JP3878086B2 - Balance control device for tandem rolling mill - Google Patents

Description

【００６３】
ここで、上記（２４）式の＊部分には、影響係数、ミル剛性係数等から成る値が入る。例えば、Ａm&c の６行、７列目の要素ａ6,7は、次式であらわされる。
【００６４】
【数２】

【００６５】
上記（２３）式は、変数３８個、式３８本の線形連立方程式であり、Ａm&c がフルランクであり、かつ外乱ｄが既知であれば、解は次式から一意に求められる（尚、通常の圧延では、Ａm&c はフルランクである）。
ｘm&c ＝Ａm&c^-1・ｄ （２６）
上記外乱ｄには、原板板厚変動・変形抵抗変動などのタンデム圧延機１の外部からの外乱ｄextと、バランス制御の操作量による外乱ｄmbcとが含まれていると考えることができる。すなわち、外乱ｄは、次式で表わされる。
ｄ＝ｄext＋ｄmbc （２７）
上記バランス制御の操作量は、４つのスタンド間目標板厚と４つのスタンド間目標張力である。このときバランス制御の操作量による外乱ｄmbcは、次の式（２２）のように表される。
ｄmbc ＝Ａpart・ｕFF （２８）
ここで、行列Ａpart（３８×８）は、制御対象の静特性を表わす行列Ａm&c から、上記バランス制御の操作量の拘束条件に相当する行のみを抜き出し、他の行の成分はすべて０とし、さらにバランス制御の操作量に相当する列のみを取り出したものである。具体的には上記（２４）式のＡm&c の１６〜１９行及び２１〜２４行を抜き出し、他の行の成分はすべて０とし、さらに２〜５列及び８〜１１列のみを取り出したものである。また、ベクトルｕFF（８×１）は、バランス制御の操作量を表わすベクトルであり、ベクトルｕFF＝（ｕ1、ｕ2、…、ｕ8）^Tの各成分は、
ｕ1：圧延スタンド１１の目標出側板厚
ｕ2：圧延スタンド１２の目標出側板厚
ｕ3：圧延スタンド１３の目標出側板厚
ｕ4：圧延スタンド１４の目標出側板厚
ｕ5：圧延スタンド１１の目標出側張力
ｕ6：圧延スタンド１２の目標出側張力
ｕ7：圧延スタンド１３の目標出側張力
ｕ8：圧延スタンド１４の目標出側張力
である。
【００６６】
従って、上記制御対象の状態量の変化は、次の（２９）式のようになる。
ｘm&c＝Ａm&c^-1・Ａpart・ｕFF＋Ａm&c^-1・ｄext （２９）
また、出力方程式を次の（３０）式のように定義する。
ｙm&c＝Ｃ・ｘm&c （３０）
ここで、行列Ｃ （８×３８）は、制御対象の状態方程式の係数行列であり、ベクトルｙm&c（８×１）は、制御対象への出力、すなわち、バランス制御の制御量である。この例では、行列Ｃは、次の（３１）式のようになる。
【００６７】
【数３】

【００６８】
ここで、上記（３１）式において＊印で表されている係数のうち、圧延荷重関係の係数は、以下の通りである。
ｃ1,29＝１／５ ｃ1,30＝−１／５
ｃ2,30＝１／５ ｃ2,31＝−１／５
ｃ3,31＝１／５ ｃ3,32＝−１／５
ｃ4,32＝１／５ ｃ4,33＝−１
また、モータ電流関係の係数は、以下の通りである。
ｃ5,34＝１／５ ｃ5,35＝−１／５
ｃ6,35＝１／５ ｃ6,36＝−１／５
ｃ7,36＝１／５ ｃ7,37＝−１／５
ｃ8,37＝１／５ ｃ8,38＝−１
このとき、出力ベクトルｙm&cの各成分は、以下のようになる。
ｙ1：ΔＰ1／（５×Ｐ1）−ΔＰ2／（５×Ｐ2）
（圧延スタンド１１の圧延荷重偏差−圧延スタンド１２の圧延荷重偏差）
ｙ2：ΔＰ2／（５×Ｐ2）−ΔＰ3／（５×Ｐ3）
（圧延スタンド１２の圧延荷重偏差−圧延スタンド１３の圧延荷重偏差）
ｙ3：ΔＰ3／（５×Ｐ3）−ΔＰ4／（５×Ｐ4）
（圧延スタンド１３の圧延荷重偏差−圧延スタンド１４の圧延荷重偏差）
ｙ4：ΔＰ4／（５×Ｐ4）−ΔＰ5／Ｐ5
（圧延スタンド１４の圧延荷重偏差−圧延スタンド１５の圧延荷重偏差）
ｙ5：ΔＧ1／（５×Ｇ1）−ΔＧ2／（５×Ｇ2）
（圧延スタンド１１のモータ電流偏差−圧延スタンド１２のモータ電流偏差）
ｙ6：ΔＧ2／（５×Ｇ2）−ΔＧ3／（５×Ｇ3）
（圧延スタンド１２のモータ電流偏差−圧延スタンド１３のモータ電流偏差）
ｙ7：ΔＧ3／（５×Ｇ3）−ΔＧ4／（５×Ｇ4）
（圧延スタンド１３のモータ電流偏差−圧延スタンド１４のモータ電流偏差）
ｙ8：ΔＧ4／（５×Ｇ4）−ΔＧ5／Ｇ5
（圧延スタンド１４のモータ電流偏差−圧延スタンド１５のモータ電流偏差）
なお、上記係数行列Ｃは、一例であり、出力ベクトルｙm&cの各成分が、板厚張力制御装置２の目標値となる変数及び制御不可となる変数とを除いた３８の変数から組み合わせた互いに独立な変数であるならば、それらの線形結合として任意に選ぶことができるのは既に述べた通りである。
【００６９】
（２９）式及び（３０）式より、制御対象の影響係数は、次の（３２）式で与えられる。
ｙm&c＝Ｃ・Ａm&c^-1・Ａpart・ｕFF＋Ｃ・Ａm&c^-1・ｄext （３２）
従って、フィードフォワード制御の制御則は、次の（３３）式で与えられる。
ｕFF＝（Ｃ・Ａm&c^-1・Ａpart）^-1・ｙm&c−（Ｃ・Ａm&c^-1・Ａpart）^-1・Ｃ・Ａm&c^-1・ｄext （３３）
ここで、フィードフォワード制御のゲイン行列ＧmbcFF（８×８）を次に（３４）式で定義する。
ＧmbcFF＝（Ｃ・Ａm&c^-1・Ａpart）^-1 （３４）
（３３）式に（３４）式を代入して、次の（３５）式が得られる。
ｕFF＝ＧmbcFF・ｙm&c−（Ｃ・Ａm&c^-1・Ａpart）^-1・Ｃ・Ａm&c^-1・ｄext （３５）
（３５）式により、目標とする出力ベクトルｙm&cを得るためには、出力ベクトルｙm&cにゲイン行列ＧmbcFFを乗じたもの（第１項）と、外乱ｄextに関する補償分（第２項）との和を操作量ｕとすればよいことが分かる。
【００７０】
しかし、実際には、モデル化の誤差や原板の硬度変動等の外乱ｄextは未知であることから、第２項を無視して、次の（３６）式を制御に用いることとする。
ｕFF＝ＧmbcFF・ｙm&c （３６）
この（３６）式によって、目標とする出力ベクトルｙm&cを得るための操作量ｕFF（フィードフォワード補償量）が求められる。すなわち、フィードフォワード補償部３１は、（３６）式を用いてフィードフォワード補償量ｕFFを算出するものである。
【００７１】
なお、図２に示すフィードフォワード補償部３１は、ゲイン行列ＧmbcFFの前後に、フィードフォワード補償量が急激に変動することを防止するためにローパスフィルタを付与したり、圧延速度等に応じてフィードフォワード補償量を調整するために別のゲインを付加したり、安全等のためにフィードフォワード補償量の大きさを制限するリミッタを付加する形態でもよい。
【００７２】
フィードバック補償部３２は、フィードバック補償量を公知の方法で求めるものである。例えば、特開２００１−９５１４号公報に開示されているように、制御対象を動的にモデル化した動特性モデルを用いて設計された制御則を用いてフィードバック補償量を求めるものである。
【００７３】
図３は、バランス制御装置３の動作を表わすフローチャートである。まず、バランス制御を開始するか否かの判定が行われる（ステップＳ１）。例えば、圧延開始後の加速完了時、または、圧延開始から所定時間経過後にバランス制御が開始される。この判定が否定された場合には、この判定が肯定されるまで待機する。この判定が肯定された場合には、目標荷重算出部３４によって目標圧延荷重が求められ、目標電流算出部３６によって目標モータ電流が求められる（ステップＳ３）。ついで、目標値算出部３７によって目標値が求められる（ステップＳ５）。そして、フィードフォワード補償部３１によって、目標圧延荷重と目標モータ電流とを用いて（３６）式に基づいてフィードフォワード補償量が求められる（ステップＳ７）。
【００７４】
次いで、フィードバック補償部３２によって、目標圧延荷重と目標モータ電流とを用いてフィードバック補償量が求められる（ステップＳ９）。次に、加算部３３によって、フィードバック補償量とフィードフォワード補償量とが加算されて操作量が求められる（ステップＳ１１）。そして、この操作量が制御対象に対して出力される（ステップＳ１３）。その後、バランス制御を終了するか否かの判定が行われる（ステップＳ１５）。例えば、圧延終了前の減速開始時、または、圧延開始から所定時間経過後にバランス制御が終了される。この判定が否定された場合には、ステップＳ７に戻り、制御が継続して実施される。この判定が肯定された場合には、処理が終了される。
【００７５】
図４は、バランス制御装置３のフィードフォワード制御の効果を示す図である。（ａ−１）は、フィードフォワード制御を行なわない場合（１自由度制御系の場合）の外乱応答であり、（ａ−２）は、フィードフォワード制御を行なわない場合（１自由度制御系の場合）の目標値応答である。また、（ｂ−１）は、フィードフォワード制御を行なう場合（２自由度制御系の場合）の外乱応答であり、（ｂ−２）は、フィードフォワード制御を行なう場合（２自由度制御系の場合）の目標値応答である。ただし、フィードフォワード制御に用いる（３６）式のフィードフォワード補償量ｕFFに誤差が無い場合を示している。
【００７６】
（ａ−１）及び（ａ−２）に示すように１自由度制御系の場合には、外乱応答の応答速度と目標値応答の応答速度とは同じである。これに対して、（ｂ−１）及び（ｂ−２）に示すように２自由度制御系の場合には、外乱応答の応答速度と目標値応答の応答速度とを独立に制御することが可能であり、目標値応答の応答性を高めることができる。（ｂ−２）では、目標値をステップ状に変化させているが、所定時間の間でランプ状に変化させる形態でも良いし、フィードバック制御の安定性に影響を与えない程度の滑らかに値の変化する関数で変化させた後一定値とする形態でも良い。
【００７７】
図５は、バランス制御装置３のフィードバック制御の効果を示す図である。ただし、フィードフォワード制御に用いる（３６）式のフィードフォワード補償量ｕFFに誤差がある場合を示している。（ａ）は、フィードバック補償部３２が制御量ｙと当制御量の目標値ｒとの偏差を積分演算する積分特性を有しない場合の目標値応答であり、（ｂ）は、フィードバック補償部３２が制御量ｙと当制御量の目標値ｒとの偏差を積分演算する積分特性を有する場合の目標値応答である。
【００７８】
（ａ）に示すように、フィードバック補償部３２が制御量ｙと当制御量の目標値ｒとの偏差を積分演算する積分特性を有しない場合には、フィードバック補償部３２によってフィードフォワード補償量ｕFFの誤差が修正されるものの、定常偏差を解消する（略零とする）ことができない。これに対して、（ｂ）に示すように、フィードバック補償部３２が制御量ｙと当制御量の目標値ｒとの偏差を積分演算する積分特性を有する場合には、フィードバック補償部３２によってフィードフォワード補償量ｕFFの誤差が修正され、定常偏差を解消する（略零とする）ことができる。
【００７９】
図６〜図９は、バランス制御装置３の効果を示す図である。ここでは、便宜上、（５）式の圧延スタンド１２、１３、１４の基準モータ電流は同じ値であり、係数ｍ、ｎも同じ値である。そして、バランス制御開始時のモータ電流Ｇ2、Ｇ3、Ｇ4の平均値を圧延スタンド１２、１３、１４の目標モータ電流とするものとする。すなわち、バランス制御装置３は、圧延スタンド１２、１３、１４のモータ電流を、バランス制御開始時のモータ電流Ｇ2、Ｇ3、Ｇ4の平均値に制御するものである。図６〜図９において、（ａ）は、圧延速度の変化であり、（ｂ）は、圧延スタンド１１〜１５のモータ電流Ｇiの変化であり、（ｃ）は、圧延スタンド１１〜１５の圧延荷重Ｐiの変化であり、（ｄ）は、圧延スタンド１１〜１４の出側目標板厚ｈiの変化であり、（ｅ）は、圧延スタンド１１〜１４の出側目標張力ｑfiの変化である。図６は、バランス制御装置３が無い場合であり、図７は、バランス制御装置３が、フィードフォワード制御を行なわない場合（フィードバック制御のみを行なう場合）であり、図８は、バランス制御装置３が、フィードバック制御を行なわない場合（フィードフォワード制御のみを行なう場合）であり、図９は、フィードバック制御とフィードフォワード制御との両方を行なう場合（本発明のバランス制御装置３による制御を行なう場合に相当する）である。
【００８０】
なお、ここでは、フィードフォワード制御は、目標値（目標板厚及び目標張力の値）の急激な変化によって圧延状態が不安定となることを防止するために、フィードフォワード補償部３１にフィードフォワード補償量を制限するリミッタが設けられているものとする。また、フィードフォワード制御による目標値の変更は、バランス制御開始から所定の時間（目標値変更区間という）の間に行なうものとする。
【００８１】
図６に示すように、バランス制御装置３が無い場合は、モータ電流のバランスが制御されず、圧延スタンド１３のモータ電流Ｇ3が定格電流を超えたままであり、圧延スタンド１３のモータに過大な負荷を与え、圧延停止となる場合がある。
【００８２】
図７に示すように、フィードバック制御のみを行なう場合（従来のバランス制御装置による制御を行なう場合に相当する）は、バランス制御がＯＮとなった後、目標値（目標板厚及び目標張力の値）が徐々に変更されて、圧延スタンド１２、１３、１４のモータ電流Ｇ2、Ｇ3、Ｇ4は、同じ値に収束されるが、その応答速度は外乱応答の応答速度と同じである。
【００８３】
図８に示すように、フィードフォワード制御のみを行なう場合は、バランス制御がＯＮとなった後、目標値（目標板厚及び目標張力の値）が図７の場合と比較して速く変更されて、圧延スタンド１２、１３、１４のモータ電流Ｇ2、Ｇ3、Ｇ4は、同じ値に収束するように制御されるが、フィードフォワード補償量ｕFFの誤差（モデル化の誤差や原板の硬度変動等の外乱ｄext）があるために、同じ値に収束されることは保証されない。目標値（目標板厚及び目標張力の値）が図７の場合と比較して速く変更されることによって、圧延スタンド１３のモータ電流Ｇ3が定格電流以下に制御されるまでに要する時間が短くなっている。そのため、圧延スタンド１３のモータへの負荷が軽減され、モータの損傷又は圧延停止等が防止される。また、圧延スタンド１３のモータ電流Ｇ3が圧延速度のネックとなっている場合には、早期に圧延速度をアップすることが可能となり、生産性が向上される。
【００８４】
図９に示すように、フィードバック制御とフィードフォワード制御との両方を行なう場合（本発明のバランス制御装置３による制御を行なう場合に相当する）は、図８の場合と同様に、フィードフォワード制御の効果として、目標値（目標板厚及び目標張力の値）が図７の場合と比較して速く変更されることによって、圧延スタンド１３のモータ電流Ｇ3が定格電流以下に制御されるまでに要する時間が短くなっている。そのため、圧延スタンド１３のモータへの負荷が軽減され、モータの損傷又は圧延停止等が防止される。圧延スタンド１３のモータ電流Ｇ3が圧延速度のネックとなっている場合には、早期に圧延速度をアップすることが可能となり、生産性が向上される。また、フィードバック制御の効果として、圧延スタンド１２、１３、１４のモータ電流Ｇ2、Ｇ3、Ｇ4は、同じ値に収束される。
【００８５】
図１０及び図１１は、板厚張力制御装置２が、張力制御として、目標張力を基準とするバンド幅を有するバンド制御を行なう場合のバランス制御装置３のフィードフォワード制御の効果を示す図である。図１０及び図１１において、（ａ）は、目標張力及び実績張力の変化を示す図であり、（ｂ）は、目標モータ電流及び実績モータ電流の変化を示す図である。ここでは、フィードフォワード制御は、目標値（目標張力の値）の急激な変化によって圧延状態が不安定となることを防止するために、フィードフォワード補償部３１にフィードフォワード補償量を制限するリミッタが設けられているものとする。また、フィードフォワード制御による目標値の変更は、バランス制御開始から所定の時間（目標値変更区間という）の間に行なうものとする。図１０は、張力制御のバンド幅の補償を行わない場合であり、図１１は、張力制御のバンド幅の補償を行なう場合である。
【００８６】
図１０に示すように、張力制御のバンド幅の補償を行わない場合は、フィードフォワード制御によって目標張力の値の変更が行われるが、張力制御がバンド制御を行なうため、実績張力が、バンド幅の上限値（目標張力上限値という）より大となるか、または、バンド幅の下限値（目標張力下限値という）より小となるまで、張力制御は行われない。そのため、バランス制御装置によるモータ電流の制御の応答速度が遅くなる場合がある。
【００８７】
そこで、目標値変更区間の開始時に、バンド幅の補償を行えば、上記のモータ電流の制御の応答速度が遅くなることを防止することができる。具体的には、目標値変更区間の開始時に、フィードフォワード補償量が正である場合には、次式によってバンド幅補償量を算出して、目標張力にバンド幅補償量を加算する。
（バンド幅補償量）＝（実績張力）−（目標張力下限値） （３７）
また、目標値変更区間の開始時に、フィードフォワード補償量が負である場合には、次式によってバンド幅補償量を算出して、目標張力にバンド幅補償量を加算する。
（バンド幅補償量）＝−[（実績張力）−（目標張力上限値）] （３８）
目標値変更区間の開始時に、実績張力が目標張力と一致する場合には、バンド幅補償量は零として、目標張力は変更しない。なお、計算誤差等によりバンド幅の補償が過度に行われ圧延状態が不安定となることを防止するために、上記バンド幅補償量に０より大で１より小の調整係数を乗じたものを目標張力に加算する形態でもよい。
【００８８】
図１１に示すように、張力制御のバンド幅の補償を行なう場合は、目標値変更区間の開始時に、目標張力にバンド幅補償量が加算され、バランス制御の開始直後から実績張力が変更され、モータ電流の制御の応答性を向上することができる。すなわち、張力制御のバンド幅の補償を行なうことによって、張力のバンド制御が行なわれる場合のバランス制御装置３の目標値応答の低下が防止される。
【００８９】
（第２実施形態：請求項１０〜請求項１３に記載のバランス制御装置の実施形態の一例）
図１２は、本発明の第２実施形態に係るバランス制御装置３ａの制御ブロックである。バランス制御装置３ａの構成は、目標荷重算出部３４、荷重記憶部３５及び目標電流算出部３６に代えて、板厚、張力、圧延荷重及びモータ電流の理想的な値である理想値を格納する理想値記憶部３８１と、板厚、張力、圧延荷重及びモータ電流の理想値を求める理想値算出部３８２と、制約条件を格納する制約条件記憶部３８４と、板厚、張力、圧延荷重及びモータ電流の実績値を取得する初期値取得部３８３と、後述する最適値計算を行なうことによって目標モータ電流及び目標圧延荷重を算出する最適値計算部３８５（最適値計算手段に相当する）とを備えることを除き、第１実施形態のバランス制御装置３の構成と同一である。ここでは、第１実施形態のバランス制御装置３と異なる点について説明し、同一の点については説明を省略する。
【００９０】
理想値記憶部３８１は、安定圧延及び品質確保の観点から理想的であると考えられる各圧延スタンド間の板厚及び張力と、各圧延スタンドの圧延荷重及びモータ電流との値（理想値）を格納するものである。ここでは、被圧延材の鋼種及び圧延ロールの表面区分（ダル、ブライト等）毎に、各圧延スタンド間の板厚及び張力と、各圧延スタンドの圧延荷重及びモータ電流との理想値（それぞれ、理想板厚、理想張力、理想荷重、理想電流という）を格納するものである。
【００９１】
理想値算出部３８２は、被圧延材の鋼種及び圧延ロールの表面区分（ダル、ブライト等）に対応する理想板厚、理想張力、理想荷重及び理想電流を理想値記憶部３８１から読み出して、最適値計算部３８５に出力するものである。
【００９２】
初期値取得部３８３は、各圧延スタンド間の板厚及び張力と各圧延スタンドの圧延荷重及びモータ電流との実績値（それぞれ、初期板厚、初期張力、初期荷重、初期電流という）をタンデム圧延機１から取得して、最適値計算部３８５に出力するものである。
【００９３】
制約条件記憶部３８４は、最適値計算部３８５が目標モータ電流及び目標荷重を算出する際の制約条件を格納するものである。制約条件は、例えば、各圧延スタンドの圧下率（または圧延荷重またはモータ電流）が所定値以上であり且つ所定値以下であること等である。
【００９４】
最適値計算部３８５は、理想値算出部３８２から入力される理想板厚、理想張力、理想荷重及び理想電流と、初期値取得部３８３から入力される初期板厚、初期張力、初期荷重及び初期電流とを用いて最適値計算を行ない目標モータ電流及び目標圧延荷重を算出するものである。ただし、最適値計算部３８５は、制約条件記憶部３８４に制約条件が格納されている場合（すなわち制約条件がある場合）には、その制約条件を満たす範囲内で最適値計算を行なうものである。
【００９５】
ここで、最適値計算部３８５によって行なわれる最適値計算について具体的に説明する。なお、ここでは便宜上、制約条件が無い場合について説明する。後述する式（３９）〜（４９）で用いられる記号の意味は、次の通りである。
ｕ：操作量ベクトル
（４つのスタンド間目標板厚ｕ1〜ｕ4と４つのスタンド間目標張力ｕ5〜ｕ8との計８成分からなるベクトル）
ｕd：理想操作量ベクトル
（４つの理想板厚ｕd1〜ｕd4と４つの理想張力ｕd5〜ｕd8との計８成分からなるベクトル）
ｕ0：初期操作量ベクトル
（４つの初期板厚ｕ01〜ｕ04と４つの初期張力ｕ05〜ｕ08との計８成分からなるベクトル）
ｒ'：変換前目標値ベクトル
（５つの目標圧延荷重ｒ'1〜ｒ'5と５つの目標モータ電流ｒ'6〜ｒ'10との計１０成分からなるベクトル）
ｒ'd：理想変換前目標値ベクトル
（５つの理想荷重ｒ'd1〜ｒ'd5と５つの理想電流ｒ'd6〜ｒ'd10との計１０成分からなるベクトル）
ｒ'0：初期変換前目標値ベクトル
（５つの初期荷重ｒ'01〜ｒ'05と５つの初期電流ｒ'06〜ｒ'010との計１０成分からなるベクトル）
Ｃr：目標値変換行列
（（３１）式で定義される行列Ｃの第２９〜３８列部分を取り出すことによって生成される８行１０列の行列）
ＧmbcFF：（３４）式で定義されるフィードフォワード制御のゲイン行列
αi：操作量ｕiに関する重み（ｉ＝１〜８）
Ａ：重みαiを対角成分とし他の成分が０の８行８列の重み行列
βi：変換前目標値ｒi'に関する重み（ｉ＝１〜１０）
Ｂ：重みβiを対角成分とし他の成分が０の１０行１０列の重み行列
Ｊ：評価関数
λi：ラグランジュの未定乗数（ｉ＝１〜８）
λ：ラグランジュの未定乗数λiを成分とする８成分からなるベクトル
まず、評価関数Ｊを次の（３９）式で定義する。
【００９６】
【数４】

【００９７】
以下の計算においては、（３９）式で定義される評価関数Ｊを最小とする変換前目標値ベクトルｒ'及び操作量ベクトルｕを求めるための最適値計算を行なう。なお、最適値計算の結果得られる操作量ベクトルｕは使用しないので、以下の説明においては、変換前目標値ベクトルｒ'の算出方法について説明する。
【００９８】
最適値計算の結果得られる目標圧延荷重及び目標モータ電流は、変換前目標値ベクトルに含まれる目標圧延荷重及び目標モータ電流と、操作量ベクトルに含まれるスタンド間目標板厚及びスタンド間目標張力とがそれぞれの理想値に近い値となるため、圧延荷重及びモータ電流のバランスに加えて板厚及び張力のバランスをも確保するような値となる。そこで、圧延スタンド間の板厚及び張力のバランスが確保され、チャタリング等の圧延トラブルが防止されると共に被圧延材の表面品位の向上が図られる。
【００９９】
次に、（３９）式で定義される評価関数Ｊを最小とする変換前目標値ベクトルｒ'及び操作量ベクトルｕを求めるための最適値計算の具体的な方法について説明する。圧延理論等より（３６）式と同様にして、次の（４０）式が得られる。ｕ−ｕ0＝ＧmbcFF・Ｃr・（ｒ'−ｒ'0） （４０）
そこで、（４０）式を満たす条件のもとで、（３９）式で定義される評価関数Ｊを最小とする最適値計算を行なう。ここで、ラグランジュの未定乗数λiを導入すると、次の（４１）式で定義される関数Ｊ’を最小とする最適値計算を行なえばよいことになる。
【０１００】
【数５】

【０１０１】
最適性の条件より次の（４２）〜（４４）式が得られる。
【０１０２】
【数６】

【０１０３】
（４１）式を（４２）〜（４４）式に代入することによって、次の（４５）〜（４７）式が得られる。
２Ａ・（ｕ−ｕd）＋λ＝０ （４５）
２Ｂ・（ｒ'−ｒ'd）−Ｃｒ^T・ＧmbcFF^T・λ＝０ （４６）
ｕ−ｕ0＝ＧmbcFF・Ｃr・（ｒ'−ｒ'0） （４７）
この（４５）〜（４７）式より、λ及びｕを消去すると、次の（４８）式が得られる。
〔Ｃｒ^T・ＧmbcFF^T・Ａ・ＧmbcFF・Ｃr＋Ｂ〕・（ｒ'−ｒ'0）＝Ｂ・（ｒ'd−ｒ'0）＋Ｃｒ^T・ＧmbcFF^T・Ａ・（ｕd−ｕ0） （４８）
ここで、８行８列の行列〔Ｃｒ^T・ＧmbcFF^T・Ａ・ＧmbcFF・Ｃr＋Ｂ〕が正則であるとして、（４８）式より次の（４９）式が得られる。
ｒ'＝ｒ'0＋〔Ｃｒ^T・ＧmbcFF^T・Ａ・ＧmbcFF・Ｃr＋Ｂ〕^-1・〔Ｂ・（ｒ'd−ｒ'0）＋Ｃｒ^T・ＧmbcFF^T・Ａ・（ｕd−ｕ0）〕 （４９）
この（４９）を用いて評価関数Ｊを最小とする変換前目標値ベクトルｒ'が求められる。
【０１０４】
ここでは、制御対象の線形のモデルを使用しているため最適値計算において収束計算等は行なう必要がないが、制御対象のモデルとして非線形のモデルを使用する場合には、収束計算を含む非線形の最適値計算を行なう必要がある。非線形の最適値計算は、例えば、公知の逐次２次計画法を用いて行なうことができる（「ＦＯＲＴＲＡＮ７７最適化プログラミング」茨木俊秀・福島雅夫著、岩波書店ｐｐ１６７〜１７１参照）。この方法を用いる場合には、所定の制約条件を満たす範囲内で最適値計算を行なうことも可能である。また、ここでは板厚に関して最適値計算を行なう場合について説明したが、板厚に代えて圧下率に関して最適化計算を行なう形態でもよい。
【０１０５】
図１３は、バランス制御装置３ａの動作を表わすフローチャートである。まず、バランス制御を開始するか否かの判定が行われる（ステップＳ１０１）。例えば、圧延開始後の加速完了時、または、圧延開始から所定時間経過後にバランス制御が開始される。この判定が否定された場合には、この判定が肯定されるまで待機する。この判定が肯定された場合には、理想値算出部３８２によって理想板厚、理想張力、理想荷重及び理想電流が理想値記憶部３８１から読み出される（ステップＳ１０３）。そして、初期値取得部３８３によって初期板厚、初期張力、初期荷重及び初期電流がタンデム圧延機１から取得される（ステップＳ１０５）。ついで、最適値計算部３８５によって目標モータ電流及び目標圧延荷重（変換前目標値ベクトルｒ'）が算出される（ステップＳ１０７）。つぎに、目標値算出部３７によって目標値（目標値ベクトルｒ）が求められる（ステップＳ１０９）。そして、フィードフォワード補償部３１によって、目標圧延荷重と目標モータ電流とを用いて（３６）式に基づいてフィードフォワード補償量が求められる（ステップＳ１１１）。
【０１０６】
次いで、フィードバック補償部３２によって、目標圧延荷重と目標モータ電流とを用いてフィードバック補償量が求められる（ステップＳ１１３）。次に、加算部３３によって、フィードバック補償量とフィードフォワード補償量とが加算されて操作量が求められる（ステップＳ１１５）。そして、この操作量が制御対象に対して出力される（ステップＳ１１７）。
【０１０７】
その後、バランス制御を終了するか否かの判定が行われる（ステップＳ１１９）。例えば、圧延終了前の減速開始時、または、圧延開始から所定時間経過後にバランス制御が終了される。この判定が肯定された場合には、処理が終了される。この判定が否定された場合には、目標値を再計算するか否かの判定が行われる（ステップＳ１２１）。例えば、所定時間間隔毎（あるいは被圧延材の圧延長の所定長さ間隔毎）に目標値の再計算を行なう。この判定が否定された場合には、ステップＳ１１１に戻って制御が継続して実施される。この判定が肯定された場合には、ステップＳ１０５に戻って、目標値が再度計算され（ステップＳ１０５〜Ｓ１０９）、制御が継続して実施される。
【０１０８】
このように、例えば、所定時間間隔毎（あるいは被圧延材の圧延長の所定長さ間隔毎）に目標値の再計算が行なわれるため、圧延条件（例えば、原板の硬度）が変化した場合にも適正な目標値が設定される。ただし、バランス制御の安定性の観点から、目標値の変更の速度はバランス制御の応答速度と比較して充分に遅くする必要がある。
【０１０９】
（第３実施形態：請求項１４〜請求項１６に記載のバランス制御装置の実施形態の一例）
図１４は、本発明の第３実施形態に係るバランス制御装置３ｂの制御ブロックである。バランス制御装置３ｂの構成は、フィードフォワード補償部３１、フィードバック補償部３２に代えて、フィードフォワード補償量を求める第１フィードフォワード補償部３１ａ（第１フィードフォワード補償手段に相当する）及び第２フィードフォワード補償部３１ｂ（第２フィードフォワード補償手段に相当する）と、フィードバック補償量を求める第１フィードバック補償部３２ａ（第１フィードバック補償手段に相当する）及び第２フィードバック補償部３２ｂ（第２フィードバック補償手段に相当する）と、バランス制御に使用する補償部を切り換える切換部３９（切換手段に相当する）とを備えることを除き、第１実施形態のバランス制御装置３の構成と同一である。ここでは、第１実施形態のバランス制御装置３と異なる点について説明し、同一の点については説明を省略する。
【０１１０】
第１フィードフォワード補償部３１ａは、第１実施形態のバランス制御装置３におけるフィードフォワード補償部３１と同一の構造を有し、第１フィードバック補償部３２ａは、第１実施形態のバランス制御装置３におけるフィードバック補償部３２と同一の構造を有するものである。
【０１１１】
第１フィードフォワード補償部３１ａ及び第１フィードバック補償部３２ａは、操作量ｕが４つの圧延スタンド間目標板厚及び４つの圧延スタンド間目標張力であって、制御量ｙが４つの荷重変動差及び４つの電流変動差である場合のフィードフォワード補償量及びフィードバック補償量をそれぞれ求めるものである。
【０１１２】
一方、第２フィードフォワード補償部３１ｂ及び第２フィードバック補償部３２ｂは、操作量ｕが４つの圧延スタンド間目標板厚であって、制御量ｙが４つの荷重変動差である場合のフィードフォワード補償量及びフィードバック補償量をそれぞれ求めるものである。このような第２フィードフォワード補償部３１ｂ及び第２フィードバック補償部３２ｂは、第１フィードフォワード補償部３１ａ及び第１フィードバック補償部３２ａと同様の方法で構成することが可能であり、第１フィードフォワード補償部３１ａ及び第１フィードバック補償部３２ａの構成方法については第１実施形態において説明しているため、ここでは構成方法についての説明は省略する。
【０１１３】
切換部３９は、所定のタイミングで第１フィードフォワード補償部３１ａと第２フィードフォワード補償部３１ｂとを交互に切り換えると共に、第１フィードバック補償部３２ａと第２フィードバック補償部３２ｂとを交互に切り換えてバランス制御に使用するものである。
【０１１４】
具体的には、圧延速度が略一定であるか否かを判定して、圧延速度が略一定である状態から圧延速度が略一定ではない状態に変化したタイミングで、第２フィードフォワード補償部３１ｂ及び第２フィードバック補償部３２ｂをバランス制御に使用するように切り換え、圧延速度が略一定ではない状態から圧延速度が略一定である状態に変化したタイミングで、第１フィードフォワード補償部３１ａ及び第１フィードバック補償部３２ａをバランス制御に使用するように切り換えるものである。ここで、第１フィードフォワード補償部３１ａ及び第２フィードフォワード補償部３１ｂによって求められたフィードフォワード補償量を、それぞれ第１ＦＦ補償量及び第２ＦＦ補償量という。また、第１フィードバック補償部３２ａ及び第２フィードバック補償部３２ｂによって求められたフィードバック補償量を、それぞれ第１ＦＢ補償量及び第２ＦＢ補償量という。
【０１１５】
すなわち、一定速圧延中は第１フィードフォワード補償部３１ａ及び第１フィードバック補償部３２ａをバランス制御に使用し、加速中または減速中は第２フィードフォワード補償部３１ｂ及び第２フィードバック補償部３２ｂをバランス制御に使用するものである。そこで、モータ負荷の変化が大きい加速中または減速中には、圧延スタンド毎の圧延荷重のみが制御される（モータ負荷が制御されない）ため、圧延スタンド毎の圧延荷重を安定して制御することが可能となる。また、モータ負荷の変化が小さい一定速圧延中には、圧延スタンド毎の圧延荷重及びモータ負荷が制御されるため、圧延スタンド毎の圧延荷重に加えて圧延スタンド毎のモータ負荷も制御することが可能となる。
【０１１６】
また、第１フィードフォワード補償部３１ａ、第２フィードフォワード補償部３１ｂ、第１フィードバック補償部３２ａ及び第２フィードバック補償部３２ｂを速度型に構成することによって、バンプレス切換が実現される（「ＰＩＤ制御」システム制御情報学会編、朝倉書店ｐｐ４８〜５０参照）。
【０１１７】
図１５は、バランス制御装置３ｂの動作を表わすフローチャートである。まず、バランス制御を開始するか否かの判定が行われる（ステップＳ２０１）。例えば、圧延開始後の加速完了時、または、圧延開始から所定時間経過後にバランス制御が開始される。この判定が否定された場合には、この判定が肯定されるまで待機する。この判定が肯定された場合には、目標荷重算出部３４によって目標圧延荷重が求められ、目標電流算出部３６によって目標モータ電流が求められる（ステップＳ２０３）。ついで、目標値算出部３７によって目標値が求められる（ステップＳ２０５）。そして、切換部３９によって、圧延速度が略一定であるか否かの判定が行なわれる（ステップＳ２０７）。この判定が肯定された場合にはステップＳ２０９へ進み、この判定が否定された場合には、ステップＳ２１５へ進む。
【０１１８】
ステップＳ２０７における判定が肯定された場合（一定速圧延中である場合）には、第１フィードフォワード補償部３１ａによって、目標圧延荷重と目標モータ電流とを用いて第１ＦＦ補償量が求められる（ステップＳ２０９）。次いで、第１フィードバック補償部３２ａによって、目標圧延荷重と目標モータ電流とを用いて第１ＦＢ補償量が求められる（ステップＳ２１１）。次に、加算部３３によって、第１ＦＦ補償量と第１ＦＢ補償量とが加算されて操作量が求められ（ステップＳ２１３）、ステップＳ２２１へ進む。
【０１１９】
ステップＳ２０７における判定が否定された場合（加速中または減速中である場合）には、第２フィードフォワード補償部３１ｂによって、目標圧延荷重を用いて第２ＦＦ補償量が求められる（ステップＳ２１５）。次いで、第２フィードバック補償部３２ｂによって、目標圧延荷重を用いて第２ＦＢ補償量が求められる（ステップＳ２１７）。次に、加算部３３によって、第２ＦＦ補償量と第２ＦＢ補償量とが加算されて操作量が求められ（ステップＳ２１９）、ステップＳ２２１へ進む。
【０１２０】
ステップＳ２１３またはステップＳ２１９において操作量が求められると、この操作量が制御対象に対して出力される（ステップＳ２２１）。その後、バランス制御を終了するか否かの判定が行われる（ステップＳ２２３）。例えば、圧延終了前の減速開始時、または、圧延開始から所定時間経過後にバランス制御が終了される。この判定が否定された場合には、ステップＳ２０７に戻り、制御が継続して実施される。この判定が肯定された場合には、処理が終了される。
【０１２１】
図１６は、バランス制御装置３ｂの動作を表わすタイミングチャートである。（ａ）は圧延速度の変化であり、（ｂ）は切換部３９の動作である。圧延速度が略一定である期間Ｔ１、Ｔ３、Ｔ５においては第１フィードフォワード補償部３１ａ及び第１フィードバック補償部３２ａが使用され、圧延速度が略一定では無い期間（加速中または減速中の期間）Ｔ２、Ｔ４においては第２フィードフォワード補償部３１ｂ及び第２フィードバック補償部３２ｂが使用される。すなわち、切換部３９によって、期間Ｔ２の開始時点ｔ１及び期間Ｔ４の開始時点ｔ３において、第２フィードフォワード補償部３１ｂ及び第２フィードバック補償部３２ｂをバランス制御に使用するように切り換えられ、期間Ｔ３の開始時点ｔ２及び期間Ｔ５の開始時点ｔ４において、第１フィードフォワード補償部３１ａ及び第１フィードバック補償部３２ａをバランス制御に使用するように切り換えられる。
【０１２２】
ここでは、圧延速度が略一定では無い期間（加速中または減速中の期間）において第２フィードフォワード補償部３１ｂ及び第２フィードバック補償部３２ｂをバランス制御に使用する形態について説明したが、圧延速度が略一定では無い期間（加速中または減速中の期間）に加えて、圧延速度が略一定では無い期間から圧延速度が略一定である期間に移行した後（加速完了または減速完了後）所定時間の間も、第２フィードフォワード補償部３１ｂ及び第２フィードバック補償部３２ｂをバランス制御に使用する形態でもよい。この場合には、モータ電流が不安定となる場合のある加速完了（または減速完了）後所定時間の間は、圧延スタンド毎の圧延荷重のみが制御される（モータ負荷が制御されない）ため、更に圧延スタンド毎の圧延荷重を安定して制御することが可能となる。
【０１２３】
また、ここでは、圧延速度に基づいて第１フィードフォワード補償部３１ａ及び第１フィードバック補償部３２ａと第２フィードフォワード補償部３１ｂ及び第２フィードバック補償部３２ｂとを切り換える形態について説明したが、第２フィードフォワード補償部３１ｂ及び第２フィードバック補償部３２ｂを備えず、制御量の内電流変動差を強制的に「０」とし、操作量の内スタンド間張力をホールドすることによって、第１フィードフォワード補償部３１ａ及び第１フィードバック補償部３２ａをそれぞれ第２フィードフォワード補償部３１ｂ及び第２フィードバック補償部３２ｂと同様に機能させることも可能である。
【０１２４】
【発明の効果】
請求項１に記載の発明によれば、フィードフォワード補償手段によって、制御量のフィードフォワード制御に用いるフィードフォワード補償量が求められ、フィードバック補償手段によって、制御量のフィードバック制御に用いるフィードバック補償量が求められ、加算手段によって、フィードフォワード補償量とフィードバック補償量とが加算されて操作量が求められ、この操作量が板厚張力制御装置に供給される。このようにして、バランス制御装置が２自由度制御系となっているため、目標値応答と外乱応答とを同時に最適化することが可能となり、安定性が良好で目標値応答の良好なバランス制御装置を実現できる。そして、板厚張力制御装置によって、目標張力を基準とするバンド幅を有するバンド制御が行われ、バランス制御装置の操作量に、目標張力が含まれ、フィードフォワード補償手段によって、バンド幅を補償するためのバンド幅補償量を加算したフィードフォワード補償量が求められるため、張力のバンド制御が行なわれる場合のバランス制御装置の目標値応答の低下を防止できる。
【０１２５】
請求項２に記載の発明によれば、フィードフォワード補償手段によって、制御対象を静的にモデル化した静特性モデルに基づいてフィードフォワード補償量が求められるため、適切なフィードフォワード補償量を容易に求めることができる。
【０１２６】
請求項３に記載の発明によれば、フィードバック補償手段が、制御量と当該制御量の目標値との偏差を積分演算する積分特性を有するため、バランス制御の目標値に対する定常偏差が解消され、良好な制御特性が得ることができる。
【０１２９】
請求項４に記載の発明によれば、荷重記憶手段に、被圧延材の単位板幅当たりの圧延荷重である単位幅荷重を少なくとも被圧延材の鋼種及び圧延ロールの表面区分毎に格納され、目標荷重算出手段によって、単位幅荷重に被圧延材の板幅を乗じることにより目標圧延荷重が求められるため、適正な目標圧延荷重が簡単に求められ、制御量が、圧延スタンド毎の圧延荷重に関するものであるため、バランス制御装置が、適正な目標圧延荷重を用いて圧延荷重を制御できる。また、制御量が、圧延スタンド毎の圧延荷重に関するものであるため、タンデム圧延機の圧延状態のバランスの重要な指標である圧延荷重が制御され、タンデム圧延機の圧延状態のバランスを保つことができる。
【０１３０】
請求項５に記載の発明によれば、荷重記憶手段に、被圧延材の単位板幅当たりの圧延荷重である単位幅荷重が少なくとも被圧延材の鋼種及び圧延ロールの表面区分毎に格納され、目標荷重算出手段によって、バランス制御開始時の実績圧延荷重が単位幅荷重に被圧延材の板幅を乗じたものに所定の値を加算した荷重上限値より大きい場合には、荷重上限値が目標圧延荷重とされ、バランス制御開始時の実績圧延荷重が単位幅荷重に被圧延材の板幅を乗じたものに所定の値を減算した荷重下限値より小さい場合には、荷重下限値が目標圧延荷重とされ、バランス制御開始時の実績圧延荷重が荷重上限値以下であり且つ荷重下限値以上である場合には、バランス制御開始時の実績圧延荷重を目標圧延荷重とされるため、適正な荷重下限値と荷重上限値とを求めることができる。制御量が、圧延スタンド毎の圧延荷重に関するものであるため、バランス制御装置が圧延荷重について荷重下限値から荷重上限値までの範囲をバンド幅とするバンド制御を行なうことができる。
【０１３１】
請求項６に記載の発明によれば、制御量が、圧延スタンド毎の圧延荷重及び圧延スタンド毎のモータ負荷に関するものであり、目標負荷算出手段によって、モータの定格負荷以下の所定の値を目標モータ負荷とされるため、バランス制御装置が、モータ負荷をモータの定格負荷値以下に制御し、モータ負荷が圧延速度のネックとなっている場合には、圧延速度をアップすることができる。また、制御量が、圧延スタンド毎のモータ負荷に関するものであるため、タンデム圧延機の圧延状態のバランスの重要な指標であるモータ負荷が制御され、タンデム圧延機の圧延状態のバランスを保つことができる。ただし、モータトルク、モータ電流、モータパワー及び圧延トルクを総称してモータ負荷というものとする。
【０１３２】
請求項７に記載の発明によれば、制御量が、圧延スタンド毎のモータ負荷に関するものであり、目標負荷算出手段によって、少なくとも１つのスタンドの目標モータ負荷が、当該スタンドを含む複数スタンドの実績モータ負荷の平均値として求められるため、バランス制御が複数スタンドのモータ負荷を所定の値以下に制御し、モータ負荷が圧延速度のネックとなっている場合には、圧延速度をアップすることができる。また、制御量が、圧延スタンド毎のモータ負荷に関するものであるため、タンデム圧延機の圧延状態のバランスの重要な指標であるモータ負荷が制御され、タンデム圧延機の圧延状態のバランスを保つことができる。
【０１３３】
請求項８に記載の発明によれば、制御量に含まれる圧延状態量に加えて、操作量に含まれる圧延状態量の内、評価関数の変数とされた圧延状態量に関しても適正な制御を実現可能とする制御量の目標値を設定できる。その結果、更に安定した圧延を可能とするバランス制御装置を実現できる。そして、圧延速度等の圧延条件が変化されたタイミング等で最適値計算手段によって制御量の目標値を求めることが可能となるため、更に適正な制御量の目標値を設定できる。
【０１３４】
請求項９に記載の発明によれば、圧延スタンド毎の圧延荷重及びモータ負荷に加えて、圧延スタンド間の目標板厚及び目標張力の内、評価関数の変数とされた圧延状態量に関しても適正な制御を実現可能とする圧延スタンド毎の圧延荷重及びモータ負荷の目標値を設定できる。その結果、圧延スタンド間の板厚及び張力のバランスを確保でき、チャタリング等の圧延トラブルを防止できると共に被圧延材の表面品位の向上を図ることができる。
【０１３５】
請求項１０に記載の発明によれば、板厚、張力、モータ負荷等に設備上の制約条件がある場合にも、その制約条件を満たす制御量の目標値を求めることができる。
【０１３７】
請求項１１に記載の発明によれば、圧延条件等に適したフィードフォワード補償手段及びフィードバック補償手段が選択的に使用され得るため、更に適正なバランス制御を実現可能である。
【０１３８】
請求項１２に記載の発明によれば、加速中または減速中の制御に適した（圧延速度が略一定である場合とは異なる）フィードフォワード補償手段及びフィードバック補償手段を使用するため、更に適正なバランス制御を実現できる。
【０１３９】
請求項１３に記載の発明によれば、モータ負荷の変化が大きい加速中または減速中にも、圧延スタンド毎の圧延荷重を安定して制御することできる。
【図面の簡単な説明】
【図１】 本発明の実施の形態に係るタンデム圧延機のバランス制御装置の概略構成を示す図である。
【図２】 本発明の第１実施形態に係るバランス制御装置の制御ブロック図である。
【図３】 第１実施形態に係るバランス制御装置の動作を表わすフローチャートである。
【図４】 第１実施形態に係るバランス制御装置のフィードフォワード制御の効果を示す図である。
【図５】 第１実施形態に係るバランス制御装置のフィードバック制御の効果を示す図である。
【図６】 バランス制御装置の効果を示す図である（バランス制御装置が無い場合）。
【図７】 バランス制御装置の効果を示す図である（フィードバック制御のみを行なう場合）。
【図８】 バランス制御装置の効果を示す図である（フィードフォワード制御のみを行なう場合）。
【図９】 第１実施形態に係るバランス制御装置の効果を示す図である（フィードバック制御とフィードフォワード制御との両方を行なう場合）。
【図１０】 張力制御としてバンド制御を行なう場合のフィードフォワード制御の効果を示す図である（バンド幅の補償を行わない場合）。
【図１１】 張力制御としてバンド制御を行なう場合のフィードフォワード制御の効果を示す図である（張力制御のバンド幅の補償を行なう場合）。
【図１２】 本発明の第２実施形態に係るバランス制御装置の制御ブロックである。
【図１３】 第２実施形態に係るバランス制御装置の動作を表わすフローチャートである。
【図１４】 本発明の第３実施形態に係るバランス制御装置の制御ブロックである。
【図１５】 第３実施形態に係るバランス制御装置の動作を表わすフローチャートである。
【図１６】 第３実施形態に係るバランス制御装置の動作を表わすタイミングチャートである。
【図１７】 バランス制御の必要性を説明するための図である。
【符号の説明】
１ タンデム圧延機
２ 板厚張力制御装置
３、３ａ、３ｂ バランス制御装置
１１〜１５ 圧延スタンド
３１ フィードフォワード補償部（フィードフォワード補償手段）
３１ａ 第１フィードフォワード補償部（第１フィードフォワード補償手段）
３１ｂ 第２フィードフォワード補償部（第２フィードフォワード補償手段）
３２ フィードバック補償部（フィードバック補償手段）
３２ａ 第１フィードバック補償部（第１フィードバック補償手段）
３２ｂ 第２フィードバック補償部（第２フィードバック補償手段）
３３ 加算部（加算手段）
３４ 目標荷重算出部（目標荷重算出手段）
３５ 荷重記憶部（荷重記憶手段）
３６ 目標電流算出部（目標負荷算出手段）
３７ 目標値算出部
３８５ 最適値計算部（最適値計算手段）
３９ 切換部（切換手段）[0001]
BACKGROUND OF THE INVENTION
The present invention relates to a balance control device for a tandem rolling mill, and more specifically, a tandem rolling mill having a plurality of rolling stands, and each rolling so as to obtain at least one of a target plate thickness and a target tension set for each rolling stand. The present invention relates to a balance control device that controls a system including a plate thickness tension control device that controls a stand and maintains the balance of the rolling state of a tandem rolling mill.
[0002]
[Prior art]
For example, in a tandem rolling mill provided with a plurality of rolling stands # 1 to # 5 as shown in FIG. 17A, the initial values of the thickness between the rolling stands and the tension on the entry / exit side of each rolling stand are determined. When the result of draft schedule calculation to be performed is inappropriate, or when there are fluctuations in the plate thickness, deformation resistance of the material to be rolled, changes in the coefficient of friction between the rolling roll and material to be rolled, etc. , Rolling load, motor current, motor torque, motor power, rolling torque (hereinafter collectively referred to as motor load), etc., changes the state quantity of each rolling stand, the balance of the rolling state of the tandem rolling mill is disrupted and specified The amount of state of the rolling stand may fluctuate greatly, adversely affecting the plate thickness accuracy and plate shape, and may hinder stable operation.
[0003]
Conventionally, an operation (referred to as manual intervention) for correcting the balance by changing the roll speed or the roll gap is mainly performed by an operator (operator). As shown in FIG. 17B, it is assumed that the rolling load distribution for each rolling stand, that is, the balance is good in a steady rolling state, which is a desirable state. Thereafter, it is assumed that a disturbance such as a variation in deformation resistance acts and only the rolling load of the rolling stand # 5 is reduced as shown in FIG. At this time, when the operator reduces the tension between the rolling stand # 4 and the rolling stand # 5 mainly by changing the roll gap of the rolling stand # 5, as shown in FIG. The load can be returned to the original state. However, when the balance is corrected by manual intervention, the burden on the operator is large, and when the manual intervention is abrupt and large, there is a problem that the plate thickness accuracy deteriorates.
[0004]
Therefore, various balance control devices that maintain the balance of rolling conditions such as rolling load and motor load of a tandem rolling mill have been proposed. Japanese Patent Laid-Open Nos. 56-109107, 60-166112, Hei 10 -5832 and JP-A-2001-9514. Here, the balance control device includes a tandem rolling mill having a plurality of rolling stands, and a plate thickness tension control device that controls each rolling stand so as to obtain at least one of a target plate thickness and a target tension set for each rolling stand. State quantities not controlled by the plate thickness tension control device, i.e. rolling load, motor load, plate thickness between rolling stands and tension between rolling stands not controlled by the plate thickness tension control device, etc. Is a device that controls a control amount selected from the linear combination (for example, (rolling load of rolling stand # 5) + (motor current of rolling stand # 5) × 2)). Further, the operation amount of the balance control device is selected according to the control amount, and is, for example, a target plate thickness, a target tension, or the like.
[0005]
For example, Japanese Patent Laid-Open No. 2001-9514 has an integration characteristic that integrates a control deviation between a control amount of balance control and a balance control target value with respect to the control amount, thereby ensuring the stability of the balance control. However, a balance control device for a tandem rolling mill that includes a multivariable feedback control system that can eliminate the steady-state deviation has been proposed.
[0006]
[Problems to be solved by the invention]
In recent years, high-strength steel sheets (hereinafter referred to as high-tensile materials) have been frequently used in automobiles and the like from the viewpoints of weight reduction and collision safety, and the types of steel materials to be rolled are increasing. When rolling a new steel grade, the deformation resistance, etc. is unknown, so it is necessary to obtain the parameters used for the above-mentioned draft schedule calculation from multiple rolling data by multiple regression calculations, etc., which takes a lot of time and labor. Cost.
[0007]
In cold rolling of high-tensile materials, the strength characteristics of the original sheet (hot rolled sheet) change depending on the rolling conditions such as the coiling temperature during hot rolling. Based on the parameters determined by the above method Even in the draft schedule, there is a problem that appropriate rolling conditions, that is, appropriate rolling load, motor load, and the like cannot be ensured. Therefore, there is a need for a responsive balance control device that can correct the balance of rolling conditions such as rolling load and motor load in a short time after the start of rolling.
[0008]
On the other hand, since the response speed to disturbance of the conventional balance control device needs to be slower than the response speed of the plate thickness tension control device from the viewpoint of stability, the responsiveness when changing the target load or target motor load (target There was a limit to increasing the value response.
[0009]
The present invention has been made in view of the above problems, and it is an object of the present invention to provide a balance control device for a tandem rolling mill that has good stability and good target value response.
[0010]
[Means for Solving the Problems]
  The balance control device for a tandem rolling mill according to claim 1 includes: a tandem rolling mill having a plurality of rolling stands; and each rolling stand so as to obtain at least one of a target plate thickness and a target tension set for each rolling stand. An operation amount calculation means for obtaining an operation amount based on a control amount selected from a rolling state amount obtained from the control object and representing a rolling state is provided. A balance control device for maintaining a balance of a rolling state of a tandem rolling mill by supplying the operation amount to the plate thickness tension control device, wherein the operation amount calculation means is a feed used for feedforward control of the control amount. A feedforward compensation means for obtaining a forward compensation amount, and a feedback compensation amount for use in feedback control of the control amount. Yes and fed back compensation means, and an adding means for adding to obtaining an operation amount and the feedback compensation amount and the feedforward compensation amountThe plate thickness tension control device performs band control having a bandwidth based on the target tension, the operation amount includes the target tension, and the feedforward compensation means compensates the bandwidth. The feedforward compensation amount is calculated by adding the bandwidth compensation amount forIt is characterized by that.
[0011]
  According to the above invention, the feedforward compensation amount used for the feedforward control of the control amount is obtained by the feedforward compensation means, the feedback compensation amount used for the feedback control of the control amount is obtained by the feedback compensation means, and the addition means Thus, the operation amount is obtained by adding the feedforward compensation amount and the feedback compensation amount, and this operation amount is supplied to the plate thickness tension control device. In this way, since the balance control device is a two-degree-of-freedom control system, it is possible to simultaneously optimize the target value response and the disturbance response, and the balance control has good stability and good target value response. A device is realized.Then, band control having a bandwidth based on the target tension is performed by the plate thickness tension control device, the target tension is included in the operation amount of the balance control device, and the bandwidth is compensated by the feedforward compensation means. Therefore, since the feedforward compensation amount obtained by adding the bandwidth compensation amount is obtained, the target value response of the balance control device is prevented from being lowered when the tension band control is performed.
[0012]
The balance control device for a tandem rolling mill according to claim 2, wherein the feedforward compensation means obtains the feedforward compensation amount based on a static characteristic model in which the controlled object is statically modeled. .
[0013]
According to the above invention, since the feedforward compensation amount is obtained by the feedforward compensation means based on the static characteristic model in which the controlled object is statically modeled, an appropriate feedforward compensation amount can be easily obtained.
[0014]
The balance control device for a tandem rolling mill according to a third aspect is characterized in that the feedback compensation means has an integration characteristic for integrating and calculating a deviation between the control amount and a target value of the control amount.
[0015]
According to the above invention, since the feedback compensation means has an integral characteristic for integrating the deviation between the control amount and the target value of the control amount, the steady deviation with respect to the balance control target value is eliminated, and the good control characteristic is obtained. Is obtained.
[0019]
  Claims 4-7According to the invention, since the control amount relates to at least one of the rolling load for each rolling stand and the motor load for each rolling stand, the rolling load and motor which are important indicators of the balance of the rolling state of the tandem rolling mill At least one of the loads is controlled, and the balance of the rolling state of the tandem rolling mill is maintained. However, the motor current, motor torque, motor power, and rolling torque are collectively referred to as a motor load.
[0020]
  Claim4The balance control device of the tandem rolling mill described inA control system includes a tandem rolling mill having a plurality of rolling stands and a plate thickness tension control device that controls each rolling stand so as to obtain at least one of a target plate thickness and a target tension set for each rolling stand. An operation amount calculating means for obtaining an operation amount based on a control amount selected from a rolling state amount obtained from the control target and representing a rolling state, and supplying the operation amount to the plate thickness tension control device Is a balance control device that maintains the balance of the rolling state of the tandem rolling mill, wherein the operation amount calculation means includes a feedforward compensation means for obtaining a feedforward compensation amount used for feedforward control of the control amount, and a control amount Feedback compensation means for obtaining a feedback compensation amount used for feedback control, and the feedforward compensation Wherein and an adding means for adding the feedback compensation amount determining the manipulated variable and,The control amount relates to a rolling load for each rolling stand, and is a target load calculating means for obtaining a target rolling load that is a target value of the rolling load for each rolling stand, and a rolling load per unit plate width of the material to be rolled. Load storage means for storing a certain unit width load at least for each steel type of the material to be rolled and each surface section of the rolling roll, and the target load calculating means multiplies the unit width load by the plate width of the material to be rolled. It is characterized by obtaining a target rolling load.
[0021]
According to the above invention, the load storage means stores the unit width load, which is the rolling load per unit plate width of the material to be rolled, for at least the steel type of the material to be rolled and the surface section of the rolling roll, and the target load calculation means. Since the target rolling load is obtained by multiplying the unit width load by the plate width of the material to be rolled, an appropriate target rolling load is easily obtained, and the control amount is related to the rolling load for each rolling stand. The rolling load is controlled by the balance control device using an appropriate target rolling load.
[0022]
  Claim5The balance control device of the tandem rolling mill described inA control system includes a tandem rolling mill having a plurality of rolling stands and a plate thickness tension control device that controls each rolling stand so as to obtain at least one of a target plate thickness and a target tension set for each rolling stand. An operation amount calculating means for obtaining an operation amount based on a control amount selected from a rolling state amount obtained from the control target and representing a rolling state, and supplying the operation amount to the plate thickness tension control device Is a balance control device that maintains the balance of the rolling state of the tandem rolling mill, wherein the operation amount calculation means includes a feedforward compensation means for obtaining a feedforward compensation amount used for feedforward control of the control amount, and a control amount Feedback compensation means for obtaining a feedback compensation amount used for feedback control, and the feedforward compensation Wherein and an adding means for adding the feedback compensation amount determining the manipulated variable and,The control amount relates to a rolling load for each rolling stand, and is a target load calculating means for obtaining a target rolling load that is a target value of the rolling load for each rolling stand, and a rolling load per unit plate width of the material to be rolled. Load storage means for storing a unit width load at least for each steel type of the material to be rolled and each surface section of the rolling roll, and the target load calculating means is configured to apply the actual rolling load at the start of balance control to the unit width load. If it is larger than the load upper limit value obtained by multiplying the rolled material sheet width by a predetermined value, the load upper limit value is set as the target rolling load, and the actual rolling load at the start of balance control is applied to the unit width load. If it is smaller than the load lower limit value obtained by subtracting a predetermined value to the product of the width of the rolled material, the load lower limit value is set as the target rolling load, and the actual rolling load at the start of balance control is less than the load upper limit value. If there is and the more load lower limit is characterized in that the actual rolling load during balance control start and target rolling load.
[0023]
According to the above invention, the unit width load, which is the rolling load per unit plate width of the material to be rolled, is stored in the load storage means at least for each steel type of the material to be rolled and the surface section of the rolling roll, and the target load calculating means. Therefore, if the actual rolling load at the start of balance control is greater than the load upper limit obtained by multiplying the unit width load by the plate width of the material to be rolled and adding a predetermined value, the load upper limit is set as the target rolling load. When the actual rolling load at the start of balance control is smaller than the load lower limit value obtained by subtracting a predetermined value from the product width multiplied by the plate width of the material to be rolled, the load lower limit value is set as the target rolling load, If the actual rolling load at the start of balance control is less than or equal to the upper limit of load and greater than or equal to the lower limit of load, the actual rolling load at the start of balance control is set as the target rolling load. Find the upper limit It is. In addition, since the control amount relates to the rolling load for each rolling stand, the balance control device performs band control with the range from the load lower limit value to the load upper limit value for the rolling load.
[0024]
  Claim6The balance control device for a tandem rolling mill described in the above, the control amount isRolling load for each rolling stand andThe present invention relates to a motor load for each rolling stand, and includes target load calculation means for obtaining a target motor load that is a target value of the motor load for each rolling stand, and the target load calculation means has a predetermined value that is equal to or less than the rated load of the motor. Is a target motor load.
[0025]
According to the above invention, the control amount relates to the motor load for each rolling stand, and the target load calculation means sets a predetermined value equal to or lower than the rated load of the motor as the target motor load. When the motor load is controlled to be equal to or less than the rated load value of the motor and the motor load becomes a bottleneck of the rolling speed, the rolling speed can be increased.
[0026]
  Claim7The balance control device of the tandem rolling mill described inA control system includes a tandem rolling mill having a plurality of rolling stands and a plate thickness tension control device that controls each rolling stand so as to obtain at least one of a target plate thickness and a target tension set for each rolling stand. An operation amount calculating means for obtaining an operation amount based on a control amount selected from a rolling state amount obtained from the control target and representing a rolling state, and supplying the operation amount to the plate thickness tension control device Is a balance control device that maintains the balance of the rolling state of the tandem rolling mill, wherein the operation amount calculation means includes a feedforward compensation means for obtaining a feedforward compensation amount used for feedforward control of the control amount, and a control amount Feedback compensation means for obtaining a feedback compensation amount used for feedback control, and the feedforward compensation Wherein and an adding means for adding the feedback compensation amount determining the manipulated variable and,The control amount relates to a motor load for each rolling stand, and includes target load calculation means for obtaining a target motor load that is a target value of the motor load for each rolling stand, and the target load calculation means includes at least one stand. The target motor load is obtained as an average value of the actual motor loads of a plurality of stands including the stand.
[0027]
According to the above invention, the control amount is related to the motor load for each rolling stand, and the target motor calculating means calculates the average motor load of a plurality of stands including the stand as the target motor load of at least one stand. Since it is calculated | required as a value, when the motor load of several stands is controlled below to a predetermined value by balance control and a motor load becomes the bottleneck of rolling speed, rolling speed can be raised.
[0028]
  Claim8The balance control device of the tandem rolling mill described inA control system includes a tandem rolling mill having a plurality of rolling stands and a plate thickness tension control device that controls each rolling stand so as to obtain at least one of a target plate thickness and a target tension set for each rolling stand. An operation amount calculating means for obtaining an operation amount based on a control amount selected from a rolling state amount obtained from the control target and representing a rolling state, and supplying the operation amount to the plate thickness tension control device Is a balance control device that maintains the balance of the rolling state of the tandem rolling mill, wherein the operation amount calculation means includes a feedforward compensation means for obtaining a feedforward compensation amount used for feedforward control of the control amount, and a control amount Feedback compensation means for obtaining a feedback compensation amount used for feedback control, and the feedforward compensation Wherein and an adding means for adding the feedback compensation amount determining the manipulated variable and,The target value of the control amount based on the value of the control amount that maximizes or minimizes the evaluation function whose variable is at least one of the rolling state amount included in the control amount and the rolling state amount included in the operation amount. Equipped with an optimal value calculation meansThe optimal value calculation means is a target value of the control amount at at least two timings between the start of balance control and the end of balance control at a predetermined timing other than the start of balance control and the start of balance control. SeekingIt is characterized by that.
[0029]
  According to the above invention, the optimum value calculating means is configured to control the control amount that maximizes or minimizes the evaluation function having at least one of the rolling state amount included in the control amount and at least one of the rolling state amount included in the operation amount as a variable. Based on the value, the target value of the control amount is obtained. Therefore, in addition to the rolling state quantity included in the control amount, the target value of the control amount that enables appropriate control to be realized with respect to the rolling state quantity included in the operation amount as a variable of the evaluation function. Is set. For example, when all the rolling state quantities included in the manipulated variable are used as variables in the evaluation function, appropriate control is performed for all the rolling state quantities included in the manipulated variable in addition to the rolling state quantity included in the controlled variable. The target value of the control amount that makes it possible to achieve is set. As a result, a balance control device that enables more stable rolling is realized.Then, the optimum value calculation means sets the target value of the control amount at at least two timings between the start of balance control and the end of balance control, at a predetermined timing other than the start of balance control and the start of balance control Desired. For example, the target value of the control amount can be obtained by the optimum value calculating means at the timing when the rolling conditions such as the rolling speed are changed, and further, the target value of the appropriate control amount is set.
[0030]
  Claim9The balance control device for a tandem rolling mill according to claim 1, wherein the rolling state amount included in the control amount is a rolling load and a motor load for each rolling stand, and the rolling state amount included in the operation amount is a target between the rolling stands. It is characterized by the plate thickness and target tension.
[0031]
According to the above invention, the rolling state amount included in the control amount is a rolling load and a motor load for each rolling stand, and the rolling state amount included in the operation amount is the target plate thickness and target tension between the rolling stands. Therefore, in addition to the rolling load and motor load for each rolling stand, a rolling stand capable of realizing appropriate control with respect to the rolling state quantity, which is a variable of the evaluation function, among the target plate thickness and target tension between the rolling stands. Target values for each rolling load and motor load are set. For example, when all the rolling state quantities included in the manipulated variable are used as variables in the evaluation function, in addition to the rolling load and motor load for each rolling stand, the target plate thickness and target tension between the rolling stands are also appropriate. A target value of the rolling load and the motor load for each rolling stand that can realize the control is set. As a result, the balance between the thickness and tension between the rolling stands is ensured, rolling troubles such as chattering are prevented, and the surface quality of the material to be rolled is improved.
[0032]
  Claim 10The balance control device for a tandem rolling mill according to claim 2, wherein the optimum value calculation means obtains a target value of the control amount that satisfies a constraint condition regarding at least one of the rolling state amounts included in the control amount or the operation amount. It is characterized by.
[0033]
According to the above invention, the target value of the control amount that satisfies the constraint condition regarding at least one of the rolling state amounts included in the control amount or the operation amount is obtained by the optimum value calculating means. Therefore, for example, even when there are constraints on equipment such as plate thickness, tension, motor load, etc., a target value of the control amount that satisfies the constraints is obtained.
[0036]
  Claim 11The balance control device of the tandem rolling mill described inA control system includes a tandem rolling mill having a plurality of rolling stands and a plate thickness tension control device that controls each rolling stand so as to obtain at least one of a target plate thickness and a target tension set for each rolling stand. An operation amount calculating means for obtaining an operation amount based on a control amount selected from a rolling state amount obtained from the control target and representing a rolling state, and supplying the operation amount to the plate thickness tension control device Is a balance control device that maintains the balance of the rolling state of the tandem rolling mill, wherein the operation amount calculation means includes a feedforward compensation means for obtaining a feedforward compensation amount used for feedforward control of the control amount, and a control amount Feedback compensation means for obtaining a feedback compensation amount used for feedback control, and the feedforward compensation Wherein and an adding means for adding the feedback compensation amount determining the manipulated variable and,The feedforward compensation means includes a first feedforward compensation means and a second feedforward compensation means, and the feedback compensation means comprises a first feedback compensation means and a second feedback compensation means, and the first feedforward compensation means is provided at a predetermined timing. The feedforward compensation means and the second feedforward compensation means are alternately switched, and the first feedback compensation means and the second feedback compensation means are alternately switched to be used for balance control. .
[0037]
According to the above invention, the feedforward compensation means comprises the first feedforward compensation means and the second feedforward compensation means, the feedback compensation means comprises the first feedback compensation means and the second feedback compensation means, and the switching means. Thus, the first feedforward compensation means and the second feedforward compensation means are alternately switched at a predetermined timing, and the first feedback compensation means and the second feedback compensation means are alternately switched and used for balance control. The Therefore, for example, when the rolling conditions such as the rolling speed change, the feedforward compensation means and the feedback compensation means suitable for the rolling conditions can be used, so that more appropriate balance control is realized.
[0038]
  Claim 12In the balance control device for a tandem rolling mill described in 1), the switching unit determines whether or not the rolling speed is substantially constant, and the first feedforward compensation unit and the second feed at a timing when the determination result changes. The forward compensation means is alternately switched, and the first feedback compensation means and the second feedback compensation means are alternately switched.
[0039]
According to the above invention, whether or not the rolling speed is substantially constant is determined by the switching means, and at the timing when this determination result changes, the first feedforward compensation means and the second feedforward compensation means are While being switched alternately, the first feedback compensation means and the second feedback compensation means are alternately switched. When the rolling speed is not substantially constant (accelerating or decelerating), the rolling state tends to become unstable, so it is suitable for control during acceleration or decelerating (different from the case where the rolling speed is substantially constant). By using the compensation means and the feedback compensation means, more appropriate balance control is realized.
[0040]
  Claim 13In the balance control device for a tandem rolling mill according to the first aspect, the first feedforward compensation unit and the first feedback compensation unit are configured such that the rolling state amount included in the control amount is a rolling load and a motor load for each rolling stand. A feedforward compensation amount and a feedback compensation amount are obtained, respectively, and the second feedforward compensation means and the second feedback compensation means provide feedforward compensation when the rolling state quantity included in the control quantity is a rolling load for each rolling stand. A second feedforward compensation unit and a second feedback compensation unit at a timing when the switching unit changes from a state in which the rolling speed is substantially constant to a state in which the rolling speed is not substantially constant. To use for balance control, rolling speed There at the timing when the rolling speed is changed to the state which is substantially constant from the state not substantially constant, is characterized in that switching to use the first feedforward compensation means and the first feedback compensation means to balance control.
[0041]
According to the above invention, the feedforward compensation amount and the feedback compensation when the rolling state amount included in the control amount is the rolling load and the motor load for each rolling stand by the first feedforward compensation means and the first feedback compensation means. The feedforward compensation amount and the feedback compensation amount when the rolling state amount included in the control amount is a rolling load for each rolling stand are obtained by the second feedforward compensation means and the second feedback compensation means, respectively. It is done. Then, the switching means switches the second feedforward compensation means and the second feedback compensation means to use for balance control at the timing when the rolling speed is changed from the substantially constant state to the non-constant state. Then, at the timing when the rolling speed is changed from a state that is not substantially constant to a state where the rolling speed is substantially constant, the first feedforward compensation means and the first feedback compensation means are switched to be used for balance control.
[0042]
That is, when the rolling speed is not substantially constant (acceleration or deceleration), the rolling load for each rolling stand is controlled, and when the rolling speed is substantially constant (during constant speed rolling), for each rolling stand. The rolling load and motor load are controlled. Therefore, during acceleration or deceleration with a large change in motor load, only the rolling load for each rolling stand is controlled (the motor load is not controlled), so that the rolling load for each rolling stand can be controlled stably. It becomes possible. In addition, during constant speed rolling with a small change in motor load, the rolling load and motor load for each rolling stand are controlled, so that the motor load for each rolling stand can be controlled in addition to the rolling load for each rolling stand. It becomes possible.
[0043]
DETAILED DESCRIPTION OF THE INVENTION
FIG. 1 is a diagram showing a schematic configuration of a balance control device for a tandem rolling mill according to an embodiment of the present invention. The control targets of the balance control device 3 (3a, 3b) are the tandem rolling mill 1 and the plate thickness tension control device 2 that controls the plate thickness and tension of the tandem rolling mill 1. The tandem rolling mill 1 is configured by continuously arranging five rolling stands 11 to 15. Each of the rolling stands 11-15 includes rolling mills 111, 121, ..., 151, tension meters 112, 122, ..., 152 for measuring the tension, and thickness gauges 113, 123 for measuring the thickness of the material to be rolled. ..., 153. In addition, although the case where the tandem rolling mill 1 is a cold rolling mill will be described here, the balance control device of the present invention can also be applied to a hot rolling mill. Furthermore, each rolling stand 11-15 is provided with the load meter which measures a rolling load, and the ammeter which measures a motor current (illustration omitted).
[0044]
The plate thickness tension control device 2 uses the roll gaps (5) of the rolling stands 11 to 15 and the roll speeds (4) of the rolling stands 11 to 14 as operation amounts (9 in total), The plate thickness (five) and the tension between the rolling stands (four) are controlled as control amounts (total nine). However, the configuration of the sheet thickness tension control device 2 is not limited to the above-described form. For example, the tension between the rolling stands (four) is not controlled, and the thickness (5 ) May be a control amount, or only the plate thickness on the final rolling stand exit side may be a control amount.
[0045]
The balance control device 3 (3a, 3b) obtains an operation amount based on a control amount selected from the rolling state amount representing the rolling state of the tandem rolling mill 1 and the sheet thickness tension control device 2, and calculates the operation amount. The balance of the rolling state of the tandem rolling mill 1 is maintained by supplying the sheet thickness tension control device 2.
[0046]
(1st Embodiment: An example of embodiment of the balance control apparatus of Claims 1-9)
FIG. 2 is a control block diagram of the balance control device 3 according to the first embodiment of the present invention. The balance control device 3 includes a feedforward compensation unit 31 (corresponding to a feedforward compensation unit) that calculates a feedforward compensation amount used for feedforward control of a control amount, and feedback compensation that calculates a feedback compensation amount used for feedback control of the control amount. A unit 32 (corresponding to feedback compensation means) and an adder 33 (corresponding to addition means) for adding the feedforward compensation amount and the feedback compensation amount to obtain the manipulated variable u. It is composed. Realizing a two-degree-of-freedom control system with other types, that is, a loop compensation type, a feedback compensation type, a target value filter type, and a general formula type (see “PID Control”, System Control Information Society, Asakura Shoten p.75) Is also possible by equivalent conversion of the control system. Note that the feedback compensation unit 32 has an integration characteristic that integrates a deviation between the control amount y and the target value r of the control amount y. Therefore, the steady deviation with respect to the balance control target value r is eliminated (becomes substantially zero), and good control characteristics are obtained.
[0047]
Further, the balance control device 3 includes a target load calculation unit 34 (corresponding to a target load calculation unit) that obtains a target rolling load that is a target value of the rolling load of each of the rolling stands 11 to 15, and a target load calculation unit 34. A load storage unit 35 (corresponding to load storage means) that stores a unit width load that is a rolling load per unit plate width of the material to be rolled used for obtaining the rolling load, and motor currents of the respective rolling stands 11 to 15 Target current calculation unit 36 (corresponding to target load calculation means) for obtaining a target motor current which is a target value of the load, and target values of load fluctuation difference and current fluctuation difference used in feedforward compensation part 31 and feedback compensation part 32 And a target value calculation unit 37 for calculating. The load fluctuation difference and the current fluctuation difference will be described later.
[0048]
The load storage unit 35 stores a unit width load, which is a rolling load per unit plate width of the material to be rolled, at least for each steel type of the material to be rolled and each surface section (dull, bright, etc.) of the rolling roll. This unit width load is set based on the past rolling performance and the like. Also, by using the unit width load, it is possible to set an appropriate target rolling load when the steel grade of the material to be rolled and the surface section of the rolling roll are the same and the plate width of the material to be rolled is different. Become. For example, even when rolling a material having a sheet width with no past rolling record, an appropriate target rolling load is obtained by using the same steel type as the material to be rolled and the unit width load of the surface section of the rolling roll. It becomes possible to set.
[0049]
The target load calculation unit 34 reads the corresponding steel type and the unit width load of the surface section of the rolling roll from the load storage unit 35, and obtains the target rolling load by multiplying the unit width load by the plate width of the material to be rolled. It is. Alternatively, when the actual rolling load at the start of balance control is greater than the load upper limit value obtained by adding a predetermined value to the product of the unit width load and the sheet width of the material to be rolled, the load upper limit value is set to the target rolling load. If the actual rolling load at the start of balance control is smaller than the load lower limit value obtained by subtracting a predetermined value obtained by multiplying the unit width load by the sheet width of the material to be rolled, the load lower limit value is set as the target rolling load. In the case where the actual rolling load at the start of balance control is equal to or lower than the upper limit value of the load and equal to or higher than the lower limit value of the load, the actual rolling load at the start of balance control may be set as the target rolling load.
[0050]
The target current calculation unit 36 sets a predetermined value equal to or lower than the rated current of the motor as the target motor current. Or the form which calculates | requires the target motor current of an at least 1 stand as an average value of the performance motor current of the some stand containing the said stand may be sufficient. For example, an average value of the motor currents of the rolling stands 12, 13 and 14 is set as the target motor current of the rolling stands 12, 13 and 14.
[0051]
The target value calculation unit 37 uses the target rolling load calculated by the target load calculation unit 34 and the target current calculated by the target current calculation unit 36 to use the load used in the feedforward compensation unit 31 and the feedback compensation unit 32. The target value of the fluctuation difference and the current fluctuation difference is calculated. Specifically, an 8-row 10-column matrix Cr (referred to as a target value conversion matrix) generated by taking out the 29th to 38th column portions of the matrix C defined by the later-described equation (31) is used as a target load ( The target value vector of the load fluctuation difference and the current fluctuation difference is calculated by multiplying a vector (referred to as a pre-conversion target value vector) composed of a total of ten components of five) and the target current (five).
[0052]
Here, the operation amount u is a target plate thickness between four rolling stands and a target tension between four rolling stands. However, the operation amount can be changed in a timely manner according to the form of the plate thickness tension control device 2.
[0053]
The controlled variable y is a load fluctuation difference between the rolling stand 11 and the rolling stand 12, a load fluctuation difference between the rolling stand 12 and the rolling stand 13, a load fluctuation difference between the rolling stand 13 and the rolling stand 14, and the rolling stand 14 and the rolling stand. 15, load fluctuation difference between the rolling stand 11 and the rolling stand 12, current fluctuation difference between the rolling stand 12 and the rolling stand 13, current fluctuation difference between the rolling stand 13 and the rolling stand 14, and the rolling stand 14 The eight current fluctuation differences from the rolling stand 15 are selected. Here, the reason why the load fluctuation difference and the current fluctuation difference are selected as the control amount y is that the control amount is limited to eight because the balance control operation amount is eight. In other words, when the load fluctuation and the current fluctuation are selected as the control amount y, it is necessary to match the number of control amounts with the number of operation amounts (here, 8). It becomes impossible to control.
[0054]
Next, the above-described load fluctuation difference will be described. The difference in load fluctuation between the rolling stand 1i (i = 1 to 4) and the rolling stand 1j (j = 2 to 5) is the difference ΔPi and ΔPj of the actual rolling load from the target rolling load. For example, it is the difference between what is normalized by the rated rolling load (Pi, Pj) and multiplied by the reciprocal of appropriate coefficients m and n. That is, it is expressed by the following formula.
ΔPi / (m × Pi) −ΔPj / (n × Pj) (1)
The feedback compensation unit 32 performs control so as to satisfy the following expression.
ΔPi / (m × Pi) −ΔPj / (n × Pj) = 0 (2)
Further, as described above, the feedback compensation unit 32 has an integral characteristic that integrates and calculates the deviation between the control amount y and the target value r of the control amount, and therefore performs control so that the following equation is established.
ΔPi / Pi: ΔPj / Pj = m: n (3)
Therefore, for example, in the case of m = 5 and n = 1, when the rolling load of each rolling stand fluctuates due to disturbance such as the hardness fluctuation of the original plate, the deviation of the rolling load between the rolling stand 1i and the rolling stand 1j The ratio is a value normalized by the reference rolling load and is controlled to 5: 1.
[0055]
Next, the above-described current fluctuation difference will be described. The difference in current fluctuation between the rolling stand 1i (i = 1 to 4) and the rolling stand 1j (j = 2 to 5) is the difference ΔGi and ΔGj of the actual motor current from the target motor current. For example, it is the difference between what is normalized by the rated current values Gi and Gj and multiplied by the reciprocal of appropriate coefficients m and n. That is, it is expressed by the following formula.
ΔGi / (m × Gi) −ΔGj / (n × Gj) (4)
The feedback compensation unit 32 performs control so as to satisfy the following expression.
ΔGi / (m × Gi) −ΔGj / (n × Gj) = 0 (5)
Further, as described above, the feedback compensation unit 32 has an integral characteristic that integrates and calculates the deviation between the control amount y and the target value r of the control amount, and therefore performs control so that the following equation is established.
ΔGi / Gi: ΔGj / Gj = m: n (6)
Therefore, for example, in the case of m = 5 and n = 1, when the motor current of each rolling stand fluctuates due to disturbance such as the hardness variation of the original plate, the ratio of the current deviation between the rolling stand 1i and the rolling stand 1j is The value normalized by the reference current value is controlled to 5: 1.
[0056]
Thus, by selecting the load fluctuation difference and the current fluctuation difference as the control amount y of the balance control, the ratio of the rolling load of each rolling stand and the deviation of the motor current (difference from the target value of the actual value) is obtained. It can be made constant, and the rolling load or motor current of a specific rolling stand can be prevented from becoming too large or too small to make the rolling state unstable. That is, the balance control device 3 can maintain the balance of the rolling state of the tandem rolling mill 1.
[0057]
The feedforward compensation unit 31 obtains a feedforward compensation amount uFF based on a static characteristic model that statically models a control target. Hereinafter, a specific method for obtaining the feedforward compensation amount will be described. The meanings of symbols used in formulas (7) to (36) described later are as follows.
vi: Stand exit side plate speed
b: Rolled material sheet width
U: Volume velocity
fi: Advanced rate
vRi: Roll speed
Si: Roll gap
Pi: Rolling load
Mi: Mill stiffness coefficient
Qi: Plastic coefficient
Ri: Roll radius
Ni: Roll speed setting value
Gi: Motor current
Zi *: Motor speed reduction coefficient due to rolling torque increment
H1: Original plate thickness
hi: Rolling stand outlet side plate thickness
Hi: Thickness on the entrance side of the rolling stand
qfi: Rolling stand outlet tension
qbi: Rolling stand entry side tension
μi: Friction coefficient
ki: Rolling material deformation resistance
-SV represents a set value in a steady state.
[0058]
First, the basic equation of cold rolling is as follows. For details, see, for example, “Theory and Practice of Sheet Rolling” (issued by the Japan Iron and Steel Institute, September 1, 1984), pp. 112-114. Here, the steel type and temperature of the material to be rolled, the type of rolling roll, and the rolling length of the rolling roll (accumulated length after rolling the rolled material with the same rolling roll after roll reassignment) are clearly shown in the following equation. There is no impact on each variable. For example, as the temperature of the material to be rolled increases, the deformation resistance ki of the material to be rolled decreases. Further, it is assumed that the sheet width b of the material to be rolled is constant during rolling. An error between the following basic equation and an actual physical phenomenon, for example, an error of a value or an error caused by a phenomenon not represented in the equation (for example, a change in the friction coefficient μi during rolling, etc.) will be described later (27 ) In the disturbance dext in the equation.
[0059]
○ Constant volume velocity:
vi × hi × b = U (i = 1, 2,..., 5) (7)
○ Stand exit side plate speed formula:
vi = (1 + fi) * vRi (i = 1, 2,..., 5) (8)
○ Stand outlet side plate thickness formula:
hi = Si + Pi / Mi (i = 1, 2,..., 5) (9)
○ Roll speed formula:
(ΔvR / vR) i = (Δ (Ri × Ni) / (Ri × Ni)) + Zi * × ΔGi (i = 1, 2,..., 5) (10)
○ Advanced rate, rolling load, rolling torque formula: Here, “Theory and practice of plate rolling” (published by the Japan Iron and Steel Institute, September 1, 1984) p. Unlike 113, Gi represents motor current, not rolling torque. The formula for converting rolling torque into motor current varies depending on the type of motor, but in the case of the most basic DC motor, (motor current) = (rolling torque) / (torque constant) (third edition steel handbook III (2) Steel bar, steel pipe, rolling common equipment p.1339). In addition, in the case of induction motors, the third edition Steel Handbook III (2) Steel bar, steel pipe and rolling common equipment p. If the relationship as shown in FIG. 18.4 of 1340 is obtained, the rolling torque can be converted into a motor current.
fi = fi (H1, Hi, hi, qfi, qbi, μi, ki) (i = 1, 2,..., 5) (11)
Pi = Pi (H1, Hi, hi, qfi, qbi, μi, ki, b) (i = 1, 2,..., 5) (12)
Gi = Gi (H1, Hi, hi, qfi, qbi, μi, ki, b) (i = 1, 2,..., 5) (13)
○ Properties of tandem rolling mill:
hi = Hi + 1 (i = 1, 2,..., 5) (14)
qfi = qbi + 1 (i = 0, 1,..., 4) (15)
○ Deformation resistance and friction formula:
ki = ki (h0, hi-1, hi, vi) (i = 1, 2,..., 5) (16)
μi = μi (vi) (i = 1, 2,..., 5) (17)
○ Plate thickness tension control system: The plate thickness tension control device 2 controls the plate thickness on the exit side of each rolling stand and the tension between each rolling stand to the target plate thickness and target tension, respectively. Equations (18) and (19) are obtained. In the case where the plate thickness tension control device 2 performs band control with a band width, the tension variation within the band width may be regarded as zero.
hi = hi-SV (i = 1, 2,..., 5) (18)
qfi = qfi-SV (i = 1, 2,..., 4) (19)
O Uncontrollable amount: The raw sheet thickness, the entrance tension of the rolling stand 11 and the like are amounts that cannot be controlled by a tandem rolling mill. The value of these uncontrollable amounts is considered to be constantly controlled by an apparatus other than the tandem rolling mill 1 (if it is not constant, it will be included in the disturbance), and the uncontrollable amount is (20), It is assumed that (21) and (22) are given.
hi = hi-SV (i = 0) (20)
qfi = qfi-SV (i = 0, 5) (21)
Ni = Ni-SV (i = 5) (22)
In consideration of the above formulas (10) to (17), formulas (7) to (9) and formulas (18) to (22) are expanded to Taylor around a steady rolling state in which balance control is operated. Then, the following simultaneous equations can be obtained.
Am & c ・ xm & c = d (23)
Here, the matrix Am & c (38 × 38) is a matrix representing the static characteristics of the controlled object, the vector xm & c (38 × 1) is a vector representing the state quantity of the controlled object, and the vector d (38 × 1) Is a disturbance vector (a vector in which all elements are zero when there is no disturbance).
[0060]
Expression (23) is an expression that defines a change in rolling state with respect to disturbance. Vector xm & c = (x1, x2, ..., x38)^TThe elements of are described below. x1 to x6 are the original plate thickness deviation and rolling stand delivery side thickness deviation Δhk / hk (k = 0, 1,..., 5), and x7 to x12 are the entry side tension deviation of the rolling stand 11 and between the rolling stands. Tension deviation Δqfk / qfk (k = 0, 1,..., 5), x13 to x17 are rolling stand exit side plate speed deviations Δvk / vk (k = 1, 2,..., 5), and x18 to x22 Is a roll speed set value deviation ΔNk / Nk (k = 1, 2,..., 5), and x23 to x27 are roll gap deviations ΔSk / hk (k = 1, 2,..., 5), and x28. Is a volume velocity deviation ΔU / U, x29 to x33 are rolling load deviations ΔPk / Pk (k = 1, 2,..., 5), and x34 to x38 are motor current deviations ΔGk / Gk (k = 1, 2, ..., 5).
[0061]
Am & c is as follows.
[0062]
[Expression 1]

[0063]
Here, a value consisting of an influence coefficient, a mill rigidity coefficient, etc. is entered in the * part of the above equation (24). For example, the elements a6 and 7 in the sixth row and seventh column of Am & c are expressed by the following equations.
[0064]
[Expression 2]

[0065]
The above equation (23) is a linear simultaneous equation with 38 variables and 38 equations, and Am & c is full rank and the disturbance d is known, the solution can be uniquely obtained from the following equation (normally, In the case of rolling, Am & c is full rank).
xm & c = Am & c^-1・ D (26)
It can be considered that the disturbance d includes a disturbance dext from the outside of the tandem rolling mill 1 such as a fluctuation of the original sheet thickness and deformation resistance, and a disturbance dmbc due to an operation amount of balance control. That is, the disturbance d is expressed by the following equation.
d = dext + dmbc (27)
The operation amount of the balance control is the target plate thickness between the four stands and the target tension between the four stands. At this time, the disturbance dmbc due to the operation amount of the balance control is expressed by the following equation (22).
dmbc = Apart · uFF (28)
Here, the matrix Apart (38 × 8) is extracted from the matrix Am & c representing the static characteristics of the controlled object, and only the row corresponding to the constraint condition of the operation amount of the balance control is extracted, and the components of the other rows are all set to 0. Further, only the column corresponding to the operation amount of balance control is extracted. Specifically, the lines 16 to 19 and 21 to 24 of Am & c in the above formula (24) are extracted, all the other rows are set to 0, and only 2 to 5 and 8 to 11 are extracted. is there. The vector uFF (8 × 1) is a vector representing the amount of operation for balance control, and the vector uFF = (u1, u2,..., U8).^TEach component of
u1: Target exit side thickness of the rolling stand 11
u2: Target outlet side thickness of the rolling stand 12
u3: Target outlet side thickness of the rolling stand 13
u4: Target exit side thickness of the rolling stand 14
u5: Target exit side tension of the rolling stand 11
u6: Target exit tension of the rolling stand 12
u7: Target exit side tension of the rolling stand 13
u8: Target exit side tension of the rolling stand 14
It is.
[0066]
Therefore, the change in the state quantity of the controlled object is expressed by the following equation (29).
xm & c = Am & c^-1・ Apart ・ uFF + Am & c^-1Dext (29)
The output equation is defined as the following equation (30).
ym & c = C ・ xm & c (30)
Here, the matrix C (8 × 38) is a coefficient matrix of a state equation to be controlled, and the vector ym & c (8 × 1) is an output to the controlled object, that is, a control amount of balance control. In this example, the matrix C is represented by the following equation (31).
[0067]
[Equation 3]

[0068]
Here, among the coefficients represented by * in the above formula (31), the coefficients related to the rolling load are as follows.
c1,29 = 1/5 c1,30 = -1 / 5
c2,30 = 1/5 c2,31 = -1 / 5
c3,31 = 1/5 c3,32 = -1 / 5
c4,32 = 1/5 c4,33 = -1
In addition, the coefficients relating to the motor current are as follows.
c5,34 = 1/5 c5,35 = -1 / 5
c6,35 = 1/5 c6,36 = -1 / 5
c7,36 = 1/5 c7,37 = -1 / 5
c8,37 = 1/5 c8,38 = -1
At this time, each component of the output vector ym & c is as follows.
y1: ΔP1 / (5 × P1) −ΔP2 / (5 × P2)
(Rolling load deviation of rolling stand 11-rolling load deviation of rolling stand 12)
y2: ΔP2 / (5 × P2) −ΔP3 / (5 × P3)
(Rolling load deviation of rolling stand 12-rolling load deviation of rolling stand 13)
y3: ΔP3 / (5 × P3) −ΔP4 / (5 × P4)
(Rolling load deviation of rolling stand 13-rolling load deviation of rolling stand 14)
y4: ΔP4 / (5 × P4) −ΔP5 / P5
(Rolling load deviation of rolling stand 14-rolling load deviation of rolling stand 15)
y5: ΔG1 / (5 × G1) −ΔG2 / (5 × G2)
(Motor current deviation of rolling stand 11−Motor current deviation of rolling stand 12)
y6: ΔG2 / (5 × G2) −ΔG3 / (5 × G3)
(Motor current deviation of rolling stand 12−Motor current deviation of rolling stand 13)
y7: ΔG3 / (5 × G3) −ΔG4 / (5 × G4)
(Motor current deviation of rolling stand 13−Motor current deviation of rolling stand 14)
y8: ΔG4 / (5 × G4) −ΔG5 / G5
(Motor current deviation of rolling stand 14−Motor current deviation of rolling stand 15)
The coefficient matrix C is an example, and each component of the output vector ym & c is mutually independent from 38 variables excluding the variable that becomes the target value of the plate thickness tension control device 2 and the variable that cannot be controlled. As described above, it can be arbitrarily selected as a linear combination of these variables.
[0069]
From the equations (29) and (30), the influence coefficient of the controlled object is given by the following equation (32).
ym & c = C ・ Am & c^-1・ Apart ・ uFF + C ・ Am & c^-1Dext (32)
Therefore, the control law of feedforward control is given by the following equation (33).
uFF = (C ・ Am & c^-1・ Apart)^-1・ Ym & c- （C ・ Am & c^-1・ Apart)^-1・ C ・ Am & c^-1Dext (33)
Here, a feed-forward control gain matrix GmbcFF (8 × 8) is defined by the following equation (34).
GmbcFF = (C ・ Am & c^-1・ Apart)^-1  (34)
By substituting the equation (34) into the equation (33), the following equation (35) is obtained.
uFF = GmbcFF · ym & c− (C ・ Am & c^-1・ Apart)^-1・ C ・ Am & c^-1Dext (35)
In order to obtain the target output vector ym & c from equation (35), the sum of the output vector ym & c multiplied by the gain matrix GmbcFF (first term) and the compensation for the disturbance dext (second term) It can be seen that the operation amount u may be used.
[0070]
However, in practice, disturbance dext such as modeling errors and fluctuations in hardness of the original plate is unknown, so the second term is ignored and the following equation (36) is used for control.
uFF = GmbcFF · ym & c (36)
The operation amount uFF (feed forward compensation amount) for obtaining the target output vector ym & c is obtained by the equation (36). That is, the feedforward compensation unit 31 calculates the feedforward compensation amount uFF using the equation (36).
[0071]
Note that the feedforward compensation unit 31 shown in FIG. 2 provides a low-pass filter before or after the gain matrix GmbcFF to prevent the feedforward compensation amount from fluctuating rapidly, or feedforward according to the rolling speed or the like. Other gains may be added to adjust the compensation amount, or a limiter that limits the magnitude of the feedforward compensation amount may be added for safety or the like.
[0072]
The feedback compensation unit 32 obtains a feedback compensation amount by a known method. For example, as disclosed in Japanese Patent Laid-Open No. 2001-9514, a feedback compensation amount is obtained using a control law designed using a dynamic characteristic model that dynamically models a controlled object.
[0073]
FIG. 3 is a flowchart showing the operation of the balance control device 3. First, it is determined whether or not to start balance control (step S1). For example, the balance control is started upon completion of acceleration after the start of rolling, or after a predetermined time has elapsed since the start of rolling. If this determination is negative, the system waits until this determination is positive. When this determination is affirmed, the target rolling load is obtained by the target load calculating unit 34, and the target motor current is obtained by the target current calculating unit 36 (step S3). Next, a target value is obtained by the target value calculation unit 37 (step S5). And the feedforward compensation part 31 calculates | requires the feedforward compensation amount based on (36) Formula using a target rolling load and a target motor current (step S7).
[0074]
Next, the feedback compensation unit 32 obtains a feedback compensation amount using the target rolling load and the target motor current (step S9). Next, the addition unit 33 adds the feedback compensation amount and the feedforward compensation amount to obtain an operation amount (step S11). Then, this manipulated variable is output to the controlled object (step S13). Thereafter, it is determined whether or not to end the balance control (step S15). For example, the balance control is ended at the start of deceleration before the end of rolling, or after a predetermined time has elapsed since the start of rolling. If this determination is negative, the process returns to step S7 and the control is continued. If this determination is affirmative, the process ends.
[0075]
FIG. 4 is a diagram illustrating the effect of the feedforward control of the balance control device 3. (A-1) is a disturbance response when the feedforward control is not performed (in the case of the one-degree-of-freedom control system), and (a-2) is a case where the feedforward control is not performed (in the one-degree-of-freedom control system). ) Target value response. In addition, (b-1) is a disturbance response when performing feedforward control (in the case of a two-degree-of-freedom control system), and (b-2) is when performing feedforward control (of a two-degree-of-freedom control system). ) Target value response. However, the case where there is no error in the feedforward compensation amount uFF of the equation (36) used for the feedforward control is shown.
[0076]
As shown in (a-1) and (a-2), in the case of the one-degree-of-freedom control system, the response speed of the disturbance response and the response speed of the target value response are the same. On the other hand, as shown in (b-1) and (b-2), in the case of the two-degree-of-freedom control system, the response speed of the disturbance response and the response speed of the target value response can be controlled independently. This is possible, and the responsiveness of the target value response can be improved. In (b-2), the target value is changed stepwise. However, the target value may be changed in a ramp shape for a predetermined time, or the value may be changed smoothly so as not to affect the stability of the feedback control. It may be a form in which a constant value is obtained after changing with a changing function.
[0077]
FIG. 5 is a diagram illustrating the effect of the feedback control of the balance control device 3. However, there is shown a case where there is an error in the feedforward compensation amount uFF in the equation (36) used for feedforward control. (A) is a target value response when the feedback compensation unit 32 does not have an integral characteristic for integrating the deviation between the control amount y and the target value r of the control amount, and (b) is a feedback compensation unit 32. Is a target value response in the case of having an integral characteristic for integrating the deviation between the control amount y and the target value r of the control amount.
[0078]
As shown in (a), when the feedback compensation unit 32 does not have an integral characteristic for integrating the deviation between the control amount y and the target value r of the control amount, the feedback compensation unit 32 feeds the feedforward compensation amount uFF. However, the steady-state deviation cannot be eliminated (substantially zero). On the other hand, as shown in (b), when the feedback compensation unit 32 has an integration characteristic for integrating the deviation between the control amount y and the target value r of the control amount, the feedback compensation unit 32 feeds the feedback compensation unit 32. The error of the forward compensation amount uFF is corrected, and the steady deviation can be eliminated (substantially zero).
[0079]
6-9 is a figure which shows the effect of the balance control apparatus 3. FIG. Here, for the sake of convenience, the reference motor currents of the rolling stands 12, 13, and 14 in the equation (5) have the same value, and the coefficients m and n have the same value. And let the average value of motor current G2, G3, G4 at the time of balance control start be a target motor current of the rolling stands 12,13,14. That is, the balance control device 3 controls the motor currents of the rolling stands 12, 13, and 14 to the average value of the motor currents G2, G3, and G4 at the start of balance control. 6-9, (a) is a change in rolling speed, (b) is a change in motor current Gi of rolling stands 11-15, and (c) is a rolling of rolling stands 11-15. The change of the load Pi, (d) is the change of the delivery target plate thickness hi of the rolling stands 11-14, and (e) is the change of the delivery target tension qfi of the rolling stands 11-14. FIG. 6 shows a case where the balance control device 3 is not provided, FIG. 7 shows a case where the balance control device 3 does not perform feedforward control (when only feedback control is performed), and FIG. However, FIG. 9 shows a case where both feedback control and feedforward control are performed (when control by the balance control device 3 of the present invention is performed). Equivalent).
[0080]
Here, the feedforward control performs feedforward compensation in the feedforward compensation unit 31 in order to prevent the rolling state from becoming unstable due to sudden changes in the target values (target plate thickness and target tension values). It is assumed that a limiter for limiting the amount is provided. Further, the target value is changed by feedforward control during a predetermined time (referred to as a target value changing section) from the start of balance control.
[0081]
As shown in FIG. 6, in the absence of the balance control device 3, the balance of the motor current is not controlled, the motor current G3 of the rolling stand 13 remains over the rated current, and the motor of the rolling stand 13 is overloaded. May stop rolling.
[0082]
As shown in FIG. 7, when only feedback control is performed (corresponding to control by a conventional balance control device), after balance control is turned on, target values (target plate thickness and target tension values). ) Is gradually changed so that the motor currents G2, G3, and G4 of the rolling stands 12, 13, and 14 are converged to the same value, but the response speed is the same as the response speed of the disturbance response.
[0083]
As shown in FIG. 8, when only the feedforward control is performed, after the balance control is turned on, the target values (target plate thickness and target tension values) are changed faster than in the case of FIG. The motor currents G2, G3, and G4 of the rolling stands 12, 13, and 14 are controlled so as to converge to the same value, but errors in the feedforward compensation amount uFF (disturbances such as modeling errors and original plate hardness fluctuations) dext) is not guaranteed to converge to the same value. By changing the target values (target plate thickness and target tension values) faster than in the case of FIG. 7, the time required until the motor current G3 of the rolling stand 13 is controlled below the rated current is shortened. ing. Therefore, the load on the motor of the rolling stand 13 is reduced, and the motor is prevented from being damaged or stopped from rolling. Further, when the motor current G3 of the rolling stand 13 becomes a bottleneck of the rolling speed, the rolling speed can be increased at an early stage, and the productivity is improved.
[0084]
As shown in FIG. 9, when both the feedback control and the feedforward control are performed (corresponding to the case where the control by the balance control device 3 of the present invention is performed), as in the case of FIG. As an effect, the time required for the motor current G3 of the rolling stand 13 to be controlled below the rated current by changing the target values (target plate thickness and target tension values) faster than in the case of FIG. Is shorter. Therefore, the load on the motor of the rolling stand 13 is reduced, and the motor is prevented from being damaged or stopped from rolling. When the motor current G3 of the rolling stand 13 becomes a bottleneck of the rolling speed, it is possible to increase the rolling speed at an early stage, and productivity is improved. As an effect of feedback control, the motor currents G2, G3, G4 of the rolling stands 12, 13, 14 are converged to the same value.
[0085]
FIGS. 10 and 11 are diagrams illustrating the effect of the feedforward control of the balance control device 3 when the plate thickness tension control device 2 performs band control having a bandwidth with reference to the target tension as tension control. . 10 and 11, (a) is a diagram showing changes in the target tension and the actual tension, and (b) is a diagram showing changes in the target motor current and the actual motor current. Here, the feedforward control has a limiter for limiting the feedforward compensation amount in the feedforward compensation unit 31 in order to prevent the rolling state from becoming unstable due to a sudden change in the target value (target tension value). It shall be provided. Further, the target value is changed by feedforward control during a predetermined time (referred to as a target value changing section) from the start of balance control. FIG. 10 shows a case where the tension control bandwidth is not compensated, and FIG. 11 shows a case where the tension control bandwidth is compensated.
[0086]
As shown in FIG. 10, when compensation of the bandwidth of the tension control is not performed, the target tension value is changed by the feedforward control. However, since the tension control performs the band control, the actual tension is the band width. The tension control is not performed until the value becomes larger than the upper limit value (referred to as the target tension upper limit value) or smaller than the lower limit value (referred to as the target tension lower limit value) of the bandwidth. Therefore, the response speed of the motor current control by the balance control device may be slow.
[0087]
Therefore, if the bandwidth is compensated at the start of the target value changing section, it is possible to prevent the response speed of the motor current control from slowing down. Specifically, when the feedforward compensation amount is positive at the start of the target value changing section, the bandwidth compensation amount is calculated by the following equation, and the bandwidth compensation amount is added to the target tension.
(Bandwidth compensation amount) = (Actual tension) − (Target tension lower limit) (37)
If the feedforward compensation amount is negative at the start of the target value changing section, the bandwidth compensation amount is calculated by the following equation, and the bandwidth compensation amount is added to the target tension.
(Bandwidth compensation amount) =-[(Actual tension)-(Target tension upper limit value)] (38)
If the actual tension matches the target tension at the start of the target value changing section, the bandwidth compensation amount is set to zero and the target tension is not changed. In order to prevent the bandwidth from being compensated excessively due to a calculation error or the like and the rolling state becoming unstable, the bandwidth compensation amount is multiplied by an adjustment factor larger than 0 and smaller than 1. It may be added to the target tension.
[0088]
As shown in FIG. 11, when compensating the bandwidth for the tension control, the bandwidth compensation amount is added to the target tension at the start of the target value changing section, and the actual tension is changed immediately after the start of the balance control. The response of the motor current control can be improved. That is, by compensating the tension control bandwidth, a decrease in the target value response of the balance control device 3 when the tension band control is performed is prevented.
[0089]
(2nd Embodiment: An example of embodiment of the balance control apparatus of Claims 10-13)
FIG. 12 is a control block of the balance control device 3a according to the second embodiment of the present invention. The configuration of the balance control device 3a stores ideal values, which are ideal values of sheet thickness, tension, rolling load, and motor current, instead of the target load calculation unit 34, the load storage unit 35, and the target current calculation unit 36. Ideal value storage unit 381, ideal value calculation unit 382 for obtaining ideal values of sheet thickness, tension, rolling load and motor current, constraint condition storage unit 384 for storing constraint conditions, plate thickness, tension, rolling load and motor An initial value acquisition unit 383 that acquires an actual current value and an optimal value calculation unit 385 (corresponding to an optimal value calculation unit) that calculates a target motor current and a target rolling load by performing optimal value calculation described later. Except for this, it is the same as the configuration of the balance control device 3 of the first embodiment. Here, a different point from the balance control apparatus 3 of 1st Embodiment is demonstrated, and description is abbreviate | omitted about the same point.
[0090]
The ideal value storage unit 381 stores values (ideal values) of the sheet thickness and tension between the rolling stands considered to be ideal from the viewpoint of stable rolling and quality assurance, and the rolling load and motor current of each rolling stand. To store. Here, for each steel grade of the material to be rolled and the surface section of the rolling roll (dull, bright, etc.), the ideal values of the sheet thickness and tension between the rolling stands and the rolling load and motor current of each rolling stand (respectively, (Ideal plate thickness, ideal tension, ideal load, ideal current).
[0091]
The ideal value calculation unit 382 reads the ideal plate thickness, ideal tension, ideal load, and ideal current corresponding to the steel type of the material to be rolled and the surface classification (dull, bright, etc.) of the rolling roll from the ideal value storage unit 381, and optimizes it. This is output to the value calculation unit 385.
[0092]
The initial value acquisition unit 383 tandem-rolls the actual values (referred to as initial plate thickness, initial tension, initial load, and initial current, respectively) of the plate thickness and tension between the rolling stands and the rolling load and motor current of each rolling stand. It is acquired from the machine 1 and output to the optimum value calculation unit 385.
[0093]
The constraint condition storage unit 384 stores constraint conditions when the optimum value calculation unit 385 calculates the target motor current and the target load. The constraint condition is, for example, that the rolling reduction (or rolling load or motor current) of each rolling stand is not less than a predetermined value and not more than a predetermined value.
[0094]
The optimum value calculation unit 385 includes the ideal plate thickness, ideal tension, ideal load and ideal current input from the ideal value calculation unit 382, and the initial plate thickness, initial tension, initial load and initial current input from the initial value acquisition unit 383. The optimum value is calculated using the current and the target motor current and the target rolling load are calculated. However, when the constraint condition is stored in the constraint condition storage unit 384 (that is, when there is a constraint condition), the optimum value calculation unit 385 performs the optimum value calculation within a range that satisfies the constraint condition. .
[0095]
Here, the optimum value calculation performed by the optimum value calculation unit 385 will be specifically described. Here, for the sake of convenience, a case where there is no constraint condition will be described. The meanings of symbols used in formulas (39) to (49) to be described later are as follows.
u: Manipulation vector
(Vector consisting of a total of 8 components, including the target plate thickness u1 to u4 between the four stands and the target tension u5 to u8 between the four stands)
ud: ideal manipulated variable vector
(Vector consisting of a total of 8 components, 4 ideal plate thicknesses ud1 to ud4 and 4 ideal tensions ud5 to ud8)
u0: Initial manipulated variable vector
(Vector consisting of a total of 8 components of 4 initial plate thicknesses u01 to u04 and 4 initial tensions u05 to u08)
r ′: target value vector before conversion
(Vector consisting of a total of 10 components of 5 target rolling loads r′1 to r′5 and 5 target motor currents r′6 to r′10)
r'd: target value vector before ideal conversion
(Vector consisting of a total of 10 components of 5 ideal loads r'd1 to r'd5 and 5 ideal currents r'd6 to r'd10)
r′0: target value vector before initial conversion
(Vector consisting of a total of 10 components of 5 initial loads r′01 to r′05 and 5 initial currents r′06 to r′010)
Cr: target value conversion matrix
(8 × 10 matrix generated by taking out the 29th to 38th column portions of the matrix C defined by the equation (31))
GmbcFF: Feedforward control gain matrix defined by equation (34)
αi: Weight related to the operation amount ui (i = 1 to 8)
A: 8-by-8 weight matrix in which the weight αi is a diagonal component and the other components are 0
βi: Weight for target value ri ′ before conversion (i = 1 to 10)
B: Weight matrix of 10 rows and 10 columns with the weight βi as a diagonal component and the other components being 0
J: Evaluation function
λi: Lagrange's undetermined multiplier (i = 1 to 8)
λ: Vector consisting of 8 components with Lagrange's undetermined multiplier λi
First, the evaluation function J is defined by the following equation (39).
[0096]
[Expression 4]

[0097]
In the following calculation, the optimum value calculation for obtaining the target value vector r ′ before conversion and the manipulated variable vector u that minimize the evaluation function J defined by the equation (39) is performed. Since the manipulated variable vector u obtained as a result of the optimum value calculation is not used, a method for calculating the pre-conversion target value vector r ′ will be described in the following description.
[0098]
The target rolling load and target motor current obtained as a result of the optimum value calculation are the target rolling load and target motor current included in the target value vector before conversion, the target plate thickness between stands and the target tension between stands included in the operation amount vector. Since these are values close to their ideal values, in addition to the balance between the rolling load and the motor current, the value is such that the balance between the plate thickness and the tension is ensured. Therefore, a balance between the thickness and tension between the rolling stands is ensured, rolling troubles such as chattering are prevented, and the surface quality of the material to be rolled is improved.
[0099]
Next, a specific method for calculating the optimum value for obtaining the pre-conversion target value vector r ′ and the manipulated variable vector u that minimize the evaluation function J defined by the equation (39) will be described. The following equation (40) is obtained in the same manner as equation (36) from rolling theory or the like. u−u0 = GmbcFF · Cr · (r′−r′0) (40)
Therefore, the optimum value calculation that minimizes the evaluation function J defined by the equation (39) is performed under the condition that satisfies the equation (40). Here, when the Lagrange's undetermined multiplier λ i is introduced, the optimum value calculation that minimizes the function J ′ defined by the following equation (41) may be performed.
[0100]
[Equation 5]

[0101]
From the optimality conditions, the following equations (42) to (44) are obtained.
[0102]
[Formula 6]

[0103]
By substituting the equation (41) into the equations (42) to (44), the following equations (45) to (47) are obtained.
2A · (u−ud) + λ = 0 (45)
2B · (r'-r'd) -Cr^T・ GmbcFF^T・ Λ = 0 (46)
u−u0 = GmbcFF · Cr · (r′−r′0) (47)
From the equations (45) to (47), when λ and u are eliminated, the following equation (48) is obtained.
[Cr^T・ GmbcFF^T* A * GmbcFF * Cr + B] * (r'-r'0) = B * (r'd-r'0) + Cr^T・ GmbcFF^T・ A ・ (ud−u0) (48)
Here, an 8 × 8 matrix [Cr^T・ GmbcFF^TAssuming that A · GmbcFF · Cr + B] is regular, the following equation (49) is obtained from the equation (48).
r ′ = r′0 + [Cr^T・ GmbcFF^T・ A ・ GmbcFF ・ Cr ＋ B]^-1・ [B ・ (r'd-r'0) + Cr^T・ GmbcFF^T・ A ・ (ud−u0)] (49)
Using this (49), a pre-conversion target value vector r ′ that minimizes the evaluation function J is obtained.
[0104]
Here, since a linear model of the controlled object is used, it is not necessary to perform a convergence calculation or the like in the optimum value calculation. However, when a nonlinear model is used as the controlled object model, a nonlinear model including the convergence calculation is used. It is necessary to calculate the optimum value. Nonlinear optimal value calculation can be performed using, for example, a known sequential quadratic programming method (see “FORTRAN77 optimization programming” by Toshihide Ibaraki and Masao Fukushima, Iwanami Shoten pp 167 to 171). When this method is used, it is possible to perform optimum value calculation within a range that satisfies a predetermined constraint condition. Further, here, the case where the optimum value calculation is performed with respect to the plate thickness has been described, but an optimization calculation may be performed with respect to the rolling reduction instead of the plate thickness.
[0105]
FIG. 13 is a flowchart showing the operation of the balance control device 3a. First, it is determined whether or not to start balance control (step S101). For example, the balance control is started upon completion of acceleration after the start of rolling, or after a predetermined time has elapsed since the start of rolling. If this determination is negative, the system waits until this determination is positive. If this determination is affirmed, the ideal value calculation unit 382 reads the ideal plate thickness, ideal tension, ideal load, and ideal current from the ideal value storage unit 381 (step S103). Then, the initial plate thickness, initial tension, initial load, and initial current are acquired from the tandem rolling mill 1 by the initial value acquisition unit 383 (step S105). Next, the optimal value calculation unit 385 calculates the target motor current and the target rolling load (pre-conversion target value vector r ′) (step S107). Next, a target value (target value vector r) is obtained by the target value calculation unit 37 (step S109). And the feedforward compensation part 31 calculates | requires the feedforward compensation amount based on (36) Formula using a target rolling load and a target motor current (step S111).
[0106]
Next, the feedback compensation unit 32 obtains a feedback compensation amount using the target rolling load and the target motor current (step S113). Next, the addition unit 33 adds the feedback compensation amount and the feedforward compensation amount to obtain an operation amount (step S115). Then, this operation amount is output to the control target (step S117).
[0107]
Thereafter, it is determined whether or not to end the balance control (step S119). For example, the balance control is ended at the start of deceleration before the end of rolling, or after a predetermined time has elapsed since the start of rolling. If this determination is affirmative, the process ends. If this determination is negative, it is determined whether to recalculate the target value (step S121). For example, the target value is recalculated every predetermined time interval (or every predetermined length interval of the rolling length of the material to be rolled). If this determination is negative, the process returns to step S111 and the control is continued. When this determination is affirmed, the process returns to step S105, the target value is calculated again (steps S105 to S109), and the control is continued.
[0108]
Thus, for example, since the target value is recalculated every predetermined time interval (or every predetermined length interval of the rolling length of the material to be rolled), when the rolling conditions (for example, the hardness of the original sheet) change. An appropriate target value is set. However, from the viewpoint of balance control stability, the speed of changing the target value needs to be sufficiently slower than the response speed of the balance control.
[0109]
(Third embodiment: an example of an embodiment of a balance control device according to claims 14 to 16)
FIG. 14 is a control block of the balance control device 3b according to the third embodiment of the present invention. The configuration of the balance control device 3b is, instead of the feedforward compensation unit 31 and the feedback compensation unit 32, a first feedforward compensation unit 31a (corresponding to a first feedforward compensation means) for obtaining a feedforward compensation amount and a second feed. Forward compensation unit 31b (corresponding to the second feedforward compensation unit), first feedback compensation unit 32a (corresponding to the first feedback compensation unit) for obtaining a feedback compensation amount, and second feedback compensation unit 32b (second feedback compensation unit) And a switching unit 39 (corresponding to a switching unit) that switches a compensation unit used for balance control, and is the same as the configuration of the balance control device 3 of the first embodiment. Here, a different point from the balance control apparatus 3 of 1st Embodiment is demonstrated, and description is abbreviate | omitted about the same point.
[0110]
The first feedforward compensation unit 31a has the same structure as the feedforward compensation unit 31 in the balance control device 3 of the first embodiment, and the first feedback compensation unit 32a is in the balance control device 3 of the first embodiment. The feedback compensation unit 32 has the same structure.
[0111]
In the first feedforward compensation unit 31a and the first feedback compensation unit 32a, the operation amount u is a target plate thickness between four rolling stands and a target tension between four rolling stands, and a control amount y is four load fluctuation differences and The feedforward compensation amount and the feedback compensation amount in the case of four current fluctuation differences are respectively obtained.
[0112]
On the other hand, the second feedforward compensation unit 31b and the second feedback compensation unit 32b provide feedforward compensation when the operation amount u is a target plate thickness between four rolling stands and the control amount y is four load fluctuation differences. The amount and the feedback compensation amount are obtained respectively. The second feedforward compensation unit 31b and the second feedback compensation unit 32b can be configured in the same manner as the first feedforward compensation unit 31a and the first feedback compensation unit 32a. Since the configuration method of the compensation unit 31a and the first feedback compensation unit 32a has been described in the first embodiment, the description of the configuration method is omitted here.
[0113]
The switching unit 39 alternately switches between the first feedforward compensation unit 31a and the second feedforward compensation unit 31b at a predetermined timing, and alternately switches between the first feedback compensation unit 32a and the second feedback compensation unit 32b. Used for balance control.
[0114]
Specifically, it is determined whether or not the rolling speed is substantially constant, and at the timing when the rolling speed is changed from the substantially constant state to the state where the rolling speed is not substantially constant, the second feedforward compensation unit 31b. The second feedback compensator 32b is switched to use for balance control, and the first feedforward compensator 31a and the first feedforward compensator 31a and the first feedback are changed at a timing when the rolling speed is changed from a substantially non-constant state to a substantially constant rolling speed. The feedback compensator 32a is switched to be used for balance control. Here, the feedforward compensation amounts obtained by the first feedforward compensation unit 31a and the second feedforward compensation unit 31b are referred to as a first FF compensation amount and a second FF compensation amount, respectively. The feedback compensation amounts obtained by the first feedback compensation unit 32a and the second feedback compensation unit 32b are referred to as a first FB compensation amount and a second FB compensation amount, respectively.
[0115]
That is, the first feedforward compensation unit 31a and the first feedback compensation unit 32a are used for balance control during constant speed rolling, and the second feedforward compensation unit 31b and the second feedback compensation unit 32b are balanced during acceleration or deceleration. Used for control. Therefore, during acceleration or deceleration with a large change in motor load, only the rolling load for each rolling stand is controlled (the motor load is not controlled), so that the rolling load for each rolling stand can be controlled stably. It becomes possible. In addition, during constant speed rolling with a small change in motor load, the rolling load and motor load for each rolling stand are controlled, so that the motor load for each rolling stand can be controlled in addition to the rolling load for each rolling stand. It becomes possible.
[0116]
Further, bumpless switching is realized by configuring the first feedforward compensation unit 31a, the second feedforward compensation unit 31b, the first feedback compensation unit 32a, and the second feedback compensation unit 32b in a speed type (“PID Control ", edited by System Control Information Society, Asakura Shoten pp 48-50).
[0117]
FIG. 15 is a flowchart showing the operation of the balance control device 3b. First, it is determined whether or not to start balance control (step S201). For example, the balance control is started upon completion of acceleration after the start of rolling, or after a predetermined time has elapsed since the start of rolling. If this determination is negative, the system waits until this determination is positive. When this determination is affirmed, the target rolling load is obtained by the target load calculating unit 34, and the target motor current is obtained by the target current calculating unit 36 (step S203). Next, a target value is obtained by the target value calculation unit 37 (step S205). Then, the switching unit 39 determines whether or not the rolling speed is substantially constant (step S207). If this determination is positive, the process proceeds to step S209, and if this determination is negative, the process proceeds to step S215.
[0118]
If the determination in step S207 is affirmative (when constant-speed rolling is in progress), the first feedforward compensation unit 31a obtains the first FF compensation amount using the target rolling load and the target motor current (step S207). S209). Next, the first feedback compensation unit 32a obtains the first FB compensation amount using the target rolling load and the target motor current (step S211). Next, the addition unit 33 adds the first FF compensation amount and the first FB compensation amount to obtain an operation amount (step S213), and proceeds to step S221.
[0119]
If the determination in step S207 is negative (when accelerating or decelerating), the second FF compensation amount is obtained by using the target rolling load by the second feedforward compensation unit 31b (step S215). Next, the second feedback compensation unit 32b obtains the second FB compensation amount using the target rolling load (step S217). Next, the addition unit 33 adds the second FF compensation amount and the second FB compensation amount to obtain an operation amount (step S219), and proceeds to step S221.
[0120]
When the operation amount is obtained in step S213 or step S219, the operation amount is output to the control target (step S221). Thereafter, it is determined whether or not to end the balance control (step S223). For example, the balance control is ended at the start of deceleration before the end of rolling, or after a predetermined time has elapsed since the start of rolling. If this determination is negative, the process returns to step S207 and control is continued. If this determination is affirmative, the process ends.
[0121]
FIG. 16 is a timing chart showing the operation of the balance control device 3b. (A) is a change in rolling speed, and (b) is an operation of the switching unit 39. In periods T1, T3, and T5 where the rolling speed is substantially constant, the first feedforward compensation unit 31a and the first feedback compensation unit 32a are used, and the rolling speed is not substantially constant (a period during acceleration or deceleration). In T2 and T4, the second feedforward compensation unit 31b and the second feedback compensation unit 32b are used. That is, the switching unit 39 switches the second feedforward compensation unit 31b and the second feedback compensation unit 32b to use for balance control at the start time t1 of the period T2 and the start time t3 of the period T4. At the start time t2 and the start time t4 of the period T5, the first feedforward compensation unit 31a and the first feedback compensation unit 32a are switched to be used for balance control.
[0122]
Here, the embodiment has been described in which the second feedforward compensation unit 31b and the second feedback compensation unit 32b are used for balance control in a period where the rolling speed is not substantially constant (a period during acceleration or deceleration). In addition to a period that is not substantially constant (a period during acceleration or deceleration), after a transition from a period in which the rolling speed is not substantially constant to a period in which the rolling speed is substantially constant (after completion of acceleration or deceleration), a predetermined time In the meantime, the second feedforward compensation unit 31b and the second feedback compensation unit 32b may be used for balance control. In this case, only the rolling load for each rolling stand is controlled (the motor load is not controlled) for a predetermined time after completion of acceleration (or completion of deceleration) in which the motor current may become unstable. It becomes possible to stably control the rolling load for each rolling stand.
[0123]
Moreover, although the form which switches 1st feedforward compensation part 31a and 1st feedback compensation part 32a, 2nd feedforward compensation part 31b, and 2nd feedback compensation part 32b based on rolling speed was demonstrated here, 2nd The feedforward compensation unit 31b and the second feedback compensation unit 32b are not provided, and the first feedforward compensation is performed by forcibly setting the inner current fluctuation difference of the control amount to “0” and holding the inner inter-stand tension of the operation amount. The unit 31a and the first feedback compensation unit 32a can also function in the same manner as the second feedforward compensation unit 31b and the second feedback compensation unit 32b, respectively.
[0124]
【The invention's effect】
  According to the first aspect of the present invention, the feedforward compensation amount used for the feedforward control of the control amount is obtained by the feedforward compensation means, and the feedback compensation amount used for the feedback control of the control amount is obtained by the feedback compensation means. Then, the operation amount is obtained by adding the feedforward compensation amount and the feedback compensation amount by the adding means, and this operation amount is supplied to the plate thickness tension control device. In this way, since the balance control device is a two-degree-of-freedom control system, it is possible to simultaneously optimize the target value response and the disturbance response, and the balance control has good stability and good target value response. A device can be realized.Then, band control having a bandwidth based on the target tension is performed by the plate thickness tension control device, the target tension is included in the operation amount of the balance control device, and the bandwidth is compensated by the feedforward compensation means. Therefore, since the feedforward compensation amount obtained by adding the bandwidth compensation amount is obtained, it is possible to prevent the target value response of the balance control device from being lowered when the tension band control is performed.
[0125]
According to the second aspect of the present invention, since the feedforward compensation amount is obtained by the feedforward compensation means based on the static characteristic model in which the controlled object is statically modeled, an appropriate feedforward compensation amount can be easily obtained. Can be sought.
[0126]
According to the invention described in claim 3, since the feedback compensation means has an integral characteristic for integrating the deviation between the control amount and the target value of the control amount, the steady deviation with respect to the target value of the balance control is eliminated, Good control characteristics can be obtained.
[0129]
  Claim4According to the invention described in the above, the load storage means stores the unit width load, which is the rolling load per unit plate width of the material to be rolled, at least for each steel type of the material to be rolled and the surface section of the rolling roll, and calculates the target load. Since the target rolling load is obtained by multiplying the unit width load by the sheet width of the material to be rolled by the means, an appropriate target rolling load is easily obtained, and the control amount relates to the rolling load for each rolling stand. Therefore, the balance control device can control the rolling load using an appropriate target rolling load.In addition, since the control amount relates to the rolling load for each rolling stand, the rolling load, which is an important indicator of the balance of the rolling state of the tandem rolling mill, is controlled, and the balance of the rolling state of the tandem rolling mill can be maintained. it can.
[0130]
  Claim5According to the invention described in the above, the load storage means stores the unit width load, which is the rolling load per unit plate width of the material to be rolled, at least for each steel type of the material to be rolled and the surface section of the rolling roll, and calculates the target load. If the actual rolling load at the start of balance control is greater than the load upper limit obtained by multiplying the unit width load by the plate width of the material to be rolled and adding a predetermined value, the load upper limit is the target rolling load. If the actual rolling load at the start of balance control is smaller than the load lower limit value obtained by subtracting a predetermined value from the product of the unit width load and the sheet width of the material to be rolled, the load lower limit value is set as the target rolling load. When the actual rolling load at the start of balance control is equal to or lower than the upper limit of load and equal to or higher than the lower limit of load, the actual rolling load at the start of balance control is set as the target rolling load. Load upper limit value It is Mel possible. Since the control amount relates to the rolling load for each rolling stand, the balance control device can perform band control with the band width in the range from the load lower limit value to the load upper limit value for the rolling load.
[0131]
  Claim6According to the invention described in the above, the control amount isRolling load for each rolling stand andThis is related to the motor load for each rolling stand. Since the target load calculation means sets a predetermined value equal to or lower than the rated load of the motor as the target motor load, the balance control device makes the motor load equal to or lower than the rated load value of the motor. When the motor load is controlled and the rolling speed becomes a bottleneck, the rolling speed can be increased.In addition, since the control amount relates to the motor load for each rolling stand, the motor load, which is an important indicator of the balance of the rolling state of the tandem rolling mill, is controlled, and the balance of the rolling state of the tandem rolling mill can be maintained. it can. However, the motor torque, motor current, motor power, and rolling torque are collectively referred to as a motor load.
[0132]
  Claim7According to the invention described in the above, the control amount relates to the motor load for each rolling stand, and the target motor calculating means calculates the target motor load of at least one stand of the actual motor loads of the plurality of stands including the stand. Since it is obtained as an average value, the balance control controls the motor load of a plurality of stands below a predetermined value, and when the motor load becomes a bottleneck of the rolling speed, the rolling speed can be increased.In addition, since the control amount relates to the motor load for each rolling stand, the motor load, which is an important indicator of the balance of the rolling state of the tandem rolling mill, is controlled, and the balance of the rolling state of the tandem rolling mill can be maintained. it can.
[0133]
  Claim8According to the invention described in the above, in addition to the rolling state amount included in the control amount, it is possible to realize appropriate control with respect to the rolling state amount which is a variable of the evaluation function among the rolling state amounts included in the operation amount. The target value of the controlled variable can be set. As a result, a balance control device that enables more stable rolling can be realized.And since it becomes possible to obtain | require the target value of control amount by the optimal value calculation means at the timing etc. when rolling conditions, such as rolling speed, were changed, the target value of further appropriate control amount can be set.
[0134]
  Claim9According to the invention described in (2), in addition to the rolling load and motor load for each rolling stand, among the target plate thickness and target tension between the rolling stands, appropriate control is also performed with respect to the rolling state amount that is a variable of the evaluation function. The target value of the rolling load and motor load for each rolling stand that can be realized can be set. As a result, the balance between the thickness and tension between the rolling stands can be secured, rolling troubles such as chattering can be prevented, and the surface quality of the material to be rolled can be improved.
[0135]
  Claim 10According to the invention described in (1), even when there are constraints on equipment such as plate thickness, tension, motor load, etc., it is possible to obtain the target value of the control amount that satisfies the constraints.
[0137]
  Claim 11Since the feedforward compensation means and the feedback compensation means suitable for the rolling conditions and the like can be selectively used, more appropriate balance control can be realized.
[0138]
  Claim 12According to the invention described in the above, since the feedforward compensation means and the feedback compensation means suitable for control during acceleration or deceleration (different from the case where the rolling speed is substantially constant) are used, further appropriate balance control is performed. realizable.
[0139]
  Claim 13According to the invention described in, the rolling load for each rolling stand can be stably controlled even during acceleration or deceleration with a large change in motor load.
[Brief description of the drawings]
FIG. 1 is a diagram showing a schematic configuration of a balance control device of a tandem rolling mill according to an embodiment of the present invention.
FIG. 2 is a control block diagram of the balance control device according to the first embodiment of the present invention.
FIG. 3 is a flowchart showing the operation of the balance control device according to the first embodiment.
FIG. 4 is a diagram illustrating an effect of feedforward control of the balance control device according to the first embodiment.
FIG. 5 is a diagram illustrating an effect of feedback control of the balance control device according to the first embodiment.
FIG. 6 is a diagram showing the effect of the balance control device (when there is no balance control device).
FIG. 7 is a diagram showing the effect of the balance control device (when only feedback control is performed).
FIG. 8 is a diagram showing the effect of the balance control device (when only feedforward control is performed).
FIG. 9 is a diagram showing the effect of the balance control device according to the first embodiment (when both feedback control and feedforward control are performed).
FIG. 10 is a diagram showing the effect of feedforward control when band control is performed as tension control (when bandwidth compensation is not performed).
FIG. 11 is a diagram showing the effect of feedforward control when band control is performed as tension control (when the bandwidth of tension control is compensated).
FIG. 12 is a control block of a balance control device according to a second embodiment of the present invention.
FIG. 13 is a flowchart showing the operation of the balance control device according to the second embodiment.
FIG. 14 is a control block of a balance control device according to a third embodiment of the present invention.
FIG. 15 is a flowchart showing the operation of the balance control device according to the third embodiment.
FIG. 16 is a timing chart showing the operation of the balance control device according to the third embodiment.
FIG. 17 is a diagram for explaining the necessity of balance control.
[Explanation of symbols]
1 Tandem rolling mill
2 Thickness control device
3, 3a, 3b Balance control device
11-15 Rolling stand
31 Feedforward compensation unit (feedforward compensation means)
31a 1st feedforward compensation part (1st feedforward compensation means)
31b 2nd feedforward compensation part (2nd feedforward compensation means)
32 Feedback compensation unit (feedback compensation means)
32a First feedback compensation unit (first feedback compensation means)
32b Second feedback compensation unit (second feedback compensation means)
33 Adder (addition means)
34 Target load calculation unit (target load calculation means)
35 Load storage unit (load storage means)
36 Target current calculation unit (target load calculation means)
37 Target value calculator
385 Optimum value calculation unit (optimum value calculation means)
39 Switching section (switching means)

Claims (13)

A control system includes a tandem rolling mill having a plurality of rolling stands and a plate thickness tension control device that controls each rolling stand so as to obtain at least one of a target plate thickness and a target tension set for each rolling stand. And an operation amount calculating means for obtaining an operation amount based on a control amount selected from a rolling state amount obtained from the control object and representing a rolling state, and supplying the operation amount to the plate thickness tension control device. Is a balance control device that maintains the balance of the rolling state of the tandem rolling mill, wherein the operation amount calculation means includes a feedforward compensation means for obtaining a feedforward compensation amount used for feedforward control of the control amount, and a control amount Feedback compensation means for obtaining a feedback compensation amount used for feedback control, and the feedforward compensation Wherein by adding the feedback compensation amount possess an adding means for obtaining the operation amount and the thickness tension control device performs a band control having a band width relative to the said target tension, the operation amount, wherein comprises a target tension, said feedforward compensation means balance control apparatus of a tandem rolling mill, characterized in Rukoto seek feedforward compensation amount obtained by adding the bandwidth compensation amount for compensating the bandwidth.   The balance control apparatus for a tandem rolling mill according to claim 1, wherein the feedforward compensation means obtains the feedforward compensation amount based on a static characteristic model in which the controlled object is statically modeled.   The balance control device for a tandem rolling mill according to claim 1 or 2, wherein the feedback compensation means has an integral characteristic for integrating the deviation between the control amount and a target value of the control amount. A control system includes a tandem rolling mill having a plurality of rolling stands and a plate thickness tension control device that controls each rolling stand so as to obtain at least one of a target plate thickness and a target tension set for each rolling stand. An operation amount calculating means for obtaining an operation amount based on a control amount selected from a rolling state amount obtained from the control target and representing a rolling state, and supplying the operation amount to the plate thickness tension control device Is a balance control device that maintains the balance of the rolling state of the tandem rolling mill, wherein the operation amount calculation means includes a feedforward compensation means for obtaining a feedforward compensation amount used for feedforward control of the control amount, and a control amount Feedback compensation means for obtaining a feedback compensation amount used for feedback control, and the feedforward compensation Wherein and an adding means for adding the feedback compensation amount determining the manipulated variable and,
The control amount relates to a rolling load for each rolling stand, and is a target load calculating means for obtaining a target rolling load that is a target value of the rolling load for each rolling stand, and a rolling load per unit plate width of the material to be rolled. Load storage means for storing a certain unit width load at least for each steel grade of the material to be rolled and each surface section of the rolling roll, and the target load calculating means is configured to multiply the unit width load by the plate width of the material to be rolled. balancing controller features and to filter tandem rolling mill to seek a target rolling load. A control system includes a tandem rolling mill having a plurality of rolling stands and a plate thickness tension control device that controls each rolling stand so as to obtain at least one of a target plate thickness and a target tension set for each rolling stand. An operation amount calculating means for obtaining an operation amount based on a control amount selected from a rolling state amount obtained from the control target and representing a rolling state, and supplying the operation amount to the plate thickness tension control device Is a balance control device that maintains the balance of the rolling state of the tandem rolling mill, wherein the operation amount calculation means includes a feedforward compensation means for obtaining a feedforward compensation amount used for feedforward control of the control amount, and a control amount Feedback compensation means for obtaining a feedback compensation amount used for feedback control, and the feedforward compensation Wherein and an adding means for adding the feedback compensation amount determining the manipulated variable and,
The control amount relates to a rolling load for each rolling stand, and is a target load calculating means for obtaining a target rolling load that is a target value of the rolling load for each rolling stand, and a rolling load per unit plate width of the material to be rolled. Load storage means for storing a certain unit width load at least for each steel type of the material to be rolled and each surface section of the rolling roll, and the target load calculating means is configured to apply the actual rolling load at the start of balance control to the unit width load. When the load upper limit value obtained by multiplying the rolled material sheet width by a predetermined value is larger than the load upper limit value, the load upper limit value is set as the target rolling load, and the actual rolling load at the start of balance control is applied to the unit width load. If it is smaller than the load lower limit value obtained by subtracting a predetermined value to the product of the width of the rolled material, the load lower limit value is set as the target rolling load, and the actual rolling load at the start of balance control is equal to or less than the load upper limit value. There and wherein when at least the load limit value, balance control device features and to filter tandem rolling mill to the actual rolling load during balance control start and target rolling load. The control amount relates to a rolling load for each rolling stand and a motor load for each rolling stand, and includes target load calculation means for obtaining a target motor load that is a target value of the motor load for each rolling stand, and the target load calculation 6. The balance control apparatus for a tandem rolling mill according to claim 4 , wherein the means sets a predetermined value equal to or less than a rated load of the motor as a target motor load. A control system includes a tandem rolling mill having a plurality of rolling stands and a plate thickness tension control device that controls each rolling stand so as to obtain at least one of a target plate thickness and a target tension set for each rolling stand. An operation amount calculating means for obtaining an operation amount based on a control amount selected from a rolling state amount obtained from the control target and representing a rolling state, and supplying the operation amount to the plate thickness tension control device Is a balance control device that maintains the balance of the rolling state of the tandem rolling mill, wherein the operation amount calculation means includes a feedforward compensation means for obtaining a feedforward compensation amount used for feedforward control of the control amount, and a control amount Feedback compensation means for obtaining a feedback compensation amount used for feedback control, and the feedforward compensation Wherein and an adding means for adding the feedback compensation amount determining the manipulated variable and,
The control amount relates to a motor load for each rolling stand, and includes target load calculation means for obtaining a target motor load that is a target value of the motor load for each rolling stand, and the target load calculation means includes at least one stand. target motor load, balancing controller features and to filter tandem rolling mill to be determined as the average of the actual motor load multiple stand including the stand. A control system includes a tandem rolling mill having a plurality of rolling stands and a plate thickness tension control device that controls each rolling stand so as to obtain at least one of a target plate thickness and a target tension set for each rolling stand. An operation amount calculating means for obtaining an operation amount based on a control amount selected from a rolling state amount obtained from the control target and representing a rolling state, and supplying the operation amount to the plate thickness tension control device Is a balance control device that maintains the balance of the rolling state of the tandem rolling mill, wherein the operation amount calculation means includes a feedforward compensation means for obtaining a feedforward compensation amount used for feedforward control of the control amount, and a control amount Feedback compensation means for obtaining a feedback compensation amount used for feedback control, and the feedforward compensation And an adding means for obtaining the feedback compensation amount and adding to the operation amount of the, the rolling state quantity contained in the control amount, evaluated according to at least one variable of the rolling state amount included in the operation amount Optimum value calculating means for obtaining a target value of the control amount based on the value of the control amount that maximizes or minimizes the function, and the optimum value calculating means is between the start of balance control and the end of balance control. , balance control start and the control amount of the target value balance control device features and to filter tandem rolling machine Rukoto seek at least 2 or more timings of a predetermined timing other than the balance control start. The rolling state amount included in the control amount is a rolling load and a motor load for each rolling stand, and the rolling state amount included in the operation amount is a target plate thickness and a target tension between the rolling stands. The balance control apparatus of the tandem rolling mill according to claim 8 . The optimum value calculation means, according to claim 8 or 9, characterized in that for obtaining a target value of at least one related constraints satisfying the control amount of the rolling state quantity contained in the controlled variable or the manipulated variable Balance control device for tandem rolling mill. A control system includes a tandem rolling mill having a plurality of rolling stands and a plate thickness tension control device that controls each rolling stand so as to obtain at least one of a target plate thickness and a target tension set for each rolling stand. An operation amount calculating means for obtaining an operation amount based on a control amount selected from a rolling state amount obtained from the control target and representing a rolling state, and supplying the operation amount to the plate thickness tension control device Is a balance control device that maintains the balance of the rolling state of the tandem rolling mill, wherein the operation amount calculation means includes a feedforward compensation means for obtaining a feedforward compensation amount used for feedforward control of the control amount, and a control amount Feedback compensation means for obtaining a feedback compensation amount used for feedback control, and the feedforward compensation Wherein and an adding means for adding the feedback compensation amount determining the manipulated variable and,
The feedforward compensation means includes first feedforward compensation means and second feedforward compensation means, and the feedback compensation means includes first feedback compensation means and second feedback compensation means, and the first feedback compensation means includes a first feedback compensation means at a predetermined timing. The apparatus further comprises switching means for alternately switching between the feedforward compensation means and the second feedforward compensation means, and switching between the first feedback compensation means and the second feedback compensation means for use in balance control. Balance control device for tandem rolling mill. The switching means determines whether the rolling speed is substantially constant, and at the timing when the determination result changes, the first feedforward compensation means and the second feedforward compensation means are alternately switched, and first feedback compensation means and balance control apparatus of a tandem rolling mill of claim 1 1, wherein the alternately switching a second feedback compensation means. The first feedforward compensation means and the first feedback compensation means determine a feedforward compensation amount and a feedback compensation amount when the rolling state amount included in the control amount is a rolling load and a motor load for each rolling stand, respectively. The second feedforward compensation unit and the second feedback compensation unit obtain a feedforward compensation amount and a feedback compensation amount when the rolling state amount included in the control amount is a rolling load for each rolling stand, respectively, and the switching unit. Is switched to use the second feedforward compensation means and the second feedback compensation means for balance control at a timing when the rolling speed is changed from a substantially constant state to a non-constant state. The rolling speed is almost constant from the state where That state at a timing changes, balance control apparatus of a tandem rolling mill according to claim 1 2, characterized in that switching to use the first feedforward compensation means and the first feedback compensation means to balance control.

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