C, and D, and _{Using T 0} , which summarizes terms not related to _{H p, t} and f _{sp, t} on the right side of the equation (23), it can be expressed as the following equations (24) and (25).

Here, H _t, each f _{st is, H i, j, t,} f si, j, reordered the _{t (I + 1) (J} + 1) is a column vector of components. 1 _{(I + 1) (J + 1)} is a matrix vector having (I + 1) (J + 1) 1s as components. T _a is a column vector of with ambient temperature component (I + J + 1) component. T _{B, t} is a matrix vector of (I + J + 1) components in which _{the temperatures T i, j, t} of the calculation points on the surface of the cross section to be calculated (quarter cross section) are appropriately rearranged.

_{A H} and A _f in the equation (24) are square matrices of (I + 1) (J + 1) rows (I + 1) (J + 1) columns. B _T is a matrix of (I + 1) (J + 1) rows (I + J + 1) columns. _BT is located on the right side of the same equation (22) for the row of the equation (24) corresponding to the equation relating to the calculation point on the surface of the calculation target cross section (quarter cross section) among the equations of the equation (22). Of the appearing temperature T _t , it is a matrix whose component is a coefficient multiplied by _{the temperature T t} of the calculation point on the surface of the cross section to be calculated (quarter cross section). E _t-1 is a matrix of (I + 1) (J + 1) rows (I + J + 1) columns. E _t-1 is a T-1 in the column direction for the row of the equation (24) corresponding to the equation relating to the calculation point on the surface of the calculation target cross section (quarter cross section) among the equations of the formula (22). _{The component corresponding to the calculation point of t-1} is the heat transfer coefficient correction parameter ε _{i, j, t-1 at} time t, and the other components are 0 (zero). Further, 1 _{(I + 1) (J + 1)} × _{(I + J + 1)} is a matrix of (I + 1) (J + 1) rows (I + J + 1) columns in which all components are 1. Further, ○ is the next symbol B _T in equation (24) is a matrix representing the calculation (Hadamard product) for calculating a product of each component of the matrix of the same size. Further, the matrices C and D are matrices of (I + 1) (J + 1) rows (I + 1) (J + 1) columns. The matrices C and D are the coefficients of _{H p, t} and (1-f _{sp, t} ) appearing on the right side of the equation of the same equation (23) in the row of the equation (25) corresponding to each equation of the equation (23). Is a matrix whose components are. T _{0, t-1} is a column vector having (I + 1) (J + 1) components and arranging terms unrelated to _{H and f s in the equation (23).}

<Calculation procedure of state estimation method>
In the present embodiment, in order to respond to changes in the indicated values of the casting speed and the amount of cooling water, the cross section to be calculated is newly set at the molten metal surface position (z = 0) in the mold 1 every time the slab 5 is pulled out by a certain distance. Generate in. Then, for each cross section to be calculated, the calculation by the heat transfer solidification model is performed from the molten metal surface (molten steel meniscus 4) in the mold 1 to at least the position of the outlet of the secondary cooling zone. In the following description, this calculation target cross section will be referred to as a tracking surface as necessary. In addition, the generation interval of the tracking surface is represented _{by Δz tp.} The occurrence interval Δz _tp of the tracking surface is a value obtained by multiplying the above-mentioned Δz by an integer (L times), and is represented by the following equation (26).

Further, in the following description, a position where the position z in the casting direction is _{an integral multiple of the generation interval Δz tp} of the tracking surface is referred to as a temperature evaluation position as necessary. The number tp is assigned from the upstream side, and the temperature evaluation position is represented _{by z tp.} tp = 0 is the position of z = 0 (the position of the molten metal surface in the mold 1). The maximum value of tp is represented _{by tp max.} The temperature evaluation positions are the temperature inside the cross section of the slab, which is the temperature inside the cross section perpendicular to the casting direction of the slab 5, the surface temperature of the slab, which is the temperature of the surface of the slab 5 in the cross section, and the inside of the cross section. It is a position to evaluate the solid phase ratio distribution in the cross section of the slab, which is the solid phase ratio distribution of. In the present embodiment, the distance between the temperature evaluation positions in the casting direction is set to half or less of the length of the longest cooling zone in the casting direction. By doing so, at least two temperature evaluation positions can be present in each of the cooling zones. As a result, as will be described later, it is possible to control the heat transfer coefficient correction parameters ε _x and ε _y and the fluctuation of the temperature at the center of the slab in the casting direction (profile of the casting direction) in one cooling zone. .. Further, from the casting speed v _{c at} the current time and the generation interval of the tracking surface (that is, the interval of the temperature evaluation position) Δz _tp , the time for the tracking surface to move between the two temperature evaluation positions z _{tp adjacent to each other.} Is represented by Δtp (= Δz _tp ÷ v _c ).

The heat transfer coefficient correction parameters ε _x and ε _y are set for each interval of the temperature evaluation position z _tp. In the following description, the heat transfer coefficient correction parameters ε _x and ε _y when the position z in the casting direction is z _tp ≤ z <z _{tp + 1} are represented by ε ^{tp as necessary.} FIG. 3 is a diagram conceptually showing an example of the installation position of the thermometer 7. In FIG. 3, the casting length (length in the z-axis direction) corresponding to the installation position of the thermometer 7 is shown as the temperature measuring casting length 1, the temperature measuring casting length 2, ... In order from the direction closer to the mold 1. In the example shown in FIG. 3, the thermometers 7 are installed at two locations in the casting direction, and the temperature measurement casting length 1 and the temperature measurement casting length 2 are defined. Further, in the following description, on each tracking surface, the position corresponding to the position of the thermometer 7 in the width direction (x-axis direction) or the thickness direction (y-axis direction) of the slab 5 is set in the circumferential direction as necessary. It is called the temperature measurement position. The number of temperature measurement casting lengths is determined according to the number of installation locations of the thermometer 7 in the casting direction, but when the number is plural, the circumferential temperature measurement position is at each thermometer installation position. It is assumed that they are in the same circumferential position.

For each of the tracking planes, the time change is calculated with the enthalpy H, the solid phase ratio f _{s, and the temperature T in the tracking plane as variables.} That is, the state variable of each tracking surface is updated according to the equations (24) and (25) every time the casting advances by the interval Δz. _{For ε i, j, t-1} in equation (22), the ^{heat transfer coefficient correction parameter ε tp} corresponding to the position of the tracking surface at time t-1 is selected. The update model of the state variable related to the tracking surface k shall be represented by the following equations (27) and (28) in which k indicating the number of the tracking surface is attached to the right shoulder of each symbol of the equations (24) and (25). And. In addition, "1" in the formulas (27) and (28) represents a matrix in which all the components in the formula (24) are 1. Since the size of the matrix is the same as the corresponding "1" in the equation (24), the subscript at the lower right indicating the number of rows and columns of the matrix is omitted in order to prevent the notation from becoming complicated.

In this embodiment, the tracking surface reaches all the temperature evaluation positions at the same time by setting the calculation model of the equation (26). Therefore, the temperature distribution of the entire slab 5 at the time when the tracking surface reaches the temperature evaluation position is estimated. Can be done. FIG. 4 shows the enthalpies h ^k , h ^k-1 , temperature τ ^k , and τ ^k-1 when the tracking surface k is the temperature evaluation position z _tp and the tracking surface k-1 is the temperature evaluation position z _tp-1. ^{, Is} a diagram showing an example of the relationship between the heat transfer coefficient correction parameters ε tp and ε ^tp-1. In FIG. 4, the tracking surfaces k and k-1 are tracking surfaces adjacent to each other. The enthalpy h ^k and the temperature τ ^k are controlled by the tracking surface k. On the other hand, the heat transfer coefficient correction parameters ε ^tp and ε ^tp-1 are managed at the temperature evaluation positions tp and tp-1. The heat transfer coefficient correction parameters ε ^tp and ε ^tp-1 are used as values at _{the temperature evaluation positions z tp} and z _tp-1 even if the tracking surfaces k and k-1 transition. That is, when the tracking surface k-1 reaches the temperature evaluation position z _tp , the tracking surface k-1 is calculated by changing the subscript k on the right shoulder to k-1 in the equations (27) and (28). Update enthalpy and temperature.

(Secondary cooling control device for continuous casting machine (cooling control device))
Next, an example of the cooling control device of this embodiment will be described. FIG. 5 is a diagram showing an example of a functional configuration of the cooling control device 100. FIG. 6 is a flowchart illustrating an example of a secondary cooling control method for a continuous casting machine. The flowchart of FIG. 6 is repeated every _{time the casting advances by the generation interval Δz tp of the} tracking surface in all or a part of the time from the start of casting to the complete drawing of the slab from the continuous casting machine. (See equation (26)). Further, it is assumed that the heat transfer coagulation model described above is stored in the heat transfer coagulation model storage unit 500 in advance. The hardware of the cooling control device 100 is realized by using, for example, a CPU, a ROM, a RAM, an HDD, an information processing device having various interfaces, or dedicated hardware.

<Cast surface temperature acquisition unit 501, step S601>
The slab surface temperature acquisition unit 501 acquires the measured value of the surface temperature of the slab 5 during casting measured by the thermometers 7a to 7f (see FIG. 3). The slab surface temperature acquisition unit 501 receives, for example, data of the measured value of the surface temperature of the slab 5 from a data processing device (not shown), and the surface of the slab 5 measured by the thermometers 7a to 7f. The measured value of temperature can be obtained.

<Operation data acquisition unit 502, step S602>
The operation data acquisition unit 502 acquires the operation data of the continuous casting machine. The operation data of the continuous casting machine includes, for example, the size of the slab 5 in the direction perpendicular to the casting direction, the casting speed v _c , the temperature of the molten steel in the mold 1, the concentration of the solute component in the molten steel, and the solute component. _{The liquidus temperature TL of the} molten steel calculated using the concentration, the flow rate of the cooling water sprayed from the cooling sprays 2a to 2t arranged in each cooling zone of the secondary cooling zone, and the surface of the slab 5. Cooling conditions at each point of are included. The operation data acquisition unit 502 can acquire the operation data of the continuous casting machine by receiving the operation data of the continuous casting machine from, for example, an upper procon or a lower instrumentation device (not shown).

Here, the cooling conditions include data indicating a range in which the cooling water jetted from the cooling sprays 2a to 2t collides with the surface of the slab 5. The operation data acquisition unit 502 includes data indicating the flow rate of the cooling water injected from the cooling sprays 2a to 2t and data indicating the range in which the cooling water injected from the cooling sprays 2a to 2t collides with the surface of the slab 5. , The distribution of the flow density of the cooling water over the entire surface of the slab 5 is calculated by using the number and arrangement of the cooling sprays 2a to 2t.

<Temperature evaluation position setting unit 503, step S603>
The temperature evaluation position setting unit 503 sets the position of the molten metal surface in the mold 1 to z = 0, and sets the position in the casting direction in which the position z in the casting direction of the slab 5 is an integral multiple _{of the generation interval Δz tp of the tracking surface.} Set as the evaluation position z _tp. The interval in the casting direction of the temperature evaluation position z _{tp is a predetermined constant interval.}

<Heat transfer coefficient estimation unit 504, step S604>
The heat transfer coefficient estimation unit 504 uses the cooling conditions acquired by the operation data acquisition unit 502 and the measured values of the surface temperature of the slab 5 acquired by the slab surface temperature acquisition unit 501 to obtain the slab 5. Estimate the heat transfer coefficient at each calculation point on the surface.
In the present embodiment, the heat transfer coefficient estimation unit 504 is divided into a portion where the cooling water collides and another portion at each of _{the positions z = 0, ..., Z max in the slab direction.} The heat transfer coefficient estimator 504, and flow density w _d spray water impinging in part the heat transfer coefficient at the calculation point on the boundary of the tracking surface belonging to each section, the cooling water collides, cooling spray 2a~ using an air flow rate v _a of 2t, the surface temperature T _s of the slab 5 of the collision portion is calculated based on a predetermined model equation. In the present embodiment, the case where the following equations (29) and (30) are used as the model equation will be shown as an example.

_{Here, K x0} (0, y, z, t) shown in the equation (29) is the heat transfer coefficient at the position y in the thickness direction of the short side surface of the slab 5 at the time t and the position z in the casting direction. is there. _{Further, K y0} (x, 0, z, t) shown in the equation (30) is a heat transfer coefficient at the position x in the width direction of the long side surface of the slab 5 at the time t and the position z in the casting direction. .. Further, the heat transfer coefficient estimation unit 504 calculates the heat transfer coefficient at the calculation point on the boundary of the tracking surface belonging to the portion of the surface of the slab 5 where the cooling water does not collide (the "other portion"). In 29) and equation (30), w _d = 0 and v _a = 0, and the calculation is based on a model equation using only _{the surface temperature T s of the slab 5.}

Next, the heat transfer coefficient estimation unit 504 uses the equation (29) using _{the heat transfer coefficient correction parameters ε x} and ε _y to correct the error between the estimated heat transfer coefficient and the true heat transfer coefficient of the slab 5. ) and the heat transfer coefficient K _x0 (0 estimated in equation (30), y, z, t), K y0 (x, 0, z, by correcting t), the heat transfer coefficient of the corrected K _x (0, y, z, t) and K _y (x, 0, z, t) are derived. _{Specifically, the heat transfer coefficient estimation unit 504 sets the heat transfer coefficient correction factor parameters ε x} and ε _y for each of the width direction and the longitudinal direction of the slab 5 corrected at the time of the previous calculation of the indicated value of the cooling water amount as follows. _{The corrected heat transfer coefficients K x} (0, y, z, t) and K _y (x, 0, z, t) are calculated by acting as in the equations (31) and (32).

<Temperature solid phase ratio distribution calculation unit 505, step S605>
At each of the temperature evaluation positions, the temperature solid phase ratio distribution calculation unit 505 determines the temperature inside the slab cross section, which is the temperature inside the cross section perpendicular to the casting direction of the slab 5, and the temperature of the surface of the slab 5 in the cross section. Heat transfer solidification each time the first calculated value including the surface temperature of a certain slab and the solid phase ratio distribution in the cross section of the slab, which is the distribution of the solid phase ratio in the cross section, is advanced by the interval between the temperature evaluation positions. Calculate using a model.
In the present embodiment, the temperature solid phase ratio distribution calculation unit 505 uses the operation data acquired by the operation data acquisition unit 502 and the corrected heat transfer coefficient heat transfer coefficient K _x (calculated by the heat transfer coefficient estimation unit 504). Using 0, y, z, t) and _Ky (x, 0, z, t), the distribution of the surface temperature of the slab 5, the distribution of the internal temperature of the slab 5, and the inside of the slab 5. The distribution of the solid phase ratio f _{s in} the above is derived.

Specifically, the temperature solid phase ratio distribution calculation unit 505 first generates a new tracking surface at the molten metal surface position (z = 0) in the mold 1. Next, the temperature solid phase ratio distribution calculation unit 505 sets the initial values of the enthalpy, temperature, and solid phase ratio calculated by the heat transfer solidification model managed by the tracking surface of the molten steel in the mold 1 at the current time t. Set based on temperature. Next, the temperature solid phase ratio distribution calculation unit 505 updates the enthalpy of each tracking surface to be calculated at the current time according to the discretized heat conduction equation of Eq. (22) using the corrected heat transfer coefficient. .. Next, the temperature solid phase rule distribution calculation unit 505 calculates the temperature and solid phase rate for the updated enthalpy by calculating the convergence of the equations (9), (13), and (14), or the temperature and solidity. The phase ratio and the solute concentration at the solid-liquid interface can be determined by calculating the convergence of equations (9), (13), (15), and (16) to obtain a numerical solution to obtain the temperature in each tracking plane. , Calculate the surface temperature of each tracking surface and the distribution of the solid phase ratio in each tracking surface.

<Heat transfer coefficient correction unit 506, step S606>
The heat transfer coefficient correction unit 506 is a measured value of the surface temperature of the slab 5 at the temperature measurement position and an estimated value of the surface temperature of the slab 5 at the temperature measurement position. The heat transfer coefficient correction parameter is derived using the estimated value of the surface temperature of the slab 5 calculated based on the above.
In the present embodiment, the heat transfer coefficient correction unit 506 obtains the measured value of the surface temperature of the slab 5 acquired by the slab surface temperature acquisition unit 501 and the estimated value of the surface temperature of the slab 5 at the temperature measurement position. Use to derive heat transfer coefficient correction parameters. The estimated value of the surface temperature of the slab 5 at the temperature measurement point is calculated based on the calculated value of the temperature of the slab 5 at the temperature evaluation position derived by the temperature solid phase ratio distribution calculation unit 505. In the present embodiment, the distance between the temperature evaluation positions in the casting direction is set to half or less of the length of the longest cooling zone in the casting direction. Therefore, the heat transfer coefficient correction parameters can be calculated at a plurality of positions in one cooling zone. Therefore, it is possible to estimate the fluctuation of the heat transfer coefficient correction parameter in the casting direction in one cooling zone, and it is possible to estimate the temperature at the center of the slab 5 more accurately.

In the following description, the measured value of the surface temperature of the slab 5 at the temperature measuring position is referred to as a surface temperature measured value, if necessary. Further, the calculated value of the temperature of the slab 5 at the temperature evaluation position derived by the temperature solid phase ratio distribution calculation unit 505 is referred to as a surface temperature calculated value, if necessary.

When the temperature measurement position matches any temperature calculation position at any temperature evaluation position, the surface temperature calculation value derived by the temperature solid phase ratio distribution calculation unit 505 is used as the surface temperature estimation value. On the other hand, the position of the temperature measurement position in the casting direction matches any of the temperature evaluation positions, but the position on the surface side of the tracking surface of the temperature measurement position (circumferential temperature measurement position) is at any calculation point. If they do not match, the heat transfer coefficient correction unit 506 derives the surface temperature at the temperature measurement position by interpolating using the calculated surface temperature values at the temperature evaluation positions where the positions in the casting direction match. When the position of the temperature measurement position in the casting direction does not match any of the temperature evaluation positions, the heat transfer coefficient correction unit 506 interpolates using the surface temperature calculation values at different positions in the casting direction to obtain the temperature. The surface temperature at the measurement position is derived. In this case, as the surface temperature calculation value used for interpolation, the value interpolated as described above within the surface side of the tracking surface may be used.

In the present embodiment, the heat transfer coefficient correction unit 506 optimizes the estimated value of the heat transfer coefficient correction parameter by performing an optimization calculation that minimizes the difference between the surface temperature calculated value and the surface temperature measured value at the temperature measurement position. Derive a solution. Specifically, in the present embodiment, the heat transfer coefficient correction unit 506 uses the algorithm of the extended Kalman filter to minimize the estimated value of the minimum error dispersion (the error dispersion between the surface temperature calculated value and the surface temperature measured value at the temperature measurement position is the minimum). The case where the estimated value of the heat transfer coefficient correction parameter) is derived as the optimum solution will be described as an example.

In the heat transfer solidification models of the formulas (27) and (28), the row corresponding to the surface of the slab 5 at the temperature evaluation position is taken out, and the change in enthalpy due to the movement of the tracking surface is described by the following formulas (33) to (33). Rewritten as in (35), the enthalpy and heat transfer coefficient correction parameters at the circumferential temperature measurement position are random numbers according to a normal distribution with an average of 0, which represents the error between each variable of the heat transfer coagulation model and the actual value. ^Let it be the sum of ^k _{h, t} or w tp ε _{, t.} It is assumed that the variance of w ^k _{h, t} ^{is Q k} _ht , and the variance of ^{w tp} ε _{, t} ^{is Q tp} ε _{, t} .

Here, h ^k _t is the enthalpy of the calculation point corresponding to the circumferential temperature measurement position on the tracking surface k. a ^k _h and b ^k _T are constructed by extracting the coefficients for ^{the corresponding h k} _t-1 and ε ^k _t-1 from the right side of the formula obtained by extracting the rows corresponding to the circumferential temperature measurement positions in the formula (27). It is a matrix. Furthermore, H ^'k _t-1, in the right side of the equation obtained by extracting a row corresponding to the circumferential temperature measurement position in the formula (27), the circumferential temperature detecting all related non calculation points enthalpy and solid fraction corresponds to the position Represents the sum of terms. ^T'k ₀ and _t-1 in the equation (35) are the enthalpy of the calculation points that do not correspond to the circumferential temperature measurement position and the enthalpy of the calculation points that do not correspond to the circumferential temperature measurement position on the right side of the equation obtained by extracting the line corresponding to the circumferential temperature measurement position in the equation (28). Represents the sum of all terms related to solid phase ratio.

Further, τ ^k _t-1 represents the surface temperature of the circumferential temperature measurement position on each tracking surface k. In equation (35), (c ^k _T ) ^T is a row vector obtained by extracting rows at the circumferential temperature measurement position for the coefficient matrix C in equation (25). In the portion of the slab 5 downstream of the outlet of the mold 1, the solid phase ratio at the calculation point on the surface of the slab 5 can be regarded as 1, so that the term derived from latent heat release is excluded in the equation (33). There is.
In the following equations (36) to (38), the subscript t of each variable in equations (33) to (35) is transmitted based on the calculation result at time t-1 in accordance with the notation of Non-Patent Document 1. It is expressed as t | t-1, which means that the result is predicted for time t based on the thermal solidification model. Further, the subscripts t-1 of each variable in the equations (33) to (35) are predicted, and the result of the prediction calculation by the heat transfer solidification model at the time t-1 is based on the result of the temperature measurement at the time t-1. It is expressed as t-1 | t-1, which means that it has been corrected.

Here, the actual value h ^k _t, ε ^tp _t, and h ^k _t for _{^{τ k t | t-1,}} ε tp t | t-1, and τ ^k _{t | t-1} of the error Delta] h ^k _{t | t-1} , Δε ^tp _{t | t-1} , and Δτ ^k _{t | t-1} are expressed by the following equation (39).

From the differences between Eqs. (33) and (36) on both sides, Eqs. (34) and (37), and Eqs. (35) and (38), Δh ^k _{t | t-1} , Δε ^tp _{t. | t-1} and Δτ ^k _{t | t-1} follow the time evolution models of the following equations (40), (41), and (42), respectively.

^{The Δh k} _{t-1 | t-1} , Δε ^tp _{t-1 | t-1} , and Δτ ^k _{t-1 | t-1} appearing in the equations (40) and (41) are at the previous time t-1. This is the result calculated by the following procedure.
First, the estimated values of the enthalpy, temperature, and solid phase ratio in all the tracking surfaces k in the slab 5 during casting by the heat transfer solidification model are calculated. For the calculation points of the circumferential temperature measurement position of each tracking surface k, h ^k _{t | t-1} and τ ^k _{t | t-1} are calculated.
Next, using the relationship of Eq. (42), Δτ ^k _{t-1 | t-1} is eliminated from Eq. (40), and Δh ^k _{t | t-1} and Δε ^tp _{t | t-} 1 are Kalman filters. According to the algorithm, the difference between the measured value and the calculated value of the surface temperature of the slab 5 at the temperature measuring point is used for correction. Here, the model estimation deviation state variable is defined by the following equation (43) in which ^{Δh k} _{t | t-1 of} each tracking surface k and Δε ^tp _{t | t-1} of each temperature evaluation position z _{tp are arranged.}

The same applies to _{X t-1 | t-1. Further, the estimated value Y t | t-1} of the surface temperature of the slab 5 at the temperature measurement point is expressed by the following equation (44).

In equations (43) and (44), T represents a transposed matrix. By rearranging the coefficients of Eqs. (40) and (41), the relationship between _{X t | t-1} and X _{t-1 | t-1} can be determined by using the _{coefficient matrices AX} and _{t as follows.} It can be expressed as (45).

In the Kalman filter algorithm, the model estimated deviation state variable X _{t | t-1} is set to the deviation _{between the measured value U t} of the surface temperature of the slab 5 at the temperature measurement point and the estimated value Y _{t | t-1 at time t.} By modifying based on this, each state variable X _{t | t} at time t is estimated. Also, each state variable X _{t |} estimation error _t is the average is 0 (zero), the covariance matrix V _{t |} and assumed to follow a multidimensional normal distribution of _t, covariance matrix V _{t |} a _t, each Estimate at the same time as the state variable X _{t | t.} However, in the present embodiment, the update calculation of _{each state variable X t | t} is different between the time when each tracking surface k reaches the temperature evaluation position and the time in the middle between the temperature evaluation positions. It will be explained separately.

(A) Processing at the time when the tracking surface k reaches the temperature evaluation position The following processing is performed at the time when each tracking surface k reaches the temperature evaluation position.
_{(1) The covariance matrix V t | t-1} of the prediction error by the heat transfer coagulation model according to Eqs. (40) and (41) is the estimation result of the covariance matrix at time t-1 V _{t-1 | t-. Using 1} , it is updated and calculated by the following formula (46).

Here, Q _t is the variance Q ^k _ht ^{of the noise w k} _ht in the equation (40) and the variance Q ^tp ε _t ^{of the noise w tp} ε and _t in the equation (41) diagonally in the same order as in the equation (43). It is a covariance matrix of noise vectors arranged side by side and with the off-diagonal component set to 0 (zero).
(2) [Calculation of Kalman gain]
The Kalman gain Ψ _{t that modifies the model estimation deviation state variable X t | t-1} obtained by the equation (45) from the surface temperature measured value and the surface temperature calculated value is calculated by the following equation (47). Here, _Cy and _t ^{are matrices in which the coefficients c k} _T of the equation (42) are arranged in the column direction in the same order as the equation (44) for k. R _y is a covariance matrix when the measurement error of the surface temperature of the slab 5 has an average of 0 (zero) and follows the multidimensional normal distribution of _{the covariance matrix R y.}

(3) [Update of prediction result of model estimation deviation state variable]
_{The estimation result X t |} t of the model estimation deviation state variable at time t, _{the prediction result X t | t-1} of the model estimation deviation state variable by Eq. (43), and the surface temperature of the slab 5 at the temperature measurement point. Using the deviation between the measured value U _t and the estimated value Y _{t | t-1} , and the Kalman gain Ψ _t , the calculation is performed by updating with the following equation (48).

(4) [Update of prediction error covariance matrix]
Prediction error covariance matrix V _t according to equation (46) _| a _t-1, using the Kalman gain [psi _t, and updated by the following equation (49), the prediction error covariance matrix V _{t |} calculating the _t.

(5) [Enthalpy at the circumferential temperature measurement position, heat transfer coefficient correction parameters, temperature correction]
Calculation values of enthalpy at the circumferential temperature measurement position of each tracking surface k in equations (36), (37), and (38), heat transfer coefficient correction parameters at _{each temperature evaluation position z tp, and each tracking.} The calculated values of the surface temperature of the slab 5 at the circumferential temperature measurement position of the surface k are calculated by the following equations (50) to (50) using the corresponding values of the estimation results of _{the model estimation deviation state variable X t | t.} It is corrected by 53).

(B) Processing at the time when the tracking surface k reaches the intermediate position of the temperature evaluation position On the other hand, the following processing is performed at the time when each tracking surface k reaches the intermediate position of the temperature evaluation position.
(1) [Update of prediction error covariance matrix]
_{The covariance matrix V t | t-1} of the prediction error by the heat transfer coagulation model according to the equations (40) and (41) is used, and _{the estimation result V t-1 | t-1} of the covariance matrix at time t-1 is used. Then, it is updated and calculated by the following formula (54).

Here, Q _t is the covariance of the noise vector in which the variance Q ^k _ht ^{of the noise w k} _ht in the equation (40) is arranged diagonally in the same order as in the equation (43) and the off-diagonal component is 0 (zero). It is a matrix.

(2) [Calculation of Kalman gain]
At the time when the intermediate position of the temperature evaluation position is reached, the observation matrix for calculating the temperature at the temperature measurement point is 0 (zero), so the Kalman gain Ψ _t is all 0 (zero) as shown in the following equation (55). ).

(3) [Update of prediction result of model estimation deviation state variable]
Since the Kalman gain Ψ _t is 0 (zero), the prediction result of the model estimation deviation state variable is not updated, and the estimation result X _{t | t} of the model estimation deviation state variable at time t is as shown in the following equation (56). Become.

(4) [Update of prediction error covariance matrix]
Since the Kalman gain Ψ _t is 0 (zero), the covariance matrix of the prediction result of the model estimation deviation state variable is not updated, and the prediction error covariance matrix V _{t | t} is as shown in the following equation (57).

(5) [Enthalpy at the circumferential temperature measurement position, heat transfer coefficient correction parameters, temperature correction]
Since the model estimation deviation state variable X _{t | t} is not updated, the calculated value of the enthalpy at the circumferential temperature measurement position of each tracking surface k and each temperature evaluation position are as shown in the following equations (58) to (60). The heat transfer coefficient correction parameter at z _tp and the calculated value of the surface temperature of the slab 5 at the circumferential temperature measurement position of each tracking surface k are also not corrected.

<Target temperature setting unit 507 at the center of the slab, step S607>
The slab center target temperature setting unit 507 sets the target temperature of the slab 5 center for each of the temperature evaluation positions. In the following description, the target temperature at the center of the slab 5 will be referred to as the target temperature at the center of the slab, if necessary. In the present embodiment, the target temperature at the center of the slab is set for each operating condition category determined from the representative values of the steel type to be cast, the size of the mold 1, and the casting speed. Further, in the casting direction, the target temperature at the center of the slab is set for each temperature evaluation position. The target temperature at the center of the slab is set at least at the center position in the width direction (x-axis direction in FIG. 2) and the thickness direction (y-axis direction in FIG. 2) of the slab 5. The slab center target temperature setting unit 507 may set a plurality of slab center target temperatures at a position at the center in the thickness direction other than the center in the width direction of the slab 5. _{The target temperature r c} ^{tp at the} center of the slab at the temperature evaluation position z _tp is derived by simulation calculation using a heat transfer solidification model based on the representative values of the steel type, mold 1 size, and casting speed for each operating condition category described above. It is set based on the calculation result of the temperature of the slab 5. In the following description, the position of the slab 5 in which the target temperature of the slab center portion is set is referred to as a slab center portion, if necessary.

<Future Prediction Unit 508, Step S608>
For each of the temperature evaluation positions, the future prediction unit 508 sets a range from the temperature evaluation position to a predetermined position on the downstream side in the casting direction from the temperature evaluation position as the future prediction range of the temperature evaluation position. To do. Further, the future prediction unit 508 sets the positions in which each of the temperature evaluation positions within the future prediction range with respect to the temperature evaluation position is ordered based on the casting direction for each of the temperature evaluation positions in the future with respect to the temperature evaluation position. Set as the predicted position. Then, the future prediction unit 508 determines the temperature inside the slab cross section, the slab cross section surface temperature, and the slab cross section surface temperature at the future prediction position when each of the temperature evaluation positions advances from the current time to each of the future prediction positions. The second calculated value including the solid phase ratio distribution in the cross section of the slab is calculated using the heat transfer solidification model. At this time, the future prediction unit 508 _{assumes that the casting speed v c} and the amount of cooling water do not change from the values at the current time. In addition, the future prediction unit 508 calculates the temperature inside the slab cross section, the slab cross section surface temperature, and the slab cross section solid phase ratio distribution at the current time at each of the temperature evaluation positions calculated using the heat transfer solidification model. Use the initial value.

In the present embodiment, first, the future prediction unit 508 sets the number of future predictions for predicting the distribution of the surface temperature of the slab 5, the temperature inside the slab 5, and the solid phase ratio as N _{tp at the future time.} .. The future prediction unit 508 has the temperature evaluation position z _tp to the temperature evaluation position z _{tp + ntp} (n _tp = 1) for each of the plurality of temperature evaluation positions z _tp of tp = 1, 2, 3, ..., Tp _max. , ..., N _tp ) is set as the future prediction range. When the temperature evaluation position z _{tp + Ntp} is located on the downstream side of the most downstream temperature evaluation position, only the most downstream temperature evaluation position or the temperature evaluation position on the upstream side is within the future prediction range. To be included. In the future prediction range of temperature evaluation position z _tp, as the predicted future position with respect to the temperature evaluation position z _tp, it includes a plurality of temperature evaluation positions included in the future prediction range. It is assumed that the future prediction number N _tp is set in advance. Further, as described above, the casting speed v _c at the current time and the generation interval of the tracking surface (that is, the interval of the temperature evaluation position) Δz _tp are used to track between the two temperature evaluation positions z _{tp adjacent to each other.} The time it takes for the surface to move is represented _{by Δtp (= Δz tp} ÷ v _c).

For each of the _{temperature evaluation positions z tp} , the future prediction unit 508 calculates the _{enthalpy at the current time t of the temperature evaluation position z tp} , the temperature of the slab 5, and the temperature solid phase ratio distribution calculation unit 505. By repeatedly solving the heat transfer solidification model, assuming that the casting speed and the amount of cooling water for the slab 5 in each cooling zone are the same as those at the current time t, each tracking surface will be in the future. The enthalpy, the temperature of the slab 5, and the solid phase ratio are derived at the _{time t + n tp} Δtp at which each of the predicted positions (future predicted positions with respect to the temperature evaluation position z _{tp) is reached.}

In the present embodiment, the future prediction unit 508 uses the heat transfer solidification model as described above to obtain the temperature in the cross section of the slab and the slab at each of the temperature evaluation positions and the future prediction position with respect to the temperature evaluation position. Calculate the surface temperature. Then, the future prediction unit 508, together with this calculation, for each of the temperature evaluation positions, the slab cross section with respect to the amount of cooling water in the cooling zone corresponding to the future prediction position within the future prediction range with respect to the temperature evaluation position. The partial differential coefficient of the internal temperature is calculated as a future temperature influence coefficient, which is a coefficient representing the effect of the amount of the cooling water on the internal temperature of the slab cross section.

Specifically, in the present embodiment, the future prediction unit 508 repeatedly solves the heat transfer solidification model as described above, and in the process of repeatedly solving the heat transfer solidification model, each tracking surface for a minute change from the current value of the amount of cooling water in each cooling zone. The temperature response gain of the central part of the slab of k (ie, the temperature of each calculation point in the slab cross section of each tracking surface k with respect to the change from the current value of the amount of cooling water in each cooling zone, of the cooling zone. Predict the future temperature influence coefficient, which is a coefficient when expressed by a linear equation depending on the amount of change in the amount of cooling water. Specifically, the future prediction unit 508 casts a certain tracking surface k when it is cut in a direction perpendicular to the casting direction at the future prediction position at the time when the tracking surface reaches the future prediction position. Predicted values of enthalpy, temperature, and solid phase ratio at the internal and surface coordinates (i, j) of the cross section of piece 5 _{Hi , j, t + ntpΔtp} , Ti, j, t + ntpΔtp, f _{si, j,} the _{t + ntpΔtp,} to calculate using the heat transfer solidification model, to a temperature of the slab center part at the same time t + n _tp [Delta] tp, the future temperature of the water volume u _xm coolant for slab long side surface of the first m cooling zone Variables that appear on both sides of equations (22) and (23) are partially differentiated by _{u xm} in order to calculate the influence coefficient ∂T _{i, j, t + ntpΔtp} / ∂u _{xm ∂H i, j, t} The variables appearing on both sides of the following equations (61), (62) and (14), which are the equations satisfied by _{+ ntpΔtp} / ∂u _xm and ∂f _{si, j, t + ntpΔtp} / ∂T _{i, j} The following equation (63), which is an equation satisfied _{by the variable ∂T i, j, t + ntpΔtp} / ∂u _xm , which is partially differentiated by _{T i, j , is expressed by ∂H i, j, t + ntpΔtp} / ∂u _xm , ∂ It is calculated by solving f _{si, j, t + ntpΔtp} / ∂T _{i, j} , and ∂T _{i, j, t + ntpΔtp} / ∂u _{xm simultaneously.} For the tracking surface at the temperature evaluation position z _tp at time t + n _tp Δtp, ∂T _{i, j, t + ntp Δtp} / ∂u _{xm at the temperature evaluation position z tp} is the future temperature influence coefficient ∂T ^tp _{i, j, t + As ntpΔtp} / ∂u _xm , the temperature evaluation position tp and the time t + n _tp Δtp are stored in association with each other. The future temperature influence coefficient ∂T ^tp _{i, j, t + ntpΔtp} / ∂u _xm will be used in the cooling water amount change amount instruction value calculation unit 510 described later.

<Refer to the center of the slab Temperature calculation unit 509, step S609>
The slab center reference temperature calculation unit 509 sets the slab center target temperature set by the slab center target temperature setting unit 507 and the slab center target temperature set by the slab center target temperature setting unit 507 for each of the temperature evaluation positions set by the temperature evaluation position setting unit 503. Using the calculated value of the temperature at the center of the slab 5 at the current time calculated based on the first calculated value, the calculated value of the temperature at the center of the slab 5 and the target temperature at the center of the slab 5 are used. The temperature between the above and the future predicted position on the downstream side in the casting direction is calculated as the reference temperature at the center of the slab, which is a temperature closer to the target temperature at the center of the slab.

In the present embodiment, the slab center reference temperature calculation unit 509 has the slab center target temperature r ^tp _{c at the temperature evaluation position z tp} set by the slab center target temperature setting unit 507, and the temperature solid phase ratio. _{Using the temperature of the slab center at the temperature evaluation position z tp} at the current time t derived by the distribution calculation unit 505, the future prediction unit 508 predicts the temperature of the slab center at the future time. The temperature that approaches the target temperature r ^tp _c at the center of the slab is derived as the reference temperature at the center of the slab.

The slab center reference temperature was derived by the slab center target temperature r ^tp _{c at the temperature evaluation position z tp} set by the slab center target temperature setting unit 507 and the temperature solid phase ratio distribution calculation unit 505. It takes a value between the temperature at the _{temperature evaluation position z tp} at the current time t and the temperature at the center of the slab. Further, as the reference temperature of the slab center portion, at least the temperature for the future predicted number n _{tp at each temperature evaluation position z tp} (that is, the temperature at each future predicted position with respect to each _{temperature evaluation position z tp) is derived.}

Specifically, the slab center reference temperature calculation unit 509 casts the tracking surface at the current time t, which the future prediction unit 508 predicts to reach the future prediction position z _{tp at the time t + n tp Δtp at the current time t.} Using the temperature T ^tp-ntp _{c, t at the center of one piece and the target temperature r c} ^{tp at the} center of the slab at the predicted future position z _{tp , each temperature evaluation position z tp} is based on the following equation (64). Calculate the slab center reference temperature T ^{tp *} _{c, t + ntpΔtp at each future predicted position.}

Here, β is a constant of 0 ≦ β ≦ 1. β is determined for each future prediction position (future prediction number n _tp). Further, c is a cross section of the slab 5 cut perpendicular to the casting direction, and is an abbreviation symbol representing the coordinates of the position of the slab center within the cross section at the position of the ^{slab center target temperature r tp} _c. is there. When the slab center target temperature setting unit 507 sets the slab center target temperature at a position in the width direction other than the center in the thickness direction of the slab 5, the slab center reference temperature calculation unit 509 calculates the reference temperature not only for the center of the slab but also for these positions.

<Cooling water amount change amount instruction value calculation unit 510, step S610>
The cooling water amount change amount instruction value calculation unit 510 calculates the cooling water amount change amount instruction value by solving the optimization problem for obtaining the determination variable that maximizes or minimizes the value of the objective function. The determinant is the cooling water amount change amount instruction value, which is the instruction value of the change amount of the cooling water amount from the actual value of the cooling water amount at the current time, and is the cooling water amount change amount instruction value for each of the cooling zones. is there. The objective function is the temperature of the center of the slab at each of the predicted future positions and the reference temperature of the center of the slab at each of the predicted future positions when the amount of cooling water is changed according to the indicated value of the amount of cooling water. Includes a term that represents the difference between. This difference is the predicted value of the temperature of the slab center at each of the future predicted positions, the reference temperature of the slab center at each of the future predicted positions, and the slab center which is the future temperature influence coefficient at the future predicted position. It is expressed using the part temperature influence coefficient and the indicated value for changing the amount of cooling water. Further, the predicted value of the temperature of the slab center portion at each of the future predicted positions is calculated based on the second calculated value at each of the future predicted positions with respect to the temperature evaluation position. Further, the objective function has a term including the square of the difference between the temperature of the slab center portion at each of the future predicted positions and the slab center reference temperature at each of the future predicted positions.

In the present embodiment, the cooling water amount change amount instruction value calculation unit 510 calculates the temperature of the slab center portion at each future prediction position with respect to each temperature evaluation position derived by the future prediction unit 508 by referring to the slab center portion temperature. Cooling water from the actual value of the amount of cooling water in each cooling zone at the current time t so as to approach the ^{reference temperature T tp *} _{c, t + ntpΔtp} at the center of the slab at the predicted future position calculated in part 509. Derived the amount of change in the amount of water in. In the following description, the amount of change in the amount of cooling water from the actual value of the amount of cooling water in each cooling zone at the current time t is referred to as an indicated value for the amount of cooling water change, if necessary. Further, the temperature of the slab center portion derived by the future prediction unit 508 is referred to as a slab center temperature prediction value, if necessary.

An objective function including the deviation between the slab center temperature predicted value at each future predicted position for each temperature evaluation position and the slab center reference temperature at the future predicted position, and the cooling water amount change amount indicated value is determined and cooled. It is calculated by obtaining the solution of the optimization problem that minimizes or maximizes the value of the objective function using the water amount change amount indication value as the determinant.

In the present embodiment, the cooling water change amount command value calculation portion 510, a cooling water change amount command value Delta] u _xm in each cooling zone and decision variables in the future prediction range, billet core temperature of each temperature evaluation position The deviation between the predicted value of and the reference temperature T ^{tp *} _{c, t + ntpΔtp} at the center of the slab corresponding to the predicted value is minimized under the constraint condition regarding the amount of cooling water in each cooling zone. Solve the planning problem.

Specifically, the objective function J of this quadratic programming problem is formulated as the following equation (65). The cooling water amount change amount instruction value calculation unit 510 stores the objective function J of the equation (65) in advance.

The first term on the right side of the equation (65) _{assumes that the cooling water amount change indication value Δu xm} in each cooling zone is sufficiently small, and at the time t + n _tp Δtp within the future prediction range, the cooling water amount change amount indication value Δu Predicted value of slab center temperature at _{temperature evaluation position z tp} when the flow rate of cooling water in the cooling zone is changed by _xm ^{T tp} _{c, t + ntpΔtp} + (∂T ^tp _{c, t + ntpΔtp} / ∂u _xm ) ・_{Calculate the deviation between Δu xm} ^{and the reference temperature T tp *} _{c, t + ntpΔtp} at the center of the slab corresponding to the time and the temperature evaluation position, and calculate the deviation of the entire slab within the future prediction range. The magnitude of the deviation is determined by the number of times predicted in the future n _tp corresponding to the time when the tracking surface reaches the predicted position in the future, the number tp representing the temperature evaluation position, and the deviation at the position c at the center of the slab. the square of the value obtained by multiplying the weight coefficient W _c of _{positive, tp,} the _ntp, the Forecasts and number n _tp, the number tp representing the temperature evaluation position, as the sum of the position c of the slab center This is the item to be evaluated. On the other hand, the second term of the right side of equation (65), the cooling water quantity change amount instruction value is a term which gives a penalty relating to the size, square and positive cooling water change amount instruction value of the m cooling zone Delta] u _xm Is the sum of the products of the weighting coefficients W _{u and m for each cooling zone.} Cooling water change amount command value calculation section 510, expand equation (65) for cooling water change amount command value Delta] u _xm, calculates the coefficient of the secondary and the primary term of the cooling water change amount command value Delta] u _xm. Then, the cooling water amount change amount instruction value calculation unit 510 minimizes the value of the objective function J of the equation (65) within a range satisfying the constraint equation expressing the constraint on the amount of cooling water in each cooling zone. It calculates the quantity of cooling water change amount command value Delta] u _xm when calculated as an optimal solution of equation (65).

Here, the case where c is a number representing the position of the center of the slab has been described as an example. However, when the slab center target temperature setting unit 507 sets the slab center target temperature at a position in the width direction other than the center in the thickness direction of the slab 5, c is set to the position in the thickness direction. In the equation (65), the sum of each c may be taken.

Here, W _{c, t + ntpΔtp} and W _{u, m} are weighting coefficients indicating the balance of the evaluation terms of the first term on the right side and the second term on the right side of the equation (65). For example, when the evaluation term of the right side first term of the equation (65) is more important than the evaluation term of the right side second term, the weighting coefficient W _{c, t + ntpΔtp with respect to the right side first term of the equation (65).} Is made larger than the size _{of the weighting coefficient W u, m} with respect to the second term on the right side.

Further, as the above-mentioned constraint equation, for example, a constraint equation indicating that the amount of cooling water in each cooling zone is equal to or less than the upper limit of the amount of the cooling water can be adopted.
Equation (65) is a quadratic programming problem. Therefore, the cooling water change amount command value calculation section 510 numerically solving calculate the amount of cooling water change amount command value Delta] u _xm coefficient matrix for when the value of the objective function J is minimized. As a method for solving the quadratic programming problem, known techniques such as the active constraint method and the Lagrange undetermined multiplier method can be used, and therefore detailed description thereof will be omitted here.

<Cooling water amount change instruction unit 511, S611>
Coolant level change instruction unit 511, derived by the cooling water amount change instruction unit 511, the optimum value of the cooling water change amount command value Delta] u _xm in each cooling zone, the actual current time t of the quantity of cooling water of the cooling zone The value _{added to the values u xm and t} is derived as the water amount indication value for the next control cycle, and the water amount indication value to be derived is a meter that controls the amount of cooling water in each cooling zone via the upper process computer or directly. Send to the device.
In the present embodiment, the distance between the temperature evaluation positions in the casting direction is set to half or less of the length of the longest cooling zone in the casting direction. By doing so, at least two temperature evaluation positions can be present in each of the cooling zones, and the target value of the temperature at the center of the slab at a plurality of positions in one cooling zone (in the present embodiment). , Target temperature at the center of the slab), and the profile of the temperature at the center of the slab in the casting direction within one cooling zone can be controlled. Therefore, it is possible to accurately control the temperature of the center of the slab in one cooling zone.

(Summary)
As described above, in the present embodiment, _{the tracking surface is generated according to the casting speed v c} , and the temperature evaluation position is set at a position that is an integral multiple of the generation interval of the tracking surface in the casting direction. En tal peak at the current time of the temperature evaluation position, the temperature of the slab 5, and the solid fraction, derived using the heat transfer solidification model based on heat conduction equation. For each temperature evaluation position, the temperature evaluation position, en tal peak at a future time when there is a movement in the future predicted position of the downstream side in the casting direction, the temperature of the slab 5, and the solid fraction, the heat transfer solidification model Is derived using. At this time, based on the heat transfer solidification model, the partial differential coefficient of the temperature of the slab center portion with respect to the cooling water amount change amount indicated value is derived as the influence coefficient of the cooling water amount change amount indicated value with respect to the temperature of the slab center portion. In addition, starting from the temperature at the center of the slab at the current time, the reference temperature at the center of the slab, which is closer to the target temperature at the center of the slab as the future predicted position on the downstream side, is derived. Then, when the amount of cooling water is changed based on the temperature at the center of the slab at each future predicted position at each temperature evaluation position, the influence coefficient corresponding to the future predicted value, and the cooling water amount change amount indicated value. Formulate the temperature of the center of the slab at each future predicted position at each temperature evaluation position. The smaller the deviation between the temperature at the center of the slab at each future prediction position at each temperature evaluation position when the amount of cooling water is changed and the reference temperature at the center of the slab corresponding to the future prediction position, the smaller the value. Find the cooling water amount change amount indication value when the value of the objective function J to be taken becomes the minimum.

Therefore, even if the casting speed is changed during casting, the temperature at the center of the slab can be brought close to the reference temperature at the center of the slab over the entire slab. As shown in the above, fluctuations in the distribution of the solid phase ratio in the casting direction at the center of the slab can also be reduced. That is, it is possible to reduce the fluctuation of the position of the slab portion where the solid phase ratio at the center of the slab is equal to or higher than the flow limit. Therefore, even if the reduction rate is reduced due to the decrease in the casting rate, the reduction rate of the slab portion where the solid phase ratio at the center of the slab is equal to or higher than the flow limit is equal to or higher than the value capable of preventing V segregation. By keeping the amount of reduction of the slab 5 constant, it is possible to prevent linear segregation while preventing V segregation and reverse V segregation. Therefore, the solid phase ratio at the center of the slab does not change significantly, and the amount of reduction with respect to the slab when the slab is lightly reduced before and after the change in the casting speed can be kept constant.

Further, in the present embodiment, the temperature at the center of the slab at the current time is used as the starting point, and the reference temperature at the center of the slab that is closer to the target temperature at the center of the slab as the future predicted position on the downstream side is used. Therefore, when the target temperature at the center of the slab is used directly, the deviation between the predicted temperature and the target temperature in the future near the current time is strongly evaluated and the amount of cooling water manipulated becomes excessive depending on the manufacturing conditions. Hunting of the operation of the amount of cooling water may occur due to the repetition of the above, and such a phenomenon can be prevented by using the reference temperature at the center of the slab as described above.

Further, in the present embodiment, based on the heat transfer solidification model, the partial differential coefficient of the temperature of the center of the slab with respect to the indicated value of the amount of cooling water is changed to the influence coefficient of the indicated value of the amount of cooling water with respect to the temperature of the center of the slab. Ask as. Therefore, without assuming that the change in the temperature at the center of the slab with respect to the indicated value for changing the amount of cooling water is expressed by a specific function, the coefficient of influence of the indicated value for changing the amount of cooling water with respect to the temperature at the center of the slab is obtained. be able to. Therefore, the deviation between the temperature of the center of the slab at the predicted future position and the reference temperature of the center at the predicted future position (in the parentheses of the first term on the left side of the equation (65) in the present embodiment) is more accurate. Can be evaluated.

Further, in the present embodiment, with respect to the enthalpy of the slab 5 and the heat transfer coefficient correction parameter, the error between the actual value and the value calculated based on the heat transfer solidification model is included in the state variable (Equation (43)). , The temperature of the slab 5 based on the error between the actual value of the temperature of the slab 5 and the value calculated based on the heat transfer solidification model and the temperature of the slab 5 calculated based on the heat transfer solidification model. (Equation (44)), and the heat transfer coefficient correction parameter is estimated by modifying the state variable based on the difference between the temperature estimate and the measured value of the slab 5 using the extended Kalman filter. Derive the optimal solution of the value. Therefore, since it is not necessary to solve the non-linear equations according to the equations (36) to (38), the optimum solution of the estimated value of the heat transfer coefficient correction parameter can be derived by using the extended Kalman filter.

(Modification example)
In the present embodiment, as shown in FIG. 2, a case where a so-called quarter cross section from the corner of the slab 5 to the center of the slab 5 is set as the calculation target region is taken as an example. explained. However, the calculation target area is not limited to this. For example, a so-called half cross section from the short side surface of the slab (the surface of x = 0 or x = X) to the center (x = X / 2) in the width direction of the slab 5, the long side surface of the upper slab of the slab 5. It may be a half cross section from (a surface of y = 0 or y = Y) to a center (y = Y / 2) in the thickness direction, or the entire calculation target region. Even in the case of so-called near-net shape casting for producing slabs for railway rails or H-shaped steel, by setting a symmetry line using symmetry and setting a calculation target area, the present embodiment can be used. A similar technique can be applied. Further, when the shape of the cross section of the slab is a distant view, one dimension in the thickness direction may be the calculation target.

In the present embodiment, since the models (Equations (27) and (28)) representing the enthalpy and the time change of the heat transfer coefficient correction parameter at the circumferential temperature measurement position are non-linear, the case where the extended Kalman filter algorithm is used is taken as an example. I mentioned and explained. However, for example, the optimum solution of the estimated value of the heat transfer coefficient correction parameter is obtained for each temperature evaluation position so as to optimize the value of the objective function including the deviation between the calculated surface temperature value and the surface temperature measurement as an evaluation index. If possible, it is not always necessary to use the extended Kalman filter algorithm. For example, a state estimation algorithm for a nonlinear system such as an ensemble Kalman filter or a particle filter may be used. Further, a downhill simplex method or a genetic algorithm may be used to search for the optimum solution by giving a heat transfer coefficient correction parameter as a candidate for the optimum solution to the objective function.

In this embodiment, the deviation of the actual heat transfer coefficient value from the model formula is formulated in the form of multiplying the heat transfer coefficient by the correction parameter. However, the deviation itself from the model formula of the actual heat transfer coefficient value may be calculated by using the extended Kalman filter algorithm similar to this embodiment or the state estimation algorithm for a nonlinear system such as an ensemble Kalman filter or a particle filter. .. Further, the deviation of the heat transfer coefficient is formulated as an optimization problem in which the deviation between the calculated surface temperature value and the surface temperature measurement is used as a variable of the objective function including the deviation as an evaluation index. A genetic algorithm or the like may be used.

In this embodiment, a case where the amount of cooling water with respect to the long side surface of the slab is manipulated (controlled) has been described as an example. However, in addition to this, the amount of cooling water from the cooling spray that injects cooling water onto the short side surface of the slab may be manipulated (controlled). In this case, in the above description, the variable x may be the variable y. For example, the future prediction unit 508 determines the amount of cooling water for the short side surface of the slab in the m-th cooling zone to the temperature of the central part of the slab at the future temperature evaluation position _{by n tp for a certain tracking surface k.} Calculate the influence coefficient ∂T _{i, j, t + ntpΔtp} / ∂u _ym of u _ym.

It is preferable to use the slab center reference temperature as in the present embodiment because it is possible to suppress a sudden change in the slab center temperature at a future predicted position. However, it is not always necessary to do this. For example, the target temperature at the center of the slab may be used instead of the reference temperature at the center of the slab. In this case, the future prediction unit 508 stores the temperature at the center of the slab among the predicted values of the temperature of the slab 5.

Further, in the present embodiment, the case where the optimization problem is a minimization problem that minimizes the value of the objective function J has been described as an example. However, the optimization problem may be a minimization problem that maximizes the value of the objective function J. For example, the optimization problem can be made a maximization problem by multiplying the right side of the equation (65) by (-1).

Further, in the present embodiment, the objective function J of the optimization problem is a weighted sum of the squared deviations of the predicted temperature at the center of the slab and the reference temperature at the center of the slab, so that the optimization problem is changed by changing the amount of cooling water in the cooling zone. The case of formulating as a quadratic programming problem regarding the quantity indicated value has been described as an example. However, instead of replacing the square deviation between the predicted temperature at the center of the slab and the reference temperature at the center of the slab with an absolute value, and using the penalty term for the indicated value for the amount of cooling water change, the absolute value of the amount of cooling water change is used. The optimization problem can also be a linear planning problem by replacing it with a constrained conditional expression.

In the present embodiment, the distance between the temperature evaluation positions in the casting direction is set to half or less of the length of the longest cooling zone in the casting direction. By doing so, at least two temperature evaluation positions are present in each of the cooling zones, and the target value of the temperature at the center of the slab at a plurality of positions in one cooling zone (in the present embodiment, casting). An example was shown in which the target temperature of one cooling zone) was set to control the profile of the temperature of the center of the slab in one cooling zone in the casting direction, but when the length of one cooling zone in the casting direction was sufficiently short. May be set so that there is only one temperature evaluation position in each of the cooling zones.

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

Next, an embodiment will be described.
In this embodiment, the cooling control device 100 of the present embodiment is applied to the continuous casting machine (slab continuous casting machine) shown in FIG. 1, and simulation calculation is performed. With the steel type and slab size assumed in this example, the continuous casting machine targeted in this example casts at a casting speed of 1.1 m / min. However, the casting speed may be reduced due to a delay in the arrival of the subsequent molten steel ladle for continuous casting. Therefore, as an example of the invention, the secondary cooling control by the method of the present embodiment is shown, and by controlling the amount of cooling water in each cooling zone of the secondary cooling zone, the slab of the entire slab is formed even before and after the change of the casting speed. It is confirmed that it is not necessary to change the reduction amount of the slab by keeping the temperature of the central portion at the center in the width direction and the 1/4 width position at the center in the thickness direction at the target value. Further, as a comparative example, a secondary cooling control method by the method of Patent Document 3 for the purpose of controlling the temperature of the surface of the slab is shown.

Based on the casting speed of the material assumed in this example in normal operation and the distribution of the amount of cooling water in each cooling zone of the secondary cooling zone, the temperature distribution in the casting direction of the slab was calculated, and from the calculated result, The temperature at the center of the slab in the thickness direction at the temperature evaluation position was extracted, and the extracted temperature was set as the target value in the invention example and made constant. In the comparative example, as described in Patent Document 3, a target value is set for the surface temperature of the slab to keep the surface temperature of the slab constant.

Further, due to the delay in the arrival of the subsequent molten steel ladle, the casting speed was changed from 1.1 m / min to 1.05 m / min and 1.1 m / min to 1.0 m / min, respectively. The time change of the temperature of the central part of the slab was calculated in each of the invention example and the comparative example.
In both the comparative example and the invention example, it was assumed that the entire slab after changing the casting speed was cast at the same casting speed, and the temperature and solid phase ratio at the center of the slab in that state were investigated.

(1) Comparative example: Simulation result of constant control of slab surface temperature FIGS. 7A to 7C show the results of the comparative example. Specifically, FIG. 7A shows the relationship between the temperature of the center of the slab (center temperature) before and after the change of the casting speed and the distance of the molten steel in the mold in the casting direction from the molten metal surface (distance from the molten metal surface). Is shown. FIG. 7B shows the deviation between the temperature at the center of the slab and the target value (deviation of the center temperature target value) and the distance of the molten steel in the mold from the molten metal surface in the casting direction (from the molten metal surface) before and after the change in the casting speed. The relationship with (distance) is shown. FIG. 7C shows the relationship between the solid phase ratio at the center of the slab (solid phase ratio at the center) and the distance of the molten steel in the mold in the casting direction from the molten metal surface (distance from the molten metal surface).

From FIGS. 7A and 7B, it can be seen that after the casting speed is lowered, the temperature at the center of the slab in the solid-liquid coexisting portion is lowered, and the amount of the decrease is larger as the casting speed is lower. In FIG. 7C, when the casting speed is reduced from 1.1 m / min to 1.0 m / min, the point where the central solid phase ratio is 0.8 of the flow limit solid phase ratio is 1.5 m upstream. Showed that it is retreating.

FIG. 8 shows a problem when the roll interval distribution is set so that the rolling speed does not cause V segregation, reverse V segregation, and central segregation at a reference casting speed of 1.1 m / min based on Patent Document 1. It is a figure explaining. It is assumed that the slab is reduced by the optimum reduction amount 802 when the casting speed is 1.1 m / min on the downstream side of the position of the liquidus line 801 of the slab. In this state, when the casting speed is lower than 1.1 m / min, the interface of the solid phase ratio, which is the flow limit, recedes from the interface 803a to the upstream side like the interface 803b, and the solid phase line becomes a solid phase. It recedes upstream like lines 804a to 804b. In this state, when the same rolling reduction amount 802 as when the casting speed is 1.1 m / min is maintained, the rolling speed is excessive in the region 805 where the solid phase ratio has increased, so that the spot-shaped central segregation is linear segregation. This may cause defects or cracks in the central part of the rolled steel material.

The reduction of the slab is carried out in units of segments holding the rolls according to the gradient in the casting direction (see the reduction segment roll group 9 in FIG. 1). Therefore, as described above, when the position of the solid phase ratio that becomes the flow limit recedes to the upstream side, the position of the solid phase ratio that becomes the flow limit is not always at the boundary of the segment, so the reduction amount is effectively changed. It is considered that this is not possible and a central segregation defect of the slab occurs.

(2) Example of Invention: Simulation Results of Constant Control of Temperature at the Center of Shards FIGS. 9A-9C show the results of the invention. 9A, 9B, and 9C are diagrams corresponding to FIGS. 7A, 7B, and 7C, respectively. Specifically, FIG. 9A shows the relationship between the temperature of the center of the slab (center temperature) before and after the change of the casting speed and the distance of the molten steel in the mold in the casting direction from the molten metal surface (distance from the molten metal surface). Is shown. FIG. 9B shows the deviation between the temperature at the center of the slab and the target value (deviation of the center temperature target value) and the distance of the molten steel in the mold from the molten metal surface in the casting direction (from the molten metal surface) before and after the change in the casting speed. The relationship with (distance) is shown. FIG. 9C shows the relationship between the solid phase ratio at the center of the slab (solid phase ratio at the center) and the distance of the molten steel in the mold in the casting direction from the molten metal surface (distance from the molten metal surface).

From FIGS. 9A and 9B, it can be seen that the fluctuation range of the temperature at the center of the slab in the solid-liquid coexisting portion is smaller than that in FIGS. 7A and 7B even after the casting speed is lowered. Further, from FIG. 9C, it can be seen that the solid phase ratio of the central portion is kept substantially constant over the entire solid-liquid coexisting portion in the range in which the casting speed is changed. Therefore, even when the casting speed is reduced from 1.1 m / min to 1.0 m / min, for example, as shown in Patent Document 1, the reduction speed in the region where the solid phase ratio at the center is below the flow limit is 1.0 m. When it is maintained at / min or more, the reduction amount can be kept constant to prevent V segregation and inverse V segregation from occurring, and linear segregation can also be prevented from occurring.

1: Mold, 2a to 2t: Cooling spray, 3a to 3e: Flow control valve, 4: Molten steel meniscus, 5: Shard, 6a to 6f: Cooling zone boundary line, 7: Thermometer, 8: Casting speed measurement roll, 9: Reduction segment roll group, 100: Cooling control device, 501: Shard surface temperature acquisition unit, 502: Operation data acquisition unit, 503: Temperature evaluation position setting unit, 504: Heat transfer coefficient estimation unit, 505: Temperature solid phase Rate distribution calculation unit, 506: Heat transfer coefficient correction unit, 507: Target temperature setting unit at the center of the slab, 508: Future prediction unit, 509: Reference temperature calculation unit at the center of the slab, 510: Indicated value for the amount of cooling water change Calculation unit, 511: Cooling water amount change instruction unit

Claims (10)

The secondary cooling zone for cooling the slabs drawn from the mold of the continuous casting machine is divided into a plurality of cooling zones in the casting direction of the slabs, and the cooling water injected from the cooling spray contained in each cooling zone. It is a secondary cooling control device of a continuous casting machine that controls the temperature of the slab by controlling the flow rate of the slab.
Based on the heat transfer equation, the temperature inside the slab cross section, which is the temperature inside the cross section of the slab perpendicular to the casting direction, the slab cross section surface temperature, which is the temperature of the surface of the slab in the cross section, and the above. A model storage means for storing the heat transfer solidification model, which is a calculation formula for calculating at least the solid phase ratio distribution in the cross section of the slab, which is the distribution of the solid phase ratio in the cross section.
A slab surface temperature acquisition means for acquiring a measured value of the surface temperature of the slab measured during casting of the slab at a predetermined temperature measurement position.
An operation data acquisition means for acquiring operation data including the casting speed of the continuous casting machine and the flow rate of the cooling water, and
The temperature evaluation position in the mold, which is the position for evaluating the temperature in the cross section of the slab, the surface temperature in the cross section of the slab, and the solid phase ratio distribution in the cross section of the slab, which is the position in the casting direction of the slab. Temperature evaluation position setting means that sets a predetermined interval from the position of the hot water surface to the position of the machine end outlet,
The heat transfer coefficient of the surface of the slab used in the calculation of the heat transfer solidification model, the amount of the cooling water included in the operation data, the measured value of the temperature of the surface of the slab at the temperature measurement position, and the measured value. A heat transfer coefficient estimation means calculated using the heat transfer coefficient correction parameter for correcting the heat transfer coefficient, and a heat transfer coefficient estimation means.
The first calculated value including the temperature in the slab cross section, the surface temperature in the slab cross section, and the solid phase ratio distribution in the slab cross section at each of the temperature evaluation positions is obtained by casting only the interval between the temperature evaluation positions. As the process progresses, the temperature solid phase distribution calculation means calculated using the heat transfer solidification model and
The first measured value of the surface temperature of the slab at the temperature measuring position and the estimated value of the surface temperature of the slab at the temperature measuring position, which are calculated by the temperature solid phase ratio distribution calculating means. Using the estimated value of the surface temperature of the slab calculated based on the calculated value of 1, the heat transfer coefficient correction means for deriving the heat transfer coefficient correction parameter, and the heat transfer coefficient correction means.
A slab center target temperature setting means for setting a slab center target temperature, which is a target value of the slab center temperature, which is the temperature of the slab center, for each of the temperature evaluation positions.
For each of the temperature evaluation positions, a range from the temperature evaluation position to a predetermined position on the downstream side in the casting direction from the temperature evaluation position is set as a future prediction range of the temperature evaluation position. For each of the temperature evaluation positions, each of the temperature evaluation positions within the future prediction range with respect to the temperature evaluation position is set as the future prediction position with respect to the temperature evaluation position, and then the casting speed and the casting speed and the above. Assuming that the amount of the cooling water does not change from the value at the current time, the temperature in the cross section of the slab at the current time at each of the temperature evaluation positions calculated using the heat transfer solidification model, the slab. With the cross-sectional surface temperature and the solid phase ratio distribution in the cross section of the slab as initial values, the slab at the future predicted position when each of the temperature evaluation positions advances from the current time to each of the future predicted positions. A future prediction means for calculating a second calculated value including the temperature in the cross section, the surface temperature in the cross section of the slab, and the solid phase ratio distribution in the cross section of the slab using the heat transfer solidification model.
It is a cooling water amount change amount instruction value which is an instruction value of the change amount of the cooling water amount from the actual value of the cooling water amount at the present time, and is the cooling water amount change amount instruction value for each of the cooling zones. As a determinant, the slab center temperature at each of the future predicted positions and the slab center at each of the future predicted positions when the amount of cooling water is changed according to the indicated value for changing the amount of cooling water. Cooling that calculates the cooling water amount change amount indication value by solving the optimization problem that obtains the cooling water amount change amount instruction value that maximizes or minimizes the value of the objective function including the term representing the difference from the target temperature. Water amount change amount indicated value calculation means and
Based on the cooling water amount change instruction value for each of the cooling zones calculated by the cooling water amount change amount instruction value calculation means and the actual value of the cooling water amount of each cooling water amount at the current time. It has a cooling water amount changing means for changing the amount of the cooling water in each of the cooling zones.
The objective function is calculated based on the second calculated value at each of the future predicted positions with respect to the temperature evaluation position, the predicted value of the slab center temperature at each of the future predicted positions, and the casting. It is expressed using the slab center target temperature at each of the future predicted positions set by the single center target temperature setting means and the cooling water amount change amount indicated value.
Every time the casting progresses at least by the interval between the temperature evaluation positions, the slab surface temperature acquisition means, the operation data acquisition means, the temperature evaluation position setting means, the heat transfer coefficient estimation means, and the temperature solid phase ratio distribution calculation. means, the heat transfer coefficient correcting means, the billet center target temperature setting means, the future prediction unit, the cooling water amount change amount instruction value calculation means, and by is repeated the cooling water amount changing means, the casting A secondary cooling control device for a continuous casting machine, characterized in that the temperature of the center of the slab at the predicted future position at an arbitrary time is brought close to the target temperature of the center of the slab. For each of the temperature evaluation positions set by the temperature evaluation position setting means, the target temperature of the slab center set by the slab center target temperature setting means and the temperature solid phase ratio distribution calculation means are calculated. Using the calculated value of the slab center temperature at the current time calculated based on the first calculated value, the calculated value of the slab center temperature and the slab center target temperature The slab center for calculating the slab center reference temperature, which is a temperature between the two, and the temperature at the future predicted position on the downstream side in the casting direction is closer to the slab center target temperature. It also has a unit reference temperature calculation means,
The objective function is expressed by using the slab center reference temperature calculated by the slab center reference temperature calculation means instead of the slab center target temperature. The secondary cooling control device for the continuous casting machine according to the above. The future prediction means uses the heat transfer solidification model to calculate the temperature in the cross section of the slab and the surface temperature of the slab at each of the temperature evaluation positions and the future prediction position with respect to the temperature evaluation position. For each of the temperature evaluation positions, the partial differential coefficient of the temperature in the cross section of the slab with respect to the amount of the cooling water in the cooling zone corresponding to the future prediction position within the future prediction range with respect to the temperature evaluation position. Calculated as the slab center temperature influence coefficient, which is a coefficient representing the effect of the amount of cooling water on the slab center temperature.
The objective function includes a predicted value of the slab center temperature at the future predicted position within the future predicted range for each of the temperature evaluation positions, a slab center target temperature at the future predicted position, and the like. The continuous casting according to claim 1 or 2, wherein the temperature influence coefficient of the center of the slab in the cooling zone corresponding to the predicted position in the future and the indicated value of the amount of change in the amount of cooling water are used. Secondary cooling control device for the machine. The optimization problem includes the predicted value of the slab center temperature at each of the future predicted positions, the slab center target temperature, the slab center temperature influence coefficient, and the cooling water amount change amount instruction. It is a term expressed using a value, and is the temperature of the center of the slab at each of the predicted future positions when the amount of the cooling water is changed according to the indicated value of the amount of the cooling water change, and the future. The objective function having a term including the square of the difference from the target temperature at the center of the slab at each of the predicted positions and a term including the square of each of the indicated values of the amount of change in the amount of cooling water, which is the determinant, is described above. This is a quadratic planning problem used as an objective function.
The cooling water amount change amount instruction value calculation means calculates a coefficient matrix for the determinant variable in the quadratic programming problem and numerically solves the determinant variable when the value of the objective function is minimized. The secondary cooling control device for a continuous casting machine according to claim 3, wherein the value is calculated as an optimum value of the cooling water amount change amount indicated value for each of the cooling zones. The heat transfer coefficient correction parameter is multiplied by the heat transfer coefficient calculated by the heat transfer coefficient estimation means.
The heat transfer coefficient correction means is a measured value of the surface temperature of the slab at the temperature measuring position and an estimated value of the surface temperature of the slab at the temperature measuring position, and is the temperature solid phase ratio distribution. The heat transfer coefficient correction parameter is performed by performing an optimization calculation that minimizes the difference between the estimated value of the surface temperature of the slab calculated based on the first calculated value calculated by the calculation means and the estimated value of the surface temperature of the slab. The secondary cooling control device for a continuous casting machine according to any one of claims 1 to 4, wherein the optimum solution is calculated. The heat transfer coefficient correction means is a measured value of the surface temperature of the slab at the temperature measuring position and an estimated value of the surface temperature of the slab at the temperature measuring position, and is the temperature solid phase ratio distribution. By the extended Kalman filter using the estimated value of the surface temperature of the slab calculated based on the first calculated value calculated by the calculating means, the error dispersion between the measured value and the estimated value is minimized. The secondary cooling control device for a continuous casting machine according to claim 5, wherein the heat transfer coefficient correction parameter at the time of becoming is calculated as an optimum solution of the heat transfer coefficient correction parameter. The distance between the temperature evaluation positions in the casting direction is at least one half or less of the length of the cooling zone having the longest length in the casting direction in the casting direction among the plurality of cooling zones. The secondary cooling control device for a continuous casting machine according to any one of claims 1 to 6, wherein the continuous casting machine is characterized in that. The secondary cooling control device for a continuous casting machine according to any one of claims 1 to 7, wherein the casting speed changes during casting of the slab. The secondary cooling zone for cooling the slabs drawn from the mold of the continuous casting machine is divided into a plurality of cooling zones in the casting direction of the slabs, and the cooling water injected from the cooling spray contained in each cooling zone. This is a secondary cooling control method for a continuous casting machine that controls the temperature of the slab by controlling the flow rate of the slab.
Based on the heat transfer equation, the temperature inside the slab cross section, which is the temperature inside the cross section of the slab perpendicular to the casting direction, the slab cross section surface temperature, which is the temperature of the surface of the slab in the cross section, and the above. A model storage process for storing a heat transfer solidification model, which is a calculation formula for at least calculating the solid phase ratio distribution in a slab cross section, which is the distribution of the solid phase ratio in the cross section,
A slab surface temperature acquisition step of acquiring a measured value of the surface temperature of the slab measured during casting of the slab at a predetermined temperature measurement position, and a slab surface temperature acquisition step.
An operation data acquisition process for acquiring operation data including the casting speed of the continuous casting machine and the flow rate of the cooling water, and
The temperature evaluation position, which is the position for evaluating the temperature in the slab cross section, the surface temperature in the slab cross section, and the solid phase ratio distribution in the slab cross section, which is the position in the casting direction of the slab, is set in the mold. A temperature evaluation position setting process that sets a predetermined interval from the position of the hot water surface to the position of the machine end outlet.
The heat transfer coefficient of the surface of the slab used in the calculation of the heat transfer solidification model, the amount of the cooling water included in the operation data, the measured value of the temperature of the surface of the slab at the temperature measurement position, and the measured value. A heat transfer coefficient estimation step calculated using the heat transfer coefficient correction parameter for correcting the heat transfer coefficient, and a heat transfer coefficient estimation step.
The first calculated value including the temperature in the slab cross section, the surface temperature in the slab cross section, and the solid phase ratio distribution in the slab cross section at each of the temperature evaluation positions is obtained by casting only the interval between the temperature evaluation positions. As the process progresses, the temperature solid phase distribution calculation step calculated using the heat transfer solidification model and
The first measured value of the surface temperature of the slab at the temperature measurement position and the estimated value of the surface temperature of the slab at the temperature measurement position, which was calculated in the temperature solid phase ratio distribution calculation step. The heat transfer coefficient correction step of deriving the heat transfer coefficient correction parameter using the estimated value of the surface temperature of the slab calculated based on the calculated value of 1 and the heat transfer coefficient correction step.
A slab center target temperature setting step of setting a slab center target temperature, which is a target value of the slab center temperature, which is the temperature of the slab center, for each of the temperature evaluation positions.
For each of the temperature evaluation positions, a range from the temperature evaluation position to a predetermined position on the downstream side in the casting direction from the temperature evaluation position is set as a future prediction range of the temperature evaluation position. For each of the temperature evaluation positions, each of the temperature evaluation positions within the future prediction range with respect to the temperature evaluation position is set as the future prediction position with respect to the temperature evaluation position, and then the casting speed and the casting speed and the above. Assuming that the amount of the cooling water does not change from the value at the current time, the temperature in the cross section of the slab at the current time at each of the temperature evaluation positions calculated using the heat transfer solidification model, the slab. With the cross-sectional surface temperature and the solid phase ratio distribution in the cross section of the slab as initial values, the slab at the future predicted position when each of the temperature evaluation positions advances from the current time to each of the future predicted positions. A future prediction step of calculating a second calculated value including the temperature in the cross section, the surface temperature in the cross section of the slab, and the solid phase ratio distribution in the cross section of the slab using the heat transfer solidification model.
It is a cooling water amount change amount instruction value which is an instruction value of the change amount of the cooling water amount from the actual value of the cooling water amount at the present time, and is the cooling water amount change amount instruction value for each of the cooling zones. As a determinant, the slab center temperature at each of the future predicted positions and the slab center at each of the future predicted positions when the amount of cooling water is changed according to the indicated value for changing the amount of cooling water. Cooling that calculates the cooling water amount change amount indication value by solving the optimization problem that obtains the cooling water amount change amount instruction value that maximizes or minimizes the value of the objective function including the term representing the difference from the target temperature. The process of calculating the indicated value for the amount of water change and
Based on the cooling water amount change instruction value for each of the cooling zones calculated by the cooling water amount change amount instruction value calculation step and the actual value of the cooling water amount of each cooling water amount at the current time. It has a cooling water amount changing step of changing the amount of the cooling water in each of the cooling zones.
The objective function is calculated based on the second calculated value at each of the future predicted positions with respect to the temperature evaluation position, the predicted value of the slab center temperature at each of the future predicted positions, and the casting. It is expressed using the target temperature of the center of the slab at each of the predicted positions in the future and the indicated value of the amount of change in the amount of cooling water, which are set by the target temperature setting step of the center of the piece.
Every time the casting progresses at least by the interval between the temperature evaluation positions, the slab surface temperature acquisition step, the operation data acquisition step, the temperature evaluation position setting step, the heat transfer coefficient estimation step, and the temperature solid phase ratio distribution calculation. step, the heat transfer coefficient correction step, the billet center target temperature setting step, the future prediction step, the cooling water amount change amount command value calculation step, and the by cooling water amount changing step are repeated, casting A secondary cooling control method for a continuous casting machine, characterized in that the temperature of the center of the slab at the predicted future position at an arbitrary time is brought close to the target temperature of the center of the slab. A program characterized in that a computer functions as each means of the secondary cooling control device of the continuous casting machine according to any one of claims 1 to 8.

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