JP2005028435A - Strip width control method for continuous rolling mill - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To enable a strip width control with a superior stability and accuracy. <P>SOLUTION: In the strip width control method of a continuous rolling mill with a plurality of rolling stands, a plurality of strip width estimation models are prepared. At least one out of the plurality of strip width estimation models is selected taking account of an entry tension, and then a delivery strip width on the stand is calculated based on the selected strip width estimation model. An evaluation function taking the calculated delivery strip width as a parameter is established, and the entry tension of the stand at each estimation time is calculated so as to minimize the evaluation function through the entire estimation period. <P>COPYRIGHT: (C)2005,JPO&NCIPI

Description

  The present invention relates to a sheet width control method for a continuous rolling mill.

Conventionally, a rolled material such as a thin steel plate has been manufactured by introducing a heated slab into a continuous rolling mill and continuously rolling it with a plurality of rolling stands. A looper or the like for adjusting the tension in the sheet is provided, and the sheet width or the like of the rolled material is controlled by adjusting the tension with the looper (tension control system).
Such a tension control system is complex per se and forms a complex control system in cooperation with the plate thickness control system. Therefore, conventionally, techniques such as the PID control method and the optimal control method have been used to control the plate width and the like by controlling the tension control system.

For example, the sheet width control method described in Patent Document 1 is based on the sheet width time series data of the rolled material after rough rolling, the sheet width time series data after finish rolling, and a single dynamic model. The rolling conditions for finish rolling are set so that the evaluation function for the time series data and the dynamic model is minimized.
Japanese Patent No. 3175560 (Pages 2-5, FIG. 1)

However, in a rolled material rolled on a rolling stand, there is no linearity seen in the relationship between the rolling load and the plate thickness, for example, between the plate width variation and the tension variation, and there may be a strong nonlinear relationship. It is well known.
Therefore, as in Patent Document 1, even if the sheet width control of the continuous rolling mill is performed using a single model, the accuracy is very poor in a portion where the nonlinearity is strong, and the sheet width is stabilized. It was difficult to control.
It is also conceivable to prepare a plurality of models, that is, a plurality of control means, and use them by switching them. However, each model cannot be handled uniformly, and the plate width is changed when the plurality of models are switched. Control could become unstable.

  Therefore, in view of the above problems, the present invention expresses the relationship between tension fluctuation and sheet width fluctuation of a highly nonlinear rolled material using a plurality of sheet width prediction models, and uses such a plurality of sheet width control models. It is an object of the present invention to provide a sheet width control method for a continuous rolling mill that enables stable and accurate sheet width control.

In order to achieve the above object, the present invention takes the following technical means.
That is, the technical means for solving the problems in the present invention is a continuous rolling mill that performs rolling while applying tension to the rolled material at a plurality of rolling stands, and the deviation between the actual value and the target value of the exit side plate width of the stand is calculated. In the sheet width control method of the continuous rolling mill for controlling the entry side tension of the stand so as to eliminate, a plurality of sheet width prediction models using the exit side sheet width and the entry side tension of the stand as parameters are set according to the input tension level. Set and select at least one of the plurality of plate width prediction models according to the entry side tension, and calculate the exit side plate width of the stand at a plurality of future prediction times using the selected plate width prediction model Then, by setting an evaluation function using the calculated exit side plate width as a parameter, the entry side tension of the stand at each prediction time is set so that the evaluation function is minimized over the entire prediction time. Out, the calculated entry side tension, characterized in that the inlet side tension of the stand.

According to this technical means, in a continuous rolling mill, one of a plurality of sheet width prediction models is selected according to the entry side tension without switching a plurality of control means (models) as in the prior art. Using this, the exit side plate width of the stand at a plurality of predicted times in the future is calculated, and the entry side tension obtained so that the evaluation function with the exit side plate width as a parameter is minimized is defined as the entry side tension of the rolling stand. This makes it possible to perform stable and accurate plate width control.
Specifically, even if the range of the inlet side tension changes during rolling, the plate width prediction model corresponding to the inlet side tension is used to predict the outlet side plate width and the inlet side tension. It is possible to realize highly efficient plate width control.

Further, the technical means for solving the problems in the present invention is characterized in that the evaluation function has a square integral of a deviation between a predicted value of the delivery side plate width and a target value as a parameter.
According to this technical means, an evaluation function is set with the square integral of the deviation between the predicted value of the exit side plate width and the target value as a parameter, and the stand of each stand at each predicted time is minimized so that this evaluation function is minimized. By calculating the entry side tension, it is possible to perform stable and accurate plate width control.
Further, the technical means for solving the problem in the present invention is that the exit side plate of the stand at a plurality of prediction times is input to the plate width prediction model by inputting the exit side plate width and the entrance side tension at the current time. The width is calculated.

According to this technical means, the exit side plate width of the stand can be predicted based on the exit side plate width and the entry side tension at the current time.
The technical means for solving the problems in the present invention is characterized in that, among the predicted entry side tensions, an input tension at the next time is set as an input tension of the stand.
According to this technical means, by adopting the incoming side tension at the next time as the incoming side tension of the rolling stand in the predicted incoming side tension time-series data, stable and accurate plate width control can be performed. Is possible.

Further, the technical means for solving the problems in the present invention calculates the inclination amount of an approximate straight line obtained by linearly approximating the relationship between the input tension and the exit side plate width change amount in the stand, and predicts the plate width. The model is characterized in that it has a linear form having the amount of inclination as a parameter.
According to this technical means, the plate width prediction model can be in a line format reflecting the relationship between the input tension and the exit side plate width change amount in the stand.

  According to the present invention, the relationship between the tension fluctuation and the board width fluctuation of a rolled material with strong nonlinearity is expressed using a plurality of board width prediction models, and by using such a board width control model, stable and accurate Good board width control is possible.

Hereinafter, a sheet width control method for a continuous rolling mill according to the present invention will be described by exemplifying a hot continuous rolling mill for thin steel sheets.
A rolled material such as a thin steel plate is manufactured by first introducing a heated slab material into a rough rolling stand and then introducing it into a finishing rolling stand which is a continuous rolling mill.
Between each rolling stand, a looper (tension adjusting means) for adjusting the longitudinal tension (hereinafter referred to as tension) of the rolled material is provided. By adjusting the tension by this tension adjusting means, the sheet width of the rolled material is controlled.

FIG. 1 shows a part of the configuration of the continuous rolling mill 1. The rolled material 2 rolled by the rolling stand A is further rolled by a rolling stand B (the corresponding stand) arranged on the downstream side in the longitudinal direction of the rolled material 2, and both rolling stands A, B A looper as the tension adjusting means 3 is provided between them.
The looper 3 is provided with a looper roll 4 in contact with the rolled material 2 in a cantilevered manner, and the looper roll 4 can move in the direction of lifting the rolled material 2 around its fulcrum. When the looper roll 4 lifts and presses the rolled material 2, the tension of the rolled material 2 increases, and the looper 3 can adjust the tension of the rolled material 2.

In addition, a load meter and an accelerometer are attached to the looper 3 (not shown), and based on data from these, it is possible to measure the current tension on the entrance side of the rolling stand B, that is, the entrance side tension. It has become.
On the exit side of the rolling stand B, a sheet width meter 5 for measuring the sheet width on the exit side is installed, and the measurement data, that is, the actual sheet width on the exit side is stored in the control means 6 provided in the continuous rolling mill 1. Based on the plate width control method described later, the entry side tension in the next control cycle is predicted, and the entry side tension of the rolling stand B is set via the tension adjusting means 3.

The sheet width control method of the continuous rolling mill processed in the control means 6 will be described based on the block diagram of FIG. 2 and the flowcharts of FIGS.
As shown in FIG. 2, the plate width control method of the present embodiment is largely divided into a prediction function and a tension determination function. The prediction function receives a current exit side width, a current entry side tension, and time-series data of a future entry side tension, and inputs a plurality of sheet width prediction models according to the entry side tension level (details will be described later). ) To obtain time-series data of the future width of the delivery side plate.
The tension determination function is to obtain time-series data of the future entry side tension using the plurality of sheet width prediction models so that the evaluation function using the predicted exit side plate width as a parameter is minimized. It is.

Hereinafter, the processing procedure of the prediction function will be described based on FIG.
First, in the rolling stand B, the delivery side actual sheet width w (0) at the current time (t = 0) is obtained from the sheet width meter 5, and the entry side actual tension σ (0) at the current time is obtained from the tension adjusting means 3. get. (S31)
Based on the acquired w (0) and σ (0), a plate width prediction model corresponding to the tension σ (0) is selected and used, and one control cycle ahead, that is, the next time (t = 1). The exit predicted plate width w (1) is calculated. (S32)
Here, an arbitrary time can be adopted as the control cycle, and it may be set to several tens of milliseconds, for example.

  The plurality of sheet width prediction models used in the processing step S31 are three mathematical models shown in (1) to (3) of [Equation 1], and the exit side sheet width and input tension of the rolling stand B are parameters. It is included as (variable). Each equation of [Equation 1] is composed of one state equation (x (t + 1) =...) And an output equation (w (t) =...).

Here, σ is the entry side tension (kg / mm), w is the exit side plate width (mm), and x is a state variable. A1 to A3, b1 to b3, c1 to c3 are coefficient matrices, and t is time.
The coefficient b indicates the amount of inclination of the approximate straight line (linearized model) shown in FIG.
FIG. 5 shows the relationship between the input tension σ (t) of the rolled material 2 rolled on the rolling stand and the plate width reduction amount Δw (t) when the temperature, thickness, and transfer speed of the rolled material are constant. Is shown. As can be seen from the figure, the two have a relationship indicated by a curve, that is, a non-linear relationship, and when the entry side tension is increased, the influence on the exit side plate width is increased.

In the case of the present embodiment, this curve is approximated by three straight lines (linearization models 1 to 3), and the inclination of each straight line is b1, b2, and b3.
When performing the calculation using the plate width prediction model, any one of (1) to (3) of [Equation 1] is used according to the range of the entry side tension value σ (0). . For example, when the entry side tension σ (0) is 1.3 (kg / mm) or less, (1) of [Equation 1] is used.
In the processing step of S31, the state variable x (0) is set appropriately.
Next, the exit predicted plate width w (2) of two control periods ahead (second time, t = 2) in the rolling stand B is calculated. (S33)
At this stage, since the time-series data of the future entry side tension has not been obtained, an arbitrary and realistic value is set as the entry side tension σ (1). Using this arbitrary entry side tension σ (1) and w (1) obtained in the previous processing step (S31), t = 2 based on the plate width prediction model corresponding to the value of σ (1). The exit side predicted plate width w (2) at is calculated.

Thereafter, by following the same processing procedure, an arbitrary entry side tension σ (t−1) is given until t = T, and this σ (t−1) and w ( Based on the plate width prediction model corresponding to the value of σ (t−1), the exit side predicted plate width w (t) at the prediction time t is calculated using t−1). (S34)
By repeatedly performing the above processing, it is possible to calculate the outgoing predicted plate width w (t) from t = 1 to T, that is, at a plurality of times in the future.
Next, based on the calculated predicted delivery side widths w (1) to w (T) based on the steps shown in FIG. 4, the incoming side tension σ (1) at a plurality of future times based on the concept of optimal control. ˜σ (T) is determined (tension determination function).

  First, the plate width prediction model [Equation 1] using the exit side plate width and the entry side tension of the rolling stand B as parameters is combined into one, and equivalent deformation is performed to derive [Equation 2].

Here, A, B1 to B3, C, D1 to D3, and E1 to E5 are coefficient matrices, d is a binary variable, and z is a continuous value auxiliary variable. The binary variable d is a variable that takes a value of 0 or 1. When d = 0, there is no term multiplied by it. That is, it corresponds to “if σ <1.3 (if σ is less than 1.3)” in [Equation 1] and the like.
For this [Equation 2], an evaluation function of [Equation 3] is introduced. This evaluation function J is obtained by adding (integrating) the square of the difference between the exit side plate width w (t) and the target value w1 (waim) at each prediction time from t = 0 to T−1, and using the parameter ( Variable).

Here, T is a value that determines how many steps ahead are predicted, Q1 to Q5 are weight matrices, and a value with a subscript 1 is a target value. ‖X‖ _Q refers to the x ^T · Q · x.
By solving [Equation 2] under the constraint condition that the evaluation function J takes the minimum value, the time-series data of the optimum entry side tension at a plurality of times in the future, that is, the error from the target value will continue in the future. The smallest entry side tensions σ (1) to σ (T) can be obtained. (S41)
Specifically, [Equation 4] can be derived by simultaneously combining [Equation 2] and [Equation 3]. By solving this [Equation 4], the input tension time series σ (1) to σ (T) can be predicted.

Here, S1 to S3, F1 to F3 are coefficient matrices obtained from A, B1 to B3, C, D1 to D3, E1 to E5, Q1 to Q5, and the matrix with “′” is a transposed matrix. . “Subj to” in [Expression 4] means “in such a constraint”, and “min _v ” means “search for the minimum V in this equation”.
Solving [Equation 4] is called a mixed integer quadratic programming problem in mathematics, and it is possible to obtain a solution from recent research results. Therefore, by solving [Equation 4] for each control period and using σ (t), which is the first element of V, as a tension command, the evaluation function J for the plate width prediction model [Equation 1] is minimized. The optimum control input is obtained.

The sheet width control is performed by applying the time series data σ (1) to σ (T) of the predicted entry side tension thus obtained to the rolling stand B.
In the case of this embodiment, among the time-series data σ (1) to σ (T) of the incoming predicted tension, the incoming predicted tension σ (1) at the next time, that is, the first σ of the time-series data, This is applied as the entry side tension of the rolling stand B. (S42)
In other words, σ (1) is output from the control means 6 and input to the tension adjusting means 3. The tension adjusting means 3 adjusts the pressing force of the looper roll 4 so that the entry side tension of the rolled material 2 becomes the predicted value σ (1).

After applying the entry side predicted tension σ (1) to the rolling stand B, the prediction calculation in the next control cycle (t = 1) is considered to be the exit side at a plurality of times in the future, assuming t = 1 as the current time. Predicted plate widths w (2) to w (T) are calculated.
At that time, as shown in FIG. 6, in the iterative calculation for determining the tension, σ (1) to σ (T) predicted in the previous control cycle are adopted as the initial value of the input tension. As the current exit side plate width, w (1) predicted in the previous control cycle is used. Thereafter, by sequentially performing the above-described processing steps, the entry-side tension time series data σ (2) to σ (T) can be predicted, and the entry-side predicted tension σ (2) is applied to the rolling stand B. To.

Similarly, the prediction calculation in the next control cycle (t = 2) adopts σ (2) to σ (T) predicted in the previous control cycle as the initial value of the entry side tension, As the exit side plate width at the current time, w (2) predicted in the immediately preceding control cycle is used as the initial value. Thereafter, by sequentially performing the above-described processing steps, the entry-side tension time series data σ (3) to σ (T) can be obtained, and the entry-side predicted tension σ (3) is applied to the rolling stand B. To do.
For each control cycle, the data shift process and the prediction calculation by the plate width prediction model selected from a plurality are sequentially repeated to obtain time-series data of the input predicted tension in each control cycle. By setting the initial entry side tension σ to the entry side tension of the rolling stand B, the rolling stand B is controlled.

Thereby, stable and accurate plate width control is possible. Specifically, as in the conventional case, the control means is designed for each plate width prediction model, and it is much more stable than the method of switching the control means or changing the control gain according to the entry side tension. Control becomes possible.
In the present embodiment, the control method is performed online through the control means, but there is no problem even if offline calculation is performed and the rolling stand is controlled based on the obtained data.
FIG. 7 shows an example of the measured sheet width when the sheet width control method according to the present embodiment is applied to the rolling stand B.

In this figure, the horizontal axis indicates the reduction amount of the plate width, and the vertical axis indicates, for example, a plate width control error calculated from a deviation between the predicted plate width and the actual plate width after control.
When using a single model in which the plate width reduction amount is linearized in the vicinity of 2 mm, the plate width control increases as the entry side tension increases and the exit side plate width reduction amount increases (as the plate width reduction amount approaches 4 mm). It can be seen that the error has increased.
Conversely, when using a single model in which the plate width reduction amount is linearized in the vicinity of 4 mm, as the entry side tension decreases and the exit side plate width reduction amount decreases (as the plate width reduction amount approaches 2 mm), It can be seen that the plate width control error once decreases but increases again.

However, when the plate width control method according to the present embodiment is used, it can be seen that in any case, the value of the plate width control error is smaller than in the case of a single model, and good control is performed.
FIG. 8 and FIG. 9 show examples of results when a simulation of plate width control is performed using the plate width control method according to the present embodiment.
The simulation conditions are as follows.
The conditions of the plate width prediction model are as follows: when multiple (three) models are used (three divisions), when the optimal model is used when the entry side tension is around 1 kg / mm (no division (I)), the entry side Consider three patterns when an optimal model is used at a tension of around 3 kg / mm (no division (II)).

The plate width target value is 2 when the plate width is increased by 2 mm from the current target plate width (when +2 mm) and when the plate width is +4 mm from the current target plate width (when +4 mm). Thinking about patterns.
By considering these patterns, the effect of the plate width control method can be achieved when the entry tension level changes, that is, when all the mathematical models of (1) to (3) in [Equation 1] are used. The difference can be examined.
When the plate width target value is +2 mm, in the case of no division (II), clear overshoot is observed in the control of the process approaching the target value, and when the plate width target value is +4 mm, there is no division ( In case I), a similar large overshoot is seen. In any case, the plate width control method according to the present embodiment controls the plate width satisfactorily without overshoot.

In addition, the board width control method of the continuous rolling mill concerning this invention is not limited to the said embodiment.
That is, the hot continuous rolling of a thin steel plate has been described as an example, but a thick steel plate or cold rolling may be used.
Further, instead of using a looper as the tension adjusting means 3, the tension (incoming side tension) of the rolled material 2 may be adjusted by making a difference in the rotation speed of the work rolls of the rolling stands A and B. .

  The sheet width control method according to the present invention is effective for a control object having a strong nonlinearity such as a tension and a sheet width in a rolled material, and can also be applied to another control object having a strong nonlinearity.

It is the figure which showed the structure of the continuous rolling mill to which this embodiment is applied. It is a block diagram of this embodiment. It is a flowchart of a prediction function. It is a flowchart of a tension | tensile_strength determination function. It is a figure which shows linearizing the relationship between an entrance side tension | tensile_strength and an exit side board width reduction amount. It is a figure which shows using the time series data of the predicted entrance tension for the prediction of the next time. It is a figure which shows an example of the result of this embodiment. It is a figure which shows an example of the result of this embodiment. It is a figure which shows an example of the result of this embodiment.

Explanation of symbols

DESCRIPTION OF SYMBOLS 1 Continuous rolling mill 2 Rolled material 3 Tension adjusting means 6 Control means

Claims (5)

Continuous rolling mill that controls the entry side tension of the stand so as to eliminate the deviation between the actual value and the target value of the exit side plate width of the stand in a continuous rolling mill that rolls while rolling the rolled material with multiple rolling stands. In the plate width control method of the machine,
A plurality of plate width prediction models using the exit side plate width and the entry side tension of the stand as parameters are set according to the input tension level, and at least one is selected from the plurality of plate width prediction models according to the entry side tension. Then, using the selected plate width prediction model, calculate the exit side plate width of the stand at a plurality of future prediction times, set an evaluation function using the calculated exit side plate width as a parameter, and set the entire prediction time The entrance side tension of the stand at each prediction time is calculated so that the evaluation function becomes the minimum over the continuous time, and the calculated entrance side tension is set as the entrance side tension of the stand. Machine width control method.   2. The sheet width control method for a continuous rolling mill according to claim 1, wherein the evaluation function includes, as a parameter, a square integral of a deviation between the predicted value of the delivery side sheet width and the target value.   3. The exit side plate width of the stand at a plurality of prediction times is calculated by inputting the exit side plate width and the entry side tension at the current time into the plate width prediction model. The sheet width control method of the continuous rolling mill described.   The strip width control method for a continuous rolling mill according to any one of claims 1 to 3, wherein an input tension at the next time among the predicted entry side tensions is set as an input tension of the stand.   By calculating the amount of inclination of an approximate straight line obtained by linearly approximating the relationship between the input tension and the exit side plate width change amount in the stand, the plate width prediction model is made into a linear form having the amount of inclination as a parameter. A sheet width control method for a continuous rolling mill according to any one of claims 1 to 4.

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