JP5500061B2 - Method for controlling shape of rolled material in roll cross type rolling mill and method for producing rolled material - Google Patents

Description

  The present invention relates to a shape control method for controlling the shape of a rolled material using a roll cloth type rolling mill, and a method for manufacturing a rolled material using the shape control method.

  In the rolling of a plate material, shape control is performed in order to obtain a desired value for the shape of the rolled material during rolling (flatness, plate crown or edge drop which is a plate thickness distribution in the width direction). In this shape control, the amount of operation of the shape control actuator is determined based on a measurement result value or an estimated value of the shape of the rolled material, or a measurement result value of a rolling load change that becomes a disturbance to the shape of the rolled material.

  As a technique relating to the shape control of the rolled material, for example, in Patent Document 1, the flatness of the rolled material is measured with a flatness meter installed on the delivery side of the rolling mill, and the measured flatness of the rolled material and a preset flatness are measured. A method for determining an operation amount of a shape control actuator based on a difference from a degree target value is disclosed. Patent Document 2 discloses a shape control method for operating a shape control actuator based on the amount of change in rolling load from a reference rolling load.

JP 2000-61520 A JP 2005-161373 A

  As an actuator for shape control performed during the rolling described above, a roll bender that is fast in response because it is hydraulically operated is most widely used. A general method for obtaining the operation amount of the roll bend force in the method similar to Patent Document 1 when the roll bender is an actuator will be described as follows.

The actual shape value of the rolled material is expressed as ε _act (in the case of flatness, the end elongation direction is positive and the middle elongation direction is negative, and the elongation ratio is expressed. If the target value is ε _aim , the operation amount of the roll bend force required to correct ε _act to ε _aim is expressed by the following formula 1. Is done.

Here, ∂ε / ∂J (<0) is a coefficient representing the influence of the roll bend force J on the rolled material shape ε. In general, in a control method in which a control amount (in this application, the shape of a rolled material) is detected and fed back to an operation amount, integral control is required to make the steady position deviation (offset) of the control amount zero. When integral control is applied to Equation 1 with a period of Δt, an operation amount ΔJ ₁ (t) of the roll bend force in the control period is expressed by Expression 2 below.

式２において、Ｋ_Ｉ（＞０）は下記式３で与えられる積分制御ゲイン、ｋ_ｉは形状の検出むだ時間等に応じて決められる積分制御の動特性を表すパラメータ、ΔＪ_１（ｔ−１）は前制御周期におけるロールベンド力の操作量であり、制御開始時の制御周期ｔ＝１ではΔＪ_１（０）＝０とする。

In Equation 2, K I _(> 0) is integral control gain, given by the following formula 3, k _i is a parameter representing the dynamic characteristic of the integral control is determined in accordance with the detected waste time like shape, ΔJ 1 _(t-1 ) Is an operation amount of the roll bend force in the previous control cycle, and ΔJ ₁ (0) = 0 in the control cycle t = 1 at the start of control.

  A general method for obtaining the operation amount of the roll bend force in the method similar to Patent Document 2 when the roll bender is an actuator will be described as follows.

  When the change in rolling load from the reference rolling load is ΔP, the influence of ΔP on the shape of the rolled material is expressed by the following formula 4.

式４において、∂ε／∂Ｐ（＞０）は、圧延荷重Ｐの圧延材形状εへの影響を表す係数である。式４の形状変化Δεをうち消すためのロールベンド力の操作量ΔＪ_２（ｔ）は、下記式５で表される。

In Equation 4, ∂ε / ∂P (> 0) is a coefficient representing the influence of the rolling load P on the rolled material shape ε. The operation amount ΔJ ₂ (t) of the roll bend force for eliminating the shape change Δε in Equation 4 is expressed by Equation 5 below.

式５において、Ｋ_Ｐ（＞０）は下記式６で与えられる比例制御ゲインである。

In Equation 5, K _P (> 0) is a proportional control gain given by Equation 6 below.

積分 ε / ∂J and ∂ε / ∂P included in the integral control gain K _{I of} the above formula 3 and the proportional control gain K _P of the above formula 6 are the setup calculation values of J and P in the setup calculation before the start of rolling. Since the value obtained by the difference calculation in the vicinity is used, the control gains K _I and K _P are fixed and not changed during rolling. Actually, since the relationship between the roll bend force J and the rolled material shape ε and the relationship between the rolling load P and the rolled material shape ε are substantially linear, there is no problem with such a fixed control gain.

  By the way, steel materials used for automobiles and structural materials are required to have excellent mechanical properties such as strength, workability, and toughness. To comprehensively improve these mechanical properties, It is effective to refine the grains. As a method of refining crystal grains of hot-rolled steel sheets, particularly in the latter stage of hot finish rolling, high pressure rolling (finish rolling with a higher reduction ratio of the latter stage stand) is performed to refine the austenite grains and within the grains. There is known a method for accumulating rolling strain and quenching immediately after finish rolling to refine the ferrite grains obtained. In order to manufacture a hot-rolled steel sheet having fine crystal grains (hereinafter referred to as “fine-grained steel”) by this method, the reduction ratio of the rear stage stand of the tandem finish rolling mill in the hot rolling line is made higher than before. Need to increase. However, if the reduction ratio of the rear stage stand is increased, the rolling load of the rear stage stand increases, and the work roll axial deflection and flattening deformation increase and the shape of the rolled material deteriorates. A roll cross type rolling mill having a shape control capability is suitable.

  In the roll-cross type rolling mill, the upper work roll, the upper backup roll, the lower work roll, and the lower backup roll are paired, respectively, and the pair cross-type rolling mill that crosses the roll axis of the upper roll pair and the lower roll pair, There is a work roll cross type rolling mill that crosses only the roll axis.

FIG. 2 is a schematic diagram showing the arrangement of work rolls in a roll-cross type rolling mill, FIG. 2 (a) is a plan view, and FIG. 2 (b) is an AA cross section and a BB cross section of FIG. 2 (a). The figure which shows the relative position of the roll axis center of the upper work roll 2 in FIG. 2, FIG.2 (c) shows the relative position of the roll axis center of the lower work roll 3 in the AA cross section and BB cross section of FIG. FIG. In FIG. 2B, O _Au is the center of the upper work roll 2 in the AA cross section (central part in the roll axis direction), and O _Bu is the center of the upper work roll 2 in the BB cross section (end part in the roll axial direction). It is. Further, in FIG. 2 _{(c), O Al} center of the lower work roll 3 in the A-A cross-section (the roll axis direction central _{portion), O Bl} is lower work roll 3 in the section B-B (roll axis direction end portion) Represents the center of 2B and 2C, the dotted line is an AA cross section, and the solid line is a BB cross section. In addition, although the cross section of the upper work roll 2 and the lower work roll 3 becomes an ellipse in an AA cross section or a BB cross section, in FIG. 2B and FIG. ing.

As shown in FIGS. 2 (a) to 2 (c), the shape control by the roll cross type rolling mill is made to cross the upper and lower roll axes in a plan view, and the gap between the upper and lower work rolls at the end in the roll axis direction is changed. This is done by adjusting the gap difference between the upper and lower work rolls at the end in the roll axis direction and at the center in the roll axis direction. This gap difference is geometrically determined by the arrangement of the upper and lower work rolls. By changing the cross angle θ, which is the angle between the upper and lower roll axes, the same effect as if the initial grinding crown was given to the roll was obtained. Therefore, it is called an equivalent roll crown, and the equivalent roll crown C _eq is expressed by the following formula 7.

式７において、Ｏ_ＡｕＯ_ＢｕはＯ_ＡｕとＯ_Ｂｕとの間の距離、Ｏ_ＡｕＯ_ＡｌはＯ_ＡｕとＯ_Ａｌとの間の距離、Ｏ_ＢｕＯ_ＢｌはＯ_ＢｕとＯ_Ｂｌとの間の距離を表す。

In Equation 7, O _Au O _Bu is the distance between O _Au and O _Bu , O _Au O _Al is the distance between O _Au and O _Al, and O _Bu O _Bl is between O _Bu and O _Bl . Represents the distance.

Here, the cross angle θ is on the order of 10 ⁻² rad, and O _Au O _Bu is much smaller than O _Au O _Al, and therefore Equation 7 is approximated by Equation 8 below.

式８において、Ｌはワークロール胴長、Ｒはワークロール半径、θはクロス角を表す。

In Equation 8, L is the work roll body length, R is the work roll radius, and θ is the cross angle.

  In the case of a pair cross type rolling mill, the effect of the equivalent roll crown appears only between the upper and lower work rolls, and in the case of the work roll cross type rolling mill, it is equivalent between the backup roll and the work roll in addition to the upper and lower work rolls. Although there is a difference that the effect of the roll crown occurs, in any rolling mill, a very large shape control effect can be obtained by operating a slight cross angle. However, since the change speed of the cross angle is considerably slower than the change speed of the roll bend force, the roll cross type rolling mill usually has a roll bender, and the control capability is large in the setup before starting rolling. In general, a slow cross angle is set as an initial response, and a roll bender that has a small control capability but a quick response is generally used as an actuator for shape control during rolling.

  However, in the production of fine-grained steel as described above, since the rolling reduction is high, the change in rolling load during rolling also increases. Therefore, the roll bender alone has insufficient control capability, and the cross angle θ may have to be manipulated by shape control during rolling. However, the coefficient ∂ε / ∂θ representing the change in the rolled material shape ε with respect to the cross angle θ of the roll cross type rolling mill can be understood from the fact that the equivalent roll crown is proportional to the square of θ as shown in Equation 8. Thus, it does not become constant like ベ ン ε / ∂J of the roll vendor, and varies greatly depending on the cross angle θ. Therefore, when using the cross angle of the roll cross type rolling mill as the operation amount for shape control during rolling, the control gain is set to a constant fixed gain during rolling as in the case of using the conventional roll bend force as the operation amount. The shape control effect changes depending on the value of the cross angle θ, the operation amount becomes too small and the control effect appears late, or the operation amount becomes excessive and the control hunting occurs, resulting in high accuracy. There was a problem that it was impossible to control the shape.

  In addition, since the change speed of the cross angle is slow, when the integration control is applied, the change of the cross angle cannot follow the change of the cross angle operation amount obtained by integration by the integration control. Due to the wind-up phenomenon, the amount of cross angle operation becomes excessive, and control hunting may occur.

  Accordingly, the present invention is a method for controlling the shape of a rolled material in a roll cloth rolling mill, which can increase the accuracy when controlling the shape of the rolled material by operating the cross angle of the roll cloth rolling mill during rolling. It is another object of the present invention to provide a rolled material manufacturing method using the shape control method.

  The present invention will be described below. In order to facilitate understanding of the present invention, reference numerals in the attached drawings and symbols used in the description of the present invention to be described later are added in parentheses, but the present invention is thereby limited to the illustrated embodiments. is not. In the following, the shape control method of the rolled material in the roll cross type rolling mill according to the present invention may be simply referred to as “the shape control method of the present invention”.

The first aspect of the present invention is a method for controlling the shape of the rolled material (10) by operating the cross angle (θ) of the roll cross type rolling mill (1), and determining the amount of operation of the cross angle. By setting the control gain (K _I , K _P ) as a function of the cross angle and substituting the actual value of the cross angle (θ _act (t)) into the above function, the cross gain is changed every moment. Is a shape control method for a rolled material in a roll-cross type rolling mill, characterized in that the operation amount (Δθ ₁ (t), Δθ ₂ (t)) is determined.

In the first aspect of the present invention, the control gain (K _I , K _P ) is preferably a monotonically decreasing function of the cross angle (θ).

According to a second aspect of the present invention, in the method of controlling the shape of the rolled material (10) by operating the cross angle (θ) of the roll cross type rolling mill (1), the amount of operation of the cross angle is determined. By setting the integral control gain (K _I ) as a function of the cross angle and substituting the actual value of the cross angle (θ _act (t)) into the above function, the integral control gain is changed from moment to moment. When determining the manipulated variable (Δθ ₁ (t)), the value (K) obtained by dividing the maximum change speed (V _max ) of the cross angle by the absolute value of the integrand (| ε _act (t) −ε _aim |). _Imax (t)) is a method for controlling the shape of a rolled material in a roll-cross type rolling mill, wherein the integral control gain is limited to be equal to or less than _Imax (t)).

In the second aspect of the present invention, the integral control gain (K _I ) is preferably a monotone decreasing function of the cross angle (θ).

  In the third aspect of the present invention, the shape of the rolled material is controlled using the method for controlling the shape of the rolled material in the roll-cross type rolling mill according to the first aspect of the present invention or the second aspect of the present invention. It is a manufacturing method of a rolling material characterized by having a process.

In the present invention, since the control gain (K _P ) and the integral control gain (K _I ) are appropriately changed from moment to moment according to the actual value (θ _act (t)) of the cross angle, the value of the cross angle (θ) It is possible to obtain the cross angle operation amount (θ ₂ (t), θ ₁ (t)) while reflecting the influence of the cross angle on the rolled material shape, which varies depending on the angle of the angle. Therefore, there is no possibility that the operation amount of the cross angle becomes excessively small and the control effect appears late, or the control amount of the cross angle becomes excessive and control hunting does not occur. Therefore, according to the present invention, it is possible to increase the accuracy of shape control of the rolled material, and it is possible to manufacture a rolled material having an excellent shape. Further, according to the present invention, it is possible to reduce a portion that has been cut off instead of being a product as a defective shape, so that it is possible to improve the yield.

In the present invention, the control gain (K _P ) and the integral control gain (K _I ) are monotonically decreasing functions of the cross angle (θ), so that the cross angle per unit change amount increases as the cross angle increases. Since the phenomenon that the shape change of the rolled material becomes large can be reflected in the calculation of the operation amount of the cross angle, the control accuracy is improved.

In the second aspect of the present invention, the integral control gain (K _I ), the maximum change speed of cross angle (V _max ), and the absolute value of the integrand (| ε _act (t) −ε _aim |) Since the limit is set to be equal to or less than the divided value (K _Imax (t)), it is possible to prevent the wind-up phenomenon of the integral controller from occurring, and the cross angle operation amount does not become excessive.

It is a figure which shows the form example of the apparatus with which the rolling mill which applies the shape control method of this invention, and its periphery is equipped. It is a schematic diagram which shows arrangement | positioning of the work roll of a roll cross type rolling mill. It is a graph which shows the rolling state at the time of controlling by the shape control method of this invention. It is a graph which shows the rolling state at the time of applying the shape control method other than this invention to a roll bender. It is a graph which shows the rolling state at the time of applying the shape control method other than this invention to a roll cross type rolling mill. It is a graph which shows the rolling state at the time of controlling by the shape control method of this invention. It is a graph which shows the rolling state at the time of applying the shape control method other than this invention to a roll bender. It is a graph which shows the rolling state at the time of applying the shape control method other than this invention to a roll cross type rolling mill. It is a graph which shows the rolling state at the time of controlling by the shape control method of this invention. It is a graph which shows the rolling state at the time of applying the shape control method other than this invention to a roll bender. It is a graph which shows the rolling state at the time of controlling by a comparison method. It is a graph which shows the rolling state at the time of controlling by the shape control method of this invention. It is a graph which shows the rolling state at the time of applying the shape control method other than this invention to a roll bender. It is a graph which shows the rolling state at the time of applying the shape control method other than this invention to a roll cross type rolling mill.

  Hereinafter, with reference to the drawings, an example of controlling the flatness of a rolled material (hereinafter, the elongation ratio is used as an index representing the flatness, and the flatness is sometimes referred to as the elongation ratio). Next, embodiments of the present invention will be described. In the case of controlling the sheet crown and edge drop of the rolled material, the present invention can be implemented in exactly the same manner by replacing the flatness with the sheet crown and edge drop. The shape control method of the present invention can be used when producing a rolled material, and can be suitably used particularly when producing fine-grained steel.

  FIG. 1 is a diagram showing a simplified example of the form of a rolling mill to which the shape control method of the present invention is applied and equipment provided around the rolling mill. As shown in FIG. 1, a rolling mill 1 that is a pair cross type rolling mill has an upper work roll 2, a lower work roll 3, an upper backup roll 4, and a lower backup roll 5. The rolling mill 1 includes an upper work roll 2 and an upper backup roll 4 (hereinafter, these may be collectively referred to as “upper roll pair”), and a lower work roll 3 and a lower backup roll 5 (hereinafter referred to as “upper roll pair”). Collectively referred to as “lower roll pair”)), with the roll axis of the upper roll pair and the roll axis of the lower roll pair crossed in plan view, from the left side to the right side of FIG. The rolled material 10 conveyed is rolled. In the shape control method of the present invention according to this embodiment, the flatness of the rolled material 10 rolled by the rolling mill 1 is controlled.

  The rolling mill 1 is provided with a cross angle detector 6 and a load cell 7, and a flatness meter 20 is provided on the rolling direction exit side of the rolling mill 1. The actual cross angle value detected by the cross angle detector 6, the actual rolling load value detected by the load cell 7, and the actual elongation value of the rolled material 10 detected by the flatness meter 20 are the shape control device 30. Given to. Further, the setup computer 40 obtains control parameters necessary for the calculation of the cross angle manipulated variable performed by the shape control device 30 prior to rolling of the rolled material 10, and provides the control parameters to the shape control device 30.

  In the shape control device 30, the actual cross angle value given from the cross angle detector 6, the actual rolling load value given from the load cell 7, the actual elongation difference value of the rolled material 10 given from the flatness meter 20, and The cross angle manipulated variable is calculated using the control parameter given from the setup computer 40. The calculated cross angle operation amount is given to a cross angle control device (not shown) provided in the rolling mill 1. And the flatness of the rolling material 10 is controlled by changing the cross angle of an upper roll pair and a lower roll pair based on the control command given from the cross angle control apparatus.

  The operation | movement at the time of controlling the flatness of the rolling material 10 using the rolling mill 1 comprised as mentioned above is demonstrated below.

Prior to rolling the rolled material 10, the setup computer 40 flattenes the rolling load set value P _set and the rolled material 10 by a known method based on the rolling conditions such as the dimensions and material of the rolled material 10. An initial set value θ _set of an appropriate cross angle for rolling is calculated, and the influence of the rolling load on the elongation ratio and the influence of the cross angle on the elongation ratio are calculated in the vicinity of P _set and θ _set . At this time, with respect to the rolling load, the effect on the elongation ratio is almost linear, and the relationship between the rolling load P and the amount of change δε _{P in the} elongation ratio is

と表されるので、例えば、下記式１０の差分法により、上記式９における係数ａ（＝∂ε／∂Ｐ＞０）を計算する。

Therefore, for example, the coefficient a (= ∂ε / ∂P> 0) in Equation 9 is calculated by the difference method of Equation 10 below.

式１０において、ε（Ｐ，θ）は圧延荷重がＰ、クロス角がθであるときの伸差率、δＰは圧延荷重の微少変化を表す。一方、クロス角については、等価ロールクラウンが上記式８で表されることから分かるように、クロス角θと伸差率の変化量δε_θとの関係は、

In Expression 10, ε (P, θ) represents the elongation difference when the rolling load is P and the cross angle is θ, and δP represents a slight change in the rolling load. On the other hand, regarding the cross angle, as can be seen from the fact that the equivalent roll crown is expressed by the above equation 8, the relationship between the cross angle θ and the change amount δε _θ of the elongation difference is

と表されるので、例えば、下記式１２の差分法により、上記式１１における係数ｂ（≠∂ε／∂θ＜０）を計算する。

Therefore, for example, the coefficient b (≠ ∂ε / ∂θ <0) in the above equation 11 is calculated by the difference method of the following equation 12.

式１２において、δθはクロス角の微少変化を表す。以上のように、セットアップ計算機４０は、式１０、式１２で制御パラメータａ、ｂを計算し、形状制御装置３０に与える。

In Expression 12, δθ represents a slight change in the cross angle. As described above, the setup computer 40 calculates the control parameters a and b using Expressions 10 and 12, and supplies them to the shape control apparatus 30.

  Next, a control operation performed after the rolling of the rolled material 10 is started will be described. There are two methods, that is, a method that uses the actual value of the elongation difference of the rolled material detected by the flatness meter 20 and a method that uses the actual value of the rolling load detected by the load cell 7. Hereinafter, it demonstrates in order.

As a first method, a method of using the actual difference value detected by the flatness meter 20 will be described. The actual elongation value of the rolled material 10 detected by the flatness meter 20 is given to the shape control device 30 as ε _act (t) every control cycle Δt of the shape control device 30 and detected by the cross angle detector 6. The actual cross angle value is given to the shape control device 30 as θ _act (t) every control cycle Δt of the shape control device 30. The shape control device 30 uses the integral control gain K _I (> 0) of integral control as a function of the cross angle θ.

のように設定しておき、式１３のθにクロス角検出器６によって検出されたクロス角実績値θ_ａｃｔ（ｔ）を代入することにより、当該制御周期における積分制御ゲインＫ_Ｉ（ｔ）を計算し、伸差率実績値ε_ａｃｔ（ｔ）と予め定めておいた伸差率目標値ε_ａｉｍとの差である伸差率偏差を求め、その積分制御の出力として当該制御周期におけるクロス角操作量Δθ_１（ｔ）を下記（１４）式で演算する。

By substituting the cross angle actual value θ _act (t) detected by the cross angle detector 6 into θ in Expression 13, the integral control gain K _I (t) in the control cycle is set. The elongation difference deviation, which is the difference between the actual elongation ratio value ε _act (t) and the predetermined elongation ratio target value ε _aim , is calculated, and the cross angle in the control cycle is output as the integral control output. The operation amount Δθ ₁ (t) is calculated by the following equation (14).

式１４において、Δθ_１（ｔ−１）は前制御周期におけるクロス角操作量であり、制御開始時の制御周期ｔ＝１ではΔθ_１（０）＝０とする。式１３において、ｋ_ｉ（＞０）は平坦度の検出むだ時間、すなわち、圧延材１０が圧延機１の直下から平坦度計２０まで移動する時間、に応じて決められる積分制御の動特性を表すパラメータである。また、ｍａｘ（θ，θ_ｍｉｎ）はθと予め定められた微少量θ_ｍｉｎとの大きい方を取ることを意味する演算子であり、θ_ａｃｔ（ｔ）によるゼロ割り（式１３の右辺の分母がゼロになること）を回避するために導入されている。

In Expression 14, Δθ ₁ (t−1) is a cross angle operation amount in the previous control cycle, and Δθ ₁ (0) = 0 in the control cycle t = 1 at the start of control. In Equation 13, k _i (> 0) is a dynamic characteristic of integral control determined according to a dead time for detecting the flatness, that is, a time required for the rolled material 10 to move from directly under the rolling mill 1 to the flatness meter 20. It is a parameter to represent. Further, max (θ, θ _min ) is an operator that means the larger of θ and a predetermined minute amount θ _min, and is divided by zero by θ _act (t) (the denominator on the right side of Equation 13). Has been introduced to avoid zero).

Since 2b · θ in the denominator of Equation 13 matches the derivative ∂ε / ∂θ from Equation 11, K _I (t) is accurately normalized under the current cross angle actual value θ _act. Therefore, the shape control effect can be prevented from changing depending on the value of the cross angle θ. Equation 13 is an integral control gain that is accurately normalized with respect to an arbitrary θ. However, since ∂ε / ∂θ (<0) is proportional to the cross angle, the integral control gain is proportional to the cross angle. Therefore, it is a monotonically decreasing function such as inverse proportion.

Further, when the integral value of integral control ε _act (t) −ε _aim is large or k _i is large, the change of the cross angle can follow the change of the cross angle manipulated variable Δθ ₁ of Expression 14. In other words, a so-called integral controller windup phenomenon may cause an excessive amount of cross angle operation. In order to avoid this, an upper limit constraint is placed on the integral control gain K _I (t) obtained by substituting θ _act (t) for θ in Equation 13, and K _Imax where K _I (t) is calculated by Equation 15 below. When (t) is exceeded, K _I (t) is replaced with K _Imax (t).

式１５において、Ｖ_ｍａｘはクロス角の最大変更速度である。このように積分制御ゲインをクロス角の最大変更速度を積分制御の被積分量で除した値以下になるように制限すれば、式１４及び式１５より、当該制御周期におけるクロス角操作量の変化の絶対値は、

In Formula 15, V _max is the maximum change speed of the cross angle. As described above, if the integral control gain is limited to be equal to or less than the value obtained by dividing the maximum change speed of the cross angle by the integral amount of the integral control, the change in the cross angle manipulated variable in the control cycle is obtained from the equations 14 and 15. The absolute value of is

となり、クロス角操作量Δθ_１の変化を、クロス角の最大変更速度で追従できる範囲内に抑制することができる。

Thus, the change in the cross angle operation amount Δθ ₁ can be suppressed within a range that can be followed at the maximum change speed of the cross angle.

Then, the method of using the rolling load track record value detected by the load cell 7 as a 2nd method is demonstrated. The actual rolling load value detected by the load cell 7 is given to the shape control device 30 as P _act (t) every control cycle Δt of the shape control device 30, and the actual cross angle value detected by the cross angle detector 6 is Then, it is given to the shape control device 30 as θ _act (t) every control cycle Δt of the shape control device 30. The shape control device 30 uses the proportional control gain K _P (> 0) as a function of the cross angle θ,

のように設定しておき、式１７のθにクロス角検出器６により検出されたクロス角実績値θ_ａｃｔ（ｔ）を代入することにより、当該制御周期における比例制御ゲインＫ_Ｐ（ｔ）を計算し、圧延荷重変化に対する比例制御の出力として当該制御周期におけるクロス角操作量Δθ_２（ｔ）を下記式１８で演算する。

By substituting the cross angle actual value θ _act (t) detected by the cross angle detector 6 into θ in Expression 17, the proportional control gain K _P (t) in the control cycle is obtained. The cross angle operation amount Δθ ₂ (t) in the control cycle is calculated by the following equation 18 as an output of proportional control with respect to the rolling load change.

式１８において、Δθ_２（ｔ−１）は前制御周期におけるクロス角操作量であり、制御開始時の制御周期ｔ＝１ではΔθ_２（０）＝０、Ｐ_ａｃｔ（０）＝Ｐ_ａｃｔ（１）とする。式１７の分母にある２ｂ・θは、式１１より、導関数∂ε／∂θに一致するので、Ｋ_Ｐ（ｔ）は現在のクロス角実績値θ_ａｃｔのもとでの−（∂ε／∂Ｐ）／（∂ε／∂θ）に一致し、クロス角θの値によって形状制御効果が変化することを防止できる。なお、式１７は任意のθに対して正確に正規化された比例制御ゲインであるが、∂ε／∂θ（＜０）がクロス角に比例することから、比例制御ゲインはクロス角に対して、反比例のような単調減少関数とする。

In Equation 18, Δθ ₂ (t−1) is the cross angle operation amount in the previous control cycle, and Δθ ₂ (0) = 0, P _act (0) = P _act () at the control cycle t = 1 at the start of control. 1). Since 2b · θ in the denominator of Equation 17 matches the derivative ∂ε / ∂θ from Equation 11, K _P (t) is − (∂ε under the current actual cross angle value θ _act. / ∂P) / (∂ε / ∂θ), and the shape control effect can be prevented from changing depending on the value of the cross angle θ. Equation 17 is a proportional control gain that is accurately normalized with respect to an arbitrary θ. However, since ∂ε / ∂θ (<0) is proportional to the cross angle, the proportional control gain is proportional to the cross angle. Therefore, it is a monotonically decreasing function such as inverse proportion.

As described above, the shape control device 30 calculates the cross angle operation amount Δθ ₁ (t) by the first method and the cross angle operation amount Δθ ₂ (t) by the second method, and sums them (first, first, When only one of the second methods is adopted, a value calculated by that method) is given to a cross angle control device (not shown) provided in the rolling mill 1, and the cross angle control device determines the cross angle of the upper roll pair. The flatness of the rolled material 10 is controlled by changing the cross angle of the lower roll pair.

The shape control method of the present invention will be described more specifically with reference to simulation results. As values common to the following simulations, Δt = 0.01 s, a = 5 × 10 ⁻⁷ kN ⁻¹ , b = −6.57 rad ⁻² , V _max = 0.00148 rad · s ⁻¹ , θ _min = 0.00175 rad, ε _aim = 0, and ∂ε / ∂J = −10 ⁻⁶ kN ⁻¹ were used.

<Simulation 1>
The flattening meter 20 measures the actual elongation ratio value ε _act (t) of the rolled material 10 to obtain an elongation ratio deviation that is a difference from the target elongation ratio value ε _aim, and the cross-angle manipulated variable is controlled by the integral control. A simulation applying only the first method for obtaining Δθ ₁ (t) was performed. The initial value of the elongation difference actual value was ε _act (1) = 0.001, and the initial setting value of the cross angle was θ _set = 0.00524 rad. The flatness detection dead time was 4 s, and the parameter k _i representing the dynamic characteristic of integral control obtained in consideration of the flatness detection dead time was set to 0.12.

  FIG. 3 shows the rolling state when the shape control method of the present invention is applied. FIG. 4 shows a rolling state when a conventional roll bender is used as an actuator. In any case, the elongation difference deviation was set at 10.2 s without overshooting. That is, even when the cross angle is used as the operation amount, the same control as when the conventional roll bend force is used as the operation amount has been realized.

On the other hand, the cross angle is set as the operation amount, but instead of using the integral control gain K _I (t) calculated every moment by substituting the actual value of the cross angle into Equation 13, the roll bend force is used as the operation amount. As is done in the method, the rolling state in the case of using the fixed control gain set by the following equation 19 based on ∂ε / 求 め θ obtained in the vicinity of the initial setting value θ _set of the cross angle is shown in FIG. As shown in FIG.

As shown in FIG. 5, the elongation difference deviation fluctuates and is not settled. This is cross angle theta is larger than the initial set value theta _{The set} by the cross angle operation, even though larger than the value that the value of ∂ε / ∂θ is determined in the vicinity of the theta _{The set,} theta _{The set} This is because an excessive control gain obtained in the vicinity of is used. On the other hand, in FIG. 3 (shape control method of the present invention) in which the integral control gain is changed from moment to moment according to the actual value of the cross angle, the elongation difference deviation can be controlled well without overshooting.

<Simulation 2>
The simulation was performed under the same conditions as in the simulation 1 except that the initial value of the elongation difference actual value was changed to ε _act (1) = − 0.001 and the initial setting value of the cross angle was changed to θ _set = 0.0140 rad. I did it.

  FIG. 6 shows the rolling state when the shape control method of the present invention is applied. FIG. 7 shows a rolling state when a conventional roll bender is used as an actuator. In any case, the elongation difference deviation was set at 10.2 s without overshooting. That is, even when the cross angle is used as the operation amount, the same control as when the conventional roll bend force is used as the operation amount has been realized.

On the other hand, the cross angle is set as the operation amount, but instead of using the integral control gain K _I (t) calculated every moment by substituting the actual value of the cross angle into Equation 13, the roll bend force is used as the operation amount. As is done by the method, the rolling state in the case of using the fixed control gain set by the above equation 19 based on ∂ε / 求 め θ obtained in the vicinity of the initial setting value θ _set of the cross angle is shown in FIG. It is shown in FIG. As shown in FIG. 8, the settling time of the elongation difference deviation was 24.0 s, which was later than when the present invention was applied (10.2 s). This is because the cross angle θ is smaller than the initial set value θ _set by the cross angle operation, and the value of ∂ε / ∂θ is smaller than the value obtained in the vicinity of θ _set , even though θ _set. This is because an excessive control gain obtained in the vicinity of is used. On the other hand, in FIG. 6 (shape control method of the present invention) in which the integral control gain is changed from moment to moment according to the actual value of the cross angle, the elongation difference deviation can be controlled well without increasing the settling time. .

<Simulation 3>
The simulation was performed under the same conditions as the simulation 2 except that the flatness detection dead time was changed to 1 s. Along with changing the detection dead time of flatness was 0.45 parameters k _i representing the dynamic characteristics of the integration control obtained by considering the detection dead time of flatness.

The rolling state when the shape control method of the present invention is applied is shown in FIG. The elongation difference deviation was set at 5.9 s without overshooting. FIG. 10 shows a rolling state in the case where a conventional roll bender is used as an actuator. The elongation difference deviation was set at 2.9 s without overshooting. In the simulation 2, the settling time is the same when the cross angle is set as the operation amount and when the roll bend force is set as the operation amount in the shape control method of the present invention. The settling time was longer when the cross angle was the manipulated variable. This is because k _i increases from 0.12 to 0.45 in response to the reduction in the flatness detection dead time, and the integral control gain K calculated by substituting the actual cross angle value into Equation 13 is as follows. _{This is because the time that I} (t) is constrained by the upper limit value K _Imax (t) calculated by Expression 15 occurs, and is due to the difference in the response between the roll bend force and the cross angle.

  On the other hand, as a comparative example, the integral control gain is changed from moment to moment according to the actual cross angle value as in Equation 13, but the rolling state when there is no upper limit constraint in Equation 15 is shown in FIG. A large overshoot occurred in the vicinity of 10 s, and the settling time of the elongation difference deviation became long as 18.0 s. This is because the change of the cross angle cannot follow the change of the cross angle operation amount obtained by integration by the integration control, and the cross angle operation amount becomes excessive due to the so-called windup phenomenon of the integration controller. On the other hand, in FIG. 9 (the shape control method of the present invention) in which the upper limit constraint of the integral control gain is provided, the elongation difference deviation can be controlled well without overshooting.

<Simulation 4>
A simulation was performed in which only the second method of measuring the actual rolling load value P _act (t) with the load cell 7 and obtaining the cross angle operation amount Δθ ₂ (t) by proportional control with respect to the change in the actual rolling load value was performed. The initial value of the elongation difference was ε _act (1) = 0, and the initial setting value of the cross angle was θ _set = 0.00698 rad. Further, a sinusoidal fluctuation having an amplitude of 650 kN and a period of 30 s was given to the rolling load.

  FIG. 12 shows the rolling state when the shape control method of the present invention is applied. FIG. 13 shows a rolling state when a conventional roll bender is used as an actuator. In any case, the elongation difference deviation was controlled to almost zero, and even when the cross angle was the operation amount, the same control as when the conventional roll bend force was the operation amount could be realized.

On the other hand, the cross angle is used as the operation amount, but instead of using the proportional control gain K _P (t) calculated every moment by substituting the actual value of the cross angle in Equation 17, the roll bend force is used as the operation amount. As is done in the method, the rolling state when a fixed control gain set by the following equation 20 is used based on ∂ε / ∂θ obtained in the vicinity of the initial set value θ _set of the cross angle is shown in FIG. 14 shows.

As shown in FIG. 14, the change amount of the cross angle with respect to the rolling load change is completely proportional, and the elongation difference deviation cannot be controlled to zero. In the time period from 0 s to 15 s, the cross angle θ is larger than the initial set value θ _set by the cross angle operation, and the value of ∂ε / ∂θ is larger than the value obtained in the vicinity of θ _set. First, since an excessive control gain obtained in the vicinity of θ _set was used, the amount of increase in the cross angle with respect to θ _set was excessive, and the elongation difference deviation was negative (medium elongation). In the time period of 15 s to 30 s, the cross angle θ is smaller than the initial setting value θ _set by the cross angle operation, and the value of ∂ε / ∂θ is smaller than the value obtained in the vicinity of θ _set . Nevertheless, since an excessive control gain obtained in the vicinity of θ _set was used, the amount of decrease in the cross angle with respect to θ _set became excessive, and the elongation difference deviation became negative (medium elongation). On the other hand, in FIG. 12 (the shape control method of the present invention) in which the proportional control gain is changed every moment according to the actual value of the cross angle, the rolling load is applied in the time zone of 0 s to 15 s where the cross angle is larger than θ _set. The change amount of the cross angle with respect to the change is made smaller than that in FIG. 14, and the change amount of the cross angle with respect to the change in rolling load is made larger than that in FIG. 14 in the time zone of 15 to 30 s where the cross angle is smaller than θ _set . Thus, the elongation difference deviation could be controlled to almost zero.

  The method for controlling the shape of a rolled material in the roll cloth rolling mill of the present invention and the method for producing a rolled material of the present invention can be used for manufacturing a plate material typified by fine-grained steel.

DESCRIPTION OF SYMBOLS 1 ... Rolling mill 2 ... Upper work roll 3 ... Lower work roll 4 ... Upper backup roll 5 ... Lower backup roll 6 ... Cross angle detector 7 ... Load cell 10 ... Rolled material 20 ... Flatness meter 30 ... Shape control device 40 ... Setup calculator

Claims (5)

In the method of controlling the shape of the rolled material by operating the cross angle of the roll cross type rolling mill,
A control gain for determining the operation amount of the cross angle is set as a function of the cross angle, and the cross gain is changed every moment by substituting the actual value of the cross angle into the function. A method for controlling the shape of a rolled material in a roll-cross type rolling mill, wherein an operation amount of a corner is determined. The shape control method of the rolling material in the roll cross type rolling mill according to claim 1, wherein the control gain is a monotonously decreasing function of the cross angle. In the method of controlling the shape of the rolled material by operating the cross angle of the roll cross type rolling mill,
An integral control gain at the time of determining the operation amount of the cross angle is set as a function of the cross angle, and the integral control gain is changed every moment by substituting the actual value of the cross angle into the function. The roll cross is characterized in that, when determining the operation amount of the cross angle, the integral control gain is limited to be equal to or less than a value obtained by dividing the maximum change speed of the cross angle by the absolute value of the integrand. A method for controlling the shape of a rolled material in a rolling mill. The shape control method of the rolling material in the roll cross type rolling mill according to claim 3, wherein the integral control gain is a monotonously decreasing function of the cross angle. A method for producing a rolled material, comprising a step of controlling the shape of the rolled material using the method for controlling the shape of the rolled material in the roll-cross type rolling mill according to any one of claims 1 to 4. .

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