## 1 Introduction  
The primary function of a temperature control valve system [1, 2] is to control the opening and closing of a butterfly valve under specified temperature or pressure conditions, thereby controlling the flow of gas flowing through a heat exchanger and realizing the temperature regulation of a cabin. The traditional temperature control system uses the mixing of hot and cold gas for heat exchange, which is a complex system with time-varying, nonlinear, and large time constants [3]. It is difficult to obtain satisfactory results using the traditional control method. We propose a temperature control valve system in which the air at the hot path and the cold path exchange heat through a heat exchanger without mixing. In order to design a control strategy suitable for a temperature control valve system and achieve servo control, it is necessary to study the working principle and characteristics of each system component in which the characteristics of the heat exchanger are analyzed, and the dynamic time constant suitable for the heat exchanger is obtained, proving the feasibility of the adaptive temperature control system. The temperature of an aircraft cabin is mainly regulated by hot gas and cold gas simultaneously, and the temperature and flow of the cold gas are affected by the flight conditions of the aircraft. While the engine provides hot gas, it is affected by the engine speed. Therefore, the key point of controlling cabin temperature by mixing cold-side and hot-side gas is controlling the hot-side gas flow. A CE525 CJ1 cabin heating control system uses engine bleed air to provide hot gas for the cabin and then cools down the cabin twice through a pre-cooler and a heat exchanger to adjust the cabin temperature. In recent years, research on cabin temperature control strategy mainly has included fuzzy control [4], expert-PID decoupling control [5], and a neural network algorithm [6]. [PERSON] et al. [7] used table-based LPID (Lookup PID) controllers to control the temperature and pressure of the aircraft bleed air in a simulation test. The dynamic test errors were within 10%, and the steady-state accuracies were within \(\pm\)2%. [PERSON] [8] proposed a new aircraft cabin temperature control system based on PID control and LQG (Linear Quadratic Regulator) control, effectively reducing the energy consumption of keeping the temperature difference as small as possible. Currently, Chinese aviation factories generally mix cold and hot gas to cool the gas discharged from the engine and control the flow of cold gas by controlling the rotation angle of the butterfly valve in the temperature control valve to control the outlet temperature. Then, the mixed outlet gas is used to adjust the temperature of the cabin. The advantage of this gas mixing method is that the response speed is fast, and the cabin temperature can be quickly adjusted to the reference temperature. However, the disadvantage is that the temperature and flow of the gas in the hot path cannot be directly controlled by the engine [9], so the outlet temperature is mainly affected by the temperature and flow of the gas in the cold path. The hot gas flow at the hot path's inlet remains stable, resulting in an unstable flow at the outlet of the hot path. [PERSON] et al. [10] simulated the air conditioning system of the Boeing 737-800 under two different operating conditions. They concluded that changes in the aircraft's environmental conditions have a significant impact on the steady-state outlet temperature and have a significant impact on the heat transfer efficiency in the primary and secondary heat exchangers. The method of temperature control by mixing hot-side gas and cold-side gas is unstable under variable environmental conditions. [PERSON] and [PERSON]. [11] discovered that the cabin inlet temperature would fluctuate more during the substantial change in aircraft flight altitude stage by using AMESim simulation, which means that the traditional method cannot effectively control the hot-side gas under variable conditions.