JP2014111269A - Frequency estimation device, method and program in molten metal surface level control system of continuous casting machine - Google Patents

Abstract

PROBLEM TO BE SOLVED: To allow a frequency component of periodic disturbance causing fluctuation of molten metal surface level to be estimated accurately and with high responsiveness.SOLUTION: A frequency estimation device 108, which estimates a frequency component of a periodic disturbance causing fluctuation of molten metal surface level, in a molten metal surface level control system that detects the molten metal surface level inside a mold during operation of a continuous casting machine and controls the molten metal surface level y to be maintained at a target level r using deviation between the detection level and a predetermined target level r, comprises: an initial frequency searching portion 108a that inputs a signal of the detection level y or a signal required depending on the detection level y to estimate frequency by the iterative least squares technique; and a nonlinear optimization portion 108b that inputs the frequency estimated by the initial frequency searching portion 108a to estimate the frequency component of periodic disturbance causing fluctuation of the molten metal surface level by a nonlinear optimization technique.

Description

  The present invention relates to a frequency estimation device, method, and program in a continuous casting machine level control system for controlling the molten metal level in a mold so as to maintain a target level without periodic fluctuations in a continuous casting machine. About.

  FIG. 10 shows an outline of the continuous casting machine. A tundish 20 for storing a molten metal (molten metal) 2 is arranged above the mold 1 having openings on the top and bottom. A pouring nozzle 3 is connected to the bottom surface of the tundish 20 and extends to the inside of the mold 1, and the molten metal 2 in the tundish 20 passes through the sliding gate 30 of the pouring nozzle 3 into the mold 1. It is poured. The molten metal 2 poured into the mold 1 is cooled by contact with the water-cooled inner wall of the mold 1 and solidifies from the outside, and becomes a slab 4 coated on the outside with a solidified shell, below the mold 1. It is pulled out continuously. The slab 4 is pulled out while maintaining a predetermined casting speed while being guided by a plurality of pairs of guide rolls 5 arranged in parallel at predetermined intervals below the mold 1. During this drawing, the slab 4 is cooled by cooling water sprayed from a spray band (not shown), cut to a predetermined dimension when solidification has progressed to the innermost part, and used in subsequent processes such as rolling. Product slab.

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

  During the operation of the continuous casting machine, the molten metal level inside the mold 1 is detected by a level meter 6 facing the surface of the molten metal 2, and this detected level y is given to the molten metal level control device C. Further, the hot water level control device C is given a target value (target level r) of the hot water level to be maintained inside the mold 1 set in the target level setting unit 7. The hot water surface level control device C obtains a deviation between the detection level y detected by the level meter 6 and the target level r set in the target level setting device 7, and the amount of change in the opening of the sliding gate 30 for eliminating this deviation is obtained. Ask. An opening / closing command u is issued to the opening / closing actuator (hydraulic cylinder) 31 of the sliding gate 30 in order to obtain the obtained opening change amount, and the opening of the sliding gate 30 is controlled by the operation of the actuator 31 according to the opening / closing command u. Change and adjust the pouring amount to the mold 1.

  In general, the amount of change in opening is required to increase the low-frequency gain in order to keep the steady level constant, and is obtained by PI calculation or PID calculation using the deviation as an input, and includes a control system including a control target. Is trying to stabilize.

However, in the operation of the continuous casting machine, there are periodic disturbances that cause fluctuations in the molten metal surface level, such as bulging of the slab 4 drawn from the mold 1. In bulging, as shown in FIG. 11, the solidified shell on the outside of the slab 4 drawn out below the mold 1 swells outward between the holding portions of a large number of guide rolls 5 arranged along the drawing path. This is a phenomenon that deforms. At this time, the fluctuation of the molten metal level inside the mold 1 occurs when the molten metal inside the solidified shell enters and leaves the mold 1 due to deformation accompanying bulging, and the temporal change in the bulging amount is periodic. It is supposed to cause level fluctuation. In particular, when the guide rolls 5 are arranged in parallel at the same pitch, the amount of bulging in each guide roll 5 changes in the same phase, so that periodic level fluctuations having a large fluctuation range occur.
It is difficult to suppress the periodic level fluctuation generated in the mold 1 due to such disturbance by the above-described general hot water level control.
Under such circumstances, various hot water surface level control methods have been conventionally proposed in which periodic level fluctuations are suppressed (see, for example, Patent Document 1).

Japanese Patent No. 3591422

“System Identification for Control by MATLAB” Shuichi Adachi (Chapter 6) Tokyo Denki University Press November 1996

To quickly detect the frequency component (frequency component of periodic disturbance that causes the fluctuation of the molten metal level) to be removed and change the controller adaptively according to the fluctuation level of the molten metal level that actually occurs during operation. Thus, it is possible to suppress the periodic level fluctuation generated in the mold 1 due to the disturbance with high accuracy.
For example, Patent Document 1 discloses a configuration in which a disturbance estimated value obtained from a detection level y and an opening degree command u or a detection level y is subjected to fast Fourier transform (FFT) to estimate frequency distribution thereof.
However, in FFT, it is necessary to average the data or spectrum for noise removal. In principle, it is necessary to use a window function, and the S / N ratio cannot be improved unless the region containing the frequency component in the window becomes large.
Moreover, when considering an adaptive control system that eliminates the level fluctuations generated in the mold 1 due to disturbance, it is necessary to estimate the frequency online. Since FFT requires a number of samples such as 512 and 1024, it cannot be said that the FFT estimation method has satisfactory responsiveness.

  The present invention has been made in view of the above points, and it is an object of the present invention to accurately and accurately estimate frequency components of periodic disturbances that cause fluctuations in the molten metal surface level.

The frequency estimation apparatus according to the present invention detects a molten metal level inside a mold during operation of a continuous casting machine, and uses the deviation between the detected level and a predetermined target level to determine the detected molten metal level. In a hot water surface level control system that controls to maintain a level, a frequency estimation device that estimates a frequency component of a periodic disturbance that causes fluctuations in the hot water surface level, the signal of the detection level, or the detection level The signal obtained according to the input is used as an input, the initial frequency search means for estimating the frequency by the recursive least-squares method (RLS method), and the frequency estimated by the initial frequency search means as inputs, and the nonlinear optimum And non-linear optimization means for estimating a frequency component of a periodic disturbance that causes fluctuations in the molten metal surface level.
According to the frequency estimation method of the present invention, the molten metal level inside the mold is detected during operation of the continuous casting machine, and the detected molten metal level is detected using the deviation between the detected level and a predetermined target level. A level estimation method for estimating a frequency component of a periodic disturbance that causes fluctuations in the molten metal surface level in a molten metal surface level control system that is controlled so as to maintain the level, wherein the detected level signal or the detected level The signal obtained according to the input is used as an input, the initial frequency search step for estimating the frequency by the recursive least-squares method (RLS method), and the frequency estimated in the initial frequency search step as an input, and the nonlinear optimum And a non-linear optimization step for estimating a frequency component of a periodic disturbance that causes fluctuations in the molten metal surface level.
The program of the present invention detects a molten metal level in the mold during operation of the continuous casting machine, and uses the deviation between the detected level and a predetermined target level to set the detected molten metal level to the target level. In the hot water level control system for controlling to maintain, a program for estimating a frequency component of a periodic disturbance that causes fluctuations in the hot water level, according to the signal of the detection level or the detection level An initial frequency search process for estimating a frequency by a recursive least-squares method (RLS method) using the required signal as an input, and a nonlinear optimization method using the frequency estimated by the initial frequency search process as an input This causes the computer to execute nonlinear optimization processing for estimating the frequency component of periodic disturbance that causes fluctuations in the molten metal surface level.

  According to the present invention, it is possible to accurately estimate a frequency component of a periodic disturbance that causes fluctuations in the molten metal surface level with good responsiveness.

It is a block diagram showing the hot_water | molten_metal surface level control system containing the hot_water | molten_metal surface level control apparatus and frequency estimation apparatus which concern on embodiment. It is a figure which shows the hot_water | molten_metal surface level fluctuation process model transfer function P (s) of the continuous casting machine in embodiment. It is a figure which shows the structure of the process part of a correction amount calculating part. It is a block diagram showing the other example of the hot_water | molten_metal surface level control system containing the hot_water | molten_metal surface level control apparatus and frequency estimation apparatus which concern on embodiment. (A) is a characteristic diagram which shows input data, (b) is a characteristic diagram which shows the result of having performed the FFT and estimating the frequency distribution. It is a characteristic view which shows the result of having estimated the frequency by RLS, ERLS, and GLS. It is a characteristic view which shows the result of applying the algorithm which minimizes the evaluation function using the signal after a notch filter. It is a figure which shows the relationship between the steepness of a notch filter, and search space. It is a figure which shows the relationship between the steepness of a notch filter, and search space. It is a characteristic view which shows the result of having searched for the optimal solution by searching for the initial frequency by RLS and then switching to the nonlinear optimization method. It is a figure which shows the outline | summary of a continuous casting machine. It is a figure for demonstrating bulging.

Preferred embodiments of the present invention will be described below with reference to the accompanying drawings. For convenience of explanation, components corresponding to the components described above will be described with the same reference numerals.
FIG. 1 is a block diagram showing a hot water level control system including a hot water level control device C according to the embodiment. The target level set in the target level setting unit 7 is r, and the detection level by the level meter 6 is y. In addition, the transfer function of the molten steel level fluctuation process model of the continuous casting machine to be controlled is P (s) (s is a Laplace operator). In addition, a disturbance that causes fluctuations in the hot water level during operation is defined as d (converted to the nozzle opening).
The molten metal level control device C detects the molten metal level y inside the mold 1 during operation of the continuous casting machine, and the opening degree command obtained by using the deviation between the detected level y and a predetermined target level r. According to u, the opening degree of the sliding gate 30 of the pouring nozzle 3 which is the pouring means is changed, and the hot water level is controlled to be maintained at the target level r.

Here, as also in Patent Document 1, the transfer function P (s) of the molten steel surface level fluctuation process model of the continuous casting machine which receives the opening degree command u and outputs the detection level y is the pouring nozzle 3. It is assumed that a dead time element required for pouring water in the interior of the mold (dead time element required for pouring water into the mold 1) P _d (s) = exp (−Ls) is included. L is a dead time required for hot water to drop inside the pouring nozzle 3.
In the present embodiment, as shown in FIG. 2, not only the waste time element P _d (s) required for the pouring of the hot water inside the pouring nozzle 3 is added to the hot water level fluctuation process model transfer function P (s), Including the dynamic characteristic of the sliding gate 30 of the pouring nozzle 3 (approximated as a first-order lag) P _sn (s) and the dynamic characteristic of the level meter 6 (approximated as a first-order lag) P _se (s) Is assumed. That is, the transfer function P (s) of the molten metal surface level fluctuation process model is expressed as the following equation (1). K is a coefficient, T _sn is a primary delay time constant of the sliding gate 30 of the pouring nozzle 3, and T _se is a primary delay time constant of the level meter 6.
In detail, the disturbance d includes a d ₁ (bulging) that occurs at the position of the current molten metal level and a d ₂ (nozzle clogging) that occurs at the pouring position of the molten metal 2.

As shown in FIG. 1, the hot water level control device C includes an addition point 101, an opening degree calculation unit 102, an addition point 103, and a correction amount calculation unit 104. Since the molten metal level control device C is normally calculated in a digital controller, it is handled as a discrete transfer function.
The addition point 101 outputs a deviation signal e between the target level r and the detection level y given as an input.
The opening calculation unit 102 receives the deviation signal e output from the addition point 101 as input, and calculates and outputs the opening change amount u ₀ .
The addition point 103 adds the opening change amount u ₀ output from the opening calculation unit 102 and the opening correction amount v output from the correction amount calculation unit 104 and outputs the addition as an opening command u.
The correction amount calculation unit 104 receives the opening degree command u and the detection level y, calculates the opening degree correction amount v, and outputs it.

The transfer function of the opening calculation unit 102 is C (q ⁻¹ ). Since the molten metal level control device C processes in a discrete system, it is expressed as a transfer function using the operator q when the discrete time system is used (hereinafter, the molten metal level control device C is the same). In general, the transfer function C (q ⁻¹ ) needs to increase the low frequency gain in order to keep the steady level constant, and a PID controller is used. However, the configuration of the opening calculation unit 102 is not limited, and for example, an RST type controller as shown in FIG. 4 may be used.

The correction amount calculation unit 104 has a delay unit 104a that delays the opening degree command u output from the molten metal level control device C and a detection level y as inputs, and is a nominal model of the molten metal level fluctuation process model (design ideal). Model) An arithmetic unit 104b that outputs a result calculated by the discretized inverse transfer function model of P _n (s), and a disturbance estimated value d ^ (d) that is a difference between the output of the arithmetic unit 104b and the output of the delay unit 104aは is added on top of d) and an estimated value dｄ output from the addition point 104c is input, and an opening correction amount v is output. A processing unit 104d is provided.

The delay unit 104a delays and outputs the opening degree command u output from the molten metal level control device C by a step m corresponding to the dead time L. When the calculation cycle in the hot water level control device C is ΔT, L / ΔT = m.
Although there is a method of expressing the dead time by an approximation method such as Padé approximation, the use of Padé approximation results in a non-minimum phase system, which causes problems such as a shift in phase characteristics in a high frequency band. On the other hand, when the notation in the discrete system is used, a quantization error corresponding to the maximum sample time may occur in the dead time, but the approximation accuracy is good in the case where the sample time is short.

In the calculation unit 104b, the transfer function is represented by an inverse transfer function model P ⁻¹ _n (q ⁻¹ ) obtained by discretizing the nominal model P _n (s) of the molten metal surface level fluctuation process model. Since the molten metal level control device C processes in a discrete system, it is expressed as a transfer function using the operator q when the discrete time system is used.
Here, the current detection level y is the result of the transfer function P (s) of the molten metal level fluctuation process model based on the sum of the opening degree command u which is an input L seconds before and the disturbance input d. The transfer function of the calculation unit 104b is a discrete transfer function model obtained by discretizing the nominal model P _n (s). In other words, from the calculation unit 104b, the current detection level y results in L seconds. The sum of the previous opening command u and the disturbance input d is output.
The nominal model in this case shows a structure that does not include dead time, and here, exp (−Ls) · P (q ⁻¹ ) ≈q ^−m · P _n (q ⁻¹ ) is set.
In some cases, nominal models use equipment design values or values obtained from independent test results, but sequential system identification methods, subspace identification methods, etc. are methods that estimate models that minimize the square error from input and output data. Good results can be obtained by using the model obtained by using this method.
Usually, the process model is strictly proper (the denominator order is larger than the numerator order), and the inverse transfer function is not a proper function. For this reason, in order to implement the inverse transfer function model in which the nominal model is discretized, it is general to express a combination of first-order and second-order lag functions. In this case, in order to maintain the identity of the signal, it is necessary to combine the same function with the delay unit 104a. The time constant of the combination function at this time is preferably 5 to 10 times higher than the disturbance frequency band.

  As a result of inputting the output of the delay unit 104a and the output of the calculation unit 104b, the addition point 104c is the result of the opening degree command u before m steps (corresponding to the dead time L) and the detected level y detected now. The estimated disturbance value d ^ which is the difference from the opening degree command u before L seconds is output.

The processing unit 104d receives the estimated disturbance value d ^ output from the addition point 104c and outputs an opening correction amount v. The transfer function of the processing unit 104d is V (q ⁻¹ ). Since the molten metal level control device C processes in a discrete system, it is expressed as a transfer function using the operator q when the discrete time system is used.
Here, in the processing unit 104d, it is necessary to extract a frequency component to be removed, that is, a frequency component of a periodic disturbance that causes fluctuations in the molten metal surface level, from the disturbance estimated value d ^ including a plurality of frequency components.
The estimated disturbance value d ^ output from the addition point 104c is an estimate of the disturbance before m steps (corresponding to the dead time L). Since the output of the processing unit 104d should be the opening correction amount v with respect to the current opening command u output from the molten metal level control device C, it is necessary to estimate the current disturbance.

As a method for designing such a transfer function V (q ⁻¹ ) of the processing unit 104d, there is a method of performing an inverse matrix calculation using a Bezout equation.
The transfer function G _yd (q ⁻¹ ) at the disturbance → water surface level is expressed by equation (2). In the equation (2), [1-V (q ⁻¹ ) q ^−m ] is a term added when the correction amount calculation unit 104 is provided.
Then, V (q ⁻¹ ) may be set as in equation (3), and the transfer function V (q ⁻¹ ) may be designed so as to be in equation (4). In the equation (4), [(1-2 cos ω · q ⁻¹ + q ⁻² ) / (1−α · 2 cos ω · q ⁻¹ + α ² · q ⁻² )] is a filter that attenuates the disturbance frequency (α: attenuation) This is a term that is a steepness of ω is adaptively estimated using FFT or the like.

Here, in the Bezout equation shown in Equation (5), J (q ⁻¹ ) and N _v (q ⁻¹ ) are obtained by coefficient comparison on the left and right. In the coefficient comparison formulas shown in Equations (6) and (7), J (q ⁻¹ ) and N _v (q ⁻¹ ) are obtained by applying an inverse matrix of M from the left to both sides.

As described above, according to the fluctuation state of the hot water surface level actually generated during operation, by appropriately changing the frequency component to be removed (frequency component of the periodic disturbance causing the fluctuation of the hot water surface level), Periodic level fluctuations occurring inside the mold 1 due to disturbance can be suppressed with high accuracy.
However, when the frequency component to be removed (frequency component of periodic disturbance that causes fluctuations in the molten metal surface level) is changed, the above calculation is executed in the actual machine of the correction amount calculation unit 104 each time. The calculation load is large, and it is practically difficult to execute the calculation in an actual calculation cycle (about several tens of msec).

As shown in FIG. 3A, originally, in order to remove periodic disturbance, the processing unit 104d has functions as a band-pass filter 105 that passes a specific frequency band and an m-step ahead predictor 106. Necessary.
However, the input of the m-step ahead predictor 106, that is, the specific frequency signal that has passed through the band-pass filter 105 is a periodic disturbance that causes fluctuations in the molten metal surface level, and particularly when the steepness of the band-pass filter is high. Can be regarded as a sine wave. Therefore, predicting m steps ahead is equivalent to advancing the phase of the sine wave by m steps. Therefore, as shown in FIG. 3B, a phase advancer 107 that advances the phase of the sine wave by m steps may be used as the m step ahead predictor 106.
As a result, when changing the frequency component to be removed (frequency component of periodic disturbance that causes fluctuations in the molten metal surface level), it is only necessary to change the frequency range through which the bandpass filter 105 passes. Therefore, it is not necessary to solve the Bezout equation as described above, and the calculation load in the correction amount calculation unit 104 is reduced.

  In the hot water level control system described above, the frequency estimation device 108 determines the frequency component to be removed (the frequency of periodic disturbances causing the hot water level fluctuation) according to the hot water level fluctuation state actually generated during operation. Component). The frequency band that passes through the bandpass filter 105 is changed according to the frequency component to be removed, and an output signal in a direction to remove the estimated disturbance is added to the output of the opening calculation unit 102, thereby causing the template due to the disturbance. It becomes possible to suppress the periodic level fluctuation generated inside 1 with high accuracy.

  The frequency estimation device 108 receives a disturbance estimated value d ^ output from the addition point 104c as an input and estimates a frequency component to be removed, and includes an initial frequency search unit 108a and a nonlinear optimization unit 108b.

The initial frequency search unit 108a uses the disturbance estimated value d ^ as an input to estimate the frequency by a recursive least-squares method (RLS method).
First, the sequential least square method will be described. This method is a parameter adaptive identification method that derives an adaptive law from the internal model principle.
D (k) composed of sinusoidal signals of frequencies w1 and w2 satisfies equation (8) when the internal model principle is used. When this equation (8) is expanded, the following equation (9) is obtained. If the sample time is T _s , the time at k steps is t = k · Ts, which is a function of time = k.
Here, an example in which two frequencies w1 and w2 are targeted will be described, but one or three or more may be used. The number of frequencies to be processed needs to be determined in advance, but the number of frequencies generated in the molten steel level control of the continuous casting machine can be grasped from operational experience.

  Using equation (9), the estimated values of a1 and a2 are a1 ^ and a2 ^, and the parameter vector θ ^ and regression vector φ (k) used in the adaptive law are obtained as in expression (10).

  Next, the estimated error ε (k) is considered, and a cost function J composed of error sums of squares is considered as shown in equations (11) and (12).

  Here, when the parameter vector θ ^ where ∂J / ∂θ ^ = 0 is obtained and the expression is manipulated by introducing the idea of the forgetting factor λ, the following recursive PAA (Parameter Adaptation Algorithm) is obtained (Non-Patent Document) 1).

In the above PAA method, it is known that the estimated value is biased unless the estimation error is whitened. As countermeasures, extended methods ERLS (Extended RLS) and GLS (Generalized Least Square) of the successive least square method in consideration of the polynomial C (q ⁻¹ ) of the error term have been proposed. In the case of frequency estimation, the signal is only d (k) (corresponding to y) and ε derived therefrom, and B (q ⁻¹ ) = 0 because there is nothing called the input signal u (k).

  That is, the estimation error is whitened by transforming the parameter vector θ ^ and the regression vector φ (k) from the equation (10) to the equation (14).

  In the case of GLS, equation (15) is obtained, and −α (ki) for i = 0... N may be used instead of the regression vector ε (ki).

FIG.5 (b) shows the result of having estimated the frequency distribution by carrying out FFT of the hot_water | molten_metal surface level data (FIG.5 (a)) of the continuous casting machine in actual operation. Moreover, the result of having estimated the frequency by RLS, ERLS, and GLS from the same data in FIG. 6 is shown. In FIG. 6, the horizontal axis represents time (s) and the vertical axis represents frequency (Hz). In terms of convergence speed, there are cases where the data to be used converge at about 100 points (using data of 1 second / point), and it can be seen that the convergence speed is faster than that of FFT.
As shown in FIG. 6, it can be seen that a bias occurs in the estimated value in RLS and ERLS. On the other hand, an estimated value without bias can be obtained with GLS. However, a high-order term (8th order) is required for C (q ⁻¹ ) for accurate estimation, and it is difficult to say that it is realistic. GLS is effective because it has periodic components other than the detection target in the data, and the periodic component having a denominator component in the error term can be expressed with the minimum order.

Next, the nonlinear optimization unit 108b receives the frequency estimated by the initial frequency search unit 108a as an input, and uses a nonlinear optimization method (Gauss-Newton method) to generate frequency components of periodic disturbances that cause fluctuations in the molten metal surface level. presume.
First, the nonlinear optimization method will be described.
Let the discrete transfer function of the notch filter be H _O (wi, q ⁻¹ ) as in equation (16). This is a filter having two poles αe ± ^jwi and βe ± ^{jwi. When} β is set close to 1 while satisfying the relationship of α <β <1, the input frequency wi is strongly attenuated.

Here, θi = cos (wi), A _O = (θi, γq ⁻¹ ) = 1−2γq ⁻¹ θi + q ⁻² . Thus, the n notch filters can be expressed as in Expression (17).

The output error is e ⁰ (k) obtained by notching the signal d (k). Consider the parameter estimation problem of equations (18) and (19) that minimizes this sum of squares as an evaluation function. This problem is a nonlinear optimization problem because H _O (wi, q ⁻¹ ) is a nonlinear function of θ, but a solution can be obtained by using the concept of nonlinear optimization.

  In obtaining the nonlinear optimization solution, a partial differential vector ψi (k−1) for minimizing the evaluation function is calculated as in Expression (20) and Expression (21).

By rearranging the equation (21), the partial differential vector of the equation (22) is finally obtained. If ψ (k−1) = [ψ ₁ (k−1)... ψ _n (k−1)] ^T and an adaptive law is obtained in the same manner as PAA, the recursion of equation (23) can be obtained even in a nonlinear optimization problem. A parameter estimation formula is obtained.

FIG. 7 shows the result of applying the above algorithm for minimizing the evaluation function J _k using the signal after the notch filter. In FIG. 7, the horizontal axis represents time (s) and the vertical axis represents frequency (Hz). In FIG. 7, the initial value is in the vicinity of the optimal solution and converges to the optimal solution (dotted characteristic line), and the initial value is greatly deviated and one of them does not converge (solid characteristic line). Is shown.
The difference in convergence depending on the initial value will be described with reference to FIGS. 8A and 8B showing evaluation function values of signals including white noise of 0.1 Hz and 0.33 Hz. First, the search space has a structure having a local solution in which only one notch filter matches and a global solution in which two notch filters match. The partial differential coefficient of this space is the steepness of the notch filter. It can be seen that α is related, ie, FIG. 8A is less steep than FIG. 8B. Considering the case where the initial value is on the top of a mountain, it can be understood that the solution converges to the bottom of the valley when the procedure of gradually increasing α from a small state (FIG. 8A → FIG. 8B) is taken. Although this method has the advantage of ensuring an unbiased solution, if the initial value is not in the vicinity of the global solution, the local solution (only one notch filter is hit: the case of the dotted characteristic line in FIG. 7) And converge.

  From the above idea, it can be seen that the above two methods work in principle. That is, an algorithm is adopted in which an initial frequency is searched for with an RLS with a low order and then an optimal solution is searched by switching to a nonlinear optimization method.

  Specifically, the initial frequency search unit 108a sets the estimated disturbance value d ^ as an input to d (k) and estimates the parameter vector θ ^ to obtain estimated values a1 ^ and a2 ^. In this calculation, initial values of the frequencies w1 and w2 need to be given, but the initial values are arbitrary. As a result, Equation (9) is solved using the obtained estimated values a1 ^ and a2 ^, and the frequencies w11 and w21 are calculated backward.

  Then, the nonlinear optimization unit 108b receives the frequencies w11 and w21 searched by the initial frequency search unit 108a as input, and estimates and outputs a frequency component of a periodic disturbance that causes fluctuations in the molten metal surface level that is an optimal solution.

  Switching from the initial frequency search unit 108a to the nonlinear optimization unit 108b may be performed based on time and parameter convergence. The convergence of the parameter may be determined by whether or not all the data is within ± a% (a is about 5 to 10) of the average value of sampling of 10 scans, for example.

  FIG. 9 shows a result of searching for an optimal solution by searching for an initial frequency with RLS and then switching to a nonlinear optimization method. In FIG. 9, the horizontal axis represents time (s), and the vertical axis represents frequency (Hz). The frequency component of the periodic disturbance causing the fluctuation of the molten metal surface level can be accurately estimated with good responsiveness.

As mentioned above, although this invention was demonstrated with various embodiment, this invention is not limited only to these embodiment, A change etc. are possible within the scope of the present invention.
For example, in the above embodiment, the disturbance estimation value d ^ is input to the frequency estimation device 108, but the present invention is not limited to this. That is, any signal that reflects the frequency component to be removed (frequency component of a periodic disturbance that causes fluctuations in the molten metal surface level) may be used. For example, the detection level y itself may be used, or the deviation obtained according to the detection level y. It may be a signal e, an opening change amount u ₀ , an opening correction amount v, or the like.
1 and 4 are merely examples. For example, a frequency estimation method in which the present invention is applied to the molten metal level control system disclosed in Patent Document 1 may be used.

A frequency estimation apparatus to which the present invention is applied is realized by a computer apparatus including a CPU, a ROM, a RAM, and the like, for example.
The present invention also provides software (program) that implements the functions of the present invention to a system or apparatus via a network or various storage media, and the system or apparatus computer reads out and executes the program. It is feasible.

  C: molten metal level control device, 1: mold, 2: molten metal (molten metal), 20: tundish, 3: pouring nozzle, 30: sliding gate, 31: actuator for opening and closing (hydraulic cylinder), 4: cast slab 5: guide roll, 6: level meter, 101: addition point, 102: opening calculation unit, 103: addition point, 104: correction amount calculation unit, 104a: delay unit, 104b: calculation unit, 104c: addition Matching point, 104d: processing unit, 105: band pass filter, 106: m step ahead predictor, 107: phase advancer, 108: frequency estimation device, 108a: initial frequency search unit, 108b: nonlinear optimization unit

Claims (3)

During operation of the continuous casting machine, the molten metal level inside the mold is detected, and control is performed to maintain the detected molten metal level at the target level by using a deviation between the detected level and a predetermined target level. In the hot water level control system, a frequency estimation device for estimating a frequency component of a periodic disturbance that causes fluctuations in the hot water level,
An initial frequency search means for estimating a frequency by a recursive least-squares method (RLS method) with the detection level signal or a signal obtained according to the detection level as an input;
Non-linear optimization means for estimating a frequency component of a periodic disturbance that causes fluctuations in the molten metal surface level by a non-linear optimization method using the frequency estimated by the initial frequency search means as an input. Estimating device. During operation of the continuous casting machine, the molten metal level inside the mold is detected, and control is performed to maintain the detected molten metal level at the target level by using a deviation between the detected level and a predetermined target level. In the hot water surface level control system, a frequency estimation method for estimating a frequency component of a periodic disturbance that causes fluctuations in the hot water surface level,
An initial frequency search step of estimating a frequency by a recursive least-squares method (RLS method) with the detection level signal or a signal obtained according to the detection level as an input;
A frequency estimation method comprising: a nonlinear optimization step for estimating a frequency component of a periodic disturbance that causes fluctuations in the molten metal surface level by a nonlinear optimization method using the frequency estimated in the initial frequency search step as an input Method. During operation of the continuous casting machine, the molten metal level inside the mold is detected, and control is performed to maintain the detected molten metal level at the target level by using a deviation between the detected level and a predetermined target level. In the hot water level control system, a program for estimating frequency components of periodic disturbances that cause fluctuations in the hot water level,
An initial frequency search process for estimating a frequency by a recursive least-squares method (RLS method) with the detection level signal or a signal obtained according to the detection level as an input;
A program for causing a computer to execute a nonlinear optimization process for estimating a frequency component of a periodic disturbance that causes fluctuations in a molten metal surface level by a nonlinear optimization method using the frequency estimated in the initial frequency search process as an input.

Images