WO2018158828A1 - シート材生産ラインの数学モデル算出装置および制御装置 - Google Patents
シート材生産ラインの数学モデル算出装置および制御装置 Download PDFInfo
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- WO2018158828A1 WO2018158828A1 PCT/JP2017/007823 JP2017007823W WO2018158828A1 WO 2018158828 A1 WO2018158828 A1 WO 2018158828A1 JP 2017007823 W JP2017007823 W JP 2017007823W WO 2018158828 A1 WO2018158828 A1 WO 2018158828A1
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- mathematical model
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- roll
- sheet material
- production line
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B65—CONVEYING; PACKING; STORING; HANDLING THIN OR FILAMENTARY MATERIAL
- B65H—HANDLING THIN OR FILAMENTARY MATERIAL, e.g. SHEETS, WEBS, CABLES
- B65H23/00—Registering, tensioning, smoothing or guiding webs
- B65H23/04—Registering, tensioning, smoothing or guiding webs longitudinally
- B65H23/18—Registering, tensioning, smoothing or guiding webs longitudinally by controlling or regulating the web-advancing mechanism, e.g. mechanism acting on the running web
- B65H23/182—Registering, tensioning, smoothing or guiding webs longitudinally by controlling or regulating the web-advancing mechanism, e.g. mechanism acting on the running web in unwinding mechanisms or in connection with unwinding operations
- B65H23/185—Registering, tensioning, smoothing or guiding webs longitudinally by controlling or regulating the web-advancing mechanism, e.g. mechanism acting on the running web in unwinding mechanisms or in connection with unwinding operations motor-controlled
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B65—CONVEYING; PACKING; STORING; HANDLING THIN OR FILAMENTARY MATERIAL
- B65H—HANDLING THIN OR FILAMENTARY MATERIAL, e.g. SHEETS, WEBS, CABLES
- B65H23/00—Registering, tensioning, smoothing or guiding webs
- B65H23/04—Registering, tensioning, smoothing or guiding webs longitudinally
- B65H23/18—Registering, tensioning, smoothing or guiding webs longitudinally by controlling or regulating the web-advancing mechanism, e.g. mechanism acting on the running web
- B65H23/195—Registering, tensioning, smoothing or guiding webs longitudinally by controlling or regulating the web-advancing mechanism, e.g. mechanism acting on the running web in winding mechanisms or in connection with winding operations
- B65H23/198—Registering, tensioning, smoothing or guiding webs longitudinally by controlling or regulating the web-advancing mechanism, e.g. mechanism acting on the running web in winding mechanisms or in connection with winding operations motor-controlled (Controlling electrical drive motors therefor)
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B65—CONVEYING; PACKING; STORING; HANDLING THIN OR FILAMENTARY MATERIAL
- B65H—HANDLING THIN OR FILAMENTARY MATERIAL, e.g. SHEETS, WEBS, CABLES
- B65H2557/00—Means for control not provided for in groups B65H2551/00 - B65H2555/00
- B65H2557/20—Calculating means; Controlling methods
- B65H2557/24—Calculating methods; Mathematic models
- B65H2557/242—Calculating methods; Mathematic models involving a particular data profile or curve
Definitions
- the mathematical model calculation device for a sheet material production line is arranged between a plurality of roll devices on the basis of a history of actual measurement values of the sheet material production line and directed from one of the plurality of roll devices to the other.
- the torque of the second motor device that drives the other of the plurality of roll devices and the plurality of roll devices
- a mathematical model calculation unit is provided that calculates a mathematical model using a deviation from the torque of the first motor device that drives one as an input and using a measurement value of the tensiometer as an output.
- the mathematical model calculation device for a sheet material production line is arranged between a plurality of roll devices on the basis of a history of actual measurement values of the sheet material production line and directed from one of the plurality of roll devices to the other.
- the plurality of roll devices at a rotational angular velocity of a second motor device that drives the other of the plurality of roll devices with respect to a sheet material production line controlled based on a measurement value of a tensiometer that measures the tension of the traveling sheet material
- the tensiometer is inputted with a deviation between a value obtained by multiplying the other radius of the first roll and the rotation angular velocity of the first motor device that drives one of the plurality of roll devices by one radius of the plurality of roll devices.
- a mathematical model calculation unit that calculates a mathematical model using the measured value of as an output.
- the mathematical model calculation device receives the torque of the first motor device and the torque of the second motor device as inputs while the sheet material production line is in operation.
- the control part which acquires the tension
- the mathematical model is calculated based on the history of actual measurement values of the sheet material production line. For this reason, it is possible to calculate a highly accurate mathematical model for controlling the tension of the sheet material.
- FIG. 1 is a configuration diagram of a winder slit facility to which a mathematical model calculation apparatus according to Embodiment 1 of the present invention is applied.
- the sheet material production line in Fig. 1 is a winder slit facility.
- the unwinder 1 is provided upstream of the winder slit facility as one of the roll devices.
- the winder 2 is provided on the downstream side of the winder slit facility as the other of the roll devices.
- the winder 2 includes a front drum 3, a rear drum 4, and a rider roll 5.
- the slitter 6 is provided between the unwinder 1 and the winder 2.
- the intermediate roll 7 is provided between the unwinder 1 and the slitter 6.
- the control device 21 includes a mathematical model calculation device 22.
- the mathematical model calculation device 22 includes a mathematical model calculation unit 23.
- the mathematical model calculation unit 23 is provided so that a mathematical model of the winder slit facility can be calculated based on a history of actual measurement values of the winder slit facility.
- the control device 21 includes a control unit 24.
- the control unit 24 is provided so as to control the operation of the winder slit facility based on the mathematical model calculated by the mathematical model calculation unit 23.
- the paper material 25 is disposed between the unwinder 1 and the winder 2.
- the paper material 25 advances from the unwinder 1 toward the winder 2.
- the paper material 25 is wound around the unwinder 1 in advance as a sheet material.
- the winding diameter of the paper material 25 is large.
- the paper material 25 is heavy.
- the paper material 25 is cut into a preset width by the slitter 6 via the intermediate roll 7.
- the paper material 25 is wound around the winder 2.
- the paper material 25 is wound up to a preset outer diameter. The winding diameter of the paper material 25 at this time is smaller than the winding diameter of the paper material 25 in the unwinder 1.
- FIG. 2 is a diagram for explaining the control of the winder slit facility to which the mathematical model calculation apparatus according to Embodiment 1 of the present invention is applied.
- the input unit of the control device 21 includes an output unit of the tension meter 20, an output unit of the front drum drive unit 15, an output unit of the rear drum drive unit 16, and an output of the rider roll drive unit 17. Connected to the part.
- the output unit of the control device 21 includes an input unit of the unwinder drive unit 14, an input unit of the front drum drive unit 15, an input unit of the rear drum drive unit 16, an input unit of the rider roll drive unit 17, and a slitter unit.
- the input unit of the drive unit 18 and the input unit of the intermediate roll drive unit 19 are connected.
- speed control is performed. Specifically, the control unit 24 outputs the rotational angular velocity reference value ⁇ fd ref (rad / s) to the front drum drive device 15.
- the front drum drive device 15 drives the front drum motor 9 based on the rotational angular velocity reference value ⁇ fd ref .
- the front drum motor 9 drives the front drum 3.
- speed control is performed. Specifically, the control unit 24 outputs the rotational angular velocity reference value ⁇ rr ref (rad / s) to the rider roll drive device 17.
- the rider roll drive device 17 drives the rider roll motor 11 based on the rotational angular velocity reference value ⁇ rr ref .
- the rider roll motor 11 drives the rider roll 5.
- speed control is performed. Specifically, the control unit 24 outputs the rotation angular velocity reference value ⁇ sl ref (rad / s) to the slitter drive device 18.
- the slitter drive device 18 drives the slitter motor 12 based on the rotational angular velocity reference value ⁇ sl ref .
- the slitter motor 12 drives the slitter 6.
- speed control is performed. Specifically, the control unit 24 outputs the rotation angular velocity reference value ⁇ int ref (rad / s) to the intermediate roll drive device 19.
- the intermediate roll drive device 19 drives the intermediate roll motor 13 based on the rotation angular velocity reference value ⁇ int ref .
- the intermediate roll motor 13 drives the intermediate roll 7.
- the control unit 24 receives an input of the torque reference value ⁇ fd ref (N ⁇ m) from the front drum drive device 15.
- the control unit 24 receives an input of the torque reference value ⁇ rd ref (N ⁇ m) from the rear drum drive device 16.
- the control unit 24 receives an input of the torque reference value ⁇ rr ref (N ⁇ m) from the rider roll drive device 17.
- the control unit 24 receives an input of a tension response value T res (MPa) that is a measurement value of the tension meter 20.
- tension control is performed. Specifically, the control unit 24 applies the torque reference to the unwinding drive device 14 based on the torque reference value ⁇ fd ref , the torque reference value ⁇ rd ref , the torque reference value ⁇ rr ref, and the tension response value T res.
- the value ⁇ uw ref (N ⁇ m) is output.
- the unwinder drive device 14 drives the unwinder motor 8 based on the torque reference value ⁇ uw ref .
- the unwinder motor 8 drives the unwinder 1.
- the paper material 25 receives a certain tension when being wound up by the winder 2.
- the tension applied to the paper material 25 is constant, wrinkles of the paper material 25 and cutting of the paper material 25 are suppressed.
- the operation of the winder slit facility is stabilized.
- the winder slit equipment is stably operated, product quality is improved.
- FIG. 3 is a block diagram for explaining tension control of a paper material using a mathematical model calculated by the mathematical model calculation apparatus according to Embodiment 1 of the present invention.
- control unit 24 includes a tension predictor 26 and a PI controller 27.
- the tension predictor 26 uses the transfer function G T (s) corresponding to the mathematical model, and the sum of the torque reference value ⁇ fd ref , the torque reference value ⁇ rd ref, and the torque reference value ⁇ rr ref and the torque reference value ⁇ uw. calculating the tension predicted value T m (MPa) from the deviation between ref.
- PI controller 27 calculates a proportional gain K p and the integral gain K I and the Laplace operator s torque reference value from the deviation between the tension reference value T ref (MPa) and tensile predicted value T m based on the tau uw ref To do.
- FIGS. 4 to 6 are block diagrams for explaining an outline of a mathematical model calculation method performed by the mathematical model calculation apparatus according to Embodiment 1 of the present invention.
- the mathematical model calculation unit 23 creates a mathematical model for estimating the tension applied to the paper material 25 from experimentally obtained data. Specifically, the mathematical model calculation unit 23 calculates the torque response value ⁇ fd res (N ⁇ m) of the front drum motor 9, the torque response value ⁇ rd res (N ⁇ m) of the rear drum motor 10, and the rider roll the difference between the torque response value of the motor 11 ⁇ rr res (N ⁇ m ) torque response value of the sum and the unwinder motor 8 and ⁇ uw res (N ⁇ m) as an input, the tension meter 20 of the tension response value T res Is used as an output to calculate a differential equation, transfer function, and state equation from input to output.
- a (z) in the expression (1) is expressed by the following expression (2).
- G (z) is a transfer function from the input u (k) to the output y (k). Specifically, G (z) is expressed by the following equation (5).
- the predicted value of the output y (k) at the current time k is expressed by the following equation (8) using past data up to the time (k ⁇ 1).
- Equation (8) The second term on the right side of equation (8) is defined by the following equation (9).
- the current output is calculated as a linear combination of past input and output.
- the prediction error ⁇ using the one-step predicted value is defined by the following equation (12).
- a (z), B (z), and C (z) are determined by the prediction error method using the equation (12). Specifically, A (z), B (z), and C (z) are determined so as to minimize the evaluation function composed of the prediction error ⁇ .
- the transfer function G ′ (s) from the input u (k) to the output y (k) can be obtained by converting the equation (13).
- the transfer function G ′ (s) is expressed by the following equation (14).
- FIGS. 7 to 9 are diagrams for explaining an example of a mathematical model calculation method by the mathematical model calculation apparatus according to Embodiment 1 of the present invention.
- FIG. 7 shows the unwinding motor and the sum of the torque response value ⁇ fd res of the front drum motor 9, the torque response value ⁇ rd res of the rear drum motor 10, and the torque response value ⁇ rr res of the rider roll motor 11.
- 8 shows a deviation from the torque response value ⁇ uw res of 8. 7
- the torque response value ⁇ fd res of the front drum motor 9 the torque response value ⁇ rd res of the rear drum motor 10
- the torque response value ⁇ rr res of the rider roll motor 11 and the torque of the unwinder motor 8.
- the response value ⁇ uw res is a value converted with the rated torque as 100%.
- the upper part of FIG. 8 is a diagram showing a transient state from the start in the upper part of FIG. 7 to the target tension. Specifically, the upper part of FIG. 8 is an enlarged view from time 0 (s) to 20 (s). In the upper part of FIG. 8, a dotted line is a line obtained by linearly approximating data.
- the lower part of FIG. 8 is a diagram showing a transitional state from the start of the lower part of FIG. 7 to the target tension. Specifically, the lower part of FIG. 8 is an enlarged view of the time from 0 (s) to 20 (s). In the lower part of FIG. 8, a dotted line is a line obtained by linearly approximating data.
- the lower part of FIG. 9 is data obtained by removing the average value and the slope, which are low-frequency disturbances, from the lower part of FIG. 8 as preprocessing of data before being input to the mathematical model.
- the mathematical model calculation unit 23 performs processing corresponding to the upper and lower stages of FIG. 9 offline after data collection.
- the mathematical model calculation unit 23 calculates a transfer function using the upper and lower data in FIG.
- the transfer function G T (s) is expressed by the following equation (15).
- the obtained transfer function G T (s) is used for tension control of the paper material 25 from the next time onward.
- the mathematical model calculator 23 removes from the input data when estimating the transfer function G T (s) in the previous paper 25 from the deviation data of the winding and rewinding torques calculated from the torque reference value of each motor. Remove the average value and slope online.
- the mathematical model calculation unit 23 inputs the value to the transfer function G T (s).
- the mathematical model calculation unit 23 calculates a value obtained by adding the average value and the slope removed from the output data when calculating the transfer function G T (s) to the output of the transfer function G T (s). Calculate as m .
- the predicted tension value Tm is calculated so as to be along the actual tension response value Tres .
- the tension of the paper material 25 is controlled with high accuracy.
- the mathematical model is calculated based on the history of the actual measurement values of the sheet material production line. For this reason, it is possible to calculate a highly accurate mathematical model for controlling the tension of the sheet material.
- the mathematical model is the sum of the torque response value ⁇ fd res of the front drum motor 9, the torque response value ⁇ rd res of the rear drum motor 10, and the torque response value ⁇ rr res of the rider roll motor 11.
- the deviation from the torque response value ⁇ uw res of the unwinder motor 8 is used as an input, and the tension response value T res of the tensiometer 20 is calculated as an output. For this reason, a highly accurate mathematical model can be calculated for the winder slit installation.
- the mathematical model may be calculated after weighting the value ⁇ uw res . In this case, a highly accurate mathematical model can be calculated according to the actual situation.
- the mathematical model is calculated using a value obtained by approximating an input and an output with a linear line and subtracting the corresponding linear line from the input and the output. For this reason, a more accurate mathematical model can be calculated.
- the mathematical model is calculated by using a value obtained by applying a low-pass filter to the measured value of the tensiometer 20 as an output. For this reason, the noise contained in the measured value in the tension meter 20 can be removed. As a result, a more accurate mathematical model can be calculated.
- a mathematical model may be calculated by using an average value of a plurality of sampling values of the measurement value of the tension meter 20 as an output. In this case, noise included in the measurement value obtained by the tensiometer 20 can be removed. As a result, a more accurate mathematical model can be calculated.
- the value obtained by multiplying the roll radius corresponding to the fastest rotation speed among the front drum motor 9, the rear drum motor 10, and the rider roll motor 11 by the rotation of the unwinder motor 8 is calculated.
- a deviation from a value obtained by multiplying the speed by the radius of the unwinder 1 may be input.
- a transfer function from the peripheral speed of the roll to the tension of the paper material 25 may be calculated as a transfer function corresponding to the mathematical model. Also in this case, a highly accurate mathematical model can be calculated.
- FIG. 11 is a hardware configuration diagram of a control device including the mathematical model calculation device according to Embodiment 1 of the present invention.
- Each function of the control device 21 can be realized by a processing circuit.
- the processing circuit comprises at least one processor 28a and at least one memory 28b.
- the processing circuit comprises at least one dedicated hardware 29.
- each function of the control device 21 is realized by software, firmware, or a combination of software and firmware.
- At least one of software and firmware is described as a program.
- At least one of software and firmware is stored in at least one memory 28b.
- the at least one processor 28a reads out and executes the program stored in the at least one memory 28b, thereby realizing each function of the control device 21.
- the at least one processor 28a is also referred to as a CPU (Central Processing Unit), a central processing unit, a processing unit, an arithmetic unit, a microprocessor, a microcomputer, and a DSP.
- the at least one memory 28b is a nonvolatile or volatile semiconductor memory such as a RAM, a ROM, a flash memory, an EPROM, or an EEPROM, a magnetic disk, a flexible disk, an optical disk, a compact disk, a mini disk, or a DVD.
- a nonvolatile or volatile semiconductor memory such as a RAM, a ROM, a flash memory, an EPROM, or an EEPROM, a magnetic disk, a flexible disk, an optical disk, a compact disk, a mini disk, or a DVD.
- the processing circuit comprises at least one dedicated hardware 29, the processing circuit is implemented, for example, as a single circuit, a composite circuit, a programmed processor, a parallel programmed processor, an ASIC, an FPGA, or a combination thereof.
- the control device 21 is realized by a processing circuit.
- each function of the control device 21 is collectively realized by a processing circuit.
- a part of each function of the control device 21 may be realized by dedicated hardware 29, and the other part may be realized by software or firmware.
- the function of the mathematical model calculation unit 23 is realized by a processing circuit as dedicated hardware 29, and at least one processor 28a is stored in at least one memory 28b for functions other than the function of the mathematical model calculation unit 23. It may be realized by reading out and executing the program.
- the processing circuit realizes each function of the control device 21 by hardware 29, software, firmware, or a combination thereof.
- the mathematical model calculation unit 23 converts each calculated transfer function into a state equation, and improves the prediction accuracy by using a Kalman filter.
- the Kalman filter is an online algorithm that sequentially estimates the state of the system using a state equation indicating the dynamic characteristics of the system and measured data that is given every moment.
- the Kalman filter uses an assumption that the influence of the disturbance applied to the system and the noise contained in the sensor follows a normal distribution.
- the state at the current time is estimated based on the information of the time before one sampling.
- the correct state is estimated by correcting the predicted tension value based on the actual measurement value at the current time.
- the mathematical model calculation unit 23 converts each transfer function calculated in the first embodiment into a state equation of Expression (17), and implements a Kalman filter. Mathematical model calculating unit 23 sequentially corrects the tension predicted value T c m by using a deviation between the tension response value T res and tension predicted value T c m for obtaining at each sampling. Specifically, the mathematical model calculating unit 23 calculates the tension prediction value T c m by performing at each sampling operations (18) from equation (22).
- the mathematical model calculation unit 23 converts the mathematical model into a state equation, and uses the Kalman filter to calculate the mathematical model based on the measurement value of the tensiometer 20 during the operation of the winder slitter facility. model by correcting the tension predicted value T c m. For this reason, the precision of tension control of paper material 25 can be raised more.
- control device similar to the control device 21 of the first embodiment may be applied to the film production line.
- the accuracy of tension control can be increased based on a highly accurate mathematical model.
- FIG. FIG. 13 is a configuration diagram of rolling equipment to which the mathematical model calculating apparatus according to Embodiment 3 of the present invention is applied.
- symbol is attached
- the forward rolling stand 30 is provided on the upstream side of the rolling equipment as one of the roll devices.
- the front rolling roll 31 is provided on the front rolling stand 30.
- the forward reduction device 32 is provided above the forward rolling stand 30.
- the rear rolling stand 33 is provided on the downstream side of the rolling equipment as the other of the roll devices.
- the rear rolling roll 34 is provided on the rear rolling stand 33.
- the rear reduction device 35 is provided above the rear rolling stand 33.
- the front motor 36 is provided corresponding to the front rolling stand 30 as a first motor device.
- the rear motor 37 is provided corresponding to the rear rolling stand 33 as a second motor device.
- the tension meter 40 is provided between the front rolling stand 30 and the rear rolling stand 33.
- the mathematical model calculation unit 23 receives the deviation between the torque response value of the rear motor 37 and the torque response value of the front motor 36 and calculates the mathematical model using the tension response value of the tensiometer 40 as an output.
- the mathematical model is calculated based on the history of the actual measurement values of the rolling equipment. For this reason, a mathematical model with high accuracy can be calculated for the rolling equipment.
- the deviation between the value obtained by multiplying the rotational speed of the rear motor 37 by the radius of the rear rolling roll 34 and the value obtained by multiplying the rotational speed of the front motor 36 by the radius of the front rolling roll 31 is input. Also good.
- a transfer function from the peripheral speed of each roll to the tension of the rolled material 41 may be calculated as a transfer function corresponding to the mathematical model. Also in this case, a highly accurate mathematical model can be calculated.
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- Controlling Rewinding, Feeding, Winding, Or Abnormalities Of Webs (AREA)
- Control Of Metal Rolling (AREA)
Abstract
Description
図1はこの発明の実施の形態1における数学モデル算出装置が適用されるワインダスリット設備の構成図である。
図2はこの発明の実施の形態1における数学モデル算出装置が適用されるワインダスリット設備の制御を説明するための図である。
図3はこの発明の実施の形態1における数学モデル算出装置により算出された数学モデルを用いた紙材の張力制御を説明するためのブロック図である。
図4から図6はこの発明の実施の形態1における数学モデル算出装置による数学モデルの算出方法の概要を説明するためのブロック図である。
図7から図9はこの発明の実施の形態1における数学モデル算出装置による数学モデルの算出方法の例を説明するための図である。
図10はこの発明の実施の形態1における数学モデル算出装置による数学モデルに基づいた張力予側値の例を説明するための図である。
図11はこの発明の実施の形態1における数学モデル算出装置を備えた制御装置のハードウェア構成図である。
図12はこの発明の実施の形態2におけるシート材生産ラインの数学モデル算出装置が算出した数学モデルによるシミュレーション結果を示す図である。なお、実施の形態1の部分と同一又は相当部分には同一符号が付される。当該部分の説明は省略される。
図13はこの発明の実施の形態3における数学モデル算出装置が適用される圧延設備の構成図である。なお、実施の形態1の部分と同一又は相当部分には同一符号が付される。当該部分の説明は省略される。
Claims (12)
- シート材生産ラインの実測値の履歴に基づいて、複数のロール装置の間に配置されて前記複数のロール装置の一方から他方へ向けて進行するシート材の張力を計測する張力計の計測値に基づいて制御されるシート材生産ラインに対し、前記複数のロール装置の他方を駆動する第2モータ装置のトルクと前記複数のロール装置の一方を駆動する第1モータ装置のトルクとの偏差を入力とし、前記張力計の計測値を出力として数学モデルを算出する数学モデル算出部、
を備えたシート材生産ラインの数学モデル算出装置。 - 前記複数のロール装置の一方は、シート材を巻き戻すアンワインダであり、
前記複数のロール装置の他方は、フロントドラムとリアドラムとライダーロールとを用いてシート材を巻き取るワインダであり、
前記第1モータ装置は、前記アンワインダを駆動するモータを有し、
前記第2モータ装置は、前記フロントドラムと前記リアドラムと前記ライダーロールとをそれぞれ駆動する複数のモータを有し、
前記数学モデル算出部は、前記フロントドラムと前記リアドラムと前記ライダーロールとをそれぞれ駆動する複数のモータのトルクの和と前記アンワインダを駆動するモータのトルクとの偏差を入力として数学モデルを算出する請求項1に記載のシート材生産ラインの数学モデル算出装置。 - 前記数学モデル算出部は、前記フロントドラムと前記リアドラムと前記ライダーロールとをそれぞれ駆動する複数のモータのトルクに対して重み付けを行った上で前記フロントドラムと前記リアドラムと前記ライダーロールとをそれぞれ駆動する複数のモータのトルクの和と前記アンワインダを駆動するモータのトルクとの偏差を入力として数学モデルを算出する請求項2に記載のシート材生産ラインの数学モデル算出装置。
- 前記複数のロール装置は、複数の圧延スタンドであり、
前記第1モータ装置は、前記複数の圧延スタンドの一方のロールを駆動するモータを有し、
前記第2モータ装置は、前記複数の圧延スタンドの他方のロールを駆動するモータを有し、
前記数学モデル算出部は、前記複数の圧延スタンドの他方のロールを駆動するモータのトルクと前記複数の圧延スタンドの一方のロールを駆動するモータのトルクとの偏差を入力として数学モデルを算出する請求項1に記載のシート材生産ラインの数学モデル算出装置。 - シート材生産ラインの実測値の履歴に基づいて、複数のロール装置の間に配置されて前記複数のロール装置の一方から他方へ向けて進行するシート材の張力を計測する張力計の計測値に基づいて制御されるシート材生産ラインに対し、前記複数のロール装置の他方を駆動する第2モータ装置の回転角速度に前記複数のロール装置の他方の半径を乗じた値と前記複数のロール装置の一方を駆動する第1モータ装置の回転角速度に前記複数のロール装置の一方の半径を乗じた値との偏差を入力とし、前記張力計の計測値を出力として数学モデルを算出する数学モデル算出部、
を備えたシート材生産ラインの数学モデル算出装置。 - 前記複数のロール装置の一方は、シート材が巻かれているアンワインダであり、
前記複数のロール装置の他方は、フロントドラムとリアドラムとライダーロールとを用いてシート材を巻き取るワインダであり、
前記第1モータ装置は、前記アンワインダを駆動するモータを有し、
前記第2モータ装置は、前記フロントドラムと前記リアドラムと前記ライダーロールとをそれぞれ駆動する複数のモータを有し、
前記数学モデル算出部は、前記フロントドラムと前記リアドラムと前記ライダーロールとをそれぞれ駆動する複数のモータの回転速度のうちの最も速い回転角速度に対応したロールの半径を乗じた値と前記アンワインダを駆動するモータの回転角速度に前記アンワインダの半径を乗じた値との偏差を入力として数学モデルを算出する請求項5に記載のシート材生産ラインの数学モデル算出装置。 - 前記複数のロール装置は、複数の圧延スタンドであり、
前記第1モータ装置は、前記複数の圧延スタンドの一方のロールを駆動するモータを有し、
前記第2モータ装置は、前記複数の圧延スタンドの他方のロールを駆動するモータを有し、
前記数学モデル算出部は、前記複数の圧延スタンドの他方を駆動するモータの回転角速度に前記複数の圧延スタンドの他方のロールの半径を乗じた値と前記複数の圧延スタンドの一方を駆動するモータの回転角速度に前記複数の圧延スタンドの一方のロールの半径を乗じた値との偏差を入力として数学モデルを算出する請求項5に記載のシート材生産ラインの数学モデル算出装置。 - 前記数学モデル算出部は、入力と出力とを1次直線で近似し、当該入力と当該出力とから対応した1次直線を差し引いた値を用いて数学モデルを算出する請求項1から請求項7のいずれか一項に記載のシート材生産ラインの数学モデル算出装置。
- 前記数学モデル算出部は、前記張力計の計測値にローパスフィルタを施した値を出力として数学モデルを算出する請求項1から請求項8のいずれか一項に記載のシート材生産ラインの数学モデル算出装置。
- 前記数学モデル算出部は、前記張力計の計測値の複数のサンプリング値の平均値を出力として数学モデルを算出する請求項1から請求項9のいずれか一項に記載のシート材生産ラインの数学モデル算出装置。
- 前記シート材生産ラインの稼働中において、請求項1から請求項10のいずれか一項に記載の数学モデル算出装置が前記第1モータ装置のトルクと前記第2モータ装置のトルクとを入力として数学モデルに基づいて算出した張力予測値を取得し、当該張力予測値に基づいて前記第1モータ装置のトルクを制御する制御部、
を備えたシート材生産ラインの制御装置。 - 前記数学モデル算出装置は、数学モデルを状態方程式に変換し、カルマンフィルタを用いて、前記シート材生産ラインの稼働中における前記張力計の計測値に基づいて数学モデルによる張力予測値を補正する請求項11に記載のシート材生産ラインの制御装置。
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