JPH059166B2 - - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION [Field of Industrial Application] The present invention relates to a method for controlling strip width in hot rolling.

[Conventional technology]

In rolling using hard rolls, changes in rolling temperature, rolling model errors, etc. cause errors in calculating the amount of width return after width reduction by hard rolls and the amount of width expansion by horizontal mills. As a result, the actual range differs from the target range.
Therefore, in order to guarantee the width requested by the next process or the customer, it is common to add an allowance to the target width and then shear it to a predetermined width after rolling. Therefore, the larger the variation in the actual width with respect to the target width, the larger the margin needs to be, which leads to a reduction in rolling yield. Therefore, a method has been invented in which the width variation during rolling is measured or estimated using a width detector or other means, and is reflected in subsequent rolling to reduce the error variation in actual width (Japanese Patent Publication No. 50-24907).

[Problem to be solved by the invention]

However, these methods require the installation of a width gauge before the final rolling mill, or estimate the width deviation at the stand from the rolling load, making it difficult to maintain model accuracy as they cannot follow changes in various rolling conditions. was difficult. In addition, width deviation occurs again on the rough output side due to the width expansion after the stand and the error in the width return amount model.

The present invention aims to solve this type of conventional problem.

[Means to solve the problem]

The gist of the present invention is to control strip width in a hot rolling mill in which at least two sets of rigid rolls and horizontal rolls are arranged as one set, and a strip width detector is installed on the outlet side of the final rolling stand. , the step of predicting the width deviation at the end of rolling when rolling is performed with the currently determined rolling set-up based on the rolling load of the existing rolling stand, and the setting of hard rolls in the next and subsequent stages based on the prediction.・The width deviation is calculated using the sequential least squares method based on the step of correcting the plate width, the actual plate width detected by the plate width detector after rolling, and the actual rolling load and rolled material information of the existing rolling stand. The present invention is a method for controlling strip width in hot rolling, which is characterized by comprising a step of correcting parameters of an estimated model.

[Effect]

Since the rough side width of the hot rolling mill is directly estimated during rolling, the estimation of the width deviation also includes model errors after that stand, so it is possible to compensate for control deviations at subsequent stands. Since the parameters of this width deviation estimation model are adaptively corrected based on the actual width at the time of exit from the hot rolling mill, width control accuracy can be improved by improving the followability of the parameters to various conditions.

〔Example〕

The present invention can be implemented by attaching a rolling load detection device to any edger. However, control using the detected load at the front stage deteriorates the final width detection accuracy, so it is preferable to perform detection at the rear edger as much as possible. However, in the later stages, there is no margin for control costs. Therefore, an example using the load by the edger 4 will be shown below.

FIG. 1 is a partial layout diagram of a rough rolling mill in one embodiment of the method of the present invention. In FIG. 1, a slab (not shown) is sent to a finishing mill where it is rolled to a predetermined thickness and width by horizontal rolls and an edger. Load detector 11 during rolling of edger 3
The actual rolling load was measured at horizontal mill 8, 9, 1.
The actual set-up value of 0 is measured with a position detector, the width deviation at the exit side of the final stage horizontal mill 10 is estimated, and the set-up of the edgers 4 and 5 is corrected to reduce fluctuations in the actual value. After rolling, width detector 1
The parameters of the width variation prediction formula are updated based on the actual width value, actual rolling schedule, and rolled material information measured in step 3, and are stored in the calculator 12 and used for predicting the width variation of the next rolled material. In this way, it is broadly divided into two parts: processing content and updating of prediction formulas. First, the prediction method will be explained.

The width deviation at the exit side of the final stage horizontal mill 10 can be divided into those that occur before the edger 3 is bitten and those that occur after that. The former (∆W ₂ ) is expressed by the equation (1) below.
This is the variation in the rolling reduction amount (ΔΔE ₃ ).

ΔW ₂ = Wcal ₂ − Wrcal ₂ = ΔEcal ₃ − ΔErcal ₃ = ΔΔE ₃ ...(1) Here, Wcal ₂ , Wrcal ₂ : Calculated width of Edger 3 bite, actual value ΔEcal ₃ , ΔErcal ₃ : Calculated reduction of Edger 3 amount, actual reduction amount.

The error in the rolling amount of the edger 2 (ΔΔE ₂ ), that is, the error in the width of the entrance plate of the edger 2 (ΔW ₂ ) multiplied by the width return rate of each stand is the final stand exit width error (ΔW _2-5 ) remains as.

ΔW ₂ = ΔΔE ₃ ΔW _2-3 = ΔW ₂ (1-η ₃ ) ΔW _2-4 = ΔW _2-3 (1-η ₄ ) ΔW _2-5 = ΔW _2-4 (1-η ₅ ) = ΔΔE ₃₅ 〓 ⁱ⁼³ (1−ηi) …(2) Here, ΔW _2-5 : Effect of ΔW ₂ on the width deviation at the exit side of the last stage horizontal mill 10 1−η ₁ : In rolling at edger i The width return rate ₅ 〓 ⁱ⁼³ (1−ηi)=(1−η ₃ )(1−η ₄ )(1−η ₅ ).

The latter (width fluctuation after rolling on edger 3) is the influence (ΔWh) on width fluctuation due to the error of the width return model at edger 3, 4, and 5 and the horizontal mill set change, and is expressed by the following equation (3). be able to.

ΔWh= ₅ 〓 ⁱ⁼⁵ αi (Δhcali−Δhrcali) ₅ 〓 ⁱ⁼ⁱ⁺¹ ……(3) where, αi: Width expansion rate due to horizontal mill reduction Δhcali, Δhrcali: Horizontal mill calculated reduction amount, actual reduction amount i: Stand No.

The width deviation (ΔW ₅ ) on the exit side of the final stand can be expressed as the sum of the width deviation (ΔWh) caused by the horizontal mill set variation and the width deviation (ΔW _2-5 ) caused by the input width deviation. Therefore, from equations (2) and (3), the final stage horizontal mill 1
The width deviation (ΔW ₅ ) on the 0 output side can be expressed by the following equation (4).

ΔW ₅ = ΔWh + ΔW _2-5 ...(4) Here, the reduction amount deviation (ΔΔE ₃ ) at edger 3 is estimated from the rolling load (F), but the actual reduction amount (ΔE ₃ rcal) is Since this is not possible, multiple regression analysis was performed directly from equation (4), and the following equation (5) was obtained.

f=aΔWh+(b ₁ ΔEcal ₃ +b ₂ RT+b ₃ Ceq+b ₄ F/h ₂
+b ₅ h ₂ /F) ₅ 〓 ⁱ⁼ⁱ⁺¹ (1−η _i )+c ……(5) Here, f: Estimated width deviation at the exit side of the final stage horizontal mill 10, multiple regression analysis This is a linear regression equation derived from

RT: Estimated rolling temperature value F: Actual rolling load value of Ezier 3 Ceq: Carbon equivalent h ₂ : Ezier rolled plate thickness The width return rate (1-η) is calculated based on off-line experiments.

a: Coefficient related to ΔWh (theoretically 1) b ₁ to b ₅ : Coefficient c: Constant.

From this width deviation estimated value f, the target width (Wcal ₅ ) is calculated as (6)
The deviation in the actual range can be compensated by correcting the equation as shown in the equation and performing the set-up calculation again for the edgers 4 and 5 as shown in the following equation (6a). Wcal ₅ ′ obtained from equation (6) is the corrected target width, and “′” means the corrected value.

Wcal ₅ ′=Wcal ₅ −f ……(6) ΔE ₅ ′=ΔW ₅ ΔE ₅ / (ΔE ₅ η ₅ +ΔE ₅ η ₄ ) ΔE ₄ ′=ΔW ₅ ΔE ₄ /(ΔE ₅ η ₅ +ΔE ₅ η ₄ ) Wcal ₄ ′=Wcal ₅ ′+ΔE ₅ ′η ₅ −Δh ₅ α ₅ Wcal ₃ ′=Wcal ₄ ′+ΔE ₄ ′η ₄ −Δh ₄ α ₄ E ₅ ′=Wcal ₄ ′+ΔE ₅ ′η ₅ E ₄ ′ ＝Wcal ₃ ′＋ΔE ₄ ′η ₄
...(6a) Set Edger 4 and 5 to the above revised target values.

Next, updating of the parameters of the prediction formula will be explained. The parameters of prediction formula (6) are thought to vary depending on various conditions, and control accuracy is thought to deteriorate. Therefore, it becomes necessary to adaptively modify the parameters of the prediction formula using actual measured values. With the development of modern control theory, many online sequential system identification methods have been proposed, but here we will use the sequential least squares method, which has fast convergence and a stable forgetting coefficient.

If the prediction formula (6) is expressed as the following formula (7) using a vector, the parameter update formula is the following formula (8), the correction gain is the following formula (9), and the covariance matrix update formula is the following ( Ten)
The forgetting coefficient is expressed by the following equation (11).

_{f o = A} ^T _{o _ _ _ _ _ _ _} ^_ _{_ _} ) ...( _{9 ) P o + 1} ⁼ ₍ ¹ _- ^K _{o o} X _o )
...(11) Here, A _o = (a, b ₁ , b ₂ , ..., b ₅ , c) ^T X _o = (ΔWh, ΔEcal ₃ ′, RT′, Ceq′, F/h ₂ ′,
h ₂ /F', 1) ^T g: constant n: rolling order T: transposition': ₅ 〓 multiplied by ⁱ⁼³ (1-ηi). A _o is each multiple regression coefficient vector (a,
b ₁ , b ₂ , . . . , b ₅ , c), and P _o is a 7×7 estimation error covariance matrix.

In this method, the only constant to be adjusted is g in equation (11), so online adjustment can be done relatively quickly and easily.

Equation (1) explained above represents the width deviation of the rolled material located between 6 and 2 in Figure 1, and equation (2) represents the deviation of the width of the rolled material located at 10 in Figure 1. Expression (3) expresses the contribution of the setting error of 6 to 10 to the width deviation of the rolled material located at 10 in Fig. 1, and expression (4) expresses the contribution of the setting error of 6-10. Expression (5) represents the width deviation of the rolled material located at 10 in Figure 1, and formula (5) is calculated by the calculator 12 in Figure 1.
Expressions (6) and (6a) express the width correction expressions of the calculator 12 in FIG. 1, and (7) to
Equation (11) represents the parameter calculation formula for the width deviation estimation formula of the calculator 12 in FIG.

The processing functions of the computer 12 shown in FIG. 1 are summarized in FIG. 3.

FIG. 2 shows an example of board width control using the control method described above. Figure 2 is a plot of 750 points, and many short horizontal lines that cross the slope line are
It can be seen as a line due to a series of many points. In the example shown in Figure 2, the slab dimensions are 250 mm thick.
~240mm, width 900~1400mm, Ceq=0.02~55, horizontal roll 10 exit dimension is 30~36mm thick,
It was rolled to a width of 750 to 1350 mm, and as is clear from the figure, the predicted width deviation correlates well with the actual width deviation, and it can be seen that extremely high control accuracy can be obtained.

〔Effect of the invention〕

As described in detail above, according to the present invention, the final width deviation can be estimated and compensated for without using a width detector during rolling, and the variation in actual width can be reduced. The cost can be reduced and the yield can be improved.

Furthermore, by adaptively correcting the estimation model based on the measured value of the actual range, control accuracy can be easily maintained, which is an excellent industrial effect.

[Brief explanation of the drawing]

FIG. 1 is a side view of a portion of a roughing mill arrangement implementing one embodiment of the present invention. FIG. 2 is a graph showing the relationship between predicted width deviation and actual width deviation by sheet width control of the present invention. FIG. 3 is a block diagram showing the functions of the computer 12 shown in FIG. 1. 1-5: Edger, 6-10: Horizontal roll,
11: Load detector, 12: Calculator, 13: Width detector.

Claims (1)

[Claims] 1 The currently determined rolling set when controlling the strip width in a hot rolling mill with at least two sets of hard rolls and horizontal rolls and a strip width detector installed on the exit side of the final rolling mill stand. - A step of predicting the width deviation at the end of rolling in the case of up-rolling based on the rolling load of the existing rolling stand, and a step of correcting the set-up of the hard rolls in the next and subsequent stages based on the prediction, A step of correcting the parameters of the width deviation estimation model using the sequential least squares method based on the actual plate width detected by the plate width detector after rolling, the actual rolling load of the existing rolling stand, and the rolled material information. A method for controlling strip width in hot rolling, characterized by comprising the steps of: