JP2006043726A - Method for controlling thickness in rolling mill - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a control method of thickness in a rolling mill by which the steady-state deviation of thickness is reduced even to ramp-type disturbance such as the increase of thermal expansion of a roll and the increase or decrease of rolling speed in the thickness controlling method in the rolling mill by which the screw down location of the rolling roll or the rolling speed of a preceding stand is adjusted by measuring the thickness after rolling and feeding back the measured value of thickness. <P>SOLUTION: This method is a control method of thickness in the rolling mill by which the transfer function K<SB>C</SB>of control action for operating the screw down location of the roll on the basis of thickness deviation consists of K<SB>C</SB>(1+T<SB>C</SB>S)/S<SP>2</SP>substantially. Where, K<SB>C</SB>is a proportional constant, Tc is a time constant and S is a Laplace operator. By selecting an angular frequency ω<SB>C</SB>where the phase lag between the transfer function G<SB>P</SB>of a screw down device and a frequency transfer function (G<SB>P</SB>×G<SB>h</SB>(jω)) of the feed-back transfer function G<SB>h</SB>is ≤30° and making it as T<SB>C</SB>≥3/ω<SB>C</SB>, a proportional constant K<SB>C</SB>is determined so the gain of an open-loop frequency transfer function at ω=ω<SB>C</SB>is approximately 1. <P>COPYRIGHT: (C)2006,JPO&NCIPI

Description

  The present invention relates to a sheet thickness control method for a rolling mill that measures a sheet thickness after rolling and feeds back a measured value of the sheet thickness to adjust a rolling roll reduction position and a rolling speed of a front stand.

  In general, in sheet rolling, automatic sheet thickness control AGC (Automatic Gage Control) for controlling the sheet thickness over the entire length of the rolled product is performed. The automatic sheet thickness control method includes a monitor AGC that measures the sheet thickness after rolling and feeds it back to the roll reduction position, a gauge meter AGC that adjusts the roll reduction position from the measured rolling load and mill constant, and a combination control of these. Etc. are adopted. In the monitor AGC, the value detected by the rolling mill outlet side thickness gauge is used as the plate thickness value used for feedback, so it is difficult to construct a highly responsive control system with a large dead time. Therefore, feedback control by the monitor AGC is essential (Non-patent Document 1).

The monitor AGC is a hot rolling mill or a cold rolling mill for rolling a strip of steel, aluminum, copper or the like, and a plate thickness detector 4 installed on the exit side of the rolling mill roll stand 2 as shown in FIG. used to detect differences in thickness results h and the plate thickness set value h _a after rolling (thickness deviation Delta] h), the here detected the thickness deviation so becomes zero, the roll of the rolling mill by the control unit 5 This is a feedback plate thickness control method in which the plate thickness after rolling is controlled to match the plate thickness set value by correcting the rolling position or the rolling speed of the front stand. FIG. 1A is a diagram illustrating a case where the roll reduction position is used as the operation amount, and FIG. 1B is a diagram illustrating a case where the rolling speed U of the front stand is used as the operation amount.

  As the rolling proceeds, roll thermal expansion and roll wear progress. In Patent Document 1, in sheet thickness control using a gauge meter AGC as a main component and measuring a sheet thickness after rolling, a roll rolling position (roll gap) offset amount used in the gauge meter AGC is set, and a sheet measured during rolling A method is described in which the roll rolling position offset amount is estimated using the thickness and this estimated value is reflected in the next rolling. Roll offset position offset is corrected with roll thermal expansion and roll wear, but the estimated value is only reflected in the next rolling, so it corresponds to roll thermal expansion that progresses while rolling one sheet. Thus, the plate thickness cannot be controlled.

  On the other hand, in the case of the monitor AGC, the plate thickness control is performed by feeding back the measured thickness value during rolling, so even in the case where the rolled plate thickness is affected by roll thermal expansion that proceeds during rolling. It is possible to control the plate thickness following the thermal expansion.

  In the conventional monitor AGC, an integral element is used as a control operation element when determining the correction target value of the roll reduction position or rolling speed of the rolling mill using the detected thickness deviation. By using an integral element as a control operation element, it is possible to control the plate thickness without causing a steady deviation of the plate thickness even when a step-like disturbance occurs, and to follow even if a ramp-like disturbance occurs. Thus, the plate thickness can be controlled. When an integral element is used as a control operation element, an unstable state occurs when the gain of the control system becomes excessive, but it does not become unstable when the gain of the control system becomes excessive. For this reason, when determining the gain, there is an advantage that stable control can be easily realized at all times by selecting a slightly smaller gain with an allowance for the magnitude of the gain.

JP-A-8-155515 "Fourth Edition Steel Handbook 3-1, 7/6/5 Dynamic Control" issued by Japan Iron and Steel Institute, July 2002

  In rolling using the monitor AGC, roll thermal expansion may proceed with the progress of rolling, and the steady deviation of the rolled sheet thickness may increase. Further, in the process of accelerating the rolling speed immediately after the start of rolling and the process of sequentially reducing the rolling speed before the end of rolling, the steady deviation of the rolled sheet thickness may also increase.

  An increase in the thermal expansion amount of the roll and an increase / decrease in the rolling speed during rolling are disturbances given to the controlled object as a ramp function. When an integral element is used as a control operation element in the monitor AGC, it is possible to follow the disturbance against such a ramp-shaped disturbance. However, with such control, the steady deviation of the plate thickness cannot be made zero with respect to the ramp-like disturbance.

  In the rolling of aluminum plates used in recent aluminum cans, the demand for plate thickness accuracy has become increasingly severe. Thus, in rolling materials with strict sheet thickness accuracy, not only the steady-state deviation of the sheet thickness that occurs when the rolling speed increases or decreases, but also the steady-state deviation that occurs due to the thermal expansion of the roll during rolling at a constant speed, It has become a cause.

  If a second-order integration element is used as a control operation element in the monitor AGC, the steady thickness deviation can be made as close to zero as possible with respect to a ramp-like disturbance. However, when a second order integral element is used as the control operation element, not only the control system becomes unstable when the gain of the control system becomes excessive, but also it becomes unstable even when the gain becomes too small. In other words, since the system is poor in stability, the second order integration element has not been used as a control operation element of the monitor AGC.

  The present invention is a rolling mill that measures the thickness after rolling and feeds back the measured thickness value to adjust the rolling roll reduction position of the rolling or the rolling speed of the front stand (hereinafter also referred to as “roll reduction position etc.”). In the sheet thickness control method, a sheet thickness control method for a rolling mill that can reduce the steady deviation of the sheet thickness against ramp-like disturbances such as an increase in the thermal expansion of the roll and a reduction in the rolling speed is provided. The purpose is to do.

That is, the gist of the present invention is as follows.
(1) In a sheet thickness control method for a rolling mill that measures the sheet thickness after rolling and feeds back the measured value of the sheet thickness to adjust the roll roll reduction position of the rolling mill, control for operating the roll reduction position based on the sheet thickness deviation A sheet thickness control method for a rolling mill, characterized in that the transfer function G _{C of} operation substantially consists of K _C (1 + T _C S) / S ² .
Here, K _C is a proportionality constant, T _C is a time constant, and S is a Laplace operator.
(2) roll pressing position operation amount G _P a transfer function of the controlled object to the rolled plate thickness control amount, the transfer function of the feedback portion G _h Distant, frequency transfer function of G _P and G _h (G _P Select an angular frequency ω _{C at} which the phase lag of G _h (jω)) is 30 ° or less, use a constant α such that α ≧ 3, and set T _C = α / ω _C, and a round frequency at ω = ω _C The sheet thickness control method for a rolling mill as described in (1) above, wherein the proportionality constant K _C is determined so that the gain of the transfer function (G _C · G _P · G _h (jω)) is approximately 1.
Here, j is an imaginary number and ω is an angular frequency.
(3) The proportional constant between the roll reduction position and the rolled sheet thickness is K _P ,
K _C0 = ω _C ² / (K _P · √ (1 + α ² ))
K _C0 is determined, and K _C is set in the range of 0.8 × K _{C0 to} 1.2 × K _C0 .
(4) The transfer function G _{P to} be controlled is represented by K _P / (1 + T _P S), and the transfer function G _h of the feedback portion is represented by e ^−LS . Plate thickness control method.
Here, T _P is the time constant of the rolling control device, e is the base of the natural logarithm, and L is the dead time that occurs when detecting the plate thickness.
(5) The thickness control method for a rolling mill according to any one of (1) to (4), wherein the control operation amount is set to the rolling speed of the front stand instead of the roll reduction position.

The present invention relates to a roll thickness control method (monitor AGC) for measuring the thickness of a rolled sheet and feeding back the measured thickness value to adjust the rolling roll reduction position and the like. The transfer function G _C of the control operation for manipulating the reduction position substantially consists of K _C (1 + T _C S) / S ² . Thereby, even when a ramp-like disturbance such as an increase in the thermal expansion amount of the roll or an increase or decrease in the rolling speed occurs, the steady thickness deviation can be reduced.

FIG. 2 shows a block diagram of a control method for performing monitor AGC. The difference between the plate thickness h and the plate thickness target value h _a after rolling by the plate thickness detector 4 is measured as Delta] h, an operation on the transfer function of the control operations in the control device 5 has performed the control operations is G _C An amount correction target value ΔC _a is calculated. As the operation amount, the roll reduction position or the rolling speed of the front stand is used.

When the roll reduction position is used as the operation amount, in the roll stand 2, the roll reduction position correction target value ΔC _a is given to the reduction control device 3 as the operation amount target value, and the roll reduction position correction actual value ΔC is determined. In the reduction control device 3, a transfer function between ΔC _a and ΔC is expressed as G _P1 . Based on the roll reduction position correction actual value ΔC, the sheet thickness h after rolling is determined. The relationship in which the plate thickness h changes due to the change in ΔC can be grasped as a proportional relationship, and the proportionality constant is set as K _P here. G _P1 and K _P are collectively expressed as G _P. The transfer function when the plate thickness deviation Δh detected by the plate thickness detector 4 is fed back to the control device 5 is set to G _h .

If the mill rigidity coefficient of the rolling device is M and the plasticity coefficient is Q, in a rolling device that does not employ a gauge meter AGC,
K _P = M / (M + Q) (1)
Can be determined. Further, in a rolling machine employing a gauge meter AGC, the positive feedback rate of the gauge meter AGC is set to β (≦ 1),
K _P = M / (M + Q (1-β)) (2)
Can be determined. Usually, a value around 0.7 is used as β.

In FIG. 2, regarding the transfer function G _P1 between the roll roll down position target value ΔC _a and the roll roll down position actual value ΔC, G _P1 = 1 / (1 + T _P S) in consideration of the delay of the roll roll down control device 3. (3)
Can be described approximately. T _P is a time constant when the reduction control device is approximated to a first-order lag element. Since G _P = K _P · G _P1 ,
G _P = K _P / (1 + T _P S) (4)
It can be expressed as.

As for the transfer function G _h of the feedback portion normally comprises only dead time element L occurring during thickness measurement,
G _h = e ^-LS (5)
Can be described.

When the distance from the rolling roll to the plate thickness measuring device is X and the rolling speed is V, the dead time L is L = X / V (6)
It can be determined as follows.

  Conventionally, in a sheet thickness control method for a rolling mill that employs a monitor AGC, an integral element has been used as a control operation element in the control device 5. For this reason, when a ramp-like disturbance such as an increase in the thermal expansion amount of the roll or an increase or decrease in the rolling speed occurs, the steady thickness deviation cannot be made zero. It is known that if the second-order integral is used as a control operation element, the steady-state deviation of the plate thickness will approach zero as much as possible. However, in this case, it is difficult to ensure the stability of the control, so it is actually used. Was not.

In the present invention, stable plate thickness control is achieved by substantially using K _C (1 + T _C S) / S ² as the transfer function G _C of the control operation for manipulating the roll reduction position based on the plate thickness deviation. In addition, even when a ramp-like disturbance occurs, it is possible to reduce the steady deviation of the plate thickness. Here, K _C is a proportionality constant, T _C is a time constant, and S is a Laplace operator. When the transfer function G _C consists only of K _C (1 + T _C S) / S ^2, it can be expressed as the following equation (7).
G _C = K _C (1 + T _C S) / S ² (7)

Since S ² appears in the denominator of the transfer function G _C of the control operation in the present invention, which means a second order integral, it is possible to make the steady thickness deviation zero even if a ramp-like disturbance occurs. It is. In addition, (1 + T _C S) appears in the numerator of the transfer function G _C. Hereinafter, this term may be referred to as “primary advance element”. By including a first-order advance element in the transfer function, appropriately setting the time constant T _C of the first-order advance element, and appropriately selecting a proportional constant K _C of the transfer function, the transfer function includes a second-order integral element. Nevertheless, the control system can be kept stable.

In the present invention, the transfer function G _C of the control operation may be substantially K _C (1 + T _C S) / S ² . Therefore, elements other than K _C (1 + T _C S) / S ² may be included in the transfer function G _C as long as the effects of the present invention are not adversely affected.

Next, a preferred method for determining the time constant T _C and the proportional constant K _C for stably maintaining the control system in the present invention will be described. Here, G _{P is} a transfer function to be controlled with the roll reduction position as the operation amount, and the rolled plate thickness as the control amount, and G _h is the transfer function of the feedback portion.

In the feedback control system, when the circuit is opened at one point of the loop, the round-trip frequency transfer function can be expressed as G _C · G _P · G _h (jω). Here, j is an imaginary number and ω is an angular frequency. Hereinafter, unless otherwise specified, the round transfer function indicates a round transfer function in an open circuit.

First, select the angular frequency omega _C the phase delay becomes 30 ° or less of the frequency transfer function of the combined G _P and _{G h (G P · G h} (jω)). In general, the transfer function G _P of control object defines a transfer function G _h feedback part as a fixed functional form, by drawing the Bode diagram as shown in FIG. 3 (a) These transfer functions, G _P It is possible to select an angular frequency ω _{C at} which the phase delay of G _h (jω) is 30 ° or less.

Next, the time constant T _C is selected so that T _C ≧ 3 / ω _C. This means that T _c = α / ω _C (8) using a constant α such that α ≧ 3.
In other words.

Finally, as shown in FIG. 3B, the proportionality constant K _C is determined so that the gain of the cyclic frequency transfer function (G _C · G _P · G _h (jω _C )) at ω = ω _C is approximately 1. . The gain of approximately 1 is preferably in the range of 0.8 to 1.2. More preferably, the gain is in the range of 0.9 to 1.1.

As described above, by determining the proportionality constant K _C and the time constant T _C in the above equation (7), which is a transfer function of the control operation, the plate thickness control of the rolling mill by the monitor AGC of the present invention can be stably performed. Is possible. The reason will be specifically described below.

  FIG. 4 shows a Bode diagram of a general loop frequency transfer function. The point where the gain curve cuts the 0 dB line in the frequency characteristic of the round-trip frequency transfer function is called a gain intersection. A value indicating how much the phase of the circular frequency transfer function has a margin with respect to −180 ° at the angular frequency of the gain intersection is called a phase margin. It is known that the control system is more stable as the phase margin is larger. The phase margin is said to be 30 ° or more.

  The point at which the phase curve cuts the −180 ° line in the frequency characteristic of the round-trip frequency transfer function is called a phase intersection. A value indicating how much the gain of the one-round frequency transfer function is 1 with respect to the angular frequency at the phase intersection is referred to as a gain margin. It is known that the control system is more stable as the gain margin is larger. It is said that the gain margin is desirably -8 dB or less.

  In order for the control system to operate stably, both the phase margin and the gain margin must satisfy the stability condition. This point will be described below.

  First, the phase margin will be described.

In the above equation (7), which is a transfer function of the control operation, the second order integral (1 / S ² ) has a constant phase delay of 180 ° as shown in FIG. Further, the element of the primary advance (1 + T _C S) is as shown in FIG. 3D, and the phase advance angle φ _{C at} the angular frequency ω _C is expressed as φ _C = tan ⁻¹ (ω _C T _C ). The Since T _C = α / ω _C , φ _C = tan ⁻¹ (α), and since α ≧ 3, it can be seen that φ _C ≧ 71 °.

As described above, it can be seen that the phase delay of the transfer function G _C (jω _C ) of the control operation is 180 ° −71 ° = 109 ° or less at the angular frequency ω = ω _C. Further, as described above, the angular frequency ω _C is selected such that the phase delay of G _P · G _h (jω _C ) is 30 ° or less. Therefore, the phase delay of the round-trip frequency transfer function G _C · G _P · G _h (jω _C ) is 109 ° + 30 ° = 139 ° or less.

In the above-described present invention, since the gain of the open-loop frequency transfer function in omega = omega _C is determined proportionality constant K _C so as to be substantially 1, that is, the vicinity of the angular frequency omega = omega _C has a gain crossover . As described above, the phase delay of the circular frequency transfer function at the angular frequency ω _C is determined to be 139 ° or less, that is, the phase margin is 41 ° or more. Therefore, the present invention has a sufficiently good phase margin.

Next, in the present invention, by determining the proportional constant K _C and the time constant T _C in the transfer function G _C = K _C (1 + T _C S) / S ² of the control operation as described above, the one-round frequency transfer function It has been found that the gain margin can always be maintained within a good range. A specific description will be given below.

The transfer function _GP in the roll reduction device can be approximately expressed by the above equation (4). Further, the transfer function G _h of the feedback part can be described by the equation (5) as described above, and the size of the dead time L can be obtained by the equation (6). At this time, the phase ∠G _h phase ∠G _P of the frequency transfer function G _P at angular frequency ω (jω) (jω) and the frequency transfer function G _h (jω) (jω) is that each expressed as follows it can.
∠G _P (jω) = − tan ⁻¹ (ωT _P ) (9)
∠G _h (jω) = − ωL = −180 ωL / π (°) (10)

In the present invention, as described above, the angular frequency ω _{C at} which the phase delay of G _P · G _h (jω) is 30 ° or less is selected. At this time, seek ∠G _P · G _{h (jω)} by adding the ∠G was calculated as described above _P (j [omega]) and ∠G _h (j [omega]), the ∠G _P · G _{h (jω)} is Ω that is −30 ° or more, that is, the phase delay is 30 ° or less is determined, and this ω is set to ω _C.

Although the size of the dead time L can be obtained by the above equation (6), it is generally larger than the value of T _P , so the angular frequency ω _C is mainly influenced by the above equation (10). And is in inverse proportion to L and a relatively small value. As a result, the gain of the transfer function G _P near the angular frequency ω _C can be approximately set to a constant K _P. The gain of G _h = e ^−LS is 1 at all angular frequencies.

Based on the above assumption, the proportionality constant K _C when the gain of the round-frequency transfer function (G _C · G _P · G _h (jω _C )) at ω = ω _C is 1 is set as K _C0 in particular. Then, K _C0 can be determined as follows.
｜ G _C・ G _P・ G _h (jω _C ) |
= | K _C0 · ((1 + jαω _C / ω _C ) / (jω _C ) ² ) · K _P | = 1 (11)
This equation can be solved for K _C0
K _C0 = ω _C ² / (K _P · √ (1 + α ² )) (12)
Is obtained. That is, the proportionality constant K _C when the gain of the round-trip frequency transfer function at ω = ω _C is 1 is represented by K _C0 in the above equation (12).

Next, using the above equations (12) and (5), G _P = K _P , the round-trip frequency transfer function (G _C · G _P · G _h (jω)) is expressed as follows:
(G _C , G _P , G _h (jω))
= [Ω _C ² · (1 + jαω / ω _C ) · K _P ] / [K _P · √ (1 + α ² ) · (jω _C ) ² ] e ^−jωL
= {[Ω _C ² · (1 + jαω / ω _C )] / [√ (1 + α ² ) · (jω _C ) ² ]} · e ^−jωL (13)
It becomes. When the condition of α ≧ 3 is considered in this expression, the gain in the vicinity of ω = ω _{C in the} expression (13) is inversely proportional to ω. Further, since ω = ω _C and the gain is 1 (0 dB), the angular frequency ω at which the gain of the one-cycle frequency transfer function is −8 dB (0.398 times) necessary as a gain margin is
ω = ω _C × (1 / 0.398) ≈2.51 × ω _C (14)
become.

Next, it is confirmed that the gain at ω = 2.51 × ω _C is −8 dB or less and the phase lag is less than 180 ° at the same time, and therefore the gain margin at the phase intersection (phase lag is 180 °) is −8 dB or less. Check. Here, since the angular frequency ω is in a frequency range larger than the above-described ω _C , the transfer function _GP of the roll reduction control is not a constant, but the following first-order lag transfer function of the time constant T _P is used. I will do it.
G _P = K _P / (1 + T _P S) (4)

As a general example, when the rolling speed V is changed from 200 m / min to 2000 m / min using a distance X from the roll stand to the plate thickness detector of 2 m, T _P = 0.07 sec, α = 3 Was examined. Table 1 shows the gain and phase delay angle at the dead time L, ω _C , ω = 2.51 × ω _{C at} each rolling speed.

As shown in Table 1, even when the rolling speed V is significantly changed to 200 to 2000 m / sec, the gain at ω = 2.51 × ω _C is −8 dB or less by determining ω _C for each rolling speed. Thus, it can be seen that the phase lag is less than about 173 ° and there is a margin up to 180 °. This indicates that the gain further decreases at the angular frequency where the phase lag is 180 °, and therefore it is clear that a sufficient gain margin can be secured in the present invention.

As described above, by setting the proportionality constant K _C and the time constant T _C in the transfer function G _C = K _C (1 + T _C S) / S ² of the control operation as in the present invention, Both the gain margin and the phase margin can be in a favorable range, and stability can be ensured in feedback control. That is, by providing a second order integral element in the control operation, it is possible to control the plate thickness without having a steady deviation against a ramp-like disturbance, and a stable plate thickness despite having a second order integral element. Control can be performed.

In the present invention, when determining the time constant T _C , T _C = α / ω _C and α ≧ 3. The reason why α ≧ 3 is that, as a result of calculating the magnitude of the change in the plate thickness with respect to the disturbance having various frequency components, it has been found that the magnitude of α is desirably 3 or more. In particular, the adverse effect of promoting the change in the plate thickness with respect to the disturbance having an angular frequency higher than ω _C tends to appear, but it has become clear that such an adverse effect can be prevented by setting α ≧ 3.

Further, in the present invention, when the proportionality constant K _C is determined so that the gain of the cyclic frequency transfer function (G _C · G _P · G _h (jω _C )) at ω = ω _C is substantially 1, it is preferable as described above. The gain is in the range of 0.8 to 1.2. By setting the gain to 0.8 or more, it is possible to keep the gain margin within the favorable range of the present invention. Further, by setting the gain to 1.2 or less, it is possible to maintain the phase margin within the preferable range of the present invention. More preferably, the gain is in the range of 0.9 to 1.1.

The preferred determination method of the proportionality constant K _C and the time constant T _C has been described above. Conversely, when the proportionality constant K _C , time constants T _C , G _P , and G _h in G _C = K _C (1 + T _C S) / S ² are determined, this control system is within the scope of the present invention. Whether it exists or not can be verified as follows.

First, the angular frequency ω at which the gain of the round-frequency transfer function (G _C · G _P · G _h (jω)) is 1 (0 dB) is obtained and set as ω _C. Next, it is confirmed that the phase delay of G _P · G _h (jω) at ω = ω _C is 30 ° or less. Further, it is confirmed that T _C ≧ 3 / ω _C. If all these conditions are satisfied, this feedback control system is within the preferable range of the present invention, and it is proved that the plate thickness can be controlled stably.

Next, a preferred method of the present invention for determining the proportionality constant K _C so that the gain of the cyclic frequency transfer function is approximately 1 at ω = ω _C will be described.

As described above, in the region of ^ω≈ω _C , the gain of the transfer function G _P can be approximately set to the constant K _P, and the gain of G _h = e ^−LS is 1 at all angular frequencies. the original, when the gain of the open-loop frequency transfer function at _{ω = ω C (G C ·} G P · G h (jω C)) is placed especially K _C0 the constant of proportionality K _C when it is 1, the K _C0 It can be determined as shown in equation (12).
K _C0 = ω _C ² / (K _P · √ (1 + α ² )) (12)
That is, the proportionality constant K _C when the gain of the round-trip frequency transfer function at ω = ω _C is 1 is represented by K _C0 in the above equation (12).

Therefore, by setting the proportionality constant K _C to a value substantially close to K _C0 in the present invention, the gain of the round-trip frequency transfer function at ω = ω _C can be made substantially 1.

That is, in the present invention, preferably, K _C0 is determined using the above equation (12), and then K _C is determined within the range of 0.8 × K _{C0 to} 1.2 × K _C0 . As a result, the gain of the one-cycle frequency transfer function (G _C · G _P · G _h (jω _C )) at ω = ω _C can be automatically set to about 1. By setting K _C to 0.8 × K _C0 or more, it is possible to maintain the gain margin within the favorable range of the present invention. In addition, by setting K _C to 1.2 × K _C0 or less, the phase margin can be maintained within the favorable range of the present invention. The K _C and more preferably in the range of _{0.9 × K C0 ~1.1 × K C0} .

In the present invention, for example, K _{C is changed} to K _C = ω _C ² / (α · K _P ) (15)
It can be determined as follows. At this time, since α ≧ 3, K _C is in the range of 0.8 × K _{C0 to} 1.2 × K _C0 .

In the present invention, it is preferable that the transfer function G _P to be controlled is represented by K _P / (1 + T _P S), and the transfer function G _h of the feedback part is represented by e ^−LS . Here, T _P is the time constant of the rolling control device, e is the base of the natural logarithm, and L is the dead time that occurs when detecting the plate thickness. In this case, specifically described how to select the angular frequency omega _C the phase delay becomes 30 ° or less of the frequency transfer function of G _P and _{G h (G P · G h} (jω)).

When the distance from the rolling roll to the plate thickness measuring device is X and the rolling speed is V, the dead time L can be determined as in the above equation (6). That is, since the dead time L changes when the rolling speed V changes, the angular frequency ω _C also needs to be determined according to the rolling speed V. As the rolling speed V increases, the angular frequency ω _C increases.

Since the frequency transfer function G _P (jω) = K _P / (1 + jωT _P ) has a first-order lag element, the gain and phase at the angular frequency ω can be expressed as follows.
| G _P (jω) | = 20 log ₁₀ (K _P / √ (1+ (ωT _P ) ² )) (dB) (16)
∠G _P (jω) = − tan ⁻¹ (ωT _P ) (9)

Further, since the transfer function G _h (jω) = e ^−jωL is a ^dead time element, the gain is 1 regardless of ω. Therefore,
| G _h (jω) | = 0 dB (17)
∠G _h (jω) = − ωL = −180 ωL / π (°) (10)
It becomes.

Thus seek ∠G _P · G _h (jω) were combined by adding the ∠G _P which is calculated by (j [omega]) and ∠G _h (jω), the ∠G _P · G _h (jω) is -30 ° or more That is, ω at which the phase delay is 30 ° or less is determined, and this ω is defined as ω _C. As described above, since the angular frequency ω _C changes according to the rolling speed V, it is necessary to obtain the angular frequency ω _C for each rolling speed.

As described above, in the present invention, it is necessary to obtain the angular frequency ω _C for each rolling speed. At this time, in the present invention, preferably, the proportionality constant K _C is determined as a value in the vicinity of K _{C0 in the} equation (12) as described above. As a result, even if the rolling speed is changed and the value of the angular frequency ω _C is changed, the gain at ω _C of the round frequency transfer function can always be automatically maintained at about 1. In this way, when ω _C is changed and the phase advance time constant T _C is changed, the gain (proportional constant K _C ) of the control device is also changed so as to change in conjunction therewith. It became possible to maintain and guarantee stability.

  In the above description, only the case where the roll reduction amount is used as the operation amount for the plate thickness control has been described. On the other hand, in the plate thickness control, the rolling speed of the front stand can be used as the operation amount. Hereinafter, the case where the rolling speed of the front stand is used as the operation amount of the plate thickness control will be described.

Even when the plate thickness control is performed by adjusting the rolling speed of the front stand, the present invention can be applied as it is. The only difference is how to determine the proportionality constant K _P.

In the above-described method in which the sheet thickness control is performed by manipulating the roll reduction amount, a proportional constant between the roll reduction position and the rolled sheet thickness is used as K _P. As described above, the value of the constant K _P is the above formula (1) in a rolling apparatus that does not employ a gauge meter AGC, and the positive feedback of the gauge meter AGC in a rolling apparatus that employs a gauge meter AGC. The rate can be defined as the equation (2) with β (≦ 1).

In the method of controlling the plate thickness by operating the rolling speed U of the front stand 2b, the proportionality constant between U and the plate thickness h can be defined as K _P for the rolling speed of the front stand 2b. And, the value of this constant K _P is that the thickness before rolling of the stand 2a (= thickness after rolling of the front stand 2b) is H,
K _P = H / U (18)
It can be determined as follows.

  Except for the above points, the same processing may be performed when the roll reduction amount is used as the operation amount and when the rolling speed of the front stand is used.

The present invention was applied in the cold rolling of an aluminum plate using a two-stand tandem rolling mill. An aluminum strip having an original plate thickness of 0.81 mm, a finished plate thickness of 0.32 mm, and a plate width of 1087 mm is rolled by a 2-stand tandem rolling mill. The allowable value of the plate thickness error is ± 1% (± 3.2 μm PP). The rolling speed varies between 150 and 900 m / min. Constant T _P 0.07 seconds when the pressure control device, the mill stiffness coefficient M is 440ton / mm.

Thickness control uses only the monitor AGC, and a plate thickness detector 4 is provided at a position 2000 mm from the roll stand 2 as the second stand as shown in FIG. The plate thickness was controlled by feeding back the thickness to the control device 5. The rolling roll reduction position was used as the operation amount for controlling the plate thickness. For plasticity factor Q,
Q = P / [2 (H−h)]
Determine as follows. Here, H: plate thickness on the roll stand entrance side, h: roll stand exit side plate thickness, P: rolling load.

In the plate thickness control according to the present invention, the transfer function G _C = K _C (1 + T _C S) / S ² of the control operation is set, T _C = α / ω _C , α = 3, and K _C = ω _C ² / (K _P · √ (1 + α ² )).

First, using a Q obtained as described above, determining the _{K P = M / (M +} Q) as K _P. Further, the dead time L of the plate thickness measurement is determined from the rolling speed V as L = X / V.

Next, a Bode diagram is drawn for the frequency transfer function G _P (jω) = K _P / (1 + jωT _P ) and the frequency transfer function G _h (jω) = e ^−jωL , and ∠G _P · G _h (jω) is ^calculated . The ω G _P · G _h (jω) is −30 ° or more, that is, the phase delay is 30 ° or less is determined, and this ω is set to ω _C. If ω _C is determined in this way, the transfer function of the control operation is determined.

FIG. 5 shows a Bode diagram of a circular frequency transfer function when rolling at a rolling speed of 2000 m / min. At the angular frequency ω _C = 4.03, the gain is 1, that is, the angular frequency ω _C is the gain intersection, and the phase margin at this angular frequency is 41 °, and a stable region is secured. In addition, the phase delay is 180 ° at the angular frequency 12.8, that is, this angular frequency is the phase intersection, and the gain margin at this angular frequency is 10.8 dB, thus ensuring a stable region. From this, it can be seen that stable control is possible by using the control transfer function of the method of the present invention.

  In the plate thickness control of the conventional method, the control element is only the integral element.

Example 1
In rolling immediately after replacing the roll, the steady state error was compared between the case where the sheet thickness was controlled by the conventional method and the case where it was controlled by the present invention. Since it is immediately after the roll exchange, the thermal expansion of the roll proceeds during rolling, and a lamp-like disturbance is added.

  FIG. 6A shows a plate thickness error in the case of control by the conventional method. A steady error of about −0.2 μm is generated, and the steady deviation with respect to the lamp-like disturbance due to the thermal expansion of the roll. It can be seen that has occurred. On the other hand, FIG. 6B shows the case where the control according to the present invention is used, and the occurrence of steady-state error is extremely small, −0.02 μm. That is, it is apparent that the application of the plate thickness control method of the present invention can suppress the occurrence of a steady deviation against a lamp-like disturbance due to the thermal expansion of the roll.

(Example 2)
Compare the situation of plate thickness error due to mill deceleration. In general, when the rolling speed is reduced, the plastic coefficient of the strip increases, and the thickness increases accordingly. That is, the reduction of the rolling speed becomes a ramp-like disturbance factor in the plate thickness control.

  The plate thickness error when the rolling speed was linearly reduced from 750 mpm and stopped was compared between the case where the conventional method was used for the plate thickness control and the case where the method of the present invention was used. FIG. 7A shows a plate thickness error in the case where deceleration is performed while controlling the plate thickness by the conventional method. FIG. 7 (b) shows the plate thickness error when the same deceleration as described above is performed in the system according to the present invention.

  As can be seen by comparing FIG. 7 (a) and FIG. 7 (b), when the plate thickness is controlled by the present invention, the occurrence of a plate thickness error is greatly suppressed. In the above rolling, the length of the strip in which an error exceeding the allowable value occurred during deceleration was about 54 m in the conventional method, but 18 m in the method according to the present invention. The strip length with poor plate thickness accuracy at that time could be reduced to about 1/3.

It is the schematic which shows the rolling mill using monitor AGC, (a) shows the case where the rolling reduction position of a front stand is used as an operation amount, when the roll reduction position is used as an operation amount. It is a figure which shows the control block diagram of monitor AGC. It is a figure which shows the Bode diagram used in order to define the suitable control conditions of this invention. It is a figure which shows the Bode diagram of a general cyclic frequency transfer function. It is a figure which shows an example of the Bode diagram of a round frequency transfer function using this invention. It is a figure which shows the time change of the plate | board thickness actual value in Example 1, (a) is a case where a conventional method is used, (b) is a case where this invention method is used. It is a figure which shows the time change of the plate | board thickness actual value in Example 2, (a) is a case where the conventional method is used, (b) is a case where this invention method is used.

Explanation of symbols

DESCRIPTION OF SYMBOLS 1 Rolled sheet 2 Roll stand 3 Roll reduction control apparatus 4 Sheet thickness detector 5 Control apparatus 6 Drive motor 7 Speed control apparatus 8 Winding machine

Claims (5)

In the sheet thickness control method of a rolling mill that measures the sheet thickness after rolling and feeds back the measured thickness value to adjust the roll roll reduction position of the rolling mill. A thickness control method for a rolling mill, wherein the function G _C substantially consists of K _C (1 + T _C S) / S ² .
Here, K _C is a proportionality constant, T _C is a time constant, and S is a Laplace operator. The transfer function of the controlled object with the roll reduction position as the manipulated variable and the rolled sheet thickness as the controlled variable is G _P , and the transfer function of the feedback part is G _h .
Phase lag of the frequency transfer function G _P and _{G h (G P · G h} (jω)) selects the angular frequency omega _C to be 30 ° or less,
T _C = α / ω _C using a constant α such that α ≧ 3,
2. The rolling mill according to claim 1, wherein the proportionality constant K _C is determined so that the gain of the round-trip frequency transfer function (G _C · G _P · G _h (jω)) at ω = ω _C is approximately unity. Thickness control method.
Here, j is an imaginary number and ω is an angular frequency. The proportional constant between the roll reduction position and the rolled sheet thickness is K _P ,
K _C0 = ω _C ² / (K _P · √ (1 + α ² ))
The thickness control method for a rolling mill according to claim 2, wherein K _C0 is determined and K _C is set in a range of 0.8 × K _{C0 to} 1.2 × K _C0 . The sheet thickness control method for a rolling mill according to claim 3, wherein the transfer function G _{P to} be controlled is represented by K _P / (1 + T _P S), and the transfer function G _h of the feedback portion is represented by e ^-LS. .
Here, T _P is the time constant of the rolling control device, e is the base of the natural logarithm, and L is the dead time that occurs when detecting the plate thickness.   The thickness control method for a rolling mill according to any one of claims 1 to 4, wherein a control operation amount is set to a rolling speed of the front stand instead of the roll reduction position.

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