JP3798239B2 - Multivariable model predictive control apparatus, method, and storage medium thereof - Google Patents

Description

【００１２】
又は
【００１３】
【数１１】

【００１４】
を用いて各制御量の変化を予測するように構成される。
また、上記制御量感度計算手段は、例えば請求項３記載のように、ｊ番目の操作量ｕ_jk+1が現在操作量ｕ_jkと同じ場合のｉ番目のニューロモデルによる制御量予測値をｙ_ik+dとし、これに対して操作量をｕ_jk+1＝ｕ_jk＋ε_j としたとき制御量予測値がｙ’_ik+dに変化したとして、時点、時点での感度ｒ_ijを、
【００１５】
【数１２】

【００１６】
として、各制御量の変化量の感度を計算するように構成される。
上記最適化計算・決定手段は、例えば請求項４記載のように、制御量の行列Ｙ、その感度の行列Ｒ、操作量の行列Ｘによる連立一次方程式Ｙ＝Ｒ・Ｘを用い、Ｘの解法として最小二乗最小ノルム解を用いて上記操作量の最適化計算を行うように構成される。
【００１７】
次に、請求項５記載の発明の多変数モデル予測制御方法は、制御対象プロセスの操作量、外乱、及び制御量を含む状態量を入力とし制御量を出力とするニューラルネットワークモデルにより制御しようとする時点から先の各制御量の変化を予測し、上記制御しようとする時点の上記状態量によって、これから先に与える各上記操作量の変化量に対する各上記制御量の変化量の感度を計算し、この計算によって得られた感度行列を用いて、各上記制御量が所定の目標値に可及的に一致し且つ各上記操作量の変化量が可及的に小さく成るように最適化計算して、この最適化計算によって得られた各上記操作量を上記制御対象プロセスへの上記操作量として決定し、この決定された上記操作量を含む状態量を入力として上記制御量を予測出力する。
【００１８】
そして、請求項６記載の記憶媒体は、制御対象プロセスの操作量、外乱、及び制御量を含む状態量を入力とし制御量を出力とするニューラルネットワークモデルにより制御しようとする時点から先の各制御量の変化を予測する機能と、上記制御しようとする時点の上記状態量によって、これから先に与える各上記操作量の変化量に対する各上記制御量の変化量の感度を計算する機能と、この計算によって得られた感度行列を用いて、各上記制御量が所定の目標値に可及的に一致し且つ各上記操作量の変化量が可及的に小さく成るように最適化計算する機能と、この最適化計算によって得られた各上記操作量を上記制御対象プロセスへの上記操作量として決定する機能と、を実行させるための多変数モデル予測制御プログラムをコンピュータによる読取りが可能なように記録している。
【００１９】
【発明の実施の形態】
以下、本発明の実施の形態を図面を参照しながら説明する。
図１は、一実施の形態における多変数モデル予測制御システムの構成を示すブロック図である。同図に示すように、この多変数モデル予測制御システム１は、プラント２と、このプラント２の出力を制御する多変数モデル予測制御装置（以下、単に制御装置という）３から成る。制御装置３は、データ処理部４、ニューロモデル部５、感度計算部６、及び最適化計算部７で構成される。このように、制御装置３には、ニューロモデルを用いたモデル予測制御機能が組み込まれている。また、上記のデータ処理部４、ニューロモデル部５、感度計算部６、及び最適化計算部７は、各部一体に構成されたものでも良く、あるいは個々に独立した各部の構成を連結して全体として一つの制御機構を構成するものであっても良い。
【００２０】
尚、説明を分かり易くするために仮に設定すれば、上記のプラント２は、例えばゴミ焼却炉と、このゴミ焼却炉によるゴミ焼却熱で蒸気を発生するボイラー装置とから成り、この発生する蒸気によって例えばタービンを回して発電をする、あるいは温水等を他へ供給するような、ゴミ焼却熱の有効利用を目的としたプラントである。勿論、化学プラント、セメントプラントなど他の処理を行うプラントであっても良いが、以下の説明ではゴミ焼却炉とボイラーとから成るプラントであるとする。
【００２１】
上記のデータ処理部４には、一方では外部から、上記プラント２の出力を制御する制御量の目標値ＳＶと、そのプラント２の出力、すなわち現在制御量ＰＶと、演算器８によって演算された「ＳＶ（制御量目標値）−ＰＶ（現在制御量）」とが入力され、他方では内部から、上記プラント２を制御すべく出力された過去の操作量ＭＶが分岐して入力され、更に、外乱ＤＪが入力される。尚、ＰＶ（ならびにＳＶ）、ＭＶ、ＤＶはそれぞれ、ｍ、ｎ、ｌ個あるものとする。ｍ≧１、ｎ≧１、ｌ≧１である。
【００２２】
制御量目標値ＳＶ又は現在制御量ＰＶは、例えばボイラーから出力すべき又は出力された蒸気量等であり、操作量ＭＶは、その蒸気量を安定して得るための焼却炉の安定な燃焼状態を維持するために操作される例えば焼却炉の各所に設けられている通風調節弁によって調節される空気量等であり、外乱は例えば焼却炉内の計測可能な箇所で検出される温度等である。また、上記の操作量は立場を変えると制御量になり、制御量は立場を変えると操作量になるものである。
【００２３】
データ処理部４は、上記の入力を処理してニューロモデル部５にデータａを出力する。ニューロモデル部５は、データ処理部４の出力値に基づいて各制御量の変化を予測して、その予測値ｃを感度計算部６に出力する。感度計算部６は、ニューロモデル部５の出力値ｃに基づいて各操作量に対する予測値の感度を計算し、その計算によって得られた感度データｄを最適化計算部７に出力する。最適化計算部７は、感度計算部６の出力値ｄに基づいて、制御量と操作量の最適化計算を行って、この計算によって得られた操作量ＭＶをプラント２及びデータ処理部４に出力する。
【００２４】
図２は、上記の多変数モデル予測制御システムにおける制御装置３の主要部の入出力データの詳細を示す図である。同図に示すように、ニューロモデル部５には、図１に示したデータ処理部４から、データａ（外乱ｘk 、制御量ｙk 、操作量ｕk ）が入力する。ここでｋは制御周期Δｔの時間ステップを表している。
【００２５】
ニューロモデル部５は、これらの入力に基づいて、τ時間後の処理装置３の出力すなわち制御量ｙ_k+d （ｄ＝τ／Δｔ）を制御量予測値ｃ（以下、ニューロ出力ｃともいう）として感度計算部６に出力する。この制御量ｙ_k+d を予測するモデルは過去の経験データに基づいて予めニューロモデル部５に設定されている。そのモデルは、次式
【００２６】
【数１３】

【００２７】
によって表わされる。左辺の記号は複数のベクトル量を表わし、右辺のｆはニューラルネットワークそのものを表わし、括弧内には、上述した外乱ｘk 、制御量ｙk 、操作量ｕk の各時間ステップ毎の値からなる入力変数を表している。各変数の添字ｋは現在時間ステップを表わし、ｋ＋１は次の時間ステップを表わし、ｋ−１は直前の時間ステップを表している。
【００２８】
上記のニューロモデルは、Δｙ＝ｙ_k+d −ｙ_k をニューロ出力とすれば、
【００２９】
【数１４】

【００３０】
として表わすこともできる。なお、ニューロモデルは予め設定しておいたものを常時用いてもよいし、逐次オンラインデータで学習更新してもよい。
ニューロモデル部５は、この数１又は数２（以下の説明では数１を用いる）に示すニューロモデルを用い、入力変数それぞれの現在値及び過去値を使用してニューロ出力ｃとしての制御量予測値を計算して、その算出されたニューロ出力ｃを感度計算部６に出力する。また、これと共に、ニューロモデル部５は、操作量ｕ_k が現在値のままの場合の制御量予測値ｙ_k+1 （ｙ_k+d ＝ｆ（ｕ_k+1 ，ｘ_k ，ｙ_k ，ｕ_k ，・・・））を、ニューロ出力ｇとして、不図示の表示装置（制御用コンピュータの表示画面）に出力すると共に、記録用データとして不図示の記憶装置に格納する。
【００３１】
次に、感度演算部６は、上記のニューロ出力ｃを用いて、各操作量に対する制御量予測値（ニューロ出力ｃ）の感度を計算する。感度は動作点によって変わるので、操作量を或る幅だけ変え、他の入力値は固定して、感度を求める。すなわち、ｊ番目の操作量ｕ_jk+1が、現在操作量ｕ_jkと同じ場合の、ｉ番目のニューロモデルによる制御量予測値をｙ_ik+dとし、これに対して操作量をｕ_jk+1＝ｕ_jk＋ε_j としたとき、制御量予測値がｙ’_ik+dに変化したとすれば、時点、時点での感度ｒ_ijは、次のようになる。
【００３２】
【数１５】

【００３３】
ここで、最適化計算部７において、制御量の数をｍ、操作量の数をｎとし、操作量の変化量をΔｕ_j 、制御量予測値の変化量をΔｙ_i とすると、前述の［数１］に示すモデルは、上記の感度ｒ（ｒ_ij）を使って、次のような線形の式で表わすことができる。
【００３４】
【数１６】

【００３５】
上記の式、数４において、τ時間後のｉ番目の制御量予測値に対応したプロセス変数の設定値（目標値）をｓ_ik+dとすると、ニューロモデルによる制御量予測値との偏差はｅ_i ＝ｓ_ik+d−ｙ_ik+dとなる。τ時間後にこれらを一致させるためには、Δｙ_i ＝ｅ_i とすればよい。ただし、ｅ_i が不感帯内にある場合はΔｙ_i ＝０とする。
【００３６】
また、上記の式、数４において、▲１▼：ｎ＝ｍ＝１のときは、上記の条件を満たすΔｕ₁ は，Δｕ₁ ＝Δｙ₁ ／ｒ₁₁となる。また、▲２▼：ｎ＝ｍ＞１のときは、上記の条件を満たすΔｕ_j は、数４の連立方程式を解くことにより一義的に求まる。また、▲３▼：ｎ＞ｍのときは、上式の条件を満たすΔｕ_j の組み合わせは複数あるので、それを一義的に決めるために、評価関数Ｊを次のようにおき、上式を満たし且つ評価関数を最小化するΔｕ_j を求める。これは次式に示すように各操作量の変分の二乗和にする。但しＷ_j は重みである。
【００３７】
【数１７】

【００３８】
ここで求まったΔｕ_j に制御の安定のための調整値α（０≦α≦１）を乗ずる。すなわち、
Δｕ_j ’＝α・Δｕ_j
とする。さらに、Δｕ_j ’の絶対値が、操作量変化率の経験上予め設定されている上限±ｖ_j を超える場合は、Δｕ_j ’をその上限値とする。すなわち、
Δｕ_j ’＞ｖ_j のとき、 Δｕ_j ’＝ｖ_j
Δｕ_j ’＜−ｖ_j のとき、 Δｕ_j ’＝−ｖ_j
とする。
【００３９】
しかる後、現在の操作量ｕ_jkに、上記求まった変化量Δu _j ’を加算して得られるｕ_jk+1＝ｕ_jk＋Δu _j ’を、次の操作量として決定する。そして、この決定した次の操作量ｕ_jk+1を、ニューロモデルに入力し、改めてτ時間後の制御量予測値
ｙ”_ik+d
を計算して確認する。このｙ”_ik+1は、最適化計算部７の出力ｈとして、不図示の表示装置（制御用コンピュータの表示画面）に出力されると共に、記録用データとして不図示の記憶装置に格納される。
【００４０】
そして、上記決定した次の操作量ｕ_jk+1が、最適化計算部７からの出力ＭＶとしてプラント２に出力される。
図３(a),(b) は、上記の演算過程を模式的に図式化して示す図である。同図(a) は、横軸に時間ｔを示し、縦軸に制御量ｙを示している。図における原点は、制御開始からｋステップ目の時点である現在時点と、このｋステップ目におけるｉ番目の制御対象の制御量ｙ_ikすなわち太い実線で示す現在制御量ＰＶとの交点を示している。また、縦軸ｙには制御量目標値ＳＶを破線で示している。
【００４１】
同図(b) は、横軸に同図(a) に対応する時間ｔを示し、縦軸に操作量ｕを示している。原点は上記と同様に制御開始からｋステップ目の時点である現在時点と、このｋステップ目におけるｉ番目の操作対象の操作量ｕ_jkすなわち太い実線で示す現在操作量ＭＶとの交点を示している。
【００４２】
ここで、同図(a) において、τ時間後、換言すればｋステップ目の現在時点から更にｄステップ目、すなわち制御開始からｋ＋ｄステップ目の制御量を予測する。先ず、同図(b) に示すように、太線で示す現在操作量ＭＶをそのままｋ＋１ステップまで継続したとすると、ｙ_ik+dが予測された。これは制御量目標値ＳＶよりもｅ_i だけ低い。
【００４３】
そこで、同図(b) に示すように、現在操作量ＭＶを＋ε_j だけ変化させてみると、同図(a) に示すように、より制御量目標値ＳＶに近いｙ’_ik+dが予測された。この結果、あとどのくらい操作量を変化させれば、その予測値ｙ”_ik+dが制御量目標値ＳＶに近似するかが判明する。すなわち現在操作量ＭＶに付加すべき操作量の変分＋Δｕ_j が判明する。
【００４４】
ここで、上述した最適化の演算、すなわち評価関数を最小にする演算方法につてい更に説明する。尚、以下の説明では、大文字の英文字は全て行列式を表わすものとする。すなわち、次の連立方程式
Ｙ＝Ｒ・Ｘ ．．．．．．．．．（１）
における、Ｙ、Ｒ、及びＸは、それぞれ上述した数４を書き換えた下記の行列式
【００４５】
【数１８】

【００４６】
を表わしたものである。尚、ここでは、一般的に記述するために、操作量ｕを変数ｘに置き換えている。また、上述してきた制御量の数ｍを、式の数ｍとし、操作量の数ｎを、未知数ｎとしている。また、以下の説明では、ｒは行列Ｒのランクを示し、上述してきた感度ｒは行列Ｒで示される。上記の数７に示す行列式のもとで、Ｘを解く方法を以下に説明する。
【００４７】
第１に、行列Ｒのランクｒ＝ｍ＜ｎのとき、
【００４８】
【数１９】

【００４９】
を最小にするＸを求める。解法は、最小二乗法（最小ノルム）を用いる。
第２に、行列Ｒのランクｒ＝ｍ＝ｎのとき、
連立一次方程式（１）を解いて、
Ｘ＝Ｒ^-1・Ｙ ．．．．．．．．．（２）
を得る。尚、Ｒ^-1は行列Ｒの逆行列である。ここでは、上述したように感度の行列Ｒと変化させるべき制御量の行列Ｙ（ベクトル）がすでに分かっているので、操作量の行列Ｘ（ベクトル）を一義的に求めることができる。
【００５０】
第３に、行列Ｒのランクｒ＝ｎ＜ｍのとき、
Ｊ＝‖Ｙ−Ｒ・Ｘ‖₂
を最小にするＸを求める。解法は、最小二乗法を用いる。尚、この式は、一つ一つのＹに対する誤差、つまり、本例のように、未知数の数ｎよりも式の数ｍが多い場合、本質的に式（１）を満たすＸは存在しないから、誤差「Ｙ−Ｒ・Ｘ」の二乗和を最小化するものである。
【００５１】
第４に、行列Ｒのランクｒ≦Ｍｉｎ（ｍ，ｎ）のとき（但し、ｍ≧１、ｎ≧１とし、ｍ、ｎの大小関係は任意であり、小さい方をｒとする）、これは、上記の第１、第２、及び第３の解法を含む一般的な解法となる。尚、上述した最適化計算部７における演算において、▲１▼、▲２▼及び▲３▼でｎ＝ｍ＝１、ｎ＝ｍ＞１及びｎ＞ｍのときの解法を示し、ｎ＜ｍのときの解法を示さなかったが、この一般解で示される。
【００５２】
先ず、Ａ・Ｚ＝ｂの最小二乗最小ノルム解をＺ⁺ とおく。
このＺ⁺ は‖ｂ−Ａ・Ｚ‖₂ が最小となるＺの中で‖Ｚ‖₂ がが最小となるＺである。評価関数を‖Ｚ‖₂ の形式にするため
ｚ_i ＝ｘ_i ・√ｗ_i
とおく。ｘ_i ＝ｚ_i ／σ_i 、σ_i ＝√ｗ_i 、ｗ_i ≠０として
【００５３】
【数２０】

【００５４】
Ｘ＝Ｃ・Ｚ
したがって、式（１）は、
Ｙ＝Ｒ・Ｃ・Ｚ
となる。ここで、
ｂ＝Ｙ
Ａ＝Ｒ・Ｃとおいて、Ｚ⁺ を求めればよい。Ｚ⁺ が求まれば、
Ｘ＝Ｃ・Ｚ⁺
よりＸが求まる。
【００５５】
【発明の効果】
以上詳細に説明したように、本発明によれば、ニューラルネットワークを用いて予測される予測制御量を求め、この求められた予測制御量の評価関数を求め、これらの評価関数を最小とする操作量を決定して、その決定した操作量を目標制御量に対応する操作量としてプラントへ出力するので、物理法則で簡単にモデル化できないプラントでも、これをニュートラルネットワークでモデル化して、単に数値を予測するのではなく、予測された変数から目標とする制御量に対応する最適な操作量を決定して出力することができ、これにより、各種のプラントに対して常に最適な制御を行うことが可能となる。
【図面の簡単な説明】
【図１】一実施の形態における多変数モデル予測制御システムの構成を示すブロック図である。
【図２】多変数モデル予測制御システムにおける多変数モデル予測制御装置の主要部における入出力データの詳細を示す図である。
【図３】多変数モデル予測制御装置による予測値の算出方法を模式的に示す図である。
【符号の説明】
１ 多変数モデル予測制御システム
２ プラント
３ 多変数モデル予測制御装置（制御装置）
４ データ処理部
５ ニューロモデル部
６ 感度計算部
７ 最適化計算部
８ 演算器[0001]
BACKGROUND OF THE INVENTION
The present invention relates to a multivariable model predictive control apparatus, a method, and a storage medium for receiving a control variable as an input and a control variable as an output.
[0002]
[Prior art]
Conventionally, input / output systems called neuron computers or neural networks have been used in many fields such as control, prediction, and diagnosis. The biggest feature of this neural network is its ability to learn, and even when it is difficult to find a clear relationship between input data and output data, it learns a combination of input data and output data. If you do, the system can create its own rules. That is, it has characteristics such as excellent pattern matching while handling nonlinear data.
[0003]
The above learning is performed by adjusting the connection weight inside the neural network so as to obtain a desired function based on given data. In other words, when a correct output is determined with respect to the input, it is determined internally whether the neural network has correctly output it and adjusting the coupling weight so that there is no error.
[0004]
In the neural network thus learned, when the same input data as the learning data given at the time of learning is given, the same data as at the time of learning data is outputted. Further, when input data close to learning data is given, there is a feature that outputs close to learning data. Therefore, if the input case is the same as that given at the time of learning, the output value is sufficiently reliable, but if it is different from the case used for learning, it is not 100% reliable. Therefore, it is important to evaluate the reliability of the output value, which evaluates whether the output value obtained for a given input case is appropriate. Various methods have been proposed as evaluation methods, and in recent years, the reliability of neural networks has increased.
[0005]
Various control processes for performing the above-described control, prediction, diagnosis and the like using a neural network having such characteristics have been proposed. Examples of models to which such control processes such as control, prediction, and diagnosis can be applied include various plants such as chemical plants, cement plants, and waste incineration plants.
[0006]
[Problems to be solved by the invention]
By the way, as described above, it has been generally performed to predict an event using a neural network, and various event control methods using a neural network have been considered. However, in terms of prediction, what could not be predicted easily by the laws of physics can be modeled by incorporating non-linearity by learning with a neural network, so that prediction can be performed. However, it was only a prediction.
[0007]
As for control methods, most of them use a neural network to obtain the operation amount itself for the control object of one input and one output, and control at the present time is performed based on the obtained operation amount. In the method and the PID control method, a method of appropriately tuning the proportional gain, the integration time, and the derivative time is known.
[0008]
An object of the present invention is to provide a multivariable model predictive control device that determines a plurality of optimum operation amounts corresponding to a control amount based on a plurality of prediction change amounts obtained using a neural network in view of the above-described conventional situation. It is to be.
[0009]
[Means for Solving the Problems]
First, the multivariable model predictive control apparatus according to claim 1 is further from a point of time when control is to be performed by a neural network model in which a manipulated variable, disturbance, and state quantity including a controlled variable of a process to be controlled are input and a controlled variable is output. The control amount change predicting means for predicting the change in each control amount and the state amount at the time when the control is to be performed are used to calculate the sensitivity of the change amount of each control amount with respect to the change amount of each operation amount to be applied in the future. Each control amount predicted by the change predicting means matches with a predetermined target value as much as possible using the control amount sensitivity calculating means and the sensitivity matrix obtained by the calculation by the control amount sensitivity calculating means. And an optimization calculation / determination means for determining each operation amount by performing an optimization calculation so that a change amount of each operation amount is as small as possible, and determined by the optimization calculation / determination means It constituted a manipulated variable to output as the operation amount of the control target process.
[0010]
For example, as described in claim 2, the control amount change prediction means sets _k of y _{k + d} as a time step up to the present time, d as a time step from the present time to a time point to be predicted, and as a neuro model,
[0011]
[Expression 10]

[0012]
Or [0013]
[Expression 11]

[0014]
Is used to predict a change in each controlled variable.
Further, the control amount sensitivity calculation means calculates the control amount predicted value based on the i-th neuro model when the j-th operation amount u _{jk + 1} is the same as the current operation amount u _jk as described in claim 3, for example. _{ik + d,} and when the manipulated variable is u _{jk + 1} = u _jk + ε _j , assuming that the control amount prediction value has changed to y ′ _{ik + d} , the sensitivity r _ij at the time point and time point is
[0015]
[Expression 12]

[0016]
Is configured to calculate the sensitivity of the change amount of each control amount.
The optimization calculation / determination means uses a simultaneous linear equation Y = R · X with a control amount matrix Y, a sensitivity matrix R thereof, and an operation amount matrix X as described in claim 4, for example, to solve X As described above, an optimization calculation of the manipulated variable is performed using a least squares minimum norm solution.
[0017]
Next, the multivariable model predictive control method according to the invention described in claim 5 tries to control by a neural network model in which the manipulated variable, disturbance, and state quantity including the controlled variable of the process to be controlled are input and the controlled variable is output. Predict the change of each control amount from the point of time, and calculate the sensitivity of the amount of change of each control amount to the amount of change of each operation amount to be given from now on according to the state amount at the time of the control. Using the sensitivity matrix obtained by this calculation, an optimization calculation is performed so that each control amount matches the predetermined target value as much as possible and the change amount of each operation amount becomes as small as possible. Then, each operation amount obtained by the optimization calculation is determined as the operation amount to the process to be controlled, and the control amount is predicted and output with the state amount including the determined operation amount as an input.
[0018]
In the storage medium according to claim 6, each control from the point of time when control is to be performed by a neural network model in which the operation amount, disturbance, and state amount including the control amount of the control target process are input and the control amount is output. A function for predicting a change in the amount, a function for calculating the sensitivity of the amount of change in each control amount with respect to the amount of change in each operation amount to be given earlier, and the calculation based on the state amount at the time of the control. A function for performing an optimization calculation so that each of the control amounts matches a predetermined target value as much as possible and a change amount of each of the manipulated variables becomes as small as possible using the sensitivity matrix obtained by A function of determining each operation amount obtained by the optimization calculation as the operation amount for the process to be controlled, and a multivariable model predictive control program for executing the program on a computer Reading is recorded so as to be capable of that.
[0019]
DETAILED DESCRIPTION OF THE INVENTION
Embodiments of the present invention will be described below with reference to the drawings.
FIG. 1 is a block diagram illustrating a configuration of a multivariable model predictive control system according to an embodiment. As shown in the figure, the multivariable model predictive control system 1 includes a plant 2 and a multivariable model predictive control device (hereinafter simply referred to as a control device) 3 that controls the output of the plant 2. The control device 3 includes a data processing unit 4, a neuro model unit 5, a sensitivity calculation unit 6, and an optimization calculation unit 7. Thus, the control device 3 incorporates a model predictive control function using a neuro model. In addition, the data processing unit 4, the neuro model unit 5, the sensitivity calculation unit 6, and the optimization calculation unit 7 described above may be configured integrally with each other, or may be configured by individually connecting the configurations of the individual units. A single control mechanism may be configured.
[0020]
If it is set for the sake of easy understanding, the plant 2 includes, for example, a waste incinerator and a boiler device that generates steam by the waste incineration heat generated by the waste incinerator. For example, it is a plant for the purpose of effective use of waste incineration heat, such as generating electricity by turning a turbine or supplying warm water to others. Of course, a plant that performs other processing such as a chemical plant or a cement plant may be used, but in the following description, it is assumed that the plant is composed of a waste incinerator and a boiler.
[0021]
On the other hand, the data processing unit 4 is operated from the outside by the arithmetic unit 8 with the target value SV of the control amount for controlling the output of the plant 2 and the output of the plant 2, that is, the current control amount PV. “SV (control amount target value) −PV (current control amount)” is input, and on the other hand, the past operation amount MV output to control the plant 2 is branched and input from the inside. A disturbance DJ is input. Note that there are m, n, and l PV (and SV), MV, and DV, respectively. m ≧ 1, n ≧ 1, and l ≧ 1.
[0022]
The control amount target value SV or the current control amount PV is, for example, the steam amount to be output from the boiler or the like, and the operation amount MV is a stable combustion state of the incinerator for stably obtaining the steam amount. For example, the amount of air adjusted by a ventilation control valve provided in each place of the incinerator is operated, and the disturbance is, for example, a temperature detected at a measurable place in the incinerator. . Further, the operation amount becomes a control amount when the position is changed, and the control amount becomes an operation amount when the position is changed.
[0023]
The data processing unit 4 processes the above input and outputs data a to the neuro model unit 5. The neuro model unit 5 predicts a change in each control amount based on the output value of the data processing unit 4 and outputs the predicted value c to the sensitivity calculation unit 6. The sensitivity calculation unit 6 calculates the sensitivity of the predicted value for each manipulated variable based on the output value c of the neuro model unit 5, and outputs sensitivity data d obtained by the calculation to the optimization calculation unit 7. The optimization calculation unit 7 performs an optimization calculation of the control amount and the operation amount based on the output value d of the sensitivity calculation unit 6, and supplies the operation amount MV obtained by this calculation to the plant 2 and the data processing unit 4. Output.
[0024]
FIG. 2 is a diagram showing details of input / output data of the main part of the control device 3 in the multivariable model predictive control system. As shown in the figure, data a (disturbance xk, control amount yk, manipulated variable uk) is input to the neuro model unit 5 from the data processing unit 4 shown in FIG. Here, k represents a time step of the control cycle Δt.
[0025]
Based on these inputs, the neuro model unit 5 uses the output of the processing device 3 after τ time, that is, the control amount y _{k + d} (d = τ / Δt) as a control amount predicted value c (hereinafter also referred to as a neuro output c). ) To the sensitivity calculation unit 6. A model for predicting the control amount y _{k + d} is preset in the neuro model unit 5 based on past experience data. The model has the following formula:
[Formula 13]

[0027]
Is represented by The symbol on the left side represents a plurality of vector quantities, the symbol f on the right side represents the neural network itself, and the parentheses indicate input variables consisting of values for each time step of the disturbance xk, control amount yk, and manipulated variable uk described above. Represents. The subscript k of each variable represents the current time step, k + 1 represents the next time step, and k-1 represents the previous time step.
[0028]
In the above neuro model, if Δy = y _{k + d} −y _k is a neuro output,
[0029]
[Expression 14]

[0030]
Can also be expressed as Note that a neuro model that is set in advance may be used at all times, or learning may be updated and updated sequentially with online data.
The neuro model unit 5 uses the neuro model shown in Equation 1 or 2 (Equation 1 is used in the following description), and predicts the control amount as the neuro output c using the current value and the past value of each input variable. The value is calculated, and the calculated neuro output c is output to the sensitivity calculator 6. Further, the same time, the neuro-model unit 5, the operation amount u _k control amount prediction value when remained in the current value _{y k + 1 (y k +} d = f (u k + 1, x k, y k, u _k ,...)) are output as a neuro output g to a display device (not shown) (display screen of a control computer) and stored as a recording data in a storage device (not shown).
[0031]
Next, the sensitivity calculation unit 6 calculates the sensitivity of the control amount predicted value (neuro output c) for each manipulated variable using the above-described neuro output c. Since the sensitivity changes depending on the operating point, the sensitivity is obtained by changing the operation amount by a certain width and fixing other input values. That is, when the j-th manipulated variable u _{jk + 1} is the same as the current manipulated variable u _jk , the control amount predicted value by the i-th neuro model is y _{ik + d,} and the manipulated variable is u _{jk +} Assuming that ₁ = u _jk + ε _j , if the control amount prediction value changes to y ′ _{ik + d} , the sensitivity r _ij at the time point and time point is as follows.
[0032]
[Expression 15]

[0033]
Here, in the optimization calculation unit 7, assuming that the number of controlled variables is m, the number of manipulated variables is n, the manipulated variable change amount is Δu _j , and the controlled variable predicted value change amount is Δy _i , the above-mentioned [ The model shown in Equation 1] can be expressed by the following linear expression using the sensitivity r (r _ij ).
[0034]
[Expression 16]

[0035]
In the above equation (4), if the set value (target value) of the process variable corresponding to the i-th control amount predicted value after τ time is s _{ik + d} , the deviation from the control amount predicted value by the neuro model is e _i = s _{ik + d} −y _{ik + d} In order to match these after τ time, Δy _i = e _i may be set. However, if e _i is in the dead zone, Δy _i = 0.
[0036]
In the above equation (4), when (1): n = m = 1, Δu ₁ satisfying the above condition is Δu ₁ = Δy ₁ / r ₁₁ . Further, when {circle over (2)} n = m> 1, Δu _j satisfying the above condition is uniquely obtained by solving the simultaneous equations of Equation 4. In addition, when (3): n> m, there are a plurality of combinations of Δu _{j that} satisfy the condition of the above expression. In order to uniquely determine it, the evaluation function J is set as follows, and the above expression is Find Δu _j that satisfies and minimizes the evaluation function. This is the sum of squares of the variation of each manipulated variable as shown in the following equation. However, _Wj is a weight.
[0037]
[Expression 17]

[0038]
The Δu _j obtained here is multiplied by an adjustment value α (0 ≦ α ≦ 1) for stabilizing the control. That is,
Δu _j '= α ・ Δu _j
And Furthermore, when the absolute value of Δu _j ′ exceeds an upper limit ± v _j set in advance based on experience with the manipulated variable change rate, Δu _j ′ is set as the upper limit value. That is,
When Δu _j ′> v _j , Δu _j ′ = v _j
When Δu _j ′ <−v _j , Δu _j ′ = −v _j
And
[0039]
After that, u _{jk + 1} = u _jk + Δu _j ′ obtained by adding the obtained change amount Δu _j ′ to the current operation amount u _jk is determined as the next operation amount. Then, the determined next operation amount u _{jk + 1} is input to the neuro model, and the control amount predicted value y ” _{ik + d} after τ time is again obtained.
Calculate and confirm. This y ″ _{ik + 1} is output as an output h of the optimization calculation unit 7 to a display device (not shown) (display screen of a control computer) and stored as a recording data in a storage device (not shown). .
[0040]
Then, the determined next operation amount u _{jk + 1} is output to the plant 2 as an output MV from the optimization calculation unit 7.
3 (a) and 3 (b) are diagrams schematically showing the above calculation process. In FIG. 4A, the horizontal axis indicates time t, and the vertical axis indicates the control amount y. The origin in the figure indicates the intersection of the current time point at the k-th step from the start of control and the control amount y _ik of the i-th control target at the k-th step, that is, the current control amount PV indicated by a thick solid line. . On the vertical axis y, the control amount target value SV is indicated by a broken line.
[0041]
In FIG. 4B, the horizontal axis indicates the time t corresponding to FIG. 4A, and the vertical axis indicates the operation amount u. Similarly to the above, the origin indicates the intersection of the current time point at the k-th step from the start of the control and the operation amount u _jk of the i-th operation object at the k-th step, that is, the current operation amount MV indicated by a thick solid line. Yes.
[0042]
Here, in FIG. 9A, after τ time, in other words, the control amount at the d step, that is, the k + d step from the start of the control, is predicted from the current point of the k step. First, as shown in FIG. 5B, assuming that the current operation amount MV indicated by a bold line is continued up to k + 1 steps, y _{ik + d} is predicted. This lower by e _i than the control amount target value SV.
[0043]
Therefore, when the current manipulated variable MV is changed by + ε _j as shown in FIG. 8B, y ′ _{ik + d} closer to the control amount target value SV is obtained as shown in FIG. Predicted. As a result, it becomes clear how much the operation amount is changed, and the predicted value y ″ _{ik + d} approximates the control amount target value SV. That is, the variation + Δu of the operation amount to be added to the current operation amount MV. _j becomes clear.
[0044]
Here, the above-described optimization calculation, that is, the calculation method for minimizing the evaluation function will be further described. In the following description, all uppercase English letters represent determinants. That is, the following simultaneous equations Y = R · X. . . . . . . . . (1)
, Y, R, and X are the following determinants obtained by rewriting the above equation 4, respectively:
[Formula 18]

[0046]
It represents. Here, the manipulated variable u is replaced with a variable x for general description. In addition, the number m of the control amounts described above is the number m in the equation, and the number n of the manipulated variables is the unknown number n. In the following description, r indicates the rank of the matrix R, and the sensitivity r described above is indicated by the matrix R. A method for solving X based on the determinant shown in Equation 7 will be described below.
[0047]
First, when rank r = m <n of matrix R,
[0048]
[Equation 19]

[0049]
Find X to minimize. As a solution method, a least square method (minimum norm) is used.
Second, when the rank r of the matrix R is r = m = n,
Solving the simultaneous linear equations (1)
X = R ⁻¹ · Y. . . . . . . . . (2)
Get. R ⁻¹ is an inverse matrix of the matrix R. Here, as described above, since the sensitivity matrix R and the control amount matrix Y (vector) to be changed are already known, the operation amount matrix X (vector) can be uniquely determined.
[0050]
Third, when rank r = n <m of matrix R,
J = ‖Y-R · X‖ ₂
Find X to minimize. The least square method is used for the solution. Note that this equation has an error with respect to each Y, that is, there is essentially no X that satisfies equation (1) when the number m of equations is larger than the number n of unknowns, as in this example. , Which minimizes the sum of squares of the error “YR · X”.
[0051]
Fourth, when the rank r of the matrix R is r ≦ Min (m, n) (however, m ≧ 1, n ≧ 1, the magnitude relationship between m and n is arbitrary, and the smaller one is r). Is a general solution including the above first, second and third solutions. In the calculation in the optimization calculation unit 7 described above, (1), (2) and (3) show solutions when n = m = 1, n = m> 1 and n> m, and n <m We did not show a solution for, but this general solution shows it.
[0052]
First, the least square minimum norm solution of A · Z = b is set as Z ⁺ .
The Z ⁺ is a Z to ‖Z‖ in Z which ‖b-A · Z‖ ₂ is minimum ₂ becomes the minimum. Z _i = x _i · √w _i to make the evaluation function ‖Z‖ ₂
far. x _i = z _i / σ _i , σ _i = √w _i , w _i ≠ 0
[Expression 20]

[0054]
X = C ・ Z
Therefore, equation (1) is
Y = R ・ C ・ Z
It becomes. here,
b = Y
If A = R · C, Z ⁺ may be obtained. If Z ⁺ is found,
X = C · Z ⁺
X can be obtained.
[0055]
【The invention's effect】
As described above in detail, according to the present invention, a predicted control amount predicted using a neural network is obtained, an evaluation function of the obtained predicted control amount is obtained, and an operation for minimizing these evaluation functions is performed. Since the determined operation amount is output to the plant as an operation amount corresponding to the target control amount, even a plant that cannot be easily modeled by the laws of physics is modeled by a neutral network, and a numerical value is simply set. Rather than predicting, it is possible to determine and output the optimum manipulated variable corresponding to the target controlled variable from the predicted variable, and to always perform optimal control for various plants. It becomes possible.
[Brief description of the drawings]
FIG. 1 is a block diagram illustrating a configuration of a multivariable model predictive control system according to an embodiment.
FIG. 2 is a diagram showing details of input / output data in a main part of the multivariable model predictive control apparatus in the multivariable model predictive control system.
FIG. 3 is a diagram schematically showing a prediction value calculation method by the multivariable model predictive control apparatus;
[Explanation of symbols]
1 Multivariable model predictive control system 2 Plant 3 Multivariable model predictive control device (control device)
4 Data processing unit 5 Neuro model unit 6 Sensitivity calculation unit 7 Optimization calculation unit 8 Operator

Claims (3)

As a neuro model that inputs the manipulated variable, disturbance, and controlled variable of the controlled process as input and outputs the controlled variable, _k of y _{k + d} should be assumed to be the time step up to the present, and d should be predicted from the present Time step to the point in time,

Or

It was used, and a control amount change predicting means for predicting a change in the control amount of the above from the point to be controlled,
In calculating the sensitivity of the amount of change of each control amount with respect to the amount of change of each operation amount to be given from now on, according to the state amount at the time to be controlled , the j-th operation amount u _{jk + 1} is the current operation amount. When the control amount predicted value based on the i-th neuro model in the same case as u _jk is y _{ik + 1} and the manipulated variable is u _{jk + 1} = u _jk + ε _j , the control amount predicted value is y ′ _ik as was changed to _+1, the time, the sensitivity r _ij at time,

Control amount sensitivity calculation means for calculating the sensitivity of the change amount of each control amount, and
Using the sensitivity matrix obtained by the calculation by the control amount sensitivity calculation means, each control amount predicted by the change prediction means matches the predetermined target value as much as possible, and the change amount of each operation amount. Are determined so as to be as small as possible, and each manipulated variable is determined by using a control equation matrix Y, a sensitivity matrix R thereof, and a simultaneous linear equation Y = R · X using the manipulated variable matrix X. , Optimization calculation / determination means for determining each manipulated variable by performing optimization calculation of the manipulated variable using a least squares minimum norm solution as a solution of X ,
With
A multivariable model predictive control apparatus, characterized in that each operation amount determined by the optimization calculation / determination means is output to the outside as the operation amount of the process to be controlled. As a neuro model that inputs the manipulated variable, disturbance, and controlled variable of the controlled process as input and outputs the controlled variable, _k of y _{k + d} should be assumed to be the time step up to the present, and d should be predicted from the present Time step to the point in time,

Or

The used to predict the change in the control amount of the first from the control should do the time,
The control should do Ri by the state quantity at the time, when calculating the sensitivity of the variation of each of the control amount with respect to a change amount of each of the manipulated variables given to from now on, j-th manipulated variable u _{jk + 1} is now The control amount predicted value based on the i-th neuro model when y is the same as the operation amount u _jk is y _{ik + 1,} and when the operation amount is u _{jk + 1} = u _jk + ε _j , the control amount predicted value is y as changes to _{'ik + 1,} the time, the sensitivity r _ij at time,

Calculate the sensitivity of the amount of change in each controlled variable ,
Using the sensitivity matrix obtained by this calculation, it is optimal that each of the predicted control amounts matches the predetermined target value as much as possible, and the change amount of each manipulated variable becomes as small as possible. In determining each manipulated variable by performing the calculation , the minimum square minimum norm solution is used as a method of solving X by using the control quantity matrix Y, the sensitivity matrix R, and the simultaneous linear equation Y = R · X based on the manipulated variable matrix X. To perform the optimization calculation of the manipulated variable to determine each manipulated variable,
A multivariable model predictive control method characterized in that each determined operation amount is output to the outside as the operation amount of the process to be controlled. As a neuro model that inputs the manipulated variable, disturbance, and controlled variable of the controlled process as input and outputs the controlled variable, _k of y _{k + d} should be assumed to be the time step up to the present, and d should be predicted from the present Time step to the point in time,

Or

A function used to predict the change in the control amount of the first from the control should do when a
The control should do Ri by the state quantity of time, per To calculate the sensitivity of the variation of each of the control amount with respect to a change amount of each of the manipulated variables given to from now on, j-th manipulated variable u _{jk + 1} is now The control amount predicted value based on the i-th neuro model when y is the same as the operation amount u _jk is y _{ik + 1,} and when the operation amount is u _{jk + 1} = u _jk + ε _j , the control amount predicted value is y as changes to _{'ik + 1,} the time, the sensitivity r _ij at time,

As a function to calculate the sensitivity of the change amount of each control amount ,
Using the sensitivity matrix obtained by this calculation, it is optimal that each of the predicted control amounts matches the predetermined target value as much as possible, and the change amount of each manipulated variable becomes as small as possible. In determining each manipulated variable by performing the calculation , the minimum square minimum norm solution is used as a method of solving X by using the control quantity matrix Y, the sensitivity matrix R, and the simultaneous linear equation Y = R · X based on the manipulated variable matrix X. A function for determining each manipulated variable by performing optimization calculation of the manipulated variable using
A function of outputting each determined operation amount to the outside as the operation amount of the control target process;
The computer-readable storage medium which recorded the multivariable model predictive control program for performing this.

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