JPH0751257B2 - Twin-belt continuous casting level control method - Google Patents

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a molten metal level control method for twin belt continuous casting.

[0002]

2. Description of the Related Art There are the following methods for detecting the level of molten metal.

1. Method of using a float A method of floating a float on the surface of the molten metal and detecting the position of this float with a stick or a chain.

2. Optical (photoelectric conversion) method Focusing on the difference in brightness at the contact position between the molten metal surface and the container,
A method of measuring this boundary line by a triangulation method using, for example, an array sensor or a television camera. 3. Method using ultrasonic wave A method of measuring the distance to the surface of the molten metal by irradiating it with ultrasonic waves and measuring the time it takes for the reflected sound waves to return.

4. Method of using radiation A method of transmitting radiation diagonally to the surface of the molten metal and detecting the level of the molten metal by the attenuation of this radiation.

5. Immersion electrode method A method of detecting the level of the molten metal by creating an ON-OFF state of the electric circuit with the electrode and the molten metal.

6. Electromagnetic Induction Method The method disclosed in Japanese Patent Laid-Open No. 48-93539 is a method in which a coil long in the depth direction is provided on the outer wall surface of the mold and this coil is connected to one side of an impedance bridge circuit. A method for detecting the level of the molten metal surface by detecting the change in the molten metal surface level as a change in the temperature of the mold wall and utilizing the change in the eddy current generated in the mold due to the change in the specific resistance of the mold wall caused thereby. Is.

The molten metal level control method for twin-belt continuous casting is based on the measured molten metal level at one location measured by the above-mentioned molten metal level detector, and the measured molten metal level and the molten metal level target. A conventional portable technique is to input a difference from the value to a PI controller or a PID controller, calculate a pouring amount command value, and output the pouring amount command value to a pouring amount operation device.

[0009]

In the twin-belt continuous casting liquid level control method using the PI controller or the PID controller based on the measured value of the molten metal level at one place, the vibration of the molten metal level may be taken into consideration. Since it is not possible, changes in the pouring amount due to the calculated pouring amount command value may cause vibration of the molten metal surface,
This causes problems in terms of product quality or yield, operating rate, and safety during operation.

The present invention provides a control method that compensates for disturbances that affect the average level of the molten metal surface, makes the average level of the molten metal surface follow a target value, and positively suppresses vibration of the molten metal surface. With the goal.

[0011]

Means for Solving the Problems The present invention provides a molten metal surface control method for a twin-belt continuous casting, measured in (b) molten metal surface level two places or more at different positions in the horizontal direction, (b) Mo - by Dal filtering, and have use of melt surface level measurement at the two locations on or vibration mode of the average level and single Kumi以 Kaminoyu surface of the molten metal surface - calculating the de average of (c) above the melt surface The pouring amount command value 1 is calculated from the level and the vibration mode, and (d) the pouring command value 2 is obtained from one of the melt level target value and the melt level measured value measured in (a). (E) The pouring amount command value is calculated from the pouring amount command value 1 and the pouring amount command value 2 described above, and (f) the pouring amount command value calculated in (e) is output to the pouring amount controller. By doing so, the disturbance that affects the average level of the molten metal surface is compensated, and the average level of the molten metal surface is set Together is to follow, which comprises suppressing the vibration of the molten metal surface.

[0012]

The present invention will be described in detail below. Taking a point on the left end of the mold as an origin toward the mold, a horizontal y-axis and a vertical upward z-axis are set, and the displacement of the molten metal surface at time t and position y is z = ζ (y , T), ζ (y, t) [m] is the sum of N + 1 terms (N ≧ 1)

[0013]

[Equation 1]

Is approximated by "'" Represents a time derivative.
k _n [1 / m] is represented by the following equation.

K _n = nπ / L (1 ≦ n ≦ N) (2) L [m] is a mold width. x ₀ (t) [m] is the average level of the molten metal surface, and x _n ′ (t) [m] is the mode displacement of the nth-order vibration mode of the molten metal surface, which is expressed by the following differential equations. To be done.

X ₀ ′ (t) = U ₀ u (t) −W (t), x _n ″ (t) + gk _n x _n (t) = U _n u (t) (1 ≦ n ≦ N) · .. (3) g is the gravitational acceleration, and g = 9.8 [m / s ² ].

W (t) [m / s] is a drawing speed.

U _o [m / s] and U _n [m / s] are expressed by the following equations.

[0019]

[Equation 2]

The distribution of the pouring speed from the nozzle in the y direction is U
(Y) is represented by u (t), and the dimension of U (y) is [m /
s], u (t) are dimensionless. U (y) is u (t)
It is the distribution of the pouring speed from the nozzle in the y direction when = 1 and is determined by the size and shape of the nozzle and the position in the mold. From the equation (3), u (t) affects the average level of the molten metal surface with the weight U ₀ , and affects the n-th order vibration mode of the molten metal surface with the weight U _n .

The present invention is based on the above findings. The operation of the present invention will be described in detail below with reference to FIG.

FIG. 1 shows the configuration of a pouring amount control system for controlling the level of the molten metal when the measured values of the molten metal level at two points are used in the present invention. This is based on the case of N = 1 in the above model. Figure 1
, The one with the integral symbol written in the triangle is the integrator, the one with the variable written in the large circle is the multiplier that multiplies the value of the variable, the one with the addition symbol written in the small circle is the adder, A subtraction symbol written in a small circle represents a subtractor. Of these, the subtractor is provided with an addition symbol and a subtraction symbol to clearly indicate the order of subtraction. The "plant" is composed of a pouring amount operation device that receives a pouring amount command value, a pouring nozzle, a pouring process element such as a mold, and a pouring detector that outputs a pouring level measurement value. .

Using the two types of molten metal level detectors, the molten metal levels are horizontally different from each other at positions y = y ₁ and y = y _2.
(Y ₁ ≠ y ₂ ), and the melt level measurement values are measured at the melt level level 1 ζ ₁ (t) = ζ (y ₁ , t) (5) Level measurement value 2 ζ ₂ (t) = ζ (y ₂ , t) (6) Surface level measurement value 1 and surface level measurement value 2
Is from equation (1)

[0024]

[Equation 3]

It is expressed as From this, x ₀ (t), x
₁ '(t) is

[0026]

[Equation 4]

It is expressed as follows. here,

[0028]

[Equation 5]

[0029]

From the molten metal level measured value 1 and the molten metal level measured value 2 input to the modal filter, a in the equation (9) is obtained.
_{Using the} multiplier and the adder that multiply ₁₁ , a ₁₂ , a ₂₁ , and a ₂₂ , the average level x ₀ of the molten metal surface is calculated by the equation (8).
(T) and the mode displacement x of the primary vibration mode of the molten metal surface
₁ '(t) is required. The mode displacement x ₁ ′ (t) is
It is calculated by an integrator and x ₁ (t) is obtained. x
₁ '(t), x ₁ (t) is called the state of the first vibration mode of the molten metal surface. x ₀ (t), x ₁ ′ (t), x ₁ (t) are called states. That is, the modal filter calculates the state from the melt level measurement value 1 and the melt level measurement value 2. Calculated state x ₀ (t), x ₁ ′ (t), x ₁
From (t), the pouring amount command value 1 is calculated by the multiplier and the adder.

Disturbances that affect the average level of the molten metal surface are considered to be fluctuations in the characteristics of the pouring amount operation device, fluctuations in the casting speed, and the like. Target surface level and measured surface level 1
Then, the pouring amount command value 2 is calculated using a subtractor, an integrator, and a multiplier, and from the pouring amount command value 2 and the pouring amount command value 1,
A pouring amount command value is calculated using a subtractor. This part is
The average level of the molten metal surface is made to follow the target value, and the disturbance that affects the average level of the molten metal surface is compensated.

The purpose of the molten metal level control is to cause the molten metal level to follow a given target value, compensate for disturbances that affect the molten metal level, and suppress vibration of the molten metal level. That is,
At x ₀ (t), x ₁ ′ (t), the average level x
_The disturbance that affects ₀ (t) is compensated, the average level x ₀ (t) of the molten metal surface is made to follow the target value, and the vibration mode displacement x
_The desired control is achieved by asymptotically approaching ₁ '(t) to zero. According to the present invention, the pouring amount command value 1 causes the average level x ₀ (t) of the molten metal surface to follow the target value, and the vibration mode displacement x ₁ ′ (t) asymptotically approaches zero. The command value 2 achieves the target control by compensating for the disturbance that affects the average level x ₀ (t) of the molten metal surface.
In the multiplier that multiplies k, k ₀ , k ₁₁ , and k ₁₀ , k, k
The values of ₀ , k ₁₁ , and k ₁₀ have important effects that affect the vibration of the molten metal surface and the speed at which the average level of the molten metal surface converges to the target value (response speed). It is desirable to determine an appropriate value.

The case where the molten metal level is measured at two points and the measured values at two points are used has been described above with reference to FIG. FIG. 3 shows a case where the molten metal level is measured at three locations and the measured molten metal level at three locations is used. This is based on the case of N = 2 in the above model. In this case, the modal filter has nine multipliers, four adders, and two integrators, and the melt level measured at three points is input to the modal filter.
Status is output. From the 5 states output from the modal filter, the pouring amount command value 1 is calculated using 5 multipliers and 4 adders. The pouring amount command value 2 is calculated in exactly the same manner as when the measured values of the molten metal level at two places are used. The pouring amount command value is calculated from the pouring amount command value 2 and the pouring amount command value 1 using a subtracter.

The above expansion is extended to the general N (N ≧ 1) when using the melt level measurement values at N + 1 places. In this case, the modal filter is (N + 1)
Has ² multipliers, N ² adders, N integrators,
The bath level measured at N + 1 places is input and 2N + 1
Status is output. From the 2N + 1 states output from the modal filter, the pouring amount command value 1 is calculated using 2N + 1 multipliers and 2N adders. The pouring amount command value 2 is calculated in exactly the same manner as when the measured values of the molten metal level at two places are used. The pouring amount command value is calculated from the pouring amount command value 2 and the pouring amount command value 1 using a subtracter.

[0035]

FIG. 2 shows an example in which the present invention is carried out by simulation. FIG. 2 is an example in which FIG. 1 is used, that is, the case where the measured values of the molten metal level at two locations are used. The solid line shows the level transition of the level in the case of the level control method of the present invention,
The broken line shows the transition of the molten metal level in the case of the molten metal level control by the conventional PI control method. In FIG. 2A, time t <
At a steady state with a drawing speed of 0.1 [m / s] at 0, t
2 (b), the drawing speed is changed to +1 [c] at t = 0 when the target level value is changed by +1 [cm] at = 0.
m / s] shows the level of the molten metal at the left end of the mold when a disturbance is applied. The horizontal axis is time and the unit is [se
c], the vertical axis is the level of the molten metal at the left end, and the unit is [cm]. The width of the mold is L = 1 [m] and 0.25 [m]
The nozzle of the width is positioned so that the left end of the nozzle and the center of the mold coincide with each other. Control method of the present invention (example of the present invention)
Then, since the molten metal level is measured at both ends of the mold, by setting y ₁ = 0 and y ₂ = L in the equation (9), a ₁₁ = 0.5, a ₁₂ = 0.5 , A ₂₁ = 0.5, a ₂₂ = −0.5 (10) are obtained. In consideration of the stability and quick response of the measured value of the molten metal surface level by performing various simulations, each parameter is k ₀ = 40, k ₁₀ = -240, k ₁₁ = -80 k = 45・ ・ (11) was set. In the PI control method (comparative example), the molten metal level was measured at one location on the left end of the mold, and the transfer function of the PI controller was (c ₀ + c ₁ p) / p (12). At this time, so that the quick response is similar to that of the example of the present invention,
Each parameter was set as c ₀ = 15, c ₁ = 5 ... (13).

FIG. 2A shows how the target value is followed, and FIG. 2B shows how the disturbance is compensated. In the PI control method (comparative example), the measured level of the molten metal surface is oscillating in both cases of following the target value and compensating for the disturbance. Both the tracking of the value and the compensation of the disturbance are performed promptly, and the molten metal level does not substantially vibrate.

[0037]

According to the present invention, the average level of the molten metal surface can be made to follow the target value, the disturbance can be compensated, and the vibration of the molten metal surface can be actively suppressed. It also has the effects of improving yield, improving the operating rate, and improving the safety during operation.

[Brief description of drawings]

FIG. 1 is a block diagram showing a calculation system of a molten metal level control system for carrying out the present invention in a mode in which measured values of molten metal level at two places are used.

FIG. 2 is a graph showing a time series transition of a molten metal level when the present invention is carried out and when a conventional example is carried out.
(A) shows the fluctuation of the molten metal level immediately after the target value is changed,
FIG. 2B shows the fluctuation of the molten metal level when the slab drawing speed temporarily changes.

FIG. 3 is a block diagram showing an arithmetic system of a molten metal level control system for carrying out the present invention in a mode using the measured molten metal level at three points.

Claims (1)

[Claims] 1. A molten metal surface level control method for a twin-belt continuous casting, measured in (b) molten metal surface level two places or more at different positions in the horizontal direction, (b) mode - by Dal filtering, the two- calculates the de average level and the vibration mode of (c) above the melt surface - - vibration mode of the mean level and single Kumi以 Kaminoyu surface of the molten metal surface by have use the melt surface level measurement at least on the locations from de The pouring amount command value 1 is calculated, and (d) the pouring command value 2 is calculated from one of the melt surface level target value and the melt surface level measured value measured in (a). The pouring amount command value is calculated from the pouring amount command value 1 and the pouring amount command value 2, and the pouring amount command value calculated in (f) and (e) is output to the pouring amount controller, whereby the average level of the pouring surface It compensates for disturbances that affect the A molten metal level control method for twin-belt continuous casting characterized by suppressing surface vibration.