图7：制定一控制计划驱动误差为零
上图所示为1个MV，1个CV系统详细控制动作开发。控制作用所需效果应由与CV稳态目标（CV.SP）相关的CV预测值镜像限定。
如果控制作用与期望效果完全相同，错误将被精确地抵消。CV将立即进入稳态目标值并在未来时域内得到保持。
因为我们知道需要从控制操作中得到所需的效果，以及过程模型描述了自变量的移动对因变量变化影响，可以合理假设模型可用于规划MV未来动作。
上图还显示了MV计划的控制作用。需要注意的是CV曲线显示了“在控制作用下的CV预测图”。曲线是加入了计算控制作用影响的CV预测值。（仅基于自变量过去的动作）。
图8：复杂精馏塔被控变量动作
图9：复杂精馏塔操作变量动作计划
上面两图显示了复杂精馏塔控制器解决方案的简介。这些图将被用于展示DMCplus控制器的主要特点。
每一栏包含了一个CV或MV的信息。Y轴是CV或MV的工程单位，x轴是时间。每栏最左侧表示的是当前时间。需要注意的是计算出的未来动作将使其大约经过时间轴一半时间到达稳态。
还需要注意每一栏右侧超出稳态时间的部分，称为“控制器时域”。这一扩展时间用来观察大部分未来动作的影响。因此“控制器时域”等同于稳态时间加未来大部分动作时间。
每个CV的预测值曲线用虚线表示。这些预测值是基于5个自变量历史值及本节前述所示模型得到的（图4）。
这些预测值代表没有任何控制动作下对3个CVs的预测。
还需要注意到所有MVs和CVs都有上下操作限。这些限制定义可接受操作区。CVs预测稳态值和MVs当前值定义了当前稳态操作点。
通过这一个点、经济信息，和操作限制定义的可接受操作区，稳态求解器计算出最优稳态操作点。这表现为每一栏右侧的稳态目标。控制器中每一MV和CV都有一个稳态目标值。
下一步是制定详细的控制作用计划。如图9所示，每一MV未来一系列动作都被计算出来。这些动作经历大约一半的稳态时间，并达到MV稳态目标值。
这些动作通过使所有3个CVs的预测值与稳态目标错误值最小化计算得到。图8所示为每一CV的“预测控制动作”。该曲线表示基于图9 MV控制动作的未来预测CV响应值。
需要注意的是根据稳态求解器计算得到的所有MVs和CVs预测值最终都在它们各自的稳态目标值。这并不是偶然的；如果MVs最终停在各自所需的稳态目标值，CVs也会停在稳态目标值。
最后需要提一点，图8和图9仅表示一个控制器在一个控制周期内的计算值。每一MV计算出的14步中第一步将被送入监督控制系统，剩下的部分将被舍弃。
如果下一控制周期中，没有干扰进入系统并且模型失配是可以忽略的，其解决方案将与上一周期解决方案的剩余部分非常相似。
然而，如果系统进入一主要干扰，正如预测本身一样，最佳稳态操作点将会改变（干扰反应）。这将需要对控制方案作出立即改变，因此这一情况下控制方案将不会像前一控制周期的方案一样。
正是因为这个原因，除了第一步动作以外，其它所有动作都将被舍弃。鉴于第一步控制动作将受到预测未来违反MV约束的影响，这些未来动作的计算依旧是必不可少的。换句话说，一个特殊的MV可能需要较现在移动地更多以避免未来违反限制。如果未来整个动作轨迹未被计算，操作限制问题将无法得到答案。
附原文：
The figure above shows the development of a detailed control action for a one MV,one CV system.The desired effect of the control action is defined by the mirror image of the CV Prediction about the CV Steady-State Target (CV Set Point).
If control action could be found that had exactly the desired effect, the error would be exactly canceled out. The CV would go immediately to the steady-state target and remain there across the future time horizon.
Since we know the effect needed from the control action, and since the model of the process describes the effect on a dependent variable of a move in an independent variable, it is reasonable to assume that the model can be used in planning the future MV control moves.
The figure above also shows the control action planned for the MV. Note that the CVplot displays a "CV Prediction with Control Moves". This curve is theresult of adding the effect of the calculated control action to the CV Prediction (based only on past moves in the independent variables).
The two figures above show a snap shot of a controller solution for the Complex Fractionator. These figures will be used to demonstrate the key features of the DMCplus controller.
Each box contains information on one CV or MV. The y-axis is in engineering units ofthe CV or MV, while the x-axis is time. The left side of each box represents current time. Notice that the future moves are calculated approximately halfway across the time to reach steady state.
Also notice that the right hand side of each box is beyond the steady-state time,referred to as the "controller time horizon".This extension of time is required to allow the entire effect of the future most move to be seen. So the"controller time horizon" is equal to the steady-state time plus the time of the future most move.
Each of the three CVs has a prediction denoted by the dotted line. These predictions are based on the past history of the five independent variables and the model shown previously in this section (Figure 4).
Thesepredictions represent where the three controlled variables are predicted to goin the absence of any control action.
Also note that all of the MVs and CVs have upper and lower operating limits. These limits define an acceptable operating region. The predicted steady-state values of the CVs and the current values of the MVs define the current steady-state operating point.
Using this point, economic information, and the acceptable operating region defined by the operating limits, the Steady-State solver calculates the optimal steady-state operating point. This appears as the steady-state target on the right side of each box. There is a steady-state target for every MV and CV inthe controller.
The next step is to develop a detailed plan of control action. This plan can beseen in Figure 9, where a series of future moves has been calculated for each MV. These moves extend about half way across the steady-state time, and are required to reach the MV steady-state target.
These moves are calculated by minimizing the errors for all three CVs between the Predictions and the CV steady-state targets. Figure 8 shows a "Prediction with Control Moves" for each CV. This curve represents how that CV is predicted to respond in the future,based on the control action shown in Figure 9.
Notice that all MVs and CVs are predicted to end up at their respective steady-state targets, calculated by the Steady-State solver. This is no accident; if the MVs are required to end up at their steady-state target, the CVs must end up at their targets also.
A final point to make is that Figures 8 and 9 represent a single calculation of the controller at one control interval only. The first move of the 14 calculated in each MV is sent to the regulatory control system, and the rest of the moves are thrown away.
If,at the next control cycle, no disturbances have entered the system and model mismatch is negligible, the solution will be very similar to the remainder of the solution from the previous cycle.
However,if a major disturbance has entered the system, the optimal steady-state operating point will change, as will the predictions themselves (reflecting the disturbance). This will require an immediate change in control strategy, so the control action in this scenario will not resemble the solution from the previous control cycle.
It is for this reason that all the moves except for the first one are thrown away.It is still essential that these future moves be calculated, since the size ofthe first control move will be affected by projected MV constraint violations in the future.In other words, a particular MV might have to be moved more now in order to prevent a future limit violation. This would not be known if the entire trajectory of future moves was not calculated,subject to the operating limits.
2015.9.11
