Meandering correction device and meandering correction method for metal strip

Abstract

Provided are a meandering correction apparatus and a meandering correction method that can control meandering of a metal strip with high responsiveness even when the distance between a steering roll and a control target position is substantial, resulting in prolonged transfer dead time. Specifically, the meandering correction apparatus for a metal strip includes a first meandering amount detection unit, a steering roll, a tilting device for the steering roll, a second meandering amount detection unit, a first control unit that corrects the shift amount at the meandering control target position based on the first meandering amount by taking into consideration the conveyance time taken from the position of the steering roll to the meandering control target position, and a second control unit that controls the position of the metal strip in the width direction with the steering roll based on the second meandering amount and the corrected shift amount.

Description

Technical Field

[0001] The present invention relates to a meandering correction apparatus and a meandering correction method for suppressing the meandering of a metal strip with the use of a steering roll in an annealing or working facility for metal strips.Background Art

[0002] In the production process of a strip-shaped metal sheet (also referred to as a "metal strip"), the metal strip is conveyed with the use of a plurality of rolls to efficiently perform plastic working, heat treatment, and surface conversion treatment, for example, on the metal sheet. In this case, however, the metal strip meanders due to the asymmetry (defective shape and residual stress) of the metal strip and the asymmetry (alignment of the rolls) of the facility.

[0003] In order to suppress the meandering of the metal strip, conventional techniques have included centering each roll by providing a crown (profile) thereto or controlling the meandering with a steering roll based on the meandering amount measured with a meandering meter.

[0004] Patent Literature 1 discloses a method capable of controlling the meandering amount at a target position with a single steering roll. This method involves predicting the meandering amount at the position of a reference roll with a plurality of meandering detection units, and then correcting the measured amount of a master meandering amount detection unit.

[0005] Patent Literature 2 discloses a method capable of controlling a steering roll on the upstream side by predicting the meandering amount on the downstream side of the steering roll using a model formula, while considering the meandering on the downstream side in a meandering correction zone.Citation ListPatent Literature

[0006] Patent Literature 1: JP-2020-164284A Patent Literature 2: JP-H05-208763A Summary of InventionTechnical Problem

[0007] However, if the conventional technologies are applied to suppress the meandering of a metal strip, the following problems arise.

[0008] Regarding Patent Literature 1, the conveyance time of a metal strip between the master (meandering amount detection unit at the position of the reference roll for the meandering amount) and the slave (meandering amount detection unit on the downstream side of the steering roll along the threading line) is not taken into consideration, and if a metal strip shakes in a vibrating manner and if there are about two detection units, there is a possibility that the meandering amount at the position of the reference roll may diverge.

[0009] Regarding Patent Literature 2, there is no mechanism of making correction based on the actual meandering amount on the downstream side of the steering roll, and thus, it is not necessarily the case that meandering on the downstream side is corrected.

[0010] Further, as illustrated in Fig. 2, conventional technology exhibits "a dead time", during which the meandering amount at a detector at a control target position is corrected. If the control time interval is sufficiently shorter than this dead time, the controller will perform repeated operations before the meandering amount is corrected, resulting in more operations than are necessary. This may induce vibration or divergence, and may lead to fracture if a metal strip comes into contact with a peripheral facility.

[0011] The present invention has been developed in view of the foregoing problems of the conventional technologies, and an object of the present invention is to provide a meandering correction apparatus and a meandering correction method that can control meandering with high responsiveness even under restricted conditions where a steering roll cannot be disposed near a meandering amount control target position on a metal strip, and where the distance between the steering roll and the control target (meandering amount control target position on a metal strip) is substantial and the conveyance time of the metal strip over that distance is prolonged.Solution to Problem

[0012] To solve the foregoing problems, the inventor has conducted feedback by considering the dead time due to the meandering amount at a control target position as illustrated in Fig. 3. Then, the inventor arrived at the present invention by finding that it is possible to stably correct meandering without the occurrence of vibration or divergence by calculating an appropriate operation amount even when the dead time exceeds the control time interval.

[0013] The meandering correction apparatus according to the present invention that advantageously solves the foregoing problems has the following features. [1] A meandering correction apparatus for correcting meandering of a metal strip conveyed along a threading line, including a first meandering amount detection unit that is disposed at a meandering control target position of the metal strip and detects a first meandering amount of the metal strip; a steering roll that is disposed to correct the first meandering amount; a tilting device for the steering roll; a second meandering amount detection unit that is disposed on a downstream side of the steering roll along the threading line and on an upstream side of the meandering control target position along the threading line, and detects a second meandering amount of the metal strip; a first control unit that corrects a shift amount at the meandering control target position based on the first meandering amount by taking into consideration a conveyance time taken from a position of the steering roll to the meandering control target position; and a second control unit that controls a position of the metal strip in a width direction with the steering roll based on the second meandering amount and the corrected shift amount. The meandering correction method according to the present invention that advantageously solves the foregoing problems has the following features. [2] A method for correcting meandering of a metal strip conveyed along a threading line, including a step of detecting a first meandering amount at a meandering control target position of the metal strip; a step of tilting a steering roll to control a shift amount at the meandering control target position; a step of detecting a second meandering amount on a downstream side of the steering roll along the threading line and on an upstream side of the meandering control target position along the threading line; a step of correcting a shift amount at the meandering control target position based on the first meandering amount by taking into consideration a conveyance time taken from a position of the steering roll to the meandering control target position; and a step of controlling a position of the metal strip in a width direction with the steering roll based on the second meandering amount and the corrected shift amount. Advantageous Effects of Invention

[0014] According to the present invention, it is possible to stably control meandering with a single steering roll by taking the conveyance time into consideration when the steering roll cannot be disposed around a reference roll for the meandering amount ( meandering control target position of the metal strip) due to facility constraints, and also when the distance between the reference roll for the meandering amount and the available steering roll is long.Brief Description of Drawings

[0015] [Fig. 1] is a schematic view illustrating the configuration of a meandering correction apparatus for a metal strip according to an embodiment of the present invention. [Fig. 2] is an explanatory view of the correction of the meandering of a metal strip based on the meandering control of the conventional technologies. [Fig. 3] is an explanatory view of the correction of the meandering of a metal strip based on the meandering control of the present invention. [Fig. 4] (a) is a graph of variation ΔS 2 in the shift amount input (S 2 ) with respect to the passage of time at the point of a second detector, and Fig. 4(b) is a graph of variation ΔS 1 in the shift amount input (S 1 ) with respect to the passage of time at the point of a first detector. [Fig. 5] is an explanatory view of an example of a meandering prediction model for a meandering correction method of the present invention. [Fig. 6] illustrates a calculation flow of an expression (6,4) for predicting the position of a metal strip. [Fig. 7] is a graph illustrating the results of evaluating (comparing) the maximum meandering amount between the track record data and each of Case A (Comparative Example): proportional control (without compensation for the conveyance time), Case B (Invention Example): a combination of proportional control (with compensation for the conveyance time) and Smith compensation, and Case C (Invention Example): a combination of sliding mode control (with compensation for the conveyance time) and Smith compensation, when the conveyance time after the meandering control is L=60 seconds. Description of Embodiments

[0016] Hereinafter, a meandering correction apparatus and a meandering correction method for a metal strip according to the present embodiment will be described.

[0017] In the present invention, an apparatus equipped with two or more meandering detectors performs feedback control that takes conveyance time into account, based on a first meandering amount measured by a detector (hereinafter referred to as a "first detector") disposed at a meandering control target position (on the downstream side along the threading line). The resulting feedback is then reflected in the shift amount at the position of another detector (hereinafter referred to as a "second detector") used for the main control. Next, the target value at the position of the metal strip is shifted in advance at the second detector, such that the metal strip reaches the intended position at the first detector at the control target position. This enables meandering to be controlled with high responsiveness, even under restricted conditions where the steering roll cannot be disposed near the control target, and even when the distance between the steering roll and the control target is substantial and the conveyance time over that distance is prolonged. This can reduce troubles, such as fractures of the metal strip.<Meandering correction apparatus>

[0018] The meandering correction apparatus for a metal strip according to the present embodiment includes: a first meandering amount detection unit that is disposed at a meandering control target position of the metal strip and detects a first meandering amount of the metal strip; a steering roll disposed to correct the first meandering amount; a tilting device for the steering roll; and a second meandering amount detection unit that is disposed on the downstream side of the steering roll along the threading line and on the upstream side of the meandering control target position along the threading line and detects a second meandering amount of the metal strip. Furthermore, the meandering correction apparatus includes a first control unit that corrects the shift amount at the meandering control target position based on the first meandering amount, taking into consideration the conveyance time taken from the position of the steering roll to the meandering control target position, and a second control unit that controls the position of the metal strip in the width direction with the steering roll based on the second meandering amount and the corrected shift amount.[First meandering amount detection unit]

[0019] As illustrated in Fig. 1, a first meandering amount detection unit M1 includes a first meandering amount detector 1 at a target position of a metal strip for controlling meandering (meandering control target position), that is, at the position of a reference roll 8 along the threading line. The control target position in the first meandering amount detection unit M1 is the reference position for controlling the meandering amount of a metal strip. The first detector 1 may be a detector selected from the measurement environment or facility.[Steering roll and tilting device]

[0020] As illustrated in Fig. 1, a steering roll 3 and a tilting device 4 including an actuator 41 and a cylinder 42 therefor are disposed on the upstream side (which means the upstream side on the threading line along a line travel direction 11) of the position (control target position) of the first meandering amount detector 1 in the first meandering amount detection unit M1 along the threading line, in order to correct the meandering of a metal strip at the position of a second detector 2. The distance between the steering roll 3 and the first meandering amount detector 1 is not limited to a particular value. In addition, a threading facility 9 may be provided between the steering roll 3 and the first meandering amount detector 1.[Second meandering amount detection unit]

[0021] As illustrated in Fig. 1, the second meandering amount detector 2 in a second meandering amount detection unit M2 is disposed at the upstream position thereof, in order to measure the meandering amount on the upstream side of the position (meandering control target position) of the first meandering amount detector 1 in the first meandering amount detection unit M1 along the threading line. The second meandering amount detector 2 is intended to control the meandering amount by the steering roll and is disposed on the downstream side of the steering roll 3 along the threading line and on the upstream side of the position (meandering control target position) of the first meandering amount detector 1 along the threading line.[Control unit]

[0022] As illustrated in Fig. 1, the control unit includes a first control unit and a second control unit.

[0023] A first control unit 6 measures the position of a metal strip by the first meandering amount detector 1, which is disposed at the target position for controlling meandering (meandering control target position). The unit 6 then calculates the meandering amount based on the relationship between the center line 12 and the shift amount of the metal strip at the meandering control target position, and then transmits the calculated meandering amount to an arithmetic unit. Smith compensation is added to the arithmetic operation process because the conveyance time is sufficiently longer than the control interval.

[0024] Further, to compensate for the low disturbance resistance, which is one of the drawbacks of the Smith compensation, the operation amount is determined using the sliding mode control, which exhibits excellent robustness, thereby achieving stable meandering control.

[0025] However, as long as the performance required for the meandering control is fully achieved, the intended effect can be obtained with the common PID control.

[0026] Correction is performed by adding variation in the shift amount of the metal strip calculated with the foregoing method to the currently set shift amount of the metal strip, so that an updated shift amount at the position (meandering control target position) of the first meandering amount detector 1 is obtained.

[0027] The second control unit 7 controls the position of the second meandering amount detector 2 so as to reduce the meandering amount at the meandering control target position (position of the first meandering amount detector 1) based on the meandering amount at the position of the second meandering amount detector and the updated shift amount (corrected shift amount) transmitted from the first control unit 6. Based on this controlled value, the second control unit 7 issues an instruction related to the operation state of the steering roll so as to attain the target position of the second meandering amount detector 2 (set threading position). In this manner, the threading position at the position of the second meandering amount detector 2 is changed.<Meandering correction method>

[0028] The meandering correction method for a metal strip according to the present embodiment is a method of correcting the meandering of a metal strip conveyed along the threading line, and includes: a step of detecting a first meandering amount at a meandering control target position of the metal strip; a step of tilting the steering roll to control the shift amount at the meandering control target position; a step of detecting a second meandering amount on the downstream side of the steering roll along the threading line and on the upstream side of the meandering control target position along the threading line; a step of correcting the shift amount at the meandering control target position based on the first meandering amount by taking into consideration the conveyance time taken from the position of the steering roll to the meandering control target position; and a step of controlling the position of the metal strip in the width direction with the steering roll based on the second meandering amount and the corrected shift amount.[First meandering amount detection step]

[0029] The first meandering amount detector 1 in the first meandering amount detection unit M1 measures the first meandering amount at the target position of the metal strip for controlling meandering (meandering control target position).[Second meandering amount detection step]

[0030] The second meandering amount detector 2 in the second meandering amount detection unit M2 measures the second meandering amount at a position on the upstream side of the target position of the metal strip for controlling meandering (meandering control target position) along the threading line and on the downstream side of the steering roll along the threading line. The measurement performed with the second meandering amount detector 2 is intended to control the meandering with the steering roll.[Control step]

[0031] Fig. 1 illustrates the details of a control step for correcting meandering.

[0032] The shift amount at the meandering control target position is corrected based on the first meandering amount measured in the first meandering amount detection step by taking the conveyance time into consideration to allow the metal strip to pass through the set threading position in the second meandering amount detection unit M2. Next, the position of the metal strip in the width direction is controlled by the steering roll based on the meandering amount at the set threading position and the corrected shift amount.

[0033] The preparation for introducing the control and a calculation flow will be described hereinafter.

[0034] Fig. 4 illustrates changes in the position of a metal strip at the position of the first detector when the set value of the shift amount at the second detector is changed in a stepwise manner. In response to a change in the shift amount, the position of the metal strip at the position of the first detector starts to change in a delayed manner (t 1 ) from the time when the set value was changed by an amount corresponding to the conveyance time L (=D / V) determined by the distance D from the steering roll to the first detector and the feed speed V of the metal strip. The response is further delayed due to the operation of the cylinder and friction between the metal strip and rolls disposed at positions up to the first detector, for example.

[0035] A model for predicting the position of the metal strip is created, taking the foregoing into consideration.

[0036] First, delays in response that occur due to the operation of the cylinder and friction with the rolls are all considered as a primary delay.

[0037] The transfer function for the first detector herein, inclusive of the conveyance time e -Ls< , is represented by Expression (1) below. [Math. 1] G s = e − L s K ∏ n 1 1 + T i s

[0038] Herein, n represents the number of rolls, including the steering roll, over which the metal strip travels until it reaches the first detector, and Ti represents the time constant of a delay in a change that occurs due to the operation of the cylinder or friction with the rolls. In addition, K represents the ratio of the actual variation ΔS 1 in the position of the metal strip at the position of the first detector to the variation ΔS 2 in the set value of the shift amount, and can be represented by Expression (2). [Math. 2] K = ΔS 1 Δ S 2

[0039] If there are two or more rolls, multi-order delays that are tertiary or higher-order delays will occur. However, such delays are approximated to a secondary delay in the usual control design. Therefore, Expression (1) is approximated to Expression (3) below. [Math. 3] G s ≈ K 1 + T c + T R s + T c T R s 2 e − Ls

[0040] In this context, T C represents the time constant of a delay that occurs due to the cylinder, while T R represents the time constant of a delay in response that occurs due to friction with the rolls. T C is determined directly from the operation of the cylinder, or can be, if the steering roll and the second detector are located sufficiently close to each other, estimated from a change in the position of the metal strip at the position of the second detector when the shift amount was input in a stepwise manner. As T R , variation at the first detector when the shift amount was input in a stepwise manner is compared with a value obtained by substituting the determined T C into the transfer function of Expression (3) through simulation, for example, and then, a value closer to the actual behavior is selected. From the thus determined transfer function, the meandering amount of the metal strip in the future is predicted.

[0041] A value obtained by excluding the conveyance time element e -Ls< from the determined transfer function of Expression (3) is subjected to inverse Laplace transform to determine an equation of state. Expression (4) below represents the equation of state. Expression (4) is used when the sliding mode control is used. x = A x + B u 4 x = x x ˙ 4 1 A = 0 1 − 1 T c T R − T c + T R T c T R 4 2 B = 0 K T c T R 4 3

[0042] Herein, x and x (where symbol x represents x with a dot above it) respectively represent the meandering amount and the meandering speed measured by the first detector 1, and u represents the amount of change in the shift amount.

[0043] As the Smith compensation control includes using the predicted value of the position of the metal strip after the conveyance time L has elapsed, a formula for predicting the position of the metal strip is considered. As illustrated in Fig. 5, it takes the conveyance time L until the position of the metal strip at the position of the first detector 1 changes in response to a change in the shift amount. Symbol u (i-n) in Fig. 5 represents the amount of change in the shift amount in the past, and a greater value of n indicates the earlier time point. Therefore, the amount of change in the position of the metal strip until L seconds have elapsed is proportional to the total amount of change in the shift amount for the past L seconds. In addition, the position of the metal strip will not immediately change in response to the total amount of change in the shift amount, and a delay in response occurs. Thus, Expression (5) below is used. [Math. 5] X = x e A L + ∫ t − L t e A t − τ B u τ dτ

[0044] Typically, the relationship between the operation amount (which is the amount of change in the shift amount in the present embodiment) and the control amount (which is the meandering amount in the present embodiment) can be represented by Expression (5), where t represents the current time, while the predicted value of the position of the metal strip (including the corrected speed) can be represented by Expression (6) below, using the current measured value and a past track record of the operation amount. Herein, X i and X i (where symbol X represents X with a dot above it) respectively represent the meandering amount and the meandering speed measured with the first detector 1 at the current time. At this time, the conveyance time L is set to the integral multiple of the control interval Δt(L=NΔt). X i = A * x i + B * 6 X i = x i x ˙ i 6 1 x i = x i x ˙ i 6 2 A * = − ω 2 ω 1 − ω 2 e − ω 1 L + ω 1 ω 1 − ω 2 e − ω 2 L − 1 ω 1 − ω 2 e − ω 1 L + 1 ω 1 − ω 2 e − ω 2 L ω 1 ω 2 ω 1 − ω 2 e − ω 1 L − ω 1 ω 2 ω 1 − ω 2 e − ω 2 L ω 1 ω 1 − ω 2 e − ω 1 L − ω 2 ω 1 − ω 2 e − ω 2 L 6 3 B * = ∑ j = i − N j = i − 1 − Kω 1 ω 2 ω 1 − ω 2 e − ω 1 i − j Δ t + Kω 1 ω 2 ω 1 − ω 2 e − ω 2 i − j Δ t u j ∑ j = i − N j = i − 1 Kω 1 2 ω 2 ω 1 − ω 2 e − ω 1 i − j Δ t − Kω 1 ω 2 2 ω 1 − ω 2 e − ω 2 i − j Δ t u j 6 4

[0045] In the present embodiment, ω 1 =1 / T C and ω 2 =1 / T R .

[0046] For the second term, four arithmetic operations alone can be used instead of the numerical solution of the following differential equation. Fig. 6 illustrates an example of the calculation flow. Finally, the difference between the current track record and the predicted value of L seconds earlier in the Smith compensation is added as feedback to Expression (6), and the result is input as Expression (7) to the controller. [Math. 7] X i * = X i + x i − X i − N

[0047] When the sliding mode control (SMC) is used, the amount of change in the shift amount is represented by Expression (8), using Expression (4). u i = − SA X i * SB − G σ σ + δ 8 S = S 1 S 2 8 1 σ = S X i * 8 2

[0048] Symbol S in Expression (8) represents a parameter that determines a hyperplane in the sliding mode control, symbol δ represents a parameter for preventing chattering, and symbol G represents the set value of gain. Finally, the output u(i) (amount of change in the shift amount) from the controller is added to the current set value of the shift amount so that the shift amount is updated.Example

[0049] Hereinafter, the advantageous effects of the present embodiment will be specifically described based on an Example, but the present invention is not limited thereto.

[0050] Fig. 7 illustrates the results of simulations performed with the track record data on the maximum meandering amount when the conveyance time at the meandering control target position is L=60 seconds. Case A represents proportional control performed without compensation for the conveyance time and corresponds to a comparative example as a conventional technology. Cases B and C correspond to examples of the invention. Specifically, proportional control was used for Case B, and sliding mode control (SMC) was used for Case C. Regarding each of Cases B and C, the maximum meandering amount was predicted to be improved by a maximum of 12% as compared to Case A where compensation for the conveyance time was not performed.

[0051] The correction of meandering was actually performed for each of Cases A, B, and C, using a threading line including the facility of Fig. 1. As in the foregoing simulation, the maximum meandering amount was improved by up to 12% when using the meandering control method of the present invention, which considers the conveyance time, compared to a meandering control method that does not consider the conveyance time.

[0052] According to the foregoing Example, it is possible to stably control meandering with a steering roll when the steering roll cannot be disposed around a reference roll for the meandering amount due to facility constraints, and also when the distance between the reference roll for the meandering amount and the steering roll is long.Reference Signs List

[0053] M1first meandering amount detection unit M2second meandering amount detection unit 1first meandering amount detector 2second meandering amount detector 3steering roll 4tilting device 41actuator 42cylinder 6first control unit 7second control unit 8reference roll 9facility 11line travel direction 12center line

Claims

1. A meandering correction apparatus for correcting meandering of a metal strip conveyed along a threading line, characterized in that the meandering correction apparatus comprises: a first meandering amount detection unit that is disposed at a meandering control target position of the metal strip and detects a first meandering amount of the metal strip; a steering roll disposed to correct the first meandering amount; a tilting device for the steering roll; a second meandering amount detection unit that is disposed on a downstream side of the steering roll along the threading line and on an upstream side of the meandering control target position along the threading line and detects a second meandering amount of the metal strip; a first control unit that corrects a shift amount at the meandering control target position based on the first meandering amount by taking into consideration a conveyance time taken from a position of the steering roll to the meandering control target position; and a second control unit that controls a position of the metal strip in a width direction with the steering roll based on the second meandering amount and the corrected shift amount.

2. A method for correcting meandering of a metal strip conveyed along a threading line, characterized in that the method comprises: a step of detecting a first meandering amount at a meandering control target position of the metal strip; a step of tilting a steering roll to control a shift amount at the meandering control target position; a step of detecting a second meandering amount on a downstream side of the steering roll along the threading line and on an upstream side of the meandering control target position along the threading line; a step of correcting a shift amount at the meandering control target position based on the first meandering amount by taking into consideration a conveyance time taken from a position of the steering roll to the meandering control target position; and a step of controlling a position of the metal strip in a width direction with the steering roll based on the second meandering amount and the corrected shift amount.

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