JP2000322106A - Control of molten metal level in mold of continuous casting machine - Google Patents

Abstract

PROBLEM TO BE SOLVED: To realize a control method capable of suppressing the variation of a molten metal level in a mold more effectively as compared with a conventional method even when errors exist in a numerical model of a continuous casting machine or the frequency characteristic of the casting machine is unknown. SOLUTION: A molten metal level in the mold 3 of the continuous casting machine is measured by a level sensor 4 and a deviation of the measured value from a set value is supplied to a feedback controller 6 and a disturbance estimation type adaptive controller 7. The controller 7 estimates periodical disturbance from the deviation and outputs an adaptive controlled variable for canceling the disturbance and the controller 6 outputs a feedback controlled variable. These two controlled variables are mutually added and the added value is supplied to an actuator 5. Then the aperture of a sliding nozzle 2 is controlled by a driving output from the actuator 5 and the molten metal level in the mold 3 is controlled.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method for controlling the level of molten metal in a mold by adjusting the amount of molten steel supplied from a tundish into a mold by the opening of a sliding nozzle in a continuous casting process. is there.

[0002]

2. Description of the Related Art In a continuous casting machine, the amount of molten steel supplied from a tundish into a mold (hereinafter referred to as a mold) is adjusted by the opening of a sliding nozzle so that the level of the molten metal in the mold matches the set level. Control. Fluctuations in the level of the molten steel in the mold are the main cause of product surface defects caused by powder entrainment, and controlling the level of the molten metal to a constant level is an important technology that directly leads to improvement in yield and product quality. It is. Conventionally, as a molten steel level control in a mold in a continuous casting machine, for example, PID control (combination control of a proportional operation, an integral operation, and a differential operation) as disclosed in JP-A-64-53747 is generally used.

[0003] However, in a continuous casting machine, the disturbance of the molten steel surface caused by the fluctuation of the drawing speed when the molten steel whose surface layer is solidified is pulled out of the mold, the fluctuation of the molten steel surface due to the fluctuation of the flow rate of the molten steel in the tundish, and the pinching roll called bulging. There are various disturbances such as periodic fluctuations in the molten metal level due to unsolidified volume fluctuations, and fluctuations in the flow rate characteristics of molten steel in the nozzle due to adhesion and detachment of alumina in the sliding nozzle, and ripples when modeling is difficult. Due to such factors as fluctuations in the parameters to be controlled and parasitic elements such as the occurrence and non-linear flow characteristics of the sliding nozzle, it is difficult to reduce fluctuations in the level of the molten metal in ordinary PID control. To solve the above-mentioned problem, for example, Japanese Patent Laid-Open No. 7-2
Japanese Patent No. 32252 proposes an automatic tuning method using a disturbance observer, and Japanese Patent Application Laid-Open No. Hei 9-146608 discloses a method that is stable with respect to the characteristic fluctuation of the above-mentioned controlled object and suppresses the amount of molten metal fluctuation with respect to the above-mentioned disturbance. Is attempted by a method of determining a control system that realizes the above as a solution to the mixed sensitivity problem of the robust (H∞) control theory.

[0004]

However, in each of the above publications, the controller is derived based on the mathematical model of the object to be controlled. Therefore, when an accurate mathematical model is obtained, the effect is exhibited. However, the control effect cannot be sufficiently exhibited when it is difficult to form an accurate mathematical model or when there is a variation factor in the control target. Furthermore, in the molten metal level control system of the continuous casting machine, the characteristics of the sliding nozzle are nonlinear, and the flow coefficient varies depending on the operating point. Also, phenomena such as alumina adhesion and dropping in the sliding nozzle and fluctuations in the flow rate of molten steel in the tundish also cause changes in the flow coefficient. Therefore, the control system configuration based on the robust (H∞) control theory requires a control system with a model error. There is a problem that the performance of the system cannot be determined at the design stage.

[0005] The present invention avoids the above-mentioned problems, and employs a control system configuration in which adaptive feedforward control is added to conventional feedback control. An object of the present invention is to provide a method for controlling a level of a metal level in a mold of a continuous casting machine, which effectively suppresses a change in the level of the metal level due to disturbance such as bulging without being affected by a model error.

[0006]

According to a first aspect of the present invention, there is provided a method for controlling a mold level in a mold of a continuous casting machine, the method comprising measuring a mold level in the mold of the continuous caster and feedback-controlling a deviation of the measured value from a set value. A method for controlling the level of the molten metal by controlling the actuator by the output of the feedback controller, operating the actuator by the output of the actuator, adjusting the opening of a sliding nozzle provided on the tundish for supplying molten steel by the drive output of the actuator And estimating and calculating an adaptive control operation amount for estimating a periodic disturbance that causes a change in the level of the molten metal from the deviation of the measured level of the molten metal from the set value, and canceling the level of the molten metal due to the estimated periodic disturbance. And the calculated adaptive control operation amount as a feedforward amount of the sliding nozzle opening change. , Those having an operation step of operating the actuator by adding the control output of the feedback controller.

According to a second aspect of the present invention, there is provided a method for controlling a level in a mold of a continuous casting machine according to the first aspect, wherein a frequency characteristic of the continuous casting machine is known. , The estimating / calculating step calculates the transfer function G (jω) of the continuous casting machine model as G (j
ω) = Ae ^jθ (where ω indicates the angular frequency of the level-level vibration), and the deviation of the level-level measurement from the set value is e
(T) (where t represents time), and the feedforward control input r to the continuous caster model is given by r = α (t) sin
(Ωt) + β (t) cos (ωt), the above e
(T) are individually multiplied by sin (ωt) and cos (ωt), and outputs n ₁ (t) and n obtained by individually low-pass filtering the products.
₂ (t), and then Fourier coefficients α (t), β of the input r for stabilizing the n ₁ (t) and n ₂ (t).
A linear adaptation algorithm for obtaining (t) by the following equations (a) and (b) (where k represents the number of sampling counts) is used. α (k + 1) = α (k) - (cos (θ) n 1 (k) + sin (θ) n 2 (k)) / A ... (a) β (k + 1) = β (k) - (cos (θ ) N ₂ (k) + sin (θ) n ₁ (k)) / A (b)

According to a third aspect of the present invention, there is provided a method for controlling a level in a mold of a continuous casting machine according to the first aspect, wherein the frequency characteristic of the continuous casting machine is unknown. , The estimating / calculating step calculates the transfer function G (jω) of the continuous casting machine model as G (j
ω) = Ae ^jθ (where ω indicates the angular frequency of the level-level vibration), and the deviation of the level-level measurement from the set value is e
(T) (where t represents time), and the feedforward control input r to the continuous caster model is given by r = α (t) sin
(Ωt) + β (t) cos (ωt), the above e
(T) are individually multiplied by sin (ωt) and cos (ωt), and outputs n ₁ (t) and n obtained by individually low-pass filtering the products.
₂ (t), and then Fourier coefficients α (t), β of the input r for stabilizing the n ₁ (t) and n ₂ (t).
(T) is calculated by the following equations (c) and (d) (where k represents the number of sampling counts), and μ ₁ ,
mu ₂ is expressed by the following equation as a step size (e), it is to use a nonlinear adaptive algorithm obtained by (f). α (k + 1) = α (k) -μ ₁ (k + 1) n ₁ (k) (c) β (k + 1) = β (k) -μ ₂ (k + 1) n ₂ (k) ... (d) μ _{1 (k + 1) = μ 1} (k) sgn (n 1 2 (k-1) -n 1 2 (k)) ... (e) μ 2 (k + 1) = μ 2 (k) sgn (n 2 2 (k- ^{_{1) -n 2 2 (k)}} ) ... (f)

As a result, even when there is an error in the mathematical model of the continuous casting machine to be controlled, the control performance does not deteriorate as in the prior art, and when the frequency characteristics of the continuous casting machine are known or unknown. In addition, by obtaining the feedforward control operation amount in each case and adding the amount to the conventional feedback control operation amount to operate the actuator, it is possible to more effectively suppress the fluctuation of the molten metal level than before, Quality and yield can be improved.

[0010]

FIG. 1 is a view showing an entire continuous casting system according to an embodiment of the present invention. In FIG. 1, 1 is a tundish, 2 is a sliding nozzle for adjusting the flow rate of molten steel, 3 is a mold, and 4 is a mold. Is a level sensor for measuring the level of the molten metal, 5 is an actuator for adjusting the nozzle opening, 6 is a conventional feedback controller (for example, a PID controller, etc.), 7
Is a disturbance estimation type adaptive controller of the present invention, 8 is, for example, a water-cooled cooler, and 18 is a roll. FIG. 2 to FIG.
1 is a block diagram showing a specific configuration of each part of the system of FIG. 1, and the configuration of each drawing will be described first.

FIG. 2 is a diagram showing a control system based on the disturbance estimation type adaptive controller shown in FIG. 1. In FIG. 2, 9 is a continuous casting machine model, 10 is a periodic disturbance estimation type adaptive algorithm, d is a level fluctuation disturbance, and e is Is the level error signal, r is the feedforward adaptive control input, and y is the output of the continuous casting machine model. In addition, the adaptive algorithm 10 of the periodic disturbance estimation type
Ω of sin (ωt) and cos (ωt) are angular frequencies of the level-level vibration, for example, bulging-type level fluctuation frequency, and the value of ω is known or measurable.

FIG. 3 is a view showing a control model of the continuous casting machine by the feedback controller of FIG. 1. The figure shows a model linearized near the casting operating point (fluid level -80 mm). In FIG. 3, 11 is a Pad approximation of the dead time, 12 is a first-order lag characteristic of the sliding nozzle system,
(T ₁ is an actuator time constant), 13 is a sliding nozzle opening coefficient K _a , 14 is a mold end area K _A , 1
5 is an integral characteristic of the mold, 16 is a first-order lag characteristic of the level sensor (t ₂ is a time constant of the level sensor), 17 is a feedback controller (for example, a PID controller), and y is a level value measured. is there.

In the control system shown in FIG. 3, the mold in which the input signal is the molten steel injection flow rate and the output signal is the level of the molten metal is an integral system, and the dynamic characteristics of the sliding nozzle system are first-order lag +
Dead time (time constant: 0.1 s, dead time: 0.4
s). The dynamic characteristic of the level sensor is set as a first-order lag (time constant: 0.15 s). The output signal is a deviation of the measured level value from the target value, and the control input is a nozzle opening operation amount. It is assumed that the following disturbance and fluctuation factors exist in this control system. (A) Ripple due to oscillation (frequency range: 2 to 2)
(3 Hz) (b) Standing wave excited by movement of the immersion nozzle (frequency range: 0.6 to 0.9 Hz) (c) Steady and unsteady bulging-fluctuation of the molten metal level (frequency range: 0.05 to 0. 3 Hz) 15Hz)

FIG. 4 is a diagram showing an example of the configuration of the disturbance estimation type adaptive controller shown in FIG. 1. In FIG. 4, reference numeral 21 denotes a fluid level fluctuation error signal filtering device; 22, an adaptive estimation device; and 23, an adaptive control output device. is there. It should be noted that n ₁ (t) and n ₂ (t) output from the fluid level fluctuation error signal filtering device 21 are output signals of low-pass filters 31 and 32 in FIG. 5 described later, and t is time. is there. K in () of the input / output signal of the adaptive estimation device 22 is a sampling count number. That is, when data is sampled at each sampling period (ΔT), the product ΔT · k of the sampling period ΔT and the sampling count number k is in a relationship of the time t. The output r (t) of the adaptive control output device 23 is r (t) =
It is output as α (t) sin (ωt) + β (t) cos (ωt), where α (t) and β (t) are the Fourier coefficients of the adaptive rule in the adaptive estimation device 22.

FIG. 5 is a diagram showing an example of the configuration of the apparatus for filtering the level-of-fluctuation error signal shown in FIG. 4. Reference numerals 31 and 32 denote independent low-pass filters (LPFs). In FIG. 5, the deviation e (t) with respect to the set value of the measured level of the molten metal level is individually multiplied by sin (ωt) and cos (ωt), and the output obtained by individually low-pass filtering the product is n.
₁ (t) and n ₂ (t).

First, the operation of FIG. 1 will be schematically described. In the continuous casting system, as shown in FIG. 1, molten steel is injected from a tundish 1 into a mold 3 through a sliding nozzle 2 whose molten steel supply amount is adjusted by a drive output of an actuator 5. The level of the molten metal in the mold 3 is measured by the level sensor 4, and the deviation of the measured value from the set value is input to both the conventional feedback controller 6 and the disturbance estimation type controller 7 of the present invention.
The feedback controller 6 outputs a feedback control output based on the control system model of FIG. 3 as a sliding nozzle opening command, and the disturbance estimation type adaptive controller 7
An adaptive control operation amount to be described later is output as a feedforward amount for changing the opening degree of the sliding nozzle.

The two control outputs output from the feedback controller 6 and the disturbance estimation type adaptive controller 7 are added together, and the added value is supplied to the actuator 5.
The actuator 5 adjusts the opening of the sliding nozzle 2 by a drive output based on the operation input of the addition result,
The amount of molten steel supplied into the mold 3 is controlled. In this way, the level of the molten metal in the mold 3 is controlled to be constant. Cooled by the cooler 8 in the mold 3 (for example, water-cooled)
The molten steel whose surface layer has solidified is sequentially pulled out by the roll 18. Hereinafter, an embodiment of the present invention will be described mainly with reference to FIGS.

In FIG. 2, the molten metal level change control system in the mold of the continuous casting machine proposed by the present invention uses the periodic disturbance estimation type adaptive algorithm 10 to calculate the deviation of the measured molten metal level from the set molten metal level e. The disturbance (vibration width and phase) is directly estimated, and the control is performed by determining, in a feed-forward manner, the opening operation amount r of the sliding nozzle for canceling the fluctuation of the molten metal level due to the disturbance.

Next, a method of designing a control system will be described. In the control block diagram of FIG. 2, periodic disturbance d is assumed as in the following equation (1). d = α _d sin (ωt) + β _d cos (ωt) .. (1) Here, ω is an angular frequency of the above-mentioned level-level vibration, for example, a bulging-type level fluctuation angular frequency, and its value is known or measurable. It is assumed that the transfer function of the continuous casting machine model 9 is the following equation (2). G (jω) = Ae ^jθ (2) Feedforward control input r to the continuous casting machine model 9
Is given by the following equation (3). r = α (t) sin (ωt) + β (t) cos (ωt) (3)

In response to the above input, the continuous casting machine model 9
Is the following equation (4), and the error signal e obtained by adding the disturbance d of the equation (1) to the steady output y is the following equation (5).
become that way. y = A (α (t) sin (ωt + θ) + β (t) cos (ωt + θ)) ... (4) e = A (α (t) sin (ωt + θ) + β (t) cos (ωt + θ)) + α d sin ( ωt) + β _d cos (ωt) (5) Here, θ is the phase of the continuous casting machine model 9 as shown in Expression (2).

The error signal e obtained by the equation (5) is multiplied by sin (ωt) and cos (ωt) as shown in FIG. 5, and the products are processed by the low-pass filters 31 and 32. And remove high frequency components. Low-pass filter 3
The steady state outputs of 1, 32 are approximately given by the following equation (6):
It becomes like (7). _{n 1 (t) = 0.5 (} Aαcos (θ) + α d -Aβsin (θ)) ... (6) n 2 (t) = 0.5 (Aβcos (θ) + β d -Aαsin (θ)) ... ( 7) However, the cutoff frequency ω _B of the low-pass filters 31 and 32 is designed so as to satisfy the following equation (8). ω _B << 2ω (8) The processing of the above equations (6) and (7) is performed in the fluid level fluctuation error signal filtering processor 21 of FIG.

Next, the processing in the adaptive estimating device 22 shown in FIG. 4, that is, the adaptive law for stabilizing the equations (6) and (7) (the Fourier coefficient α (t) of the input r shown in the equation (3)) ,
A method of obtaining β (t)) will be described. (A) When the phase θ of the continuous casting machine model is known When the frequency characteristics of the continuous casting machine model can be identified, the adaptive correction coefficient is expressed by the following equations (9) and (1).
0). α (k + 1) = α (k) - (cos (θ) n 1 (k) + sin (θ) n 2 (k)) / A ... (9) β (k + 1) = β (k) - (cos (θ ) N ₂ (k) + sin (θ) n ₁ (k)) / A (10) Here, k in () is the sampling count. The output of the internal filter of the control system using the adaptive law of the above equation is as in the following equations (11) and (12). _{n 1 (k + 1) =} 0.5n 1 (k) ... (11) n 2 (k + 1) = 0.5n 2 (k) ... (12) Equation (11) and (12), the system is a linear It can be seen that the eigenvalues are all asymptotically stable at -0.5.

(B) When the phase θ of the continuous casting machine model is unknown When the frequency characteristics of the continuous casting machine model cannot be obtained,
Even if this frequency characteristic is obtained, when the phase is a non-linear object whose frequency depends on the frequency, and when there is uncertainty in the phase, the adaptive rules of the equations (9) and (10) become unstable. There is a risk of becoming. To prevent this, the following adaptive law that does not depend on the phase characteristics of the continuous casting machine model is used. α (k + 1) = α (k) −μ ₁ (k + 1) n ₁ (k) (13) β (k + 1) = β (k) −μ ₂ (k + 1) n ₂ (k) (14) Μ ₁ and μ ₂ in the equations are step sizes, which are obtained as in the following equations (15) and (16).

[0024] _{μ 1 (k + 1) =} μ 1 (k) sgn (n 1 2 (k-1) -n 1 2 (k)) ... (15) μ 2 (k + 1) = μ 2 (k) sgn (n ₂ ² (k−1) −n ₂ ² (k)) (16) Note that “sgn” is called “signum” and sgnx is sg
For n0 = 0 and x ≠ 0, sgnx = x / | x |.
According to the above equations (13) to (16), this system is nonlinear. As a result of examining the phase plane locus of this nonlinear system for various phases θ by simulation, the following equation (1) is obtained.
Asymptotic stability of this nonlinear system can be guaranteed within the parameter range of 7). | Μ ₁ | <1 / A, i = 1,2 ... (17)

In the adaptive control output device 23 shown in FIG. 4, the equations (9) and (10) for the linear control system calculated by the adaptive estimator 22 or the formula (1) for the non-linear control system are used.
3) For α (k) and β (k) based on (14),
First, the sampling period ΔT and the sampling count k
Are obtained, and α (t) and β (t) are sequentially obtained. Next, r (t) is sequentially calculated by the above equation (3), and this r (t) is sequentially output as a feedforward adaptive control operation amount. The feedforward adaptive control operation amount is added to the feedback control operation amount output from the feedback controller 6 in FIG. As a result, the fluctuation of the level of the molten metal in the mold 3 is suppressed as described above.

The control effect on the measured data of the level of the molten metal level in the mold of the continuous casting machine using the above adaptive algorithm will be described below. The control system was configured as shown in FIG. 1, and the simulation for the change in the level of the molten metal level in the mold was performed using the following parameters. Disturbance frequency: 0.0851 Hz Initial value: n ₁ (0) = n ₂ (0) = 0, α (0) = 6
β (0) = 0 Step size: | μ ₁ | <0.6 / A, i = 1,2

FIG. 6 is a diagram showing a change in the molten metal level when the control method according to the embodiment of the present invention is not performed.
FIG. 6 is a diagram showing a simulation result of a change in the level of the molten metal when the control method according to the embodiment of the present invention is performed.
From the simulation showing the control results in FIG. 7, it can be seen that the amplitude of the level change of the metal surface is suppressed as time elapses from the start of the control, and that after a certain time elapses, 50 to 60% of the amplitude of the level fluctuation at the start of the control can be suppressed. .

As described above, according to the present embodiment, in the method for controlling the level of the molten metal in the mold in the continuous casting, the sliding placed on the tundish according to the deviation of the measured value of the molten metal level from the set value. When designing a control system for controlling the level of the molten metal according to the nozzle opening command, the adaptive algorithm for periodic disturbance estimation is applied, and the level of the molten metal is controlled without being affected by the error of the mathematical model of the continuous casting machine. Periodic disturbances (vibration width and phase) that cause fluctuations in the level of the bath surface from the deviation of the measured value from the set value
And an adaptive control operation amount for canceling the level change caused by the estimated periodic disturbance is calculated, and this is added to the conventional feedback control operation amount as a feedforward amount for changing the opening of the sliding nozzle. In the conventional control method, it is possible to effectively control the level change of the bulging property without causing deterioration of the control performance in the presence of the mathematical model error, which is problematic in the conventional control method, and to improve the product quality and yield. Can contribute to improvement.

[0029]

As described above, according to the present invention, the mold level in the mold of the continuous casting machine is measured, the deviation of the measured value from the set value is input to the feedback controller, and the control output of the feedback controller is used. In the method of operating an actuator, adjusting the opening of a sliding nozzle provided on a tundish for supplying molten steel by the actuator drive output and controlling the level of the molten metal, when the frequency characteristic of the continuous casting machine is known, Uses a linear adaptation algorithm, and if the frequency characteristics are unknown, uses a non-linear adaptation algorithm to estimate a periodic disturbance that causes a change in the level of the molten metal from the deviation from the set value of the measured level of the molten metal. Calculating adaptive control manipulated variables for canceling the level change caused by the estimated periodic disturbance, The control operation amount is added to the control output of the feedback controller as the feedforward amount of the sliding nozzle opening change to operate the actuator, so that the mathematical expression model of the continuous casting machine to be controlled is Even when there is an error, it is possible to more effectively suppress the fluctuation of the molten metal level than before, without causing the deterioration of the control performance as in the related art, and to contribute to the improvement of the product quality and the yield.

[Brief description of the drawings]

FIG. 1 is a diagram showing an entire continuous casting system according to an embodiment of the present invention.

FIG. 2 is a diagram showing a control system by a disturbance estimation type adaptive controller of FIG. 1;

FIG. 3 is a view showing a control model of a continuous casting machine by the feedback controller of FIG. 1;

FIG. 4 is a diagram illustrating a configuration example of a disturbance estimation type adaptive controller in FIG. 1;

FIG. 5 is a diagram showing a configuration example of a fluid level fluctuation error signal filtering device of FIG. 4;

FIG. 6 is a diagram illustrating a change in the level of the molten metal when the control method according to the embodiment of the present invention is not performed.

FIG. 7 is a diagram showing a change in the level of the molten metal when the control method according to the embodiment of the present invention is performed.

[Explanation of symbols]

 DESCRIPTION OF SYMBOLS 1 Tundish 2 Sliding nozzle 3 Mold 4 Level sensor 5 Actuator 6, 17 Feedback controller 7 Disturbance estimation type adaptive controller 8 Cooler 9 Continuous casting machine model 10 Periodic disturbance estimation type adaptive algorithm 18 Roll 21 Metal surface level fluctuation error signal Filtering device 22 Adaptive estimator 23 Adaptive control output device 31, 32 Low-pass filter

Continued on front page F-term (reference) 4E004 MB02 MB09 5H004 GA07 GA40 GB03 HA05 HB05 JB30 KA31 KB02 KB04 KB06 KB33 KC33 KC55 LA01 LA03 LA13 MA12

Claims (3)

[Claims] 1. A level of molten metal in a mold of a continuous casting machine is measured, a deviation of the measured value from a set value is input to a feedback controller, an actuator is operated by a control output of the feedback controller, and a drive output of the actuator is output. In the method for controlling the level of the molten metal level by adjusting the opening of a sliding nozzle provided in a tundish for supplying molten steel, a periodic disturbance that causes a variation of the molten metal level from a set value of the measured molten metal level is provided. Estimating and calculating an adaptive control operation amount for canceling the level change due to the estimated periodic disturbance; anda feed-forward amount for changing the sliding nozzle opening degree by calculating the adaptive control operation amount. The operation of adding the control output of the feedback controller to operate the actuator. Caster mold molten steel surface level control method characterized by a step. 2. When the frequency characteristic of the continuous casting machine is known, the estimating / calculating step is performed by setting the transfer function G (jω) of the continuous casting machine model to G (jω) =
Ae ^j.theta. (Where ω denotes the angular frequency of the molten metal surface level oscillation), the deviation for the set value of the molten metal surface level measured value e (t) (where t represents time), the feedforward to the continuous casting machine model When the control input r is r = α (t) sin (ωt) + β (t) cos (ωt), e (t) is multiplied by sin (ωt) and cos (ωt), respectively. Output n of low-pass filtered products
₁ (t) and n ₂ (t) are obtained, respectively. Next, the Fourier coefficients α (t) and β (t) of the input r for stabilizing the n ₁ (t) and n ₂ (t) are given by the following equations. (A), (b)
2. The method according to claim 1, wherein a linear adaptive algorithm obtained by (where k represents a sampling count number) is used. α (k + 1) = α (k) - (cos (θ) n 1 (k) + sin (θ) n 2 (k)) / A ... (a) β (k + 1) = β (k) - (cos (θ ) N ₂ (k) + sin (θ) n ₁ (k)) / A (b) 3. When the frequency characteristic of the continuous casting machine is unknown, the estimating / calculating step is performed by setting the transfer function G (jω) of the continuous casting machine model to G (jω) =
Ae ^j.theta. (Where ω denotes the angular frequency of the molten metal surface level oscillation), the deviation for the set value of the molten metal surface level measured value e (t) (where t represents time), the feedforward to the continuous casting machine model When the control input r is r = α (t) sin (ωt) + β (t) cos (ωt), e (t) is multiplied by sin (ωt) and cos (ωt), respectively. Output n of low-pass filtered products
₁ (t) and n ₂ (t) are obtained, respectively. Next, the Fourier coefficients α (t) and β (t) of the input r for stabilizing the n ₁ (t) and n ₂ (t) are given by the following equations. (C), (d)
(Where k represents the number of sampling counts), and μ ₁ and μ ₂ in the equations (c) and (d) are used as a step size using a nonlinear adaptive algorithm obtained by the following equations (e) and (f). The method for controlling the level of a molten metal in a mold of a continuous casting machine according to claim 1, characterized in that: α (k + 1) = α (k) -μ ₁ (k + 1) n ₁ (k) (c) β (k + 1) = β (k) -μ ₂ (k + 1) n ₂ (k) ... (d) μ _{1 (k + 1) = μ 1} (k) sgn (n 1 2 (k-1) -n 1 2 (k)) ... (e) μ 2 (k + 1) = μ 2 (k) sgn (n 2 2 (k- ^{_{1) -n 2 2 (k)}} ) ... (f)