# Temperature Regulation of Hot Vapor Preservation Treatment of Litch Based on PSO-Fuzzy PID
## 4 Analysis and Modeling of The Hot Vapor Treatment Process of Litchi
### Equipment Preheating Link  
In this link, heat transfer will occur between vapor and pipes, boxes, conveyor chains, and air, including heat convection, conduction, and radiation. The heat transfer process is too complex to describe the equipment heating process accurately with a single heat transfer formula. Therefore, the transfer function of this segment was established by the experimental method.  
The test was carried out on 20 April 2022. The testing procedure involved emptying the processing room of the equipment (without lithti) and suspending the conveyor chain motor to achieve the fastest heating effect. The electric control valve was opened and maintained at maximum opening when the pressure of the vapor generator became saturated, so that the temperature of the treatment chamber could rise rapidly. An RX6020C paperless recorder from Hangzhou Meikong Automation Technology Co., Ltd. (Hangzhou, China) was used to access 18 temperature measurement points of the device, read the resistance value of Pt100 thermal resistance, convert it into temperature value, and record it. The data were analyzed using Origin Pro 2021b software, which generated the temperature change curve of the heating link. The abnormal temperature measurement point 00 data was eliminated and the average temperature rise curve of the vapor treatment room was drawn. Figure 8 shows the temperature rise curve of the equipment. Due to incomplete equipment sealing, heat transfer occurred between vapor and air at the inlet and outlet of the conveyor chain, making it impossible to achieve the ideal temperature of 100 \({}^{\circ}\)C.  
The vapor valve opens at the time of point A, and the vapor enters the vapor treatment room from the nozzle through the pipeline. It is atmospheric pressure, which can be regarded as the temperature of the vapor being 100 \({}^{\circ}\)C. Therefore, the instantaneous system of opening the valve inputs a step signal of 100 \({}^{\circ}\)C (\(\Delta M=100\)). The point is set to \(t_{0}\), and the curve begins to change after about 8 s. It can be seen that there is a lag between the temperature sensor detection and the actual temperature change. The mathematical  
Figure 8: Equipment temperature rise curve. Note: Point A is the time node at which the valve opens.  
model of the controlled object of the temperature control system can be expressed by the first-order delay link [29], and the transfer function can be expressed as:  
\[G(s)=\frac{K}{Ts+1}e^{-Ts} \tag{4}\]  
where _K is_ the static gain of the object; _T is_ the time constant; _\(\tau\)_ is the pure lag time; _\(s\)_ is a complex variable.  
The approximate transfer function of the step response is determined by the Cohen-Coon formula. The formula is as follows:  
\[\left\{\begin{aligned} & K=\frac{\Delta C}{\Delta M}\\ & T=1.5(t_{0.632}-t_{0.28})\\ &\tau=1.5\Big{(}t_{0.28}-\frac{t_{0.632}}{3}\Big{)}\end{aligned}\right. \tag{5}\]  
where \(\Delta M\) is the step input signal to the system; \(\Delta C\) is the output response, \(\Delta C=T_{max}-T_{0}\), which is the difference between the temperature maximum \(T_{max}\) and the initial temperature \(T_{0}\); \(t_{0.28}\) is the time when the temperature value rises by 0.28 times \(\Delta C\); and \(t_{0.632}\) is the time when the temperature value rises by 0.632 times \(\Delta C\).  
The curve was sampled according to the required data, and the corresponding sampling time and temperature values are shown in Table 2. According to the sampling data, the transfer function of the heating link can be calculated by substituting it into the Formula (5) as follows:  
\[G(s)=\frac{0.655}{37.2s+1}e^{-6.8s} \tag{6}\]