Molten metal surface level controller and molten metal surface control method

Abstract

To provide a molten metal surface level controller and a molten metal surface level control method which can suppress periodic bulging disturbance while maintaining a wide control bandwidth of feedback control.SOLUTION: A molten metal surface level controller CT according to the present invention, controls a molten metal surface level of a continuous casting machine CM by using feedback control to control an adjustment device that adjusts a molten steel quantity supplied to a casting mold of the continuous casting machine CM. The molten metal surface level controller CT includes: an FF compensator 12 that determines a feed-forward compensation amount composed of a sinusoidal wave component having an amplitude, a period, and a phase for eradicating outer disturbance to be applied to a molten metal surface level on the basis of the molten metal surface level, a manipulation amount of the adjustment device, and a transfer function of the continuous casting machine CM related to the molten metal surface level: and an adder 13 that, when performing control by using the feedback control, adds the feed-forward compensation amount determined by the FF compensator 12 to a feedback compensation amount in the feedback control.SELECTED DRAWING: Figure 2

Description

[Technical field]

[0001] The present invention relates to a molten metal level control device and a molten metal level control method for controlling the molten metal level in a mold in a continuous casting machine. [Background technology]

[0002] In a continuous casting machine that produces steel slabs, which are semi-finished products with a certain shape, by continuously solidifying molten steel, a phenomenon called bulging occurs. This bulging is a phenomenon in which the solidified shell bulges outward due to the static pressure of the molten steel inside, and this bulge is then depressed when the slab being cast is pulled out, and such bulging and depression are repeated periodically. This bulging causes the surface of the molten steel in the solidified shell (molten metal surface) to move up and down (the molten metal surface level fluctuates). For this reason, in order to maintain good quality of the slab (steel slab), it is important to suppress the molten metal surface level fluctuation caused by bulging and to keep the molten metal surface level in the mold constant. Technologies for keeping the molten metal surface level constant are disclosed, for example, in Patent Document 1 and Patent Document 2.

[0003] The mold level control device for a continuous casting machine disclosed in Patent Document 1 is a device that measures the mold level in a mold with a continuous casting machine for molten metal, and controls the opening of a pouring means for the mold in accordance with an opening command calculated using the deviation between the measured mold level and a target mold level so as to maintain the mold level at the target mold level. The device is equipped with an opening control unit that adjusts the opening of the pouring means based on the measured mold level and the target mold level, a disturbance estimation unit that estimates disturbances when the molten metal is poured into the mold and calculates an estimated disturbance amount value based on the measured mold level and the past opening of the pouring means, and a bulging visualization monitoring unit that calculates a fluctuation period of unsteady bulging based on the estimated disturbance amount calculated by the disturbance estimation unit and the casting speed of the continuous casting machine. The bulging visualization monitoring unit calculates a fluctuation period of unsteady bulging based on the estimated disturbance amount value. and the casting speed; an oversampling unit that converts time series data of the disturbance amount estimate value acquired by the data acquiring unit over a predetermined period into pre-oversampling data based on a casting length which is an integral value of the casting speed and oversamples the pre-oversampling data based on the casting length to generate post-oversampling data; an FFT processing unit that performs fast Fourier transform analysis on the post-oversampling data based on the casting length to calculate a distance frequency spectrum of an unsteady bulging occurrence roll pitch at which unsteady bulging occurs; and a peak detection unit that detects a peak of the distance frequency spectrum to calculate the unsteady bulging occurrence roll pitch and calculates a fluctuation period of the unsteady bulging based on the unsteady bulging occurrence roll pitch and the casting speed.

[0004] Such a mold level control device for a continuous casting machine disclosed in Patent Document 1 estimates disturbances using a disturbance estimation unit (disturbance estimation observer). At this estimation stage, the estimation of the disturbance is not based on the casting length, and the disturbance estimation observer itself has dynamic characteristics, so that a phase lag occurs in the estimated disturbance. For this reason, even if the frequency (or period), amplitude, and phase of the disturbance based on the slab length are accurately obtained, the phase lag occurs and the amplitude becomes small, making it impossible to obtain the phase and amplitude accurately.

[0005] On the other hand, the molten metal level control device disclosed in Patent Document 2 detects the molten metal level in the mold of the continuous casting machine, determines the deviation between the detected molten metal level and a predetermined target level, calculates an amount of change in the opening of the inlet of the molten metal into the mold based on the determined deviation, changes the opening in accordance with the calculated amount of change, and controls the molten metal level to be kept at the target level. The device is equipped with a frequency detection unit that detects the frequency of periodic level fluctuations contained in the molten metal level, an oscillator that oscillates a signal at the frequency detected by the frequency detection unit, a phase / amplitude calculation unit that calculates a phase and amplitude so as to cancel out the periodic level fluctuation, and an adder that adds a signal oscillated by the oscillator and having the phase and amplitude calculated by the phase / amplitude calculation unit to the calculated amount of change to correct the amount of change in the opening.

[0006] The molten metal level control device for a continuous casting machine disclosed in Patent Document 2 adds a signal separate from the feedback control, and therefore may be able to suppress high-frequency disturbances and disturbances of multiple frequencies that are difficult to control with feedback control. However, Patent Document 2 detects only the frequency of fluctuations "contained in the signal of the molten metal level," and does not include the frequency of fluctuations in the manipulated variable or the frequency of fluctuations in the opening degree of the flow regulator. Therefore, if the disturbances are suppressed and the vibration-related level fluctuations disappear, the molten metal level control device for a continuous casting machine disclosed in Patent Document 2 cannot be applied. In addition, there is a possibility that the level fluctuations caused by the manipulated variable may be recognized as level fluctuations caused by the disturbance. In other words, the influence of the manipulated variable is not taken into consideration. [Prior art documents] [Patent documents]

[0007] [Patent Document 1] JP 2011-143414 A [Patent Document 2] JP 2002-059249 A Summary of the Invention [Problem to be solved by the invention]

[0008] Conventionally, there have been the following problems with controlling the molten metal level. The first problem is the limit of feedback control. Since the control target in controlling the molten metal level is an integral system, there is a phase delay of 90 degrees. For this reason, in feedback control, it is necessary to advance the phase and increase the gain at the frequency of the fluctuation in the molten metal level caused by bulging. This makes it possible to suppress disturbances of a specific frequency, but it has been confirmed that in order to ensure stability, the control band is narrowed. For this reason, it is difficult to respond when disturbances of multiple frequencies are applied, when the frequency changes, or when high-frequency disturbances are applied.

[0009] There are two possible countermeasures. The first countermeasure is to sacrifice the control band to narrow it, and suppress disturbances at specific frequencies, but it becomes more difficult to suppress disturbances at low frequencies. The second countermeasure is to ensure a wide control band and suppress disturbances at low frequencies, but there is a limit to how much disturbance suppression at specific frequencies can be achieved.

[0010] This second measure (method) was able to keep the fluctuations in the molten metal level small by mainly suppressing the low-frequency disturbances, even when multiple frequency disturbances were applied, the frequency changed, or a high-frequency disturbance was applied. However, it was not possible to suppress the disturbances caused by bulging to nearly zero, and there is a need to address the recent tightening of quality standards and the need to ensure production capacity.

[0011] The present invention has been made in consideration of the above-mentioned circumstances, and an object of the present invention is to provide a molten metal level control device and a molten metal level control method that can suppress periodic bulging disturbances while maintaining a wide control band of feedback control. [Means for solving the problem]

[0012] As a result of various investigations, the present inventors have found that the above object can be achieved by the present invention described below. That is, a mold level control device according to one embodiment of the present invention is a device that controls the mold level of a continuous casting machine by controlling an adjustment device that adjusts the amount of molten steel supplied to a mold of the continuous casting machine using feedback control, and includes an FF compensation unit that calculates a feedforward compensation amount consisting of sine wave components having an amplitude, period and phase for canceling out disturbances applied to the mold level, based on the mold level, an operation amount of the adjustment device, and a transfer function of the continuous casting machine related to the mold level, and an adder that adds the feedforward compensation amount calculated by the FF compensation unit to the feedback compensation amount of the feedback control when controlling using the feedback control. When the mold level and the operation amount of the adjustment device are a plurality of values ​​that are arranged in a time domain in a chronological order at predetermined time intervals, the FF compensation unit converts each value of the mold level and the operation amount of the adjustment device in the time domain into each value in a spatial domain having a coordinate axis in the longitudinal direction of a slab produced by the continuous casting machine, and converts the transfer function from the time frequency domain to the spatial frequency domain before calculating the feedforward compensation amount.

[0013] Since this type of molten metal level control device determines not only the amplitude and period but also the phase in order to cancel out the disturbance, it is possible to suppress fluctuations in the molten metal level due to the disturbance by feedforward compensation. Since the above-mentioned molten metal level control device adds a feedforward compensation amount to the feedback compensation amount, it is unlikely to affect the feedback control, and therefore the feedback control band can be maintained wide. Therefore, the above-mentioned molten metal level control device can suppress periodic bulging disturbances while maintaining a wide control band of the feedback control.

[0014] In the above-mentioned molten metal level control device, when the molten metal level and the operation amount of the adjustment device are a plurality of values ​​arranged in a time domain in a chronological order at a predetermined time interval, the FF compensation unit converts each value of the molten metal level and the operation amount of the adjustment device in the time domain into each value in a spatial domain having a coordinate axis in the longitudinal direction of the slab produced by the continuous casting machine, and converts the transfer function from the time frequency domain to the spatial frequency domain, and then calculates the feedforward compensation amount.

[0015] When the casting speed is changed, the intervals between the values ​​on the slab are also changed in the time domain, which affects the casting speed. Since the above-mentioned molten metal level control device changes from the time frequency domain to the spatial frequency domain, it is possible to appropriately determine the feedforward compensation amount without being affected by such an effect, and to appropriately control the molten metal level.

[0016] In another aspect, in the above-mentioned molten metal surface level control device, the FF compensation unit obtains a plurality of the sine wave components for a plurality of frequencies different from each other, obtains an amount of cancellation of the disturbance for each of a first phase of a first sine wave component having a peak from among the plurality of sine wave components, a second phase of a second sine wave component on the low frequency side relative to the first sine wave component, and a third phase of a third sine wave component on the high frequency side relative to the first sine wave component, and selects, from the first to third phases, the phase that cancels out the disturbance the most as the phase of the feedback compensation amount.

[0017] The feedforward compensation amount may be composed of a first sine wave component having a peak, but the first sine wave component may have an opposite phase to a desired phase for canceling the disturbance. The above-mentioned molten metal level control device selects the phase that best cancels the disturbance from among the first to third phases of the first to third sine wave components as the phase of the feedforward compensation amount, so that a more appropriate phase can be selected. The above-mentioned molten metal level control device can handle even when disturbances of multiple frequencies are applied. For example, when peaks are adjacent to each other, the phase also changes significantly near the frequency of the adjacent peaks, but the above-mentioned molten metal level control device can select an appropriate phase by determining the phase that cancels the disturbance by calculating the amount of cancellation of the disturbance.

[0018] In another aspect, the above-mentioned molten metal surface level control device further includes a gain type changing unit that changes the gain of the feedback control to be smaller than a current value when the absolute value of the rate of the manipulated variable of the adjustment device is larger than a predetermined first threshold, and changes the gain of the feedback control to be larger than the current value when the absolute value of the rate of the manipulated variable of the adjustment device is smaller than a predetermined positive second threshold that is smaller than the first threshold.

[0019] Such a molten metal level control device can perform feedback control with an appropriate gain according to the absolute value of the rate of the manipulated variable of the adjusting device, and can control the molten metal level within the rate limit (within the operating speed) of the actuator that drives the valve. Also, the above-mentioned molten metal level control device can prevent the control system from becoming unstable due to modeling errors, etc.

[0020] In another aspect, in the above-mentioned molten metal level control devices, feedforward compensation is performed in a time-frequency domain that is lower than the time frequency at which the phase difference of the modeling error of the controlled object is π / 3 and lower than the time frequency of the surface wave of the molten metal surface in the mold.

[0021] In such a mold level control device, the feedforward compensation is robust against modeling errors.

[0022] A method for controlling a molten steel level according to one aspect of the present invention is a method for controlling the molten steel level of a continuous casting machine by controlling, using feedback control, an adjustment device that adjusts the amount of molten steel supplied to a mold from a tundish of the continuous casting machine. The method includes an FF compensation step of determining a feedforward compensation amount composed of a sine wave component having an amplitude, period and phase for canceling out a disturbance applied to the molten steel level, based on the molten steel level, an operation amount of the adjustment device, and a transfer function of the continuous casting machine related to the molten steel level, and an adding step of adding the feedforward compensation amount determined in the FF compensation step to the feedback compensation amount of the feedback control when controlling using the feedback control. When the molten steel level and the operation amount of the adjustment device are a plurality of values ​​that are arranged in a time domain in a chronological order at predetermined time intervals, the FF compensation step converts each value of the molten steel level and the operation amount of the adjustment device in the time domain into each value in a spatial domain having a coordinate axis in the longitudinal direction of a slab produced by the continuous casting machine, and converts the transfer function from the time frequency domain to the spatial frequency domain before determining the feedforward compensation amount.

[0023] In this type of molten metal level control method, not only the amplitude and period but also the phase are calculated to cancel out the disturbance, so that the molten metal level fluctuations caused by the disturbance can be suppressed by feedforward compensation. Since the above-mentioned molten metal level control method adds a feedforward compensation amount to the feedback compensation amount, it is unlikely to affect the feedback control, so that the feedback control band can be maintained wide. Therefore, the above-mentioned molten metal level control method can suppress periodic bulging disturbances while maintaining a wide control band of the feedback control. Since the above-mentioned molten metal level control method changes from the time frequency domain to the spatial frequency domain, it is possible to properly calculate the feedforward compensation amount without being affected by such influences, and the molten metal level can be properly controlled. Effect of the Invention

[0024] The molten metal level control device and molten metal level control method according to the present invention can suppress periodic bulging disturbances while maintaining a wide control band of feedback control. [Brief description of the drawings]

[0025] [Figure 1] FIG. 1 is a schematic diagram showing a configuration of a continuous casting machine in an embodiment. [Diagram 2] FIG. 2 is a block diagram of the continuous casting machine relating to control of the molten metal surface level. [Diagram 3] 3 is a block diagram showing a configuration of an FB compensator shown in FIG. 2. [Figure 4] 1 is a graph showing a Bode diagram and a frequency shaping result of an FB compensator including a PID control unit and a second-order filter unit, the Bode diagram being obtained by solving a mixed sensitivity problem of the FB compensator. [Diagram 5] 1 is a graph showing a Bode plot and a frequency shaping result of an H∞ controller obtained by solving a mixed sensitivity problem in the H∞ controller. [Figure 6] 1 is a lookup table showing each parameter in the FB compensator for each Kf / A and each gain type. [Figure 7] FIG. 13 is a diagram for explaining an example of an interpolation technique for each parameter Kp in the FB compensator. [Figure 8] FIG. 1 is a diagram for explaining a transformation from the time domain to the spatial domain. [Figure 9] As an example, this figure shows the results of a simulation of a value (a value equivalent to a disturbance manipulated variable) obtained by back-calculating an unknown disturbance to a manipulated variable. [Figure 10] FIG. 13 is a diagram illustrating a gain for reducing the amount of feedforward compensation for high-frequency disturbance. [Figure 11] 4 is a flowchart showing the operation of the molten metal surface level control device in the embodiment. [Figure 12] 12 is a flowchart showing a process for calculating a feedforward compensation amount shown in FIG. 11. [Figure 13]FIG. 13 is a diagram showing a simulation result in the case of a constant casting speed. [Figure 14] FIG. 13 shows simulation results for the case of variable casting speed. [Figure 15] FIG. 13 is a diagram showing a simulation result in a comparative example. [Figure 16] FIG. 13 is a diagram showing a simulation result when modeling error is taken into consideration. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0026] Hereinafter, one or more embodiments of the present invention will be described with reference to the drawings. However, the scope of the invention is not limited to the disclosed embodiments. In addition, configurations with the same reference numerals in each drawing indicate that they are the same configurations, and their description will be omitted as appropriate. In this specification, when referring to a general term, a reference numeral without a subscript is used, and when referring to an individual configuration, a reference numeral with a subscript is used.

[0027] The molten steel level control device in the embodiment is a device that controls the molten steel level of the continuous casting machine by controlling a valve that adjusts the amount of molten steel supplied from a tundish of the continuous casting machine to a mold using feedback control. In the present embodiment, the molten steel level control device further includes an FF compensation unit that calculates a feedforward compensation amount consisting of a sine wave component having an amplitude, a period, and a phase for canceling a disturbance applied to the molten steel level based on the molten steel level, the valve opening or operation amount of the valve, and a transfer function of the continuous casting machine related to the molten steel level, and an adder that adds the feedforward compensation amount calculated by the FF compensation unit to the feedback compensation amount of the feedback control when controlling using the feedback control. That is, the molten steel level control device in the embodiment controls the molten steel level by adding a feedforward compensation amount for canceling a disturbance to the feedback compensation amount. Such a molten steel level control device will be described in more detail below.

[0028] Fig. 1 is a schematic diagram showing the configuration of a continuous casting machine in an embodiment, and Fig. 2 is a block diagram of the continuous casting machine relating to control of the molten metal level.

[0029] A continuous casting machine CM in which the molten metal level is controlled by the molten metal level control device CT in the embodiment includes, for example, a tundish TD, a mold MD, and multiple sets of rolls RL, which are arranged in this order from the upstream side to the downstream side, as shown in FIG.

[0030] The tundish TD is a device into which molten steel flows from a ladle (not shown) and into which predetermined inclusions are removed by floating up and being separated. The ladle is a device into which molten steel after secondary refining, in which the composition has been finely adjusted, is poured and which stores the molten steel, and is disposed at the top. Note that in the ladle as well, some of the inclusions are removed by floating up and being separated. The tundish TD is disposed next to the ladle.

[0031] A through hole is formed in the bottom of the tundish TD, and a nozzle NZ is attached to the through hole for guiding the molten steel to the mold MD. A valve VL for adjusting the amount of molten steel supplied from the tundish TD to the mold MD is attached to the nozzle NZ. The valve VL is, for example, a slide valve. An actuator AC for driving the valve VL is provided on the valve VL. The actuator AC is, for example, a stepping cylinder. Although the valve VL is used in the example shown in FIG. 1, other devices capable of adjusting the flow rate of molten steel and obtaining a transfer function, such as a stopper, may be used.

[0032] The mold MD is a device into which the molten steel flows from the tundish TD through a nozzle NZ, and the molten steel is cooled to form a cast slab Ob of a predetermined shape. The mold MD is water-cooled, and the molten steel that comes into contact with the mold MD is solidified from the outside to form a relatively thin solidified shell, which is then formed into the cast slab Ob of the predetermined shape. The mold MD is disposed next to the tundish TD.

[0033] A level measuring unit 1 is provided near the mold MD to measure the height of the surface of the molten steel in the mold (molten steel level). The level measuring unit 1 is, for example, an eddy current sensor. In controlling the molten steel level, a height value with a vertical upward direction as positive is used as the molten steel level. The level measuring unit 1 outputs the measured molten steel level to the molten steel level control device CT as a controlled variable y (y(s)). The molten steel level control device CT generates an operation variable u (u(s)) based on the molten steel level (controlled variable y) and other factors, as described below, and outputs the operation variable u to the actuator AC. The actuator AC drives the valve VL so that the valve opening v (v(s)) corresponds to the operation variable u. This adjusts the cross-sectional area of ​​the flow path of the molten steel flowing through the nozzle NZ, adjusts the amount of molten steel supplied from the tundish TD to the mold MD, and controls the molten steel level.

[0034] The rolls (rollers) RL are devices that support the slab Ob while drawing the slab Ob from the mold MD at a variable speed (casting speed). The rolls RL are arranged in pairs so as to contact both sides of the slab Ob, and are arranged at predetermined intervals from the upstream side to the downstream side at the next stage of the mold MD. The predetermined intervals may be equal or may be unequal, for example, wider on the downstream side than on the upstream side. The multiple sets of rolls RL are arranged so that the casting direction (drawing direction) is oriented from the vertical direction to the horizontal direction. The multiple sets of rolls RL are configured to include one or more driving rolls and multiple driven rolls.

[0035] The continuous casting machine CM is further equipped with various known sensors (not shown), such as a sensor for determining the mass of molten steel in the tundish, a sensor for determining the mold width, and a sensor for determining the casting speed.

[0036] It has been confirmed that when bulging occurs in such a continuous casting machine CM, its period is (roll pitch at the location where bulging occurs) / (casting speed). Therefore, in the time domain, the bulging period [s] is inversely proportional to the casting speed. On the other hand, in the spatial domain where the slab is fixed, the period [m] is the value of the roll pitch and is independent of the casting speed.

[0037] In a block diagram, for example as shown in FIG. 2, the continuous casting machine CM for controlling the molten metal level comprises a molten metal level control device CT, an actuator AC, and a block VL_MD_1 which brings together a valve VL, a mold MD, and a level measurement unit 1, and the molten metal level control device CT comprises a subtractor 10, an FB compensator 11, an FF compensator 12, and an adder 13.

[0038] The molten metal level control device CT is configured with, for example, a computer (including a PLC (Programmable Logic Controller)) equipped with a CPU (Central Processing Unit), a memory, an input / output interface, and these peripheral circuits, and the subtractor 10, the FB compensator 11, the FF compensator 12, and the adder 13 are functionally configured in the CPU by executing a predetermined program. The memory includes, for example, a ROM (Read Only Memory) which is a non-volatile memory element, an EEPROM (Electrically Erasable Programmable Read Only Memory) which is a rewritable non-volatile memory element, and a RAM (Random Access Memory) which is a so-called working memory of the CPU for storing data generated during program execution. The input / output interface inputs and outputs predetermined data between various sensors and devices higher than the molten metal level control device CT.

[0039] The subtractor 10 receives the target value of the molten metal surface level and the controlled variable y(s), calculates the deviation (difference) between these target values ​​and the controlled variable y(s), and outputs the calculated deviation to the FB compensator 11.

[0040] The FB compensator 11 determines a feedback compensation amount according to the deviation input from the subtractor 10 as described below, and outputs the determined feedback compensation amount to the adder 13 .

[0041] The FF compensator 12 determines a feedforward compensation amount consisting of a sine wave component having an amplitude, period and phase for canceling out a disturbance applied to the molten metal level based on the molten metal level, the valve opening degree of the valve VL, and a transfer function of the continuous casting machine CM related to the molten metal level, as described below, and outputs the determined feedforward compensation amount to an adder 13.

[0042] When performing control using feedback control, the adder 13 adds the feedforward compensation amount calculated by the FF compensation unit 12 to the feedback compensation amount of the feedback control input from the FB compensator 11, and outputs the sum to the actuator AC, which is a stepping cylinder AC in this embodiment.

[0043] A stepping cylinder AC as an example of an actuator AC drives a valve VL, a slide valve VL in this embodiment, so that the valve opening v(s) corresponds to the manipulated variable u(s). This adjusts the cross-sectional area of ​​the flow path of the molten steel flowing through the nozzle NZ, adjusts the amount of molten steel supplied from the tundish DT to the mold MD, and controls the molten steel level. This molten steel level is measured by a level measuring unit 1. At this time, when a disturbance d(s) is applied (superimposed) to the molten steel level, the molten steel level influenced by the disturbance d(s) is measured as a controlled variable y(s) by the level measuring unit 1. This measured controlled variable y(s) is input to a subtractor 10 of the molten steel level control device CT. Here, the disturbance d(s) is originally applied before the level measuring unit 1, but in FIG. 2, the value after passing through the level measuring unit 1 is taken as the disturbance d(s).

[0044] In the block diagram of the continuous casting machine CM regarding such control of the molten metal level, the transfer function P(s) in the block of controlled objects consisting of the actuator AC, valve VL, mold MD and level measurement unit 1 is expressed as in the following equation 1.

[0045]

number

[0046] Here, T SC is the time constant of the stepping cylinder AC (time constant of the actuator AC), and L SC is the dead time of the stepping cylinder AC (dead time of the actuator AC), and K f is the flow coefficient [m 2 / s] (the amount of molten steel flowing per unit time [m 3 / s]), A is the cross-sectional area of ​​the mold MD, and T CD is the time constant of the level measuring unit 1, which is the eddy current sensor 1 in this embodiment, and L CD is the dead time of the level measuring unit 1 (eddy current sensor 1). SC = 0.2 [s], T CD =0.3[s], L SC =0.1[s], L CD = 0.12 [s]. Of course, T SC , T CD , L SC and L CD The values ​​of the flow coefficient K are changed according to the continuous casting machine CM. f The cross-sectional area A of the mold MD varies depending on the casting conditions. For example, the range is 0.6 <K f / A<2.1. f / A can be calculated from the mass of molten steel in the tundish, the width of the mold, and the casting speed by a known calculation method. The calculation method is disclosed, for example, in "Akira Murakami, Yoshiharu Nishida, Naoji Miki, Toru Matsuura, and Masaru Nakao, "H∞ Control of Molten Steel Level in a Continuous Casting Machine," Journal of the Institute of Systems Control and Information Engineers, Vol. 10, No. 11, pp. 607-615, 1997" (Reference 1).

[0047] Feedforward compensation is used for known disturbances, such as changes in casting speed, changes in tundish molten steel mass, and changes in mold width. If necessary, it is also possible to consider changes in the molten steel level SV. A specific method is disclosed in JP 2014-200830 A. Even during unsteady conditions such as changes in casting speed, level fluctuations can be suppressed for known disturbances. Note that the amount of feedforward compensation for the known disturbances is added as a part of the manipulated variable, but is omitted from the drawings and formulas in the following description of the embodiments.

[0048] Transfer function P from valve opening v(s) to molten metal level y(s) v2l (s) is expressed as follows in Equation 2.

[0049]

number

[0050] On the other hand, as described above, since the value after passing through the level measurement unit 1 (eddy current sensor 1) is regarded as the disturbance d(s), the molten metal surface level y(s) is expressed by the following equation 3, and by rearranging the equation, the disturbance d(s) becomes the following equation 4.

[0051]

number

[0052]

number

[0053] The value obtained by back-calculating the unknown disturbance d(s) to the manipulated variable u(s) (hereinafter referred to as the "disturbance manipulated variable equivalent value") u d (s) is expressed as follows:

[0054]

number

[0055] The compensation amount (feedforward compensation amount) ff to cancel this unknown disturbance dist (s) is basically the disturbance control amount equivalent value u d The FF compensator 12 uses this feedforward compensation amount ff dist (s) is required.

[0056]

number

[0057] Here, the manipulated variable u(s) means a value equivalent to the output of the position type mold level control device CT that controls the stepping cylinder AC, etc., and is the sum of the compensation amounts such as the feedback compensation amount and the feedforward compensation amount. If the mold level control device CT is of the velocity type, the manipulated variable u(s) is the integrated or added value of the sum of the feedback compensation rate, the feedforward compensation rate, etc.

[0058] In addition, the valve opening v(s) is replaced by the operation amount u(s), and the transfer function P v2l Instead of (s), a transfer function P(s) may be used.

[0059] The amount of feedback compensation determined by the FB compensator 11 and the amount of feedforward compensation determined by the FF compensator 12 will be described in more detail below.

[0060] (Calculation of feedback compensation amount) Fig. 3 is a block diagram showing the configuration of the FB compensator shown in Fig. 2. Fig. 4 is a graph showing a Bode diagram of the FB compensator obtained by solving a mixed sensitivity problem in the FB compensator having a PID control unit and a second-order filter unit, and a frequency shaping result. In this example, the mixed sensitivity problem for additive uncertainty in Reference 1 is used. Fig. 5 is a graph showing a Bode diagram of the H∞ controller obtained by solving a mixed sensitivity problem in the H∞ controller, and a frequency shaping result.

[0061] The FB compensator 11 includes a PID control unit 111 and a filter unit 112, for example, as shown in FIG.

[0062] The PID control unit 111 executes PID control including at least P control based on the deviation between the target value input from the subtractor 10 and the controlled variable y(s). More specifically, the PID control unit 111 executes any one of P control, PI control, PD control, and PID control. The PID control unit 111 outputs its output to the filter unit 112. The PID control unit 111 may be a proportional-leading type, a differential-leading type, or the like. Furthermore, the PID control unit 111 may have an imperfect differential, or may have a filter for noise removal. The frequency at which control is performed is, for example, from frequency 0 to the Nyquist frequency in digital control.

[0063] The filter unit 112 adjusts the gain and phase. Examples of the filter unit 112 include a first-order filter (a filter expressed by a first-order rational expression) and a second-order filter (a filter expressed by a second-order rational expression). The filter unit 112 outputs its output to the adder 13 as a feedback compensation amount.

[0064] As an example, when the filter unit 112 is a second-order filter, the transfer function K(s) of the FB compensator 11 is expressed by the following equation F1.

[0065]

number

[0066] The transfer function K(s) is the transfer function K of the PID control unit 111 shown in the formula F1. PID (s) and the transfer function of the second-order filter unit 112. The PID control unit 111 has three parameters (K P , T I , T D), and the filter unit 112 has four parameters (a1, a2, b1, b2). The FB compensator 11 determines these seven parameters, not in a linear form, but by solving a mixed sensitivity problem using an optimization method, for example, in the following manner, taking into consideration the balance between robust stability and disturbance suppression.

[0067] Solving a mixed sensitivity problem using an optimization technique means, for example, finding the minimum value of an evaluation function represented by predetermined variables that is included in a weighting function constituting the mixed sensitivity problem, under constraints such as the mixed sensitivity problem.

[0068] Let frequency be f min (=0.001) [Hz] to f max (=10) [Hz], logarithmically spaced N ω (=200) points, frequency variable f i (i=1,...,N ω ) is set. When digital control is performed, the controlled frequency ranges from 0 to the Nyquist frequency, but in this example, the sampling period is set to 0.1 [s]. Therefore, the frequency ranges from 0 [Hz] to the Nyquist frequency of 5 [Hz]. The lower limit frequency is set to a small value of 0.001 [Hz] because it cannot be set to 0 logarithmically. The upper limit frequency is set to a large value of 10 [Hz] near the Nyquist frequency. The frequency f i is multiplied by 2π to obtain the angular frequency variable ω i (i=1,...,N ω )

[0069] The evaluation function J to be minimized is W1H The evaluation function J in formula F2 is set as the weighting function W of the mixed sensitivity problem expressed by formulas F3 and F4. 1H (s), W 2H This is a function that maximizes the frequency band of disturbance suppression by making the gain of (s) as large as possible.

[0070]

number

[0071]

number

[0072]

number

[0073] As a constraint condition at each angular frequency, the norm constraint of the mixed sensitivity problem is expressed as the following formula F5. Here, σ() indicates the maximum singular value. This formula F5 is converted to dB to ensure accuracy during optimization calculation, and becomes the constraint condition of the following formula F6.

[0074]

number

[0075]

number

[0076] The subscript "H" indicates a high gain type, and similar calculations will be performed later for the middle gain type "M" and the low gain type "L".

[0077] In addition, when substituting formula F3 and formula F4 into formula F5 or formula F6, W 1H (s) is substituted into W1(s), and W 2H (s) is substituted into W2(s). Similar calculations are performed for the middle gain type and low gain type described below.

[0078] Here, the parameters of the PID control unit 111 are, in order to achieve negative feedback, K p >0, T I >0, TD≧0 are essential. This optimization problem is non-convex and may fall into a local solution, so in order to make it easier to converge, a constraint condition like the following equation F7 was set for each variable. Note that K p >0, TI Constraints other than the constraints TD > 0 and TD ≥ 0 are provided for convenience in order to avoid falling into a local solution, and are not essential. For example, in the multi-start local search method of this example, an optimal solution can be found without any convenient constraints by increasing the number of initial values ​​tried during optimization.

[0079]

number

[0080] The last two equations in the constraint condition equation F7 impose restrictions on the damping coefficient of the filter unit 112. That is, the last two equations are set in order to search for an optimal value in a region where the zeros and poles are unlikely to be oscillatory and are unlikely to approach the imaginary axis.

[0081] For example, a multi-start local search method is used as the optimization method, and the initial value is tried at multiple points, and the optimization result from the initial value that does not fall into a local solution is adopted. The initial value is K W1H = 0.1, K P =0.2, T I =17.6, T D = 1.0, a1 = 1.0, a2 = 1.0, b1 = 1.0, b2 = 1.0. Here, K f / A was set to 0.6 (K f / A=0.6).

[0082] The optimization problem is to find the minimum value of the evaluation function J in formula F2 under the constraints of formulas F6 and F7. By using a publicly available nonlinear optimization method (for example, the fmincon function in the "Optimization Toolbox" (registered trademark) of The MathWorks, Inc.), W1H =0.559485, K P =1.031486, T I =17.579967, T D The results obtained were: =0.0, a1=0.604110, a2=0.229163, b1=0.495033, b2=0.074074.

[0083] The PID control unit 111 calculates the differential time T D is 0, which is essentially PI control. The Bode diagram and frequency shaping result of the FB compensator 11 using this result are shown in FIG. 4. Meanwhile, for comparison, the Bode diagram and frequency shaping result of the H∞ controller obtained by solving the mixed sensitivity problem are shown in FIG. 5. The calculation method of this H∞ controller is disclosed in, for example, the above-mentioned document 1. Comparing FIG. 4 with FIG. 5, it can be seen that the FB compensator 11 has almost the same performance as the H∞ controller.

[0084] The FB compensator 11 thus obtained is designed in advance in such a way that its control characteristics change continuously in order to adapt to the change in the continuous casting machine CM, and a plurality of them are stored in the memory. For example, f Each FB compensator 11 is obtained by changing / A from 0.6 to 2.1 in increments of 0.1. f Depending on / A, real numbers from 1 (1.0) to 16 (16.0) are assigned in order, and these are called FB compensator numbers. f When / A=0.6, the FB compensator number is 1 (1.0), and K f When / A=2.1, the FB compensator number is 16 (16.0). In the above example, K f A high-gain type FB compensator 11 was obtained with / A=0.6, but a middle-gain type FB compensator 11 with a lower gain than the high-gain type FB compensator 11 is also obtained, and a low-gain type FB compensator 11 with a lower gain than the middle-gain type FB compensator 11 is also obtained. Therefore, the FB compensator 11 has a gain of K f There are 16 types of / A and 3 types of gain type, making a total of 48 types, which are shown in the following table 1. In this table 1, high gain types are represented by "H", middle gain types are represented by "M", and low gain types are represented by "L".

[0085] [Table 1]

[0086] The above result is the FB compensator 11 for H1, so the FB compensators 11 for the remaining H2 to H16 are similarly obtained.

[0087] The middle gain type FB compensator 11 can be similarly obtained by using the following equations F8 to F10 instead of the above equations F2 to F4. W1M as small as possible, and as a result, the weighting function W 1M By increasing the gain of (s), the evaluation function maximizes the frequency band of disturbance suppression. When substituting formulas F9 and F10 into formulas F5 and F6, W 1M (s) is substituted into W1(s), and W 2M (s) is substituted into W2(s).

[0088]

number

[0089]

number

[0090]

number

[0091] The low-gain type FB compensator 11 can be similarly obtained by using the following equations F11 to F13 instead of the above-mentioned equations F2 to F4. W1L as small as possible, and as a result, the weighting function W 1L By increasing the gain of (s), the evaluation function maximizes the frequency band of disturbance suppression. When substituting formulas F12 and F13 into formulas F5 and F6, W 1L (s) is substituted into W1(s), and W 2L (s) is substituted into W2(s).

[0092]

number

[0093]

number

[0094]

number

[0095] Figure 6 shows the f FIG. 6A is a lookup table showing the parameters of the FB compensator for each K / A and gain type. f Parameter K by / A and gain type p 6B is a lookup table showing the values ​​of K f / A and gain type specific parameters T I FIG. 6C is a lookup table showing the values ​​of K f FIG. 6D is a lookup table showing the values ​​of the parameter b1 for each / A and gain type. f FIG. 6E is a lookup table showing the values ​​of the parameter b2 for each / A and gain type. f FIG. 6F is a lookup table showing the values ​​of the parameter a1 for each / A and gain type. f This is a lookup table showing the values ​​of the parameter a2 for each / A and gain type. D is omitted since it is 0.0.

[0096] The parameters K of the 48 types of FB compensators 11 obtained in this way P , T I , a1, a2, b1, b2 are shown in the form of a look-up table in FIG. 6. For example, the FB compensator 11 of M2 is P =0.435, T I=11.608, a1 =0.49, a2 =0.159, b1 =0.517, b2 =0.078. The look-up table shown in Fig. 6 is stored in the memory of the molten metal level control device CT.

[0097] In this embodiment, as shown in FIG. 2, the FB compensator 11 is configured to control the FB compensator 11 by a system (higher system) SY that is higher than the FB compensator 11. f The value of / A and the value of the gain type are given to specify and configure the FB compensator 11. For this reason, a high gain type H is defined as 1.0, a middle gain type M is defined as 2.0, and a low gain type L is defined as 3.0, so that the gain type can be continuously changed from 1.0 to 3.0.

[0098] The host system SY may be a system configured within the molten metal level control device CT, or may be a system configured outside the molten metal level control device CT. In the example shown in Fig. 2, the host system SY is a system configured within the molten metal level control device CT. In this embodiment, the host system SY changes the gain of the feedback control to be smaller than the current value when the absolute value of the rate of the operation amount of the valve VL is larger than a predetermined first threshold, and changes the gain of the feedback control to be larger than the current value when the absolute value of the rate of the operation amount of the valve VL is smaller than a predetermined positive second threshold smaller than the first threshold. The host system SY corresponds to an example of a gain type changing unit.

[0099] The lookup table shown in Figure 6 shows the K f / A, so K given by the higher-level system SY f If the value of / A and the value of the gain type are not in the lookup table shown in Figure 6, the K fThe FB compensator 11 corresponding to the value of / A and the value of the gain type is generated by interpolation from the lookup table shown in Fig. 6. For this interpolation, for example, the "nD Lookup Table" block of "Simulink" (registered trademark) of The MathWorks, Inc. can be used. As settings of this block, the number of dimensions of the table is set to "2", and "linear point and slope" is set as the interpolation method. As a method similar in principle, the interpolation is performed as follows.

[0100] FIG. 7 shows an example of each parameter K p For example, when the gain type is 1.4 and K f Assume that / A is 0.72. Gain type=1.4 is between gain type 1 (i.e., high gain type H) and gain type 2 (i.e., middle gain type M) with a ratio of 0.4:0.6, as shown in FIG. f / A=0.72 is between the FB compensator 11 (*2) with FB compensator number 2 and the FB compensator 11 (*3) with FB compensator number 3 at a ratio of 0.02:0.08=0.2:0.8 (* indicates either H, M, or L). p The value of is H2 (gain type = 1, K f / A=0.7) 0.928, H3 (Gain Type=1, K f / A=0.8) 0.845, M2 (Gain Type=2, K f / A=0.7) 0.435, M3 (Gain Type=2, K f / A=0.8) is between 0.396.

[0101] First, TMP1 is determined at the point where H2 and M2 are divided internally at a ratio of 0.4:0.6. p The value of is (0.4 0.435 + 0.6 0.928) = 0.731. Next, TMP2 is found at the point where H3 and M3 are divided internally at 0.4:0.6. pThe value of is (0.4 0.396 + 0.6 0.845) = 0.665. RESULT is then found at the point where TMP1 and TMP2 are divided internally at a ratio of 0.2:0.8. p The value of RESULT is (0.2 0.665 + 0.8 0.731) = 0.718. This RESULT value is the K p The other parameters T I , a1, a2, b1, and b2 can also be obtained by interpolation in the same way. In this case, the FB compensator number is 2.2.

[0102] This allows K f Based on the real value of / A and the real value of the gain type, the FB compensator 11 can be formed with continuously changing control characteristics. Then, the feedback compensation amount is calculated from the deviation of the molten metal surface level (the difference between the target value and the controlled amount y).

[0103] (Calculation of feedforward compensation amount) FIG. 8 is a diagram for explaining the conversion from the time domain to the space domain. The feedforward compensation amount is calculated based on the molten metal level (control amount y), the valve opening v (or the operation amount u) of the valve VL, and the transfer function of the continuous casting machine CM related to the molten metal level. Since the molten metal level y and the valve opening v (or the operation amount u) are sampled at a predetermined time interval, they become a plurality of values ​​arranged in a time series at a predetermined time interval in the time domain, and are a function of a past time t' (t'≧0. For example, if it is 1.0 [s] ago, t'=1.0.) indicating how many seconds ago it was, with the present being 0. For example, as shown in FIG. 8A, the values ​​of the molten metal level y and the valve opening v (or the operation amount u) at time 0 [s] are values ​​at the current molten metal level, and the values ​​of the molten metal level y and the valve opening v (or the operation amount u) at past time t' [s] are values ​​at a position in the slab Ob that is x' away from the current molten metal level. The following will describe the case of the valve opening v, but the same explanation can be given for the case of the operation amount u. If the casting speed is constant, the values ​​of the molten metal level y and the valve opening v are arranged at equal intervals on the slab Ob, so that the feedforward compensation amount can be obtained in this time domain. However, since the casting speed is variable, the FF compensator 12 first converts the values ​​of the molten metal level and the valve opening v of the valve VL in the time domain into values ​​in the spatial domain having coordinate axes in the longitudinal direction of the slab Ob produced by the continuous casting machine CM, as shown in FIG. 8C. This is because bulging is considered to occur at a substantially constant frequency or period in the spatial domain.

[0104] More specifically, first, the values ​​of the molten metal level y and the valve opening v in the time domain are associated with positions on the slab Ob. For example, the position x'(t') on the slab Ob at time t' can be found by integrating the casting speed Vc(t) (where t means a time t [s] before the past, t≧0) from the current time 0 to the past time t' (t'≧0) (x'(t')=∫Vc(t)dt, where the integral ∫ is from 0 to t'). Since Vc(t)≧0, x'(t')≧0.

[0105] Next, as shown in Fig. 8B, N positions X'(i) (i = 0,1,...,N-1) on the slab Ob that are equally spaced on the coordinate axis X' along the longitudinal direction of the slab Ob, with the current molten metal level position X'(0) as the coordinate origin, are associated with the values ​​of the molten metal level y in the time domain and the valve opening v. Depending on the relationship between the casting speed Vc, the sampling period, and the number of past data points to be stored in the memory, there may be cases where the values ​​of the molten metal level y and the valve opening v in the time domain corresponding to the position X'(i) (i = 0,1,...,N-1) do not exist. In this case, the values ​​of the molten metal level Y'(i) (i = 0,1,...,N-1) and the valve opening V'(i) (i = 0,1,...,N-1) in the spatial domain corresponding to the position X'(i) (i = 0,1,...,N-1) are found by interpolation or extrapolation.

[0106] Specifically, it is as follows: When the position X'(i) is monotonically increasing, the time t X’i '(t X’i '≧0) is calculated by interpolation or extrapolation. X’i At this time t X’i The time t' does not necessarily coincide with an integer multiple of the sampling period, but is a real multiple. The relationship between the time t', the molten metal level y, and the valve opening v is known, so the obtained t X’i ', the molten metal level y(t X’i ') and valve opening v(t X’i ') can be obtained by interpolation or extrapolation. These become Y'(i) and V'(i).

[0107] Here, the interpolation can be, for example, linear interpolation.

[0108] Extrapolation is necessary, for example, when, in the case of a constant velocity, Vc, sampling period, and number of accumulated data points become the maximum value of the distance in spatial coordinates, and this maximum value is smaller than X'(N-1). For example, if there is a t' corresponding to X'(1000), but no t' corresponding to X'(1001) and beyond, then the t' corresponding to X'(1000) can be used as the t' corresponding to X'(1001) and beyond. This makes it possible to find values ​​after Y'(1001) and values ​​after V'(1001) by extrapolation.

[0109] Next, although it is fine to leave it as it is, the fact that the time is reversed and difficult to understand is addressed. Therefore, to simplify handling, the positive and negative signs of the coordinate axis X' are converted as shown in FIG. 8C. Specifically, it becomes X(i) = X'(N-1-i) (i = 0, 1, . . . , N-1). For example, the coordinate axis X' becomes the coordinate axis X whose coordinate origin is the position X'(N-1) = X(0) on the slab Ob before the time N-1 [s].

[0110] Because the axis has been changed, the molten metal level and valve opening also change to Y(i) = Y'(N-1-i) (i = 0, 1, , N-1) and V(i) = V'(N-1-i) (i = 0, 1, , N-1).

[0111] Note that the positive and negative signs of the coordinate axes are reversed for the sake of simplification and are not essential, but if the positive and negative signs are not reversed, the coordinates used in the subsequent calculations will differ from those in this embodiment.

[0112] As a result, the values ​​of the molten metal level y and the valve opening v of the valve VL in the time domain are converted into values ​​in the spatial domain having a coordinate axis X in the longitudinal direction of the slab Ob produced by the continuous casting machine CM. For example, N=1024 (=2 10 ), the position X on the coordinate axis X={X0,X1,X2,...,X 1021 ,X 1022 ,X 1023}, the melt level in the spatial domain Y={Y0,Y1,Y2,...,Y 1021 ,Y1022 ,Y 1023}, the valve opening in the spatial domain V={V0, V1, V2, . . . , V 1021 ,V 1022 ,V 1023} is obtained. Here, for simplicity, numerical values ​​are replaced with variables. Note that in this example, N=1024, but this is not limited to this, and may be an appropriate number such as 512 or 2048.

[0113] The molten metal level Y and the valve opening V of the valve VL are determined by using the deviation from the equilibrium point, and each component of the molten metal level Y [m] and the valve opening V [m] (in this embodiment, the valve VL is a slide valve VL, so the unit of the valve opening V is [m]) is initialized to 0. This makes it possible to use this method even when the casting speed is very slow and 1024 points of data cannot be obtained. As the equilibrium point of the molten metal level Y, the SV (Setting Value) itself, which is the target value of the molten metal level Y, can be used. As the equilibrium point of the valve opening V, for example, a value obtained by applying a low-pass filter with a time constant of 10 [s] to the measured value of the valve opening V can be used.

[0114] The FF compensator 12 performs a fast Fourier transform (FFT) on the molten metal level Y[m] and the valve opening V[m] to obtain the frequency characteristics of the molten metal level Y[m] and the valve opening V[m]. The FFT method is disclosed, for example, in "C Language Digital Signal Processing," Akizuki, Matsuyama, and Yoshie, Baifukan Publishing, 1989, pp. 121-127 (Reference 2). The fft function of "Matlab" (registered trademark) by The MathWorks, Inc. can also be used.

[0115] The discretized frequency f[1 / m] is f={(i / 1024)·(1 / 0.004)}={f0,f1,f2,···,f 1021 ,f 1022 ,f 1023} (i = 0, 1, , 1023), and the discretized period L [m] is L = {(1024 / i) 0.004} = {L0, L1, L2, , L 1021 ,L 1022 ,L 1023} (i = 0, 1, , 1023). Here, as in the above, numerical values ​​are replaced with variables for simplification. The same applies below. Note that △X, which is the interval in the spatial domain, is set to 0.004 [m] in consideration of the frequency resolution and the number of FFT points, but other values ​​may be used.

[0116] The FFT results of the molten metal level Y[m] and the valve opening V[m] are values ​​corresponding to the frequency f or period L. The FFT result of the molten metal level Y[m] is Y FFT ={Y FFT0 ,Y FFT1 ,Y FFT2 ,···,Y FFT1021 ,Y FFT1022 ,Y FFT1023}, and the FFT result of the valve opening V[m] is V FFT ={V FFT0 ,V FFT1 ,V FFT2 ,···,V FFT1021 ,V FFT1022 ,V FFT1023}.

[0117] Each element is a complex number, Y FFTi (i=1,2,···,510,511) is Y FFT(1024-i) It is in a conjugate relationship with V. FFTi The same is true for Y FFT0 = 0, and V FFT0 = 0. Note that 511 is a value calculated as N / 2-1.

[0118] Here, in this embodiment, there are four first to fourth domains. The first domain is a time domain (amplitude [m], frequency [Hz] or period [s], phase [rad]). The second domain is a time-frequency domain (amplitude [m], frequency [Hz] or period [s], phase [rad]). The third domain is a spatial domain (amplitude [m], frequency [1 / m] or period [m], phase [rad]). And the fourth domain is a spatial frequency domain (amplitude [m], frequency [1 / m] or period [m], phase [rad]). The time domain of the first domain is transformed into the time-frequency domain of the second domain by its FFT. Thus, the time-frequency domain of the second domain is transformed into the time domain of the first domain by its inverse Fourier transform (inverse FFT). The spatial domain of the third domain is transformed into the spatial frequency domain of the fourth domain by its FFT. Thus, the spatial frequency domain of the fourth domain is transformed into the spatial domain of the third domain by its inverse FFT.

[0119] FIG. 8 shows a transformation from the first time domain to the third space domain.

[0120] Next, the FF compensator 12 calculates the transfer functions P(s), P(s) of the continuous casting machine CM related to the molten metal level y. v2l (s) from the time frequency domain to the spatial frequency domain. That is, 1021 ,f 1022 ,f 1023}, the frequency response (complex number) is calculated.

[0121] More specifically, the frequency response (complex number) is calculated as follows: FFT and valve opening V FFT Since the unit of frequency is [1 / m] in the spatial frequency domain, some ingenuity is required when calculating the value of the transfer function at the above frequency f or period L. c_n Then, the converted frequency f tf is used. f tf ={(i / 1024)·(V c_n / 0.004)}={f tf0 ,f tf1 ,f tf2 ,f tf1021 ,f tf1022 ,f tf1023} [Hz] (i = 0, 1, , 1023).

[0122] From the above, N = 1024 is the number of FFT points, and △X = 0.004 [m] is the data interval in the spatial domain with coordinate axis X. Note that the frequency in the time-frequency domain transformed from the time domain by FFT is {(i / 1024) (1 / △t)} [Hz] (i = 0, 1, , 1023), so the above formula is a virtual sampling period of △t = 0.004 / V c_n This is equivalent to changing the

[0123] V c_n can be appropriately set to the current value, the average value while the slab Ob advances a certain distance in the past, or the like, but here it is set to the current value. In other words, this is equivalent to regarding the current casting speed Vc as having been kept constant in the past.

[0124] ω tfi =2πf tfi (i=0,1,···,1023), for i=0~512, P(jω tfi ) and P v2l (jω tfi ) for i = 513 to 1023, the value is the conjugate of 1024-i, and P tf ={P tf0 ,P tf1 ,P tf2 ,···,P tf1021 ,P tf1022 ,P tf1023}, P v2ltf ={P v2ltf0 ,P v2ltf1 ,P v2ltf2 ,···,P v2ltf1021 ,P v2ltf1022 ,P v2ltf1023} is obtained. Each component is a complex number. Up to this point, the transfer function has been changed from the time-frequency domain, which is generally replaced with s = jω, to s = jωtf By replacing it with, the change to the spatial frequency domain is made. And, P tf , P v2ltf The frequency response of is obtained. Here, the discretized frequency and the discretized period are the same values ​​as f and L described above, making it possible to perform calculations in the spatial frequency domain. Note that 512 is a value calculated by N / 2.

[0125] Then, the FF compensator 12 determines a feedforward compensation amount consisting of a sine wave component having an amplitude, a period and a phase for canceling the disturbance applied to the molten metal surface level.

[0126] More specifically, since the frequency characteristics and frequency responses of each frequency were obtained in this way, the disturbance D FFT That is, D FFT ={Y FFTi -P v2ltfi ·V FFTi}={D FFT0 ,D FFT1 ,D FFT2 ,···,D FFT1021 ,D FFT1022 ,D FFT1023}. i = 0 to 512 are calculated using formula 4, and for i = 513 to 1023, the conjugate value of 1024-i is used. In order to eliminate stationary components and low-frequency components, in this example, values ​​corresponding to frequencies equivalent to periods of 1.0 [m] or more in a spatial domain having the coordinate axis X are forcibly set to 0.

[0127] Next, using Equation 5, the disturbance control amount equivalent value UD FFT In other words, UD FFT ={D FFTi / P tfi}={UD FFT0 ,UD FFT1 ,UD FFT2 ,···,UD FFT1021 ,UD FFT1022 ,UD FFT1023 As mentioned above, the disturbance control amount equivalent value UD FFT By inverting the sign of , essentially, a feedforward compensation amount for the disturbance is obtained.

[0128] As described above, the operation amount may be used instead of the valve opening. In this case, the transfer function P v2l Instead of (s), the transfer function P(s) is used.

[0129] Next, U.D. FFT The amplitude of each component of ampUD FFTi and phaseUD FFTi and can be calculated using the following Equations 7 and 8.

[0130]

number

[0131]

number

[0132] In this way, the disturbance control amount equivalent value, and its amplitude and frequency at each frequency are obtained.

[0133] Next, UD of these 512 points (N / 2) FFTi By selecting the peak amplitude from among the component values ​​of the signal, the frequency, amplitude and phase of the feedforward compensation amount are determined.

[0134] 512 points of UD FFTi From the component values, for example, frequencies that satisfy the following condition are selected. The discretized period L [m] is in the range of 0.1 to 1.0 [m]. The amplitude is 1.0 mm (= 0.001 m) or more. -Has the maximum amplitude at seven discrete frequencies including before and after.

[0135] This allows the frequency, amplitude, and phase of the disturbance control amount equivalent value, which has a peak in its amplitude, to be obtained. Note that there may be zero or multiple peaks.

[0136] It may be possible to perform feedforward compensation by directly using the frequency, amplitude, and phase obtained in this way, but in reality this is difficult because the obtained phase may be shifted by approximately π [rad] and the frequency is only obtained discretely.

[0137] FIG. 9 is a diagram showing, as an example, a simulation result of a value (disturbance manipulated variable equivalent value) obtained by back-calculating an unknown disturbance to the manipulated variable. The disturbance manipulated variable equivalent value is the basis of the feedforward compensation amount. FIG. 9A shows numerical values ​​of the simulation result, FIG. 9B shows a graph of the amplitude represented by the numerical values ​​in FIG. 9A, and FIG. 9C shows a graph of the phase represented by the numerical values ​​in FIG. 9A. The horizontal axis in each of FIGS. 9B and 9C is i, the vertical axis in FIG. 9B is the amplitude, and the vertical axis in FIG. 9C is the phase. FIG. 9 shows a simulation result in the case where the casting speed is constant and there is feedforward compensation of the disturbance. FIG. 9 shows the discrete frequency of the FFT, the discrete period of the FFT calculated in Equation 7, and the UD at a time of 200 [s] in the simulation of FIG. 13. FFT The amplitude and phase of each component are shown as a fraction from 0 to 30.

[0138] The phase shift is about π [rad] at the frequency before and after the amplitude peak. There are cases where the phase changes by π [rad] on the high frequency side of the peak frequency, and cases where the phase changes by about π [rad] on the low frequency side of the peak frequency. In Figure 9, the first u d The first amplitude peak is at i=12, and the phase changes between i=12 and i=13 on the high frequency side. The second amplitude peak is at i=25, and the phase changes between i=25 and i=24 on the low frequency side. If the phase shifts by about π [rad], the fluctuations will be amplified, so it is necessary to select an appropriate phase.

[0139] On the other hand, with discrete frequencies, errors may occur in the amount of feedforward compensation, so it is necessary to improve the frequency accuracy.

[0140] Therefore, the frequency, amplitude, and phase at each peak of the amplitude of the disturbance manipulation amount equivalent value are obtained as follows. Note that, for simplicity, the case of the first peak (i=12) in Fig. 9 will be described here, but the same applies to the case where there are multiple peaks.

[0141] First, the FF compensator 12 calculates the frequency of the feedforward compensation amount (the frequency of the value equivalent to the disturbance control amount) f peak More specifically, the frequency f f is selected from the frequencies adjacent to the peak frequency, and the frequency f peak is calculated by weighting the frequency of the peak and the selected frequency by the amplitude of the peak and the amplitude of the selected frequency. 12 (=2.92969[1 / m], its amplitude = 0.00386[m]) and its adjacent frequency f 11 , f 13 Among these, the frequency f with the largest amplitude is 13 (=3.17383[1 / m], its amplitude = 0.00290[m]) is selected, and the frequency f peak = ((0.00386·2.92969+0.00290·3.17383) / (0.00386+0.00290)) = 3.03 [1 / m]. This allows us to calculate a more accurate frequency, without being limited to the discrete frequency values ​​themselves.

[0142] Next, the FF compensator 12 calculates the amplitude of the feedforward compensation amount (the amplitude of the value equivalent to the disturbance control amount) amp peak In the above example, the peak frequency f 12 Amplitude at amp peak =0.00386. This value is the amplitude at the location of the manipulated variable u, and is filtered and multiplied by the gain of the controlled object to obtain the amplitude at the location of the disturbance d. peak = 0.00386 is different from the amplitude of the disturbance d, 0.001 [m], described below.

[0143] Although not used in this example, the amplitude can be calculated by other methods. Specifically, the square root of the sum of the squares of the amplitudes at the peak and the three frequencies before and after it is calculated. The frequency of the peak is f 12 (=2.92969[1 / m], its amplitude = 0.00386[m]), and the frequencies around it are f 11 (=2.68555[1 / m], its amplitude=0.00104[m]), f 13 (=3.17383[1 / m], its amplitude = 0.00290[m]). The amplitude in this case is √(0.00386 2 +0.00104 2 +0.00290 2 ) = 0.00494. It has been confirmed that this method can accurately determine the amplitude when the disturbance is a single-cycle sine wave and is stationary. However, control simulations have shown that robustness is likely to decrease when a disturbance consisting of multiple sine waves is applied or when the disturbance is non-stationary. Therefore, in this example, the value of the peak amplitude itself, which is a smaller value as described above, is used instead, and it has been confirmed that stable control is possible.

[0144] Here, this amplitude amp peak Since is easily changed in the case of a non-stationary part or when a sudden disturbance is applied, in this embodiment, a low-pass filter with a time constant (for example, 5 [s]) is further applied, and the application result is the amplitude amp peak This makes it possible to prevent the frequency, amplitude, and phase of the disturbance control amount equivalent value from changing frequently. For this reason, in this example, the amplitude amp peak = 0.00386, and the amplitude amp peak =0.00378.

[0145] Next, the FF compensator 12 obtains the phase of the feedforward compensation amount in the spatial frequency domain. More specifically, for each of the three phases at the peak frequency and the two adjacent frequencies in the disturbance manipulation amount equivalent value, the amount of disturbance cancellation is obtained by obtaining an inner product in the spatial domain on the coordinate axis X, and the phase that most effectively cancels the disturbance is selected.

[0146] More specifically, it is calculated as follows: First, the frequency number of the peak is set to j, the frequency adjacent to this on the low frequency side is set to pre, and the frequency adjacent to this on the high frequency side is set to post. In the above example, j=12, pre=11, and post=13.

[0147] First, let us consider the case of peak frequency j. d The phase of the disturbance d at the application point (after P(s)) is 2π (frequency) (distance from the center of the slab length at point N) + π + (u d (phase of P(s)) + (phase lag of P(s)). Here, π is added because the sign is inverted. The amount of feedforward compensation for disturbance, -u d The amplitude ff of the wave at the position X(i) (i=0,1,...,N-1) of the coordinate axis X when the disturbance d is applied _at_dj If the gain of the controlled object is ignored, it can be expressed as the following Equation 9.

[0148]

number

[0149] Here, since the gain of the controlled object is positive and is calculated commonly at frequency j, frequency pre, and frequency post, the gain of the controlled object is ignored to reduce the amount of calculation. And, since the value of the high frequency component is large at the location of the manipulated variable u and it is difficult to accurately evaluate, the inner product is calculated at the location where the disturbance d is applied. This is because the continuous casting machine CM is basically an integrator, and the location of the manipulated variable u corresponds to the value obtained by differentiating the disturbance.

[0150] Next, to obtain the inner product, the disturbance D FFT The disturbance d is obtained by inverse FFT of FFT ) = {d0,d1,d2,...,d 1021 ,d 1022 ,d 1023}. Each component represents the amplitude of the disturbance at position X(i) (i=0, 1, . . . , N-1) on the coordinate axis X. The inverse FFT technique is disclosed on pages 127 to 130 of the above-mentioned document 2. The fft function of "Matlab" (registered trademark) of The MathWorks, Inc. can also be used. Note that the imaginary components become negligibly small, and only the real components are extracted as the disturbance d, and each element of the disturbance d becomes a real number.

[0151] And the amplitude ff _at_dj and the inner product IP j is calculated using the following formula 10. That is, for i = 0 to 1023, the products of the components are calculated and then the sum of these products is calculated.

[0152]

number

[0153] Similarly, for the frequency pre, the amplitude ff of the wave at position X(i) (i=0,1,...,N-1) on the coordinate axis X is _at_dpre is calculated, and the inner product IP pre Similarly, for the frequency post, the amplitude ff of the wave at position X(i) (i=0,1,...,N-1) on the coordinate axis X is calculated as _at_dpost is calculated, and the inner product IP post is required.

[0154] If the inner product IP is smallest and negative, it is considered that it cancels the disturbance d the most. j , the inner product IP pre and the inner product IP post The phase of the smallest and most negative inner product IP is the phase of the feedforward compensation amount of the disturbance. peak That is, the inner product IP j If is minimum and negative, the phase of the feedforward compensation of the disturbance peak =phaseUD FFTj The inner product IP oreIf is minimum and negative, the phase of the feedforward compensation of the disturbance peak =phaseUD FFTpre The inner product IP post If is minimum and negative, the phase of the feedforward compensation of the disturbance peak =phaseUD FFTpost In cases other than these three cases, the disturbance is not canceled, so the amplitude is set to 0, and as a result, feedforward compensation of the disturbance of this peak is not performed. peak =phaseUD FFTj =-0.02916.

[0155] This allows the selection of an appropriate phase. This method can also be used in unsteady cases where the casting speed Vc changes or the characteristics of the controlled object change.

[0156] From the above, for one peak (peak at frequency j = 12), frequency f peak , amplitude amp peak and phase peak If there is another peak, the frequency f peak , amplitude amp peak and phase peak is required.

[0157] Although not used in this example, the phase can also be obtained by other methods. Specifically, when the i of the amplitude peak of the disturbance manipulated variable equivalent value is an odd number, the result of adding π to the phase of the peak is used as the phase. When the i of the amplitude peak of the disturbance manipulated variable equivalent value is an even number, the phase of the peak itself is used. For example, in the case of FIG. 9B, the first peak is i=12, which is an even number, so the phase -0.02916 is used as it is. On the other hand, the second peak is i=25, which is an odd number, so π is added and the phase becomes 2.83821+π=5.9798. It has been confirmed that the phase can be obtained by this method when the disturbance is a sinusoidal wave with a single cycle and in the stationary part. However, it has been found that in the non-stationary part, the phase may rarely be shifted by π. In this case, the disturbance is amplified, which is not preferable. Therefore, in this example, the above-mentioned method of selecting a phase by using an inner product is used instead, and it has been confirmed that an appropriate phase can be selected even in an unsteady portion.

[0158] Then, the FF compensator 12 determines the rate of the feedforward compensation amount in the next sampling period or the feedforward compensation amount itself in the time domain from the frequency, amplitude and phase of the feedforward compensation amount of the disturbance corresponding to each peak in the spatial frequency domain.

[0159] More specifically, the amount of disturbance feedforward compensation output in the next sampling period in the time domain is the value at the location where "current casting speed Vc × sampling period" is advanced in the spatial domain of coordinate axis X. When the molten metal level control device CT is of the velocity type, the rate dff / dt [m / s] (time derivative of dff) of the disturbance feedforward compensation amount for one peak is expressed by the following equation 11.

[0160]

number

[0161] Here, gainmp1 is a gain multiplied by the sampling period for calculating the amount of high-frequency compensation, and is represented by, for example, the line graph shown in FIG. 10. FIG. 10 is a diagram showing a gain for reducing the amount of feedforward compensation for high-frequency disturbance. The horizontal axis of FIG. 10 is the period [m], and the vertical axis is the gain. gainmp1 shown in FIG. 10 has a characteristic that the gain increases proportionally from 0 to 1.0 when the period is from 0 [m] to 0.33 [m], and the gain saturates at 1.0 when the period is 0.33 [m] or more. Therefore, when the period of the disturbance is 0.33 [m] or more, the gain is 1, and the amount of feedforward compensation for the disturbance required after one sampling period is used as is. The first peak in the above example corresponds to this.

[0162] When the molten metal level control device CT is of the velocity type, the rate of the feedforward compensation amount for the disturbance is multiplied by the gain. The rate of the feedforward compensation amount becomes smaller in proportion to the period. As a result, the feedforward compensation amount also becomes smaller in proportion to the period. This is because the higher the frequency, the less robust the system is against phase changes, making it easier for phase shifts in the feedforward compensation to occur, and so the feedforward compensation amount is restricted. Note that the second peak in the above example corresponds to this.

[0163] Feedforward compensation amount ff for disturbance at the k+1th sampling of position type k+1 is the feedforward compensation amount ff at the kth sampling k By using the above, it is expressed as in the following Equation 12. Note that other methods such as trapezoidal integration may be used.

[0164]

number

[0165] Although one peak has been described above, when there are multiple peaks, similar calculations are performed for each peak, and the rates of the disturbance feedforward compensation amount or the compensation amount itself for all peaks are summed up to obtain Equation 11, which is the rate of the final disturbance feedforward compensation amount, or Equation 12, which is the final disturbance feedforward compensation amount.

[0166] Next, the operation of this embodiment will be described. Fig. 11 is a flowchart showing the operation of the molten metal level control device in the embodiment. Fig. 12 is a flowchart showing the calculation process of the feedforward compensation amount shown in Fig. 11.

[0167] When the power is turned on, the molten metal level control device CT having such a configuration initializes each necessary part and starts its operation. The computer constituting the molten metal level control device CT functionally configures a host system SY, a subtractor 10, an FB compensator 11, an FF compensator 12 and an adder 13 by executing a program.

[0168] In FIG. 11, when the sampling timing arrives at every sampling period Δt, the molten metal level control device CT acquires a predetermined casting state from the host system SY and determines the FB compensator number (S1). In this embodiment, the casting state is K f The mass of molten steel in the tundish, the width of the mold, and the casting speed are included in order to calculate K / A, and the molten steel level and the valve opening are included in order to control the molten steel level. The host system SY calculates K from the mass of molten steel in the tundish, the width of the mold, and the casting speed by the known calculation method as described above. f The upper system SY calculates the gain type adjusted in the process S5 described later in the molten metal level control executed at the previous sampling timing, and the calculated K fThe FB compensator number according to / A is selected and determined, and this determined FB compensator number is output to the FB compensator 11. Note that at the first sampling timing after startup, any of the high gain type, middle gain type, and low gain type may be used. For example, the middle gain type may be used. f The FB compensator number according to / A is selected and determined.

[0169] Next, the molten metal level control device CT calculates the parameter K according to the gain type input from the upper system SY and the determined FB compensator number by the FB compensator 11. P , T I , T D (=0.0), a1, a2, b1, and b2 are determined based on the lookup table stored in the memory, and the feedback compensation amount (FB compensation amount) is calculated (S2).

[0170] Next, the molten metal level control device CT uses the FF compensator 12 to determine a feedforward compensation amount (FF compensation amount) consisting of a sine wave component having an amplitude, period and phase for canceling out the disturbance applied to the molten metal level, based on the molten metal level y, the valve opening v (or operation amount u) of the valve VL, and a transfer function of the continuous casting machine CM related to the molten metal level (S3).

[0171] More specifically, in process S3, in FIG. 12, first, the FF compensator 12 converts the values ​​y, v of the molten metal level level y and the valve opening v of the valve VL in the time domain into values ​​Y, V in the spatial domain having a coordinate axis X in the longitudinal direction of the slab Ob produced by the continuous casting machine CM (S31).

[0172] Next, the FF compensator 12 performs FFT on each of the molten metal level Y and the valve opening degree V to obtain the frequency characteristics of each of the molten metal level Y and the valve opening degree V in the spatial frequency domain (S32).

[0173] Next, the FF compensator 12 calculates the transfer functions P(s), P v2l(s) from the time frequency domain to the spatial frequency domain, and v2l The FF compensator 12 calculates the frequency response of the molten metal level Y and the valve opening V in the spatial frequency domain, and the transfer functions P(s) and P(s) of the continuous casting machine. v2l From the frequency response in the spatial frequency domain of (s), a disturbance control amount equivalent value, which is a value obtained by back-calculating the unknown disturbance to the control amount, is obtained (S33).

[0174] Next, the FF compensator 12 selects an amplitude peak in the disturbance control amount equivalent value in the spatial frequency domain (S34).

[0175] Next, the FF compensator 12 calculates, for each of the one or more peaks selected in step S34, a frequency of the feedforward compensation amount (a frequency of a value equivalent to a disturbance control amount) f peak (S35).

[0176] Next, the FF compensator 12 calculates the amplitude of the feedforward compensation amount (the amplitude of the value equivalent to the disturbance control amount) amp for each of the one or more peaks selected in step S34. peak (S36).

[0177] Next, the FF compensator 12 calculates the phase of the feedforward compensation amount in the spatial frequency domain for each of the one or more peaks selected in step S34. peak As described above, if a phase that cancels the disturbance cannot be found, the amplitude of the peak is set to 0, and feedforward compensation of the disturbance of the peak is not performed.

[0178] Then, the FF compensator 12 determines the rate of the feedforward compensation amount in the next sampling period or the feedforward compensation amount itself in the time domain from the frequency, amplitude, and phase of the feedforward compensation amount of the disturbance corresponding to each peak in the spatial frequency domain (S38), and ends this process S3.

[0179] When each of the steps S31 to S38 shown in FIG. 12 is completed, returning to FIG. 11, the molten metal level control device CT then adds, by the adder 13, the feedback compensation amount calculated by the FB compensator 11 in step S2 and the feedforward compensation amount calculated by the FF compensator 12 in step S3 (S4).

[0180] Next, the molten metal level control device CT adjusts the gain type by the host system SY (S5). More specifically, when the absolute value of the rate of the manipulated variable is greater than a predetermined first threshold, the host system SY changes the gain of the feedback control to be smaller than the current value, and when the absolute value of the rate of the manipulated variable is smaller than a positive predetermined second threshold smaller than the first threshold, the host system SY changes the gain of the feedback control to be larger than the current value. More specifically, in this embodiment, as described above, the high gain type H is defined as 1.0, the middle gain type M is defined as 2.0, and the low gain type L is defined as 3.0. Therefore, when the molten metal level control device CT is a velocity type, the host system SY adds a first predetermined value (e.g., 0.01, 0.02, etc.) to the numerical value of the current gain type when the absolute value is greater than the first threshold. This changes the gain type from the current gain type to the low gain type, and saturation of the rate (operation speed) due to the rate limit (operation speed limit) of the actuator AC (stepping cylinder AC in this embodiment) can be avoided. If the absolute value is smaller than the second threshold, the upper system SY subtracts a second predetermined value (e.g., 0.01, 0.02, etc.) set in advance to the numerical value of the current gain type. This changes the gain type from the current gain type to the high gain type. The first threshold is equal to or smaller than the rate limit of the actuator AC and is appropriately set in advance from a plurality of samples. The second threshold is a positive value smaller than the first threshold and is appropriately set in advance from a plurality of samples. The first and second predetermined values ​​may be the same value as each other, or may be different values ​​from each other.

[0181] Next, the molten metal level control device CT outputs the sum calculated in step S4 to the actuator AC (stepping cylinder AC in this embodiment) (S6). The actuator AC (stepping cylinder AC in this embodiment) drives the valve VL (slide valve VL in this embodiment) in response to the sum input from the molten metal level control device CT. This controls the molten metal level at the current sampling timing.

[0182] Then, the molten metal level control device CT judges whether or not the control of the molten metal level has ended (S7). If the result of this judgment is that the control of the molten metal level has ended (Yes), for example due to turning off the power or an input to end the control of the molten metal level, the molten metal level control device CT ends the control of the molten metal level. On the other hand, if the result of the judgment is that the control of the molten metal level has not ended (No), the molten metal level control device CT returns the process to step S1.

[0183] The molten metal level control device CT controls the molten metal level through such operations.

[0184] Next, the results of the simulation will be described. FIG. 13 is a diagram showing the results of the simulation in the case of a constant casting speed. FIG. 14 is a diagram showing the results of the simulation in the case of a variable casting speed. FIG. 15 is a diagram showing the results of the simulation in a comparative example. FIG. 13A, FIG. 14A, and FIG. 15A show the casting speed, with the horizontal axis being time [s] and the vertical axis being the casting speed [m / s]. FIG. 13B, FIG. 14B, and FIG. 15B show the disturbance, with the horizontal axis being time [s] and the vertical axis being the disturbance [m]. FIG. 13C, FIG. 14C, and FIG. 15C show the molten metal level, with the horizontal axis being time [s] and the vertical axis being the molten metal level [m]. FIG. 13D, FIG. 14D, and FIG. 15D show the opening degree of the slide valve, with the horizontal axis being time [s] and the vertical axis being the opening degree [m]. 13E, 14E, and 15E show the types of FB compensators 11, with the horizontal axis representing time [s], the left vertical axis representing the gain type, and the right vertical axis representing the FB compensator number.P , T I , a1, a2, b1, and b2, where the horizontal axis is time [s] and the left vertical axis is the parameter K P , a1, a2, b1, b2, and the right vertical axis represents the parameter T I 13G, 14G, and 15G show the amount of feedback compensation, with the horizontal axis being time [s] and the vertical axis being the amount of feedback compensation (FB compensation) [m]. 13H and 14H show the amount of feedforward compensation for disturbance in the position type, with the horizontal axis being time [s] and the vertical axis being the amount of feedforward compensation for disturbance (FF compensation for disturbance) [m]. As mentioned above, the amount of feedforward compensation for known disturbances such as changes in casting speed is omitted. 13I and 14I show the period of the component of the amount of feedforward compensation for disturbance (FF compensation for disturbance), with the horizontal axis being time [s] and the vertical axis being the period [m] of the component of the FF compensation for disturbance. Fig. 13J and Fig. 14J show the amplitude of the disturbance feedforward compensation amount (disturbance FF compensation amount) component, with the horizontal axis being time [s] and the vertical axis being the amplitude [m] of the disturbance FF compensation amount component. Fig. 13K and Fig. 14K show the phase of the disturbance feedforward compensation amount (disturbance FF compensation amount) component, with the horizontal axis being time [s] and the vertical axis being the phase [rad] of the disturbance FF compensation amount component.

[0185] The comparative example of the molten metal level control device is configured by removing the FF compensator 12 and the adder 13 from the molten metal level control device CT in the embodiment shown in Fig. 2. That is, the comparative example of the molten metal level control device is configured with a host system SY, a subtractor 10 and an FB compensator 11, and also has a function of adjusting the gain type by the host system SY.

[0186] In the simulation, the mass of molten steel in the tundish was 40.0×10 3The casting load is set to [kg], the mold width is set to 1.80 [m], and the casting speed is constant (uniform) at 0.02 [m / s] in the cases shown in Figures 13 and 15 (see Figures 13A and 15A), and in the case shown in Figure 14, it is constant (uniform) at 0.02 [m / s] from 0 [s] to 150 [s], changes from 0.02 [m / s] to 0.01 [m / s] between 150 [s] and 160 [s], and thereafter is constant (uniform) at 0.01 [m / s] (see Figure 14A). The disturbance applied to the molten metal level as a disturbance due to bulging is formed by superimposing a first wave with a period of 0.33 [m] and an amplitude of 0.010 [m] and a second wave with a period of 0.165 [m] and an amplitude of 0.0025 [m] in the spatial domain on the coordinate axis X (see Figs. 13B, 14B and 15B). Of course, this disturbance is not measured (cannot be observed) by the molten metal level control device CT of the embodiment and the molten metal level control device of the comparative example. The molten metal level control device CT of the embodiment performs back calculation as described above.

[0187] Under such simulation conditions, in the comparative example of the mold level control device, as shown in FIG. 15C, the mold level PV (Process Variable) fluctuates greatly due to disturbances (disturbances due to bulging), and it is found that the mold level control device of the comparative example has difficulty in suppressing disturbances (disturbances due to bulging). The mold level PV is a measured value, and the mold level SV is a target value. In the comparative example of the mold level control device, as shown in FIG. 15E, immediately after the start of the simulation, it is determined that it is difficult to saturate at the rate limit of the actuator AC, and the gain type is continuously adjusted from the middle gain type 2.0 to the high gain type 1.0. The FB compensator number is constant because the casting state (casting conditions) of the molten steel mass in the tundish, the mold width, and the casting speed are constant, as described above. On the other hand, the parameters of the FB compensator 11 change with the change in the gain type, as shown in FIG. 15F. Even if the parameters are changed in this way, as shown in FIG. 15C, the molten metal surface level PV fluctuates but remains in a steady state and is stable in this state.

[0188] In contrast, in the case of the embodiment of the molten metal level control device CT in the case of the constant casting speed, as shown in FIG. 13C, even if there is a disturbance, the molten metal level PV gradually changes to a smaller fluctuation, and it is understood that the FF compensator 12 effectively controls the molten metal level. Comparing FIG. 13D and FIG. 15D, it is understood that the valve opening has almost the same amplitude as that of the comparative example, but the phase delay is smaller than that of the comparative example. This is considered to be the reason why the fluctuation of the molten metal level gradually decreases as shown in FIG. 13C. The gain type, FB compensator number, and parameters of the FB compensator 11 are almost the same as those of the comparative example, as shown in FIG. 13E and FIG. 13F. As shown in FIG. 13G, the feedback compensation amount gradually decreases, while as shown in FIG. 13H, the feedforward compensation amount gradually increases. Therefore, it is considered that the feedforward compensation amount gradually increases so as to cancel out the disturbance (disturbance due to bulging), and the feedback compensation amount gradually decreases accordingly. As shown in Fig. 13I, the periods of the components of the feedforward compensation amount are 0.330 [m] and 0.165 [m] in the spatial domain on the coordinate axis X, and can be accurately estimated (back-calculated). As shown in Fig. 13J, the amplitudes of the components of the feedforward compensation amount change continuously. Also, as shown in Fig. 13K, the phases of the components of the feedforward compensation amount suppress level fluctuations while temporarily selecting appropriate phases discontinuously in the unsteady portion before 120 [s] in the first half. Then, in the almost steady portion after 120 [s] in the second half, the phases are changed continuously to suppress level fluctuations.

[0189] On the other hand, in the embodiment of the mold level control device CT in the case of variable casting speed, the disturbance is formed of the first and second waves defined in the spatial domain on the coordinate axis X as described above. Since the casting speed changes as described above, in the time domain, the period changes as shown in FIG. 14B. As shown in FIG. 14C, the mold level PV gradually changes to a small fluctuation even if the casting speed changes, and it can be seen that the FF compensator 12 is effectively acting on the control of the mold level. In particular, after the casting speed is decelerated, the mold level PV is suppressed to a small fluctuation. As described above, since the feedforward compensation for the casting speed change is performed, the mold level PV does not rise sharply when the casting speed is decelerated. It can be seen that the fluctuation of the mold level PV is gradually reduced by the feedforward compensation of the disturbance. In addition, the fact that the feedback control is more effective as the casting speed is smaller also has an effect. As shown in FIG. 14D, it can be seen that the valve opening becomes smaller when the casting speed is decelerated, and the valve VL is driven in the closing direction. As shown in Figs. 14E and 14F, the gain type, FB compensator number, and parameters of the FB compensator 11 are almost the same as those in the comparative example before the casting speed is reduced. However, when the casting speed is reduced, the K fSince / A also changes, the FB compensator number and the parameters of the FB compensator 11 also change, and after the casting speed is decelerated, the FB compensator number and the parameters of the FB compensator 11 after the change are constant. Even if the FB compensator number changes, the fluctuation of the molten metal level PV is suppressed, and the control of the molten metal level remains stable. As shown in FIG. 14G, the feedback compensation amount gradually decreases before and after the casting speed is decelerated, while as shown in FIG. 14H, the feedforward compensation amount gradually increases. Therefore, it is considered that the feedforward compensation amount gradually increases so as to cancel the disturbance (disturbance due to bulging), and the feedback compensation amount gradually decreases accordingly. It can be seen that the period of the feedforward control amount in the time domain is extended (lengthened) after the casting speed is decelerated. As shown in FIG. 14I, the periods of the components of the feedforward compensation amount are 0.330 [m] and 0.165 [m] in the spatial domain on the coordinate axis X, and can be accurately estimated (back-calculated). Even if the casting speed changes, since the time domain is converted to the space domain, it can be confirmed that the change in the casting speed is not affected. As shown in Fig. 14J, the amplitude of each component of the feedforward compensation amount changes before and after the casting speed is decelerated because the transfer function of the controlled object changes before and after the casting speed is decelerated. As shown in Fig. 14K, the time change rate of the phase in the time domain of each component of the feedforward compensation amount becomes smaller after the casting speed is decelerated. This corresponds to the fact that the casting speed becomes smaller and the period of the disturbance in the time domain becomes longer.

[0190] In addition, it is necessary to ensure the robustness of the feedforward compensation, i.e., to prevent the level fluctuation from increasing even if a modeling error exists. For this purpose, it is particularly effective to limit the period of the sine wave of the feedforward compensation. A specific example will be described below.

[0191] Stepping cylinder time constant T SC =0.2[s], Dead time L SC =0.1[s], time constant T of the eddy current sensor CD =0.3[s], Dead time L CD= 0.12 [s] respectively fluctuates by 20%, the time equivalent to the phase difference of the modeling error is approximately (0.2 + 0.1 + 0.3 + 0.12) × 0.2 = 0.144 [s].

[0192] Here, when canceling out a sine wave by adding a sine wave with the same amplitude but different phase, it is necessary to shift the phase from the original sine wave by π (180 degrees). When the phase shift exceeds the range of π±π / 3, the amplitude becomes larger than the original sine wave signal and is amplified. Here, π / 3 corresponds to 1 / 6 of one period.

[0193] Therefore, if the amplitude is estimated accurately, the period of the sine wave for which feedforward compensation is performed must be longer than 0.144 x 6 = 0.864 [s], which is one of the conditions for the lower limit of the period of the sine wave for which feedforward compensation is performed.

[0194] Furthermore, there are surface waves on the molten metal surface in the mold as modeling errors. The fundamental wave of the surface wave is a standing wave with antinodes at both ends of the long side, which is the width of the mold. The eddy current sensor is installed away from the center of the mold, so it detects the surface waves. However, although level control that manipulates the valve opening can control the average level of the entire molten metal surface, it cannot control the surface waves, and if the period of the surface waves is also controlled, spillover can cause the control to become unstable.

[0195] Here, the period of the fundamental wave of the surface wave is expressed as √[2π (2 mold width) / gravitational acceleration], which is 1.5 [s] in this example. This value is one of the lower limit conditions for the period of the sine wave that performs feedforward compensation.

[0196] Due to the above two conditions, the lower limit of the period of the sine wave for which feedforward compensation is performed is at least 1.5 [s]. However, taking into account a margin, in this example, the lower limit of the period of the sine wave for which feedforward compensation is performed is set to 4.0 [s].

[0197] As a result, feedforward compensation does not destabilize control even if there are modeling errors in the time constant or dead time. Also, feedforward compensation does not output a manipulated variable with the period of the surface waves, and does not excite waves with the period of the surface waves, so spillover does not occur and control does not become unstable.

[0198] The following will be described with reference to the simulation results in FIG. 16. FIG. 16 is a diagram showing the simulation results when modeling errors are taken into consideration. FIG. 16A shows the casting speed, with the horizontal axis being time [s] and each vertical axis being the casting speed [m / s]. FIG. 16B shows the disturbance, with the horizontal axis being time [s] and the vertical axis being the disturbance [m]. FIG. 16C shows the molten metal level, with the horizontal axis being time [s] and the vertical axis being the molten metal level [m]. FIG. 16D shows the opening of the slide valve, with the horizontal axis being time [s] and the vertical axis being the opening [m]. FIG. 16E shows the type of FB compensator 11, with the horizontal axis being time [s], the left vertical axis being the gain type, and the right vertical axis being the FB compensator number. FIG. 16F shows the parameter K of the FB compensator. P , T I , a1, a2, b1, and b2, the horizontal axis is time [s], and the left vertical axis is the parameter K P , a1, a2, b1, b2, and the right vertical axis is the parameter T IFIG. 16G shows the amount of feedback compensation, with the horizontal axis being time [s] and the vertical axis being the amount of feedback compensation (FB compensation) [m]. FIG. 16H shows the amount of feedforward compensation for disturbance in the position type, with the horizontal axis being time [s] and the vertical axis being the amount of feedforward compensation for disturbance (FF compensation for disturbance) [m]. As mentioned above, the amount of feedforward compensation for known disturbances such as changes in casting speed is omitted. FIG. 16I shows the period of the component of the feedforward compensation amount for disturbance (FF compensation amount for disturbance), with the horizontal axis being time [s] and the vertical axis being the period [m] of the component of the FF compensation amount for disturbance. FIG. 16J shows the amplitude of the component of the feedforward compensation amount for disturbance (FF compensation amount for disturbance), with the horizontal axis being time [s] and the vertical axis being the amplitude [m] of the component of the FF compensation amount for disturbance. FIG. 16K shows the phase of the component of the disturbance feedforward compensation amount (disturbance FF compensation amount), where the horizontal axis is time [s] and the vertical axis is the phase [rad] of the disturbance FF compensation amount component.

[0199] Figure 16 shows the simulation results when modeling errors are present, i.e., when the time constant and dead time of the stepping cylinder and eddy current sensor of the continuous casting machine increase by 20%, and in this example, a surface wave with a large amplitude of 5 mm is applied, with only sine waves with a period of 4.0 s or more being feedforward compensated.

[0200] As shown in FIG. 16A, the casting speed was 0.020 [m / s], similarly to FIGS. 13 and 15, the mass of molten steel in the tundish was 40.0×103 [kg], and the mold width was 1.80 [m].

[0201] As shown in FIG. 16B, the disturbance is formed by superimposing a first wave, which is a fundamental wave with a period of 0.33 [m] and an amplitude of 0.010 [m], and a second wave, which is a harmonic wave with a period of 0.165 [m] and an amplitude of 0.0025 [m], as in FIGS. 13 to 15, and further adding a surface wave with an amplitude of 5 [mm] and a period of 1.5 [s] as described above.

[0202] As shown in Fig. 16C, the amplitude of the molten metal level PV is stably controlled with the level fluctuation due to the first and second waves reduced. Here, as assumed, the level fluctuation due to the surface wave with a period of 1.5 [s] is not excited, and the amplitude of the level fluctuation with a period of 1.5 [s] remains almost constant. Therefore, it can be seen that the feedforward compensation is robust against modeling errors. This is because, as shown in Figs. 16I to 16K described later, the sine wave with a period of 1.5 [s], that is, the sine wave with a period of 1.5 × 0.020 = 0.03 [m] in the spatial domain of the slab length, is not included in the feedforward compensation.

[0203] In this example, the above conditions (discretized period L [m] is in the range of 0.1 to 1.0 [m]. The amplitude is 1.0 [mm] (= 0.001 [m]) or more. The period L has the maximum amplitude among the seven discrete frequencies including before and after.) are in the range of 0.1 to 1.0 [m]. Since the casting speed is 0.02 [m / s], the period is 5 to 50 [s] when converted to the time domain, and the above conditions are stricter and take precedence. However, for example, if the casting speed is 0.04 [m / s], the period condition converted to the time domain of the above conditions is 2.5 to 25 [s], and the condition for robustness of the feedforward compensation, "period 4.0 [s] or more," takes precedence. Therefore, the period (frequency) constraint in the time domain is essential.

[0204] FIG. 16D shows the valve opening.

[0205] The gain type in Figure 16E is low gain (L) (value 3.0 in the graph). This indicates that because the surface wave is set to a large value, the rate of the manipulated variable due to feedback compensation often exceeds a specified value, and the gain type is changed to lower the feedback gain. In other words, the effectiveness of feedback control is weakened. The FB compensator number remains unchanged because the conditions such as the casting speed are constant.

[0206] Figure 16F shows the change in the parameters of the PI+ filter, which can be seen to change depending on the gain type.

[0207] Fig. 16G shows the amount of feedback compensation, and Fig. 16H shows the amount of feedforward compensation. It can be seen that as the amount of feedforward compensation increases, the amount of feedback compensation decreases. Also, the feedback compensation contains a small amount of surface wave periodic components, but the feedforward compensation does not contain any surface wave periodic components.

[0208] 16I to 16K respectively show the period, amplitude, and phase of the sine wave of the feedforward compensation amount component, and as described above, no component with the period of the surface wave is included, and only sine waves corresponding to the fundamental wave of the bulging disturbance with a period of 0.33 [m] and the higher harmonic with a period of 0.165 [m] are included. And, since there is no component with the period of the surface wave, it is understood that the molten metal level fluctuation with the period of the surface wave is not excited.

[0209] From the above, it can be seen that the feedforward compensation is robust against modeling errors. That is, by performing the feedforward compensation in a time-frequency domain that is lower than the time frequency at which the phase difference of the modeling error of the controlled object is π / 3 and lower than the time frequency of the surface wave of the molten metal surface in the mold, it can be seen that the feedforward compensation has robustness against modeling errors. In the above example, the period corresponding to the time frequency at which the phase difference of the modeling error of the controlled object is π / 3 is 0.144 [s] × 6 = 0.864 [s], and the period corresponding to the time frequency of the surface wave of the molten metal surface in the mold is 1.5 [s], so that the time-frequency domain is lower than the period of 1.5 [s]. In the above simulation, the feedforward compensation is performed on the lower frequency side than the period of 4.0 [s], taking into account a margin.

[0210] As described above, the molten metal level control device CT and the molten metal level control method implemented therein in the embodiment calculate not only the amplitude and period but also the phase in order to cancel out disturbances, so that fluctuations in the molten metal level due to disturbances can be suppressed by feedforward compensation. The above-mentioned molten metal level control device CT and molten metal level control method add a feedforward compensation amount to the feedback compensation amount, so that the stability of the feedback control is not easily affected, and the feedback control band can be maintained wide. Therefore, the above-mentioned molten metal level control device CT and molten metal level control method can suppress periodic bulging disturbances while maintaining a wide control band of feedback control.

[0211] In the case of the disturbance estimation observer disclosed in Patent Document 1, a filter is used, which causes a phase delay and limits the effect of reducing the fluctuation of the molten metal level. If feedback compensation is used to deal with the periodic disturbance of bulging, the control band will become narrow.

[0212] When the casting speed is changed, the intervals between the values ​​on the slab are also changed in the time domain, which affects the casting speed. The above-mentioned molten metal level control device CT and molten metal level control method change the time domain to the spatial domain, so that the feedforward compensation amount can be appropriately calculated without being affected by the above-mentioned influence, and the molten metal level can be appropriately controlled.

[0213] The feedforward compensation amount may be composed of a first sine wave component (a component of frequency j) having a peak, but the first sine wave component may have an opposite phase to a desired phase for canceling out a disturbance. The above-mentioned molten metal level control device CT and molten metal level control method select a phase that best cancels out the disturbance from among the first to third phases of the first to third sine wave components (components of frequency j, pre, and post) as the phase of the feedforward compensation amount, so that a more appropriate phase can be selected. The above-mentioned molten metal level control device CT and molten metal level control method can handle even cases where disturbances of multiple frequencies are applied. For example, when peaks are adjacent to each other, the phase also changes significantly near the frequency of the adjacent peaks, but the above-mentioned molten metal level control device CT and molten metal level control method can select an appropriate phase by determining the phase that cancels out the disturbance by calculating the amount of cancellation of the disturbance.

[0214] Since it is determined whether or not to cancel the disturbance within a certain period (time and space) at the sampling timing, the above-mentioned molten metal level control device CT and molten metal level control method are unlikely to provide overly sensitive compensation even in unsteady cases where the disturbance or the controlled object changes.

[0215] The above-mentioned molten metal level control device CT and molten metal level control method adjust the gain type, so that feedback control can be performed with an appropriate gain according to the absolute value of the rate of the operation amount of the valve VL, and the molten metal level can be controlled within the rate limit (within the operating speed limit) of the actuator that drives the valve. In other words, the above-mentioned molten metal level control device CT and molten metal level control method can make the performance of the feedback control as high as possible without causing instability, and can continue the control.

[0216] Therefore, the above-mentioned molten metal level control device CT and molten metal level control method operate adaptively to changes in the controlled object and external disturbances, maintain stability, maintain a wide control band, and use feedforward compensation in combination with feedback compensation to suppress fluctuations in the molten metal level due to disturbances, even if the disturbances contain multiple frequency components.

[0217] In order to express the present invention, the present invention has been described adequately and sufficiently through the embodiments with reference to the drawings in the above description, but it should be recognized that those skilled in the art can easily change and / or improve the above-mentioned embodiments. Therefore, unless the changes or improvements made by those skilled in the art are at a level that departs from the scope of the claims described in the claims, the changes or improvements are interpreted as being included in the scope of the claims. [Explanation of symbols]

[0218] CT Molten metal level control device SY Upper system CM Continuous Casting Machine TD Tundish AC Actuator VL Valve MD mold RL Role 1 Level measurement section 10. Subtractor 11 FB compensator 12 FF compensator 13 Adder 111 PID control unit 112 Filter section

Claims

1. A molten steel level control device that controls a molten steel level of a continuous casting machine by controlling an adjustment device that adjusts an amount of molten steel supplied to a mold of the continuous casting machine using feedback control, an FF compensation unit that calculates a feedforward compensation amount consisting of a sine wave component having an amplitude, a period, and a phase for canceling a disturbance applied to the molten metal level, based on the molten metal level, an operation amount of the adjusting device, and a transfer function of the continuous casting machine related to the molten metal level; an adder that adds a feedforward compensation amount calculated by the FF compensation unit to a feedback compensation amount of the feedback control when performing control using the feedback control, When the molten metal level and the operation amount of the adjustment device are a plurality of values ​​arranged in a time domain at a predetermined time interval in a time series, the FF compensation unit converts each value of the molten metal level and the operation amount of the adjustment device in the time domain into each value in a spatial domain having a coordinate axis in the longitudinal direction of the slab produced by the continuous casting machine, and converts the transfer function from the time frequency domain to a spatial frequency domain, and then calculates the feedforward compensation amount. Water level control device.

2. the FF compensation unit obtains a plurality of the sine wave components for a plurality of frequencies different from each other, obtains a cancellation amount of the disturbance for each of a first phase of a first sine wave component having a peak from among the plurality of sine wave components, a second phase of a second sine wave component on the low frequency side relative to the first sine wave component, and a third phase of a third sine wave component on the high frequency side relative to the first sine wave component, and selects, from the first to third phases, a phase that cancels out the disturbance most as a phase of the feedback compensation amount. The molten metal level control device according to claim 1 .

3. a gain type changing unit that changes a gain of the feedback control to be smaller than a current value when an absolute value of a rate in the manipulated variable of the adjustment device is larger than a predetermined first threshold, and changes a gain of the feedback control to be larger than a current value when an absolute value of a rate in the manipulated variable of the adjustment device is smaller than a positive predetermined second threshold that is smaller than the first threshold, The molten metal level control device according to claim 1 or 2.

4. Feedforward compensation is performed in a time-frequency domain that is lower than the time frequency at which the phase difference of the modeling error of the control object is π / 3 and is lower than the time frequency of the surface wave of the molten metal surface in the mold. The molten metal level control device according to any one of claims 1 to 3.

5. A molten steel level control method for controlling a molten steel level in a continuous casting machine by controlling an adjustment device for adjusting an amount of molten steel supplied from a tundish of the continuous casting machine to a mold using feedback control, comprising: an FF compensation step of determining a feedforward compensation amount consisting of a sine wave component having an amplitude, a period and a phase for canceling a disturbance applied to the molten metal level, based on the molten metal level, an operation amount of the adjusting device, and a transfer function of the continuous casting machine related to the molten metal level; an adding step of adding a feedforward compensation amount calculated in the FF compensation step to a feedback compensation amount of the feedback control when performing control using the feedback control; When the molten metal level and the operation amount of the adjusting device are a plurality of values ​​arranged in a time domain at a predetermined time interval in a time series, the FF compensation step converts the values ​​of the molten metal level and the operation amount of the adjusting device in the time domain into values ​​in a spatial domain having a coordinate axis in the longitudinal direction of the slab produced by the continuous casting machine, and converts the transfer function from the time frequency domain to the spatial frequency domain, and then calculates the feedforward compensation amount. A method for controlling the molten metal level.

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