JP2003089146A - Sheet manufacturing method and sheet thickness control unit - Google Patents

Sheet manufacturing method and sheet thickness control unit

Info

Publication number
JP2003089146A
JP2003089146A JP2001288401A JP2001288401A JP2003089146A JP 2003089146 A JP2003089146 A JP 2003089146A JP 2001288401 A JP2001288401 A JP 2001288401A JP 2001288401 A JP2001288401 A JP 2001288401A JP 2003089146 A JP2003089146 A JP 2003089146A
Authority
JP
Japan
Prior art keywords
sheet
thickness
operation amount
adjusting means
manipulated variable
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Granted
Application number
JP2001288401A
Other languages
Japanese (ja)
Other versions
JP4834946B2 (en
Inventor
Masatsugu Uehara
正嗣 上原
Hajime Hirata
肇 平田
Yasuhiro Nakai
康博 中井
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Toray Industries Inc
Original Assignee
Toray Industries Inc
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Toray Industries Inc filed Critical Toray Industries Inc
Priority to JP2001288401A priority Critical patent/JP4834946B2/en
Publication of JP2003089146A publication Critical patent/JP2003089146A/en
Application granted granted Critical
Publication of JP4834946B2 publication Critical patent/JP4834946B2/en
Anticipated expiration legal-status Critical
Expired - Fee Related legal-status Critical Current

Links

Classifications

    • BPERFORMING OPERATIONS; TRANSPORTING
    • B29WORKING OF PLASTICS; WORKING OF SUBSTANCES IN A PLASTIC STATE IN GENERAL
    • B29CSHAPING OR JOINING OF PLASTICS; SHAPING OF MATERIAL IN A PLASTIC STATE, NOT OTHERWISE PROVIDED FOR; AFTER-TREATMENT OF THE SHAPED PRODUCTS, e.g. REPAIRING
    • B29C48/00Extrusion moulding, i.e. expressing the moulding material through a die or nozzle which imparts the desired form; Apparatus therefor
    • B29C48/03Extrusion moulding, i.e. expressing the moulding material through a die or nozzle which imparts the desired form; Apparatus therefor characterised by the shape of the extruded material at extrusion
    • B29C48/07Flat, e.g. panels
    • B29C48/08Flat, e.g. panels flexible, e.g. films
    • BPERFORMING OPERATIONS; TRANSPORTING
    • B29WORKING OF PLASTICS; WORKING OF SUBSTANCES IN A PLASTIC STATE IN GENERAL
    • B29CSHAPING OR JOINING OF PLASTICS; SHAPING OF MATERIAL IN A PLASTIC STATE, NOT OTHERWISE PROVIDED FOR; AFTER-TREATMENT OF THE SHAPED PRODUCTS, e.g. REPAIRING
    • B29C48/00Extrusion moulding, i.e. expressing the moulding material through a die or nozzle which imparts the desired form; Apparatus therefor
    • B29C48/25Component parts, details or accessories; Auxiliary operations
    • B29C48/92Measuring, controlling or regulating
    • BPERFORMING OPERATIONS; TRANSPORTING
    • B29WORKING OF PLASTICS; WORKING OF SUBSTANCES IN A PLASTIC STATE IN GENERAL
    • B29CSHAPING OR JOINING OF PLASTICS; SHAPING OF MATERIAL IN A PLASTIC STATE, NOT OTHERWISE PROVIDED FOR; AFTER-TREATMENT OF THE SHAPED PRODUCTS, e.g. REPAIRING
    • B29C2948/00Indexing scheme relating to extrusion moulding
    • B29C2948/92Measuring, controlling or regulating
    • B29C2948/92009Measured parameter
    • B29C2948/92114Dimensions
    • B29C2948/92152Thickness
    • BPERFORMING OPERATIONS; TRANSPORTING
    • B29WORKING OF PLASTICS; WORKING OF SUBSTANCES IN A PLASTIC STATE IN GENERAL
    • B29CSHAPING OR JOINING OF PLASTICS; SHAPING OF MATERIAL IN A PLASTIC STATE, NOT OTHERWISE PROVIDED FOR; AFTER-TREATMENT OF THE SHAPED PRODUCTS, e.g. REPAIRING
    • B29C2948/00Indexing scheme relating to extrusion moulding
    • B29C2948/92Measuring, controlling or regulating
    • B29C2948/92009Measured parameter
    • B29C2948/92114Dimensions
    • B29C2948/92171Distortion, shrinkage, dilatation, swell or warpage
    • BPERFORMING OPERATIONS; TRANSPORTING
    • B29WORKING OF PLASTICS; WORKING OF SUBSTANCES IN A PLASTIC STATE IN GENERAL
    • B29CSHAPING OR JOINING OF PLASTICS; SHAPING OF MATERIAL IN A PLASTIC STATE, NOT OTHERWISE PROVIDED FOR; AFTER-TREATMENT OF THE SHAPED PRODUCTS, e.g. REPAIRING
    • B29C2948/00Indexing scheme relating to extrusion moulding
    • B29C2948/92Measuring, controlling or regulating
    • B29C2948/92323Location or phase of measurement
    • B29C2948/92438Conveying, transporting or storage of articles
    • BPERFORMING OPERATIONS; TRANSPORTING
    • B29WORKING OF PLASTICS; WORKING OF SUBSTANCES IN A PLASTIC STATE IN GENERAL
    • B29CSHAPING OR JOINING OF PLASTICS; SHAPING OF MATERIAL IN A PLASTIC STATE, NOT OTHERWISE PROVIDED FOR; AFTER-TREATMENT OF THE SHAPED PRODUCTS, e.g. REPAIRING
    • B29C2948/00Indexing scheme relating to extrusion moulding
    • B29C2948/92Measuring, controlling or regulating
    • B29C2948/92323Location or phase of measurement
    • B29C2948/92447Moulded article
    • BPERFORMING OPERATIONS; TRANSPORTING
    • B29WORKING OF PLASTICS; WORKING OF SUBSTANCES IN A PLASTIC STATE IN GENERAL
    • B29CSHAPING OR JOINING OF PLASTICS; SHAPING OF MATERIAL IN A PLASTIC STATE, NOT OTHERWISE PROVIDED FOR; AFTER-TREATMENT OF THE SHAPED PRODUCTS, e.g. REPAIRING
    • B29C2948/00Indexing scheme relating to extrusion moulding
    • B29C2948/92Measuring, controlling or regulating
    • B29C2948/92504Controlled parameter
    • B29C2948/92523Force; Tension
    • BPERFORMING OPERATIONS; TRANSPORTING
    • B29WORKING OF PLASTICS; WORKING OF SUBSTANCES IN A PLASTIC STATE IN GENERAL
    • B29CSHAPING OR JOINING OF PLASTICS; SHAPING OF MATERIAL IN A PLASTIC STATE, NOT OTHERWISE PROVIDED FOR; AFTER-TREATMENT OF THE SHAPED PRODUCTS, e.g. REPAIRING
    • B29C2948/00Indexing scheme relating to extrusion moulding
    • B29C2948/92Measuring, controlling or regulating
    • B29C2948/92504Controlled parameter
    • B29C2948/92609Dimensions
    • B29C2948/92647Thickness
    • BPERFORMING OPERATIONS; TRANSPORTING
    • B29WORKING OF PLASTICS; WORKING OF SUBSTANCES IN A PLASTIC STATE IN GENERAL
    • B29CSHAPING OR JOINING OF PLASTICS; SHAPING OF MATERIAL IN A PLASTIC STATE, NOT OTHERWISE PROVIDED FOR; AFTER-TREATMENT OF THE SHAPED PRODUCTS, e.g. REPAIRING
    • B29C2948/00Indexing scheme relating to extrusion moulding
    • B29C2948/92Measuring, controlling or regulating
    • B29C2948/92504Controlled parameter
    • B29C2948/92609Dimensions
    • B29C2948/92666Distortion, shrinkage, dilatation, swell or warpage
    • BPERFORMING OPERATIONS; TRANSPORTING
    • B29WORKING OF PLASTICS; WORKING OF SUBSTANCES IN A PLASTIC STATE IN GENERAL
    • B29CSHAPING OR JOINING OF PLASTICS; SHAPING OF MATERIAL IN A PLASTIC STATE, NOT OTHERWISE PROVIDED FOR; AFTER-TREATMENT OF THE SHAPED PRODUCTS, e.g. REPAIRING
    • B29C2948/00Indexing scheme relating to extrusion moulding
    • B29C2948/92Measuring, controlling or regulating
    • B29C2948/92819Location or phase of control
    • B29C2948/92857Extrusion unit
    • B29C2948/92904Die; Nozzle zone

Landscapes

  • Engineering & Computer Science (AREA)
  • Mechanical Engineering (AREA)
  • Feedback Control In General (AREA)
  • Extrusion Moulding Of Plastics Or The Like (AREA)

Abstract

PROBLEM TO BE SOLVED: To provide a sheet manufacturing method capable of rapidly controlling the thickness of a sheet to a desired thickness profile with high accuracy, and a control unit for the thickness of the sheet. SOLUTION: The sheet manufacturing method uses a die equipped with a plurality of thickness adjusting means to extrude a raw material and molding the extrudate to form a sheet and controlling the thickness of the sheet, while controlling the operation quantity applied to the thickness adjusting means. A step for measuring the thickness distribution in the width direction of the sheet; a sep for leading out an operation quantity time series, wherein a predetermined evaluation function for evaluating a sheet thickness forecast formula calculated, on the basis of a process model expressing the relation between the operation quantity and the thickness of the sheet and the measured value becomes an extreme value; and a step for outputting at least the first operation quantity in the operation quantity time series to the thickness adjusting means are repeated in predetermined timing.

Description

【発明の詳細な説明】Detailed Description of the Invention

【0001】[0001]

【発明の属する技術分野】本発明は、フィルムなどのシ
ートの製造方法およびシートの厚み制御装置に関するも
のである。
BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method for manufacturing a sheet such as a film and a sheet thickness control device.

【0002】[0002]

【従来の技術】高分子フィルムなどのシートの幅方向の
厚みを所望のプロファイル、例えば均一の厚みに制御す
る従来のシート製造方法の例を図2および図3を用いて
説明する。
2. Description of the Related Art An example of a conventional sheet manufacturing method in which the thickness of a sheet such as a polymer film in the width direction is controlled to have a desired profile, for example, a uniform thickness will be described with reference to FIGS.

【0003】押出機3より押し出された原料たる重合体
は、ダイ4で図2の紙面に垂直な幅方向に拡げられ押し
出されてシート1となり、延伸機2により縦方向(シー
ト走行方向)、横方向(シート幅方向)に延伸されて巻
取機6に巻き取られる。ダイ4には厚み調整手段10が
幅方向に等間隔に複数個配設されており、これは具体的
にはヒーター、ギャップ調整具等によって重合体の吐出
量を変える働きをする。厚み計8はシート1の厚みをシ
ート幅方向の分布として測定し、制御手段9は、厚み調
整手段10のそれぞれを、これに対応する箇所の測定値
に基づいて制御する。
The raw material polymer extruded from the extruder 3 is spread by a die 4 in the width direction perpendicular to the paper surface of FIG. 2 and extruded to form a sheet 1, which is then stretched by a stretching machine 2 in the longitudinal direction (sheet running direction) The film is stretched in the lateral direction (sheet width direction) and wound up by the winder 6. The die 4 is provided with a plurality of thickness adjusting means 10 at equal intervals in the width direction, which specifically serves to change the discharge amount of the polymer by a heater, a gap adjusting tool, or the like. The thickness meter 8 measures the thickness of the sheet 1 as a distribution in the sheet width direction, and the control means 9 controls each of the thickness adjusting means 10 on the basis of the measurement value at the corresponding position.

【0004】この制御手段としては、厚み調整手段のそ
れぞれについて独立した制御ループを構成し、各制御ル
ープでは、厚み測定値と目標値の偏差に対して比例、積
分、微分演算を施した結果を操作量として厚み制御手段
に出力する周知のPID制御を行なう方法が広く利用さ
れている。
As the control means, an independent control loop is formed for each of the thickness adjusting means, and in each control loop, the results of proportional, integral, and differential operations are performed on the deviation between the thickness measurement value and the target value. A well-known method of performing PID control in which the operation amount is output to the thickness control means is widely used.

【0005】また、特公平6−75906号公報、特公
平6−75907号公報、特公平6−75908号公
報、特許第3021135号公報にはこの制御手段とし
て現代制御理論を用いた厚み制御装置が示されている。
Further, Japanese Patent Publication No. 6-75906, Japanese Patent Publication No. 6-75907, Japanese Patent Publication No. 6-75908, and Japanese Patent No. 3021135 disclose thickness control devices using modern control theory as the control means. It is shown.

【0006】[0006]

【発明が解決しようとする課題】上記、厚み調整手段の
それぞれについて独立した制御ループを構成した従来の
厚み制御系では、まだ充分に満足できる制御は行えな
い。その理由の一つは、上記厚み調整手段の一つを操作
すると、隣接する調整手段に対応する箇所のシート厚み
まで変化するという干渉現象によるものである。このた
め、厚み調整手段のそれぞれに対応した制御ループは相
互に干渉し、対応位置の厚みと目標値との偏差に基づい
て操作量を演算して制御しても、隣接する調整手段によ
る影響を受けて目標値に近づかない場合や、目標値に近
づく速度が極めて遅くなる場合があった。
SUMMARY OF THE INVENTION The conventional thickness control system in which the respective thickness adjusting means have independent control loops cannot perform sufficiently satisfactory control. One of the reasons is that when one of the thickness adjusting means is operated, the sheet thickness at a portion corresponding to the adjacent adjusting means is changed, which is an interference phenomenon. For this reason, the control loops corresponding to the respective thickness adjusting means interfere with each other, and even if the operation amount is calculated and controlled based on the deviation between the thickness at the corresponding position and the target value, the influence of the adjacent adjusting means does not occur. In some cases, the target value has not been approached, and the speed of approaching the target value has become extremely slow.

【0007】また、別の理由として、上記厚み調整手段
の一つを操作してから、その結果が対応位置での厚み測
定結果にあらわれるまでに時間的な遅れ、すなわち制御
で言うところのむだ時間があることによる。このため、
PID制御のゲインを大きくすると、厚み調整手段に操
作量を出力した結果が対応位置での厚み測定結果にあら
われる前に大きく操作しすぎることになり、制御が不安
定になる。したがって、制御が安定するように、制御の
ゲインを小さくせざるを得ず、即応性の悪い制御系とな
る。
Another reason is that there is a time lag between the operation of one of the thickness adjusting means and the appearance of the result in the thickness measurement result at the corresponding position, that is, the dead time in control. Because there is For this reason,
When the gain of the PID control is increased, the operation amount becomes too large before the result of outputting the operation amount to the thickness adjusting means appears in the thickness measurement result at the corresponding position, and the control becomes unstable. Therefore, the control gain must be reduced so that the control becomes stable, resulting in a control system with poor responsiveness.

【0008】この問題に対しては、前述の公告公報、特
許公報に提案されている現代制御による方法が効果があ
ると考えられるが、これらの方法については設計、パラ
メータチューニングに要する時間、手間に対して得られ
る効果が少ないという問題がある。
For this problem, it is considered that the methods by modern control proposed in the above-mentioned publications and patents are effective, but these methods require time and effort for designing, parameter tuning. There is a problem that the effect obtained is small.

【0009】すなわち、これらの方法では、操作量と制
御量の間の関係をプロセスモデルと呼ばれる関係式によ
って表し、これに基づいて制御系を設計していく必要が
ある。 ところが、図2に示すようなシート成形プロセ
スに含まれる縦方向の延伸、横方向の延伸等を解析的に
数式表現することは困難であり、何らかの簡略化を行う
結果として、実際に利用可能なプロセスモデルは、実際
のプロセスとの違い、すなわちモデル化誤差を含んでい
る。また、シート成形プロセスの特性自体が時間的に変
化する場合もあり、この場合にもプロセスモデルは誤差
を含むことになる。
That is, in these methods, it is necessary to represent the relationship between the manipulated variable and the controlled variable by a relational expression called a process model and design the control system based on this. However, it is difficult to express mathematically the longitudinal stretching, the lateral stretching, etc. included in the sheet forming process as shown in FIG. 2, and as a result of some simplification, it can be actually used. The process model includes a difference from the actual process, that is, a modeling error. In addition, the characteristics of the sheet forming process itself may change with time, and in this case as well, the process model includes an error.

【0010】したがって、プロセスモデルが誤差を持つ
結果として、これを用いて設計した制御系が演算した操
作量は、実際の最適値とは違ったものとなる。通常はこ
の違いは問題とならないが、長時間の運転制御の間で誤
差が積み重なったり、前述のようにプロセスの特性自体
が変化してモデル化誤差が大きくなった場合には、所望
の厚みプロファイルに制御できなくなる場合もあった。
Therefore, as a result of the process model having an error, the manipulated variable calculated by the control system designed using the process model is different from the actual optimum value. Normally, this difference is not a problem, but if the error accumulates during long-term operation control, or if the modeling characteristics increase due to changes in the process characteristics themselves as described above, the desired thickness profile is increased. In some cases, it was out of control.

【0011】この発明の目的は、従来の技術の上記問題
点を解決し、シート厚みを素早く、高精度に所望の厚み
プロファイルに制御できるシートの製造方法およびシー
トの厚み制御装置を提供することにある。
An object of the present invention is to solve the above problems of the prior art and to provide a sheet manufacturing method and a sheet thickness control apparatus capable of controlling the sheet thickness to a desired thickness profile quickly and with high accuracy. is there.

【0012】[0012]

【課題を解決するための手段】上記課題を解決するため
の本発明のシートの製造方法は、複数の厚み調整手段を
備えたダイを用いて原料を押し出し、成形してシートと
なすとともに、前記厚み調整手段に加える操作量を制御
して前記シートの厚みを制御するシートの製造方法であ
って、前記シートの幅方向の厚み分布を測定するステッ
プと、前記操作量とシート厚みとの関係を表すプロセス
モデルおよび前記シート厚み測定値に基づいて求められ
る将来のシート厚み変化を所定の評価関数を用いて評価
し、該評価関数が極小値となる操作量時系列を導出する
ステップと、導出された該操作量時系列のうち少なくと
も最初の操作量を前記厚み調整手段に出力するステップ
とを所定のタイミングで繰り返すことを特徴としてい
る。
A method for manufacturing a sheet according to the present invention for solving the above-mentioned problems is to extrude a raw material using a die provided with a plurality of thickness adjusting means and form the sheet to obtain a sheet. A method of manufacturing a sheet for controlling the thickness of the sheet by controlling the operation amount applied to a thickness adjusting means, the step of measuring the thickness distribution in the width direction of the sheet, and the relationship between the operation amount and the sheet thickness. Evaluating a future sheet thickness change obtained based on the process model and the sheet thickness measurement value using a predetermined evaluation function, and deriving a manipulated variable time series in which the evaluation function is a minimum value; The step of outputting at least the first operation amount to the thickness adjusting means in the operation amount time series is repeated at a predetermined timing.

【0013】また、本発明のシートの製造方法の好まし
い態様としては、前記所定の評価関数は、前記シート厚
み変化および前記操作量の変化に基づくものである。
In a preferred embodiment of the sheet manufacturing method of the present invention, the predetermined evaluation function is based on the sheet thickness change and the operation amount change.

【0014】また、本発明のシートの製造方法の別の好
ましい態様としては、前記所定の評価関数として、製造
開始時と製造安定時とで異なる評価関数を使用し、か
つ、製造開始時には製造安定時よりもシート厚み変化の
寄与度が操作量の寄与度に対して高くなるものを使用す
るまた、本発明のシートの製造方法の別の好ましい態様
としては、前記プロセスモデルとして、伝達関数と少な
くとも対角成分がゼロでない定数行列の積で表されるも
のを用いるものである。
As another preferred embodiment of the method for producing a sheet of the present invention, as the predetermined evaluation function, different evaluation functions are used at the start of production and at the time of stable production, and at the start of production, the production stability is improved. A sheet whose contribution to the change in the sheet thickness is higher than that to the contribution to the manipulated variable is used as another preferred embodiment of the sheet manufacturing method of the present invention. The one represented by the product of constant matrices whose diagonal elements are not zero is used.

【0015】また、本発明のシートの製造方法の別の好
ましい態様としては、前記定数行列として、シート幅方
向における端部と中央部とに対応する部分でそれぞれ異
なる定数を用いるものである。
In another preferred aspect of the method for manufacturing a sheet of the present invention, different constants are used as the constant matrix at portions corresponding to the end portion and the central portion in the sheet width direction.

【0016】また上記課題を解決するための本発明のシ
ートの厚み制御装置は、シートの幅方向の厚み分布を測
定する厚み測定手段によって測定された幅方向の各部の
シート厚み測定値に基づいて対応する位置のシートの厚
み調整手段へ操作量を与える制御装置であって、前記操
作量とシート厚みとの関係を表すプロセスモデルおよび
前記シート厚み測定値に基づいて求められる将来のシー
ト厚み変化を所定の評価関数を用いて評価し、該評価関
数が極小値となる操作量時系列を導出する操作量時系列
導出手段と、導出された該操作量時系列のうち少なくと
も最初の操作量を前記厚み調整手段に出力する操作量出
力手段とを備えたことを特徴としている。
Further, the sheet thickness control device of the present invention for solving the above-mentioned problems is based on the sheet thickness measurement value of each portion in the width direction measured by the thickness measuring means for measuring the thickness distribution of the sheet in the width direction. A control device for giving an operation amount to a sheet thickness adjusting means at a corresponding position, for a future sheet thickness change obtained based on a process model representing the relationship between the operation amount and the sheet thickness and the sheet thickness measurement value. An operation amount time series deriving means for evaluating using a predetermined evaluation function and deriving an operation amount time series in which the evaluation function has a minimum value, and at least the first operation amount of the derived operation amount time series And a manipulated variable output means for outputting to the thickness adjusting means.

【0017】また、本発明のシートの厚み制御装置の好
ましい態様としては、前記操作量時系列導出手段は、前
記所定の評価関数として、製造開始時と製造安定時とで
異なる評価関数を使用し、かつ、製造開始時には製造安
定時よりもシート厚み変化の寄与度が操作量の寄与度に
対して高くなるものを使用するものである。
In a preferred embodiment of the sheet thickness control apparatus of the present invention, the operation amount time series deriving means uses, as the predetermined evaluation function, different evaluation functions at the start of manufacturing and at the time of stable manufacturing. In addition, at the start of manufacturing, the contribution of the change in sheet thickness to the contribution of the manipulated variable is higher than that at the time of stable production.

【0018】また、本発明のシートの厚み制御装置の好
ましい態様としては、前記プロセスモデルとして、伝達
関数と少なくとも対角成分がゼロでない定数行列の積で
表されるものを用いるものである。
In a preferred embodiment of the sheet thickness control apparatus of the present invention, the process model represented by the product of a transfer function and a constant matrix in which at least a diagonal component is not zero is used.

【0019】また、本発明のシートの厚み制御装置の好
ましい態様としては、前記操作量時系列導出手段は、前
記定数行列として、シート幅方向における端部と中央部
とに対応する部分でそれぞれ異なる定数を用いるもので
ある。
In a preferred embodiment of the sheet thickness control device of the present invention, the manipulated variable time series deriving means has different constant matrices at portions corresponding to an end portion and a central portion in the sheet width direction. It uses a constant.

【0020】また、上記課題を解決するための本発明の
コンピュータ読み取り可能な記憶媒体は、シートの幅方
向の各部の厚みの測定値を入力するステップと、前記各
部の厚みの目標値と前記測定値との差を算出するステッ
プと、前記各部の差に基づいて厚み調整手段に加える操
作量を算出するステップとを所定のタイミングで繰り返
す動作をコンピュータに実現させるプログラムを記憶し
た記憶媒体であって、前記操作量を算出するステップ
は、前記操作量とシート厚みとの関係を表すプロセスモ
デルおよび前記シート厚み測定値に基づいて求められる
将来のシート厚み変化を所定の評価関数を用いて評価
し、該評価関数が極小値となる操作量時系列を導出する
ステップと、導出された該操作量時系列のうち少なくと
も最初の操作量を前記厚み調整手段に出力するステップ
を含むことを特徴としている。
Further, in the computer-readable storage medium of the present invention for solving the above-mentioned problems, the step of inputting the measured value of the thickness of each part in the width direction of the sheet, the target value of the thickness of each part and the measurement A storage medium that stores a program that causes a computer to perform an operation of repeating a step of calculating a difference with a value and a step of calculating an operation amount applied to the thickness adjusting means based on the difference between the respective parts at a predetermined timing. , The step of calculating the operation amount, the process model representing the relationship between the operation amount and the sheet thickness and future sheet thickness change obtained based on the sheet thickness measurement value is evaluated using a predetermined evaluation function, A step of deriving a manipulated variable time series in which the evaluation function has a minimum value; and a step of deriving at least a first manipulated variable in the derived manipulated variable time series. It is characterized by comprising the step of outputting the observed adjustment means.

【0021】また、上記課題を解決するための本発明の
プログラムは、シートの幅方向の各部の厚みの測定値を
入力するステップと、前記各部の厚みの目標値と前記測
定値との差を算出するステップと、前記各部の差に基づ
いて厚み調整手段に加える操作量を算出するステップと
を所定のタイミングで繰り返す動作をコンピュータに実
現させるプログラムであって、前記操作量を算出するス
テップは、前記操作量とシート厚みとの関係を表すプロ
セスモデルおよび前記シート厚み測定値に基づいて求め
られる将来のシート厚み変化を所定の評価関数を用いて
評価し、該評価関数が極小値となる操作量時系列を導出
するステップと、導出された該操作量時系列のうち少な
くとも最初の操作量を前記厚み調整手段に出力するステ
ップを含むことを特徴としている。
Further, a program of the present invention for solving the above-mentioned problem is a step of inputting a measured value of the thickness of each part in the width direction of the sheet and a difference between the target value of the thickness of each part and the measured value. A program for causing a computer to realize an operation of repeating, at a predetermined timing, a step of calculating and a step of calculating an operation amount applied to the thickness adjusting means based on a difference between the respective parts, the step of calculating the operation amount comprising: A future model change in sheet thickness obtained based on the process model and the sheet thickness measurement value, which represents the relationship between the operation amount and the sheet thickness, is evaluated using a predetermined evaluation function, and the operation amount is a minimum value. Deriving a time series, and outputting at least the first operation amount of the derived operation amount time series to the thickness adjusting means. It is a symptom.

【0022】[0022]

【発明の実施の形態】以下に図を引用しながら本発明を
シートの製造方法に適用した実施例に基づいて説明す
る。
BEST MODE FOR CARRYING OUT THE INVENTION The present invention will be described below with reference to the drawings based on an embodiment in which the present invention is applied to a sheet manufacturing method.

【0023】図2は、一般的なシートの製造設備全体概
略構成図を示す図であり、図3は図2に示すダイの要部
拡大斜視図である。
FIG. 2 is a diagram showing an overall schematic configuration of a general sheet manufacturing facility, and FIG. 3 is an enlarged perspective view of an essential part of the die shown in FIG.

【0024】押出機3より押し出された重合体は、ダイ
4で図2の紙面に垂直な幅方向に拡げられ押し出されて
シート1となり、延伸機2により縦方向、横方向に延伸
されて巻取機6に巻き取られる。
The polymer extruded from the extruder 3 is expanded by a die 4 in the width direction perpendicular to the paper surface of FIG. 2 and extruded to form a sheet 1, which is stretched in a longitudinal direction and a transverse direction by a stretching machine 2 and wound. It is taken up by the take-up machine 6.

【0025】ダイ4には厚み調整手段10が幅方向に等
間隔に複数個配設されている。厚み調整手段10として
は、ボルトを配置し、機械的または熱的にあるいは電気
的にダイ4のギャップ11を変えることにより重合体の
吐出量を変えるボルト方式、ヒーターを配置し、ヒータ
発生熱を変えることにより、その個所の重合体の粘性を
変えて流速を変えることにより吐出量を変えるヒーター
方式のいずれでも用いることができる。
A plurality of thickness adjusting means 10 are arranged on the die 4 at equal intervals in the width direction. As the thickness adjusting means 10, a bolt system in which a bolt is arranged and a discharge amount of the polymer is changed by changing the gap 11 of the die 4 mechanically or thermally or electrically is arranged. By changing the temperature, it is possible to use any of the heater methods in which the discharge amount is changed by changing the viscosity of the polymer at that location and changing the flow rate.

【0026】厚み計8はシート1の厚みをシート幅方向
の分布として測定する。厚み計8としては、β線、赤外
線、紫外線、X線等の吸収率を利用したもの、光の干渉
現象を利用したもの等、任意の厚み計を用いることがで
きる。
The thickness meter 8 measures the thickness of the sheet 1 as a distribution in the sheet width direction. As the thickness meter 8, any thickness meter such as one utilizing the absorptance of β rays, infrared rays, ultraviolet rays, X-rays and the like, one utilizing the light interference phenomenon, etc. can be used.

【0027】制御手段9は、まず、厚み計8で測定した
厚みのシート幅方向分布測定値を入力して、これから厚
み調整手段10の各操作点に対応するシート厚み測定値
を求め、次にこの各操作点に対応するシート厚み測定値
から後述する制御動作演算を行って各操作点毎の制御出
力を決定し、これを一定周期で各操作点に出力する。
The control means 9 first inputs the sheet width direction distribution measurement value of the thickness measured by the thickness gauge 8 and obtains the sheet thickness measurement value corresponding to each operation point of the thickness adjusting means 10 from this, and then The control operation calculation described later is performed from the sheet thickness measurement value corresponding to each operation point to determine the control output for each operation point, and this is output to each operation point in a fixed cycle.

【0028】この各操作点毎の制御出力は図示しないパ
ワーユニットを介して厚み調整手段10に入力され、こ
のパワーユニット出力によって、例えばボルトを熱的伸
縮させるヒートボルト方式では、ボルトに付設したヒー
タに電力が供給されてボルトが加熱され、それに応じて
ボルトが伸縮してギャップ11の幅を調整する。他の方
式でも電力が供給されて厚み調整手段10が動作するこ
とは同様であり、この厚み調整手段10の動作により、
シートは所望のプロファイルに管理される。
The control output for each operating point is input to the thickness adjusting means 10 via a power unit (not shown), and by the power unit output, for example, in the heat bolt system in which the bolt is thermally expanded and contracted, electric power is supplied to the heater attached to the bolt. Is supplied to heat the bolt, and the bolt expands and contracts accordingly to adjust the width of the gap 11. It is the same that power is supplied to the thickness adjusting means 10 in other systems as well, and the operation of the thickness adjusting means 10 causes
The sheet is managed in a desired profile.

【0029】ここで、制御手段9の作用の詳細について
説明する。
Here, the operation of the control means 9 will be described in detail.

【0030】図1は制御手段9の作用のフローチャート
を示したもので、制御開始より各時刻t(t=0、1、
2、・・・)毎に、厚み計8で測定したシート厚み分布
を入力し、これより厚み調整手段10の各操作点に対応
するシート厚み測定値を求め、後述する操作量時系列導
出ステップで操作量時系列を導き、操作量出力ステップ
で導き出された操作量時系列から実際に厚み調整手段1
0に出力する操作量を決定して出力するという過程を制
御終了まで繰り返す。
FIG. 1 shows a flow chart of the operation of the control means 9, and at each time t (t = 0, 1,
2, ...), the sheet thickness distribution measured by the thickness gauge 8 is input, and the sheet thickness measurement values corresponding to the respective operating points of the thickness adjusting means 10 are obtained from the sheet thickness distribution, and the operation amount time series deriving step described below is performed. The operation amount time series is derived with, and the thickness adjusting means 1 is actually obtained from the operation amount time series derived in the operation amount output step.
The process of determining and outputting the manipulated variable to be output to 0 is repeated until the control is completed.

【0031】なお、以下では離散時間で説明するが、制
御の時間間隔は厚み計8がシート1の厚みをシート幅方
向の分布として測定するのに要する時間もしくはその倍
数とするのが好ましい。具体的には数十秒から数分であ
る。こうした制御タイミングは、必ずしも固定周期であ
る必要はなく、プロセスの安定状態等に応じて適宜変更
してもよい。すなわち、製造開始時には短い周期で制御
を行い、製造安定時には長い周期で制御を行なってもよ
い。
In the following description, discrete time will be described, but the control time interval is preferably the time required for the thickness meter 8 to measure the thickness of the sheet 1 as a distribution in the sheet width direction, or a multiple thereof. Specifically, it is several tens of seconds to several minutes. Such control timing does not necessarily have to be a fixed cycle, and may be appropriately changed depending on the stable state of the process. That is, control may be performed in a short cycle at the start of manufacturing, and may be controlled in a long cycle at stable manufacturing.

【0032】プロセスモデルを用いれば、ある操作量時
系列を出力したときに、シート厚みがどのように変動し
ていくかを予測することができる。操作量時系列導出ス
テップは、この予測したシート厚みを最適に、すなわち
所定の評価関数が極値となるように、制御するにはどの
ような操作量を出力していけば良いかを導出するステッ
プである。
By using the process model, it is possible to predict how the sheet thickness will change when a certain operation amount time series is output. The operation amount time-series derivation step derives what operation amount should be output to control the predicted sheet thickness optimally, that is, so that the predetermined evaluation function becomes an extreme value. It is a step.

【0033】操作量時系列導出ステップにおける演算
は、測定したシート厚みとそれまでに出力した操作量を
用いて、予め定めた操作量時系列導出式より操作量時系
列を求めるものであるが、以下にこの操作量時系列導出
式に至るまでの考え方について説明する。
The operation amount time series deriving step is to obtain the operation amount time series from a predetermined operation amount time series deriving formula using the measured sheet thickness and the operation amount output up to that time. The concept leading up to this manipulated variable time series derivation formula will be described below.

【0034】まず、厚み調整手段10に操作量が加えら
れたときシート厚みがどのように変化するかを表すプロ
セスモデルを考える。このプロセスモデルは、操作量を
出力してからの厚み調整手段の動作の時間遅れ、シート
が口金を出てから厚み計の位置まで搬送される時間と厚
み計で幅方向の厚みプロファイルを測定するのに要する
時間からなるむだ時間および一つの厚み調整手段を操作
した場合に隣接する厚み調整手段に対応する位置のシー
ト厚みが変化する干渉を数式化したものである。以上の
条件を満たせば、どのようなプロセスモデルでも用いる
ことができる。しかし、各厚み調整手段に対して個々に
モデル化するのでは多大な時間と労力を要すだけでな
く、時系列導出式が煩雑になりすぎるい。そこでプロセ
スモデルを、厚み調整手段の操作量と対応する位置のフ
ィルム厚みの関係を表すスカラ伝達関数と個々の厚み調
整手段間の干渉を表す、少なくとも対角成分がゼロでな
い定数行列との積を用いて表現することが好ましい。こ
れにより、操作量時系列演算の際の演算が簡略化され
る。このようなプロセスモデルは、例えば離散時間伝達
関数を用いて下式で表される。式(1)
First, let us consider a process model showing how the sheet thickness changes when an operation amount is applied to the thickness adjusting means 10. This process model measures the time delay of the operation of the thickness adjusting means after the operation amount is output, the time when the sheet is conveyed from the mouthpiece to the position of the thickness gauge, and the thickness profile in the width direction is measured by the thickness gauge. It is a mathematical expression of the dead time consisting of the time required for and the interference that changes the sheet thickness at the position corresponding to the adjacent thickness adjusting means when one thickness adjusting means is operated. As long as the above conditions are satisfied, any process model can be used. However, if each thickness adjusting means is individually modeled, not only a great amount of time and labor is required, but also the time series derivation formula becomes too complicated. Therefore, the process model is calculated by multiplying the scalar transfer function, which represents the relationship between the film thickness at the position corresponding to the manipulated variable of the thickness adjusting means, and the constant matrix, in which at least the diagonal component is non-zero, which represents the interference between the individual thickness adjusting means. It is preferable to use and express. This simplifies the calculation in the operation amount time series calculation. Such a process model is expressed by the following equation using, for example, a discrete time transfer function. Formula (1)

【0035】[0035]

【数1】 [Equation 1]

【0036】ただし、yM、uはそれぞれ、各厚み調整
手段に対応する測定位置におけるシート厚みと操作量を
表し、厚み調整手段10の個数Nの要素を持つベクトル
である。またp、qは離散時間伝達関数の次数、a、b
はそれぞれの係数を表す値であり、実際のシート製造プ
ロセスの遅れ時間やむだ時間を考慮して決定するもので
ある。
However, y M and u respectively represent the sheet thickness and the operation amount at the measurement position corresponding to each thickness adjusting means, and are vectors having the number N of the thickness adjusting means 10. Further, p and q are the orders of the discrete time transfer function, a and b.
Is a value representing each coefficient and is determined in consideration of the delay time and dead time of the actual sheet manufacturing process.

【0037】むだ時間をdとする場合、式1は、以下の
式1’のように表すこともできる。式(1’)
When the dead time is d, the expression 1 can also be expressed as the following expression 1 '. Expression (1 ')

【0038】[0038]

【数2】 [Equation 2]

【0039】Wは個々の厚み調整手段間の干渉を表すN
×Nのマトリクスであり、下式で表される。式(2)
W represents the interference between the individual thickness adjusting means N
It is a matrix of × N and is expressed by the following equation. Formula (2)

【0040】[0040]

【数3】 [Equation 3]

【0041】上式で、α1(≧0)は隣の厚み調整手段
に対応する位置のシート厚みが変化する割合、α2(≧
0)は二つ離れた厚み調整手段に対応する位置のシート
厚みが変化する割合を表す。上式では、三つ以上離れた
厚み調整手段に対応する位置のシート厚みが変化する割
合を0とおいた例を示したが、α3(≧0)以降を考慮
しても良い。ただし、α3以降を0とした方が、演算が
簡単になるわりに、演算結果に対する影響が少ないので
好ましい。また後述するように各行のα1、α2の値は異
なるものであってもかまわない。
In the above equation, α 1 (≧ 0) is the rate at which the sheet thickness at the position corresponding to the adjacent thickness adjusting means changes, and α 2 (≧ 0
0) represents the rate of change in the sheet thickness at the position corresponding to the two thickness adjusting means. In the above formula, an example is shown in which the rate of change in the sheet thickness at the position corresponding to the thickness adjusting means separated by three or more is set to 0, but α 3 (≧ 0) or later may be considered. However, it is preferable to set α 3 and subsequent ones to 0 because the calculation is simplified and the calculation result is less affected. Further, as will be described later, the values of α 1 and α 2 in each row may be different.

【0042】以下に、式1を基にした操作量時系列の導
出の例を示すが、本発明はこれに限定されない。
An example of deriving the manipulated variable time series based on the equation 1 will be shown below, but the present invention is not limited to this.

【0043】式1で表されるプロセスモデルより、From the process model expressed by the equation 1,

【0044】[0044]

【数4】 [Equation 4]

【0045】とすると、時刻tにおけるシート厚みy
M(t)は、
Then, the sheet thickness y at time t
M (t) is

【0046】[0046]

【数5】 [Equation 5]

【0047】のように、表すことができる。Can be expressed as

【0048】さらに、 ΔyM(t)=yM(t)−yM(t−1) Δu(t) =u(t)−u(t−1) とおくと、将来の時刻t+1、t+2におけるシート厚
みyM(t+1)、yM(t+2)はそれぞれ
Further, if Δy M (t) = y M (t) −y M (t−1) Δu (t) = u (t) −u (t−1), then future times t + 1, t + 2 Sheet thicknesses y M (t + 1) and y M (t + 2) in

【0049】[0049]

【数6】 [Equation 6]

【0050】と表すことができ、これを漸化的に適用す
れば時刻t+j(j>1)におけるシート厚みyM(t+
j)は、
By applying this recursively, the sheet thickness y M (t +) at time t + j (j> 1) can be expressed as follows.
j) is

【0051】[0051]

【数7】 [Equation 7]

【0052】のように、シート厚みyM(t−1)、・・
・、yM(t−p)と操作量u(t−q)、・・・、u(t+
j−1)で表せる。
The sheet thickness y M (t-1), ...
,, y M (t−p) and manipulated variable u (t−q), ..., u (t +
j-1).

【0053】ここで、シート厚みyM(t−1)、・・
・、yM(t−p)と操作量u(t−1)、・・・、u(t−
q)は時刻tで決定しているものであり、g、hは式1
に示す伝達関数の係数a、bから求まるものであり、上
記プロセスモデルから事前に決まっているものであるか
ら、将来のシート厚みyM(t+j)は時刻t以降に出力
する操作量時系列u(t)、・・・、u(t+j−1)を決
めれば決定するといえる。
Here, the sheet thickness y M (t-1), ...
,, y M (tp) and manipulated variable u (t-1), ..., u (t-
q) is determined at time t, and g and h are expressed by Equation 1
The sheet thickness y M (t + j) in the future is calculated from the coefficients a and b of the transfer function shown in FIG. It can be said that it is decided if (t), ..., U (t + j−1) are decided.

【0054】上記シート厚みはプロセスモデルによるも
のであるが、プロセスモデルは実際のプロセスとは完全
には一致しなかったり、様々な外乱などによって実際の
シート厚みとは異なる。このため、最適な制御を行うた
めに、遠い将来までシート厚みを求めてこれより評価関
数を導いたとしても、結局は誤差の大きな不確実な情報
で操作量を決めることになるため好ましくない。そこ
で、操作量を変化させる時間をm(0より大きい整
数)、シート厚みを求める時間をP(0より大きい整
数)というように有限な時間区間を考える。すなわち、
操作量は時刻tからt+m−1まで変化させてその後は
一定に保つとしたとき、時刻(t+L)から(t+L+
P−1)まで(Lは整数)のシート厚みは、式(3)
The above-mentioned sheet thickness is based on the process model, but the process model does not completely match the actual process, or differs from the actual sheet thickness due to various disturbances. Therefore, even if the sheet thickness is obtained in the distant future and the evaluation function is derived from this in order to perform the optimal control, the operation amount is ultimately determined by uncertain information with a large error, which is not preferable. Therefore, consider a finite time interval such that the time for changing the operation amount is m (an integer greater than 0) and the time for obtaining the sheet thickness is P (an integer greater than 0). That is,
When the manipulated variable is changed from time t to t + m−1 and kept constant thereafter, from time (t + L) to (t + L +
The sheet thickness up to P-1) (L is an integer) is calculated by the formula (3).

【0055】[0055]

【数8】 [Equation 8]

【0056】で表される。これをベクトル行列表現すれ
ば下式となる。
It is represented by If this is expressed as a vector matrix, the following equation is obtained.

【0057】[0057]

【数9】 [Equation 9]

【0058】上記はプロセスモデルから導いた将来のシ
ート厚みである。一方、時刻tにおいて厚み計8により
実際のシート厚み分布が測定され、これより厚み調整手
段10の各操作点に対応する実際のシート厚みy(t)が
判るので、これを用いて時刻t+jでのシートの厚みを
予測すれば、予測式yP(t+j)は
The above are future sheet thicknesses derived from the process model. On the other hand, the actual sheet thickness distribution is measured by the thickness meter 8 at the time t, and the actual sheet thickness y (t) corresponding to each operation point of the thickness adjusting means 10 can be known from this, which is used at the time t + j. Predicting the sheet thickness of, the prediction formula y P (t + j) is

【0059】[0059]

【数10】 [Equation 10]

【0060】となる。上記と同様に時刻(t+L)から
(t+L+P−1)までのシート厚みの予測式は
It becomes Similar to the above, the prediction formula of the sheet thickness from time (t + L) to (t + L + P-1) is

【0061】[0061]

【数11】 [Equation 11]

【0062】となる。ただし、上式でyは要素数N個の
ベクトルy(t)をM個並べたベクトルである。すなわ
ち、yPは、上式により予測される将来のシート厚み変
化を表す時系列である。
It becomes However, in the above equation, y is a vector in which M vectors y (t) having N elements are arranged. That is, y P is a time series representing the future change in sheet thickness predicted by the above equation.

【0063】次にこの厚み予測式が最適になるように評
価する評価関数を考える。
Next, let us consider an evaluation function that evaluates the thickness prediction formula to be optimum.

【0064】まず、時刻t現在において測定されたシー
ト厚みプロファイルy(t)から、時刻t+jにおいて所
望の厚みプロファイルr(要素数Nのベクトル)へ至る
参照軌道yR(t+j)(j=1,2,・・・)を設定す
る。
First, the reference trajectory y R (t + j) (j = 1, j) from the sheet thickness profile y (t) measured at the time t to the desired thickness profile r (vector of the number of elements N) at the time t + j. 2, ...) is set.

【0065】この参照軌道は、常法に従い適宜設定すれ
ばよい。例えば、
This reference orbit may be set appropriately according to a conventional method. For example,

【0066】[0066]

【数12】 [Equation 12]

【0067】で表すことができ、βを0に近づければ所
望のプロファイルrにより速く近づく軌道となる。シー
ト厚み予測式とこの参照軌道の偏差(の2次形式)は、
小さい方がよい。
It can be expressed as follows. When β approaches 0, the trajectory becomes closer to the desired profile r. Sheet thickness prediction formula and deviation of this reference trajectory (secondary form of) are
The smaller the better.

【0068】一方、操作量については、操作量の変化Δ
uが小さい方がよい。以上の点を考慮し、評価関数Jと
して式(4)
On the other hand, regarding the manipulated variable, the change Δ in the manipulated variable
The smaller u is better. Considering the above points, the evaluation function J is given by the formula (4).

【0069】[0069]

【数13】 [Equation 13]

【0070】を使用し、この関数が極小値になる操作量
時系列を導出する。ただし、式(5)
By using, the time series of manipulated variables for which this function has a minimum value is derived. However, equation (5)

【0071】[0071]

【数14】 [Equation 14]

【0072】である。It is

【0073】ここで、上式の第1項は所望の厚みに至る
までの参照軌道と厚み予測式の偏差に関わるもの、第2
項は操作量に関わるものであり、Λ、Ψがそれぞれの寄
与度を決める。
Here, the first term of the above equation relates to the deviation between the reference trajectory and the thickness prediction equation until the desired thickness is reached, and the second term
The term is related to the manipulated variable, and Λ and Ψ determine their contributions.

【0074】一般に製膜開始時には所望の厚みとの偏差
が大きく、大きな操作量を加えて急速に偏差を小さくし
ていくべきであり、また製膜安定時には偏差が小さくな
り大きな操作量を与えるべきではないことから、上記Λ
とΨとの関係が異なる評価関数を準備し、製膜開始時に
は操作量に関係するΨの寄与を低く、製膜安定時にはΨ
の寄与を高くすることが好ましい。
Generally, the deviation from the desired thickness is large at the start of film formation, and the deviation should be rapidly reduced by adding a large operation amount. Also, when the film formation is stable, the deviation should be small and a large operation amount should be given. Therefore, the above Λ
And Ψ, different evaluation functions are prepared. At the start of film formation, the contribution of Ψ related to the manipulated variable is low, and when film formation is stable, Ψ
Is preferably increased.

【0075】このとき、評価関数Jが極小値をとるため
の必要条件は
At this time, the necessary condition for the evaluation function J to take the minimum value is

【0076】[0076]

【数15】 [Equation 15]

【0077】であり、これを満たすΔunAnd Δu n satisfying this is

【0078】[0078]

【数16】 [Equation 16]

【0079】となり、これが操作量時系列導出式であ
る。
This is the formula for deriving the manipulated variable time series.

【0080】すなわち、操作量時系列導出ステップで
は、前段で求めたシート厚み測定値y(t)を上式のy
およびyRに代入し、また時刻t−1までの情報からΔ
0、ΔyMを更新して操作量時系列の変化分Δunを導
出し、これよりu(t)、・・・、u(t+m−1)を決定
する。
That is, in the operation amount time series deriving step, the sheet thickness measurement value y (t) obtained in the preceding stage is converted into y in the above equation.
And y R , and from the information up to time t−1, Δ
u 0 , Δy M are updated to derive a change amount Δu n of the manipulated variable time series, and u (t), ..., U (t + m−1) are determined from this.

【0081】次に操作量出力ステップでは、上記で決定
した操作量時系列のうち、u(t)のみを実際に厚み調整
手段10に出力する。
Next, in the operation amount output step, only u (t) of the operation amount time series determined above is actually output to the thickness adjusting means 10.

【0082】この操作量時系列導出ステップと、操作量
出力ステップを時刻t、t+1、t+2・・・と繰り返
す。すなわち、時刻t+1では新たに測定したy(t+
1)および前回出力したu(t)を既知の値として、操作
量時系列導出式を用いてu(t+1)、・・・、u(t+
m)を決定し、これらのうちu(t+1)を厚み調整手段
10に出力する。
The operation amount time series deriving step and the operation amount output step are repeated at times t, t + 1, t + 2, .... That is, at time t + 1, the newly measured y (t +
1) and u (t) output last time are known values, and u (t + 1), ..., U (t +
m) is determined, and u (t + 1) of these is output to the thickness adjusting means 10.

【0083】また、この操作量時系列導出ステップは上
記のように毎時刻繰り返しても良いが、例えば2≦s≦
mなる整数sに対して、時刻t、t+s、t+2sとい
うようにs周期で操作量時系列を導出し、tからt+s
−1の間については、時刻tにおいて導出したu(t)、
・・・、u(t+s−1)を出力しても良い。
The operation amount time series deriving step may be repeated every time as described above, but for example, 2 ≦ s ≦
For an integer s of m, a manipulated variable time series is derived in s cycles, such as times t, t + s, and t + 2s, and t to t + s.
For −1, u (t) derived at time t,
..., u (t + s-1) may be output.

【0084】このような制御動作演算を行うことで、シ
ート厚みを素早く、高精度に所望の厚みプロファイルに
制御できる。すなわち、厚み調整手段の一つを操作する
と、隣接する調整手段に対応する箇所のシート厚みまで
変化するという干渉現象および、厚み調整手段の一つを
操作してから、その結果が対応位置での厚み測定結果に
あらわれるまでのむだ時間を数式化したプロセスモデル
を用いて決定した厚み予測式を最適化する操作量時系列
を決定して加えているため、シート厚みは目標値に極め
て速く、高精度に収束する。
By performing such control operation calculation, the sheet thickness can be quickly and accurately controlled to a desired thickness profile. That is, when one of the thickness adjusting means is operated, the interference phenomenon that the sheet thickness of the portion corresponding to the adjacent adjusting means is changed, and after operating one of the thickness adjusting means, the result is obtained at the corresponding position. Since the operation amount time series that optimizes the thickness prediction formula determined using the process model in which the dead time until it appears in the thickness measurement result is determined and added, the sheet thickness is extremely fast and high to the target value. Converge to accuracy.

【0085】さらに、プロセスモデルに誤差がある場合
や、他の外乱がある場合のように実際の厚み測定値yが
予測式yPと異なるものになっても、予測式の決定、最
適な操作時系列の決定を新たに測定した厚み測定値yを
用いて頻繁に行うことで、モデルの誤差か外乱による偏
差の蓄積が起こらず、制御を通して準最適な操作量を決
定することができるため、シート厚みを目標値に素早
く、高精度に制御できる。
Further, even when the actual thickness measurement value y is different from the prediction formula y P as in the case where the process model has an error or when there is another disturbance, the prediction formula is determined and the optimum operation is performed. By frequently determining the time series using the newly measured thickness measurement value y, accumulation of deviation due to model error or disturbance does not occur, and a sub-optimal manipulated variable can be determined through control. The sheet thickness can be quickly and accurately controlled to the target value.

【0086】ここで用いるプロセスモデルは上記説明に
用いた、パラメトリックモデルの他に、時刻t=0で操
作量としてインパルス状出力を厚み調整手段10与えた
ときに、シート厚みが時刻t=1,2,3,・・・でど
のように変化するかを記述したインパルス応答モデル
や、時刻t=0で操作量としてステップ状出力を厚み調
整手段10に与えたときに、シート厚みが時刻t=1,
2,3,・・・でどのように変化するかを記述したステ
ップ応答モデル、さらには状態変数を用いて、操作量と
状態変数の関係、状態変数とシート厚みの関係を記述す
る状態空間モデル等を用いることができる。
The process model used here is, in addition to the parametric model used in the above description, when the thickness adjusting means 10 is given an impulse-like output as an operation amount at the time t = 0, the sheet thickness becomes the time t = 1, When the step response is given to the thickness adjusting means 10 as the manipulated variable at time t = 0, the sheet thickness changes at time t = 1,
Step response model describing how it changes in 2, 3, ..., and further a state space model describing the relationship between the manipulated variable and the state variable and the relationship between the state variable and the sheet thickness using the state variable Etc. can be used.

【0087】またプロセスモデルはシート幅方向におい
て均一の関係としても良いが、端部と中央部にそれぞれ
対応する部分で異なるものとしても良い。すなわち、一
つの厚み調整手段を操作した結果が隣接する厚み調整手
段に対応するシート厚みに影響する干渉が、端部では広
範囲にわたることから、端部では隣接する厚み調整手段
への干渉の割合を中央部のものに対して大きくすること
が好ましい。
The process model may have a uniform relationship in the sheet width direction, but may have different relationships at the portions corresponding to the end portion and the central portion. That is, since the interference of the result of operating one thickness adjusting means on the sheet thickness corresponding to the adjacent thickness adjusting means is wide at the end portion, the ratio of the interference to the adjacent thickness adjusting means at the end portion is It is preferable to make it larger than that of the central portion.

【0088】上記実施形態例における制御手段の各動作
は、コンピュータと、それを動作させるプログラムなど
によって実現される。このようなプログラム及び各種の
記憶手段のデータはフレキシブルディスク、MO、CD
−ROM等のコンピュータ読み取り可能な有形媒体や有
線または無線のネットワークのような伝送手段を通じて
流通される。
Each operation of the control means in the above embodiment is realized by a computer and a program for operating the computer. Such programs and data in various storage means are flexible disks, MOs, CDs.
-Distributed through a computer-readable tangible medium such as a ROM or a transmission means such as a wired or wireless network.

【0089】[0089]

【実施例】ここで、本発明を用いてシートを製造した実
施例について説明する。 (実施例1)図2に示すシートの製造設備を用いて、厚
さ2.7μmのポリエステルフィルムを製造した。製膜
幅は3.5m、製膜速度は製品部で175m/分であ
る。厚み調整手段10はカートリッジヒーターを内蔵し
たボルトを熱的に膨張収縮させてギャップ11を調整す
るヒートボルト方式を用い、厚み制御に使用したヒート
ボルトの数は45本である。厚み計8としては特公平4
−522に記載の、光の干渉現象を利用した光干渉式厚
さ計を使用した。この厚み計は、フィルムの幅方向に6
0秒の周期でスキャンしながら、フィルムの幅方向に対
して15mm間隔でフィルム厚みを測定する。また、制
御を行うタイミングは、厚み計のスキャン周期と同じ6
0秒とした。
EXAMPLES Now, examples of producing a sheet by using the present invention will be described. (Example 1) A 2.7 μm-thick polyester film was manufactured using the sheet manufacturing facility shown in FIG. The film-forming width is 3.5 m, and the film-forming speed is 175 m / min in the product section. The thickness adjusting means 10 uses a heat bolt method of thermally expanding and contracting a bolt containing a cartridge heater to adjust the gap 11, and the number of heat bolts used for thickness control is 45. Special fairness as a thickness gauge 8
An optical interference type thickness gauge described in -522 using an optical interference phenomenon was used. This thickness meter is 6 in the width direction of the film.
The film thickness is measured at intervals of 15 mm in the width direction of the film while scanning at a cycle of 0 second. In addition, the control timing is the same as the scan cycle of the thickness gauge.
It was set to 0 seconds.

【0090】プロセスモデルとしては、式1’のプロセ
スモデルを用い、ある1本のヒートボルトに所定の操作
量を加えたときの、このヒートボルトに対応する測定位
置近傍のシート厚み変化から下式のように定めた。
As the process model, the process model of the formula 1'is used, and when a predetermined operation amount is applied to a certain heat bolt, the following formula is derived from the change in the sheet thickness near the measurement position corresponding to this heat bolt. I decided as follows.

【0091】[0091]

【数17】 [Equation 17]

【0092】すなわち、式1’において、p=2、q=
3、d=2、a2'=-0.012、a1'=-0.54、a0'=-0.71
4、b3=-0.315、b2=-0.012、b1=1.57、式2におい
て、α1=0.65、α2=0.25とした。
That is, in equation 1 ', p = 2 and q =
3, d = 2, a 2 '= -0.012, a 1 ' = -0.54, a 0 '= -0.71
4, b 3 = -0.315, b 2 = -0.012, b 1 = 1.57, and in Expression 2, α 1 = 0.65 and α 2 = 0.25.

【0093】また、式3のL、P、mはそれぞれ0、1
0、7とし、式5に示す評価関数Jの係数λi(i=
1,2,・・・,P)、ψj(j=1,2,・・・,
m)はそれぞれ1.0、0.8とした。
Further, L, P and m in the equation 3 are 0 and 1 respectively.
0 and 7, the coefficient λ i of the evaluation function J shown in Expression 5 (i =
1, 2, ..., P), ψ j (j = 1, 2, ..., P
m) was set to 1.0 and 0.8, respectively.

【0094】まず、複数のヒートボルトに操作量を加え
て故意に厚みむら(厚みの最大値と最小値の差を厚み平
均値で割ったもの)を作り、本発明の方法によってフィ
ルムの厚みを制御した。
First, an operation amount is applied to a plurality of heat bolts to intentionally create thickness unevenness (difference between maximum and minimum values of thickness divided by average thickness value), and the thickness of the film is measured by the method of the present invention. Controlled.

【0095】さらに比較のため、同程度の厚みムラを作
って、従来制御(PID制御)を用いてフィルムの厚み
を制御した。
Further, for comparison, the thickness of the film was controlled by using the conventional control (PID control) by making the same thickness unevenness.

【0096】図4はPID制御を用いた制御結果、図5
は本発明の技術による制御結果であり、図4では約30
分の制御で厚みむらは8.4%から7.4%までしか改
善していないが、図5では同様に約30分の制御で厚み
むらは9.1%から1.4%に改善し、本発明による技
術を用いることで、シート厚みを所望のプロファイルに
素早く、かつ精度良く制御できることが確認できた。
FIG. 4 shows the control result using PID control, and FIG.
Is a control result by the technique of the present invention, and is about 30 in FIG.
Although the thickness unevenness is improved only from 8.4% to 7.4% by controlling the minute, the thickness unevenness is similarly improved from 9.1% to 1.4% by controlling about 30 minutes in FIG. It was confirmed that the sheet thickness can be quickly and accurately controlled to a desired profile by using the technique according to the present invention.

【0097】(実施例2)次に、実施例1と同程度の厚
みむらを作り、厚みむらが大きい制御開始直後は、操作
量に関係するψの寄与を低くして大きな操作量を加える
ように、式5に示す評価関数Jの係数λi(i=1,
2,・・・,P)、ψj(j=1,2,・・・,m)を
それぞれ1.0、0.5とし、厚みむらが5%になった
時点で、それぞれを1.0、0.8に変えた。その結
果、実施例1よりも素早く厚みむらを改善することがで
きた。
(Embodiment 2) Next, thickness unevenness similar to that in Embodiment 1 is created, and immediately after the start of control with a large thickness unevenness, the contribution of ψ related to the manipulated variable is reduced to add a large manipulated variable. , The coefficient λ i of the evaluation function J shown in Expression 5 (i = 1,
2, ..., P) and ψ j (j = 1, 2, ..., M) are set to 1.0 and 0.5, respectively, and when the thickness unevenness is 5%, the values are set to 1. I changed it to 0 and 0.8. As a result, the thickness unevenness could be improved more quickly than in Example 1.

【0098】(実施例3)次に、フィルム幅方向に対し
て中心から左右それぞれ35%を中央部、残り左右それ
ぞれ15%を端部と設定し、中央部、端部それぞれ任意
のヒートボルトに所定の操作量を加え、それぞれのヒー
トボルトに対応するシート厚み測定位置近傍のシート厚
みが安定したときのシート厚み分布から、式2のα1
α2を、中央部では、α1=0.6、α2=0.2、端部
ではα1=0.7、α2=0.3と定め、実施例1、2と
同程度の、シート全幅にわたる厚みむらを作り、本発明
の方法を適用してフィルムの厚みを制御した。その結
果、実施例1、2よりもさらにフィルム全幅にわたって
厚みが均一になり、安定して製膜ができた。
(Embodiment 3) Next, with respect to the width direction of the film, 35% on each side from the center is set as a central portion, and the remaining 15% on each side is set as an end portion. From the sheet thickness distribution when the sheet thickness in the vicinity of the sheet thickness measurement position corresponding to each heat bolt is stabilized by adding a predetermined operation amount, α 1 in Equation 2
α 2 is set to α 1 = 0.6 and α 2 = 0.2 at the central portion and α 1 = 0.7 and α 2 = 0.3 at the end portions, which are similar to those of the first and second embodiments. The thickness of the film was controlled by applying the method of the present invention by making uneven thickness over the entire width of the sheet. As a result, the thickness became more uniform over the entire width of the film than in Examples 1 and 2, and stable film formation was possible.

【0099】[0099]

【発明の効果】以上説明したように、本発明のシート製
造方法は、シート厚みを素早く高速に所望の厚みプロフ
ァイルに制御できるため、シートの製造開始時に製品と
して合格する所定の厚みむらのレベルに達するまでの時
間を短縮することができ、この間に製造する不良品の量
を著しく削減できるとともに、製造効率を向上でき、シ
ートのコストダウンが可能になる。また、製膜中に例え
ば延伸装置の温度分布が変わるなどの変化があってシー
トの厚みプロファイルが変動したとしても、これを素早
く所望のプロファイルに制御できるため、結果としてシ
ートの厚み均一性が良くなり、シートの品質を向上する
ことができる。
As described above, the sheet manufacturing method of the present invention can control the sheet thickness to a desired thickness profile quickly and at a high speed, so that the sheet has a predetermined thickness unevenness level that is acceptable as a product at the start of sheet manufacturing. It is possible to shorten the time required to reach the target, significantly reduce the amount of defective products manufactured during this period, improve the manufacturing efficiency, and reduce the cost of the sheet. Even if the thickness profile of the sheet fluctuates due to changes such as the temperature distribution of the stretching device during film formation, this can be quickly controlled to the desired profile, resulting in good sheet thickness uniformity. Therefore, the quality of the sheet can be improved.

【図面の簡単な説明】[Brief description of drawings]

【図1】本発明の一実施形態例における、シートの厚み
制御のフローチャートである。
FIG. 1 is a flowchart of sheet thickness control in an embodiment of the present invention.

【図2】本発明の一実施形態例におけるシートの製造設
備の全体概略構成を示す図である。
FIG. 2 is a diagram showing an overall schematic configuration of a sheet manufacturing facility according to an embodiment of the present invention.

【図3】図2に示す口金の要部拡大斜視図である。FIG. 3 is an enlarged perspective view of a main part of the mouthpiece shown in FIG.

【図4】従来方法によるシート製造時のシート厚み制御
結果である。
FIG. 4 is a result of sheet thickness control during sheet production by a conventional method.

【図5】本発明の一実施例によるシート製造時の厚み制
御結果である。
FIG. 5 is a thickness control result at the time of manufacturing a sheet according to an embodiment of the present invention.

【符号の説明】[Explanation of symbols]

1 :シート 2 :延伸機 3 :押出機 4 :口金 5 :冷却ロール 6 :巻取機 7 :搬送ロール 8 :厚み計 9 :制御手段 10:厚み調整手段 11:間隙 1: Sheet 2: Stretching machine 3: Extruder 4: Clasp 5: Cooling roll 6: Winder 7: Transport roll 8: Thickness gauge 9: Control means 10: Thickness adjusting means 11: Gap

───────────────────────────────────────────────────── フロントページの続き Fターム(参考) 4F207 AG01 AP11 AR12 KA01 KA17 KL76    ─────────────────────────────────────────────────── ─── Continued front page    F-term (reference) 4F207 AG01 AP11 AR12 KA01 KA17                       KL76

Claims (12)

【特許請求の範囲】[Claims] 【請求項1】 複数の厚み調整手段を備えたダイを用い
て原料を押し出し、成形してシートとなすとともに、前
記厚み調整手段に加える操作量を制御して前記シートの
厚みを制御するシートの製造方法であって、前記シート
の幅方向の厚み分布を測定するステップと、前記操作量
とシート厚みとの関係を表すプロセスモデルおよび前記
シート厚み測定値に基づいて求められる将来のシート厚
み変化を所定の評価関数を用いて評価し、該評価関数が
極小値となる操作量時系列を導出するステップと、導出
された該操作量時系列のうち少なくとも最初の操作量を
前記厚み調整手段に出力するステップとを所定のタイミ
ングで繰り返すことを特徴とするシートの製造方法。
1. A sheet for controlling the thickness of a sheet by extruding a raw material using a die equipped with a plurality of thickness adjusting means to form a sheet and controlling an operation amount applied to the thickness adjusting means. A step of measuring the thickness distribution in the width direction of the sheet, which is a manufacturing method, and a future sheet thickness change obtained based on the process model and the sheet thickness measurement value representing the relationship between the operation amount and the sheet thickness. Evaluating using a predetermined evaluation function, deriving a manipulated variable time series in which the evaluated function is a minimum value, and outputting at least the first manipulated variable in the derived manipulated variable time series to the thickness adjusting means. The method for manufacturing a sheet, characterized in that the step of performing is repeated at a predetermined timing.
【請求項2】 前記所定の評価関数は、前記シート厚み
変化および前記操作量の変化に基づくものである請求項
1に記載のシートの製造方法。
2. The sheet manufacturing method according to claim 1, wherein the predetermined evaluation function is based on a change in the sheet thickness and a change in the operation amount.
【請求項3】 前記所定の評価関数として、製造開始時
と製造安定時とで異なる評価関数を使用し、かつ、製造
開始時には製造安定時よりもシート厚み変化の寄与度が
操作量の寄与度に対して高くなるものを使用する請求項
2に記載のシートの製造方法。
3. As the predetermined evaluation function, different evaluation functions are used at the start of manufacturing and at the time of stable manufacturing, and the contribution of the change in sheet thickness at the start of manufacturing is more than that at the stable manufacturing. The method for producing a sheet according to claim 2, wherein a sheet having a higher price than the sheet is used.
【請求項4】 前記プロセスモデルとして、伝達関数と
少なくとも対角成分がゼロでない定数行列の積で表され
るものを用いる請求項1〜3のいずれかに記載のシート
の製造方法。
4. The method for producing a sheet according to claim 1, wherein a process function represented by a product of a transfer function and a constant matrix in which at least a diagonal component is not zero is used.
【請求項5】 前記定数行列として、シート幅方向にお
ける端部と中央部とに対応する部分でそれぞれ異なる定
数を用いる請求項4に記載のシートの製造方法。
5. The method of manufacturing a sheet according to claim 4, wherein different constants are used for the constant matrix at portions corresponding to an end portion and a central portion in the sheet width direction.
【請求項6】 シートの幅方向の厚み分布を測定する厚
み測定手段によって測定された幅方向の各部のシート厚
み測定値に基づいて対応する位置のシートの厚み調整手
段へ操作量を与える制御装置であって、前記操作量とシ
ート厚みとの関係を表すプロセスモデルおよび前記シー
ト厚み測定値に基づいて求められる将来のシート厚み変
化を所定の評価関数を用いて評価し、該評価関数が極小
値となる操作量時系列を導出する操作量時系列導出手段
と、導出された該操作量時系列のうち少なくとも最初の
操作量を前記厚み調整手段に出力する操作量出力手段と
を備えたことを特徴とするシートの厚み制御装置。
6. A control device for giving an operation amount to a thickness adjusting means of a sheet at a corresponding position based on a sheet thickness measurement value of each portion in the width direction measured by a thickness measuring means for measuring a thickness distribution of the sheet in the width direction. The sheet thickness change in the future obtained based on the process model and the sheet thickness measurement value representing the relationship between the manipulated variable and the sheet thickness is evaluated using a predetermined evaluation function, and the evaluation function has a minimum value. And a manipulated variable output means for outputting at least the first manipulated variable in the derived manipulated variable time series to the thickness adjusting means. Characteristic sheet thickness control device.
【請求項7】 前記操作量時系列導出手段は、前記所定
の評価関数として、製造開始時と製造安定時とで異なる
評価関数を使用し、かつ、製造開始時には製造安定時よ
りもシート厚み変化の寄与度が操作量の寄与度に対して
高くなるものを使用するものである請求項6に記載のシ
ートの厚み制御装置。
7. The manipulated variable time series deriving means uses, as the predetermined evaluation function, different evaluation functions at the start of production and at the time of stable production, and at the start of production, changes in sheet thickness than at stable production. 7. The sheet thickness control device according to claim 6, wherein the contribution degree of is higher than that of the manipulated variable.
【請求項8】 前記プロセスモデルとして、伝達関数と
少なくとも対角成分がゼロでない定数行列の積で表され
るものを用いる請求項6または7に記載のシートの厚み
制御装置。
8. The sheet thickness control device according to claim 6, wherein the process model is represented by a product of a transfer function and a constant matrix in which at least a diagonal component is not zero.
【請求項9】 前記操作量時系列導出手段は、前記定数
行列として、シート幅方向における端部と中央部とに対
応する部分でそれぞれ異なる定数を用いる請求項8に記
載のシートの厚み制御装置。
9. The sheet thickness control device according to claim 8, wherein the operation amount time series deriving means uses, as the constant matrix, different constants at portions corresponding to an end portion and a central portion in the sheet width direction. .
【請求項10】 請求項1〜5のいずれかに記載のシー
ト製造方法によって製造されたシート。
10. A sheet manufactured by the sheet manufacturing method according to claim 1.
【請求項11】 シートの幅方向の各部の厚みの測定値
を入力するステップと、前記各部の厚みの目標値と前記
測定値との差を算出するステップと、前記各部の差に基
づいて厚み調整手段に加える操作量を算出するステップ
とを所定のタイミングで繰り返す動作をコンピュータに
実現させるプログラムを記憶した記憶媒体であって、前
記操作量を算出するステップは、前記操作量とシート厚
みとの関係を表すプロセスモデルおよび前記シート厚み
測定値に基づいて求められる将来のシート厚み変化を所
定の評価関数を用いて評価し、該評価関数が極小値とな
る操作量時系列を導出するステップと、導出された該操
作量時系列のうち少なくとも最初の操作量を前記厚み調
整手段に出力するステップを含むことを特徴とするコン
ピュータ読み取り可能な記憶媒体。
11. A step of inputting a measured value of the thickness of each part in the width direction of the sheet, a step of calculating a difference between a target value of the thickness of each part and the measured value, and a thickness based on the difference of each part. A storage medium that stores a program for causing a computer to perform the operation of repeating the operation amount to be added to the adjusting means at a predetermined timing, wherein the operation amount calculating step includes the operation amount and the sheet thickness. Evaluating a future sheet thickness change obtained based on the process model and the sheet thickness measurement value representing the relationship using a predetermined evaluation function, and deriving a manipulated variable time series in which the evaluation function is a minimum value, Computer readable, characterized in that it includes a step of outputting at least a first operation amount of the derived operation amount time series to the thickness adjusting means. A capable storage medium.
【請求項12】 シートの幅方向の各部の厚みの測定値
を入力するステップと、前記各部の厚みの目標値と前記
測定値との差を算出するステップと、前記各部の差に基
づいて厚み調整手段に加える操作量を算出するステップ
とを所定のタイミングで繰り返す動作をコンピュータに
実現させるプログラムであって、前記操作量を算出する
ステップは、前記操作量とシート厚みとの関係を表すプ
ロセスモデルおよび前記シート厚み測定値に基づいて求
められる将来のシート厚み変化を所定の評価関数を用い
て評価し、該評価関数が極小値となる操作量時系列を導
出するステップと、導出された該操作量時系列のうち少
なくとも最初の操作量を前記厚み調整手段に出力するス
テップを含むことを特徴とするプログラム。
12. A step of inputting a measured value of the thickness of each part in the width direction of the sheet, a step of calculating a difference between a target value of the thickness of each part and the measured value, and a thickness based on the difference of each part. A program for causing a computer to realize an operation of repeating a step of calculating an operation amount applied to the adjusting means at a predetermined timing, wherein the step of calculating the operation amount is a process model representing a relationship between the operation amount and the sheet thickness. And a step of evaluating a future sheet thickness change obtained based on the sheet thickness measurement value using a predetermined evaluation function, and deriving an operation amount time series in which the evaluation function has a minimum value, and the derived operation. A program including a step of outputting at least a first manipulated variable in a quantitative time series to the thickness adjusting means.
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JP2007296673A (en) * 2006-04-28 2007-11-15 Japan Steel Works Ltd:The Position corresponding device and position corresponding method
JP2008135010A (en) * 2006-10-02 2008-06-12 Fisher Rosemount Syst Inc Updating and utilizing dynamic process simulation for in-operating process environment
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WO2007063927A1 (en) * 2005-11-30 2007-06-07 Toray Industries, Inc. Method of producing sheet and sheet producing device
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CN112996647B (en) * 2018-11-06 2024-04-30 温德默勒及霍乐沙两合公司 Method and device for controlling nozzle gap of outlet nozzle of flat film machine
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US11964418B2 (en) 2018-11-06 2024-04-23 Windmöller & Hölscher Kg Adjusting device and method for controlling an exit thickness of a nozzle exit gap of a flat film machine
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JP7431570B2 (en) 2019-03-15 2024-02-15 株式会社日本製鋼所 Resin film manufacturing equipment and resin film manufacturing method
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JP7496940B2 (en) 2020-12-09 2024-06-07 スリーエム イノベイティブ プロパティズ カンパニー Slot die positioning with ringing constraints
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