實施DMCplus的第一步是辨識過程動態(tài)模型作箍。通過給工廠變量擾動，收集第一手數(shù)據(jù)前硫，獲得工廠模型胞得。運用DMCplus多變量控制軟件對工廠數(shù)據(jù)進行分析。分析得到包含所有顯著耦合變量間相互關系的多變量動態(tài)模型屹电。
下圖顯示了一個復雜精餾塔模型阶剑。每一格代表對應自變量在0時刻作一階躍變化，而其它自變量保持恒定時因變量響應（開環(huán)階躍響應）危号。
簡單地說牧愁，每條曲線表示自變量變化對對應因變量的影響情況。在后面部分我們將對模型進行進一步說明葱色。
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? 圖4：復雜精餾塔模型
得到過程動態(tài)模型后递宅，模型將被用于生成和預測過程中CV的未來動態(tài)。
模型是基于自變量歷史值變化數(shù)據(jù)計算出預測值的苍狰。鑒于所有這些變化會對系統(tǒng)產(chǎn)生持續(xù)影響办龄，我們近似認為自變量改變起至一個穩(wěn)態(tài)時間為需要考慮的。變化起一個穩(wěn)態(tài)時間后就不需要考慮淋昭，因為它們已經(jīng)不再影響系統(tǒng)俐填。
由于模型曲線代表了自變量變化對因變量地影響，這些自變量變化可應用于生成模型每一因變量的未來預測值翔忽。模型能計算當前時刻一個穩(wěn)態(tài)時間內(nèi)的預測值英融。控制器每次執(zhí)行時會更新因變量預測值歇式，并調(diào)和當前預測與實際因變量測量值以消除模型失配的影響驶悟。
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? 圖5：最佳穩(wěn)態(tài)計算參考要素
DMCplus算法下一步是按上圖所示計算所有MV和CV的最優(yōu)穩(wěn)態(tài)目標。計算由穩(wěn)態(tài)線性規(guī)劃（LP）或穩(wěn)態(tài)二次規(guī)劃（QP）實現(xiàn)材失。
計算的輸入包括MV（操作變量）當前值和操作限制痕鳍、CV（被控變量）穩(wěn)態(tài)預測值、產(chǎn)品價值經(jīng)濟信息、原材料和公用工程成本笼呆。
操作界限定義了一個可接受的操作區(qū)域熊响。MV當前值和CV預測穩(wěn)態(tài)值定義了假設MVs沒有移動時預測的穩(wěn)態(tài)工作點。這一點在或不在可接受操作區(qū)域內(nèi)都有可能诗赌。
穩(wěn)態(tài)求解器（LP或QP）計算出每個MV的穩(wěn)態(tài)移動汗茄，組合后系統(tǒng)給出一個可接受工作區(qū)域內(nèi)的穩(wěn)態(tài)操作點。并且從經(jīng)濟角度看此操作點是最優(yōu)的铭若。需要注意的是這一最佳穩(wěn)態(tài)操作點始終在上述幾個限制下洪碳。
下圖顯示了一包含2個MV（操作變量），3個CV（被控變量）系統(tǒng)例子奥喻。
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? 圖6：具有2個MV和3個CV系統(tǒng)的操作區(qū)域
MVs是回流流量.SP和再沸器蒸汽流量.SP偶宫。CVs是塔頂出料雜質(zhì)，塔釜出料雜質(zhì)和塔壓差环鲤。上述五個變量限制下的操作區(qū)域為可接受操作區(qū)域。
在這個例子中憎兽，當前穩(wěn)態(tài)操作點在區(qū)域內(nèi)冷离，盡管不總是這樣。同時纯命，當前穩(wěn)態(tài)操作點與當前操作點是不同的西剥；它是系統(tǒng)預測未來沒有控制作用的作用點。
知道當前穩(wěn)態(tài)操作點亿汞、五個變量限制瞭空，和經(jīng)濟信息，就能夠確定最佳穩(wěn)態(tài)工作點疗我。該點指定所有MVs和CVs最優(yōu)穩(wěn)態(tài)目標咆畏。
DMCplus算法最后一步是開發(fā)MVs控制動作的詳細計劃以使CVs預測未來性能與期望未來性能誤差最小化。CVs期望未來性能是它們的穩(wěn)態(tài)目標吴裤，由穩(wěn)態(tài)求解器計算旧找。
CVs穩(wěn)態(tài)目標通常都是CVs的設定點。為了動態(tài)驅(qū)動CVs到目標值麦牺，控制器計算出未來MV一系列動作钮蛛，一直到未來一半穩(wěn)態(tài)時間左右。這將使控制器推遲控制動作剖膳，有利于解決多變量控制問題中一個MV動作對其它MVs的影響魏颓。
當所有計算出的MV移動被加入后，MV的值必須等于線性規(guī)劃中MV穩(wěn)態(tài)目標值吱晒。如果所有的MVs達到穩(wěn)態(tài)目標甸饱，CVs也將達到穩(wěn)態(tài)目標。
附原文：
The first step in implementing DMCplus is to?model the dynamics?of the process. The plant model is obtained by first collecting plant data whileperturbing the plant. This plant data is analyzed using DMCplus MultivariableControl software. The result of this analysis is a dynamic, multivariable modelof the process that contains all significant interactions between variables.
Thefigure below shows the model for the Complex Fractionator. Each box representsthe response in time of the dependent variable to a step change at time zero ofthe corresponding independent variable, while all other independent variablesare held constant (open loop step responses).
In simple terms, each curve represents the?effect of a change?in an independent variable on that dependent variable. The model will be described inmore detail in a later section.
Once the dynamic model has been obtained, this model is used to form and maintain a?prediction?of future behavior of the controlled variables in the process.
This?prediction is maintained by using the past history of changes in the?independent variables. All independent variable changes up to one steady-state?time into the past are considered, since all of these changes still have an?effect on the system. Changes that occurred more than one steady-state time?into the past need?not be considered, since they no longer affect the system.
Since the model curves represent the effects of independent variable changes on dependent variables, these independent variable changes can be applied to the model to generate a future prediction for each dependent variable. These predictions extend from the current time out to one steady-state time into the future. These dependent variable predictions are updated at each execution of the controller, and are reconciled with the actual dependent variable measured values to eliminate model mismatch.
The next step in the DMCplus algorithm is to?calculate optimum steady-state?targets for all manipulated and controlled variables, as shown schematically in the figure above. This calculation is done by either the Steady-StateLinear Program (LP) or the Steady-State Quadratic Program (QP).
The input to this calculation consists of the MV (manipulated variable) current values and operating limits, the CV (controlled variable) steady-state predicted values, and economic information on values of products, and costs of raw materials and utilities.
The operating limits define an acceptable operating region. The MV current value sand CV predicted steady-state values define the predicted steady-state operating point, assuming no moves in the MVs. This point may or may not beinside the acceptable operating region.
Thesteady-state solver (LP or QP) calculates a steady-state move in each MV, whichtaken together, specify a steady-state operating point that is within theacceptable operating region. Further, this operating point is optimal from aneconomic standpoint. Note that this optimal steady-state operating point willalways be at several limits.
The figure below shows an example of a two MV (manipulated variable), three CV(controlled variables) system.
The MVs are reflux flow set point and reboiler steam flow set point. The CVs are overhead impurity, bottoms impurity, and tower differential pressure. The operating limits on all five variables define an acceptable operating region.
Inthis example, the current steady-state operating point is inside the region,although this is not always the case. Also, this current?steady-state?operating point is not the same as the current operating point; it is the point to which the system is predicted to go in the absence of control action.
Knowing the current steady-state operating point, the limits on all five variables, and economic information, it is possible to identify the optimal steady-state operating point. This point specifies optimal steady-state targets for all MVsand CVs.
The final step in the DMCplus algorithm is to?develop a detailed plan of
control action for the manipulated variables that minimizes the difference between the predicted future behavior and the desired future behavior of the controlled variables. The desired future behavior of the controlled variables is to have them at their steady-state targets, as calculated by the steady-state solver.
Basically,the CV steady-state targets are the set points for the CVs.In order to dynamically drive the CVs to their targets, a series of future moves is calculated for each MV, extending approximately one-half steady-state time into the future. This allows the controller to defer control action, and also to better play the effects of one MV off against the other MVs in solving the multivariable control problem.
The value of the MV, when all calculated moves are added in, must be equal to theMV steady-state target from the linear program. If all MVs reach their steady-state targets, the CVs will also reach their steady-state targets.
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?2015.9.10
