JP6256149B2 - Continuous casting machine level control device, continuous casting machine level control method, and computer program - Google Patents

Description

  The present invention relates to a molten metal level control device for a continuous casting machine, a molten metal level control method for a continuous casting machine, and a computer program, and in particular, used for controlling the molten metal level of a molten metal in a mold in a continuous casting machine. And suitable.

FIG. 10 is a diagram illustrating an example of a configuration of a continuous casting machine.
In FIG. 10, a tundish 20 for storing a molten metal (molten metal) 2 is disposed above a mold 1 having upper and lower ends opened and having a rectangular parallelepiped cavity in the height direction. An immersion nozzle 3 is connected to the bottom surface of the tundish 20. The immersion nozzle 3 is extended to a predetermined position inside the mold 1. The molten metal 2 in the tundish 20 is poured into the mold 1 through a sliding nozzle 30 attached to the immersion nozzle 3. In accordance with the opening degree of the sliding nozzle 30, the amount of pouring water into the mold 1 changes.

  The molten metal 2 poured into the mold 1 is cooled by contact with the water-cooled inner wall of the mold 1 and solidifies from the outside, and becomes a slab 4 whose outer side is covered by a solidified shell. It is pulled out continuously. The slab 4 is pulled out while maintaining a predetermined casting speed while being guided by a plurality of pairs of guide rolls 5 arranged in parallel at predetermined intervals below the mold 1. During this drawing, the slab 4 is cooled by cooling water sprayed from a spray band (not shown), cut to a predetermined size when solidification has progressed to the innermost part, and used in subsequent processes such as rolling. Product slab.

  In such a continuous casting machine, various inconveniences that impede stable operation such as overflow of the molten metal 2 from the upper part of the mold 1 and occurrence of breakout are prevented in advance and the production efficiency is improved. In order to stabilize the cooling and solidification of the inside of the mold and improve the quality of the product slab, the surface level (molten surface level) of the molten metal 2 staying inside the mold 1 has no periodic fluctuations and is appropriate. It is important to maintain the level.

  During the operation of the continuous casting machine, the level of the molten metal inside the mold 1 is detected by a level meter 6 facing the surface of the molten metal 2. The hot water level (detection level y) detected by the level meter 6 is given to the hot water level control device 7. In addition, the hot water level control device 7 is given a target value (target level r) of the hot water level to be maintained inside the mold 1 set in the target level setter 7a. The hot water surface level control device 7 obtains a hot water surface level deviation which is a deviation between the target level r set in the target level setting device 7a and the detection level y detected by the level meter 6, and calculates the hot water surface level deviation. The amount of change in the opening of the sliding nozzle 30 to be eliminated is obtained. Then, an opening / closing command u is output to the opening / closing actuator (hydraulic cylinder) 31 of the sliding nozzle 30 in order to obtain the obtained opening change amount. The actuator 31 operates according to the opening / closing command u, thereby changing the opening of the sliding nozzle 30 and adjusting the amount of pouring water into the mold 1. A stopper may be used in place of the sliding nozzle 30.

In general, the amount of change in opening is obtained by PI calculation or PID calculation using as input a molten metal level deviation that is the deviation between the target level r and the detection level y described above.
However, in the operation of the continuous casting machine, there are periodic disturbances that cause fluctuations in the molten metal surface level, such as bulging of the slab 4 drawn from the mold 1. As shown in FIG. 11, the bulging is such that the slab 4 (solidified shell) drawn out below the mold 1 bulges outward between a large number of guide rolls 5 arranged in parallel along the drawing path. It is a phenomenon that deforms. The molten metal inside the solidified shell enters and exits the mold 1 due to deformation of the slab 4 (the solidified shell) due to bulging (temporal change in the amount of bulging), and the hot water inside the mold 1 It is supposed to cause periodic fluctuations in the surface level (periodic level fluctuations). In particular, when the guide rolls 5 are arranged in parallel at the same pitch, the bulging amount in each guide roll 5 changes in the same phase, so that a periodic fluctuation of the molten metal surface level having a large fluctuation width occurs. To do.
It is difficult to suppress the periodic fluctuation of the molten metal surface level generated inside the mold 1 due to such a disturbance only by the general level control (PI control or PID control) described above.

Therefore, Patent Document 1 discloses a hot water surface level control system represented by a block diagram as shown in FIG. The hot water level control device 7 includes a subtractor 71, an adder 72, an opening degree calculation unit 73, a correction amount calculation unit 74, and an adder 75.
The subtractor 71 subtracts the detection level y from the target level r given as an input of the molten metal level control device 7 to obtain a molten metal level deviation which is a deviation between the target level r and the detected level y. A deviation signal e corresponding to the level deviation is output.
The adder 72 adds the deviation signal e output from the subtracter 71 and a hot water surface level deviation correction amount x described later, and outputs an addition signal E corresponding to the added value as a correction value of the hot water surface level deviation. .
The opening calculation unit 73 receives the addition signal E output from the adder 72 and calculates an opening change amount u ₀ . The opening calculation unit 73 is a feedback controller that performs the above-described PI calculation or PID calculation.
The correction amount calculation unit 74 receives the addition signal E output from the adder 72 as an input, and outputs the opening correction amount v to be added to the opening change amount u ₀ obtained by the opening calculation unit 73 and the subtractor 71. The molten metal level deviation correction amount x to be added to the deviation signal e is calculated.

The correction amount calculation unit 74 is configured as a filter element including a Q filter 74a, an M filter 74b, and an N filter 74c. The addition signal E is given to the Q filter 74a. The output q of the Q filter 74a is given in parallel to the M filter 74b and the N filter 74c, the M filter 74b outputs the opening degree correction amount v, and the N filter 74c outputs the hot water surface level deviation correction amount x. . As will be described later, the correction amount calculation unit 74 arranges a Q filter 74a, an M filter 74b, and an N filter 74c as shown in FIG. 12, and sets (1-N (s) · It is characterized in that the frequency characteristic of Q (s)) can be superimposed.
The adder 75 adds the opening change amount u ₀ obtained by the opening calculation unit 73 and the opening correction amount v obtained by the correction amount calculation unit 74, and an opening command corresponding to this addition value. u is output.

The opening degree command u is given to a plant model 81 that models a fluctuation level level process in a continuous casting machine. Thereby, the hot-water surface level inside the casting_mold | template 1 changes. The level obtained by adding the disturbance d by the adder 82 to the hot water surface level changing in this way is fed back as the detection level y detected by the level meter 6 and output to the subtractor 71.
In actual control, the plant model 81 and the adder 82 are replaced with an actual plant (continuous casting machine). Further, the adder 82 can be arranged between the adder 75 and the plant model 81 to represent a block diagram.
Here, in Patent Document 1, the transfer function P _M (s) of the plant model 81 is expressed by the following equation (1).

In the formula (1), s is a Laplace operator. KK [m ² · mm / sec] is a flow coefficient of the sliding nozzle 30. A [m ² ] is a horizontal cross-sectional area of the hollow portion of the mold 1. T _N [sec] is a dead time required for dropping of hot water inside the immersion nozzle 3.
In addition, (2 / T _N −s) / (2 / T _N + s) in the expression (1) is a first-order Padé approximation of the transfer function of the dead time element based on the dead time T _N.
In Patent Document 1, the transfer function N (s) of the N filter 74c and the transfer function M (s) of the M filter 74b are expressed by the following equations (2) and (3), respectively. Here, as the transfer function N (s) of the N filter 74c and the transfer function M (s) of the M filter 74b, a proper transfer function that satisfies the following expression (4) is selected.

As shown in the equations (1) to (3), the transfer function P _M (s) of the plant model 81 is a transfer function of a dead time element based on the dead time T _N and a transfer due to characteristics other than the dead time T _N. Expressed as a product with a function. Further, as shown in the equations (1) and (2), the transfer function N (s) of the N filter 74c is a dead time based on the dead time T _N of the transfer function P _M (s) of the plant model 81. Contains the transfer function of the element. Further, as shown in the equations (1) and (3), the transfer function M (s) of the M filter 74b is a dead time based on the dead time T _N of the transfer function P _M (s) of the plant model 81. It has the inverse characteristics of the transfer function due to characteristics other than the elements. In the expressions (2) and (3), (1 / (1 + T _M · s)) is T _M as a time constant for making the transfer function M (s) of the M filter 74b a proper transfer function. First-order lag element.
In Patent Document 1, the transfer function Q (s) of the Q filter 74a is expressed by the following equations (5) and (6).

In the equation (6), F (s) is a transfer function of a notch filter (band cutoff filter) having a central angular frequency ω [rad / sec]. The notch filter is a filter that cuts off a signal having a local frequency centered on the central angular frequency ω. In Equation (6), K _Q [−] is the output gain, and η [−] is the attenuation coefficient [−] of the fluctuation of the molten metal level.
In Patent Document 1, the transfer function Q (s) of the Q filter 74a is derived as follows.
FIG. 13 is a block diagram of a general hot water level control system.
In FIG. 13, the transfer function from the level d disturbance d to the detection level u coincides with the sensitivity function S (s). Therefore, the sensitivity function S (s) means how the level d disturbance d is amplified and appears in the detection level y. Further, the transfer function T ′ (s) from the melt level disturbance d to the opening command u means how the melt level disturbance d appears in the opening command u.

Here, the sensitivity function S (s) when the feedback controller 70 in FIG. 13 includes only the opening degree calculation unit 73 shown in FIG. 12 is the transfer function C (s) of the feedback controller 70. Is represented by C ₀ (s), it is expressed by the following equation (7). Further, the transfer function C of the feedback controller 70 when the feedback controller 70 in FIG. 13 includes the adder 72, the opening degree calculation unit 73, the correction amount calculation unit 74, and the adder 75 shown in FIG. (S) is expressed by the following equation (8).

  From the equations (8) and (4), the sensitivity function when the feedback controller 70 in FIG. 13 is composed of an adder 72, an opening calculation unit 73, a correction amount calculation unit 74, and an adder 75. S (s) is represented by the following equation (9).

As shown in the equations (7) and (9), when the feedback controller 70 in FIG. 13 includes an adder 72, an opening calculation unit 73, a correction amount calculation unit 74, and an adder 75. The sensitivity function S (s) is (1−N (s) · Q with respect to the sensitivity function S (s) when the feedback controller 70 in FIG. The frequency characteristic of (s)) is superimposed. In Patent Document 1, the frequency characteristic of (1-N (s) · Q (s)) is a characteristic of a notch filter having a central angular frequency ω. The center angular frequency ω is the angular frequency of the disturbance d, that is, the angular frequency corresponding to the fluctuation period of the molten metal surface level to be suppressed.
In order to make the frequency characteristic of (1-N (s) · Q (s)) the characteristic of the notch filter, it is necessary to obtain the transfer function Q (s) of the Q filter 74a as an analytical solution of the model matching problem. is there. That is, it is formulated as a problem for obtaining Q (s), which is a suboptimal solution that minimizes the value of the evaluation function J in the following equation (10).

This model matching problem is, for example, the Nevanlina Pick algorithm described in “7.3. Complementary Extreme Value Problem” in “System Control Theory for Advanced Control (Matoshi Maeda, Toshiharu Sugie, Asakura Shoten, 1990)”. It can be solved by the method described in the above.
Here, paying attention to the fact that the transfer function N (s) of the N filter 74c has one unstable zero 2 / _TN , an analytical solution shown in the following equation (11) is obtained.

However, in Equation (11), 1 / N (s) is not a proper transfer function. Therefore, the following equation (12) is obtained by superimposing a first-order lag element having a time constant T _{M on} Equation (11). As shown, the transfer function Q (s) of the Q filter 74a is a proper transfer function.

  Equation (5) is obtained from Equation (12) and Equation (2).

Japanese Patent No. 3591422

Maeda Atsushi and Sugie Shunji, “System Control Theory for Advanced Control”, Asakura Shoten, 1990

However, in the technique described in Patent Document 1, when the central angular frequency ω is high, that is, when the periodic fluctuation of the molten metal surface level is performed in a short period, the cyclic fluctuation of the molten metal surface level is effectively reduced. There is a risk that it cannot be suppressed.
FIG. 14 is a diagram showing a result of simulating the relationship between the amplitude (temperature level) of the sensitivity function S (s) and the frequency in the technique described in Patent Document 1. In FIG. FIG. 15 is a diagram showing the relationship between the amplitude (opening command) of the transfer function T ′ (s) and the frequency in the technique described in Patent Document 1. FIG. 16 is a diagram showing the relationship between the hot water level and time in the technique described in Patent Document 1.

14, 15, and 16, the center angular frequency ω is 2 × π × (1/3) [rad / sec], the output gain K _Q is 1.00 [−], and the fluctuation of the melt level is changed. The result of computer simulation with the attenuation coefficient η set to 0.33 [−] is shown. 14, 15, and 16 also show the results (without Q) when the feedback controller 70 is configured only by the opening degree calculation unit 73. In addition, the same value was used about the parameter which is common in each result.

  As shown in FIG. 14, in the technique described in Patent Document 1, the correction amount calculation unit 74 is configured as described above, so that the frequency (1/3 [1 [ In the vicinity of Hz]), the fluctuation of the molten metal surface level is warped and amplified. Further, as shown in FIG. 15, in the technique described in Patent Document 1, by configuring the correction amount calculation unit 74 as described above, the frequency corresponding to the fluctuation period of the molten metal level to be suppressed (1 / In the vicinity of 3 [Hz]), the opening degree command greatly increases. As a result, hot water level hunting occurs. Further, as shown in FIG. 16, in the technique described in Patent Document 1, the correction amount calculation unit 74 is configured as described above, so that the fluctuation of the molten metal surface level in a cycle of 3 seconds is warped and amplified.

  This invention is made | formed in view of the above problems, and it aims at enabling it to suppress the periodic fluctuation | variation of the hot_water | molten_metal surface level inside a casting_mold | template.

The first aspect example of the molten metal level control device of the continuous casting machine according to the present invention includes a detection level detected during operation by a detecting means for detecting a molten metal level inside the mold, a predetermined target level, As an input, a correction value for the molten metal level deviation, which is a deviation of the above, is input, and an opening calculation unit for obtaining an opening change amount required for the pouring means to the mold, and a correction value for the molten metal level deviation are input. A correction amount calculation unit for obtaining a hot water level deviation correction amount to be added to the hot water level deviation and an opening correction amount to be added to the opening change amount, the hot water level deviation correction amount, A first adder that derives a value obtained by adding the surface level deviation as a correction value of the molten metal level deviation and outputs the correction value to the opening calculation unit and the correction amount calculation unit; and the opening correction amount; A value obtained by adding the amount of change in the opening amount to the pouring means for the mold. A second level adder for deriving and outputting as an opening degree command, and a molten steel level control device for a continuous casting machine, wherein the correction amount calculation unit inputs a correction value for the molten metal level deviation. A Q filter that performs input, an M filter that receives the output of the Q filter and outputs the opening correction amount, and an N filter that receives the output of the Q filter and outputs the molten metal level deviation correction amount The transfer function of the M filter includes the inverse characteristic of the transfer function of the first-order lag element by the pouring means, the inverse characteristic of the transfer function of the first-order lag element by the detection means, and the transfer function of the integral element Expressed using a product of inverse characteristics, reciprocal of process gain, and transfer function of a third-order lag element introduced to make the transfer function of the M filter a proper transfer function, the transfer function of the N filter The casting Expressed by using the product of the transfer function expressing the time delay element due to the hot water drop by Padé approximation and the transfer function of the third-order lag element introduced to make the transfer function of the M filter a proper transfer function The transfer function of the Q filter is a product of a transfer function of a band pass filter having a central angular frequency corresponding to an angular frequency corresponding to a fluctuation period of the molten metal surface level to be suppressed, and a transfer function of a phase advance filter, and the product of the transfer function of the N filter and the transfer function of the Q filter, an evaluation function for evaluating the difference value is most assessment of the evaluation function takes a value that indicates that evaluation as the difference is small is high The phase advance filter transfer function has a maximum phase advance amount at the central angular frequency and a gain of 1 at the central angular frequency. It is a transfer function that expresses that the phase advance amount at the central angular frequency coincides with the phase delay amount of the third-order lag element included in the transfer function of the N filter.
The second aspect of the molten metal level control device of the continuous casting machine according to the present invention includes a detection level detected during operation by a detecting means for detecting a molten metal level inside the mold, a predetermined target level, As an input, a correction value for the molten metal level deviation, which is a deviation of the above, is input, and an opening calculation unit for obtaining an opening change amount required for the pouring means to the mold, and a correction value for the molten metal level deviation are input. A correction amount calculation unit for obtaining a hot water level deviation correction amount to be added to the hot water level deviation and an opening correction amount to be added to the opening change amount, the hot water level deviation correction amount, A first adder that derives a value obtained by adding the surface level deviation as a correction value of the molten metal level deviation and outputs the correction value to the opening calculation unit and the correction amount calculation unit; and the opening correction amount; A value obtained by adding the amount of change in the opening amount to the pouring means for the mold. A second level adder for deriving and outputting as an opening degree command, and a molten steel level control device for a continuous casting machine, wherein the correction amount calculation unit inputs a correction value for the molten metal level deviation. A Q filter that performs input, an M filter that receives the output of the Q filter and outputs the opening correction amount, and an N filter that receives the output of the Q filter and outputs the molten metal level deviation correction amount The transfer function of the M filter includes the inverse characteristic of the transfer function of the first-order lag element by the pouring means, the inverse characteristic of the transfer function of the first-order lag element by the detection means, and the transfer function of the integral element Expressed using a product of inverse characteristics, reciprocal of process gain, and transfer function of a third-order lag element introduced to make the transfer function of the M filter a proper transfer function, the transfer function of the N filter The casting Expressed by using the product of the transfer function expressing the time delay element due to the hot water drop by Padé approximation and the transfer function of the third-order lag element introduced to make the transfer function of the M filter a proper transfer function The transfer function of the Q filter is a product of a transfer function of a band pass filter having a central angular frequency corresponding to an angular frequency corresponding to a fluctuation period of the molten metal surface level to be suppressed, and a transfer function of a phase advance filter, An evaluation function for evaluating a value obtained by multiplying a difference between the product of the transfer function of the N filter and the transfer function of the Q filter by a weight function, and the smaller the value obtained by multiplying the difference by the weight coefficient, the more the evaluation is performed. is determined to a value indicating that the value of the evaluation function is high most evaluation whose values indicate a high, the transfer function of the phase advance filter are that the amount of phase lead in the center angular frequency is maximum, The gain at the central angular frequency becomes 1, and the phase advance amount at the central angular frequency is obtained by subtracting the phase advance amount of the weight function from the phase delay amount of the third-order lag element included in the transfer function of the N filter. The weighting function includes a region where the gain increases from a low frequency region to a high frequency region, and from the low frequency region to the high frequency region. A gain correction coefficient that does not include a region where the gain decreases toward the region, and that causes the gain at the central angular frequency of the transfer function of the Q filter to be 1 when the gain of the bandpass filter is 1 Is applied to the transfer function of the bandpass filter.

The first aspect example of the molten metal level control method for a continuous casting machine according to the present invention includes a detection level detected during operation by a detecting means for detecting a molten metal level inside the mold, a predetermined target level, As an input, a correction value for the molten metal level deviation, which is a deviation of the above, is input, and an opening calculation step for obtaining an opening change amount required for the pouring means to the mold, and a correction value for the molten metal level deviation is input. A correction amount calculating step for obtaining a hot water surface level deviation correction amount to be added to the hot water surface level deviation and an opening correction amount to be added to the opening degree change amount, the hot water surface level deviation correction amount, A value obtained by adding a value obtained by adding the surface level deviation as a correction value for the molten metal level deviation, a value obtained by adding the opening correction amount and the opening change amount to the mold. Derived and output as the opening command for the pouring means A level control method for a continuous casting machine, wherein the correction amount calculation step inputs a Q filter that receives the correction value of the level difference and inputs the output of the Q filter. And performing an operation using the M filter that outputs the opening correction amount and the N filter that receives the output of the Q filter and outputs the molten metal level deviation correction amount. The transfer function includes an inverse characteristic of the transfer function of the first-order lag element by the pouring means, an inverse characteristic of the transfer function of the first-order lag element by the detection means, an inverse characteristic of the transfer function of the integral element, and the inverse of the process gain. The transfer function of the M filter is expressed by using a product of the transfer function of the third-order lag element introduced to make the transfer function of the M filter into a proper transfer function, and the transfer function of the N filter is caused by the pouring of the mold into the mold. Mu Expressed using a product of a transfer function expressing a time element in Padé approximation and a transfer function of a third-order lag element introduced to make the transfer function of the M filter a proper transfer function, The transfer function is a product of a transfer function of a band pass filter having a central angular frequency corresponding to the fluctuation frequency of the molten metal surface level to be suppressed and a transfer function of the phase advance filter, and a transfer function of the N filter. an evaluation function for evaluating the product of the transfer function of the Q filter, the difference value indicating the value of the evaluation function that takes a value indicating that evaluated as the difference is small is high that most Rated The transfer function of the phase advance filter is such that the phase advance amount at the central angular frequency is maximized, the gain at the central angular frequency is 1, and the center It is a transfer function expressing that a phase advance amount at an angular frequency matches a phase delay amount of the third-order delay element included in the transfer function of the N filter.
The second aspect example of the molten metal level control method of the continuous casting machine according to the present invention includes a detection level detected during operation by a detecting means for detecting a molten metal level inside the mold, a predetermined target level, As an input, a correction value for the molten metal level deviation, which is a deviation of the above, is input, and an opening calculation step for obtaining an opening change amount required for the pouring means to the mold, and a correction value for the molten metal level deviation is input. A correction amount calculating step for obtaining a hot water surface level deviation correction amount to be added to the hot water surface level deviation and an opening correction amount to be added to the opening degree change amount, the hot water surface level deviation correction amount, A value obtained by adding a value obtained by adding the surface level deviation as a correction value for the molten metal level deviation, a value obtained by adding the opening correction amount and the opening change amount to the mold. Derived and output as the opening command for the pouring means A level control method for a continuous casting machine, wherein the correction amount calculation step inputs a Q filter that receives the correction value of the level difference and inputs the output of the Q filter. And performing an operation using the M filter that outputs the opening correction amount and the N filter that receives the output of the Q filter and outputs the molten metal level deviation correction amount. The transfer function includes an inverse characteristic of the transfer function of the first-order lag element by the pouring means, an inverse characteristic of the transfer function of the first-order lag element by the detection means, an inverse characteristic of the transfer function of the integral element, and the inverse of the process gain. The transfer function of the M filter is expressed by using a product of the transfer function of the third-order lag element introduced to make the transfer function of the M filter into a proper transfer function, and the transfer function of the N filter is caused by the pouring of the mold into the mold. Mu Expressed using a product of a transfer function expressing a time element in Padé approximation and a transfer function of a third-order lag element introduced to make the transfer function of the M filter a proper transfer function, The transfer function is a product of a transfer function of a band pass filter having a central angular frequency corresponding to the fluctuation frequency of the molten metal surface level to be suppressed and a transfer function of the phase advance filter, and a transfer function of the N filter. An evaluation function for evaluating a value obtained by multiplying a difference between the product of the transfer function of the Q filter and a weight function, and a value indicating that the smaller the value obtained by multiplying the difference by the weight coefficient is, the higher the evaluation is the value of the evaluation function that takes is determined to a value indicating that most Rated, the transfer function of the phase advance filter are that the amount of phase lead in the center angular frequency is maximized, said central angular frequency And the phase advance amount at the central angular frequency coincides with the phase delay amount of the third-order lag element included in the transfer function of the N filter minus the phase advance amount of the weight function. The weighting function includes a region where the gain increases from a low frequency region toward a high frequency region, and from a low frequency region toward a high frequency region. A gain correction coefficient that is a function that does not include a region in which the gain decreases, and that causes the gain at the central angular frequency of the transfer function of the Q filter to be 1 when the gain of the bandpass filter is 1. It is applied to the transfer function of a pass filter.

  The computer program according to the present invention causes a computer to execute each step of the molten steel level control method of the continuous casting machine.

  According to the present invention, the transfer function of the plant model is made higher order to form the transfer function of the M filter and the N filter, and the phase advance filter for compensating the phase delay amount of the third order delay element included in the N filter is introduced. Therefore, it is possible to suppress periodic fluctuations in the hot water level inside the mold.

It is a figure which shows the result of having simulated the relationship between the amplitude (water surface level) of a sensitivity function in the technique based on description of patent document 2, and a frequency. It is a figure which shows the relationship between the amplitude (opening instruction | command) and frequency of a transfer function in the technique based on description of patent document 2. FIG. It is a figure which shows the relationship between the hot_water | molten_metal surface level and time in the technique based on description of patent document 2. FIG. It is a figure which shows the result of having simulated the relationship between the amplitude (water surface level) and frequency of a sensitivity function in 1st Embodiment. It is a figure which shows the relationship between the amplitude (opening instruction | command) and frequency of a transfer function in 1st Embodiment. It is a figure which shows the relationship between the hot_water | molten_metal surface level and time in 1st Embodiment. It is a figure which shows the result of having simulated the relationship between the amplitude (hot-water surface level) and frequency of a sensitivity function in 2nd Embodiment. It is a figure which shows the relationship between the amplitude (opening instruction | command) and frequency of a transfer function in 2nd Embodiment. It is a figure which shows the relationship between the hot water surface level and time in 2nd Embodiment. It is a figure which shows an example of a structure of a continuous casting machine. It is a figure explaining bulging. It is a figure which shows an example of a structure of a level control apparatus. It is a block diagram of a general hot water level control system. It is a figure which shows the result of having simulated the relationship between the amplitude (water surface level) of a sensitivity function in the technique of patent document 1, and a frequency. It is a figure which shows the relationship between the amplitude (opening instruction | command) and frequency of a transfer function in the technique of patent document 1. FIG. It is a figure which shows the relationship between the hot_water | molten_metal surface level in the technique of patent document 1, and time.

In response to the above-described problem in the technique described in Patent Document 1, a technique described in Japanese Patent Application No. 2012-266275 has been proposed.
Before describing the embodiment of the present invention, a technique based on the description of Japanese Patent Application No. 2012-266275 will be described. In the following description, a technique based on the description in Japanese Patent Application No. 2012-266275 is referred to as a technique based on the description in Patent Document 2 as necessary.
In the technique based on the description in Patent Document 2 and the technique described in Patent Document 1, the transfer functions Q (s), M (s), and Q (s) of the Q filter 74a, the M filter 74b, and the N filter 74c shown in FIG. N (s) and the transfer function P _M (s) of the plant model 81 are different. Other configurations are the same as those shown in FIGS. 10 and 12, and thus detailed description thereof is omitted.
In the technique based on the description of Patent Document 2, the transfer function P _M (s) of the plant model 81 is expressed by the following equation (13).

In the equation (13), T _CYL [sec] is a time constant of the opening / closing actuator (hydraulic cylinder) 31. T _S [sec] is a time constant of the level meter 6.
Next, in the technology based on the description in Patent Document 2, the transfer function N (s) of the N filter 74c and the transfer function M (s) of the M filter 74b are expressed by the following equations (14) and (15), respectively. Represented by a formula. Here, as the transfer function N (s) of the N filter 74c and the transfer function M (s) of the M filter 74b, a proper transfer function that satisfies the following expression (16) is selected.

As shown in the equation (13), in the technique based on the description in Patent Document 2, the transfer function P _{M of the} plant model 81 is considered in consideration of the characteristics of the opening / closing actuator (hydraulic cylinder) 31 and the characteristics of the level meter 6. (S) is constructed, and compared with the technique described in Patent Document 1 (see equation (1)), a plant model 81 that is close to an actual machine is obtained. Furthermore, as shown in the equation (13), the technique based on the description in Patent Document 2 does not employ the first-order Padé approximation for the transfer function of the dead time element based on the dead time T _N.

As described above, the transfer function M (s) of the M filter 74b has the inverse characteristics of elements other than the dead time element based on the dead time T _N that the transfer function P _M (s) of the plant model 81 has. Therefore, if the delay function of the opening / closing actuator (hydraulic cylinder) 31 and the level meter 6 is not considered in the transfer function M (s) of the M filter 74b, a phase delay occurs. In particular, when the central angular frequency ω is high, the phase delay becomes significant. In the technique described in Patent Document 1, since these delay elements are not taken into consideration, there is a risk that the hot water surface level hunts as described above when trying to suppress the fluctuation of the hot water surface level in a short cycle. On the other hand, in the technology based on the description of Patent Document 2, in order to take account of these delay elements, it is possible to suppress hunting of the molten metal surface level when suppressing fluctuations in the molten metal surface level in a short cycle. Can do.
Next, in the technology based on the description in Patent Document 2, the transfer function Q (s) of the Q filter 74a is expressed by the following equations (17) to (19).

In the equation (19), L (s) is a transfer function of the phase advance filter. K _L [−] is the gain of the phase advance filter. γ [−] is a correction coefficient of the phase advance filter (γ <1). T _L [sec] is a time constant of the phase advance filter. The equation (18) represents the transfer function F (s) of the notch filter having the central angular frequency ω, similarly to the equation (6).
Here, in the technique based on the description of Patent Document 2, the phase advance filter is designed so that the following (A), (B), and (C) are established.
(A) The phase advance amount α is maximized at the central angular frequency ω.
(B) The gain of the phase advance filter at the central angular frequency ω is set to 1.
(C) The phase advance amount α at the center angular frequency ω is made to coincide with the phase delay amount in the transfer function N (s) of the N filter 74c.
By designing this manner phase-lead filter, the N transfer function N (s) delay elements included in the (dead time element based on dead time T _N of the filter _{74c (= exp (-T N ·} s)) The phase lag filter compensates for the phase lag caused by the ^third -order lag element (= 1 / (1 + T _M · s) ³ ) introduced to make the transfer function M (s) of the M filter 74b a proper transfer function. The frequency characteristic of (1-N (s) · Q (s)) can be made asymptotic to the transfer function F (s) of the notch filter having the central angular frequency ω.

FIG. 1 is a diagram showing a result of simulating the relationship between the amplitude (the level of the molten metal surface) of the sensitivity function S (s) and the frequency in the technique based on the description in Patent Document 2. FIG. 2 is a diagram showing the relationship between the amplitude (opening degree command) of the transfer function T ′ (s) and the frequency in the technology based on the description in Patent Document 2. FIG. 3 is a diagram showing the relationship between the molten metal level and time in the technology based on the description in Patent Document 2.
1, 2, and 3, the center angular frequency ω is 2 × π × (1/3) [rad / sec], the output gain K _Q is 1.00 [−], and the fluctuation of the melt level is changed. The result of computer simulation with the attenuation coefficient η set to 0.33 [−] is shown. 1, 2, and 3, the result (without Q) when the feedback controller 70 is configured only by the opening calculation unit 73, and the transfer function P of the plant model 81 in the technique described in Patent Document 1. The result (Patent Document 1) when _M (s) is made higher in the same manner as the technique based on the description of Patent Document 2 is also shown. In addition, the same value was used about the parameter which is common in each result.

As shown in FIG. 1, the hot water surface to be suppressed by compensating for the phase lag of the transfer function N (s) of the N filter 74c with a phase advance filter as in the technique based on the description in Patent Document 2. In the vicinity of the frequency (1/3 [Hz]) corresponding to the level fluctuation cycle, fluctuations in the molten metal surface level can be reduced.
Further, as shown in FIG. 3, by compensating for the phase lag of the transfer function N (s) of the N filter 74c with a phase advance filter as in the technique based on the description in Patent Document 2, a cycle of 3 seconds is obtained. Variations in the hot water level can be suppressed.
On the other hand, as shown in FIG. 2, as in the technique based on the description in Patent Document 2, the phase advance filter compensates for the phase lag of the transfer function N (s) of the N filter 74c and tries to suppress it. In the frequency region higher than the frequency (1/3 [Hz]) corresponding to the fluctuation level of the molten metal level, the opening degree command is greatly increased.

As described above, in the technology based on the description in Patent Document 2, the fluctuation of the molten metal surface level in a short cycle is achieved by increasing the transfer function P _M (s) of the plant model 81 and introducing a phase advance filter. Can be suppressed. However, the control output in the high frequency region is very large. Therefore, practical use may not be able to so large an output gain K _Q.
When controlling the level of the molten metal inside the mold 1, if the control output in the frequency region higher than 1/3 [Hz] is excessively increased, the ripple component caused by the flow of the molten metal 2 in the mold 1 is reduced. It has been empirically known that the fluctuation of the molten metal surface level increases due to amplification. Therefore, it is not desirable that the control output in the high frequency region becomes too large.

Therefore, it is conceivable to suppress the influence of the ripple of the molten metal surface level by providing an electromagnetic force device that suppresses the disturbance of the flow of the molten metal 2 in the mold 1 such as an electromagnetic brake. However, when electromagnetic stirring is performed using an electromagnetic force device, a stirring flow is imparted to the flow of the molten metal 2 in the mold 1, and therefore the influence of the undulation of the molten metal surface due to this stirring flow cannot be ignored. Therefore, it should be noted that high-frequency control output is suppressed.
In the technology based on the description in Patent Document 2, bilinear transformation is performed on the continuous-time transfer function described so far to convert it into a discrete-time transfer function. As shown in the equation (14), the transfer function N (s) of the N filter 74c includes a dead time element (= exp (−T _N · s)) based on a pure dead time T _N that is not approximated. include. For this reason, the order of the controller increases. When implementing a controller, it is not desirable for the order of the controller to increase.
Further, in the technology based on the description of Patent Document 2, the dead and dead time element based on the time _{T N (= exp (-T N} · s)), the transfer function M (s) the proper transmission of M filter 74b In order to compensate the ^third -order lag element (= 1 / (1 + T _M · s) ³ ) introduced to make a function with the phase advance filter, a plurality of phase advance filters are required.

Therefore, the present inventors, in addition to the above-described problems of the technique described in Patent Document 1, in order to solve these problems of the technique based on the description of Patent Document 2, The embodiment has been conceived.
Hereinafter, embodiments of the present invention will be described with reference to the drawings.
(First embodiment)
First, a first embodiment of the present invention will be described. In this embodiment and the technique described in Patent Document 1, the transfer functions Q (s), M (s), and N (s) of the Q filter 74a, the M filter 74b, and the N filter 74c shown in FIG. 81 is different from the transfer function P _M (s). Further, in the present embodiment and the technique based on the description in Patent Document 2, the transfer functions Q (s) and N (s) of the Q filter 74a and the N filter 74c shown in FIG. P _M (s) is different. Other configurations are the same as those shown in FIGS. 10 and 12, and thus detailed description thereof is omitted.
<Transfer function P _M (s) of plant model 81>
In this embodiment, the transfer function P _M (s) of the plant model 81 is expressed by the following equation (20).

As shown in the equation (1), (2 / T _N −s) / (2 / T _N + s) in the equation (20) is the first order Padé approximation of the transfer function of the dead time element based on the dead time T _N. It is.
As shown in the equation (20), in the present embodiment, as in the technique based on the description in Patent Document 2, the characteristics of the opening / closing actuator (hydraulic cylinder) 31 and the characteristics of the level meter 6 are taken into consideration. The transfer function P _M (s) of the model 81 is constructed. On the other hand, for the time delay element based on the time delay T _N , the transfer function of the plant model 81 using the first-order Padé approximation is used as in the technique described in Patent Document 1 in order to reduce the order of the controller. Build P _M (s).

<Transfer Function N (s) of N Filter 74c, Transfer Function M (s) of M Filter 74b>
In the present embodiment, the transfer function N (s) of the N filter 74c and the transfer function M (s) of the M filter 74b are represented by the following equations (21) and (22), respectively. Here, as the transfer function N (s) of the N filter 74c and the transfer function M (s) of the M filter 74b, a proper transfer function satisfying the following expression (23) is selected.

As described above, the transfer function M (s) of the M filter 74b has the inverse characteristics of elements other than the dead time element based on the dead time T _N that the transfer function P _M (s) of the plant model 81 has. Further, the transfer function N (s) of the N filter 74c has a time delay element based on the time delay T _N of the transfer function P _M (s) of the plant model 81. Further, in order to make the transfer function M (s) of the M filter 74b a proper transfer function and to satisfy the expression (23), the transfer function N (s) of the N filter 74c and the transfer function of the M filter 74b. A third-order lag element (= 1 / (1 + T _M · s) ³ ) having a time constant T _M is superimposed on _M (s).

That is, as shown in the equation (22), the transfer function M (s) of the M filter 74b is the inverse of the transfer function of the process gain (A / KK), and the inverse characteristic (s) of the transfer function of the integral element, Inverse characteristics (1 + T _CYL · s) of the transfer function of the first order lag element by the opening / closing actuator (hydraulic cylinder) 31, reverse characteristics (1 + T _S · s) of the transfer function of the first order lag element by the level meter 6, and the M filter 74b The transfer function M (s) is expressed by a product of a transfer function (= 1 / (1 + T _M · s) ³ ) of a third-order lag element for making a proper transfer function.
Further, as shown in the equation (33), the transfer function N (s) of the N filter 74c is a transfer function ((2 / T _N −s) expressing a dead time element based on the dead time T _N by a first-order Padé approximation. ) / (2 / T _N + s)), and a transfer function (= 1 / (1 + T _M · s) ³ ) of a third-order lag element for making the transfer function M (s) of the M filter 74b a proper transfer function, It is represented by the product of

<Transfer function Q (s) of Q filter 74a>
In the present embodiment, the transfer function Q (s) of the Q filter 74a is expressed by the following equations (24) to (26).

In equations (25) and (26), L (s) is the transfer function of the phase advance filter, K _L [−] is the gain of the phase advance filter, and γ [−] is the phase advance filter gain. It is a correction coefficient (γ <1), and T _L [−] is a time constant of the phase advance filter. Equation (25) represents a transfer function F _L (s) of a notch filter having a center angular frequency ω, which has been phase compensated by a phase advance filter having a transfer function _L (s).

In the present embodiment, the phase advance filter is designed so that the following (a1), (b1), and (c1) are established.
(A1) The phase advance amount α is maximized at the central angular frequency ω.
(B1) The gain of the phase advance filter at the center angular frequency ω is set to 1.
(C1) The phase advance amount α at the central angular frequency ω is matched with the phase delay amount of the third-order lag element (= 1 / (1 + T _M · s) ³ ).
By designing the phase advance filter in this way, the delay element included in the transfer function N (s) of the N filter 74c (introduced to make the transfer function M (s) of the M filter 74b a proper transfer function). The phase lag caused by the ^third -order lag element (= 1 / (1 + T _M · s) ³ ) can be compensated by the phase advance filter, and the frequency characteristic of (1−N (s) · Q (s)) It can be asymptotic to the transfer function F (s) of the notch filter of frequency ω.

<Design Method of Transfer Function Q (s) of Q Filter 74a>
Next, an example of a method for designing the transfer function Q (s) of the Q filter 74a shown in Expression (24) will be described.
As shown in the equations (7) to (9), when the feedback controller 70 in FIG. 13 includes an adder 72, an opening calculation unit 73, a correction amount calculation unit 74, and an adder 75. The sensitivity function S (s) of FIG. 13 is (1−N (s) .multidot.s) with respect to the sensitivity function S (s) when the feedback controller 70 in FIG. The frequency characteristic of Q (s)) is superimposed.
In the present embodiment, the frequency function of (N (s) · Q (s)) is expressed by the following equation (27), and the transfer function F _BL (s) of the band-pass filter that is phase-compensated by the phase advance filter: Asymptotically. Here, the band pass filter is a filter that passes a signal having a local frequency centered on the central angular frequency ω.

As shown in equation (27), the transfer function F _BL (s) of the bandpass filter that has been phase compensated by the phase advance filter is a third-order lag element (= 1) included in the transfer function N (s) of the N filter 74c. / (1 + T _M · s) ³ ) is represented by the product of the transfer function L (s) of the phase advance filter that compensates for the phase delay caused by / and the transfer function of the bandpass filter.
As a result, the frequency characteristic of (1-N (s) · Q (s)) is made asymptotic to the transfer function F (s) of the notch filter having the central angular frequency ω.
Therefore, the model matching problem for obtaining the transfer function Q (s) of the Q filter 74a of the present embodiment is a suboptimal solution that minimizes the value of the evaluation function J in the following equation (28). Is formulated as a problem to find

The evaluation function J shown in the equation (28) includes the transfer function F _BL (s) of the bandpass filter that has been phase compensated by the phase advance filter, the transfer function N (s) of the N filter 74c, and the transfer function of the Q filter 74a. The evaluation function is such that the smaller the difference between Q (s) and the product N (s) · Q (s), the smaller the value (the higher the evaluation).
The model matching problem for obtaining the transfer function Q (s) of the Q filter 74a is, for example, “7.3” in “System Control Theory for Advanced Control (by Maeda Atsushi, Toshiharu Sugie, Asakura Shoten, 1990)”. It can be solved by the method described in “The Nevanrina-Pick Algorithm Described in the Complementary Extreme Value Problem”.
Here, paying attention to the fact that the transfer function N (s) of the N filter 74c has one unstable zero 2 / _TN , an analytical solution shown in the following equation (29) is obtained.

However, in Equation (29), 1 / N (s) is not a proper transfer function. Therefore, the following equation (30) is obtained by superimposing a first-order lag element having a time constant T _{M on} Equation (29). As shown, the transfer function Q (s) of the Q filter 74a is a proper transfer function. The time constant T _M can be set to a value 5 to 10 times the time corresponding to the frequency band of the disturbance d.

From equation (30) and equation (21), equation (24) is obtained.
<Design Method of Transfer Function L (s) of Phase Advance Filter>
First, the phase advance amount α at the central angular frequency ω is expressed by the following equation (31).

Next, the correction coefficient γ of the phase advance filter that realizes the phase advance amount α at the center angular frequency ω is determined.
The phase advance amount φ in the phase advance filter L (s) is expressed by the following equation (32). Therefore, the time constant T _L of the phase advance filter that maximizes the phase advance amount φ in the phase advance filter L (s) is expressed by the following equation (33).

  From the equations (32) and (33), the phase advance amount α at the central angular frequency ω is expressed by the following equation (34).

  Therefore, when the phase advance amount α at the central angular frequency ω is given, γ in the range of γ <1 can be obtained as a solution of the quadratic equation as shown in the following equation (35).

Next, the time constant T _L of the phase advance filter in which the angular frequency that maximizes the phase advance amount is the central angular frequency ω is determined by the above-described equation (33).
Finally, the gain K _L of the phase advance filter with a gain of 1 at the central angular frequency ω is determined. Since the following equation (36) is obtained from the equation (26), the gain K _L of the phase advance filter with the gain at the central angular frequency ω being 1 is represented by the following equation (37).

As described above, the coefficients K _L , γ, and T _L of the transfer function L (s) of the phase advance filter shown in the equation (26) are obtained, and the transfer function L (s) of the phase advance filter is designed. .
Equation (26) is a transfer function L (s) of the phase advance filter when the phase advance amount α at the central angular frequency ω is π / 2 or less (α ≦ π / 2). When the phase advance amount α at the central angular frequency ω exceeds π / 2 (α> π / 2), a phase advance amount exceeding π / 2 cannot be obtained with one phase advance filter. For this reason, it is necessary to multistage the phase advance filter. For example, when the phase advance amount α at the central angular frequency ω is greater than π / 2 and less than or equal to π (π / 2 <α ≦ π), the transfer function L (s) of the phase advance filter is expressed by the following equation (38): It is represented by In this case, the phase advance amount of the one-stage phase advance filter is made to coincide with the phase delay amount that is half of the phase delay amount of the third-order delay element (= 1 / (1 + T _M · s) ³ ) (that is, the one-stage phase advance filter). The phase advance amount of the advance filter is set so that the phase advance amount α at the center angular frequency ω is ½ times the right side of (Equation 31)), and two such phase advance filters are used. May be configured.

<Concept of the present inventors up to the present embodiment>
Next, the transfer function Q (s) of the Q filter 74a, the transfer function N (s) of the N filter 74c, and the transfer function P _M (s) of the plant model 81 are determined as described above. The idea of the present inventors will be described to clarify the features of this embodiment.
[First idea]
In the technique described in Patent Document 1, the frequency characteristics of (1-N (s) · Q (s)) are transferred to the notch filter having the central angular frequency ω as shown in the equations (6) and (10). The transfer function Q (s) of the Q filter 74a is designed so as to be asymptotic to the function.
This coincides with making the frequency characteristic of (N (s) · Q (s)) asymptotic to the transfer function F _B (s) of the bandpass filter shown in the following equation (39).

  Here, only the transfer function N (s) of the N filter 74c and the transfer function M (s) of the M filter 74b are increased as shown in the equations (14) and (15). When the transfer function Q (s) of the Q filter 74a is obtained by the technique, the following expression (40) (the same result as expression (24)) is obtained as a result.

As described above, the transfer function P _M (s) of the plant model 81 is made higher order and the result is analyzed (see FIGS. 4 to 6). It has been found that the fluctuation of the hot water level in the vicinity of the cycle, which occurs when the technique is used to suppress the fluctuation of the hot water level in a short cycle, can be suppressed.
On the other hand, when the present inventors solve the model matching problem so that the frequency characteristic of (N (s) · Q (s)) is asymptotic to the transfer function F _B (s) of the bandpass filter, the sensitivity function S ( It has been found that the gain of s) does not decrease at the central angular frequency ω but decreases at an angular frequency lower than the central angular frequency ω, resulting in a phase delay. From this, the present inventors, as shown in the equations (27) and (28), have a band pass filter in which the frequency characteristics of (N (s) · Q (s)) are superimposed on the phase advance filter. The idea was to solve the model matching problem so as to be asymptotic to the transfer function F _BL (s).

[Second idea]
Further, the present inventors have considered the transfer function Q (s) of the Q filter 74a when the transfer function P _M (s) of the plant model 81 has no time delay element based on the time delay T _N. The transfer function P _M (s) of the plant model 81 in this case is expressed by the following equation (41), and the transfer functions M (s) and N (s) of the M filter 74b and the N filter 74c are respectively It is represented by the following formulas (42) and (43).

  Further, the model matching problem for obtaining the transfer function Q (s) of the Q filter 74a in this case is Q (s), which is a suboptimal solution that minimizes the value of the evaluation function J in the following equation (44). It is formulated as a problem to be sought.

  Here, since the transfer function N (s) of the N filter 74c is a transfer function having no unstable zeros, the transfer function of the Q filter 74a in which the evaluation function J of the equation (44) is 0 (J = 0). Q (s) is immediately obtained as in the following equation (45).

However, in Equation (45), 1 / N (s) is not a proper transfer function. Therefore, the following equation (46) is obtained by superimposing a third-order lag element having a time constant T _{M on} Equation (45). As shown, the transfer function Q (s) of the Q filter 74a is a proper transfer function.

At this time, the gain of the sensitivity function S (s) does not decrease at the central angular frequency ω. This is because the cause of the phase delay in the control by the transfer function Q (s) of the Q filter 74a obtained by the design based on the model matching is the third-order delay element (= 1/1 /) included in the transfer function N (s) of the N filter 74c. (1 + T _M · s) ³ ). From this, the present inventors set the third order delay element (= 1 / (1 + T _M · s) ³ ) included in the transfer function N (s) of the N filter 74c as the amount of phase delay to be compensated by the phase advance filter. I got the idea that I should do it.
On the other hand, as described above, in the technique based on the description in Patent Document 2, all the elements included in the transfer function N (s) of the N filter 74c (dead time element based on the dead time T _N ) are obtained by the phase advance filter. _{(= exp (-T N · s} )) and, since to compensate for the phase lag caused by the tertiary delay element (= 1 / (1 + T M · s) 3), dead time element based on dead time T _N (= exp ( -T _N · s), extra phase compensation is performed.

<Usefulness>
FIG. 4 is a diagram showing the result of simulating the relationship between the amplitude (water surface level) of the sensitivity function S (s) and the frequency in the present embodiment. FIG. 5 is a diagram showing the relationship between the amplitude (opening command) of the transfer function T ′ (s) and the frequency in the present embodiment. FIG. 6 is a diagram showing the relationship between the hot water level and time in the present embodiment.
Here, as described above, the transfer function T ′ (s) is a transfer function from the disturbance level d to the opening degree command u, and is defined by the following equation (47).

4, 5, and 6, the center angular frequency ω is 2 × π × (1/3) [rad / sec], the output gain K _Q is 1.00 [−], and the fluctuation of the melt level is changed. The result of computer simulation with the attenuation coefficient η set to 0.33 [−] is shown. 4, 5, and 6, the results when the feedback controller 70 is configured only by the opening degree calculation unit 73 (without Q) and the technique based on the description in Patent Document 2 are used. The results (Patent Document 2) are also shown. In addition, the same value was used about the parameter which is common in each result.

  As shown in FIG. 4, in this embodiment, compared with the technique based on the description of Patent Document 2, the sensitivity function S (s) has a frequency (1) corresponding to the fluctuation period of the molten metal surface level to be suppressed. / 3 [Hz]), that is, in the vicinity of the central angular frequency ω, the ability to reduce the fluctuation of the molten metal surface level is slightly inferior. Moreover, as shown in FIG. 6, in this embodiment, compared with the technique based on description of patent document 2, the capability to reduce the fluctuation | variation of the hot_water | molten_metal surface level of a 3 second period is a little inferior. However, as shown in FIG. 4, the present embodiment can reduce the fluctuation of the molten metal surface level in the high frequency region as compared with the technique based on the description of Patent Document 2.

On the other hand, as shown in FIG. 5, when the transfer function T ′ (s) is compared, in the present embodiment, compared to the technique based on the description in Patent Document 2, it corresponds to the fluctuation level of the molten metal level to be suppressed. An increase in the opening degree command can be suppressed in a frequency region higher than the frequency to be performed (1/3 [Hz]).
This indicates the usefulness of the transfer function Q (s) of the Q filter 74a of this embodiment. That is, in the present embodiment, the use of an electromagnetic force device that applies a stirring flow to the flow of the molten metal 2 in the mold 1 can suppress the high-frequency control output even when the influence of the ripples on the molten metal surface cannot be ignored. it can. This means that operating conditions and equipment conditions to which the transfer function Q (s) of the Q filter 74a of this embodiment can be applied are expanded.
Further, unlike the technique based on the description in Patent Document 2, the order of the controller (the order of the N filter 74c) is reduced by using the first-order Padé approximation of the transfer function of the time delay element based on the time delay T _N. can do. Furthermore, unlike the technique based on the description in Patent Document 2, using a continuous-time transfer function without converting to a discrete-time transfer function also contributes to a reduction in the order of the controller.

As described above, in the present embodiment, the process gain KK / A, the integral element 1 / s, the dead time element based on the dead time T _N as a first-order putty approximation, and the primary by the opening / closing actuator (hydraulic cylinder) 31 are used. The transfer function P _M (s) of the plant model 81 is expressed by the product of the delay element and the first-order delay element by the level meter 6. The transfer function M (s) of the M filter 74b and the transfer function N (s) of the N filter 74c are configured as an irreducible decomposition of the transfer function P _M (s) of the plant model 81. Further, the transfer function F _BL (s) of the filter formed by the product of the transfer function of the phase advance filter and the transfer function of the bandpass filter having the center angular frequency ω, the transfer function N (s) of the N filter 74c, and the Q filter 74a. The transfer function Q (s) of the Q filter 74a when the value of the evaluation function J that becomes smaller as the difference between the product and the product of the transfer function Q (s) becomes smaller is derived. Here, the phase advance filter has the maximum phase advance amount at the central angular frequency ω, the gain at the central angular frequency ω becomes 1, and the phase advance amount at the central angular frequency ω becomes the transfer function N (s) of the N filter 74c. It is designed to match the phase delay amount of the included third-order lag element (= 1 / (1 + T _M · s) ³ ).
Therefore, it is possible to simultaneously realize the suppression of the periodic fluctuation of the molten metal surface level inside the mold, the suppression of the control output in the high frequency region, and the reduction of the order of the controller.
In this embodiment, the first-order padé approximation of the transfer function of the dead time element based on the dead time T _N is used, but a second-order or higher-order Padé approximation may be adopted.

(Second Embodiment)
Next, a first embodiment of the present invention will be described. In the present embodiment, the following (a2), (b2), and (c2) are performed in order to further suppress the control output in the high frequency region and further reduce the fluctuation of the molten metal surface level at the central angular frequency ω. ).

(A2) The model matching problem is formulated by introducing a weighting factor W (s) into the evaluation function J. Thereby, the gain in the high frequency region of the transfer function Q (s) of the Q filter 74a can be suppressed.
(B2) The phase advance amount of L (s) of the phase advance filter is obtained by subtracting the phase advance amount of the weight function W (s) from the delay due to the third-order delay element of the transfer function N (s) of the N filter 74c. To do. Thereby, the gain of the sensitivity function S (s) at the central angular frequency ω can be minimized.
(C2) Q such that the gain at the center angular frequency ω of the transfer function Q of the filter 74a (s) is 1.00, corrects the output gain K _Q of the transfer function Q (s) of the Q filter 74a. As a result, when the output gain K _{Q is set} to 1.00, the gain at the central angular frequency ω of the transfer function Q (s) of the Q filter 74a can be set to 1.00, and the stability of the control is ensured. However, the gain of the sensitivity function S (s) at the central angular frequency ω can be minimized.

  Thus, the transfer function Q (s) of the Q filter 74a is mainly different between the present embodiment and the first embodiment. Therefore, in the description of the present embodiment, detailed description of the same parts as those of the first embodiment is omitted. Also in the present embodiment, description will be made using the reference numerals attached to FIGS. 10 and 12 as in the first embodiment.

The transfer function P _M (s) of the plant model 81, the transfer function N (s) of the N filter 74c, and the transfer function M (s) of the M filter 74b are the same as in the first embodiment (Equation (20)) (See formula (21), formula (22)).
<Transfer function Q (s) of Q filter 74a>
In the present embodiment, the transfer function Q (s) of the Q filter 74a is expressed by the following equations (48) to (51).

In equation (51), L (s) is the transfer function of the phase advance filter, K _L [−] is the gain of the phase advance filter, and γ [−] is the correction coefficient of the phase advance filter ( γ <1) and T _L [−] are time constants of the phase advance filter.
In the present embodiment, the phase advance filter is designed so that the following (a3), (b3), and (c3) are satisfied.
(A3) The phase advance amount α is maximized at the central angular frequency ω.
(B3) The gain of the phase advance filter at the central angular frequency ω is set to 1.
(C3) The phase advance amount α at the central angular frequency ω is made to coincide with the value obtained by subtracting the phase advance amount of the weighting function W (s) from the ^third -order lag element (= 1 / (1 + T _M · s) ³ ).

By designing the phase lead filter in this way, the delay element included in the transfer function N (s) of the N filter 74c (the transfer function M (s) of the M filter 74b is introduced to become a proper transfer function). The third-order lag element (= 1 / (1 + T _M · s) ³ ) minus the phase advance amount of the weighting function W (s) can be compensated, and (1−N (s) · Q (s) ) Can be made asymptotic to the transfer function F (s) of the notch filter having the central angular frequency ω.
Note that (a3) and (b3) are the same as (a1) and (b1), which are the design policies of the phase advance filter of the first embodiment.
In the equation (49), K _QV [−] is an output gain correction coefficient, and is expressed by the following equations (52) to (54).

The output gain correction coefficient K _QV is a Q filter 74a obtained when the product of the output gain K _Q and the output gain correction coefficient K _QV of the filter transfer function F _L (s) in equation (49) is 1.00. Is the reciprocal of the gain at the central angular frequency ω of the transfer function Q (s). By introducing the output gain correction coefficient K _QV , when the output gain K _Q is 1.00, the gain at the center angular frequency ω of the transfer function Q (s) of the Q filter 74a becomes 1.00.
In Equation (50), Z _W is the size of the zero point of the weight function W (s), and P _W is the size of the pole of the weight function W (s). The size Z _W of the zero point of the weight function W (s) is greater than 0 and takes a value less than the size of the pole of the weight function W (s) (0 <Z _W <P _W ).
Thus, the weighting function W (s) includes a region where the gain increases from the low frequency region toward the high frequency region, and the gain decreases from the low frequency region toward the high frequency region. By using a broadly monotonically increasing function that does not include a region, the gain in the high frequency region of the transfer function Q (s) of the Q filter 74a can be reduced.

<Design Method of Transfer Function Q (s) of Q Filter 74a>
Next, an example of a method for designing the transfer function Q (s) of the Q filter 74a shown in Expression (48) will be described.
As described above, the sensitivity function S (s) when the feedback controller 70 in FIG. 13 includes the adder 72, the opening calculation unit 73, the correction amount calculation unit 74, and the adder 75 is ( 9) It is expressed by the formula.
In the present embodiment, the frequency function of (1-N (s) · Q (s)) is expressed by the following equation (55), and the transfer function F _L (s ) Asymptotically.

Equation (55) is obtained by calculating the weighting function W () from the phase delay amount generated by the ^third -order delay element (= 1 / (1 + T _M · s) ³ ) included in the transfer function N (s) of the N filter 74c. 2 shows a transfer function F _L (s) of a filter to which a phase advance filter that compensates for the amount obtained by subtracting the amount of phase advance caused by s) is applied.
The model matching problem for obtaining the transfer function Q (s) of the Q filter 74a of the present embodiment obtains Q (s) that is a suboptimal solution that minimizes the value of the evaluation function J of the following equation (56). Formulated as a problem.

The evaluation function shown in the equation (56) includes the transfer function of the bandpass filter that has been phase-compensated by the phase advance filter (the second term on the right side of the equation (54)), and the transfer function N (s) and Q of the N filter 74c. Evaluation that the smaller the value obtained by multiplying the difference between the product N (s) and Q (s) by the transfer function Q (s) of the filter 74a and the weighting coefficient W (s), the smaller the value (the higher the evaluation). It is a function.
The model matching problem for obtaining the transfer function Q (s) of the Q filter 74a is, for example, “7.3” in “System Control Theory for Advanced Control (by Maeda Atsushi, Toshiharu Sugie, Asakura Shoten, 1990)”. It can be solved by the method described in “The Nevanrina-Pick Algorithm Described in the Complementary Extreme Value Problem”.
Here, paying attention to the fact that the transfer function N (s) of the N filter 74c has one unstable zero 2 / _TN , an analytical solution shown in the following equation (57) is obtained.

However, since 1 / N (s) is not a proper transfer function in the equation (57), the following equation (58) is obtained by superimposing a first-order lag element having a time constant T _{M on the} equation (57). As shown, the transfer function Q (s) of the Q filter 74a is a proper transfer function.

Equation (48) is obtained from Equation (58) and Equation (21).
<Design Method of Transfer Function L (s) of Phase Advance Filter>
The phase advance amount α at the central angular frequency ω is expressed by the following equation (59).

The other design method of the transfer function L (s) of the phase advance filter is the same as that described in the first embodiment.
That is, the correction coefficient γ of the phase advance filter that realizes the phase advance amount α at the center angular frequency ω is determined by the equation (35). The time constant T _L of the phase advance filter having the central angular frequency ω as the angular frequency that maximizes the phase advance amount is determined by the equation (33). The gain K _L of the phase-lead filter to the gain at the center angular frequency ω 1 is determined by the equation (37).
Equation (51) is a transfer function L (s) of the phase advance filter when the phase advance amount α at the central angular frequency ω is π / 2 or less (α ≦ π / 2). When the phase advance amount α at the central angular frequency ω exceeds π / 2 (α> π / 2), the phase advance filter may be multistaged as described in the first embodiment.

<Concept of the present inventors up to the present embodiment>
Next, the inventors' idea obtained up to the determination of the transfer function Q (s) of the Q filter 74a as described above will be described, and the features of the present embodiment will be clarified.
[First idea]
First, assuming that the phase advance amount α at the angular frequency ω of the phase advance filter is the equation (31), the transfer function Q (s) of the Q filter 74a shown in the equation (48) is designed. However, for the sake of simplicity, the following equation (60) is used instead of equation (49).

  At this time, the gain of the sensitivity function S (s) has a minimum value at an angular frequency higher than the central angular frequency ω. This means that phase lead occurs due to the introduction of the weight function W (s). The phase advance amount φ at the central angular frequency ω of the frequency characteristic of (1-N (s) · Q (s)) is expressed by the following equation (61).

The phase advance amount φ in the equation (61) matches the phase advance amount at the central angular frequency ω of the weighting function W (s).
From this, the inventors obtained the idea that the phase advance amount α at the central angular frequency ω should be expressed by the equation (59).

[Second idea]
First, assuming that the phase advance amount α at the angular frequency ω of the phase advance filter is the equation (59), the transfer function Q (s) of the Q filter 74a shown in the equation (48) is designed. However, here, for the sake of simplicity, the equation (60) is used instead of the equation (49).
At this time, the gain of the sensitivity function S (s) has a minimum value at the central angular frequency ω. On the other hand, the gain of the transfer function Q (s) of the Q filter 74a becomes maximum at the central angular frequency ω, but its value is less than 1.00.
The transfer function Q (s) of the Q filter 74a functions as a filter that promotes oscillation at the center angular frequency ω by positive feedback. Therefore, the frequency characteristic of (1-N (s) · Q (s)) is approximated to a notch filter having a central angular frequency ω. This means that it is desirable to make the gain at the central angular frequency ω of the frequency characteristic of the transfer function Q (s) of the Q filter 74a as close to 1.00 as possible.
Therefore, the present inventors correct the gain at the central angular frequency ω of the frequency characteristic of the transfer function Q (s) of the Q filter 74a to be 1.00 when the output gain K _{Q is set} to 1.00. The idea was to introduce an output gain correction coefficient K _QV to be used.

<Usefulness>
FIG. 7 is a diagram illustrating a result of simulating the relationship between the amplitude (water surface level) of the sensitivity function S (s) and the frequency in the present embodiment. FIG. 8 is a diagram illustrating the relationship between the amplitude (opening command) of the transfer function T ′ (s) and the frequency in the present embodiment. FIG. 9 is a diagram showing the relationship between the hot water level and time in the present embodiment.
Here, as described above, the transfer function T ′ (s) is a transfer function from the melt level disturbance d to the opening degree command u, and is defined by the equation (47).

7, 8, and 9, the center angular frequency ω is 2 × π × (1/3) [rad / sec], the output gain K _Q is 1.00 [−], and the fluctuation of the melt level is changed. The result of computer simulation with the attenuation coefficient η set to 0.33 [−] is shown. 7, 8, and 9, the result when the feedback controller 70 is configured only by the opening calculation unit 73 (without Q) and the case where the technique based on the description in Patent Document 2 is used. The results (Patent Document 2) are also shown. In addition, the same value was used about the parameter which is common in each result.

  As shown in FIG. 7, when the sensitivity function S (s) is compared, in this embodiment, the frequency (1/3 [Hz]) corresponding to the fluctuation period of the molten metal level to be suppressed, that is, the central angular frequency ω. , The ability to reduce the fluctuation of the molten metal surface level can be made equivalent to the technology based on the description in Patent Document 2. Moreover, as shown in FIG. 9, in this embodiment, the capability to reduce the fluctuation | variation of the hot_water | molten_metal surface level of a 3 second period can also be made equivalent to the technique based on description of patent document 2. FIG.

Further, as shown in FIG. 8, when the transfer function T ′ (s) is compared, in the present embodiment, compared to the technique based on the description of Patent Document 2, it corresponds to the fluctuation cycle of the molten metal level to be suppressed. An increase in the opening degree command can be suppressed in a frequency region higher than the frequency to be performed (1/3 [Hz]). Further, comparing FIG. 6 with FIG. 8, in this embodiment, compared to the first embodiment, the frequency (1/3 [Hz]) corresponding to the fluctuation period of the molten metal level to be suppressed is compared. In the high frequency range, it is possible to suppress an increase in the opening degree command.
In the present embodiment, as a result of suppressing the increase in the opening degree command as described above, as shown in FIG. 7, as compared with the technique based on the description of Patent Document 2, the fluctuation level of the molten metal level to be suppressed The ability to reduce the fluctuation of the molten metal surface level is slightly inferior in the frequency corresponding to (1/3 [Hz]), that is, in the region on the lower frequency side than the central angular frequency ω.

The above in this embodiment, as described, the output gain K _Q output gain K _Q such that the gain at the center angular frequency ω is 1.00 Q filter 74a transfer function Q (s) at 1.00 The product (the second term on the right side of the equation (49)) of the transfer function of the band pass filter and the transfer function of the phase advance filter in which the output gain correction coefficient K _QV to be corrected is introduced, and the transfer function N (s) of the N filter 74c Filter when the value of the evaluation function J, which becomes smaller as the value obtained by multiplying the difference between the product of the Q and the transfer function Q (s) of the Q filter 74a by the weighting factor W (s), becomes the smallest The transfer function Q (s) of 74a is derived. Here, the phase advance filter has the maximum phase advance amount at the central angular frequency ω, the gain at the central angular frequency ω becomes 1, and the phase advance amount at the central angular frequency ω becomes the transfer function N (s) of the N filter 74c. It is designed to coincide with the phase delay amount of the included third-order delay element (= 1 / (1 + T _M · s) ³ ) minus the phase advance amount of the weight function W (s). The weighting function W (s) includes a region where the gain increases from the low frequency region toward the high frequency region, and a region where the gain decreases from the low frequency region toward the high frequency region. It is a function that does not include.
Therefore, it is possible to further reduce the periodic fluctuation of the molten metal surface level inside the mold and the control output in the high frequency region. Further, since the gain in the high frequency region of the transfer function Q (s) of the Q filter 74a can be reduced by the weighting function W (s), the hunting of the molten metal surface level caused by the modeling error is avoided. be able to.

The embodiment of the present invention described above can be realized by a computer executing a program. Further, a computer-readable recording medium in 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 nonvolatile memory card, a ROM, or the like can be used.
In addition, the embodiments of the present invention described above are merely examples of implementation in carrying out the present invention, and the technical scope of the present invention should not be construed as being limited thereto. Is. That is, the present invention can be implemented in various forms without departing from the technical idea or the main features thereof.

1 Mold 2 Molten metal (molten metal)
DESCRIPTION OF SYMBOLS 3 Submerged nozzle 4 Cast slab 5 Guide roll 6 Level meter 7 Hot water level control device 20 Tundish 30 Sliding nozzle 31 Opening and closing actuator (hydraulic cylinder)
71 Subtractor 72 Adder 73 Opening Calculation Unit 74 Correction Amount Calculation Unit 74a Q Filter 74b M Filter 74c N Filter 75 Adder 81 Plant Model 82 Adder

Claims (5)

The correction value of the molten metal level deviation, which is the deviation between the detection level detected during operation by the detection means for detecting the molten metal level inside the mold and the predetermined target level, is input, and the injection to the mold is performed. An opening calculation unit for obtaining an opening change amount required for the hot water means;
A correction amount calculating unit for obtaining a correction value of the molten metal level deviation as input, and calculating a molten metal level deviation correction amount to be added to the molten metal level deviation and an opening correction amount to be added to the opening change amount, respectively.
A value obtained by adding the molten metal level deviation correction amount and the molten metal level deviation is derived as a correction value for the molten metal level deviation and is output to the opening calculation unit and the correction amount calculation unit. An adder;
A hot water for a continuous casting machine having a second adder for deriving and outputting a value obtained by adding the opening correction amount and the opening change amount as an opening command for the pouring means for the mold. A surface level control device,
The correction amount calculation unit includes:
A Q filter having the correction value of the molten metal level deviation as an input;
An M filter having the output of the Q filter as an input and the opening correction amount as an output;
An N filter having the output of the Q filter as an input and the hot water level deviation correction amount as an output;
Have
The transfer function of the M filter includes an inverse characteristic of the transfer function of the first-order lag element by the pouring means, an inverse characteristic of the transfer function of the first-order lag element by the detection means, an inverse characteristic of the transfer function of the integral element, and a process It is expressed using the product of the reciprocal of the gain and the transfer function of the third-order lag element introduced to make the transfer function of the M filter a proper transfer function,
The transfer function of the N filter includes a transfer function that expresses a dead time element due to dripping into the mold by Padé approximation, and a third-order lag element introduced to make the transfer function of the M filter a proper transfer function. It is expressed using the product of the transfer function and
The transfer function of the Q filter is a product of a transfer function of a band pass filter having a central angular frequency corresponding to an angular frequency corresponding to a fluctuation period of the molten metal surface level to be suppressed, and a transfer function of a phase advance filter, an evaluation function for evaluating the transfer function of the product of the transfer function of the Q filter, a difference, the value of the evaluation function that takes a value indicating that evaluated as the difference is small is high, most Rated Determined to be a value indicating that
The transfer function of the phase advance filter is such that the phase advance amount at the central angular frequency is maximized, the gain at the central angular frequency is 1, and the phase advance amount at the central angular frequency is equal to that of the N filter. A molten metal level control device for a continuous casting machine, characterized in that the transfer function represents that the phase delay amount of the third-order lag element included in the transfer function coincides. The correction value of the molten metal level deviation, which is the deviation between the detection level detected during operation by the detection means for detecting the molten metal level inside the mold and the predetermined target level, is input, and the injection to the mold is performed. An opening calculation unit for obtaining an opening change amount required for the hot water means;
A correction amount calculating unit for obtaining a correction value of the molten metal level deviation as input, and calculating a molten metal level deviation correction amount to be added to the molten metal level deviation and an opening correction amount to be added to the opening change amount, respectively.
A value obtained by adding the molten metal level deviation correction amount and the molten metal level deviation is derived as a correction value for the molten metal level deviation and is output to the opening calculation unit and the correction amount calculation unit. An adder;
A hot water for a continuous casting machine having a second adder for deriving and outputting a value obtained by adding the opening correction amount and the opening change amount as an opening command for the pouring means for the mold. A surface level control device,
The correction amount calculation unit includes:
A Q filter having the correction value of the molten metal level deviation as an input;
An M filter having the output of the Q filter as an input and the opening correction amount as an output; an N filter having the output of the Q filter as an input and an output of the molten metal level deviation correction amount;
Have
The transfer function of the M filter includes an inverse characteristic of the transfer function of the first-order lag element by the pouring means, an inverse characteristic of the transfer function of the first-order lag element by the detection means, an inverse characteristic of the transfer function of the integral element, and a process It is expressed using the product of the reciprocal of the gain and the transfer function of the third-order lag element introduced to make the transfer function of the M filter a proper transfer function,
The transfer function of the N filter includes a transfer function that expresses a dead time element due to dripping into the mold by Padé approximation, and a third-order lag element introduced to make the transfer function of the M filter a proper transfer function. It is expressed using the product of the transfer function and
The transfer function of the Q filter is a product of a transfer function of a band pass filter having a central angular frequency corresponding to an angular frequency corresponding to a fluctuation period of the molten metal surface level to be suppressed, and a transfer function of a phase advance filter, Is an evaluation function for evaluating a value obtained by multiplying a difference between the product of the transfer function of the Q and the transfer function of the Q filter by a weighting function, and the smaller the value obtained by multiplying the difference by the weighting coefficient, the higher the evaluation. is determined as the value of the evaluation function that takes a value that indicates it is a value indicating that most Rated,
The transfer function of the phase advance filter is such that the phase advance amount at the central angular frequency is maximized, the gain at the central angular frequency is 1, and the phase advance amount at the central angular frequency is equal to that of the N filter. A transfer function that represents that the phase delay amount of the third-order lag element included in the transfer function matches the value obtained by subtracting the phase advance amount of the weight function,
The weight function is a function that includes a region where the gain increases from a low frequency region toward a high frequency region, and does not include a region where the gain decreases from a low frequency region toward a high frequency region. ,
A gain correction coefficient is applied to the transfer function of the band pass filter so that the gain at the central angular frequency of the transfer function of the Q filter becomes 1 when the gain of the band pass filter is 1. A hot water level control device for a continuous casting machine. The correction value of the molten metal level deviation, which is the deviation between the detection level detected during operation by the detection means for detecting the molten metal level inside the mold and the predetermined target level, is input, and the injection to the mold is performed. An opening calculation step for obtaining an opening change amount required for the hot water means;
A correction amount calculation step for obtaining a correction value of the hot water surface level deviation as an input, and obtaining a hot water surface level deviation correction amount to be added to the hot water surface level deviation and an opening correction amount to be added to the opening change amount, respectively.
A first addition step of deriving a value obtained by adding the molten metal level deviation correction amount and the molten metal level deviation as a correction value of the molten metal level deviation;
A hot water of a continuous casting machine having a second addition step of deriving and outputting a value obtained by adding the opening correction amount and the opening change amount as an opening command for the pouring means to the mold. A surface level control method,
The correction amount calculation step includes:
A Q filter having the correction value of the molten metal level deviation as an input;
An M filter having the output of the Q filter as an input and the opening correction amount as an output;
An output using the output of the Q filter and an N filter that outputs the molten metal level deviation correction amount is performed,
The transfer function of the M filter includes an inverse characteristic of the transfer function of the first-order lag element by the pouring means, an inverse characteristic of the transfer function of the first-order lag element by the detection means, an inverse characteristic of the transfer function of the integral element, and a process It is expressed using the product of the reciprocal of the gain and the transfer function of the third-order lag element introduced to make the transfer function of the M filter a proper transfer function,
The transfer function of the N filter includes a transfer function that expresses a dead time element due to dripping into the mold by Padé approximation, and a third-order lag element introduced to make the transfer function of the M filter a proper transfer function. It is expressed using the product of the transfer function and
The transfer function of the Q filter is a product of a transfer function of a band pass filter having a central angular frequency corresponding to an angular frequency corresponding to a fluctuation period of the molten metal level to be suppressed, and a transfer function of a phase advance filter, and the N filter. an evaluation function for evaluating the transfer function of the product of the transfer function of the Q filter, a difference, the value of the evaluation function that takes a value indicating that evaluated as the difference is small is high, most Rated Determined to be a value indicating that
The transfer function of the phase advance filter is such that the phase advance amount at the central angular frequency is maximized, the gain at the central angular frequency is 1, and the phase advance amount at the central angular frequency is equal to that of the N filter. A molten metal level control method for a continuous casting machine, characterized in that the transfer function represents that the phase delay amount of the third-order lag element included in the transfer function coincides. The correction value of the molten metal level deviation, which is the deviation between the detection level detected during operation by the detection means for detecting the molten metal level inside the mold and the predetermined target level, is input, and the injection to the mold is performed. An opening calculation step for obtaining an opening change amount required for the hot water means;
A correction amount calculation step for obtaining a correction value of the hot water surface level deviation as an input, and obtaining a hot water surface level deviation correction amount to be added to the hot water surface level deviation and an opening correction amount to be added to the opening change amount, respectively.
A first addition step of deriving a value obtained by adding the molten metal level deviation correction amount and the molten metal level deviation as a correction value of the molten metal level deviation;
A hot water of a continuous casting machine having a second addition step of deriving and outputting a value obtained by adding the opening correction amount and the opening change amount as an opening command for the pouring means to the mold. A surface level control method,
The correction amount calculation step includes:
A Q filter having the correction value of the molten metal level deviation as an input;
An M filter having the output of the Q filter as an input and the opening correction amount as an output;
An output using the output of the Q filter and an N filter that outputs the molten metal level deviation correction amount is performed,
The transfer function of the M filter includes an inverse characteristic of the transfer function of the first-order lag element by the pouring means, an inverse characteristic of the transfer function of the first-order lag element by the detection means, an inverse characteristic of the transfer function of the integral element, and a process It is expressed using the product of the reciprocal of the gain and the transfer function of the third-order lag element introduced to make the transfer function of the M filter a proper transfer function,
The transfer function of the N filter includes a transfer function that expresses a dead time element due to dripping into the mold by Padé approximation, and a third-order lag element introduced to make the transfer function of the M filter a proper transfer function. It is expressed using the product of the transfer function and
The transfer function of the Q filter is a product of a transfer function of a band pass filter having a central angular frequency corresponding to an angular frequency corresponding to a fluctuation period of the molten metal level to be suppressed, and a transfer function of a phase advance filter, and the N filter. Is an evaluation function for evaluating a value obtained by multiplying a difference between the product of the transfer function of the Q and the transfer function of the Q filter by a weighting function, and the smaller the value obtained by multiplying the difference by the weighting coefficient, the higher the evaluation. the value of the evaluation function that takes a value indicating that is determined to be a value indicating that most Rated,
The transfer function of the phase advance filter is such that the phase advance amount at the central angular frequency is maximized, the gain at the central angular frequency is 1, and the phase advance amount at the central angular frequency is equal to that of the N filter. A transfer function that represents that the phase delay amount of the third-order lag element included in the transfer function matches the value obtained by subtracting the phase advance amount of the weight function,
The weight function is a function that includes a region where the gain increases from a low frequency region toward a high frequency region, and does not include a region where the gain decreases from a low frequency region toward a high frequency region. ,
A gain correction coefficient is applied to the transfer function of the band pass filter so that the gain at the central angular frequency of the transfer function of the Q filter becomes 1 when the gain of the band pass filter is 1. A method for controlling a molten metal level in a continuous casting machine.   A computer program for causing a computer to execute each step of the molten steel level control method for a continuous casting machine according to claim 3 or 4.

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