Dynamic model 动态模型 & Prediction update 预测更新

在DMCplus控制器中斜坡变量的处理方式与稳态变量不同。模型响应也有些不同。

下图10所示为缓冲罐液位斜坡响应：假设出容器流量每小时增加1 Mlb/hr，液位大约会以1%/60min的速率下降。斜坡值（如图所示为-0.0154）即液位变化率，是基于模型响应的最后两个系数计算的。在60min时响应依旧在下降，这表明系统依旧存于不平衡状态。

Figure10: Ramp Model Response

                                                                              图10：斜坡模型响应

Prediction update预测更新

为使用反馈法校正稳态变量的预测向量，观察到的预测误差将（测量值-预测值）被带入各元素的预测向量（如下图11所示）。这相当于预测向量基于一恒定值的简单移位。其假设在没有其它信息的情况下，当前观察到的偏差既不会增加也不会减少。:

另一方面对于斜坡变量，观察到的预测误差可以与系统中材料积累速率的不准确预测联系起来。在这种情况下，预测误差将不断增长，除非预测“旋转”以解决不平衡预测的错误。

Figure 11：Prediction Feedback Correction for Steady-State Variable

                                                              图11： 稳态变量的预测反馈校正

要使用反馈法校正斜坡预测，和稳态变量一样，首先对预测向量进行一等同于预测误差的移位处理。接着是对预测进行“旋转”;也就是说，一个与预测误差成正比的斜坡向量将被添加到预测向量中。旋转系数由预测旋转激烈度决定（如下图12所示）。

Figure12: Prediction Feedback Correction for Ramp Variable

                                                             图12：斜坡变量的预测反馈校正

旋转因子可以被认为是预测向量旋转误差分数（如下图13所示）。旋转因子为0代表没有旋转，而旋转因子为1代表所有观察到的预测误差都是由于不平衡预测错误的缘故。

Figure13: Rotation Factor for Ramp

                                                                             图13：斜坡旋转因子

附原文：

Ramp variables are handled differently than steady-state variables in the DMCplus controller. The model responses also look somewhat different.

Figure 10 below shows the ramp response for level in a surge tank: For a 1 Mlb/hr increase in flow out of the vessel, the level will drop by almost 1 percent after 60 minutes. The value ofthe ramp (shown as -0.0154) is calculated as the rate of change in the level,based on the last two coefficients in the model response. The response is still dropping at 60 minutes; this indicates that an imbalance in the system exists.

Prediction update

To correct the prediction vector for a steady-state variable using feedback methods, the observed prediction error (measured value-predicted value) is added to each element of the prediction vector (see Figure 11 below).This corresponds to a simple shift in the prediction vector by a constant value.What this assumes is that in the absence of other knowledge, the currently observed error will neither grow nor shrink.

For a ramp variable on the other hand,an observed prediction error can be related to an incorrect prediction in the rate of material accumulation in the system. In this case, the prediction error will continue to grow unless the prediction is "rotated" to account for this error in imbalance prediction.

To correct a ramp prediction using feedback methods,the prediction vector is first shifted by an amount equal to the prediction error, just as for steady-state variables. Next, however, the prediction is "rotated";that is, a ramp vector proportional to the prediction error is added to the prediction vector. The rotation factor determines how aggressively the prediction is rotated (see Figure 12 below).

The rotation factor can bethought of as the fraction of the error used to rotate the prediction vector(see Figure 13 below). A rotation factor of zero (0) means no rotation, while a one (1) means that all of the observed prediction error is attributed to error in the imbalance prediction.

                                                                   2015.9.29