*3.2.1.1 Characteristic variable* en*•*Δen

The product of the error *e* and the error change Δ*e* constitutes a characteristic variable describing the dynamic process of the system, and whether the value of the characteristic variable is greater than zero can describe the trend of the system dynamic process error change. Let *en* and *en*�<sup>1</sup> denote the error values of the current and previous sampling moments respectively, then Δ*en = en*�*en* � 1. For different stages of the dynamic system response curve shown in **Figure 20**, the values of the characteristic variables *en•*Δ*en* are shown in **Table 2**.

When *en•*Δ*en* > 0, as shown in the *AB* and *CD* sections in **Figure 20**, it shows that the dynamic process of the system changes in the direction of increasing error, that is, the absolute value of the error gradually increases. When *en•*Δ*en* < 0, as shown in **Figure 20**, *BC* and *DE*, it shows that the dynamic process of the system changes in the direction of decreasing error, that is, the absolute value of the error gradually decreases. In the control process, the computer can easily recognize the symbol of *en•*Δ*en,* so as to grasp the behavior characteristics of the dynamic process of the system, so as to better formulate the next control strategy.

**Figure 20.** *Curve of dynamic process.*


**Table 2.**

*Sign change of characteristic variables.*

## *3.2.1.2 Characteristic variable* e*•*Δe

The absolute value of the ratio of the error change Δ*e* to the error *e* is defined as the characteristic variable describing the error change trend in the dynamic process of the system. The combined use of |Δ*e/e*| and *en•*Δ*en* can further divide the characteristics of the dynamic process and facilitate the capture of different modes of the dynamic process. For example, in **Figure 19**, the *AB* segment of the curve can be subdivided into the following three cases:


The above-mentioned α and β are constants set according to the needs of control, and there are α > β. Similarly, readers of the BC, CD, and DE segments of the curve in **Figure 15** can perform similar analysis.
