JP3790129B2 - Process simulator application control apparatus and method - Google Patents

Description

ここで、ΔU(k)は入力Δu(k)∈R^mを１ステップづつずらしてNu²個並べたもの、D(k)は外乱d(k)∈R^kを１ステップづつずらしてNu個並べたもの、G(k)は(時間に依存する)プロセスのステップ応答(時系列データ)を１ステップづつずらしてNp³個並べたもの、Y(k)は出力y(k)∈R^pをNp個並べたもの、Yhold(k)は操作量を固定した場合の出力yhold∈R^pを１ステップづつずらしてNp個並べたもの、E(k)は外乱から出力への影響を表す行列である。なお、R*は＊次の実数の集合である。
【００５６】
また、以下のような制約条件が与えられているとする。
【００５７】
【数２】

ここで、u⁽ⁱ⁾は入力uのi番目要素、Δu⁽ⁱ⁾は入力の差分Δuのi番目の要素、y^(j)は出力yのj番目の要素であり、添え字のminとmaxは、それぞれ最小と最大を表し、入力及び出力の制約である。このとき、次の評価関数を最小にするような制御入力u(k)（あるいは、同じことであるが、入力の差分Δu(k)）を求めよ。
【００５８】
【数３】

【数４】

（６）式は、時刻k〜k+Nu間の最適操作量であるが、実際には、現在時刻ｋの操作量のみを取りだし、
△u(k)=[Im,0,…,0]Δu(k) （7)
を最適操作量とする。
【００５９】
「新モデル予測制御問題」と「新モデル予測制御問題の解」を参考にして、以下に図１に示した本実施形態の動作を説明する。
【００６０】
先ず、プロセス値記憶手段２において、プロセス外乱センサ１６、プロセス出力センサ１７１〜１７５で計測した各種水質や水量などのセンサ出力値、及びアクチュエータ１８１〜１８４の操作量値（アクチュエータの操作量値が計測できない場合は、プロセス最適化手段１０から出力される操作量指令値）に関する項目を記録する領域を確保し、これらの領域の初期化を行う。
【００６１】
次に、ある時刻において、プロセス外乱センサ１６の計測値（時系列データ）、プロセスセンサ１７１〜１７５の計測値（時系列データ）、及びアクチュエータ１８１〜１８５の操作量値（時系列データ）をプロセス値記憶手段２のプロセスデータサーバに適切なフォーマットに従って記憶する。
【００６２】
次に、プロセス外乱予測手段３によって、本実施形態の外乱である流入下水量及び流入下水水質を予測する。具体的には、以下の様なことが考えられる。
【００６３】
例えば、過去の流入下水量データや流入下水水質データを統計解析し、自己回帰モデル（ARモデル）などの統計モデルを構成して、流入下水量や流入下水水質を予測することができる。
【００６４】
また、流入下水量や流入下水水質は、図２（ａ），（ｂ）に示すように、天候と時刻に依存して一定のパターンを持つことが多いので、現在の天候と時刻を参照して過去のパターンを参照することによって予測することができる。
【００６５】
また、流入下水量や流入下水水質の典型的なパターンが認められず、さらに過去の流入下水量や流入下水水質のデータが保存されていない場合には、プロセス外乱センサ１６によって計測した流入下水量や流入下水水質をホールドし、これを未来に外挿することによってプロセス外乱の予測を行うことができる。
【００６６】
次に、プロセス値記憶手段２に記憶された所定の期間に亘る操作量の時系列データ及びプロセス外乱予測手段３によって予測された流入下水量や流入下水水質の予測値をプロセス予測手段４に引き渡す。
【００６７】
プロセス予測手段４では、例えば、以下に示すような数学モデル（非線形微分方程式）によって構築されるプロセスシミュレータによって、被制御量（あるいは観測出力）である最終沈殿池１５の水質を予測する。
【００６８】
プロセスシミュレータのモデル
図１の下水処理プロセスのプロセスシミュレータは、構成要素として最初沈殿池モデル、嫌気槽モデル、無酸素槽モデル、好気槽モデル、最終沈殿池モデル、からなり、これを物理的に結合することによって構築できる。
【００６９】
最初沈殿池（ First Clarifier) モデル
沈殿池のモデル化の方法は、例えば文献「G．A．Ekama et al,"Secondary Settling Tanks-Theory,Modeling,Design and Operation"，IAWQ Scientific Technical Report No.6,(1997)」にまとめられているが、ここでは、説明を簡単にするため、以下のような簡単なモデルを利用する。
【００７０】
【数５】

ここで、Qfcin(t)[m³/day]は外乱としての流入量、Sfcin(t)[g/m³]及びXfcin(t)[g/m³]は、それぞれ、外乱としての溶解性及び浮遊性流入水質成分、Qfcout(t)=Qfcwaste(t)＋Qfcnextoutq(t)[m³/day]（Qfcwaste(t)：初沈余剰汚泥引抜量、Qfcnextoutq(t):生物反応槽（嫌気槽）への流出量）は最初沈殿池からの流出量、Sfcin(t)[g/m³]は溶解性の水質９項目からなるベクトル、XLfc(t)[g/m³]は、沈殿部の浮遊性(固形)の水質7項目からなるベクトル、XUfc(t)[g/m³]は上澄部の浮遊性の水質7項目からなるベクトルである。溶解性の水質と浮遊性の水質は合計16個からなる。また、Vfcは最初沈殿池容量(一定と仮定)であり、αは汚泥が沈殿していると考えられる容積の最初沈殿池水量Vfcに対する割合の逆数を示す定数である。また、嫌気槽へ引き継がれる水質をZfc(t):=[Sfc(t)XUfc(t)]^Tと定義し、余剰汚泥として引き抜かれる水質をZfcwaste(t):=[Sfc(t)XLfc(t)]^Tと定義する。
【００７１】
嫌気槽 (AnAerobic Tank) モデル
嫌気槽モデルは、微生物の反応と液体の完全混合を表すモデルから成る。
【００７２】
【数６】

ここで、Qaain(t)=Qfcnextout(t)+Qscret(t)[m³/day]（Qscret(t)[m³/day]は、後述の返送汚泥量)と、Qaaout[m³/day]は、それぞれ嫌気槽への流入量(最初沈殿池からの流入量＋返送汚泥量)と嫌気槽からの流出量(無酸素槽への流入量)であり、Zaa(t)[g/m³]は嫌気槽の水質からなるベクトルであり、Zaain(t)[g/m³]={Zfc(t)Qfcout(t)+Zscret(t)}/Qaain(t)(Zscret(t)は後述の返送汚泥の水質)は嫌気槽へ流入する水質からなるベクトルであり、Vaa[m³]は嫌気槽の水量(一定と仮定)である。また、r(Zaa(t)は、微生物反応による反応速度式であり、例えば、文献「IAWQ Task Group on Mathematical Modeling for Design and Operation of Biological Wastewater Treatment Processes、"Activated Sludge Model No.2"，IAWQ Scientific Technical Report No.3,(1995)」に示されている19個の生物反応プロセスを考慮したASM2などで構成される(ただし、ASM2である必然性はなく、微生物反応を模擬できる反応速度式であれば、任意のものでよい)。
【００７３】
ASM2では、Zaa(t)の要素として、P0₄(リン酸)、NH₄(アンモニア)、NO₃(硝酸)、DO(溶存酸素)や、MLSS(浮遊固形物濃度)の構成要素としての窒素除去やリン除去に関わる微生物など、16個の水質を考慮している。また、r(Zaa(t)の各要素は、19個の各プロセスに対して定義されるモノー型と呼ばれる非線形関数の反応速度式に対する重み付き和で構成されているため、それ自身非線形の関数になっている。従って、(13)〜(15)式のASM2モデルは、16次の非線形微分方程式となっている。
【００７４】
無酸素槽 (AnOxic Tank) モデル
無酸素槽モデルは、嫌気槽モデルとほぼ同様の構成である。
【００７５】
【数７】

ここで、Qaoin(t)＋Qoxcirc(t)[m³/day]（Qoxcirc(t)は後述の循環量）とQaoout(t)[m³/day]は、それぞれ反応槽への流入量と反応槽からの流出量、Zao(t)[g/m³]は無酸素槽の水質からなるベクトル、Zaoin(t)[g/m³]={Zaa(t)Ｑaaout(t)＋Zox(t)Qoxcirc(t)}/Qaoin(t)(Zox(t)は後述の好気槽の水質)は無酸素槽へ流入する水質からなるベクトル、Vao[m³]は無酸素槽の水量(一定と仮定)である。
【００７６】
好気槽 (OXic Tank) モデル
好気槽のモデルは、嫌気槽や無酸素槽のモデルに、酸素供給のモデルを追加したものとなる。
【００７７】
【数８】

ここで、Qoxin(t)=Qaoout(t)[m³/day]とQoxout(t)=Qoxnextout(t)+Qoxcirc(t)[m³/day](Qoxnextout(t)は最終沈殿池への流出量、Qoxcirc(t)は循環量)は、それぞれ好気槽への流入量と好気槽からの流出量(循環量＋最終沈殿池への流出量)、Zoxwe (t)[g/m³]は好気槽の水質からなるベクトル、Zoxin(t)[g/m³]=Zao(t)は好気槽へ流入する水質からなるベクトルVox[m³]は好気槽の水量(一定と仮定)である。また、So2ox(t)はZox(t)の要素(ASM2では2番目の要素)である溶存酸素濃度、So2は飽和溶存酸素濃度、KLaは総括酸素移動容量係数、Qb(t)はブロワによる曝気風量、Kは曝気風量と総括酸素移動容量係数を関連づける比例定数である。
【００７８】
最終沈殿池 (Second Clari6er) モデル
最終沈殿池も、最初沈殿池のモデルと同様にモデル化できる。
【００７９】
【数９】

ここで、Qscin(t)=Qoxnextout(t)は最終沈殿池への流入量、[Sscin(t)，XLscin(t)]=Zox(t)は最終沈殿池への流入水質、Ssc(t)[g/m³]は溶解性の水質からなるベクトル、XLsc(t)[g/m³]は、沈殿部の浮遊性(固形)の水質からなるベクトル、XUsc(t)[g/m³]は上澄部の浮遊性の水質からなるベクトルである。また、Vscは最終沈殿池の水量(一定と仮定)であり、βは汚泥が沈殿していると考えられる容積の沈殿池水量Vscに対する割合の逆数を示す定数である。また、Qscout(t)=Qscwaste(t)+Qscret(t)[m³/day](Qscout(t)：余剰汚泥引抜量、Qscret(t)：返送汚泥量)である。また、嫌気槽へ返送される(及び余剰汚泥として引き抜かれる)水質をZscret:=[Ssc(t)XLsc(t)]^Tと定義し、放流水質をZsceffl(t):=[Ssc(t)XUsc(t)]^Tと定義する。以上の(8)〜(27)式の各プロセスモデルを結合し、これを例えば計算機上に実装することにより、プロセスシミュレータを構築できる。以上のモデルをまとめると、形式的には以下のようにまとめて書くことができる。
【００８０】
【数１０】

と定義し、f(x(t))，g1(x(t))，g2(x(t))は、(8)〜(27)式のx(t)に関する関数を適切に配置したものである。また、h(x(t))は観測量であり、例えば、x(t)の要素である各槽の酸素濃度S02aa(t)，S02ao(t)，S02ox(t)や各槽のMLSS濃度Xtssaa(t)，Xtssao(t)，Xtssox(t)、さらには、x(t)の要素である各槽のアンモニア性窒素濃度Snh4aa(t)，Snh4ao(t)，Snh4ox(t)や、リン酸性リン濃度Spo4aa(t)，Spo4ao(t)，Spo4ox(t)などをベクトルとして並べたものである。また、h2(x(t))は、被制御量であり、例えば、放流規制である最終沈殿池から流出する(x(t))の要素である)リン酸性リン濃度Spo4sc(t)やアンモニア性窒素濃度Snh4sc(t)、さらには、Ssc(t)の各水質要素の関数(線形和)である溶解性CODなどである。
【００８１】
さて、(28)〜(30)式のプロセスシミュレータを用いてプロセス予測を行う際には、未来の操作量は現在の操作量をそのままホールドしているとして、計算を行う。これを、所定の制御周期毎にサンプリングし、所定の予測ホライズンNpまでの時系列データとして取り出し、さらにこのデータを適切に並べることにより、(1)式のYhold(k)の下記の、
【数１１】

を得ることができる。これがプロセス予測手段４の予測方法の一例であり、これによって操作量を固定した場合のプロセスの予測値が計算できる。
【００８２】
また、(28)〜(30)式のようなプロセスモデルが得られないような場合には、過去の時系列データから統計的(数理的)な方法によってプロセスシミュレータを構築しておき、これに対して上記と同様のことを行えば、操作量を固定した場合のプロセス予測を行うことができる。
【００８３】
また、もしプロセスシミュレータが存在しない場合には、次の様に操作量を固定した場合の予測を行うこともできる。まず、運転員が現在の操作量を保った場合の最終沈殿池１５の水質がどのように変化するかを過去の経験と勘に基づいて予測し、それを図３に示すように、例えば電子的に入力できるディスプレイ(銀行のATMの様なもの)に予測軌道(予測応答)として入力をしてもらう。この入力されたデータを時系列データとして取り出し、上記と同様の方法によって、操作量を固定した場合の予測を行うことができる。
【００８４】
また、プロセスシミュレータは存在するが運転員がプロセスシミュレータの予測に不満や疑問を感じる様な場合には、以下の様にプロセス予測を行うこともできる。まず、上述したようなプロセスシミュレータにより、操作量を固定した場合の最終沈殿池１５の水質の予測を行う。次に、この予測軌道(予測応答)を、例えばディスプレイ上にグラフとして表示する。次に、このディスプレイ上にグラフとして表示された予測応答に不満がある場合には、運転員が、例えばマウスなどによってドラッグやドロップをすることにより、この予測応答波形を修正できるようにしておく。そして、この修正された予測応答波形を時系列データとして改めて保存し、これを上記と同様の方法によって、操作量を固定した場合のプロセス予測を行うことができる。これを図４に示す。
【００８５】
上述したように、プロセスの物理化学的な方法に基づいて微分方程式や偏微分方程式など用いて構築したシミュレータや、プロセス値記憶手段２に蓄積されたプロセス操作量、その外乱等から多変量解析等の統計的システム同定法を利用して構築したシミュレータを用いる方法では、プロセス出力センサ１７１〜１７５の値を用いずに予測を行っていた。このような予測では、しばしば予測精度が劣化することがある。さらに、純粋な積分を含むプロセスや不安定なプロセス(有限の値の操作量を入力しているにも関わらず、出力が有限でなくなるようなプロセス)では、そもそも予測を行うことができない。このような場合には、例えば、(28)〜(30)式の様なプロセスシミュレータに対して、プロセス出力センサ１７１〜１７５の出力値と現時点の予測値との誤差をフィードバックすることにより、より精度良くかつ高ロバストな予測を行うことができる。例えば、以下の様にセンサ値のフィードバックを持つプロセスシミュレータ(ロバストプロセス値予測器)を構成できる。
【００８６】
【数１２】

もし、f(x(t))-Kh1(x(t))を適当な動作点周りで線形近似を行い、その固有値の実部が全てマイナスになるようにKを選び、さらに対象プロセスが(28)〜(30)式で厳密に(誤差を持たずに)表現できるならば、(34)式と(35)式は、それぞれ、(局所的には)真の状態と真の出力に漸近的に収束する。従って、単に(28)〜(30)式を用いて予測を行うよりも、(34)式と(35)式を用いることによってロバストに予測を行うことができる。
【００８７】
次に、ステップ応答記憶手段５では、予めプロセスに対するステップ応答試験を行うことができる場合には、想定される複数の運転点を設定し、その複数の運転点周りでステップ応答試験を行っておき、その応答波形を対応する運転点とセットにしてデータベース化しておくことができる。また、プロセスが既に稼動状態にあり、ステップ応答試験を行うことが困難な場合には、例えば(28)〜(30)式で構成される様なプロセスシミュレータを用いて、このプロセスシミュレータを仮想的に対象プロセスとみなし、これに対して応答波形を対応する運転点とセットにしてデータベース化しておくと同様な方法でステップ応答を記憶させておくことができる。
【００８８】
また、対象プロセスに対する想定される運転点が予め不明であり、かつ、制御周期がプロセスシミュレーション計算時間と比較してそれほど短くない場合には、現在の運転点をプロセス値記憶手段２からオンラインで検出し、その近傍で循環ポンプ１８１乃至余剰汚泥引き抜きポンプ１８４のアクチュエータに微小なステップ摂動を与えた場合の応答をシミュレーションし、その応答波形を記憶することによって、ステップ応答記憶手段５を実現することができる。なお、この方法を用いた場合は、ステップ応答波形が一つであるため、以下で説明するステップ応答選択手段６は必要なくなる。
【００８９】
次に、ステップ応答選択手段６では、プロセス値記憶手段２に保存された現在の操作量を入力し、その情報からステップ応答記憶手段５に記憶されたステップ応答の集合の中から、最も近い運転点を探し出し(例えば、現在の複数の操作量の値とステップ応答記憶手段５に記憶された運転点(複数の操作量の様々な組み合わせに対する運転点)を、例えば、０〜１の値を取るように、全て正規化し、正規化した複数の操作量の値と正規化した運転点の誤差の２乗和が最小となるような運転点を最も適切な運転点として採用するなど、その運転点に対応するステップ応答を選択する。
【００９０】
また、プロセス運転員が自分でステップ応答を選択したい場合には、図５に示すように、それぞれの出力に対するステップ応答波形を複数表示しておき、この中から運転員が選択するという方法も考えられる。さらに、前述したように、管理者や運転員がグラフとして表示された予測結果を自分で修正する方法も考えられる。次に、プロセス最適化手段１０では、プロセス予測手段４による操作量を固定した場合のプロセス出力予測値と、ステップ応答選択手段６によって選択されたステップ応答波形を入力し、それぞれのデータを適切に並べることによって、Yhold(k)の予測値及びG(k)の予測値を計算する。次に、これらの予測値を用いて、例えば制約条件が無い場合には、(6)式を計算することによって最適な操作量を決定できる。この場合、プロセス評価関数及び評価重み供給手段７や目標値軌道供給手段９によって、予め評価関数や評価関数の重みや目標値軌道は外部から与えられているとする。
【００９１】
また、プロセス制約条件供給手段８による制約がある場合には、後述する「モデル予測制御問題3'」の解法として良く用いられている共役勾配法などの最適化手法を用いることによって、最適操作量を決定できる。
【００９２】
また、より効率良く最適操作量を求めるためには、制約がある場合の最適化問題をLMIの問題として再定式化して、最近のLMIの研究で得られている最新の成果を用いて、より効率良く最適操作量を求めることができる。
【００９３】
また、一連の処理を行う計算機のパワーが足りない場合やより短い周期で制御を行いたい場合には、最適化問題の最適解を求めることをあきらめ、遺伝的アルゴリズムなどのヒューリスティックな解法を用いて、準最適な操作量を求めることができる。次に、プロセス最適化手段１０で決定した最適な操作量を操作量指令値として下水処理プロセス１に与え、これに従って操作量を調整する。最後に、プロセス値記憶手段２の初期化を除いた上記の操作を制御周期毎に繰り返す。なお、人間系が介在している箇所については、必ずしも制御周期毎に繰り返す必要はなく、間欠的に介在しても構わない。
【００９４】
次に、本実施形態の効果を説明することとする。ここでは、まず本実施形態が何故効果的であるかを説明し、最後に本実施例の効果をまとめる。まず、以下の説明を行う準備として、後の説明で重要となるプロセスシミュレータ(28)〜(30)式の特徴を列挙する。
【００９５】
イ プロセスシミュレータのモデルは一見複雑であるが、要素をベクトル化して表示すると、結局(28)〜(30)式の形にまとめられる。
【００９６】
ロ しかし、(28)〜(30)式の状態方程式の次数は、ASM2を用いた場合80次(5×16次)にのぼり、高次である。
【００９７】
ハ さらに、(28)〜(30)式は、強い非線形性を持つため線形近似を行うことは難しい(fx(t)の要素はASM2による飽和型の強い非線形関数であり、さらに双線形の項も持っている)。
【００９８】
さて、本実施形態の効果を説明するために、これらの特徴を念頭において、(28)〜(30)式に対して、既存のモデル予測制御方式を適用することを考える。一般に(非線形の)モデル予測制御は、以下のように定式化される。
【００９９】
モデル予測制御問題 1( 一般系 ; 連続時間系 )
制御対象(対象プロセス)のモデルが以下のように与えられているとする。
【０１００】
【数１３】

ここで、u(t)∈R^mは入力、d1(t))∈R^lはシステム外乱、d2(t)∈R^kは観測外乱、x(t)∈Rⁿは状態、y(t)∈R^pは出力であり、R*は＊次の実数の集合である。また、以下のような制約条件が与えられているとする。
【０１０１】
【数１４】

ここで、U⁽ⁱ⁾は入力uのi番目の要素、y^(j)は出力yのj番目の要素であり、添え字のminとmaxは、それぞれ最小と最大を表し、入力及び出力の制約である。このとき、次の評価関数を最小にするような制御入力u(t)を求めよ。
【０１０２】
【数１５】

プロセス制御においては、通常、制御周期をサンプリング周期とする離散時間のモデルを用いて、以下の様な離散時間系のモデル予測制御問題として定式化することも多い。
【０１０３】
モデル予測制御問題 2( 一般系 ; 離散時間系 )
制御対象(対象プロセス)のモデルが以下の様に与えられているとする。
【０１０４】

ここで、u(t)∈R^mは入力、d1(t))∈R^lはシステム外乱、d2(t)∈R^kは観測外乱、x(t)∈Rⁿは状態、y(t)∈R^pは出力であり、R*は＊次の実数の集合である。また、以下のような制約条件が与えられているとする。
【０１０５】
【数１６】

このとき、次の評価関数を最小にするような制御入力u(k)を求めよ。
【０１０６】
【数１７】

さて、ここで、以上のモデル予測制御方式を、下水処理プロセスに対して適用することを考える。まず、上記「イ」の特徴より、(28)〜(30)式において、被制御量と観測出力を同一のものとすれば(y(t)=z(t))、本実施形態の下水処理プロセスには、(28)〜(30)式の下水処理プロセスシミュレータを使った「モデル予測制御問題1」として定式化できる。さらに、(28)〜(30)式を、例えばオイラー差分などによって、予め与えた制御周期で離散化すれば、「モデル予測制御問題2」として定式化することもできる。
【０１０７】
しかし、「モデル予測制御問題1」や「モデル予測制御問題2」は、問題として定式化することは容易であるが、実際にこの問題を解くのはそれほど容易なことではない。これに対して、現在、多くの研究者によって非線形モデル予測制御問題の研究が進められている。例えば、理論上の問題として、局所解に陥らずに最適解を求める問題や安定性を保証する問題などが残されている。さらに、莫大の計算量をどのように低減するかという実装上の問題も残されている。特に、実用上の側面からは、計算量の問題を解決することは重要である（局所解の問題や安定性の問題も非常に重要な問題である。しかし、実用的観点からは、局所解の問題は局所解を準最適解と考えて妥協してしまうことができる。また、安定性の問題に関しては、多くのプロセスでは、不安定化しないように制御系の機構面から対策することなどで避けている場合が多い。しかし、計算量が莫大になる問題は、現実の実装に関わるため、この問題を解決しなれば、産業界で使われることは難しい）。例えば、これを下水処理プロセスに適用するためには、下水処理プロセスシミュレータの特徴「ロ」のため、計算量が莫大になってしまうことは避けられない。従って、このようなモデル予測制御を下水処理プロセスのような複雑なプロセスに適用するには、まだ長い年月を必要とすると考えられる。
【０１０８】
一方、実際に既に産業分野で使われているモデル予測制御は、「モデル予測制御1」や「モデル予測制御2」の制御対象を線形なシステムに限ったものである。特に計算機上に実装することを考えて、離散時間系で用いられることが多く、これは、「モデル予測制御問題2」の特殊ケースと考えることができる。これを以下に示す。
【０１０９】
モデル予測制御問題 3( 線形状態空間モデル ; 離散時間系 )
制御対象(対象プロセス)のモデルが以下の様に与えられているとする。
【０１１０】

ここで、u(t)∈R^mは入力、d1(t))∈R^lはシステム外乱、d2(t)∈R^kは観測外乱、x(t)∈Rⁿは状態、y(t)∈R^pは出力である。また、A〜Fは適当なサイズの定数行列である。
【０１１１】
また、以下のような制約条件が与えられているとする。
【０１１２】
【数１８】

このとき、次の評価関数を最小にするような制御入力u(k)を求めよ。
【０１１３】
【数１９】

なお、通常、線形のモデル予測制御では、予め制御対象の前に積分器を挿入しておくことが多いため（ステップ目標値に対して、定常偏差をゼロに保つためである）、実際には、以下の問題を解くことが多い。ただし、以下のモデル予測制御3'とモデル予測制御3は、アルゴリズム上はほとんど同じである。
【０１１４】
モデル予測制御問題 3 、 ( 線形状態空間拡大モデル ; 離散時間系 )
制御対象(対象プロセス)の前に積分器を挿入した拡大制御対象のモデルが以下の様に与えられているとする。
【０１１５】
【数２０】

また、以下のような制約条件が与えられているとする。
【０１１６】
【数２１】

ここで、U⁽ⁱ⁾は入力uのi番目の要素、ΔU⁽ⁱ⁾は入力の差分、y^(j)は出力yのj番目の要素であり、添え字のminとmaxは、それぞれ最小と最大を表し、入力及び出力の制約である。このとき、次の評価関数を最小にするような制御入力u(k)（あるいは、同じことであるが、入力の差分Δu(k)）を求めよ。
【０１１７】
【数２２】

さて、「モデル予測制御問題3'」は、次の手順で解くことができる。
【０１１８】
1)評価関数をベクトル及び行列形式で表すこと。
【０１１９】
2)制御対象のモデルから出力予測形式を導出すること。
【０１２０】
3)評価関数を最小化する操作量を計算すること。
【０１２１】
1)については、評価関数(56)式を以下の様に書きなおす。
【０１２２】
【数２３】

一方、2)については、制御対象(51)式と(52)式のモデルから、ブスチップ先出力予測形式とよばれる次の形に変形する。
【０１２３】
【数２４】

次に、3)の最適操作量を求める。ここでは、簡単のため、制約条件が存在しない場合を考える。この場合は、解析的に最適操作量を導出できる。まず、(62)式を(57)式へ代入して、評価関数を△U(k)のみの関数として表す。すると、

となり、この(65)式を△U(k)に関して最小化するために、△U(k)に関して偏微分を行いそれをゼロとする。つまり、
【数２５】

を計算する。ここで、G，Hx(k)，Q，R及びYr(k)が△U(k)に依存しないことに注意すると、これは解析的に計算でき、その解は、
△U(k)=(G^TQG+R)^-1G^T(Yr(k)-Hx(k)) (67)
となる。これが、時刻k〜k+Nu間の最適操作量であるが、実際には、現在時刻kの操作量のみを取りだし、
△U(k)=[Im,0,…,0]△U(k) (68)
を最適操作量とし、制御周期毎に(67)式を解きなおして、閉ループ制御系とする。なお、この(68)式は、
1)状態は測定可能である。
【０１２４】
2)制約条件を考慮していない。
【０１２５】
という場合の最適操作量であるが、状態が得られない場合や制約がある場合に関しては、それぞれ、
1)状態x(k)に対するオブザーバを構成してx(k)の推定値で置きかえる。
【０１２６】
2)制約条件がある場合は、(53)式と(55)式を、(61)式などを用いて△u(k)の関数として書きなおし、これをまとめて、△U(k)に関する線形行列不等式(LMI)として書きなおす。そして、(65)式と併せて、線形制約を持つ二次形式最適化問題として、例えば共役勾配法を用いて数値的に最適操作量を求める。
【０１２７】
とすれば、容易に解決できる。
【０１２８】
以上が、産業界で既に用いられているモデル予測制御方式の一般的な定式化とその解法である。
【０１２９】
この「モデル予測制御3'」を下水処理プロセスに適用するためには、(51)式と(52)式の線形モデルを必要とする。しかしながら、(28)〜(30)式は、非線形のモデルであり、その要素としてASM2などの強い非線形関数を含むため、この線形近似モデルを導出することは難しい。つまり、前記「ハ」の性質を持つため、(51)式と(52)式の様なモデルを、近似的にも作ることが困難である。従って、「モデル予測制御3'」を本実施形態の下水処理プロセスに適用することは困難である。
【０１３０】
以上の説明により、本実施形態の下水処理プロセスの様な複雑なプロセスには、従来のモデル予測制御を適用することが難しいことがわかる。
【０１３１】
本発明では、このような複雑なプロセスに対しても、適用できるようなモデル予測制御方式を提供している。以下では、このアイデアを説明しよう。
【０１３２】
さて、前述の「モデル予測制御問題3'」において、その解法の過程を再考してみると、評価関数をベクトル形式で表すことや出力予測形式を導出することが、「モデル予測制御問題3'」を具体的に解くために必要となる操作であった。逆に、もし予め、「評価関数をベクトル形式で表現」し、「出力予測形式で表現された対象システムのモデルが与えられている」ならば、その形から直接モデル予測制御問題を定式化しても構わない。前者の「評価関数をベクトル形式で表現」することは、単に表現の形式を変えただけであるが、後者の「出力予測形式で表現された対象システムのモデルが与えられている」ことは、単に表現形式を変えただけではなく、それ以上の意味を持つ。
【０１３３】
すなわち、「モデル予測制御問題3'」では、「出力予測形式」の導出を線形状態空間モデルから行っているが、「出力予測形式」さえ存在すれば、制御対象のモデルが線形状態空間モデルでな<とも、その後の(65)〜(68)式は意味を持ち、最適操作量の決定を行うことができるということである。つまり、最適操作量(68)式を求めるために、制御対象が線形であることは(少なくとも陽には)用いていない。用いているのは、「出力予測形式」であり、(67)式を見てもわかるように、具体的には、GとHx(k)の2つを何らかの方法で得ることができれば、(65)〜(68)式の手段は実行可能である。では、(62)式のGとHx(k)は何を意味するかを考えてみることとする。
【０１３４】
Gは、(63)式の中を見ればわかるように、△uに対するインパルス応答(=uに対するステップ応答)を制御周期毎に1ステップずつずらして、予測ホライズンNpの長さだけ並べたものである。別の言葉を使えば、「予測出力応答の未来の入力に依存する成分」ということもできる。また、Hx(k)は、△u=0とした場合の出力予測値を与えるものであるから、「操作量を一定に保った場合の出力予測値からなるベクトル」であることがわかる。別の言葉を使えば、「予測出力応答の過去の入力に依存する成分」ということもできる。このことより、もし、「現在の運転点の近くでのステップ応答」と「現在の運転状態を保つ、すなわち、操作量を固定する場合の出力の予測」を行うことができれば、「モデル予測制御問題3'」の形をそのまま利用して、モデル予測制御問題を解くことができる。
【０１３５】
以上をまとめると、線形モデルを用いずに出力予測形式のモデルを用いて、先に示した「新モデル予測制御問題」の定式化に到達することができる。
【０１３６】
以上の説明から明らかなように、この「新モデル予測制御問題」の解法は、「モデル予測制御問題3'」と全く同様に行うことができる。また、「モデル予測制御問題3'」は、「新モデル予測制御問題」において、ステップ応答を固定し(線形の場合ステップ応答は全ての運転点において同一の応答となるようにし)、
【数２６】

とした特殊な場合と見なすことができる。
【０１３７】
「モデル予測制御問題3'」を「新モデル予測制御問題」に変更したことにより、以下の様にモデル予測制御の適用範囲を拡張できた。
【０１３８】
a. 「新モデル予測制御問題」では、「ステップ応答行列」と「操作量を固定した場合の出力予測応答」を、何らかの方法によって適切に供給することができれば、制御対象のモデルが線形である必要はない。
【０１３９】
b. 「モデル予測制御問題3'」では線形モデルから問題を定式化したため、ステップ応答行列Gは固定であったが、(65)〜(67)式の手順はステップ応答行列が時間と共に変化しても(kに依存しても)意味を持つため、G(k)と拡張できる。
【０１４０】
そして、「ステップ応答行列」や「操作量を固定した場合の出力予測応答」は、上記実施形態の動作として説明した方法によって供給することができる。この拡張によって、以下に列挙する本実施形態の効果が得られる。
【０１４１】
A. 制御周期毎に「プロセスのステップ応答」と「プロセスの操作量固定時のプロセス出力予測値」を外部からプロセス最適化手段に適切に供給するという操作を行う事のみで、従来の線形のモデル予測制御と同程度の演算量で、モデル予測制御の適用範囲を格段に拡張することができる。
【０１４２】
B. 「ステップ応答」や「プロセス出力予測値」等の一般の人にも容易に理解できる概念を用いて制御系の設計を行うことができるため、「ステップ応答」や「プロセス出力予測値」をディスプレイ上に表示するなどをして可視化することにより、管理者や運転員が安心して用いることのできる最適な制御系を構築することができる。
【０１４３】
C. 一般の人にも容易に理解できる概念である「ステップ応答」や「プロセス出力予測値」を人間系を介して修正することにより、プロセス最適性を適応的に向上させていくことができる。
【０１４４】
なお、既存のモデル予測制御と本発明の新しいモデル予測制御系の構成方法の考え方の相違を示した図を図6に示しておく。
【０１４５】
【発明の効果】
以上の説明により明らかな如く、本発明によれば、下水処理プロセス、上水処理プロセス、石油化学プロセスなど、特に、比較的時定数の長いプロセス系を中心とする任意の対象システムに対して、制御性能、経済性、制約などを考慮した最適な制御系を、容易に実装可能な演算量で、かつ、ヒューマンフレンドリーな形で提供することができる。
【図面の簡単な説明】
【図１】本発明に係るプロセスシミュレータ応用モデル制御装置の一実施形態の構成を適用対象である下水処理場の下水処理プロセスと併せて示した系統図。
【図２】図１に示した実施形態の動作を説明するために、流入下水量又は水質と時間との関係を示した線図。
【図３】図１に示した実施形態の動作を説明するために、人間系による予測値と時間との関係を示す線図の入力状態を示す概念図。
【図４】図３に示した人間系による予測値と時間との関係をプロセスシミュレータにより修正する場合の入力状態を示す概念図。
【図５】図１に示した実施形態の動作を説明するために、ステップ応答選択手段を人間系で行う場合の選択方法を示す概念図。
【図６】本発明のモデル予測制御装置と既存のモデル予測装置の考え方の相違を表した図
【符号の説明】
１ 下水処理プロセス
２ プロセス値記憶手段
３ プロセス外乱予測手段
４ プロセス予測手段
５ ステップ応答記憶手段
６ ステップ応答選択手段
７ プロセス評価関数及び評価重み供給手段
８ プロセス制約条件供給手段
９ 目標値軌道供給手段
１０ プロセス最適化手段
１１ 最初沈殿池
１２ 嫌気槽
１３ 無酸素槽
１４ 好気槽
１５ 最終沈殿池
１６ プロセス外乱センサ
１７１〜１７５ プロセス出力センサ
１８１〜１８４ アクチュエータ[0001]
BACKGROUND OF THE INVENTION
The present invention mainly focuses on process systems having relatively long time constants, such as biological processes such as sewage treatment processes and food processing processes, and chemical processes such as petroleum refining, and other electromagnetic systems such as motors and generators. Further, the present invention relates to a process simulator application control apparatus and method based on a simulator that simulates behaviors of various processes and systems including machine systems such as robots.
[0002]
[Prior art]
Various processes and systems in the industry (hereinafter referred to as target processes), such as water and sewage water volume processes and water quality processes, steel processes, petroleum refining processes, transportation systems, elevator systems, building air conditioning systems, urban thermal energy supply systems, etc. Conventionally, PID control and sequence control, which are a kind of classical control, have been widely used as control methods for target processes. These control methods are balanced control methods from the viewpoints of reliability, control performance, ease of design and tuning, and have established the position as the most standard control method in the industry.
[0003]
In recent years, for example, changes in the social background, such as the seriousness of environmental problems and increased awareness, and the diversification of customer demands accompanying diversification of values, have led to more severe and diverse control requirements as shown below. It has come to become something. For example, in sewage treatment, in order to reduce the burden on the environment, organic substances that are the quality of discharged water and regulations on the discharge of rivers such as nitrogen and phosphorus are becoming mandatory, and these values can be controlled quantitatively. The need to do is increasing.
[0004]
In addition, strict control performance has been demanded for strict quality requirements in steel sheet thickness control and for a comfortable ride comfort in elevators. Furthermore, as well as demands for simple control performance, as well as demands for reducing the amount of chemical injection in the water and sewage treatment process and improving the quality of treated water, economic cost reductions and energy savings are required. The demand for control is diversifying. As described above, in order to respond to various and strict requirements, the conventional PID control and sequence control are no longer sufficient, and in recent years, various advanced controls have been used.
[0005]
There are two broad approaches to advanced control. One is an approach such as fuzzy control or artificial intelligence (AI), which is a method of quantifying human senses and empirical knowledge to control, and control based on If-Then rules. This is called rule-based control. Another approach is a method of constructing a control system based on a mathematical model that expresses or simulates the behavior of a target process, and is called model-based control.
[0006]
These two approaches have their advantages and disadvantages depending on the circumstances and scope of use, but if there is a model that can adequately represent the behavior of the target process, it is potentially model-based. Control can provide better control performance than rule-based control. For details, refer to the specification of Japanese Patent Application No. 2000-059221 filed by the same applicant as the present application and the references described therein. Therefore, the presence or absence of a model that can simulate the behavior of the target process is one of the criteria for determining whether to use rule-based control or model-based control.
[0007]
In mechanical systems and electromagnetic systems such as elevators and power electronics, a model of the target process can be constructed relatively easily based on equations of motion, circuit equations, or electromagnetic laws. In addition, in the vicinity of the operating point (operating point) to be controlled, the model of the target process can be expressed by a linear differential equation, linear transfer function, or linear state equation with a relatively low order. For example, the optimal regulator theory (LQR) : Linear Quardratic Regulator / LQG: Linear Quardratic Regulator with Gaussian Input), inverse linear control theory (ILQ), or model-based control such as H-infinity control theory has already been applied. Effectiveness has been demonstrated.
[0008]
On the other hand, in so-called process control fields such as petrochemical processes and water and sewage processes, the process response is slower than mechanical and electrical systems, and operating costs such as chemicals and electric power that become operational quantities simultaneously with demands for control performance Since there is a strong demand for reducing the amount of noise, advanced control in a form different from mechanical and electrical systems has been developed. The most important of these is model predictive control, which is a type of model-based control. Model predictive control is a control method that can consider cost reduction and various constraint conditions in addition to achieving control performance, and can answer relatively diverse requirements. Model predictive control is a control system that was put into practical use in the industry by DMC (Dynamic Matrix Control), which was independent from Shell Shel1 Oi1, in the late 1970s and early 1980s. It is often used as advanced control in the industry.
[0009]
However, compared with conventional PID control and the like, such advanced control is still less applicable in the process control field. One of the technical reasons is that the target processes that can be handled by the existing model predictive control are limited. In order to apply the existing model predictive control to a certain process, some form of lumped constant linear model of the target process is required. Such a model may be derived from the laws of physicochemistry, or may be directly derived by performing a step response test or the like.
[0010]
On the other hand, as represented by the water quality process of sewage treatment, for example, the target process often has strong non-linearities or strong spatial distribution. In some cases, it is difficult to simulate the behavior of a process even approximately using a linear model. In such a case, the effectiveness of the model predictive control method currently in practical use is not clear and the scope of application is considered to be limited. In addition, research on nonlinear model predictive control has been actively conducted in the field of the latest control theory, but many of them are theoretical methods such as the construction method of model predictive control systems and the stability of closed loop systems. The main purpose of this analysis is the amount of computation that is important for implementation, and there are still many issues in terms of constraints on the nonlinear target system being handled, and practically these control systems can be easily realized. It is thought that it has not reached.
[0011]
On the other hand, models that simulate process behavior (usually called simulators) are used in various fields for purposes such as operation management, monitoring, process design, and operation training, not for direct control purposes. It has been. For example, in the field of sewage treatment, the International Association on Water Quality (IAWQ) has developed activated sludge models No. 1 to activated sludge models No. 1 representing the nitrogen and phosphorus removal processes using nonlinear differential equations. ~ Activated Sludge Model No.3) has been published, and a sewage treatment water quality process simulator can be constructed on a computer by combining it with a hydraulic model represented by partial differential equations. Such process simulators are capable of simulating processes with higher precision along with the development of computer technology, and as a result, the models themselves used to build simulators are becoming increasingly complex. ing.
[0012]
If this direction of development is extrapolated to the future as it is, the process model (simulator) for the purpose of operation management and monitoring and the process model for designing the model base (model prediction) control system will be further separated. It is estimated that. However, if a process simulator capable of more precisely capturing complex phenomena can be used for model predictive control system design, a control system that can meet strict and diverse requirements can be constructed, and its potential The ability is considered very high.
[0013]
[Problems to be solved by the invention]
Although the control method using the process simulator has a very high potential, a systematic control method using the process simulator has not been developed so far. In order to solve this problem, the inventors identified a simple model (low-dimensional linear approximation model) for control system design using a process simulator composed of complex mathematical models in Japanese Patent Application No. 2000-059221. On the other hand, a control system design method using the conventional model predictive control method was proposed. This is an indirect process simulator application control device that uses a process simulator indirectly to introduce a control system design model in order to associate a conventional model predictive control with a process simulator.
[0014]
The present invention provides a configuration method of a direct process simulator application control apparatus that constructs model predictive control using a process simulator directly instead of an indirect approach.
[0015]
[Means for Solving the Problems]
  To achieve the above object, the invention according to claim 1
  A disturbance sensor that measures process disturbances;
  A process output sensor that measures the observed output of the process;
  Process value storage means for storing measured values of the disturbance sensor and the process output sensor, and a process operation amount command value over a predetermined period;
  Process disturbance from the present time is the future point that is more than the time constant of the step response to the set of process manipulated variable and process controlled variable with the fastest change in process controlled variable with respect to process manipulated variable. (1) Predict process disturbances, such as the autoregressive model, up to a future point that is less than the time until the step response for the set of process manipulated variable and process controlled variable with the slowest amount of change converges to the final value A method for constructing a disturbance prediction model using a statistical model, (2) a method for constructing a disturbance prediction model by referring to past patterns, and (3) a method for extrapolating measured disturbance values (hold (0 Process disturbance prediction means for predicting by at least one of the following, first order,..., Nth order):
  A process model for calculating a prediction of a process controlled amount using the process manipulated variable command value stored in the process value storage means, a measured value of the process disturbance, and a predicted value of the process disturbance by the process disturbance prediction means. A process for inputting a measured value of a process output sensor other than the process disturbance stored in the process value storage means to the process model at the same time, and predicting a temporal behavior of the process controlled amount by the process model. Prediction means,
  The designer determines in advance a set of operating points consisting of a set of representative points of at least one of the manipulated variable and disturbance, and at least one set of manipulated variables and disturbance represented by the operating point. Corresponding step response time series over a predetermined period, and storing each operation point, at least one set of operation amount and disturbance represented by each operation point, and step response time series corresponding to each operation point Step response storage means;
  The current step response time series is selected from the step response time series for each operating point stored in the step response storage means based on the process manipulated variable command value of the process value storage means and the measured value of the process disturbance. Step response selection means;
  The process predicted value predicted by the process predicting means, the step response time series selected by the step response selecting means, the evaluation function, the evaluation weight constraint condition, and the target value trajectory set in advance are constrained or unconstrained. Formulate as a quadratic programming problem and (1) analytically find the solution of this quadratic programming problem, (2) use mathematical programming to solve the quadratic programming problem, (3) linear matrix inequality (LMI) The manipulated variable that satisfies the identifiable condition is obtained by applying the interior point method for LMI and (4) applying the metaheuristics typified by genetic algorithm or immune algorithm. Over the period from the arbitrary time set by the designer to the time when the process simulation is performed under the condition that the command value, disturbance measurement value, and process observation output value are included. And process optimization means for determining the optimum the operation amount command values,
  A process simulator application control device including
[0016]
According to the present invention, the process response prediction, the process step response, and the process optimization are made independent from each other, and the process response prediction and the process step response are supplied to the process optimization means from the outside, so that the nonlinear target process and distribution are It is possible to provide a model predictive control method that can flexibly cope with complex target processes such as constant target processes. Furthermore, each function (process response prediction, process step response, and process optimization) can be calculated with the same amount of computation as that used in the conventional model predictive control. It is possible to provide a control method that can be realized with the same amount of computation.
[0017]
The reason why conventional model predictive control could not do this is that the model predictive control design problem is formulated so as to minimize the constrained quadratic evaluation function after the model of the target system is given in advance. This is because (model assumption ⇒ optimization problem (model predictive control problem)), the model predictive control problem is largely restricted by the model of the target system.
[0018]
The present invention does not assume that a specific model is used for formulation of a design problem, and considers model predictive control in which a constrained quadratic evaluation function is given first, and the step response and process required at that time Since the formulation of supplying two response predictions from outside (formulation of optimization problem (model predictive control problem) ⇒ supply of required model), the scope of application of model predictive control is dramatically expanded. (The details of this idea are explained in the examples).
[0019]
Furthermore, since the process optimization means used in the present invention is always a unimodal optimization problem when the evaluation function is in quadratic form, an optimal solution can always be obtained. On the other hand, the currently studied nonlinear model predictive control generally becomes a multimodal optimization problem, and there is a possibility that an optimal solution cannot be obtained. In the present invention, the process optimization means used in the conventional model predictive control is used as it is, and the step response and the process predicted value required for solving this optimization problem are determined for each control cycle. This is because the unimodality of the optimization problem is preserved because the idea of variably giving from outside is used. On the other hand, in the normal nonlinear model predictive control, since the problem is formulated using a nonlinear model and a constrained quadratic evaluation function, the process optimization problem itself becomes complicated and generally becomes a multimodal problem.
[0020]
The invention according to claim 2 is the process simulator application control apparatus according to claim 1, wherein the process prediction means is a process simulator constructed using a differential equation or a partial differential equation based on a physicochemical law of the process. Prepare.
[0021]
According to the present invention, as the understanding of the target process deepens and the prediction accuracy of the response of the target process increases, the control performance and economic cost of the process can be more strictly optimized accordingly.
[0022]
According to a third aspect of the present invention, in the process simulator application control apparatus according to the first aspect, the process prediction means includes a process operation amount command value and a process disturbance measurement value stored in advance in the process value storage means, and a process A process simulator built using any one of statistical methods such as multivariate analysis, system identification method, and modeling method from time series data of neural network based on time series data of observation output of .
[0023]
According to the present invention, even if the physicochemical knowledge about the target process is ambiguous, the output of the target process can be predicted by systematically analyzing data that is the result of operating the target process in the past. And a model predictive control system using the prediction result can be constructed.
[0024]
According to a fourth aspect of the present invention, in the process simulator application control apparatus according to the first aspect, the process prediction means includes a human-type process simulator for externally setting a future process output prediction time series.
[0025]
According to the present invention, even if the physicochemical knowledge about the target process is ambiguous and the past operation history of the target process is not stored, the administrator who is familiar with the behavior of the target process to some extent If there is an operator or an operator, the target process can be optimized only by having the manager or operator predict as a predicted trajectory (time series data) how the process will change in the future. it can.
[0026]
The invention according to claim 5 is the process simulator application control apparatus according to claim 2 or 3, wherein the process prediction means displays the prediction result as a graph on the display device after performing the prediction by the process simulator, The prediction result which is judged from the outside from the current driving situation and displayed as a graph on the display device is corrected from the display device.
[0027]
According to the present invention, even when the predicted value of the target process by the process simulator does not match the experience or intuition of the manager or operator of the target process and the manager or operator feels uneasy, The process prediction can be easily changed from the display so that the operator can be satisfied. As a result, the process can be optimized to satisfy the manager and the operator.
[0028]
The invention according to claim 6 is the process simulator application control apparatus according to claim 2 or 3, wherein the process prediction means has a feedback mechanism from the process output value using an extended Kalman filter or the like for the process simulator. A robust process simulator with robustness is provided.
[0029]
According to the present invention, for example, when the target process includes an integral characteristic (stability limit system) or is an unstable system, the process simulator has a slight perturbation of input (disturbance and manipulated variable) or the target process. Even in the case of being sensitive to fluctuations in the dynamic characteristics of the process, the process response can be predicted robustly, and as a result, the process can be optimized even for the target process. Even when the process is stable, the sensitivity to disturbances mixed in the process can be suppressed as much as possible to improve the prediction accuracy, and as a result, more accurate process optimization can be performed.
[0030]
According to a seventh aspect of the present invention, in the process simulator application control apparatus according to the first aspect, the step response storage means performs a step response test on the process for each operating point in advance offline, and obtains from the test result. The obtained step response time series is stored in advance as a database.
[0031]
According to the present invention, when the target process is a stable system and a test signal can be input in advance, the step response test is performed a plurality of times in advance at a plurality of assumed operating points, and the dynamic characteristics of the process are detailed in advance. By grasping it, the process can be optimized more strictly.
[0032]
The invention according to claim 8 is the process simulator application control apparatus according to claim 2 or 3, wherein the step response storage means performs a virtual step response test for each operating point in advance offline using the process simulator. The step response time series obtained from the test results is stored in advance as a database.
[0033]
According to the present invention, even when the target process is already in an operating state and it is difficult to experimentally capture the dynamic characteristics of the target process, the process dynamic characteristics are virtually calculated using the process simulator. Can be captured in detail in advance and the process can be optimized.
[0034]
The invention according to claim 9 is the process simulator application control device according to claim 2 or 3, wherein the step response storage means performs a virtual step response test near the current operating point online using the process simulator. Do.
[0035]
According to the present invention, the step response in the vicinity of the operating point in the actual operating state can be obtained online, and in the case where the plant is operated at an operating point that was not assumed offline. Even the process can be optimized.
[0036]
The invention according to claim 10 is the process simulator application control apparatus according to claim 1, wherein the process optimization means is formulated as a constrained quadratic programming problem, and a standard quadratic programming problem such as a conjugate gradient method is used. The calculation is performed by using the solution of
[0037]
According to the present invention, the solution of the constrained quadratic programming problem used as a standard solution of the conventional model predictive control is used as it is only by supplying the step response and the process predicted value from the outside. A model predictive control system can be configured more flexibly. In other words, the inheritance (software) of the model prediction control that has already been realized can be inherited as it is, and its application range can be dramatically expanded.
[0038]
The invention according to claim 11 is the process simulator application control apparatus according to claim 1, wherein the process optimizing means is formulated as a constrained quadratic programming problem, and is regarded as a linear matrix inequality problem. Calculation is performed using an algorithm such as a point method.
[0039]
According to the present invention, the latest results on optimization obtained through LMI research are directly incorporated into model predictive control by re-recognizing model predictive control as LMI that has been studied at the forefront of control theory in recent years. The process can be optimized more efficiently than the conventional model predictive control.
[0040]
The invention according to claim 12 is the process simulator application control apparatus according to claim 1, wherein the process optimization means is formulated as a constrained quadratic programming problem, and a genetic algorithm, an immune algorithm, etc. Suboptimal operations are performed using the heuristic solution of.
[0041]
According to the present invention, by making use of a fast heuristic solution such as a genetic algorithm by making a compromise of giving up and sub-optimizing to strictly optimize the process, However, the process can be sub-optimized much faster. Therefore, even when a high-end high-speed computer cannot be used due to problems such as introduction costs, a model predictive control system can be constructed with a relatively low-end computer.
[0042]
According to a thirteenth aspect of the present invention, in the process simulator application control apparatus according to the first aspect, the process disturbance prediction means uses a statistical model such as a regression model for the time series data of the measured values of the process disturbance. Find the predicted value of.
[0043]
According to the present invention, by creating a disturbance prediction model with high accuracy from the past behavior of process disturbance, the process output can be predicted with higher accuracy, and as a result, the process can be optimized more strictly.
[0044]
According to a fourteenth aspect of the present invention, in the process simulator application control apparatus according to the first aspect, the process disturbance prediction means refers to the past time series data of the measured values of the process disturbance and performs process disturbance by pattern matching. Find the predicted value of.
[0045]
According to the present invention, it is possible to predict a process output with high accuracy by easily and accurately predicting a disturbance that periodically fluctuates, and as a result, it is possible to optimize the process more strictly.
[0046]
According to a fifteenth aspect of the present invention, in the process simulator application control apparatus according to the first aspect, the process disturbance predicting means holds the measured value of the current process disturbance and extrapolates it to a certain point in the future as it is. Determine the predicted value of the process disturbance.
[0047]
According to the present invention, even when there is not much a priori information on process disturbance, the process output prediction accuracy can be improved by predicting the process disturbance to some extent, compared with the case where the process disturbance prediction is not performed. As a result, the optimality of the process can be improved.
[0048]
  The invention according to claim 16 provides
  Process disturbance and process observation over a period from the time set by the designer to the time of process simulation under the condition that the manipulated variable command value, disturbance measurement value, and process observation output value satisfying the identifiable condition are included. Measure the output and store it together with the process manipulated variable command value.
  The disturbance of the process is a point in the future beyond the time constant of the step response to the set of the process operation amount and the process control amount with the fastest change in the process control amount with respect to the process operation amount from the present time. (1) Predict process disturbances to the future point below the time until the step response for the set of process manipulated variable and process controlled variable with the slowest change in control amount converges to the final value: autoregressive model, etc. (2) A method for constructing a disturbance prediction model with reference to past patterns, (3) A method for extrapolating measured disturbance values (hold ( 0th order, 1st order,..., Nth order)),
  The process manipulated variable command value, the measured value of the process disturbance, and the predicted value of the process disturbance are input to a process model for calculating the prediction of the process controlled amount, and preferably a process other than the stored process disturbance The measurement value of the output sensor is also input to the process model at the same time, and the temporal behavior of the process controlled amount is predicted by the process model,
  The designer determines in advance a set of operating points consisting of a set of representative points of at least one of the manipulated variable and disturbance, and at least one set of manipulated variables and disturbances represented by the operating point. Corresponding step response time series over a predetermined period, storing each operation point, at least one set of operation amount and disturbance represented by each operation point, and step response time series corresponding to each operation point ,
  By selecting the current step response time series from the stored step response time series for each operating point by the process manipulated variable command value and the process disturbance measurement value,
  Formulating the process predicted value, the selected step response time series, the preset evaluation function, the evaluation weight constraint condition, and the target value trajectory as a constrained or unconstrained quadratic programming problem. (1) analytically, (2) use mathematical programming to solve quadratic programming problems, (3) apply linear point inequalities (LMI) and apply interior point method for LMI, (4) The manipulated variable is obtained by any method of applying meta-heuristics represented by genetic algorithm and immune algorithm, and manipulated variable command value, disturbance measurement value and process observation output value satisfying the identifiable condition are obtained. Under the condition of including, determine the optimum manipulated variable command value over a period from the arbitrary time set by the designer to the time to perform the process simulation,
  Process simulator application control method.
[0049]
The present invention has the same effect as that of the first aspect of the invention.
[0050]
DETAILED DESCRIPTION OF THE INVENTION
Hereinafter, the present invention will be described in detail based on preferred embodiments shown in the drawings. In the following embodiments, a water quality treatment process using a sewage microbial reaction is taken up as a specific process, but the process may be arbitrary and is not an essential part of the idea of the present invention. The idea of the present invention resides in the configuration method itself (including an algorithm) that configures an optimal model predictive control system. FIG. 1 is a system diagram showing a sewage treatment system showing a sewage treatment process and a process simulator application model control apparatus to which a configuration of an embodiment of the present invention is applied.
[0051]
The sewage treatment system in FIG. 1 predicts a sewage treatment process 1 as a control target, a process value storage unit 2 that holds process measurement values in a process data server, and an inflow amount and inflow water quality that are disturbances mixed in the process. Process disturbance prediction means 3 for performing, process prediction means 4 for predicting the process state, controlled quantity and observed output, and step response memory for storing step responses in the vicinity of various operating points of the controlled quantity and observed output of the process A step response selecting means 6 for extracting an appropriate step response from the step response storage means 5, a process evaluation function and evaluation weight supply means 7, a process; Restriction condition supply means 8, target value trajectory supply means 9, and process optimization means 1 for determining an optimum operation amount of the process Provided with a door.
[0052]
Of these, the sewage treatment process 1 includes an initial sedimentation tank 11, an anaerobic tank 12, an anaerobic tank 13, an aerobic tank 14, a final sedimentation tank 15, an amount of inflow sewage considered to be a process disturbance, and various inflows. A process disturbance sensor 16 for measuring sewage water quality, process output sensors 171 to 175 for measuring various water quality values such as dissolved oxygen concentration, ammonia nitrogen concentration, respiration rate of each facility of the sewage treatment process 1, It is composed of four actuators including a circulation pump 181, a blower 182, a return pump 183, and an excess sludge extraction pump 184, which are operation amounts to each facility.
[0053]
The operation of the present embodiment configured as described above will be described below. This embodiment finally provides a specific solution to the “new model predictive control problem” shown below. The following “new model predictive control problem” itself is a method for formulating a new model predictive control that was not considered as a formulation of the existing model predictive control. The reason why the new model predictive control formulation has been invented will be described in the description of the effect of the present embodiment.
[0054]
New model predictive control problem (output prediction form; discrete time system)
Assume that a model of an expansion control target (expansion system) in which an integrator is inserted before the control target (target process) is given in the following output prediction format for each control cycle.
[0055]
[Expression 1]

Where ΔU (k) is the input Δu (k) ∈R^mStep by step to Nu²D (k) is the disturbance d (k) ∈R^kG (k) is Np by shifting the step response (time series data) of the process (time series) by 1 step.^ThreeY (k) is the output y (k) ∈R^pYhold (k) is the output yhold ∈ R when the manipulated variable is fixed.^pE (k) is a matrix representing the influence of the disturbance on the output. R * is a set of * order real numbers.
[0056]
Further, it is assumed that the following constraint conditions are given.
[0057]
[Expression 2]

Where u⁽ⁱ⁾Is the i-th element of input u, Δu⁽ⁱ⁾Is the i-th element of the input difference Δu, y^(j)Is the j-th element of the output y, and the subscripts min and max represent the minimum and maximum, respectively, and are input and output constraints. At this time, find the control input u (k) that minimizes the next evaluation function (or the input difference Δu (k), which is the same).
[0058]
[Equation 3]

[Expression 4]

Equation (6) is the optimum operation amount between times k and k + Nu, but actually only the operation amount at the current time k is taken out,
△ u (k) = [Im, 0,…, 0] Δu (k) (7)
Is the optimum operation amount.
[0059]
The operation of the present embodiment shown in FIG. 1 will be described below with reference to the “new model predictive control problem” and “solution of the new model predictive control problem”.
[0060]
First, in the process value storage means 2, sensor output values such as various water qualities and water amounts measured by the process disturbance sensor 16 and the process output sensors 171 to 175, and operation amount values of the actuators 181 to 184 (actuator operation amount values are measured. If this is not possible, areas for recording items related to the operation amount command value output from the process optimization means 10 are secured, and these areas are initialized.
[0061]
Next, at a certain time, the measurement values (time series data) of the process disturbance sensor 16, the measurement values (time series data) of the process sensors 171 to 175, and the operation amount values (time series data) of the actuators 181 to 185 are processed. The value is stored in the process data server of the value storage means 2 according to an appropriate format.
[0062]
Next, the process disturbance prediction means 3 predicts the inflow sewage amount and the inflow sewage quality that are disturbances of the present embodiment. Specifically, the following can be considered.
[0063]
For example, past inflow sewage data and inflow sewage quality data can be statistically analyzed, and a statistical model such as an autoregressive model (AR model) can be constructed to predict the inflow sewage quantity and inflow sewage quality.
[0064]
Inflow sewage volume and inflow sewage quality often have a certain pattern depending on the weather and time, as shown in Figs. 2 (a) and 2 (b), so refer to the current weather and time. Prediction by referring to the past pattern.
[0065]
In addition, when a typical pattern of inflow sewage amount or inflow sewage quality is not recognized, and inflow sewage amount data and past inflow sewage quality data are not stored, inflow sewage amount measured by the process disturbance sensor 16 The process disturbance can be predicted by holding the inflow sewage quality and extrapolating it to the future.
[0066]
Next, the operation amount time-series data stored in the process value storage unit 2 and the predicted value of the inflow sewage amount and the inflow sewage quality predicted by the process disturbance prediction unit 3 are delivered to the process prediction unit 4. .
[0067]
In the process prediction means 4, for example, the water quality of the final sedimentation basin 15 that is a controlled amount (or observation output) is predicted by a process simulator constructed by a mathematical model (nonlinear differential equation) as shown below.
[0068]
Process simulator model
The process simulator of the sewage treatment process shown in FIG. 1 includes a first sedimentation basin model, an anaerobic tank model, an anaerobic tank model, an aerobic tank model, and a final sedimentation basin model as constituent elements. Can be built.
[0069]
First settling pond ( First Clarifier) model
Methods for modeling sedimentation basins are summarized in, for example, the document “GA Ekama et al,“ Secondary Settling Tanks-Theory, Modeling, Design and Operation ”, IAWQ Scientific Technical Report No. 6, (1997)”. However, in order to simplify the explanation, the following simple model is used.
[0070]
[Equation 5]

Where Qfcin (t) [m^Three/ day] is the inflow as disturbance, Sfcin (t) [g / m^Three] And Xfcin (t) [g / m^Three] Is the solubility and floating inflow water quality components as disturbance, Qfcout (t) = Qfcwaste (t) + Qfcnextoutq (t) [m^Three/ day] (Qfcwaste (t): amount of first excess sludge extraction, Qfcnextoutq (t): outflow to biological reaction tank (anaerobic tank)) is the outflow from the first sedimentation basin, Sfcin (t) [g / m^Three] Is a vector consisting of nine soluble water quality items, XLfc (t) [g / m^Three] Is a vector consisting of 7 items of floating (solid) water quality in the sediment, XUfc (t) [g / m^Three] Is a vector consisting of seven items of floating water quality in the supernatant. There are a total of 16 soluble and floating water qualities. Vfc is the initial sedimentation tank capacity (assumed to be constant), and α is a constant indicating the reciprocal of the ratio of the volume of sludge precipitating to the initial sedimentation tank water volume Vfc. In addition, the water quality passed to the anaerobic tank is Zfc (t): = [Sfc (t) XUfc (t)]^TThe water quality extracted as excess sludge is defined as Zfcwaste (t): = [Sfc (t) XLfc (t)]^TIt is defined as
[0071]
Anaerobic tank (AnAerobic Tank) model
The anaerobic tank model consists of a model that represents microbial reactions and complete mixing of liquids.
[0072]
[Formula 6]

Where Qaain (t) = Qfcnextout (t) + Qscret (t) [m^Three/ day] (Qscret (t) [m^Three/ day] is the return sludge volume) and Qaaout [m^Three/ day] is the inflow to the anaerobic tank (inflow from the first sedimentation basin + return sludge volume) and the outflow from the anaerobic tank (inflow to the anaerobic tank), respectively. Zaa (t) [g / m^Three] Is a vector composed of anaerobic water quality, Zaain (t) [g / m^Three] = {Zfc (t) Qfcout (t) + Zscret (t)} / Qaain (t) (Zscret (t) is the quality of the return sludge described later) is a vector consisting of the quality of water flowing into the anaerobic tank, Vaa [ m^Three] Is the amount of water in the anaerobic tank (assuming constant). In addition, r (Zaa (t) is a reaction rate equation based on a microbial reaction. It is composed of ASM2 etc. considering the 19 biological reaction processes shown in `` Technical Report No.3, (1995) '' (However, it is not necessarily ASM2, and it can be a reaction rate equation that can simulate microbial reactions. Any).
[0073]
In ASM2, P0 as the element of Zaa (t)_Four(Phosphoric acid), NH_Four(Ammonia), NO_ThreeIt considers 16 water qualities such as (nitric acid), DO (dissolved oxygen) and microorganisms involved in nitrogen removal and phosphorus removal as components of MLSS (floating solids concentration). In addition, each element of r (Zaa (t) is composed of a weighted sum for the reaction rate equation of a nonlinear function called mono-type defined for each of the 19 processes, so it is a nonlinear function itself. Therefore, the ASM2 model of the equations (13) to (15) is a 16th-order nonlinear differential equation.
[0074]
Anoxic tank (AnOxic Tank) model
The anaerobic tank model has almost the same configuration as the anaerobic tank model.
[0075]
[Expression 7]

Where Qaoin (t) + Qoxcirc (t) [m^Three/ day] (Qoxcirc (t) is the circulation rate described later) and Qaoout (t) [m^Three/ day] is the amount of inflow and outflow from the reaction tank, Zao (t) [g / m^Three] Is a vector consisting of water quality in an anaerobic tank, Zaoin (t) [g / m^Three] = {Zaa (t) Qaaout (t) + Zox (t) Qoxcirc (t)} / Qaoin (t) (Zox (t) is the water quality of the aerobic tank, which will be described later) is a vector consisting of water quality flowing into the anoxic tank , Vao [m^Three] Is the amount of water in the anoxic tank (assuming constant).
[0076]
Aerobic tank (OXic Tank) model
The aerobic tank model is obtained by adding an oxygen supply model to the anaerobic tank or anoxic tank model.
[0077]
[Equation 8]

Where Qoxin (t) = Qaoout (t) [m^Three/ day] and Qoxout (t) = Qoxnextout (t) + Qoxcirc (t) [m^Three/ day] (Qoxnextout (t) is the outflow to the final sedimentation basin, Qoxcirc (t) is the circulation volume), and the inflow to the aerobic tank and the outflow from the aerobic tank (circulation volume + final sedimentation basin) ), Zoxwe (t) [g / m^Three] Is a vector of aerobic tank water quality, Zoxin (t) [g / m^Three] = Zao (t) is a vector Vox [m consisting of water quality flowing into the aerobic tank^Three] Is the amount of water in the aerobic tank (assuming constant). So2ox (t) is the dissolved oxygen concentration that is the element of Zox (t) (the second element in ASM2), So2 is the saturated dissolved oxygen concentration, KLa is the overall oxygen transfer capacity coefficient, and Qb (t) is the aeration by the blower The air volume, K, is a proportionality constant that correlates the aeration air volume with the overall oxygen transfer capacity coefficient.
[0078]
Final sedimentation basin (Second Clari6er) model
The final sedimentation basin can be modeled in the same way as the initial sedimentation basin model.
[0079]
[Equation 9]

Where Qscin (t) = Qoxnextout (t) is the inflow to the final sedimentation basin, [Sscin (t), XLscin (t)] = Zox (t) is the quality of the inflow water to the final sedimentation basin, Ssc (t) [g / m^Three] Is a vector consisting of soluble water, XLsc (t) [g / m^Three] Is a vector consisting of floating (solid) water quality in the sedimentation part, XUsc (t) [g / m^Three] Is a vector consisting of floating water quality in the supernatant. Further, Vsc is the amount of water in the final sedimentation basin (assumed to be constant), and β is a constant indicating the reciprocal of the ratio of the volume of sludge settled to the sedimentation basin water amount Vsc. Qscout (t) = Qscwaste (t) + Qscret (t) [m^Three/ day] (Qscout (t): excess sludge extraction amount, Qscret (t): return sludge amount). The water quality returned to the anaerobic tank (and extracted as excess sludge) is Zscret: = [Ssc (t) XLsc (t)]^TAnd the discharged water quality is Zsceffl (t): = [Ssc (t) XUsc (t)]^TIt is defined as A process simulator can be constructed by combining the above process models (8) to (27) and mounting them on a computer, for example. The above models can be summarized and written formally as follows.
[0080]
[Expression 10]

F (x (t)), g1 (x (t)), and g2 (x (t)) are appropriately arranged functions related to x (t) in equations (8) to (27) It is. H (x (t)) is an observed quantity, for example, the oxygen concentration S02aa (t), S02ao (t), S02ox (t) of each tank, which is an element of x (t), and the MLSS concentration of each tank Xtssaa (t), Xtssao (t), Xtssox (t), and ammonia nitrogen concentration Snh4aa (t), Snh4ao (t), Snh4ox (t), phosphorus The acid phosphorus concentration Spo4aa (t), Spo4ao (t), Spo4ox (t), etc. are arranged as a vector. Further, h2 (x (t)) is a controlled amount, for example, phosphoric acid phosphorus concentration Spo4sc (t) flowing out from the final sedimentation basin that is the discharge regulation (element of x (t)) Spo4sc (t) or ammonia And the soluble COD that is a function (linear sum) of each water quality element of Ssc (t).
[0081]
Now, when performing process prediction using the process simulators of equations (28) to (30), calculation is performed assuming that the future operation amount holds the current operation amount as it is. This is sampled every predetermined control period, taken out as time series data up to a predetermined predicted horizon Np, and further arranged this data appropriately, the following Yhold (k) of the equation (1),
## EQU11 ##

Can be obtained. This is an example of the prediction method of the process prediction means 4, whereby the predicted value of the process when the manipulated variable is fixed can be calculated.
[0082]
If a process model such as Equations (28) to (30) cannot be obtained, a process simulator is constructed using a statistical (mathematical) method from past time-series data. On the other hand, if the same thing as the above is performed, the process prediction when the operation amount is fixed can be performed.
[0083]
In addition, if no process simulator exists, it is possible to predict when the operation amount is fixed as follows. First, based on past experience and intuition, how the water quality of the final settling basin 15 changes when the operator maintains the current operation amount is predicted, for example, as shown in FIG. A display (such as an ATM at a bank) that can be input automatically is input as a predicted trajectory (predicted response). The input data is taken out as time series data, and prediction in the case where the operation amount is fixed can be performed by the same method as described above.
[0084]
If there is a process simulator but the operator feels dissatisfied or questioned about the process simulator prediction, the process prediction can be performed as follows. First, the water quality of the final sedimentation basin 15 when the manipulated variable is fixed is predicted by the process simulator as described above. Next, the predicted trajectory (predicted response) is displayed as a graph on a display, for example. Next, when the predicted response displayed as a graph on the display is unsatisfactory, the operator can modify the predicted response waveform by dragging or dropping the mouse with, for example, a mouse. Then, the corrected predicted response waveform can be stored again as time series data, and the process prediction can be performed when the manipulated variable is fixed by the same method as described above. This is shown in FIG.
[0085]
As described above, a simulator constructed using a differential equation or partial differential equation based on a physicochemical method of the process, a process variable stored in the process value storage means 2, a multivariate analysis based on the disturbance, etc. In the method using the simulator constructed by using the statistical system identification method, the prediction is performed without using the values of the process output sensors 171 to 175. In such a prediction, the prediction accuracy often deteriorates. Furthermore, a process including pure integration or an unstable process (a process in which an output is not finite despite a finite value of an operation amount being input) cannot be predicted in the first place. In such a case, for example, by feeding back an error between the output values of the process output sensors 171 to 175 and the current predicted value to a process simulator such as the equations (28) to (30), Precise and highly robust prediction can be performed. For example, a process simulator (robust process value predictor) having sensor value feedback can be configured as follows.
[0086]
[Expression 12]

If f (x (t))-Kh1 (x (t)) is linearly approximated around an appropriate operating point, K is selected so that all real parts of its eigenvalues are negative, and the target process is ( (34) and (35) are asymptotically (locally) the true state and the true output, respectively, if they can be expressed exactly (with no error) by (28) to (30). Converge. Therefore, the prediction can be performed more robustly by using the equations (34) and (35) than by simply using the equations (28) to (30).
[0087]
Next, in the step response storage means 5, when a step response test for the process can be performed in advance, a plurality of assumed operating points are set and the step response test is performed around the plurality of operating points. The response waveform can be set in a database with the corresponding operating point. Also, if the process is already in operation and it is difficult to perform a step response test, for example, use a process simulator such as that shown in Equations (28) to (30). If a response waveform is set as a set with a corresponding operating point and stored in a database, a step response can be stored in a similar manner.
[0088]
Further, when the assumed operating point for the target process is unknown in advance and the control cycle is not so short as compared to the process simulation calculation time, the current operating point is detected online from the process value storage means 2. The step response storage means 5 can be realized by simulating the response when a minute step perturbation is given to the actuator of the circulation pump 181 to the excess sludge extraction pump 184 in the vicinity and storing the response waveform. it can. Note that when this method is used, since there is only one step response waveform, the step response selecting means 6 described below is not necessary.
[0089]
Next, the step response selection means 6 inputs the current manipulated variable stored in the process value storage means 2 and the nearest operation from the set of step responses stored in the step response storage means 5 from the information. A point is searched (for example, the current values of the plurality of operation amounts and the operation points stored in the step response storage means 5 (operation points for various combinations of the plurality of operation amounts) take a value of 0 to 1, for example. Thus, all operating points are normalized, and the operating point that minimizes the sum of squares of the normalized operating point values and the normalized operating point error is adopted as the most appropriate operating point. Step response corresponding to is selected.
[0090]
In addition, when the process operator wants to select the step response himself, as shown in FIG. 5, a plurality of step response waveforms for each output are displayed, and the operator can select from these. It is done. Furthermore, as described above, a method in which the manager or the operator corrects the prediction result displayed as a graph by himself / herself is also conceivable. Next, the process optimization unit 10 inputs the process output prediction value when the operation amount by the process prediction unit 4 is fixed and the step response waveform selected by the step response selection unit 6 and appropriately inputs each data. By arranging, the predicted value of Yhold (k) and the predicted value of G (k) are calculated. Next, using these predicted values, for example, when there is no constraint condition, the optimum operation amount can be determined by calculating the equation (6). In this case, it is assumed that the evaluation function, the weight of the evaluation function, and the target value trajectory are given in advance from the outside by the process evaluation function and evaluation weight supply unit 7 and the target value trajectory supply unit 9.
[0091]
Further, when there is a restriction by the process restriction condition supply means 8, an optimum operation amount is obtained by using an optimization technique such as a conjugate gradient method that is often used as a solution of the “model predictive control problem 3 ′” described later. Can be determined.
[0092]
In addition, in order to obtain the optimum operation amount more efficiently, the optimization problem when there is a constraint is reformulated as an LMI problem, and the latest results obtained in recent LMI research are used. The optimum operation amount can be obtained efficiently.
[0093]
Also, if the power of the computer that performs a series of processing is insufficient or if you want to control in a shorter cycle, give up finding the optimal solution of the optimization problem and use a heuristic solution such as a genetic algorithm. A sub-optimal operation amount can be obtained. Next, the optimum operation amount determined by the process optimization means 10 is given to the sewage treatment process 1 as an operation amount command value, and the operation amount is adjusted accordingly. Finally, the above operation excluding the initialization of the process value storage means 2 is repeated every control cycle. In addition, about the location where the human system interposes, it does not necessarily need to be repeated for every control period, and may interpose intermittently.
[0094]
Next, the effect of this embodiment will be described. Here, first, why this embodiment is effective will be described, and finally, the effects of this embodiment will be summarized. First, as preparation for the following explanation, the characteristics of the process simulators (28) to (30) that are important in the following explanation are listed.
[0095]
The model of the process simulator is complicated at first glance, but when elements are vectorized and displayed, they are eventually put together in the form of equations (28) to (30).
[0096]
However, the order of the state equations (28) to (30) is as high as 80th order (5 × 16th order) when ASM2 is used.
[0097]
C Furthermore, it is difficult to perform linear approximation because Eqs. (28) to (30) have strong nonlinearity (the elements of fx (t) are strong nonlinear functions of saturation type by ASM2, and bilinear terms Also have).
[0098]
Now, in order to explain the effects of this embodiment, it is considered that an existing model predictive control method is applied to the equations (28) to (30) with these characteristics in mind. In general, (non-linear) model predictive control is formulated as follows.
[0099]
Model predictive control problem 1 ( General system ; Continuous time system )
Assume that the model of the control target (target process) is given as follows.
[0100]
[Formula 13]

Where u (t) ∈R^mIs the input, d1 (t)) ∈R^lIs the system disturbance, d2 (t) ∈R^kIs the observed disturbance, x (t) ∈RⁿIs the state, y (t) ∈R^pIs the output, and R * is the set of * order real numbers. Further, it is assumed that the following constraint conditions are given.
[0101]
[Expression 14]

Where U⁽ⁱ⁾Is the i th element of input u, y^(j)Is the j-th element of the output y, and the subscripts min and max represent the minimum and maximum, respectively, and are input and output constraints. Find the control input u (t) that minimizes the next evaluation function.
[0102]
[Expression 15]

In process control, usually, a discrete-time model having a control period as a sampling period is often formulated as a model predictive control problem of the following discrete-time system.
[0103]
Model predictive control problem 2 ( General system ; Discrete time system )
Assume that the model of the control target (target process) is given as follows.
[0104]

Where u (t) ∈R^mIs the input, d1 (t)) ∈R^lIs the system disturbance, d2 (t) ∈R^kIs the observed disturbance, x (t) ∈RⁿIs the state, y (t) ∈R^pIs the output, and R * is the set of * order real numbers. Further, it is assumed that the following constraint conditions are given.
[0105]
[Expression 16]

Find the control input u (k) that minimizes the next evaluation function.
[0106]
[Expression 17]

Now, consider applying the above model predictive control method to a sewage treatment process. First, from the characteristics of the above “a”, in the equations (28) to (30), if the controlled variable and the observation output are the same (y (t) = z (t)), the sewage of this embodiment The treatment process can be formulated as “Model Predictive Control Problem 1” using the sewage treatment process simulators (28) to (30). Furthermore, if the equations (28) to (30) are discretized at a control cycle given in advance by, for example, Euler differences, it can be formulated as “model predictive control problem 2”.
[0107]
However, although “model predictive control problem 1” and “model predictive control problem 2” are easy to formulate as problems, it is not so easy to actually solve this problem. In contrast, many researchers are currently studying nonlinear model predictive control problems. For example, there are theoretical problems such as a problem of obtaining an optimal solution without falling into a local solution and a problem of ensuring stability. In addition, there remains an implementation problem of how to reduce the enormous amount of calculation. In particular, from a practical aspect, it is important to solve the computational complexity problem (local solution problems and stability problems are also very important problems. This problem can be compromised by considering the local solution as a sub-optimal solution, and for many stability problems, in many processes, measures should be taken from the mechanism side of the control system to avoid destabilization. However, since the problem with a huge amount of computation is related to the actual implementation, it is difficult to use it in the industry unless this problem is solved.) For example, in order to apply this to a sewage treatment process, it is inevitable that the amount of calculation becomes enormous due to the characteristic “b” of the sewage treatment process simulator. Therefore, it is considered that it takes a long time to apply such model predictive control to a complicated process such as a sewage treatment process.
[0108]
On the other hand, model predictive control that is actually used in the industrial field is limited to a linear system for “model predictive control 1” and “model predictive control 2”. In particular, it is often used in a discrete-time system in consideration of mounting on a computer, and this can be considered as a special case of “model predictive control problem 2”. This is shown below.
[0109]
Model predictive control problem 3 ( Linear state-space model ; Discrete time system )
Assume that the model of the control target (target process) is given as follows.
[0110]

Where u (t) ∈R^mIs the input, d1 (t)) ∈R^lIs the system disturbance, d2 (t) ∈R^kIs the observed disturbance, x (t) ∈RⁿIs the state, y (t) ∈R^pIs the output. A to F are constant matrices of appropriate sizes.
[0111]
Further, it is assumed that the following constraint conditions are given.
[0112]
[Formula 18]

Find the control input u (k) that minimizes the next evaluation function.
[0113]
[Equation 19]

Normally, in linear model predictive control, an integrator is often inserted in advance before the control target (to keep the steady deviation at zero with respect to the step target value). Often, the following problems are solved. However, the following model predictive control 3 ′ and model predictive control 3 are almost the same on the algorithm.
[0114]
Model predictive control problem Three , ( Linear state space expansion model ; Discrete time system )
Assume that the model of the extended control target with the integrator inserted before the control target (target process) is given as follows.
[0115]
[Expression 20]

Further, it is assumed that the following constraint conditions are given.
[0116]
[Expression 21]

Where U⁽ⁱ⁾Is the i-th element of input u, ΔU⁽ⁱ⁾Is the input difference, y^(j)Is the j-th element of the output y, and the subscripts min and max represent the minimum and maximum, respectively, and are input and output constraints. At this time, find the control input u (k) that minimizes the next evaluation function (or the input difference Δu (k), which is the same).
[0117]
[Expression 22]

The “model predictive control problem 3 ′” can be solved by the following procedure.
[0118]
1) Express the evaluation function in vector and matrix form.
[0119]
2) Deriving the output prediction format from the model to be controlled.
[0120]
3) Calculate the manipulated variable that minimizes the evaluation function.
[0121]
For 1), rewrite the evaluation function (56) as follows.
[0122]
[Expression 23]

On the other hand, with respect to 2), the model of the control object (51) and (52) is transformed into the following form called the bus tip output prediction format.
[0123]
[Expression 24]

Next, the optimum operation amount of 3) is obtained. Here, for the sake of simplicity, let us consider a case where there is no constraint condition. In this case, the optimum operation amount can be derived analytically. First, the expression (62) is substituted into the expression (57), and the evaluation function is expressed as a function of only ΔU (k). Then

In order to minimize the equation (65) with respect to ΔU (k), partial differentiation is performed with respect to ΔU (k) and it is set to zero. That means
[Expression 25]

Calculate Note that G, Hx (k), Q, R, and Yr (k) do not depend on ΔU (k), this can be calculated analytically, and the solution is
△ U (k) = (G^T(QG + R)^-1G^T(Yr (k) -Hx (k)) (67)
It becomes. This is the optimum manipulated variable between time k and k + Nu, but actually only the manipulated variable at the current time k is taken out,
△ U (k) = [Im, 0,…, 0] △ U (k) (68)
Is the optimum manipulated variable, and the equation (67) is solved again for each control cycle to obtain a closed loop control system. This equation (68) is
1) The state can be measured.
[0124]
2) The constraints are not considered.
[0125]
In the case where the state cannot be obtained or there are restrictions,
1) Configure an observer for state x (k) and replace it with an estimate of x (k).
[0126]
2) If there are constraints, rewrite Eqs. (53) and (55) as a function of △ u (k) using Eq. (61) etc. Rewrite as linear matrix inequality (LMI). Then, together with the equation (65), as a quadratic form optimization problem having a linear constraint, for example, an optimal manipulated variable is obtained numerically using a conjugate gradient method.
[0127]
If so, it can be solved easily.
[0128]
The above is a general formulation of a model predictive control method already used in the industry and its solution.
[0129]
In order to apply this “model predictive control 3 ′” to the sewage treatment process, linear models of equations (51) and (52) are required. However, since the equations (28) to (30) are nonlinear models and include strong nonlinear functions such as ASM2 as elements, it is difficult to derive this linear approximation model. In other words, it is difficult to make models such as the equations (51) and (52) approximately because of the above-mentioned property of “c”. Therefore, it is difficult to apply “model predictive control 3 ′” to the sewage treatment process of this embodiment.
[0130]
From the above description, it can be seen that it is difficult to apply the conventional model predictive control to a complicated process such as the sewage treatment process of the present embodiment.
[0131]
The present invention provides a model predictive control method that can be applied to such complicated processes. I will explain this idea below.
[0132]
Now, in the above-mentioned “Model Predictive Control Problem 3 ′”, when the process of the solution is reconsidered, expressing the evaluation function in the vector format and deriving the output predictive form are “Model Predictive Control Problem 3 ′”. It was an operation required to solve " On the other hand, if “the evaluation function is expressed in vector format” and “the model of the target system expressed in the output prediction format is given” in advance, the model predictive control problem is formulated directly from that form. It doesn't matter. The former "representing the evaluation function in vector form" is simply changing the form of the expression, but the latter "giving the model of the target system represented in the output prediction form" It has more meaning than just changing the expression.
[0133]
In other words, in “Model Predictive Control Problem 3 ′”, the “output prediction format” is derived from the linear state space model, but if the “output prediction format” exists, the model to be controlled is a linear state space model. In particular, the following formulas (65) to (68) are meaningful and the optimum manipulated variable can be determined. That is, in order to obtain the optimum manipulated variable (68), the fact that the control target is linear is not used (at least explicitly). What is used is the `` output prediction format '', and as you can see from equation (67), specifically, if you can get both G and Hx (k) in some way, The means of the formulas (65) to (68) can be executed. Let us consider what G and Hx (k) in Equation (62) mean.
[0134]
As can be seen from the equation (63), G is an impulse response to Δu (= step response to u) shifted by one step for each control period, and arranged by the length of the predicted horizon Np. is there. In other words, it can be called “a component that depends on the future input of the predicted output response”. Further, since Hx (k) gives an output predicted value when Δu = 0, it is understood that “Hx (k) is a vector consisting of an output predicted value when the operation amount is kept constant”. In other words, it can be said to be “a component that depends on the past input of the predicted output response”. From this, if "step response near the current driving point" and "predicting output when the current operating state is maintained, that is, the operation amount is fixed" can be performed, "model predictive control" The model predictive control problem can be solved by using the form of “Problem 3 ′” as it is.
[0135]
To summarize the above, it is possible to arrive at the formulation of the “new model predictive control problem” described above by using the output prediction format model without using the linear model.
[0136]
As is clear from the above description, the solution of the “new model predictive control problem” can be performed in the same manner as the “model predictive control problem 3 ′”. In addition, the “model predictive control problem 3 ′” is a step response fixed in the “new model predictive control problem” (in the case of linear, the step response becomes the same response at all operating points)
[Equation 26]

It can be regarded as a special case.
[0137]
By changing "Model Predictive Control Problem 3 '" to "New Model Predictive Control Problem", the application range of model predictive control could be expanded as follows.
[0138]
a. In the “new model predictive control problem”, if the “step response matrix” and “output predictive response when the manipulated variable is fixed” can be appropriately supplied by some method, the model to be controlled is linear. There is no need.
[0139]
b. In “Model Predictive Control Problem 3 ′”, since the problem was formulated from the linear model, the step response matrix G was fixed. However, the steps (65) to (67) change the step response matrix with time. But it has meaning (even if it depends on k), so it can be expanded to G (k).
[0140]
The “step response matrix” and “output prediction response when the operation amount is fixed” can be supplied by the method described as the operation of the above embodiment. By this expansion, the effects of the present embodiment listed below can be obtained.
[0141]
A. By simply performing the operation of appropriately supplying “process step response” and “process output predicted value when the process operation amount is fixed” from the outside to the process optimization means at each control cycle, The scope of application of model predictive control can be greatly expanded with the same amount of computation as model predictive control.
[0142]
B. Since the control system can be designed using concepts that can be easily understood by ordinary people, such as “step response” and “process output predicted value”, “step response” and “process output predicted value” Is displayed on the display, etc., and an optimal control system that can be used with peace of mind by the manager and the operator can be constructed.
[0143]
C. Process optimization can be adaptively improved by modifying “step response” and “process output predicted value”, which are concepts that can be easily understood by ordinary people, via a human system. .
[0144]
FIG. 6 shows a diagram showing the difference in the concept of the configuration method of the existing model predictive control and the new model predictive control system of the present invention.
[0145]
【The invention's effect】
As is apparent from the above description, according to the present invention, for any target system centering on a process system having a relatively long time constant, such as a sewage treatment process, a water treatment process, and a petrochemical process, It is possible to provide an optimal control system in consideration of control performance, economy, restrictions, and the like, with a calculation amount that can be easily implemented, and in a human friendly manner.
[Brief description of the drawings]
FIG. 1 is a system diagram showing the configuration of an embodiment of a process simulator application model control apparatus according to the present invention together with a sewage treatment process to which a sewage treatment plant is applied.
FIG. 2 is a diagram showing the relationship between the inflow sewage amount or water quality and time in order to explain the operation of the embodiment shown in FIG. 1;
3 is a conceptual diagram showing an input state of a diagram showing a relationship between a predicted value by a human system and time in order to explain the operation of the embodiment shown in FIG. 1;
4 is a conceptual diagram showing an input state when a relationship between a predicted value and time by a human system shown in FIG. 3 is corrected by a process simulator;
FIG. 5 is a conceptual diagram showing a selection method when step response selection means is performed in a human system in order to explain the operation of the embodiment shown in FIG. 1;
FIG. 6 is a diagram showing the difference in concept between the model prediction control device of the present invention and the existing model prediction device.
[Explanation of symbols]
1 Sewage treatment process
2 Process value storage means
3 Process disturbance prediction means
4 Process prediction means
5 step response storage means
6 Step response selection means
7 Process evaluation function and evaluation weight supply means
8 Process constraint condition supply means
9 Target value trajectory supply means
10 Process optimization means
11 First sedimentation basin
12 Anaerobic tank
13 Anoxic tank
14 Aerobic tank
15 Final sedimentation basin
16 Process disturbance sensor
171 to 175 Process output sensor
181 to 184 Actuator

Claims (16)

A disturbance sensor that measures process disturbances;
A process output sensor that measures the observed output of the process;
Set by the designer under the condition that the measured values of the disturbance sensor and the process output sensor, and the manipulated variable command value, the measured disturbance value, and the process observation output value satisfy the identifiable condition. Process value storage means for storing over a period from the arbitrary time to the time of performing the process simulation ;
Process disturbance from the present time is the future point that is more than the time constant of the step response to the set of process manipulated variable and process controlled variable with the fastest change in process controlled variable with respect to process manipulated variable. (1) Predict process disturbances: autoregressive models, etc., to future points below the time until the step response for the set of process manipulated variable and process controlled variable with the slowest amount of change converges to the final value A method of constructing a disturbance prediction model using a statistical model, (2) A method of constructing a disturbance prediction model with reference to past patterns, and (3) A method of extrapolating measured disturbance values (hold (0 next, primary, · · ·, N order)), and process disturbances predicting means for predicting at least one,
A process model for calculating a prediction of a process controlled amount using the process manipulated variable command value stored in the process value storage means, a measured value of the process disturbance, and a predicted value of the process disturbance by the process disturbance prediction means. A process for inputting a measured value of a process output sensor other than the process disturbance stored in the process value storage means to the process model at the same time, and predicting a temporal behavior of the process controlled amount by the process model. Prediction means,
The designer determines in advance a set of operating points consisting of a set of representative points of at least one of the manipulated variable and disturbance, and at least one set of manipulated variables and disturbance represented by the operating point. Corresponding step response time series over a predetermined period, and storing each operation point, at least one set of operation amount and disturbance represented by each operation point, and step response time series corresponding to each operation point Step response storage means;
The current step response time series is selected from the step response time series for each operating point stored in the step response storage means based on the process manipulated variable command value of the process value storage means and the measured value of the process disturbance. Step response selection means;
The process predicted value predicted by the process predicting means, the step response time series selected by the step response selecting means, the evaluation function, the evaluation weight constraint condition, and the target value trajectory set in advance are constrained or unconstrained. formulated as a quadratic programming problem, the solution of the quadratic programming problem, the (1) analytically determined, (2) using the mathematical programming for solving quadratic programming problem, (3) linear matrix inequality (LMI) The manipulated variable that satisfies the identifiable condition is obtained by applying the interior point method for LMI and (4) applying the metaheuristics typified by the genetic algorithm or immune algorithm. under the condition that includes a command value and the disturbance measurement values and processes observed output value, the period from the arbitrary time by the designer set to the time for performing the process simulation And process optimization means for determining the optimum the operation amount command values over,
Process simulator application control device equipped with. The process prediction means includes a process model expressed by a differential equation or partial differential equation based on a physicochemical law of the process, an operation amount input unit for inputting an operation amount of the process, and a process measured by a sensor 2. A process simulator comprising at least a process disturbance input unit for inputting a disturbance and a process output unit for calculating a temporal change in the output of the process and outputting the calculation result. The process simulator application control apparatus described. The process predicting means uses a process operation amount command value and a process disturbance measurement value accumulated in advance in the process value storage means, and time-series data of process observation output, and an arbitrary value designated by the model creator By applying one of the algorithms included in the multivariate analysis method, the identification algorithm used in the system identification method, or the learning algorithm used in the neural network to the time series data model of A process model created from time series data, a manipulated variable input unit for inputting the manipulated variable of the process, a process disturbance input unit for inputting the process disturbance measured by the sensor, and a temporal change in the output of the process. And at least a process output unit for calculating and outputting the calculation result Characterized in that it has a b Seth simulator, a process simulator application control device according to claim 1. The process prediction means predicts the output of the process when the process operation amount and disturbance values are maintained at the current values, and stores the predicted values as predicted time series data. The process simulator application control apparatus according to claim 1, wherein the process simulator is used for process prediction . The process prediction means predicts the water quality of the final sedimentation basin when the operation amount is fixed by the process simulator , and then displays the predicted response as a graph on a display device, and the predicted response displayed on the display 4. The operation according to claim 2, wherein the operator corrects the predicted response waveform and stores the corrected predicted response waveform as time series data when the operator is dissatisfied. Process simulator application control device. The process simulator application control apparatus according to claim 2 , wherein the process prediction unit includes a robust process simulator that has a robustness by providing a feedback mechanism from the process output value to the process simulator. . The step response storage means selects a certain operating point among the operating points, changes one operation amount in steps at the selected operating point, and a plurality of predefined process outputs when changed in steps The movement data until the process output settles to a constant value is recorded as a step response in a predetermined cycle, and the other manipulated variables are sequentially changed step by step at the selected operating point. By repeating the recording of the step response according to the movement of the process output, the obtained P × N (however, the operation amount is N and the process output is P ) step response time series is stored in advance as a database. The process simulator application control apparatus according to claim 1.   The step response storage means performs a virtual step response test for each operating point in advance offline with respect to the process simulator, and stores a step response time series obtained from the test result as a database in advance. The process simulator application control device according to claim 2 or 3.   The process simulator application control apparatus according to claim 2 or 3, wherein the step response storage means performs a virtual step response test in the vicinity of a current operating point online to the process simulator. The process optimization means, the output Y (K), the output difference delta Y (K), comprising at least one or more of the input U (K) and the input difference delta U (K), and that format is secondary The process simulator according to claim 1, wherein the evaluation function described in a form is formulated as a constrained quadratic programming problem and calculation is performed by using a standard quadratic programming problem solution method such as a conjugate gradient method. Application control device. The process optimization means is to formulate as a quadratic programming problem of constrained or unconstrained, the solution of the quadratic programming problem, (1) analytically determined, mathematical programming solving (2) quadratic programming problem (3) Considering linear matrix inequalities ( LMI ) and applying the interior point method for LMI , (4) Applying metaheuristics typified by genetic and immune algorithms The process simulator application according to claim 1, wherein an operation amount is obtained, formulated as a constrained quadratic programming problem, and an arithmetic operation such as an interior point method is performed by regarding this as a linear matrix inequality problem. Control device. The process optimization means is to formulate as a quadratic programming problem of constrained or unconstrained, the solution of the quadratic programming problem, (1) analytically determined, mathematical programming solving (2) quadratic programming problem the use, (3) applying the interior point method for LMI regarded as linear matrix inequality (LMI), by (4) the method of any of, applying a Metaheuristics typified by the genetic algorithm and immune algorithm The process simulator application control apparatus according to claim 1 , wherein an operation amount is obtained . The process disturbance prediction means includes:
Statistical model d (t + 1) = f (d (t), d that collects measured values of process disturbance d (t) over a specified period specified by the designer and predicts the collected process disturbance data d (t) (t-1), ... , d (tn)) , and the statistics are calculated so as to optimize a statistical criterion in which there is a distribution of errors between the data collected over the predetermined period and the predicted value by the statistical model. Confirm the prediction model by determining the values of the parameters included in the model,
The prediction model created, by entering the value of process disturbances measured determined the predictive value of 1 step ahead, 2 steps ahead by substituting this 1 step ahead predicted value and the predicted measurement value again model By repeatedly obtaining the predicted value of, and obtaining the predicted value for a predetermined step,
The process simulator application control apparatus according to claim 1. The process disturbance prediction means includes:
Prepare multiple patterns of disturbance determined by the designer, select a pattern that matches the current conditions for the prepared pattern, and refer to the past time-series data of the measured values of the process disturbance. The process simulator application control apparatus according to claim 1, wherein a predicted value of a process disturbance is obtained by matching. The process disturbance prediction means includes:
Measures the current value of the disturbance, assumes that the current value will continue for the future, sets the future value of the disturbance as the current value, holds the measured value of the current process disturbance, and extrapolates to a future point in time The process simulator application control apparatus according to claim 1, wherein a predicted value of a process disturbance is obtained by Process disturbance and process observation over a period from an arbitrary time set by the designer to the time of process simulation under the condition that the manipulated variable command value, disturbance measurement value, and process observation output value satisfy the identifiable condition are included. Measure the output and store it together with the process manipulated variable command value.
The disturbance of the process is a point in the future beyond the time constant of the step response to the set of the process operation amount and the process control amount with the fastest change in the process control amount with respect to the process operation amount from the present time. step responses to a set of the slowest process operation amount and the process the controlled variable change in the control amount to a point of time following the future to converge to the final value, to predict the disturbance (1) process: autoregressive model such (2) A method for constructing a disturbance prediction model with reference to past patterns, (3) A method for extrapolating measured disturbance values (hold ( 0 order, 1st order,..., Nth order)),
The process manipulated variable command value, the measured value of the process disturbance, and the predicted value of the process disturbance are input to a process model for calculating the prediction of the process controlled amount, and preferably a process other than the stored process disturbance The measurement value of the output sensor is also input to the process model at the same time, and the temporal behavior of the process controlled amount is predicted by the process model,
The designer determines in advance a set of operating points consisting of a set of representative points of at least one of the manipulated variable and disturbance, and at least one set of manipulated variables and disturbance represented by the operating point. Corresponding step response time series over a predetermined period, storing each operation point, at least one set of operation amount and disturbance represented by each operation point, and step response time series corresponding to each operation point ,
By selecting the current step response time series from the stored step response time series for each operating point by the process manipulated variable command value and the process disturbance measurement value,
Said process predicted value, formulated as a quadratic programming problem of constrained or unconstrained as input and step response time series selected, the preset evaluation function and evaluation weight constraints and the target value trajectory, the secondary the solution of the programming problem, (1) analytically determine, using the mathematical programming solving (2) quadratic programming problem, applying the interior point method for LMI regarded as (3) linear matrix inequality (LMI), (4) The manipulated variable is obtained by any method of applying meta-heuristics represented by genetic algorithm and immune algorithm, and manipulated variable command value, disturbance measurement value and process observation output value satisfying the identifiable condition are obtained. Under the condition of including, determine the optimum manipulated variable command value over a period from the arbitrary time set by the designer to the time to perform the process simulation,
Process simulator application control method.

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