JP3571952B2 - 2-DOF control device - Google Patents

Description

他方、外乱Ｄによる制御量Ｙの望ましい制御応答を規定する規範モデルは既に知られているように次式とする（ＰＩＤ制御、ｐ１４（２．１１）式またはｐ３１（２．３５）式、著者：須田信英、編者：システム制御情報学会、発行所：株式会社 朝倉書店参照）。
【００３４】
Ｍ_Ｄ（ｓ）＝｛ｓ／（Ｋ_Ｐ／Ｔ_Ｉ）｝・［１／（１＋σＤｓ＋α２ＤσＤ^２ｓ^２＋α３ＤσＤ^３ｓ^３）］ ……（４）
ここで、外乱入力に対する制御応答に関する規範モデルの係数α２Ｄ，α３Ｄは 速応性とロバスト性との兼ね合いから、例えば表１に示す値とする。この表１は前述する文献ＰＩＤ制御、ｐ１４〜ｐ１５参照。
【００３５】
【表１】

【００３６】
ところで、以上のような（３）式の実制御系と（４）式の規範モデルとは等しい関係になければならない。よって、Ｗ_Ｄ（ｓ）＝Ｍ_Ｄ（ｓ）について解けば、外乱入力に対する制御応答に関する立上り時間σ_ＤおよびＰＩＤパラメータＫ_Ｐ、Ｔ_Ｉ、Ｔ_{Ｄ が}決定できる。そこで、決定されたパラメータを設定したＰＩＤフィードバック制御系に対し、制御対象の入力側にステップ状外乱を与えたとすると、図７（ａ）に示すような制御応答が得られる。
【００３７】
次に、図２（ｂ）に示す制御系に対し、決定された制御パラメータＫ_Ｐ，Ｔ_Ｉ，ＴＤを設定し、このときの目標値Ｒから制御量Ｙへの伝達関数Ｗ_Ｒ（ｓ）をもって表わすと、次式のようになる。
【００３８】
Ｗ_Ｒ（ｓ）＝［Ｋ_Ｐ｛ｂ＋１／（Ｔ_Ｉｓ）＋ｃＴ_Ｄｓ｝］・Ｍ_Ｄ（ｓ） ……（５）ここで、前段の［ ］内はフィードフォワード制御要素５の伝達関数、後段のＭ_Ｄ（ｓ）は前記（４）式の規範モデルの伝達関数である。
【００３９】
従って、この（５）式は下記する（６）式で表わせる。
【００４０】
Ｗ_Ｒ（ｓ）＝（１＋ｂＴ_Ｉｓ＋ｃＴ_ＩＴ_Ｄｓ^２）／（１＋σＤｓ＋α２ＤσＤ^２ｓ^２＋α３ＤσＤ^３ｓ^３） ……（６）
他方、目標値Ｒによる制御量Ｙの望ましい制御応答を規定する規範モデルは次式で表わすものとする（前述文献 ＰＩＤ制御、ｐ１２０（６．２）式参照）。
【００４１】
Ｍ_Ｒ（ｓ）＝１／（σＲｓ＋α２ＲσＲ^２ｓ^２＋α３ＲσＲ^３ｓ^３） …（７）
ここで、目標値変化に対する制御応答に関する規範モデルの係数α２Ｒ、α３Ｒは速応性とロバスト性との兼ね合いから、例えば前記表１に示す値とする。
【００４２】
そこで、Ｗ_Ｒ（ｓ）＝Ｍ_Ｒ（ｓ）について解くと、目標値変化に対する制御応答に関する立上り時間σＲは下式の３次方程式の最小実根から求められる。
【００４３】
（１−２α２Ｒ＋α３Ｒ）σＲ^３−（１−α２Ｒ）σＤσＲ^２＋α２ＤσＤ^２σＲ−α３ＤσＤ^３＝０ ……（８）
ここで、（６）式のＷ_Ｒ（ｓ）＝Ｂ／Ｃとし、また（７）式のＭ_Ｒ（ｓ）＝１／Ｚと置けば、Ｗ_Ｒ（ｓ）＝Ｍ_Ｒ（ｓ）の関係から、
Ｂ／Ｃ＝１／Ｚ → Ｚ＝Ｃ／Ｂ ……（９）
が導き出せる。
【００４４】
そこで、Ｃ／Ｂについて演算し、１次項および２次項まで解を導き出し、前記Ｚの１次項および２次項とそれぞれ等しい関係に置いて計算すれば、比例項用２自由度化パラメータｂは、
ｂ＝（σＤ−σＲ）／Ｔ_Ｉ ……（１０）
なる演算式から決定できる。また、微分項用２自由度化パラメータｃは、

なる演算式から決定できる。
【００４５】
なお、（１１）式においてα２Ｄ＝α２Ｒ＝０．５の場合には、
ｃ＝（σＤ−σＲ）^２／（２Ｔ_ＩＴ_Ｄ） ……（１２）となり、２自由度化パラメータｂ，ｃは（σ_Ｄ−σ_Ｒ）の関数であるとも言える。
【００４６】
従って、以上の説明から明らかなように、２自由度化パラメータｂ，ｃを求めるための入力項目Ａおよび演算式を得ることができたので、以下、その具体例について説明する。
【００４７】
図３は本発明に係る２自由度ＰＩＤ制御装置の一実施の形態を示す構成図である。
【００４８】
同図（ａ）に示す制御装置は、２自由度ＰＩＤ制御器１にパラメータ発生機構２が接続され、このパラメータ発生機構２には、入力項目Ａとして、積分時間ＴＩ、微分時間Ｔ_Ｄ、外乱入力制御応答を規定する立上り時間σＤ、目標値変更制御 応答を規定する立上り時間σＲが入力され、後記する図４に示す演算手段により ２自由度化パラメータｂ，ｃを算出し、２自由度ＰＩＤ制御器１に設定する構成である。
【００４９】
同図（ｂ）に示す制御装置は、同図（ａ）に示す入力項目の他に、さらに
外乱入力制御応答規範モデルの２次項係数α２Ｄ、目標値変更制御応答規範モデ ルの２次項係数α２Ｒも追加入力され、後記する図５に示す演算手段により２自 由度化パラメータｂ，ｃを算出し、２自由度ＰＩＤ制御器１に設定する構成である。
【００５０】
すなわち、図４（ａ）に示すパラメータ発生機構２は比較要素１１および除算要素１２からなり、比較要素１１は入力される外乱入力制御応答を規定する立上り時間σＤから同じく入力される目標値変更制御応答を規定する立上り時間σＲを減算し、その減算出力を除算要素１２に導入する。この除算要素１２は、減算結果（σＤ−σＲ）を積分時間ＴＩで除算し、前記（１０）式の比例項用２自由度化 パラメータｂを算出し、２自由度ＰＩＤ制御器１に設定する。
【００５１】
なお、外乱入力制御応答を規定する立上り時間σＤはＰＩＤパラメータを部分 的モデルマッチング法で設計する際に自動的に決定でき、或いは他の方法を用いてＰＩＤパラメータを決定する場合にはステップ外乱が入った時に制御量Ｙがピーク値に達する時間にほぼ等しいことから、この時間からも決定可能である。
【００５２】
また、目標値変更制御応答を規定する立上り時間σＲは前述したように演算に より一義的に決定でき、或いは目標値ステップ変化時の制御量がほぼ５０％に到達する時間として任意に設定できる。
【００５３】
次に、図４（ｂ）に示すパラメータ発生機構２は、比較要素１３、除算要素１４、乗算要素１５、除算要素１６および係数要素１７が設けられている。この比較要素１３および除算要素１４は、図４（ａ）と同様に比例項用２自由度化パラメータｂを算出する。さらに、乗算要素１５において比較要素１３の出力と除算要素１４の出力とを乗算し、この乗算結果を除算要素１６に導入し、ここで乗算結果を微分時間Ｔ_Ｄで除した後、係数要素１７で１／２を乗算すれば、前記（１ ２）式に基づく微分項用２自由度化パラメータｃ＝（σＤ−σＲ）^２／（２Ｔ_ＩＴ_Ｄ）を算出でき、２自由度ＰＩＤ制御器１に発信する。
【００５４】
さらに、図５は図３（ｂ）のパラメータ発生機構２の内部構成を示す図である。
【００５５】
このパラメータ発生機構２は、第１の演算要素２１および第２の演算要素２２からなり、第１の演算要素２１は（１０）式の演算により比例項用２自由度化パラメータｂを算出し、２自由度ＰＩＤ制御器１に発信する。第２の演算要素２２は（１１）式の演算により微分項用２自由度化パラメータｃを算出し、同様に２自由度ＰＩＤ制御器１に発信する。
【００５６】
次に、パラメータ発生機構２の他の例について図６を参照して説明する。
【００５７】
図６（ａ）は外乱入力および目標値変更による応答制御を規定する立上り時間σＤ、σＲの差信号（σＤ−σＲ）を除算要素１２に導き、ここで差信号を積分時間Ｔ_Ｉで除算することによって比例項用２自由度化パラメータｂを算出する例であ る。
【００５８】
図６（ｂ）は同図（ａ）と同様に両立上り時間σＤ、σＲの差信号（σＤ−σＲ）を入力する点を除けば、図４（ｂ）と同様な構成により２自由度化パラメータｂ，ｃを算出し、２自由度ＰＩＤ制御器１に発信する例である。
【００５９】
なお、以上のようにして決定された入力項目Ａのもとに２自由度化パラメータｂ，ｃを設定した場合の目標値ステップ変更時の制御応答例は図７（ｂ）に示す通りである。また、比較のため、従来のＩ−ＰＤ性御時（ｂ＝ｃ＝０）の制御応答は図７（ｃ）に、基本ＰＩＤ制御時（ｂ＝ｃ＝１）の制御応答は図７（ｄ）に示す通りである。
【００６０】
これらの制御応答図から明らかなように、ｂ＝ｃ＝０または１に限定されることなく、ｂ，ｃを任意の所定値とすることにより、目標値変更時に大きなオーバシュートを発生させることなく、追従性の優れた２自由度ＰＩＤ制御を実現できる。
【００６１】
なお、σＤ、σＲ、Ｔ_Ｉ、Ｔ_Ｄは以上記述した値に限られるものではなく、任意の定めた値を用いて、（１０）式、（１１）式の演算式により、２自由度化パラメータｂ，ｃ決定し設定してもよい。
【００６２】
従って、以上のような実施の形態によれば、予め定められた入力項目をパラメータ発生機構２に入力すれば、前述する導出された所定の演算式に基づいて２自由度化パラメータｂ，ｃを求めて２自由度ＰＩＤ制御器１に設定可能であり、従来のように長時間をかけて試行錯誤的に調整しつつ最適パラメータを決定するといった手間を省くことができ、調整作業の迅速化および熟練者によらずにパラメータを決定できる。
【００６３】
（第２の実施の形態）
第１の実施の形態では、（１）式〜（１１）式の導出過程に基づいて入力項目Ａ（σ_Ｄ、σ_{Ｒ 、Ｔ Ｉ 、Ｔ Ｄ 、}σ２_{Ｄ 、}σ２_{Ｒ ）}を選定し、これら入力項目Ａのもとに所定の演算式により２自由度化パラメータｂ，ｃを決定したが、本実施の形態では、グラフ関数を用いて２自由度化パラメータｂ，ｃを発信させる構成とするものである。
【００６４】
すなわち、本実施の形態においては、遅れ次数をもつ各種の制御対象に関し、前述する各式で求められたパラメータｂ，ｃをグラフで表わせば、図８（ａ）、（ｂ）に示すようになるので、予めパラメータ発生機構２に図８に示すような関係にあるグラフを関数として設定しておき、外部から入力される制御対象の伝達関数（テスト・バッチ）タイプ、むだ時間Ｌおよび限界周期Ｔｃ、或いはＬとＴｃとの代わりに基準化むだ時間ＬＮ（＝Ｌ／Ｔｃ）を受けたとき、関数としての ２自由度化パラメータｂ，ｃを発信するようにしてもよい。
【００６５】
図９および図１０は本発明に係る２自由度ＰＩＤ制御装置の実施の形態を示す構成図である。
【００６６】
この制御装置は図３と同様に２自由度ＰＩＤ制御器１とパラメータ発生機構２とで構成されているが、図９はパラメータ発生機構２に図８に示すようなグラフ関数が設定され、入力される制御対象タイプ、むだ時間Ｌおよび限界周期Ｔｃに基づいて２自由度化パラメータｂ，ｃを発生させる例である。
【００６７】
図１０は同じくパラメータ発生機構２に図８に示すグラフ関数が設定され、入力される制御対象タイプおよび基準化むだ時間ＬＮ（Ｌ／Ｔｃ）に基づいて同じ く２自由度化パラメータｂ，ｃを発信し、２自由度ＰＩＤ制御器１に設定する例である。
【００６８】
従って、この実施の形態によれば、各種の制御対象に関し、第１の実施の形態により決定されたパラメータｂ、ｃをグラフ関数として予めパラメータ発生機構２に設定しておけば、制御対象タイプ、むだ時間などの入力項目を入力するだけで、迅速に制御対象タイプに応じて最適な２自由度化パラメータｂ，ｃを発生することができ、煩雑な調整作業を必要とせずに目標値変更に対して追従性の優れた２自由度ＰＩＤ制御装置を実現できる。
（第３の実施の形態）
この実施の形態は、２自由度ＰＩＤ制御装置に代えて２自由度Ｉ−ＰＤ制御装置に適用した例である。Ｉ−ＰＤ制御は比例動作および微分動作とも制御量だけによって依存して動作する制御である。
【００６９】
この２自由度Ｉ−ＰＤ制御系は、基本的には図２０ないし図２２と同様な構成であることから、２自由度Ｉ−ＰＤ制御装置においても概念的には図１と同様な構成である図１１で表わすことができる。
【００７０】
すなわち、２自由度Ｉ−ＰＤ制御装置は、２自由度Ｉ−ＰＤ制御器１′にパラメータ発生機構２が接続され、このパラメータ発生機構２は入力される入力項目Ａに基づいて比例項用および微分項用２自由度化パラメータｂ，ｃを発生する機構である。
【００７１】
この２自由度ＰＩＤ制御系は、図２０の従来構成から図１２（ａ）に示すようなブロック図で表すことができる。
【００７２】
図１２において３１は２自由度Ｉ−ＰＤ制御器（２自由度ＰＩＤ制御器）、３２は制御対象、３３は加算要素、Ｒは制御量、Ｙは制御量、Ｄは外乱である。
【００７３】
この２自由度Ｉ−ＰＤ制御器３１は、目標値Ｒと制御量Ｙが入力され、外乱に対する抑制特性のためのＰＩＤパラメータである比例ゲインＫ_Ｐ、積分時間Ｔ_Ｉ、微分時間Ｔ_Ｄ、比例項用２自由度化パラメータｂおよび微分項用２自由度化パラ メータｃを用い、以下のような演算式により操作量ＭＶを求める。
【００７４】
Ｋ_Ｐ｛ｂＲ−Ｙ＋（１／Ｔ_Ｉｓ）（Ｒ−Ｙ）＋Ｔ_Ｄｓ（ｃＲ−Ｙ）｝……（１３）
このようにして求めた操作量ＭＶは外乱Ｄとともに制御対象３２に印加する。
【００７５】
ところで、図１２（ａ）に示す制御系は等価ブロック変換すると、仮想的に図１２（ｂ）のようなフィードフォワード制御要素３４とフィードバック制御要素３５とで構成される。３２は制御対象、３６は加減算要素である。
【００７６】
この制御系においてフィードフォワード制御要素３４は、入力される目標値Ｒに対し、制御要素３４の伝達関数を乗算し出力Ｗを発信する。また、フィードバック制御要素３５は、制御対象３２の出力である制御量Ｙに対し、制御要素３５の伝達関数を演算し出力Ｖを発信する。そして、加減算要素３６はフィードフォワード制御要素３４の出力Ｗからフィードバック制御要素３５の出力Ｖを減算し、得られた減算出力を制御対象３２に印加し、制御量Ｙを発生させる。このとき、外乱Ｄは加減算要素３６に加算的に加わり、制御対象３２に入力される。
【００７７】
また、制御対象３２の伝達関数をＧ_Ｐ（ｓ）とすると、フィードバック制御系 における外乱Ｄから制御量Ｙへの伝達関数Ｗ_Ｄ（ｓ）は次式で表わせる。
【００７８】

他方、外乱Ｄによる制御量Ｙの望ましい制御応答を規定する規範モデルは既に知られているように次式とする（ＰＩＤ制御、ｐ１４（２．１１）式またはｐ３１（２．３５）式、著者：須田信英、編者：システム制御情報学会、発行所：株式会社 朝倉書店）。
【００７９】
Ｍ_Ｄ（ｓ）＝｛（Ｔ_Ｉ／Ｋ_Ｐ）ｓ｝／（１＋σＤｓ＋α２ＤσＤ^２ｓ^２＋α３ＤσＤ^３ｓ^３＋α４ＤσＤ^４ｓ^４） ……（１５）
ここで、外乱入力に対する制御応答に関する規範モデルの係数α２Ｄ，α３Ｄ， α４Ｄは速応性とロバスト性との兼ね合いから、例えば表２に示す値とする。
【００８０】
【表２】

【００８１】
ここで、前述と同様にＷ_Ｄ（ｓ）＝Ｍ_Ｄ（ｓ）として解くと、外乱入力に対する制御応答に関する立上り時間σＤおよびＰＩＤパラメータＫ_Ｐ、Ｔ_Ｉ、Ｔ_Ｄが決定できる。この決定されたパラメータを設定したＩ−ＰＤフィードバック制御系に対し、制御対象の入力側にステップ状外乱を与えたとすると、図１７に示すような 制御応答が得られる。
【００８２】
次に、図１２（ｂ）に示す制御系に対し、決定された制御パラメータＫ_Ｐ，Ｔ_Ｉ，Ｔ_Ｄを設定し、このときの目標値Ｒから制御量Ｙへの伝達関数Ｗ_Ｒ（ｓ）をもって表わすと、次式のようになる。
【００８３】
Ｗ_Ｒ（ｓ）＝［Ｋ_Ｐ｛ｂ＋１／（Ｔ_Ｉｓ）＋ｃＴ_Ｄｓ｝］ ・ＭＤ（ｓ）……（１６）
ここで、前段の［ ］内はフィードフォワード制御要素３４の伝達関数、後段のＭＤ（ｓ）は前記（１５）式の規範モデルの伝達関数である。
【００８４】
従って、この（１６）式は下記する（１７）式で表わせる。
【００８５】
Ｗ_Ｒ（ｓ）＝（１＋ｂＴ_Ｉｓ＋ｃＴ_ＩＴ_Ｄｓ^２）／（１＋σＤｓ＋α２ＤσＤ^２ｓ^２＋α３ＤσＤ^３ｓ^３＋α４ＤσＤ^４ｓ^４）……（１７）
他方、目標値Ｒによる制御量Ｙの望ましい制御応答を規定する規範モデルは次式で表わすものとする（前述する文献 ＰＩＤ制御 、ｐ１２０（６．２）式参照）。
【００８６】
Ｍ_Ｒ（ｓ）＝１／（１＋σＲｓ＋α２ＲσＲ^２ｓ^２＋α３ＲσＲ^３ｓ^３）…（１８）
ここで、目標値変化に対する制御応答に関する規範モデルの係数α２Ｒ、α３Ｒは速応性とロバスト性との兼ね合いから、例えば前記表２に示す値とする。
【００８７】
そこで、Ｗ_Ｒ（ｓ）＝Ｍ_Ｒ（ｓ）とし、高次項を無視して解くと、目標値変更に対する制御応答に関する立上り時間σＲと外乱入力に対する制御応答に関する立 上り時間σＤとの立上り時間比σＲ／σＤは下式の３次方程式の最小実根から求ま る。
【００８８】
（１−２α_{２ Ｒ}＋α_{３ Ｒ}）（σ_Ｒ／σ_Ｄ）^３−（１−α_{２ Ｒ}）（σ_Ｒ／σ_Ｄ）^２＋α_２Ｄ（σ_Ｒ／σ_Ｄ）−α_{３ Ｄ}＝０ ……（１９）
また、微分時間を用いない２自由度Ｉ−Ｐ制御では、立上り時間比σＲ／σＤは次の２次方程式の最小実根として求まる。
【００８９】
（１−α２Ｒ）（σＲ／σＤ）^２−（σＲ／σＤ）＋α２Ｄ＝０ ……（２０）
次に、比例項用２自由度化パラメータｂ算出用係数βは、
β＝１−（σＲ／σＤ） ……（２１）
また、微分項用２自由度化パラメータｃ算出用係数γは、
γ＝（１−α２Ｒ）（σＲ／σＤ）^２−（σＲ／σＤ）＋α２Ｄ ……（２２）
とする。
【００９０】
よって、これらの値を用いると、比例項用２自由度化パラメータｂは、
ｂ＝βσＤ／Ｔ_Ｉ ……（２３）
と決定でき、また微分項用２自由度化パラメータｃは、
ｃ＝γσＤ^２／（Ｔ_ＩＴ_Ｄ） ……（２４）
と決定できる。
【００９１】
そこで、これら係数βおよび係数γを発生させる関数要素が必要となるが、これら係数を発生させる関数要素は以下のように作成する。
【００９２】
すなわち、ある補間係数λＤから定まる（１５）式の規範モデルＭＤ（ｓ）と、ある補間係数λＲから定まる前記（１８）式の規範モデルＭＲ（ｓ）とを用いて、前記（１９）式の方程式または前記（２０）式の方程式から立上り時間比σＲ／ σＤを求め、前記（２１）式、（２２）式から係数β、γを求める。
【００９３】
そして、これら補間係数λＤ，λＲの種々の値に対して係数β、γを求め、ｘ軸をλＤ、ｙ軸をλＲ、ｚ軸をβおよびγとした行列データテーブルを作成し、補間係数λＤ，λＲを入力すれば、係数β、γを発生する関数要素を作成できる。
【００９４】
なお、補間係数λと最大感度Ｍｓとの間には図１５に示す関係があるので、λＤ，λＲの代わりに最大感度ＭＳＤ、ＭＳＲを用いてもよい。また、２次の規範モデルを用いた場合には、λＲの代わりとして、規範モデルの分母２次項の係数α２Ｒを用いてもよい。
【００９５】
さらに、関数要素例として、例えば図１６（ａ）に示すように、ｘ軸に３次規範モデルのλＤ、ｙ軸に２次規範モデルのα２Ｒとすれば、２自由度Ｉ−Ｐ制御用の係数βを求めるための関数が得られる。また、図１６（ｂ）、（ｃ）に示すように、ｘ軸に４次規範モデルのλＤ、ｙ軸に３次規範モデルのλＲとすれば、２自由度Ｉ−ＰＤ制御用の係数β、γを求めるための関数が得られる。
【００９６】
図１３は以上のような説明を踏まえつつ具体化したパラメータ発生機構の一例を示す構成図である。
【００９７】
このパラメータ発生機構２は関数要素４１と演算要素４２とで構成されている。この関数要素４１は、外乱抑制用Ｉ−ＰＤ制御系の規範モデルの属性値ＸＤ（ λＤ、ＭＳＤなど）と目標値追従性を規定する規範モデルの属性値ＸＲ（γＲ、ＭＳＲ 、α２Ｒなど）との種々の値の組みに対して係数βの値を蓄えた行列データテーブルであって、入力される属性値ＸＤと属性値ＸＲとに基づいて、行列データテーブルから蓄えた係数βを発生させる。なお、行列データテーブルの代わりに、前記（１９）式または（２０）式と（２１）式との演算により、係数βを発生させる要素であってもよい。
【００９８】
前記演算要素４２は乗算要素４３および除算要素４４からなり、そのうち乗算要素４３は関数要素４１から発生される係数βに外乱抑制用Ｉ−ＰＤ制御系の規範モデルの立上り時間σＤを乗算し、除算要素４４に導入する。この除算要素４ ４は、乗算要素４３によって得られる乗算値を積分時間Ｔ_Ｉで除して比例項用２ 自由度化パラメータｂを算出し、２自由度Ｉ−ＰＤ制御器１′、３１に設定する。
【００９９】
図１４は２自由度化パラメータ発生機構の他の例を示す構成図である。
【０１００】
このパラメータ発生機構２は、２つの関数要素４５、４６と、これら関数要素４５，４６にそれぞれ対応する２つの演算要素４７，４８とによって構成されている。
【０１０１】
これら関数要素４５、４６は、それぞれ規範モデルの属性値ＸＤとＸＲとの種々の値の組みに対して係数βの値を蓄えた行列データテーブルであって、入力される属性値ＸＤと属性値ＸＲとに基づいて、それぞれ行列データテーブルから蓄えた係数β，γを発生させる。なお、関数要素４５である行列データテーブルの代わりに、前記（１９）式または（２０）式と（２１）式との演算により係数βを発生させ、また関数要素４６である行列データテーブルの代わりに、前記（１９）式と（２２）式の演算により係数γを発生させる要素であってもよい。
【０１０２】
前記演算要素４７は図１３に示す演算要素４２と同様に乗算要素４９および除算要素５０からなり、乗算要素４９は関数要素４５から発生される係数βに外乱抑制用Ｉ−ＰＤ制御系の規範モデルの立上り時間σＤを乗算し、除算要素５０に 導入する。この除算要素５０は、乗算要素４９にて得られた乗算値を積分時間ＴＩで除して比例項用２自由度化パラメータｂを算出する。
【０１０３】
一方の演算要素４８は、第１の乗算要素５１、第２の乗算要素５２、除算要素５３および乗算要素５４からなり、前記（２４）式の演算により微分項用２自由度化パラメータｃを算出する。具体的には、第２の乗算要素５２にて得られた立上り時間σＤの乗算値σＤ^２と係数γとを乗算要素５１にて乗算し、除算要素５３に導入する。この除算要素５３は乗算要素５１からの乗算値を乗算要素５４により得られる積分時間Ｔ_Ｉと微分時間Ｔ_Ｄとの乗算値で除算し、（２４）式により微分項用２自由度化パラメータｃを算出する。そして、各演算要素４７，４８で得られたパラメータｂ，ｃを例えば図２０に示す２自由度Ｉ−ＰＤ制御器１′に発信する。
【０１０４】
なお、２自由度Ｉ−ＰＤ制御器１′としては、図２０に示したものに限定されず、これを等価ブロック変換して得られる図２１に示す目標値フィードフォワード型や図２２に示す目標値フィルタ型、さらにはループ補償型やフィードバック補償型などであってもよい（ＰＩＤ制御、ｐ７５、著者：須田信英、朝倉書店）。
【０１０５】
また、図２０に示す微分要素１１８として完全微分型で表記したが、１次遅れ要素が付加された不完全微分型であってもよい。
【０１０６】
次に、パラメータ発生機構への入力について説明する。外乱を最も良好に抑制できるように規範モデルを用いてＰＩＤ値を設計した場合、この時に使用した規範モデルで補間係数λＤ、最大感度ＭＳＤ、分母２次項の係数α２Ｒ、立上り時間σＤは一義的に決まるので、これらを使用する。規範モデルを用いずにＰＩＤ値を調整した場合、操作端にステップ入力を加えたときの補間係数λＤを種々変えて描 いた制御応答（図１７）と比較し、形状がもっとも近い波形の補間係数λＤから 、規範モデルおよび立上り時間σＤ（制御応答がほぼピークに達する時間）を同 定して使用する。
【０１０７】
なお、図１７（ａ）は４次の規範モデルの制御応答図であって、微分動作を用いた２自由度Ｉ−ＰＤ制御系を用いる場合に使用される。また、図１７（ｂ）は３次の規範モデルの制御応答図であって、微分動作を用いない２自由度Ｉ−Ｐ制御系に使用される。
【０１０８】
また、目標値変更の過度時に発生する操作量の変化を小さくする場合やロバスト性を増やしたい場合には立上り時間σＤとして前記により定まる値よりも大き い値を、また応答を早めたい場合には小さい値を入力する。
【０１０９】
また、例えばＩ−ＰＤ制御系の規範モデルを自動的に同定する機構を付加し、Ｉ−ＰＤ制御器で用いられている積分時間Ｔ_Ｉ、微分時間Ｔ_Ｄとともに同定結果の入力項目を本発明のパラメータ発生機構に自動的に入力すれば、オート（セルフ）チューニング２自由度Ｉ−ＰＤ制御系を構成することができる。
【０１１０】
さらに、目標値変更の追従性を規定する規範モデルとしては、補間係数λＲや 分母２次項の係数α２Ｒを種々変えて描いた制御応答波形（図１８）を参照し、オーバシュート量などから、その制御系で最も適切な形状を与える補間係数λＲや 分母２次項の係数α２Ｒ、つまり規範モデルの属性値を決定して入力する。なお、図１８（ａ）は目標値単位ステップ変更時の補間係数λＲを種々変えた場合の３ 次規範モデルの制御応答図であって、２自由度Ｉ−ＰＤ制御に用いられ、図１８（ｂ）は目標値単位ステップ変更時の分母２次項の係数を種々変えた場合の２次の規範モデルの制御応答図であって、２自由度Ｉ−Ｐ制御時に用いられる。
【０１１１】
図１９は、本発明によるパラメータ発生機構２から２自由度化パラメータを発生し、２自由度Ｉ−Ｐ（Ｄ）制御器に設定し、制御対象を制御したときの制御応答の一例である。なお、比較のために、１自由度Ｉ−Ｐ（Ｄ）制御器およびＰＩ（Ｄ）制御器で制御した場合についてその制御応答を示している。
【０１１２】
この図から明らかなように、本発明によるＩ−ＰＤ制御の場合、目標値変更時に大きなオーバシュートを発生させることなく、しかも速応性をもたせて応答させることができ、目標値追従性を大幅に向上させることができる。
【０１１３】
【発明の効果】
以上説明したように本発明によれば、所定の入力項目のもとに目標値変更時の制御応答を規定する２自由度化パラメータを自動的に発生でき、従来のように長時間かけて試行錯誤的に調整する作業を省略でき、また熟練者に頼らずに短時間に２自由度化パラメータを発生できる。
【０１１４】
よって、外乱に対しても目標値変更に対しても、迅速に最適な制御性を実現できる２自由度制御装置を提供できる。
【図面の簡単な説明】
【図１】本発明に係わる２自由度制御装置の第１および第２の実施の形態を説明する概念構成図。
【図２】本発明の原理を説明する２自由度ＰＩＤ制御系のブロック線図。
【図３】本発明に係わる２自由度制御装置における入力項目を含む全体のブロック構成図。
【図４】図３に示すパラメータ発生機構の具体的な構成例を示す図。
【図５】図３に示すパラメータ発生機構の具体的な構成例を示す図。
【図６】図３に示すパラメータ発生機構の具体的な構成例を示す図。
【図７】本発明に係わる２自由度制御装置を用いた場合の制御応答例を示す図。
【図８】図３に示すパラメータ発生機構に設定する関数を説明する図。
【図９】本発明に係わる２自由度制御装置の第２の実施形態を示すブロック構成図。
【図１０】本発明に係わる２自由度制御装置の第２の実施形態の他の例を示すブロック構成図。
【図１１】本発明に係わる２自由度制御装置の第３の実施の形態を説明する概念構成図。
【図１２】本発明の原理を説明する２自由度Ｉ−ＰＤ制御系のブロック線図。
【図１３】パラメータ発生機構の具体的な構成例を示す図。
【図１４】パラメータ発生機構の具体的な構成例を示す図。
【図１５】規範モデルの補間係数と最大感度との関係を示す図。
【図１６】関数要素の関数特性を示す図。
【図１７】ＰＩＤ値設計あるいはＩ−ＰＤ制御系の特性同定に使用するステップ外乱入力時の規範モデルの制御応答を示す図。
【図１８】２自由度Ｉ−Ｐ（Ｄ）制御設計に使用する目標値単位ステップ変更時の規範モデルの制御応答を示す図。
【図１９】本発明に係わる２自由度制御装置を用いた場合の制御応答例を示す図。
【図２０】従来公知の一般的な２自由度ＰＩＤまたは２自由度Ｉ−ＰＤ制御系の概略構成を示す図。
【図２１】従来公知のフィードフォワード要素をもつ２自由度制御装置の構成図。
【図２２】従来公知の目標値フィルタ要素をもつ２自由度制御装置の構成図。
【符号の説明】
１…２自由度ＰＩＤ制御器
１′…２自由度Ｉ−ＰＤ制御器
２…パラメータ発生機構
２１、２２…演算要素
σＤ…外乱入力制御応答に関する立上り時間
σＲ…目標値変更制御応答に関する立上り時間
Ｔ_Ｉ…積分時間
Ｔ_Ｄ…微分時間
α２Ｄ…外乱入力制御応答規範モデルの２次項係数
α２Ｒ…目標値変更制御応答規範モデルの２次項係数
４１，４５，４６…関数要素
４２，４７，４８…演算要素[0001]
TECHNICAL FIELD OF THE INVENTION
The present invention relates to a two-degree-of-freedom controller used in various instrumentation fields and servo control fields of petroleum, chemical, steel, electric power, papermaking, and the like, and particularly relates to a flow rate, a pressure, a liquid level, and a composition of each part of a plant. The present invention relates to a two-degree-of-freedom control device that performs feedback control of process variables such as position, speed, and rotation speed.
[0002]
[Prior art]
Conventionally, a two-degree-of-freedom PID control device has been used to satisfactorily perform feedback control of a control amount both when a disturbance is input and when a target value is changed.
[0003]
Here, the two-degree-of-freedom PID control is PID control for simultaneously optimizing both the suppression characteristic for disturbance and the follow-up characteristic for target value change.
[0004]
FIG. 20 is a block diagram of a conventional general 2-DOF PID or 2-DOF I-PD control device.
[0005]
This control device includes a two-degree-of-freedom PID (hereinafter, including two-degree-of-freedom I-PD) controller 100 and a control target 101. The two-degree-of-freedom PID degree controller 100 includes a proportional system, an integral system, and a differential system. Has become.
[0006]
The proportional system multiplies the target value R by the two-degree-of-freedom parameter b for the proportional term of the coefficient element 111, subtracts the control amount Y from the multiplied value by the subtraction element 112, and introduces the result into the addition element 113. On the other hand, the integration system obtains a control deviation E between the target value R and the control amount Y in the comparison element 114, and calculates an integration time T for the obtained control deviation E._IAre integrated by an integration element 115 having Further, the differentiating system multiplies the target value R by the two-degree-of-freedom parameter c for the differential term of the coefficient element 116 and leads to a subtraction element 117, where the control amount Y is subtracted from the multiplied value, and the obtained subtracted value is obtained. Is differentiated by a differentiating element 118 having a differentiating time TD, and then introduced into the adding element 113.
[0007]
The output of the subtraction element 112, the output of the integration element 115, and the output of the differentiation element 118 obtained in this manner are added by the addition element 113, and the operation is performed by multiplying the added value by the proportional gain Kp of the proportional gain coefficient element 119. After obtaining the amount MV, it is applied to the control target 101 together with the amount of disturbance.
[0008]
Conventionally, as shown in FIG. 21, a feedforward control method is adopted in which a change in a target value is detected, a change in an operation amount is determined in advance in order to cancel the influence thereof, and an operation is executed ahead of schedule. A degree of freedom PID controller is used.
[0009]
The two-degree-of-freedom PID controller 100 inputs the target value R to the target value feedforward element 121, where the two-degree-of-freedom parameter b for the proportional term and the two-degree-of-freedom parameter c for the differential term are used to obtain ( b + cT_Ds) Execute the operation and transmit the obtained output. Further, after the control element E obtains the control deviation E between the target value R and the control amount Y in the comparison element 114, the integration time T_I, And is introduced into the subtraction element 122. On the other hand, in the differential system, the proportional / differential operation expression (1 + T_Ds) and introduces it into the subtraction element 122. Here, the output of the proportional / differential element 123 is subtracted from the output of the integral element 115, and the result of the subtraction is added to the proportional gain K of the proportional gain coefficient element 119._P, And the multiplied value is added to the output of the target value feedforward element 121 by the addition element 124 to obtain the manipulated variable MV applied to the control target 101 (not shown).
[0010]
Further, conventionally, as shown in FIG. 13, a two-degree-of-freedom PID control device to which a target value filter element 131 is added is used.
[0011]
The two-degree-of-freedom PID controller 100 calculates the target value R by using the two-degree-of-freedom parameters b and c of the target value filter element 131 in accordance with the following equation, and calculates the optimum target value follow-up characteristic. Calculate the target value.
[0012]
(1 + bT_Is + cT_IT_Ds²) / (1 + T)_Is) …… (1)
The control target E and the control amount Y obtained as described above are used to determine the control deviation E by the comparison element 114, and then the control deviation E is calculated by the proportional / integral element 132 to obtain {1 + 1 / (T_Is)｝ is calculated. Further, a differential operation is performed on the control amount Y by the differential element 133. Then, the subtraction element 134 subtracts the output of the differential element 133 from the output of the proportional / integral element 132, and multiplies the obtained subtracted output by the proportional gain Kp of the proportional gain coefficient element 119 to obtain the manipulated variable MV. This is applied to the control target 101 (not shown) together with the amount of disturbance.
[0013]
[Problems to be solved by the invention]
By the way, in each of the various PID controllers described above, the PID parameter (proportional gain K_P, Integration time T_I, Differentiation time T_D), It is necessary to adjust the two-degree-of-freedom parameters b and c for optimizing the follow-up characteristic to the change of the target value by trial and error. In addition, a control target model is constructed in advance, a simulation is executed under a certain evaluation function offline, and each parameter of the transfer function, that is, a PID parameter and two-degree-of-freedom parameters b and c are designed by searching for an optimum value. Has been done.
[0014]
As a result, in order to obtain the PID parameter and the two-degree-of-freedom parameters b and c that provide an optimal control response to disturbance and a change in the target value, a complicated adjustment work by a skilled person is necessary, and the adjustment work is required. There is a problem that requires a lot of time.
[0015]
SUMMARY OF THE INVENTION The present invention has been made in view of the above circumstances, and provides a two-degree-of-freedom control device that quickly and easily generates a two-degree-of-freedom parameter for obtaining an optimal control response to a change in a target value without skill. Is to provide.
[0016]
[Means for Solving the Problems]
In order to solve the above-described problems, the present invention provides a two-degree-of-freedom control device that uses a control parameter and a two-degree-of-freedom parameter to control both a disturbance suppression property and a target value tracking property with respect to a control target. A rise time σD relating to a disturbance input control response, a rise time σR relating to a target value change control response, and an integral time T which is the control parameter._IAlternatively, the integration time T_IAnd derivative time T_DAnd a parameter generating mechanism for generating the two-degree-of-freedom parameter defining the target value change control response.
[0017]
In addition, in addition to the above input items, a value proportional to a value obtained by a predetermined arithmetic expression using a second-order coefficient α2D of the disturbance input control response reference model and a second-order coefficient α2R of the target value change control response reference model. , A two-degree-of-freedom parameter defining the target value change control response.
[0018]
According to the present invention, by taking the above-described means, predetermined predetermined input items, that is, a rise time σD relating to a disturbance input control response, a rise time σR relating to a target value change control response, and an integral Time T_IAlternatively, the integration time T_IAnd derivative time T_DAnd α2D as a second-order coefficient of the disturbance input control response reference model and α2R as a second-order coefficient of the target value changing control response reference model, and a predetermined value derived from the transfer function of the actual control system and the transfer function of the reference model. By executing the above calculation, the two-degree-of-freedom parameter defining the target value change control response can be generated, and the work of adjusting by trial and error as in the related art can be omitted.
[0019]
Another invention provides the two-degree-of-freedom parameter defining a target value change control response using a transfer characteristic type of a controlled object, a dead time and a limit period, or a transfer characteristic type and a standardized dead time of a controlled object. Is provided with a parameter generating mechanism for generating the
[0020]
According to the present invention, by taking the above-described means, it is possible to previously form a graph function based on the transfer characteristic type of the controlled object, the dead time and the limit period, or the transfer characteristic type and the standardized dead time of the controlled object. It is possible to generate the two-degree-of-freedom parameter quickly and easily, and to achieve the same effect as the above-mentioned invention.
[0021]
Further, in another invention, the attribute value of the first reference model and the attribute value of the second reference model that defines the target value followability in the disturbance suppression I-PD control system are input, and both of these attribute values are input. A function element for generating a coefficient value as a function, and a calculation element for generating a two-degree-of-freedom parameter for improving target value followability using the coefficient value of the function element, the rise time and the integration time of the first reference model And a parameter generating mechanism having the following.
[0022]
According to the present invention, a coefficient value is generated as a function of an attribute value of a first reference model and an attribute value of a second reference model defining target value followability in a disturbance suppression I-PD control system. , Using the rise time and the integration time of the first reference model to generate the two-degree-of-freedom parameter for improving the followability of the target value, the two-degree-of-freedom parameter is automatically adjusted without performing trial and error adjustment work. Parameter can be generated.
[0023]
BEST MODE FOR CARRYING OUT THE INVENTION
Hereinafter, embodiments of the present invention will be described with reference to the drawings.
(First Embodiment)
Prior to describing an embodiment of the two-degree-of-freedom control apparatus according to the present invention, a basic concept for realizing the present apparatus will be described with reference to FIG.
(1) First, based on the input of the target value R and the control amount Y, the proportional gain K_P, Integration time T_I, Differentiation time T_DIn addition to the above, a two-degree-of-freedom PID controller 1 for calculating the operation amount MV by using the two-degree-of-freedom parameter b for the proportional term and the two-degree-of-freedom parameter c for the differential term is provided. The two-degree-of-freedom PID controller 1 corresponds to, for example, the two-degree-of-freedom PID controller 100 in FIG.
(2) Next, in the two-degree-of-freedom PID controller 1, the proportional gain KP, the integration time TI, and the differentiation time TD, which are PID parameters that optimize the control response to disturbance, are adjusted in advance. Set in controller 1.
(3) Further, a new parameter generating mechanism 2 is provided, and two-degree-of-freedom parameters b and c are automatically calculated under a certain input item A.
(4) It is assumed that the two-degree-of-freedom parameters b and c calculated by the parameter generating mechanism 2 are generated and set in the two-degree-of-freedom PID controller 1.
[0024]
In order to concretely realize the above concept, it is important what kind of input item A is used, and what kind of calculation the parameter generating mechanism 2 performs based on the input item A to obtain the parameters b and c. Come.
[0025]
Therefore, a procedure for deriving the input item A and the arithmetic expression will be described below.
[0026]
If a conventional general two-degree-of-freedom control system (see FIG. 20) is represented by a transfer function, a configuration as shown in FIG. 2A is obtained.
[0027]
In the figure, 1 is a two-degree-of-freedom PID controller, 3 is a control target, 4 is an addition element, R is a target value, Y is a control amount, and D is a disturbance.
[0028]
That is, the two-degree-of-freedom PID controller 1 receives the target value R and the control amount Y, and outputs a proportional gain K which is a control parameter for a suppression characteristic against disturbance._P, Integration time T_I, Differentiation time T_DUsing the two-degree-of-freedom parameter b for the proportional term and the two-degree-of-freedom parameter c for the derivative term, the manipulated variable MV can be obtained by the following arithmetic expression.
[0029]
K_P｛BR-Y + (1 / T_Is) (RY) + T_Ds (cR-Y)｝ (2)
The manipulated variable MV obtained by the above equation is applied to the control target 3 together with the disturbance D.
[0030]
Incidentally, the two-degree-of-freedom PID control system shown in FIG. 2A can be virtually represented by a control system as shown in FIG. 5 is a feedforward control element, 6 is an addition / subtraction element, and 7 is a feedback control element.
[0031]
In this control system, the feedforward control element 5 sets the input target value R to ｛K_P(B + 1 / T_Is + cT_Ds) Calculate the transfer function｝ and transmit the output W. Further, the feedback control element 7 applies ΔK to the control amount Y which is the output of the control_P(1 + 1 / T_Is + T_D) Calculate the transfer function｝ and transmit the output V. Then, the output V of the feedback control element 7 is subtracted from the output W of the feedforward control element 5 in the addition / subtraction element 6, and the obtained subtraction output is applied to the control target 3 to generate a control amount Y. At this time, the disturbance D is added to the addition / subtraction element 6 in an additive manner and input to the control target 3.
[0032]
Further, the transfer function of the control target 3 is represented by G_P(S), the transfer function W from the disturbance D to the control amount Y in the feedback control system_D(S) can be expressed by the following equation.
[0033]

On the other hand, a reference model that defines a desired control response of the control amount Y due to the disturbance D is expressed by the following equation (PID control, equation p14 (2.11) or equation p31 (2.35), author). : Nobuhide Suda, Editor: The Society of System Control and Information Engineers, Publisher: Asakura Shoten Co., Ltd.).
[0034]
M_D(S) = ｛s / (K_P/ T_I)｝ · [1 / (1 + σDs + α2DσD)²s²+ Α3DσD³s³)] …… (4)
Here, the coefficients α2D and α3D of the reference model regarding the control response to the disturbance input are set to, for example, the values shown in Table 1 in consideration of the balance between the quick response and the robustness. In Table 1, see the above-mentioned document PID control, p14 to p15.
[0035]
[Table 1]

[0036]
Incidentally, the actual control system of the above equation (3) and the reference model of the equation (4) must be in the same relation. Therefore, W_D(S) = M_DSolving for (s) gives rise time σ for control response to disturbance input_DAnd PID parameter K_P, T_I, T_{D But}Can decide. Therefore, if a step-like disturbance is applied to the input side of the control target in the PID feedback control system in which the determined parameters are set, a control response as shown in FIG. 7A is obtained.
[0037]
Next, for the control system shown in FIG._P, T_I, TD, and the transfer function W from the target value R to the control amount Y at this time is set._RWhen expressed by (s), the following equation is obtained.
[0038]
W_R(S) = [K_P｛B + 1 / (T_Is) + cT_Ds｝] ・ M_D(5) Here, [] in the preceding stage is the transfer function of the feedforward control element 5, and M in the subsequent stage_D(S) is the transfer function of the reference model of equation (4).
[0039]
Therefore, this equation (5) can be expressed by the following equation (6).
[0040]
W_R(S) = (1 + bT)_Is + cT_IT_Ds²) / (1 + σDs + α2DσD)²s²+ Α3DσD³s³) …… (6)
On the other hand, a reference model that defines a desirable control response of the control amount Y based on the target value R is represented by the following equation (see the above-mentioned document PID control, p120 (6.2) equation).
[0041]
M_R(S) = 1 / (σRs + α2RσR²s²+ Α3RσR³s³…… (7)
Here, the coefficients α2R and α3R of the reference model relating to the control response to the change in the target value are set to the values shown in Table 1 above, for example, in view of the balance between quick response and robustness.
[0042]
Then, W_R(S) = M_RWhen solving for (s), the rise time σR relating to the control response to the change in the target value is obtained from the minimum real root of the following cubic equation.
[0043]
(1-2α2R + α3R) σR³− (1-α2R) σDσR²+ Α2DσD²σR-α3DσD³= 0 (8)
Here, W in equation (6)_R(S) = B / C, and M in equation (7)_RIf (s) = 1 / Z, W_R(S) = M_RFrom the relationship (s),
B / C = 1 / Z → Z = C / B (9)
Can be derived.
[0044]
Therefore, by performing an operation on C / B, deriving a solution up to the first-order and second-order terms, and calculating the Z and B terms in the same relation as the first-order and second-order terms, respectively, the two-degree-of-freedom parameter b for the proportional term becomes
b = (σD−σR) / T_I                                  …… (10)
It can be determined from the following arithmetic expression. The two-degree-of-freedom parameter c for the differential term is

It can be determined from the following arithmetic expression.
[0045]
In the case of α2D = α2R = 0.5 in the equation (11),
c = (σD-σR)²/ (2T_IT_D) (12) and the two-degree-of-freedom parameters b and c are (σ_D−σ_R).
[0046]
Therefore, as is apparent from the above description, the input item A and the arithmetic expression for obtaining the two-degree-of-freedom parameters b and c were obtained, and a specific example will be described below.
[0047]
FIG. 3 is a configuration diagram showing one embodiment of a two-degree-of-freedom PID control device according to the present invention.
[0048]
In the control device shown in FIG. 1A, a parameter generating mechanism 2 is connected to a two-degree-of-freedom PID controller 1, and the parameter generating mechanism 2 has an integral time TI and a differential time T as input items A._D, A rise time sigma defining the disturbance input control response, and a rise time sigma R defining the target value change control response, and the calculation means shown in FIG. This is a configuration to be set in the PID controller 1.
[0049]
The control device shown in FIG. 2B further includes, in addition to the input items shown in FIG.
A quadratic term coefficient α2D of the disturbance input control response reference model and a quadratic term coefficient α2R of the target value change control response reference model are additionally input, and the calculation means shown in FIG. And the two-degree-of-freedom PID controller 1 is set.
[0050]
That is, the parameter generating mechanism 2 shown in FIG. 4A includes a comparison element 11 and a division element 12, and the comparison element 11 is a target value change control that is also input from a rise time σD that defines an input disturbance input control response. The rise time σR defining the response is subtracted, and the subtracted output is introduced to the division element 12. The division element 12 divides the subtraction result (σD−σR) by the integration time TI to calculate the two-degree-of-freedom parameter b for the proportional term in the equation (10), and sets the parameter b in the two-degree-of-freedom PID controller 1. .
[0051]
Note that the rise time σD that defines the disturbance input control response can be automatically determined when the PID parameter is designed by the partial model matching method, or when the PID parameter is determined by using another method, the step disturbance can be determined. Since the time when the control amount Y reaches the peak value upon entering, it can be determined from this time.
[0052]
Further, the rise time σR defining the target value change control response can be uniquely determined by the calculation as described above, or can be arbitrarily set as the time required for the control amount at the time of the target value step change to reach approximately 50%.
[0053]
Next, the parameter generating mechanism 2 shown in FIG. 4B includes a comparison element 13, a division element 14, a multiplication element 15, a division element 16, and a coefficient element 17. The comparison element 13 and the division element 14 calculate the proportional-term two-degree-of-freedom parameter b as in FIG. Further, the multiplication element 15 multiplies the output of the comparison element 13 by the output of the division element 14 and introduces the multiplication result into the division element 16, where the multiplication result is differentiated by the differential time T_DThen, by multiplying by で with the coefficient element 17, the two-degree-of-freedom parameter c = (σD−σR) for the differential term based on the equation (12) is obtained.²/ (2T_IT_D) Can be calculated and transmitted to the two-degree-of-freedom PID controller 1.
[0054]
FIG. 5 is a diagram showing the internal configuration of the parameter generating mechanism 2 of FIG.
[0055]
The parameter generating mechanism 2 includes a first operation element 21 and a second operation element 22. The first operation element 21 calculates the proportional term two-degree-of-freedom parameter b by the operation of Expression (10), Transmit to the two-degree-of-freedom PID controller 1. The second arithmetic element 22 calculates the differential term two-degree-of-freedom parameter c by the operation of the equation (11), and similarly sends the parameter to the two-degree-of-freedom PID controller 1.
[0056]
Next, another example of the parameter generating mechanism 2 will be described with reference to FIG.
[0057]
FIG. 6A shows a difference signal (σD−σR) between the rise times σD and σR that defines the response control by disturbance input and target value change to the division element 12, where the difference signal is integrated into the integration time T._IThis is an example of calculating the two-degree-of-freedom parameter b for the proportional term by dividing by.
[0058]
FIG. 6 (b) has two degrees of freedom by a configuration similar to that of FIG. 4 (b), except that a difference signal (σD−σR) between the rise times σD and σR is input as in FIG. This is an example in which parameters b and c are calculated and transmitted to the two-degree-of-freedom PID controller 1.
[0059]
FIG. 7B shows an example of a control response when the target value step is changed when the two-degree-of-freedom parameters b and c are set based on the input item A determined as described above. . For comparison, FIG. 7C shows a control response in the conventional I-PD control (b = c = 0), and FIG. 7C shows a control response in the basic PID control (b = c = 1). As shown in d).
[0060]
As is apparent from these control response diagrams, b and c are not limited to 0 or 1, and by setting b and c to arbitrary predetermined values, a large overshoot does not occur when the target value is changed. Thus, two-degree-of-freedom PID control with excellent followability can be realized.
[0061]
Note that σD, σR, T_I, T_DIs not limited to the values described above, and the two-degree-of-freedom parameters b and c may be determined and set according to the arithmetic expressions of Expressions (10) and (11) using any predetermined values. .
[0062]
Therefore, according to the above-described embodiment, if a predetermined input item is input to the parameter generating mechanism 2, the two-degree-of-freedom parameters b and c are calculated based on the above-described predetermined arithmetic expression. It can be set in the two-degree-of-freedom PID controller 1 and the trouble of determining the optimal parameters while adjusting by trial and error over a long period of time as in the related art can be omitted. Parameters can be determined without depending on the skilled person.
[0063]
(Second embodiment)
In the first embodiment, based on the derivation process of the equations (1) to (11), the input item A (σ_D, Σ_{R , T I , T D ,}σ2_{D ,}σ2_{R )}Is selected, and the two-degree-of-freedom parameters b and c are determined by a predetermined arithmetic expression based on these input items A. In the present embodiment, the two-degree-of-freedom parameters b and c are determined using a graph function. It is configured to transmit.
[0064]
That is, in the present embodiment, regarding the various control objects having the delay order, the parameters b and c obtained by the above-described equations can be represented by graphs as shown in FIGS. Therefore, a graph having a relationship as shown in FIG. 8 is set in advance in the parameter generating mechanism 2 as a function, and a transfer function (test / batch) type, a dead time L, and a limit period of a control target input from the outside are set. When a standardized dead time LN (= L / Tc) is received instead of Tc or L and Tc, two-degree-of-freedom parameters b and c as functions may be transmitted.
[0065]
9 and 10 are configuration diagrams showing an embodiment of a two-degree-of-freedom PID control device according to the present invention.
[0066]
This control device comprises a two-degree-of-freedom PID controller 1 and a parameter generation mechanism 2 as in FIG. 3, but FIG. 9 shows a graph function as shown in FIG. This is an example in which two-degree-of-freedom parameters b and c are generated based on a controlled object type, a dead time L, and a limit cycle Tc.
[0067]
In FIG. 10, the graph function shown in FIG. 8 is similarly set in the parameter generation mechanism 2, and the two-degree-of-freedom parameters b and c are similarly set based on the input control target type and the standardized dead time LN (L / Tc). This is an example in which a signal is transmitted and set in the PID controller 1 with two degrees of freedom.
[0068]
Therefore, according to this embodiment, if the parameters b and c determined according to the first embodiment are set in advance in the parameter generating mechanism 2 as graph functions for various control targets, the control target type, By simply inputting input items such as dead time, the optimal two-degree-of-freedom parameters b and c can be quickly generated according to the type of control object, and the target value can be changed without complicated adjustment work. On the other hand, a two-degree-of-freedom PID control device with excellent followability can be realized.
(Third embodiment)
This embodiment is an example in which the present invention is applied to a 2-DOF I-PD control device instead of a 2-DOF PID control device. The I-PD control is a control that operates depending on only the control amount in both the proportional operation and the differential operation.
[0069]
Since the two-degree-of-freedom I-PD control system has basically the same configuration as in FIGS. 20 to 22, the two-degree-of-freedom I-PD control device also has a conceptually similar configuration to FIG. This can be represented in FIG.
[0070]
That is, in the two-degree-of-freedom I-PD control device, a parameter generation mechanism 2 is connected to a two-degree-of-freedom I-PD controller 1 '. This is a mechanism for generating two-degree-of-freedom parameters b and c for the differential term.
[0071]
This two-degree-of-freedom PID control system can be represented by a block diagram as shown in FIG. 12A from the conventional configuration of FIG.
[0072]
In FIG. 12, 31 is a two-degree-of-freedom I-PD controller (two-degree-of-freedom PID controller), 32 is a control target, 33 is an addition element, R is a control amount, Y is a control amount, and D is a disturbance.
[0073]
The two-degree-of-freedom I-PD controller 31 receives a target value R and a control amount Y and receives a proportional gain K which is a PID parameter for suppressing characteristics against disturbance._P, Integration time T_I, Differentiation time T_DUsing the two-degree-of-freedom parameter b for the proportional term and the two-degree-of-freedom parameter c for the differential term, the manipulated variable MV is obtained by the following arithmetic expression.
[0074]
K_P｛BR-Y + (1 / T_Is) (RY) + T_Ds (cR-Y)｝ (13)
The operation amount MV obtained in this way is applied to the control target 32 together with the disturbance D.
[0075]
By the way, the control system shown in FIG. 12A is virtually composed of a feedforward control element 34 and a feedback control element 35 as shown in FIG. 32 is an object to be controlled and 36 is an addition / subtraction element.
[0076]
In this control system, the feedforward control element 34 multiplies the input target value R by the transfer function of the control element 34 and outputs an output W. Further, the feedback control element 35 calculates a transfer function of the control element 35 with respect to the control amount Y that is the output of the control target 32, and transmits an output V. Then, the addition / subtraction element 36 subtracts the output V of the feedback control element 35 from the output W of the feedforward control element 34 and applies the obtained subtraction output to the control target 32 to generate a control amount Y. At this time, the disturbance D is added to the addition / subtraction element 36 in an additive manner and is input to the control target 32.
[0077]
Further, the transfer function of the controlled object 32 is represented by G_P(S), the transfer function W from the disturbance D to the control amount Y in the feedback control system_D(S) can be expressed by the following equation.
[0078]

On the other hand, a reference model that defines a desired control response of the control amount Y due to the disturbance D is expressed by the following equation (PID control, equation p14 (2.11) or equation p31 (2.35); : Nobuhide Suda, Editor: The Society of Systems, Control and Information Engineers, Publisher: Asakura Shoten Co., Ltd.)
[0079]
M_D(S) = ｛(T_I/ K_P) S｝ / (1 + σDs + α2DσD)²s²+ Α3DσD³s³+ Α4DσD⁴s⁴) ...... (15)
Here, the coefficients α2D, α3D, and α4D of the reference model relating to the control response to the disturbance input are set to, for example, the values shown in Table 2 in consideration of the balance between the quick response and the robustness.
[0080]
[Table 2]

[0081]
Here, as described above, W_D(S) = M_D(S), the rise time .sigma.D and the PID parameter K for the control response to the disturbance input_P, T_I, T_DCan be determined. Assuming that a step-like disturbance is applied to the input side of the control target in the I-PD feedback control system in which the determined parameters are set, a control response as shown in FIG. 17 is obtained.
[0082]
Next, with respect to the control system shown in FIG._P, T_I, T_DIs set, and a transfer function W from the target value R to the control amount Y at this time is set._RWhen expressed by (s), the following equation is obtained.
[0083]
W_R(S) = [K_P｛B + 1 / (T_Is) + cT_Ds｝] · MD (s) ... (16)
Here, [] in the first stage is the transfer function of the feedforward control element 34, and MD (s) in the second stage is the transfer function of the reference model of the above equation (15).
[0084]
Therefore, this equation (16) can be expressed by the following equation (17).
[0085]
W_R(S) = (1 + bT)_Is + cT_IT_Ds²) / (1 + σDs + α2DσD)²s²+ Α3DσD³s³+ Α4DσD⁴s⁴) ... (17)
On the other hand, a reference model that defines a desired control response of the control amount Y based on the target value R is represented by the following equation (see the above-mentioned document PID control, p120 (6.2) equation).
[0086]
M_R(S) = 1 / (1 + σRs + α2RσR²s²+ Α3RσR³s³)… (18)
Here, the coefficients α2R and α3R of the reference model relating to the control response to the change in the target value are set to the values shown in Table 2 above, for example, in view of the balance between quick response and robustness.
[0087]
Then, W_R(S) = M_R(S) and solving with ignoring higher order terms, the rise time ratio σR / σD of the rise time σR relating to the control response to the change of the target value and the rise time σD relating to the control response to the disturbance input is represented by the following cubic equation: From the smallest real root of.
[0088]
(1-2α_{2 R}+ Α_{3 R}) (Σ_R/ Σ_D)³− (1-α_{2 R}) (Σ_R/ Σ_D)²+ Α_2D(Σ_R/ Σ_D) -Α_{3 D}= 0 (19)
In the two-degree-of-freedom IP control without using the differential time, the rise time ratio σR / σD is obtained as the minimum real root of the following quadratic equation.
[0089]
(1-α2R) (σR / σD)²− (ΣR / σD) + α2D = 0 (20)
Next, the coefficient β for calculating the two-degree-of-freedom parameter b for the proportional term is
β = 1− (σR / σD) (21)
The coefficient γ for calculating the two-degree-of-freedom parameter c for the differential term is
γ = (1−α2R) (σR / σD)²− (ΣR / σD) + α2D (22)
And
[0090]
Therefore, using these values, the two-degree-of-freedom parameter b for the proportional term is
b = βσD / T_I                                        ...... (23)
And the two-degree-of-freedom parameter c for the differential term is
c = γσD²/ (T_IT_D) ...... (24)
Can be determined.
[0091]
Therefore, a function element for generating these coefficients β and γ is required. The function elements for generating these coefficients are created as follows.
[0092]
That is, using the reference model MD (s) of the equation (15) determined from a certain interpolation coefficient λD and the reference model MR (s) of the above equation (18) determined from a certain interpolation coefficient λR, The rise time ratio σR / σD is obtained from the equation or the equation (20), and the coefficients β and γ are obtained from the equations (21) and (22).
[0093]
Then, coefficients β and γ are obtained for various values of the interpolation coefficients λD and λR, and a matrix data table is created in which the x-axis is λD, the y-axis is λR, and the z-axis is β and γ. , ΛR, a function element for generating the coefficients β and γ can be created.
[0094]
Since there is a relationship shown in FIG. 15 between the interpolation coefficient λ and the maximum sensitivity Ms, the maximum sensitivities MSD and MSR may be used instead of λD and λR. When a second-order normative model is used, a coefficient α2R of a second-order denominator of the normative model may be used instead of λR.
[0095]
Further, as an example of a function element, as shown in FIG. 16A, if the x-axis is λD of the third-order norm model and the y-axis is α2R of the second-order norm model, for two-degree-of-freedom IP control, A function for obtaining the coefficient β is obtained. Further, as shown in FIGS. 16B and 16C, if the x-axis is λD of the fourth-order norm model and the y-axis is λR of the third-order norm model, the coefficient β for two degrees of freedom I-PD control , Γ are obtained.
[0096]
FIG. 13 is a configuration diagram showing an example of a parameter generation mechanism embodied based on the above description.
[0097]
This parameter generating mechanism 2 is composed of a function element 41 and an operation element 42. The function element 41 includes an attribute value XD (λD, MSD, etc.) of the reference model of the disturbance suppression I-PD control system and an attribute value XR (γR, MSR, α2R, etc.) of the reference model that defines the target value followability. Is a matrix data table in which the values of the coefficient β are stored for various combinations of the values of the above, and the stored coefficient β is generated from the matrix data table based on the input attribute values XD and XR. Note that, instead of the matrix data table, an element that generates the coefficient β by the operation of the expression (19) or the expression (20) and the expression (21) may be used.
[0098]
The operation element 42 includes a multiplication element 43 and a division element 44. The multiplication element 43 multiplies a coefficient β generated from the function element 41 by a rise time σD of a reference model of a disturbance suppression I-PD control system, and performs division. Introduced in element 44. The division element 44 calculates the multiplication value obtained by the multiplication element 43 by an integration time T_IAnd calculate the two-degree-of-freedom parameter b for the proportional term, and set it in the two-degree-of-freedom I-PD controllers 1 'and 31.
[0099]
FIG. 14 is a configuration diagram showing another example of the two-degree-of-freedom parameter generation mechanism.
[0100]
The parameter generating mechanism 2 includes two function elements 45 and 46 and two operation elements 47 and 48 corresponding to the function elements 45 and 46, respectively.
[0101]
These function elements 45 and 46 are matrix data tables storing the values of the coefficient β for various combinations of the attribute values XD and XR of the reference model, respectively. Based on XR, the coefficients β and γ stored from the matrix data table are generated. Note that instead of the matrix data table as the function element 45, the coefficient β is generated by the operation of the equation (19) or the equation (20) and the equation (21). Alternatively, an element for generating the coefficient γ by the calculation of the above equations (19) and (22) may be used.
[0102]
The operation element 47 includes a multiplication element 49 and a division element 50 in the same manner as the operation element 42 shown in FIG. 13, and the multiplication element 49 includes a coefficient β generated from the function element 45 and a reference model of a disturbance suppressing I-PD control system. Is multiplied by the rise time σD, and is introduced into the division element 50. This division element 50 calculates the two-degree-of-freedom parameter b for the proportional term by dividing the multiplication value obtained by the multiplication element 49 by the integration time TI.
[0103]
One operation element 48 includes a first multiplication element 51, a second multiplication element 52, a division element 53, and a multiplication element 54, and calculates the two-degree-of-freedom parameter c for the differential term by the operation of the equation (24). I do. Specifically, the multiplication value σD of the rise time σD obtained by the second multiplication element 52²And a coefficient γ are multiplied by a multiplication element 51 and introduced into a division element 53. The division element 53 calculates the integration time T obtained by the multiplication element 54 by the multiplication value from the multiplication element 51._IAnd derivative time T_D, And the two-degree-of-freedom parameter c for the differential term is calculated by equation (24). Then, the parameters b and c obtained by the respective operation elements 47 and 48 are transmitted to, for example, a two-degree-of-freedom I-PD controller 1 'shown in FIG.
[0104]
Note that the two-degree-of-freedom I-PD controller 1 'is not limited to the one shown in FIG. 20, but a target value feed-forward type shown in FIG. It may be a value filter type, or a loop compensation type or a feedback compensation type (PID control, p75, author: Nobuhide Suda, Asakura Shoten).
[0105]
Although the differential element 118 shown in FIG. 20 is described in a fully differential type, it may be an incomplete differential type to which a first-order lag element is added.
[0106]
Next, the input to the parameter generating mechanism will be described. When the PID value is designed using the reference model so that disturbance can be suppressed most satisfactorily, the interpolation coefficient λD, the maximum sensitivity MSD, the coefficient α2R of the second-order denominator, and the rise time σD are uniquely determined in the reference model used at this time. Use these as they are decided. When the PID value is adjusted without using the reference model, it is compared with the control response (Fig. 17) drawn by changing the interpolation coefficient λD when a step input is applied to the operation terminal (Fig. 17), and the interpolation coefficient of the waveform having the closest shape is obtained. From λD, the reference model and the rise time σD (the time when the control response almost reaches a peak) are specified and used.
[0107]
FIG. 17A is a control response diagram of a fourth-order reference model, and is used when a two-degree-of-freedom I-PD control system using a differential operation is used. FIG. 17B is a control response diagram of a third-order reference model, which is used in a two-degree-of-freedom IP control system that does not use a differential operation.
[0108]
In addition, when the change in the manipulated variable that occurs when the target value change is excessive is reduced or when the robustness is desired to be increased, the rise time σD is set to a value larger than the value determined as described above. Enter a smaller value.
[0109]
Further, for example, a mechanism for automatically identifying a reference model of the I-PD control system is added, and an integration time T used in the I-PD controller is used._I, Differentiation time T_DIf the input items of the identification result are automatically input to the parameter generating mechanism of the present invention, an auto (self) tuning two-degree-of-freedom I-PD control system can be configured.
[0110]
Further, as a reference model for defining the followability of the target value change, a control response waveform (FIG. 18) drawn by variously changing the interpolation coefficient λR and the coefficient α2R of the denominator quadratic term is referred to. The interpolation coefficient λR that gives the most appropriate shape in the control system and the coefficient α2R of the denominator quadratic term, that is, the attribute values of the reference model are determined and input. FIG. 18A is a control response diagram of the third-order model when the interpolation coefficient λR is variously changed when the target value unit step is changed, and is used for two-degree-of-freedom I-PD control. b) is a control response diagram of the second-order normative model when the coefficient of the denominator quadratic term is variously changed at the time of changing the target value unit step, and is used in two-degree-of-freedom IP control.
[0111]
FIG. 19 is an example of a control response when a two-degree-of-freedom parameter is generated from the parameter generation mechanism 2 according to the present invention, set in a two-degree-of-freedom IP (D) controller, and a control target is controlled. For comparison, the control response is shown for a case where control is performed by a one-degree-of-freedom IP (D) controller and a PI (D) controller.
[0112]
As is clear from this figure, in the case of the I-PD control according to the present invention, it is possible to respond with a quick response without generating a large overshoot at the time of changing the target value, and it is possible to greatly improve the target value following ability. Can be improved.
[0113]
【The invention's effect】
As described above, according to the present invention, a two-degree-of-freedom parameter that defines a control response when a target value is changed can be automatically generated based on a predetermined input item. The work of adjusting by mistake can be omitted, and the two-degree-of-freedom parameter can be generated in a short time without relying on a skilled person.
[0114]
Therefore, it is possible to provide a two-degree-of-freedom control device capable of quickly realizing optimum controllability both for disturbance and target value change.
[Brief description of the drawings]
FIG. 1 is a conceptual configuration diagram illustrating first and second embodiments of a two-degree-of-freedom control device according to the present invention.
FIG. 2 is a block diagram of a two-degree-of-freedom PID control system for explaining the principle of the present invention.
FIG. 3 is an overall block diagram including input items in a two-degree-of-freedom control device according to the present invention.
FIG. 4 is a diagram showing a specific configuration example of a parameter generation mechanism shown in FIG. 3;
FIG. 5 is a diagram showing a specific configuration example of a parameter generation mechanism shown in FIG. 3;
FIG. 6 is a diagram showing a specific configuration example of a parameter generation mechanism shown in FIG. 3;
FIG. 7 is a diagram showing an example of a control response when the two-degree-of-freedom control device according to the present invention is used.
FIG. 8 is a view for explaining functions set in the parameter generation mechanism shown in FIG. 3;
FIG. 9 is a block diagram showing a two-degree-of-freedom control device according to a second embodiment of the present invention.
FIG. 10 is a block diagram showing another example of the two-degree-of-freedom control apparatus according to the second embodiment of the present invention.
FIG. 11 is a conceptual diagram illustrating a two-degree-of-freedom control apparatus according to a third embodiment of the present invention.
FIG. 12 is a block diagram of a two-degree-of-freedom I-PD control system illustrating the principle of the present invention.
FIG. 13 is a diagram showing a specific configuration example of a parameter generation mechanism.
FIG. 14 is a diagram showing a specific configuration example of a parameter generation mechanism.
FIG. 15 is a diagram showing a relationship between an interpolation coefficient of a reference model and a maximum sensitivity.
FIG. 16 is a diagram showing function characteristics of function elements.
FIG. 17 is a diagram showing a control response of a reference model at the time of a step disturbance input used for PID value design or characteristic identification of an I-PD control system.
FIG. 18 is a diagram showing a control response of a reference model when changing a target value unit step used in two-degree-of-freedom IP (D) control design.
FIG. 19 is a diagram showing an example of a control response when the two-degree-of-freedom control device according to the present invention is used.
FIG. 20 is a diagram showing a schematic configuration of a conventionally known general two-degree-of-freedom PID or two-degree-of-freedom I-PD control system;
FIG. 21 is a configuration diagram of a two-degree-of-freedom control device having a conventionally known feedforward element.
FIG. 22 is a configuration diagram of a two-degree-of-freedom control device having a conventionally known target value filter element.
[Explanation of symbols]
1 ... 2 degrees of freedom PID controller
1 '... 2-DOF I-PD controller
2. Parameter generation mechanism
21, 22 ... operation element
σD: Rise time for disturbance input control response
σR: Rise time for target value change control response
T_I… Integration time
T_D… Derivative time
α2D: second order coefficient of disturbance input control response reference model
α2R: second order coefficient of target value change control response reference model
41, 45, 46 ... function elements
42, 47, 48 ... arithmetic elements

Claims (10)

In a two-degree-of-freedom control device that controls both disturbance suppression and target value tracking with respect to a controlled object using a control parameter and a two-degree-of-freedom parameter,
Using the rise time related to the disturbance input control response, the rise time related to the target value change control response, and the integration time or the integration time and the derivative time that are the control parameters, the two freedoms that define the target value change control response are used. A two-degree-of-freedom control device comprising a parameter generation mechanism for generating a degree-of-degree parameter. The parameter generating mechanism according to claim 1,
The rise time relating to the disturbance input control response is σD, the second order coefficient of the disturbance input control response reference model is α2D, the rise time relating to the target value change control response is σR, the target value change The second order coefficient of the control response reference model is α2R, and the integration time Is T _I and the differentiation time is T _D ,
{(1−α2R) · σR ² −σD · σR + α2D · σD ² } / T _I · T _D
A two-degree-of-freedom control device, comprising: a calculating means for setting a value proportional to a value obtained by an arithmetic expression as a two-degree-of-freedom parameter defining the target value change control response. In a two-degree-of-freedom control device that controls both disturbance suppression and target value tracking with respect to a controlled object using a control parameter and a two-degree-of-freedom parameter,
A parameter generation mechanism that generates the two-degree-of-freedom parameter that defines a target value change control response using the transfer characteristic type of the controlled object, the dead time and the limit period, or the transfer characteristic type and the standardized dead time of the controlled object. A two-degree-of-freedom control device, comprising: The parameter generating mechanism according to claim 3,
4. A two-degree-of-freedom control device, wherein a two-degree-of-freedom parameter defining a target value change control response obtained in any one of claims 1 to 3 is set as a graph function for various control targets. In a two-degree-of-freedom control device that controls both disturbance suppression and target value tracking with respect to a controlled object using a control parameter and a two-degree-of-freedom parameter,
The attribute value of the first reference model and the attribute value of the second reference model that defines the target value followability in the disturbance suppression I-PD control system are input, and a coefficient value is generated as a function of these two attribute values. A parameter generation mechanism having a function element and an operation element for generating a two-degree-of-freedom parameter for improving target value followability by using a coefficient value of the function element, a rise time and an integration time of the first reference model. A two-degree-of-freedom control device, comprising: The two-degree-of-freedom control device according to claim 5,
The function element is provided with a matrix data table that holds coefficient values for various sets of attribute values of the first reference model and attribute values of the second reference model. A two-degree-of-freedom control device for generating a coefficient value. In the two-degree-of-freedom control device according to claim 5 or 6,
The first reference model is a model used for designing a PID parameter that favorably suppresses a disturbance, or a model obtained by identifying characteristics of an I-PD control system. Control device. The two-degree-of-freedom control device according to any one of claims 5 to 7,
The attribute value of the reference model uses any one of an interpolation coefficient of the reference models, a maximum sensitivity of the reference models, and a transfer function coefficient value of the reference models. Control device. The two-degree-of-freedom control device according to claim 5,
The arithmetic element generates a two-degree-of-freedom parameter by multiplying a coefficient value generated from the function element by a rise time of the first reference model, and dividing the multiplied value by an integration time. To control two degrees of freedom. The two-degree-of-freedom control device according to claim 5,
The arithmetic element multiplies the coefficient value generated from the function element by the square of the rise time of the first reference model, and divides the multiplied value by the multiplied value of the integral time and the derivative time to obtain two free elements. A two-degree-of-freedom control device for generating a degree of freedom parameter.

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