## 3 Results  
After the air supply status of the system was stable, the airflow parameters at the outlet of the system were monitored. When the airflow parameters at the outlet of the system were stable, the system records the test parameters.  
The torque motor was controlled by current, a \(0-250\) mA sweep current signal was input to the torque motor, and the valve angle and the temperature change at the outlet of the hot path were observed and recorded.  
The results in Figure 12 show that the flow of the cold gas was affected by the rotation angle of the butterfly valve, and the temperature at the outlet of the hot gas changed with the flow of the cold gas, which is consistent with the mathematical model and simulation analysis results.  
For the heat exchanger identification experiment, identification experiments were carried out in sections under the above four flow states. Preliminary tests showed that the second-order transfer function had an excellent fitting effect. Therefore, the four-part models were fitted by a second-order transfer function. The results were as following Figure 13.  
Figure 11: Steady-state identification experiment of heat exchanger: (**a**) input temperature \(T_{\text{hss}}\), and (**b**) output temperature of heat exchanger \(T_{\text{h2}}\).  
Figure 12: Experiment results of temperature control valve characteristics: (**a**) angular displacement of the butterfly valve, (**b**) gas flow at the cold path’s inlet, and (**c**) gas flow at the cold path’s inlet.  
A second-order transfer function of the heat exchanger under four flow conditions was calculated from experimental results. The transfer functions of the four-stage heat exchanger model shown above are  
\[tf_{g_{h}=5400}=\frac{1.1465(1+32.12\;\text{s})}{(1+0.685\;\text{s})(1+45.45\; \text{s})} \tag{24}\]  
\[tf_{g_{h}=3000}=\frac{0.9956(1+96.03\;\text{s})}{(1+3.401\;\text{s})(1+112.1\; \text{s})} \tag{25}\]  
\[tf_{g_{h}=2150}=\frac{0.99815(1+91.14\;\text{s})}{(1+5.458\;\text{s})(1+100.0 \;\text{s})} \tag{26}\]  
\[tf_{g_{h}=1300}=\frac{0.95321(1+7.031\;\text{s})}{(1+0.812\;\text{s})(1+23.54 \;\text{s})} \tag{27}\]  
According to the transfer function of the four-stage heat exchanger, step signals were input respectively to obtain the time constant of the heat exchanger under different flow rates.  
As shown in Figure 14, the order of the time constants of the four transfer functions are \(g_{h}=1300\;\text{kg/h}\), \(g_{h}=2150\;\text{kg/h}\), \(g_{h}=3000\;\text{kg/h}\), \(g_{h}=5400\;\text{kg/h}\), which conformed to the actual situation. The passband is \(0.05\;\text{rad/s}\), within the passband the amplitude from large to small is \(g_{h}=5400\;\text{kg/h}\), \(g_{h}=3000\;\text{kg/h}\), \(g_{h}=2150\;\text{kg/h}\), \(g_{h}=1300\;\text{kg/h}\), and the phase delay from large to small is \(g_{h}=5400\;\text{kg/h}\), \(g_{h}=3000\;\text{kg/h}\), \(g_{h}=2150\;\text{kg/h}\), \(g_{h}=1300\;\text{kg/h}\), which conformed to the actual situation.  
Figure 13: Fitting result of second-order transfer function: (**a**) \(g_{h}=5400\;\text{kg/h}\), (**b**) \(g_{h}=3000\;\text{kg/h}\), (**c**) \(g_{h}=2150\;\text{kg/h}\), (**d**) \(g_{h}=1300\;\text{kg/h}\).  
Through the simulation and identification experiment of the heat exchanger, the dynamic characteristics of heat exchanger in a temperature control system were qualitatively analyzed. The dynamic characteristics, including the time constant under various working conditions of heat exchanger system, were obtained so that the parameters of PID controller of the temperature control valve torque motor could be calculated according to the dynamic characteristics of the system and used to design the adaptive regulation of the valve and realize the adaptive temperature control system.