Unmanned aerial vehicle-mounted ultra-low temperature refrigeration system and coupling control method thereof with flight control
Patent Information
- Application Number
- CN202610968724.8
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Priority Date
- 2025-12-02
- Filing Date
- 2026-07-01
- Publication Date
- 2026-09-29
AI Technical Summary
现有技术中,制冷系统的运行状态,如压缩机排气压力、汽液分离器液位、蒸发器温度、管路振动等,完全不被无人机飞控感知,飞控仅根据重心、重量、风速等宏观参数规划飞行路径,完全不知道制冷系统是否正因倾斜或振动而处于危险状态
1、通过健康度指数实施驱动飞控与制冷系统的双向耦合,打破了传统无人机运输中飞控对负载内部状态不知情的技术壁垒,使飞控能够根据压缩机的实时健康状态动态调整飞行策略、制冷系统控制器能够根据飞行姿态变化提前前馈调节制冷参数,形成了边飞行、边感知、边调控的在线闭环协同机制,从根本上解决了静态分离监控模式下制冷系统在动态飞行环境中频繁失效的问题。
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Figure CN122835009A_ABST
Abstract
Description
Technical Field
[0001] This application relates to the field of unmanned aerial vehicle (UAV) transportation technology, specifically to a UAV-mounted cryogenic refrigeration system and its coupling control method with flight control. Background Technology
[0002] When drones transport goods such as ultra-low temperature vaccines and biological agents, a special scenario requires the attachment of a heavy-duty refrigeration system with a cooling capacity below -80°C. In existing technologies, the operational status of the refrigeration system, such as compressor discharge pressure, vapor-liquid separator level, evaporator temperature, and pipeline vibration, is completely undetectable by the drone's flight controller. The flight controller only plans the flight path based on macroscopic parameters such as center of gravity, weight, and wind speed, completely unaware that the refrigeration system may be in a dangerous state due to tilting or vibration. Simultaneously, the refrigeration system's controller is also unaware of the drone's current flight state, passively adjusting the compressor speed based solely on the internal temperature. This results in significant control lag when the drone turns, climbs, or traverses turbulent waters due to the inability to predict attitude changes.
[0003] Furthermore, the design of existing mounting structures only considers structural strength, and their vibration transmission characteristics are not quantified. The flight control system cannot accurately determine the actual amount of vibration transmitted to the cooling system. The lack of two-way data exchange between the flight control system and the cooling system means that malfunctions in the cooling system cannot be detected by the flight control system and cannot trigger an emergency response. In particular, when flammable refrigerants such as R50 leak, the flight control system continues to fly along the original route, posing a serious safety hazard.
[0004] Therefore, there is an urgent need for a mounted cryogenic refrigeration system and its control method that can achieve bidirectional data coupling between the flight control and refrigeration systems. Summary of the Invention
[0005] To address the aforementioned issues, this application provides an unmanned aerial vehicle (UAV) mounted cryogenic refrigeration system and its coupling control method with the flight control system.
[0006] To achieve this objective, the following technical solution is adopted in this application: A UAV-mounted cryogenic refrigeration system and its coupling control method with flight control are provided, including: Obtain the multiphysics state parameters of the cryogenic refrigeration system mounted on the UAV; A health index is generated based on the degree of deviation between the multiphysics state parameters and the preset safety envelope; A bidirectional data channel is dynamically established between the flight controller and the cooling system controller to transmit the health index to the flight controller and the flight attitude information of the flight controller to the cooling system controller. The flight controller adjusts the flight strategy based on the health index, and the cooling system controller adjusts the cooling parameters based on the flight attitude information. When the health index falls below the threshold or a refrigerant leak is detected, the flight controller executes an emergency landing procedure, and the refrigeration system controller simultaneously executes a safety shutdown procedure.
[0007] Preferably, the preset security envelope is calibrated in the following manner: During the operation of the refrigeration system, the compressor discharge pressure, the liquid level of the vapor-liquid separator, and the evaporator inlet temperature are collected synchronously. The product of the discharge pressure and the liquid level is used as the load characterization quantity, and the ratio of the evaporator inlet temperature to the discharge pressure is used as the efficiency characterization quantity. The values of each safety envelope boundary are dynamically adjusted according to the mapping relationship between the load characterization quantity and the efficiency characterization quantity.
[0008] Preferably, the bidirectional data channel is constructed in the following manner: The health index is used as the basis for channel priority classification. When the health index is higher than the first threshold, the channel operates at the first priority, transmitting only the health index and fault flags to minimize communication bandwidth usage. When the health index is between the first and second thresholds, the channel operates at the second priority, supplementing the transmission of multi-physics state parameters in various dimensions, enabling the flight controller to perceive the degradation trend of the cooling system. When the health index is lower than the second threshold, the channel operates at the third priority, supplementing the transmission of real-time decision logs of the cooling system controller, enabling the ground station to retrospectively review the control logic during emergency phases.
[0009] Preferably, the health index is calculated as follows: the deviation of the multiphysics state parameters of each dimension from their respective safe envelope boundaries is calculated, the weighted average of the two dimensions with the largest deviation is taken as the main score, the root mean square of the sum of the squares of the deviations of the other dimensions is taken as the fluctuation penalty term, and the health index is obtained by subtracting the fluctuation penalty term from the main score.
[0010] Preferably, the refrigeration system controller adjusts the refrigeration parameters based on the flight attitude information by: recording the refrigerant distribution recovery time after each attitude change, using the median of the recovery times as a time constant, performing linear regression on the recovery time corresponding to the same attitude change amplitude in multiple sets of historical data and the compressor speed adjustment amount, using the regression slope as the compensation coefficient for the attitude change amplitude range, and multiplying the current attitude change rate by the compensation coefficient of the corresponding range to obtain the compressor speed compensation amount.
[0011] Preferably, the emergency landing procedure makes a landing strategy decision based on a combination of the health index and the refrigerant leakage concentration, as follows: The health index is normalized to a weight coefficient between 0 and 1. The weight coefficient is multiplied by the preset maximum search radius to obtain the actual search radius. Candidate points that meet the landing conditions are searched within the actual search radius. The landing conditions are as follows: The gas concentration decay curve value at the candidate point is lower than the safety threshold, and the angle between the line connecting the candidate point and the leak source and the wind direction is greater than the first preset angle. When there is no candidate point that meets the landing conditions within the actual search radius, the safety threshold in the landing conditions is dynamically relaxed based on the health index. For every decrease of the health index by the first preset value, the safety threshold is increased by the second preset value.
[0012] Preferably, the UAV-mounted cryogenic refrigeration system and its coupling control method with the flight control system further include: The vibration transfer function of the mounting mechanism is obtained. The flight controller calculates the vibration energy transmitted to the cooling system based on the convolution result of the current airframe vibration spectrum and the vibration transfer function. When the vibration energy exceeds a preset threshold, the difference between the vibration energy and the threshold is used as the adjustment amount to proportionally reduce the setpoint of the rotational speed of each propeller, so that the vibration energy transmitted to the cooling system converges to below the threshold.
[0013] Preferably, the vibration transfer function is updated in the following manner: After each flight mission, the vibration spectrum of the aircraft recorded throughout the flight is deconvolved with the actual vibration spectrum at the refrigeration system installation point to obtain the actual vibration transfer function of the flight. The actual vibration transfer function is then weighted and averaged with the historical transfer function, and the vibration transfer function is updated with the weighted result.
[0014] Preferably, when the flight control system executes the emergency landing procedure, it calculates the maximum permissible horizontal acceleration based on the current health index. The maximum permissible horizontal acceleration is proportional to the health index. When the health index approaches "0", the maximum permissible horizontal acceleration approaches "0". The landing path planning uses the maximum permissible horizontal acceleration as a hard constraint. By discretizing the path into piecewise Bézier curves and forcibly applying acceleration continuity conditions at the boundaries of each segment, a smooth trajectory is generated.
[0015] Preferably, the mass ratio of R600a, R1150, and R50 in the refrigerant mixture discharged from the compressor of the cryogenic refrigeration system is 63.59:34.91:1.50, and the upper limit of the discharge pressure in the safety envelope is determined by the following method: The upper limit of the exhaust pressure is obtained by multiplying the exhaust pressure by a safety factor determined based on the condenser heat dissipation conditions, whereby the exhaust pressure is the same as the reference pressure when the compressor is operating at the specified mass ratio and the evaporator inlet temperature reaches the target value. The safety factor increases with increasing ambient temperature.
[0016] This application has the following beneficial effects: 1. By implementing a health index to drive the bidirectional coupling between the flight control and refrigeration systems, the technical barrier of flight control being unaware of the internal state of the load in traditional UAV transportation is broken. This enables the flight control to dynamically adjust the flight strategy based on the real-time health status of the compressor, and the refrigeration system controller to adjust the refrigeration parameters in advance based on changes in flight attitude. This forms an online closed-loop collaborative mechanism of simultaneous flight, sensing, and control, fundamentally solving the problem of frequent failures of the refrigeration system in dynamic flight environments under static separation monitoring mode.
[0017] 2. Through the deep integration of multi-physics state perception and hierarchical control strategies, the flight mode is divided into three levels: normal, protection, and emergency, based on the health index. This allows the UAV's flight envelope to elastically contract according to the real-time health status of the cooling system. When the equipment is healthy, it can fully utilize flight performance, and when the equipment degrades, it can actively limit attitude angles and flight speed to delay performance degradation. This completely changes the inherent problems of the traditional fixed threshold control mode, which is too conservative when the equipment is healthy and slow to react when the equipment degrades. It significantly improves the survivability of the cooling system and the mission completion rate under complex flight conditions.
[0018] 3. In refrigerant leak emergency scenarios, a joint decision-making mechanism of health index and leak concentration is creatively introduced. By dynamically compressing the landing search radius through health index and constraining the landing point selection with leak source diffusion model, the UAV can actively avoid downwind gas diffusion areas and areas around fire sources when performing emergency landing. This fundamentally changes the traditional single decision-making logic of emergency landing that only relies on battery power and GPS signal, and provides a customized safety guarantee solution for UAV transportation of heavy-duty ultra-low temperature refrigerators. Attached Figure Description
[0019] To more clearly illustrate the technical solutions of the embodiments of this application, the drawings used in the embodiments of this application will be briefly described below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.
[0020] Figure 1 This is a diagram illustrating the implementation steps of the UAV-mounted cryogenic refrigeration system and its coupling control method with the flight control system provided in this application embodiment. Figure 2 This is a schematic diagram of the piping structure of the ultra-low temperature refrigeration system in the heavy-duty refrigerator provided in the embodiments of this application; Figure 3 This is a schematic diagram of the bonding between the copper tube in the evaporator and the inner liner of the refrigerator in an embodiment of this application. Detailed Implementation
[0021] The technical solution of this application will be further described below with reference to the accompanying drawings and specific embodiments.
[0022] The accompanying drawings are for illustrative purposes only and are schematic diagrams, not actual images. They should not be construed as limiting the scope of this application. To better illustrate the embodiments of this application, some components in the drawings may be omitted, enlarged, or reduced, and do not represent the actual product dimensions. It is understandable to those skilled in the art that some well-known structures and their descriptions may be omitted in the drawings.
[0023] In the accompanying drawings of the embodiments of this application, the same or similar reference numerals correspond to the same or similar components. In the description of this application, it should be understood that if terms such as "upper," "lower," "left," "right," "inner," and "outer" indicate the orientation or positional relationship based on the orientation or positional relationship shown in the drawings, they are only for the convenience of describing this application and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, the terms used to describe positional relationships in the drawings are only for illustrative purposes and should not be construed as limiting this application. For those skilled in the art, the specific meaning of the above terms can be understood according to the specific circumstances.
[0024] In the description of this application, unless otherwise expressly specified and limited, the term "connection" or similar designation indicating a connection between components should be interpreted broadly. For example, it can refer to a fixed connection, a detachable connection, or an integral part; it can be a mechanical connection or an electrical connection; it can be a direct connection or an indirect connection through an intermediate medium; it can refer to the internal communication between two components or the interaction between two components. Those skilled in the art can understand the specific meaning of the above terms in this application based on the specific circumstances.
[0025] The following section provides a detailed description of the UAV-mounted cryogenic refrigeration system and its coupling control method with the flight control system, using the application scenario of heavy-duty cryogenic refrigerator transportation by UAV. In this embodiment, the UAV carries a heavy-duty refrigerator with a built-in cryogenic refrigeration system, weighing approximately 50 kg. The refrigerator uses a mixture of three hydrocarbon refrigerants—R600a, R1150, and R50—in a specific mass ratio. The UAV may be used for example to perform vaccine transportation tasks from a city disease control center to an island health station. It should be noted that the method of this application is applicable to other scenarios requiring the coupling control of precision temperature control equipment with the UAV flight control system; this embodiment is only for illustrating the technical solution.
[0026] In this embodiment, before the UAV takes off, the ground station sends a mission start command to the flight control and cooling system controllers. After completing their self-tests, the flight control and cooling system controllers begin executing the coupling control method of this application, which specifically includes the following steps: S1, acquire the multi-physics state parameters of the cryogenic refrigeration system mounted on the UAV; Figure 2 This is a schematic diagram of the piping structure of the ultra-low temperature refrigeration system in a heavy-duty refrigerator. According to... Figure 2 The ultra-low temperature refrigeration system provided in this embodiment includes a compressor 1, an anti-condensation pipe 2, a condenser 3, a cooling fan, a dryer filter 4, a vapor-liquid separator 5, a plate heat exchanger 6, a secondary capillary tube 7, a main capillary tube 8, and an evaporator 9.
[0027] The acquisition of multi-physics state parameters involves deploying a comprehensive sensing array at seven nodes in the refrigeration system: the compressor exhaust port, compressor casing, lower part and outlet pipe of the vapor-liquid separator, cold-side inlet and hot-side outlet of the plate heat exchanger, flattened copper pipe section at the evaporator inlet, and compressor return pipe. This array is then used to collect multi-physics state parameters in real time. Each sensor is fixed using adjustable clamps or magnetic bases to accommodate individual differences between different batches of refrigerators.
[0028] The specific deployment methods for each sensor are as follows: exist Figure 2 At the exhaust port copper pipe of compressor 1 shown, a thin-film pressure sensor and a PT1000 surface-mount temperature sensor are fixed with clamps. The temperature sensor is in contact with thermally conductive silicone grease. The thin-film sensor is only 1.2 mm thick, which does not affect heat dissipation. The PT1000 exhibits linear resistance change within the range of -40℃ to 150℃, and its resistance at -85℃ is approximately 18.5 ohms. Lead resistance can be eliminated through three-wire measurement. In this embodiment, a thin-film pressure sensor was chosen instead of a traditional cylindrical sensor because the compressor surface has dense heat dissipation fins, and a cylindrical sensor would obstruct airflow, leading to localized overheating.
[0029] Two 3mm diameter holes are made in the lower middle part (30mm from the bottom) of the vapor-liquid separator 5 to install dual probes of a capacitive liquid level sensor. The distance between the two probes is preferably 10mm. When the liquid R600a level is higher than the lower probe, the change in dielectric constant causes an increase in capacitance, outputting a 4-20mA signal. Simultaneously, a high-frequency pressure sensor is installed on the separator's outlet pipe via a tee connector, with a preferred response frequency of 10kHz. The liquid level sensor determines whether there is sufficient liquid refrigerant. In this embodiment, the vapor-liquid separator design relies on gravity separation. When the UAV tilts more than 10°, the liquid level drops sharply, leading to insufficient oil return from the compressor. The high-frequency pressure sensor is used to capture suction pressure pulsations caused by liquid level fluctuations, providing tilt indicators for subsequent real-time risk modeling.
[0030] Miniature NTC thermistors are secured to the cold-side inlet pipe (liquid R600a from the vapor-liquid separator 5) and hot-side outlet pipe (leading to the main capillary tube 8) of plate heat exchanger 6 using stainless steel clamps. To prevent short circuits caused by condensate, the thermistor leads and wire ends are encapsulated with thermally conductive silicone, which cures to form a waterproof protective layer. Dual-point temperature difference... , This indicates the temperature sensed by the thermistor located at the hot-side outlet of the plate heat exchanger. This indicates the temperature sensed by the thermistor located at the cold-side inlet of the heat exchanger. During normal operation... Approximately 35-40℃. When A sudden decrease, such as a drop to 20°C, indicates frost buildup or internal blockage in the heat exchanger, which is usually a chain reaction of a failed vapor-liquid separator.
[0031] At the flattened section of the inlet copper pipe of evaporator 9, preferably 50mm from the flattening start point, a 1mm diameter thermocouple is welded using a handheld welding machine. This welding method ensures a strong weld and rapid thermal response even at -85℃. Simultaneously, an ultrasonic flowmeter clamp is attached to the outside of this pipe section, and the instantaneous flow rate of liquid R50 is measured using the time-of-flight method. Since R50 is liquid at -85℃ and its density is known, the flowmeter outputs the volumetric flow rate. Traditional electromagnetic flowmeters suffer from severe electrode polarization at low temperatures and cannot function; therefore, in this embodiment, a non-invasive ultrasonic measurement method is used.
[0032] A capacitive oil level sensor is installed in the compressor's return line, preferably 100mm from the suction port, with the probe extending into one-third of the pipe's inner diameter. This sensor utilizes the difference in dielectric constant between the lubricating oil and the refrigerant; as the oil level decreases, the capacitance decreases. Simultaneously, an R50 gas concentration sensor is installed. R50 is gaseous and flammable at room temperature; a leak concentration exceeding 100ppm poses a risk. The oil level sensor is directly related to the compressor's wear life, while the R50 concentration sensor provides the trigger conditions for an emergency landing of the drone.
[0033] Through the above deployment, a comprehensive sensing array covering thermodynamic phase state and mechanical vibration is formed. The UAV flight control terminal can obtain key parameters in real time such as compressor exhaust pressure, temperature, liquid level and suction pulsation of vapor-liquid separator, heat exchanger efficiency, evaporator inlet flow and temperature, return oil level, and R50 leakage concentration, providing a data foundation for subsequent UAV attitude correction.
[0034] After being filtered by the conditioning circuit, the sensor signal is converted into a digital quantity by the ADC and transmitted to the flight control computer via a low-power wireless protocol. After receiving the data, the flight control computer adds a timestamp to each frame of data to synchronize with the flight control signal and stores the status parameters of each dimension into a memory circular queue in a unified format.
[0035] It should be noted that in this embodiment, the sensor deployment positions for heavy-duty refrigerators of the same model but different batches may differ to avoid measurement data deviating from the true value due to manufacturing tolerances of individual refrigerators or batches. In this embodiment, the integrated sensing array composed of various sensors provides the data basis for correcting the UAV's flight attitude. The UAV's correction effect directly affects the reliability of cryogenic cooling during flight. Therefore, when the sensor placement is unreasonable, it not only affects the UAV's correction effect but also indirectly affects the reliability of cryogenic cooling during flight. Therefore, the placement of each sensor... Figure 2 The effectiveness of the arrangement of sensors in the cryogenic refrigeration piping is crucial. However, different models, and even different batches of the same model, manufactured by different companies have varying manufacturing tolerances. If the same sensors are deployed in the same locations for all heavy-duty refrigerators shipped from all channels, it may be difficult to maintain the cryogenic temperature at -80°C in a drone transport scenario involving -85°C cryogenic refrigerators, which is unacceptable. Therefore, to address this issue, after each flight, this embodiment identifies sensors whose measurement deviation exceeds the deviation threshold based on the calculated cryogenic refrigeration effect score, and drives the sensors with measurement deviations to move to the corresponding step size position. Then, the flight is restarted, and this process is repeated multiple times until the measurement deviations at each node converge.
[0036] Specifically, firstly, a continuous period of time exceeding 30 seconds in a horizontal attitude is extracted from the flight data and used as an analysis window. The horizontal attitude parameters include roll angle φ ≤ 5°, pitch angle θ ≤ 5°, and ground speed stable at 2-4 meters per second. Within this window, the average and standard deviation of four key indicators—evaporator inlet temperature, compressor discharge pressure, return oil level, and compressor power—are calculated.
[0037] Then, the scores for each indicator are calculated, including the evaporator inlet temperature score S_te, the compressor discharge pressure stability score S_pr, the return oil level score S_oil, and the compressor power score S_po. The temperature score S_te is calculated based on the target evaporation temperature T_tar for this heavy-duty refrigerator model (-85℃ in this embodiment), S_te=max(0,1-|T_avg-T_tar| / 3), where a score of 0 is given if the temperature deviation exceeds 3℃. It should be noted that the 3℃ tolerance comes from the ±2℃ temperature control accuracy achieved through improvements to the evaporator structure in this embodiment, plus a ±1℃ margin due to the transportation environment; it is not arbitrarily set.
[0038] The compressor discharge pressure stability score is S_pr=max(0,1-σ_P / 0.3), where σ_P is the standard deviation of the compressor discharge pressure within the stability window, and the maximum allowable fluctuation is set to 0.3Kgf / cm2. It should also be noted that 0.3Kgf / cm2 is not arbitrarily set, but rather derived from the fluctuation range of discharge pressure during normal operation obtained through experimental analysis. Exceeding this range indicates that tilting has caused a shift in the compressor's operating point.
[0039] The return oil level score S_oil=min(1,L_avg / L_min), where L_avg is the average return oil level of the compressor within the stable window, and L_min is the minimum allowable oil level of the compressor. The time score is 0 when the oil level is below this value.
[0040] The compressor power score S_po = max(0, 1 - |P_avg - P_base | / (0.1P_base)), where P_base is the rated power of the refrigeration system under standard operating conditions, with an allowable deviation of 10%. This deviation is not arbitrarily set but is determined based on the power variation pattern with operating conditions obtained through experimental analysis. P_avg represents the average compressor power within the stable window.
[0041] Finally, the evaporator inlet temperature score (S_te), compressor discharge pressure stability score (S_pr), oil return level score (S_oil), and compressor power score (S_po) are weighted and fused to obtain the ultra-low temperature refrigeration performance score within the stability window. A higher score indicates better refrigeration performance. It should be noted that the weighting is based on a sensitivity analysis of the impact of each parameter on refrigeration performance; for example, a 1°C deviation in evaporator temperature has a much greater impact on the chamber temperature than a 5% power fluctuation. In this application, the preferred weights for S_te, S_pr, S_oil, and S_po are 0.4, 0.2, 0.2, and 0.2, respectively. Since the weighting is not within the scope of the claims in this application, it will not be specifically detailed.
[0042] In this application, the method for identifying whether the measurement deviation of the sensor exceeds the corresponding deviation threshold is as follows: When it is determined that during the same flight, the number of sensors whose cryogenic cooling effect scores for each steady-state analysis window are lower than the preset score threshold is greater than the preset number threshold, a prompt is made to optimize the sensor position, calculate the root mean square error of the sensing data of each sensor during the flight, then filter out the sensors whose root mean square error exceeds the corresponding deviation threshold, and instruct the drive mechanism to drive the selected sensors to move the corresponding step length.
[0043] For example, if the overall score for a certain steady-state analysis window is 0.42, and the preset score threshold is, for example, 0.8, the system determines that the cooling effect within that window is poor. If the number of such determinations exceeds a preset threshold during the same flight, the system determines that the sensor positions need to be optimized. Then, the system compares the measured values of each sensor with the theoretical expected values point by point, calculating the root mean square error (RMSE) for the entire flight. For example, the RMSE ranking for this flight is as follows: The root mean square (RMS) error of the evaporator inlet temperature sensor is 2.3℃, the RMS error of the compressor discharge pressure sensor is 0.38 kgf / cm², and the RMS error of the vapor-liquid separator level sensor is 3.1℃. The RMS errors of other sensors are all within the allowable range. However, the individual scores show that the pressure stability score is 0 and the evaporator temperature score is only 0.4, indicating that the system primarily focuses on the evaporator inlet temperature sensor and the vapor-liquid separator level sensor. The system then instructs the drive mechanism or prompts the operator to manually move the selected sensors by the corresponding step size. For example, if the evaporator inlet temperature sensor thermocouple is welded to the end of a flattened copper tube, with an initial position 50mm from the flattening point, system analysis reveals that the sensor's temperature reading is systematically low throughout the flight, but the response time is normal, indicating that it is not a fault but rather that the measurement point is located in a supercooled region. Therefore, it is recommended to move the sensor 2mm towards the evaporator body to get closer to the actual phase change area. The on-site operator sees a prompt on the software interface: "Evaporator inlet temperature sensor suspected of being in a supercooled region; please move it 2mm along the pipeline axis towards the evaporator." The operator only needs to loosen the clamp, move the sensor, and then tighten it again.
[0044] After the adjustment is completed, a second test flight is conducted on the same route, and the cooling effect score is calculated again until the overall score is greater than the preset score threshold.
[0045] After obtaining the multiphysics state parameters of the cryogenic refrigeration system mounted on the UAV, the coupling control method between the refrigeration system and the flight control system proceeds to the following steps: S2, generates a health index based on the degree of deviation between the multiphysics field state parameters and the preset safety envelope; The flight control computer reads the current multiphysics state parameter vector from the circular queue. In this embodiment, the preset safety envelope is a set of multidimensional boundaries, including the compressor exhaust pressure upper limit of 16.5 kgf / cm². 2 Lower limit of inspiratory pressure: 0.7 kgf / cm 2 The target value for evaporator inlet temperature is -85℃, with an allowable fluctuation of ±3℃. The maximum allowable tilt angle for the compressor is 10°. The maximum allowable vibration acceleration is 0.6g. The minimum liquid level threshold for the gas-liquid separator, the minimum oil level threshold for oil return, and the refrigerant leakage concentration threshold are set according to the experimental conditions.
[0046] For each dimension's state parameter, calculate its deviation from the corresponding safety envelope boundary. Taking exhaust pressure as an example, if the current measured value is P and the upper limit is Pmax, then the deviation dP = (P - Pref) / (Pmax - Pref), where Pref is the normal operating point reference value. When the measured value is lower than the lower limit or higher than the upper limit, the deviation is forcibly assigned a value of 1. After calculating the deviation for each dimension, take the weighted average of the two dimensions with the largest deviations as the main score, and use the root mean square of the sum of squares of the deviations for the remaining dimensions as the fluctuation penalty term. Subtract the fluctuation penalty term from the main score to obtain the health index H, where H ranges from 0 to 1. The closer the health index is to 1, the better the refrigeration system's condition; the closer it is to 0, the closer it is to failure.
[0047] In step S2, it is important to emphasize that the preset safety envelope is not a fixed value, but a dynamically adjusted value based on the load and efficiency metrics. The method for dynamically adjusting the preset safety envelope is as follows: During the operation of the refrigeration system, the compressor discharge pressure Pdis and the vapor-liquid separator level Lsep are collected simultaneously. The discharge pressure reflects the current load level of the compressor; the higher the discharge pressure, the greater the work done by the compressor, and the heavier the load on the refrigeration system. The vapor-liquid separator level reflects the circulation state of the refrigerant in the system; a low level indicates insufficient refrigerant or abnormal distribution, while a high level indicates excessive liquid return.
[0048] The product of discharge pressure and liquid level is used as the load characterization quantity L, i.e., L = Pdis × Lsep. The physical meaning of this product is as follows: when both discharge pressure and liquid level rise simultaneously, it indicates that the compressor is operating under high load and the refrigerant circulation is sufficient, meaning the system is under heavy load. When discharge pressure rises but the liquid level falls, it indicates that the system may have refrigerant leakage or abnormal throttling, representing an abnormally high load. This product relationship allows information from two dimensions to be integrated into a comprehensive indicator, avoiding misjudgments based on a single parameter.
[0049] It should be noted that the load characterization value L is not arbitrarily defined, but is derived from the experimental data in Table be of the applicant's specification in application number "CN202511796084.9" and patent title "Refrigerant Mixture and Refrigeration System Applied to Ultra-low Temperature Refrigeration System". That is, the load characterization value L defined in this application depends on the mass proportions of R600a, R1150, and R50 being controlled at 63.59%, 34.91%, and 1.50%, respectively.
[0050] Furthermore, the evaporator inlet temperature (Tev) and compressor discharge pressure (Pdis) are collected simultaneously. The evaporator inlet temperature reflects the actual cooling effect of the refrigeration system under the current operating conditions; the lower the temperature, the better the cooling effect. The discharge pressure reflects the cost of the compressor's work; the higher the pressure, the greater the energy consumption.
[0051] The ratio of evaporator inlet temperature to exhaust pressure is used as the efficiency indicator, Eff, where Eff = Tev / Pdis. The physical meaning of this ratio is: under the same exhaust pressure, the lower the evaporation temperature, the higher the system's refrigeration efficiency; and under the same evaporation temperature, the lower the exhaust pressure, the more economical the system's operation. This ratio allows for a comprehensive evaluation of the refrigeration system's operating efficiency under current conditions. The efficiency indicator Eff is derived from experimental data in Table be of the applicant's patent application (CN202511796084.9), entitled "Refrigerant Mixture and Refrigeration System Applied to Ultra-Low Temperature Refrigeration Systems," and is not arbitrarily defined.
[0052] After obtaining the load characterization quantity L and the efficiency characterization quantity Eff, the values of each safety envelope boundary are dynamically adjusted according to the mapping relationship between the load characterization quantity and the efficiency characterization quantity. The method is as follows: The system records a set of data points (load and efficiency metrics) every 10 minutes within a fixed time window to form a data point cloud on a two-dimensional plane. When the system is in a healthy state, these data points should be distributed within a specific area. Efficiency decreases slightly when the load increases but remains within an acceptable range, and efficiency recovers when the load decreases.
[0053] However, as equipment ages or operating conditions change, the distribution area of data points may drift. The system dynamically adjusts the safety envelope boundary in the following ways: For example, based on the point cloud data from the most recent 24 hours, the mean and standard deviation of the efficiency metrics within each load range are calculated. The mean ± 3 times the standard deviation is taken as the normal efficiency range within that load range. When new data points consistently fall outside the normal range, it indicates that the equipment performance has changed, and the system updates the corresponding safety envelope boundary values accordingly. For instance, if efficiency continues to decline under the same load, it indicates that the compressor or heat exchanger performance has degraded, and the system lowers the upper limit of the discharge pressure or raises the lower limit of the evaporation temperature to reflect changes in the actual load capacity of the equipment.
[0054] After generating the health index in step S2, the UAV-mounted cryogenic refrigeration system and its coupling control method with the flight control system provided in this application proceed to the following steps: S3 dynamically establishes a two-way data channel between the flight control and the cooling system controller; In this application, the main channel of the bidirectional data channel established between the flight controller and the cooling system controller uses a CAN bus wired connection, while the backup channel uses a low-power Bluetooth wireless connection. Both channels transmit the same data simultaneously, and the receiving end detects communication failures by comparing the data consistency between the two channels.
[0055] The bidirectional data channel transmits data in two directions: 1. From the cooling system controller to the flight controller, it transmits the health index H, status parameters of various dimensions, and fault indicators; 2. From the flight controller to the cooling system controller, it transmits the UAV's current attitude angles (pitch, roll, yaw), attitude angular velocity, ground speed, altitude, and vibration acceleration. All data is transmitted through the bidirectional data channel at an update frequency of no less than 10Hz.
[0056] In this application, the method for constructing a bidirectional data channel is as follows: The communication bandwidth between the flight controller and the cooling system controller is a limited resource during UAV flight, especially during long-distance flights or in complex electromagnetic environments, where the bandwidth may be further limited. To transmit the most valuable information within this limited bandwidth, this application uses a health index H as the basis for channel priority classification.
[0057] Specifically, the system presets two thresholds, for example, setting the first threshold Hhigh=0.8 and the second threshold Hlow=0.5. When H≥0.8, the channel operates at the first priority, i.e., the highest priority. At this time, the cooling system is in good condition, and there is no need to transmit a large amount of detailed data, minimizing communication bandwidth usage and reserving valuable bandwidth for the flight controller's own telemetry data. When 0.5≤H<0.8, the channel operates at the second priority (medium priority). At this time, the cooling system has shown a noticeable performance degradation, and more detailed status parameters need to be transmitted for the flight controller to assess the degradation trend. When H<0.5, the channel operates at the third priority, i.e., the lowest priority. At this time, the cooling system is in a dangerous state, and the real-time decision log of the cooling system controller is transmitted for the ground station to perform post-fault attribution analysis.
[0058] Under the first priority, the channel only transmits the health index H and fault flags, with a total data volume of no more than 4 bytes per frame. This streamlined design ensures that the flight controller can still obtain the most critical health status information when communication bandwidth is limited.
[0059] Under the second priority level, the channel, in addition to transmitting multi-physics state data across various dimensions, builds upon the first priority level. This includes real-time values for seven dimensions: compressor discharge pressure, intake pressure, evaporation temperature, liquid level, return oil level, heat exchanger temperature difference, and vibration acceleration. This enables the flight control system to perceive detailed degradation trends in the cooling system, providing data support for tiered adjustments to flight strategies.
[0060] Under the third priority level, the channel supplements the second priority level with the transmission of real-time decision logs from the refrigeration system controller. The decision logs record every control action executed by the controller within the last 60 seconds, including the time, amount, and reason for each compressor speed adjustment. This log data allows the ground station to retrospectively analyze the control logic during emergency phases, determining the timing and cause of any failures.
[0061] Different priorities correspond to different data frame structures. For example, the first-priority frame structure only contains a frame header (including a priority identifier) and a status field (including a health index and a fault flag). The third-priority frame structure appends a decision log field after the status field, significantly increasing the total frame length. The priority identifier in the frame header allows the receiver to directly identify the frame priority without unpacking the data body, thus selectively receiving or discarding low-priority frames based on the current bandwidth conditions.
[0062] It should be noted that the first threshold Hhigh is preferably the average of the maximum health index values within each time window of the preset time series, and the second threshold Hlow is preferably the average of the minimum health index values within each time window of the preset time series. For example, if a time series is 30 days long and each time window is 10 minutes, and within two consecutive time windows, the maximum health index H in the first time window is Hmax1, and the maximum health index H in the adjacent second time window is Hmax2, then the average of Hmax1 and Hmax2 is the first threshold Hhigh corresponding to the time series formed by the first and second time windows.
[0063] Therefore, in this embodiment, the boundary of the preset safety envelope is dynamically adjusted, and the health index is calculated based on the preset safety envelope. The first threshold Hhigh and the second threshold Hlow are also dynamically calculated based on historical health indices. Thus, the constructed bidirectional data channel prioritizes data transmission types using the first threshold Hhigh and the second threshold Hlow, which is also dynamically adjusted. The purpose of this design is to transmit the most valuable data under limited bandwidth conditions, based on changes in the performance of the drone and the refrigeration system. Furthermore, the dual-channel data transmission link design allows for rapid detection of communication failures through simple data consistency checks. This is crucial for scenarios where heavy-duty refrigerators are transported by drones at high altitudes and flight safety must be ensured, enabling the prediction of communication failures and early intervention to execute emergency landing procedures.
[0064] After step S3 completes the dynamic establishment of the bidirectional data channel between the flight controller and the cooling system controller, as follows: Figure 1 As shown, the UAV-mounted cryogenic refrigeration system and its coupling control method with the flight control system provided in this embodiment proceed to the following steps: S4, the flight controller adjusts the flight strategy based on the health index, and the cooling system controller adjusts the cooling parameters based on the flight attitude information; Specifically, the refrigeration system controller receives the current attitude angle and its rate of change from the flight controller at a frequency of 10Hz, and then calculates the compressor speed compensation amount at the current moment. In this application, the feedforward control table is obtained through experimental calibration and records the compressor speed adjustment amount required to maintain stable evaporation temperature under different tilt angles and tilt velocities. The feedforward adjustment amount is output in a manner that is positively correlated with the attitude change amplitude.
[0065] More specifically, when a drone undergoes attitude changes, such as turning, climbing, or descending, the refrigerant distribution inside the refrigeration system will change due to the change in the direction of gravity. Tilting may cause the liquid refrigerant in the vapor-liquid separator to shift, the compressor oil return hole to be partially exposed, and the refrigerant flow at the evaporator inlet to fluctuate. These changes will be reflected in fluctuations in the evaporator inlet temperature.
[0066] The system records the occurrence time of each attitude change event, such as the moment when the attitude angle change exceeds 2°, and the time required for the evaporator inlet temperature to recover to within ±0.5°C of the temperature before the attitude change. This time is defined as the "recovery time". The system maintains a historical record list of recovery times, which may store up to the most recent 100 events. The median of the historical recovery times is used as the time constant of the refrigeration system under the current operating conditions.
[0067] The system then divides the historical data into multiple intervals based on the magnitude of attitude change, for example, each interval has a width of 2°, such as attitude changes between 0° and 2°, 2° and 4°, 4° and 6°, etc. For each interval, historical data points within that interval are collected, and each data point contains two variables: recovery time t and compressor speed adjustment ΔRPM. Linear regression is performed on multiple sets of data (t, ΔRPM) within the same interval, with t as the independent variable and ΔRPM as the dependent variable, to fit a straight line ΔRPM = kt + b, where the slope k is the compensation coefficient for that attitude change range, and b is a constant term to be solved.
[0068] When the flight controller sends new attitude data, the cooling system controller calculates the difference in attitude angle between the current moment and the previous moment, and then divides it by the time interval to obtain the attitude change rate v. Based on the magnitude of the current attitude angle change, a specified interval is determined, and the corresponding compensation coefficient k is extracted. The compressor speed compensation amount at the current moment = v × k.
[0069] It should also be noted that the flight controller adjusts the flight strategy based on the health index as follows: The flight control computer dynamically adjusts the flight strategy based on the received health index H. When H ≥ 0.8, the flight control operates in normal flight mode, allowing a maximum roll angle ≤ 15°, a maximum pitch angle ≤ 12°, a maximum angular velocity ≤ 20° / s, and a maximum ground speed ≤ 15m / s. When 0.5 ≤ H < 0.8, the flight control operates in protective flight mode, limiting the maximum roll angle to ≤ 8°, the maximum pitch angle to ≤ 6°, the maximum angular velocity to ≤ 10° / s, and the maximum ground speed to ≤ 8m / s, and continuously outputting a "low cooling system health" message on the flight control status display. When H < 0.5, the flight control operates in emergency flight mode, automatically planning a safe landing path and triggering a landing.
[0070] The method for automatically planning a safe landing path in this application is briefly described as follows: In the automatic safe landing path planning step, the flight controller first checks the current roll rate, assuming it is 18° per second (too high), and immediately limits the roll rate command to, for example, ±5° per second. Specifically, a saturation function is set before the derivative term input of the PID controller. This saturation function defines the control limit of the roll rate to prevent excessively high angular velocity commands from causing violent sloshing of the refrigerant level inside the refrigerator.
[0071] Then, the callback rate is calculated, and the callback rate coefficient K is dynamically set based on the health index H=0.78. 回调 =1-H / 0.8=0.025 (In this embodiment, it is preferred to set the callback rate coefficient to 0 when H=0.8), and the maximum callback angular velocity is set to K. 回调 ×18° per second. Since the current angular velocity adjustment is limited to 5° per second, this upper limit will not be exceeded during the actual pullback. The design of the pullback rate being negatively correlated with the health index H ensures that when H approaches 0, the controller will pull back at the fastest speed to avoid triggering a higher-level emergency landing. K 回调 If the value is less than 0, the PID controller will directly output a callback rate of 0, which means that no adjustment of the drone's attitude is required.
[0072] When the attitude angle stabilizes within the safe range and the health index H increases to 0.5 or above, the system removes the angular velocity limit. During this correction process, the drone's altitude remains almost unchanged, avoiding other risks caused by emergency maneuvers.
[0073] While executing step S4, the flight controller continuously monitors whether the health index is below the threshold (0.5) or whether a refrigerant leak is detected. If so, the flight controller immediately executes the emergency landing procedure, and the refrigeration system controller simultaneously executes the safety shutdown procedure.
[0074] Specifically, when the health index H remains below 0.5 for more than 3 seconds, it is considered a severe system degradation fault, and the refrigeration system controller sends a fault type code, such as 00x1, to the flight controller. When the refrigerant concentration sensor detects an R50 concentration exceeding 100 ppm for more than 1 second, it is considered a refrigerant leak fault, and the refrigeration system controller sends a fault type code, such as 00x2, to the flight controller. Upon receiving fault type code 00x1, the flight controller executes a descent procedure, with a vertical descent speed not exceeding 0.5 meters per second and a horizontal acceleration not exceeding 0.3g. Upon receiving fault type code 00x2, the flight controller executes an emergency landing procedure, forcibly avoiding fire sources and areas with large crowds during the landing path planning.
[0075] After sending an emergency shutdown request, the refrigeration system controller simultaneously executes the safety shutdown procedure, first cutting off the refrigerant pipeline solenoid valve, then shutting down the compressor, and reporting the status of each actuator to the flight controller.
[0076] Specifically, when the refrigerant concentration sensor detects a leak, the system reads the current health index H value (between 0 and 1) and uses it directly as the weighting coefficient w. w=1 indicates that the refrigeration system is completely healthy but has a leak, while w=0 indicates that the refrigeration system has completely failed and has a leak, which is the most serious situation.
[0077] The system then presets a maximum search radius Rmax, which represents the maximum area that the UAV can search under ideal conditions, i.e., when w=1. The actual search radius Ra=Rmax×w.
[0078] Within the actual search radius, the system searches for candidate points that meet the following landing conditions: The gas concentration decay curve value at the candidate point is lower than the safety threshold, and the angle between the line connecting the candidate point and the leak source and the wind direction is greater than a first preset angle, such as 30°. The angle condition is used to ensure that the landing point is not on the downwind path of the leaking gas, so as to avoid the drone being continuously exposed to a high concentration of refrigerant during landing.
[0079] In this application, the gas concentration decay curve value is calculated using the following formula:
[0080] in, This represents the gas concentration decay curve value of the UAV at coordinate point (x, y); Q represents the intensity of the leak source, which is derived by inferring the gas concentration value detected by the concentration sensor, or it can be directly replaced by the gas concentration value detected by the sensor. Let y be the wind speed of the drone at coordinate point (x, y, z), y be the horizontal distance of the predicted point (candidate point) relative to the leak source in the direction perpendicular to the wind direction, i.e., the crosswind distance, and z be the height of the predicted point relative to the leak source in the vertical direction. and These represent the diffusion parameters in the crosswind and vertical directions, respectively, and the diffusion width of the gas in the corresponding direction. They are obtained by referring to tables in manuals such as the "Ambient Air Quality Standards" or by using empirical formulas, based on the atmospheric stability category and the downwind distance of the leak source.
[0081] When no candidate landing point meets the landing conditions within the actual search radius, the safety threshold in the landing conditions is dynamically relaxed based on the health index H. The preferred relaxation rule is: for every 0.1 decrease in H, the safety threshold increases by 10 ppm. The limit of relaxation is when H=0, the safety threshold increases to 100 ppm. This dynamic relaxation mechanism ensures that even in extreme cases, such as when H is very low and the search range is very small, the UAV can still find a barely acceptable landing point, rather than being forced to crash due to the inability to find a perfect landing point.
[0082] When computing power and bandwidth are sufficient, this application also provides another method for automatically planning a safe landing path, which is described in detail below: If the health index H remains below the safety threshold for m seconds, or if one or more of the following are detected: refrigerant R50 leakage or compressor overpressure, a dynamic safety equipotential surface is constructed that integrates terrain, fire source, gas diffusion model, and liquid level fluctuation. Model predictive control is used to search for the minimum potential energy path, and acceleration limits are correlated with real-time liquid level fluctuations. Finally, a smooth landing is executed and a leak diffusion warning is pushed out.
[0083] Specifically, for example, if a drone detects an R50 gas concentration of 150 ppm during flight, and the liquid level fluctuation in the vapor-liquid separator reaches 2.5 times the normal value, with a southwest wind, an emergency landing path needs to be planned. The method is as follows: On a three-dimensional grid, such as a resolution of 5m×5m×2m and a range of 500m×500m×100m, calculate the potential energy value E(x,y,z) of each grid point, where x, y, and z represent the horizontal, vertical, and z-axis coordinates of the grid point in three-dimensional space, respectively, preferably the coordinates of the center point of the grid.
[0084] In this embodiment, the potential energy value of each grid point preferably includes a weighted sum of one or more of the following: ground potential energy value, fire source potential energy value, crowd potential energy value, gas diffusion potential energy value, and liquid level sloshing potential energy value of the vapor-liquid separator. The real-time update frequency is preferably set to 2Hz.
[0085] The preferred method for calculating terrain potential energy is as follows: Set the potential energy of flat areas with an elevation 5 meters lower than the surrounding average to 0, and set the potential energy of steep slopes exceeding 15° to 1, guiding the drone to preferentially land on low-lying, flat areas. The method for calculating the potential energy of a fire source, for example, is: using the coordinates of the gas station as the center, and employing... For example, when the drone is 30 meters away from the gas station, its potential energy is 0.83, and when it is 10 meters away, its potential energy is 0.92, forcing the path away from the fire source. This represents the Euclidean distance from the drone's current location to the hazard source. The standard deviation is preferably set based on the hazard radius of the hazard source, such as that of a gas station. The distance is set at 50 meters. The calculation method for the crowd potential energy is the same as that for the fire source potential energy, and will not be repeated here. The solution method for the gas diffusion potential energy is: calculate the concentration at the ground centerline. ,in The leakage intensity is, for example, 0.5 g per second; This refers to wind speed, for example, 4 m / s. This refers to the downwind distance (the horizontal straight-line distance from the leak source point to a point in space along the wind direction), for example, 200m. , For diffusion parameters, the preferred calculation method is: , .Will =200, =0.5, Substituting 4 into the equation, we get... =0.000239g / m 3 Assume the alarm threshold is set to 0.0008 g / m³. 3 Therefore, it is preferable to express the gas diffusion potential energy value as the ratio of 0.000239 to 0.0008, i.e., 0.3.
[0086] The level of liquid sloshing potential energy in the vapor-liquid separator directly affects the precise temperature control effect of the cryogenic refrigeration system. It should be noted that the ability to control the cryogenic refrigeration at -82℃ is the result of a combination of factors, including the flattened and bonded structure of the evaporator's copper tubes, the control of liquid level sloshing potential energy, the dynamic construction of a multi-physics field real-time monitoring network, and iterative attitude correction for the UAV. Therefore, liquid level sloshing potential energy is a key factor to consider during UAV flight control and emergency landing, and is one of the core technologies of this application.
[0087] In this application, the liquid level fluctuation amplitude ΔL of the vapor-liquid separator is monitored in real time and normalized to the 0-1 range. The maximum allowable fluctuation amplitude of ΔL is set to 10mm. Then, the liquid level sloshing potential energy is normalized to ΔL / 10. The function of this liquid level sloshing potential energy is to guide the path as far away as possible from the moment of violent liquid level fluctuation. The method is as follows: Assume the prediction time N is 10 seconds and the sampling time Δt is 0.5 seconds. Define the UAV's state variables at the k-th prediction time as xk=[Xk,Yk,Zk,Vxk,Vyk,Vzk]. T Let Xk, Yk, Zk represent the x-axis, y-axis, and Z-axis coordinates of the UAV's position at time k, and Vxk, Vyk, Vzk represent the velocity components of the UAV at time k along the x-axis, y-axis, and Z-axis, respectively. Assume the acceleration control applied to the UAV at time k is ak = [axk, ayk, azk]. T axk, ayk, and azk are the control components of acceleration ak on the horizontal, vertical, and Z axes, respectively.
[0088] In this application, the constructed path planning optimization objective J is:
[0089] Indicates the number of predicted times; , These represent the potential energy values at the k-th and N-th steps, respectively, which are the weighted sums of the ground potential energy, the fire source potential energy, the crowd potential energy, the gas diffusion potential energy, and the liquid level sloshing potential energy of the vapor-liquid separator. , The weighting coefficients are preferably 0.1 and 5, respectively.
[0090] The value of is subject to the following constraints: 1. ,in =0.3 ; It is the acceleration due to gravity; 2. azk≤0.4g; In addition, the maximum landing speed Vzk ≤ 1.5 m / s; the fire source exclusion zone is preferably ≥ 30 meters, that is, the drone must always stay away from fire sources such as gas stations ≥ 30 meters away; the downwind high concentration prohibited zone, that is, the gas diffusion potential energy value must be ≤ 0.4.
[0091] In this application, the method for solving the cost function is explained by example as follows: Let the current state of the UAV (at time k=0) be: position (0,0,75) m, velocity (12,0,0) m / s, and liquid level fluctuation ΔL be 2.5 mm. 2.2 m / s2 The fire source is located at (150,0,0), downwind of the positive X-axis, i.e., the wind speed is along the X-axis, and the gas diffusion potential energy is >0.4 in the region X>100m.
[0092] The solver searches for control sequences a0, a1, a2, ..., a19 in the prediction time domain (e.g., prediction point N=20) such that: The position is recursively calculated as follows: the horizontal coordinate of the UAV at time k+1 is Xk+1 = Xk + Vxk△t + 0.5axk△t 2 The velocity of the UAV on the horizontal axis at time k+1 is Vxk+1 = Vxk + axk△t; the calculation methods for the vertical axis and Z-axis coordinates of the UAV's position at time k+1 are the same as those for Xk+1, and will not be repeated here.
[0093] The initial conditions are: X0=0, Vx0=12, Y0=0, Vy0=0, ZO=75, Vz0=0.
[0094] Hard constraints: |axk|≤2.2, |ayk|≤2.2, |azk|≤3.92, Vzk≥-1.5, negative values indicate descent speed; location is far from the fire source.
[0095] The method for solving the cost function to obtain the optimal control sequence includes the following steps: The trajectory planning is transformed into a quadratic programming problem with control acceleration as the decision variable, including dynamic safety equipotential surfaces and linear motion constraints, where the upper limit of acceleration is correlated with the liquid level fluctuation of the vapor-liquid separator in real time. For example, in an emergency landing triggered by an R50 leak, a dynamic safety equipotential surface has been established, and the liquid level fluctuation ΔL = 2.5 mm results in an upper limit for horizontal acceleration. =2.2m / s 2 The goal is to find the optimal trajectory with a prediction time domain of 10 seconds and N=20 steps within 0.5 seconds.
[0096] First, define the decision variable vector z, which contains all control accelerations: z = [ax0, ay0, az0, ax1, ay1, az1, ..., axk, ayk, azk, ..., ax19, ay19, az19] T There are a total of 60 variables.
[0097] Cost function To rewrite it as a quadratic form 0.5 × z T Hz+f T z, in this embodiment, undergoes linearization processing. Wherein, z T Let f be the transpose of the decision variable vector z, f be a column vector, and f be the coefficients of the linear terms. T Let f be the transpose of f, and H be a symmetric matrix. 0.5×zT Hz+f T z expanded as: , This represents the element in the i-th row and j-th column of matrix H. It is the i-th component of f. It is the i-th component of z. It is the j-th component of z.
[0098] This embodiment addresses the cost function. The method for linearization is as follows: A first-order Taylor expansion near the current reference trajectory yields the coefficients of the linear terms. The quadratic term H originates from the squared acceleration term; therefore, H is a diagonal matrix with diagonal elements of 0.2, due to 0.5 Hz. 2 =0.1z 2 Therefore, H = 0.2.
[0099] The equality constraint is a state recursion. For example, X(k+1) = Xk + Vxk × Δt + 0.5axk × Δt 2 Let X(k+1) represent the horizontal coordinate of the UAV's position at time k+1, and Vx(k+1) = Vxk + axk × Δt, where Vx(k+1) represents the velocity component of the UAV's velocity on the horizontal axis at time k+1. Representing Xk and Vxk at each time step as a linear combination of the initial state and ax, and substituting them into the equation, forms a linear equality constraint matrix.
[0100] The inequality constraints are: axk ≤ 2.2, ayk ≤ 2.2, and the horizontal composite acceleration ≤ 2.2. Simultaneously, azk ≤ 3.92, and the descent velocity Vzk ≥ -1.5. The location restriction constraint is, for example, a distance of ≥ 30m from the gas station. This is converted to a linear inequality approximation. All these constraints are written as lb ≤ Az ≤ ub, where A represents the constraint matrix (i.e., the linear equality constraint matrix obtained above), z is the decision variable vector, lb is the lower bound vector, and ub is the upper bound vector.
[0101] After transforming trajectory planning into a process with control acceleration as the decision variable, the method for generating the optimal control sequence proceeds to the following steps: To solve the quadratic programming problem, the gradient is calculated in each iteration using the real-time updated potential energy field, and the acceleration hard constraint is satisfied through projection. The specific method is as follows: The solver initializes the decision variable vector z as the zero vector z. (0) =0, the first iteration process is as follows: Calculate the current trajectory. For example, if the current trajectory is a uniform straight flight, the trajectory is at the 10th step, i.e., k=10, when the trajectory enters the gas diffusion forbidden zone and the potential energy is extremely high. Then, calculate the gradient ▽J, since Within the restricted area, the gradient, for example, points in the direction requiring deceleration and right yaw. The gradient ∠J is calculated as follows: based on the position coordinates of each point on the predicted trajectory using the current control sequence z, the partial derivative of the potential energy with respect to the position point in the cost function is backpropagated to each control acceleration, and the derivative of the squared acceleration term is added to obtain the partial derivative of J with respect to each decision variable, expressed by the formula: =
[0102] in, Indicates the position of the drone at step j. The partial derivative of the safety potential energy with respect to position is obtained from the numerical derivation of the dynamic safety equipotential surface. Let be the linear transfer coefficient of position to control acceleration. The gradient of the squared acceleration term, This is a preset hyperparameter, preferably 0.1.
[0103] Then, in each iteration, the decision variable z is updated by minimizing the augmented Lagrange function, which includes the objective function, the quadratic penalty for constraint violations, and the Lagrange multipliers, i.e.: The original variable update formula is expressed as: , , This is the penalty parameter, used to control the weight of constraint violations; Dual variables, the constraints in the primal problem are =b, where b is a constant vector. Let be the dual variable of step i. for The transpose of .
[0104] Then update the dual variable y, as follows: ; Finally, Projecting axk and ayk onto the interval [-2.2, 2.2] and projecting azk onto [-3.92, 3.92], we get... The projection method is as follows: if axk < -2.2, then take 2.2; if axk > 2.2, then take 2.2; otherwise, leave it unchanged. The projection principle of ayk is the same as that of axk, and will not be repeated here.
[0105] Then a second iteration is performed, based on... Recalculating the trajectory revealed that a point still entered the edge of the restricted area. The gradient guidance was further adjusted, resulting in... After repeating 20-30 times, the original residual and / or dual residuals All less than 1 The time convergence ultimately yields a smooth obstacle avoidance and deceleration trajectory.
[0106] After obtaining the smooth obstacle avoidance and deceleration trajectory, the method for generating the optimal control sequence proceeds to the following steps: Each control cycle executes the first control variable in the optimal control sequence, then re-initializes and solves with the updated refrigeration system state, forming a rolling closed-loop optimization, specifically: The flight control system retrieves the first control variable a0 from z, for example, a0=[ax0=-1.5,ay0=1.2,az0=0.0] and executes it. After 0.5 seconds, the system status is updated, and the liquid level fluctuation becomes, for example, ΔL=2.6mm. The flight control system uses the new status as the initial condition to reconstruct the equipotential surface and solve it again. The path for the next cycle is automatically adjusted to ensure flight safety.
[0107] In this application, in order to reduce the impact of UAV body vibration on the ultra-low temperature cooling effect of the refrigeration system, the vibration transfer function of the refrigerator and the UAV mounting mechanism is obtained to actively reduce the vibration of the refrigerator. The specific method is as follows: After the design and assembly of the mounting mechanism are completed, white noise is applied to the mounting mechanism using a vibrator, with the frequency range controlled between 10Hz and 200Hz. At the same time, the accelerations au(t) and ar(t) at the UAV connection point are measured. Then, Fourier transform is performed on the two sets of acceleration signals to obtain the corresponding frequency domain representations Au(f) and Ar(f), and the vibration transfer function H(f) = Ar(f) / Au(f) is designed.
[0108] In this embodiment, an acceleration sensor for collecting acceleration au(t) is installed at the connection interface between the UAV body and the mounting mechanism, i.e., at the fixing point between the upper connecting plate of the mounting mechanism and the UAV body. An acceleration sensor for collecting acceleration ar(t) is installed at the mounting point where the lower end of the mounting mechanism is fixed to the outer shell of the cooling system, i.e., at the connection point between the cooling system support and the mounting mechanism.
[0109] Accelerometers continuously acquire time-domain signals au(t) and ar(t) at a sampling frequency of 1 kHz. The acquired time-domain signals are segmented into time windows of 1 second, and a Hanning window is applied to the signal within each window to suppress spectral leakage.
[0110] A 1024-point Fast Fourier Transform (FFT) is performed on each windowed signal to obtain a complex signal in the frequency domain. The FFT Fourier algorithm, which outputs the input time-domain signal in the frequency domain, is a standard method and will not be detailed here. In the transformed result, the frequency of the k-th frequency point is fk = k × (fs / N), where fs = 1000Hz is the sampling frequency, and N = 1024 is the number of sampling points; therefore, the frequency resolution is approximately 0.976Hz. The complex result for each frequency point is X(fk) = ak + jbk. ak is the real part of the complex number in the frequency domain at the k-th frequency point, directly output by the FFT Fourier algorithm. The input to the FFT is a time-domain signal, and the output is a complex number in the frequency domain. The real part ak and the imaginary part bk are the output results of the FFT, and j is the imaginary unit.
[0111] The amplitude at each frequency point |X(fk)| = sqrt(ak) 2 +bk 2 Phase at each frequency point (fk) = atan2(bk, ak). Frequency data is updated in a 1-second window to obtain the frequency domain representations Au(f) and Ar(f) in real time. sqrt is the square root operation. Taking ak=3 and bk=4 as an example, atan2(4,3) represents the angle between the vector from the origin to point (3,4) and the positive x-axis in a rectangular coordinate system. First, calculate the ratio of bk to ak, i.e., 4 / 3 = 1.333, then calculate atan1.333 = 53.13°.
[0112] During flight, the flight controller collects the airframe vibration spectrum Au(f) in real time. The flight controller calculates the vibration energy E transmitted to the cooling system. When E exceeds the preset threshold Eth, the vibration energy is determined to be excessive.
[0113] When E is greater than Eth, the adjustment amount Δ = E - Eth is calculated. Using Δ as feedback, the setpoint speed of each propeller of the UAV is proportionally reduced by ΔRPMi = -Kpi × Δ, where Kpi is the proportional coefficient of the i-th propeller, calibrated experimentally. i = 1, 2, 3, 4 represent one of the UAV propellers. Reducing the speed will decrease the total thrust of the UAV, therefore the flight control system needs to adjust the attitude angles synchronously to maintain altitude and position. However, the reduction in overall thrust will decrease aerodynamic excitation, thus causing the vibration energy transmitted to the cooling system to gradually converge below the threshold.
[0114] The method by which the flight control system adjusts the attitude angle while reducing the propeller speed is not within the scope of the claims made in this application and will not be specifically described. It should be noted that the proportional coefficient Kpi for each propeller is calibrated separately. The calibration method is as follows: each propeller is run individually with a known speed change applied, and the change in vibration energy transmitted to the cooling system mounting point is measured. The change in transmitted vibration energy divided by the speed change is taken as the Kpi for that propeller.
[0115] In this embodiment, the vibration transfer function H(f) is dynamically updated. The vibration transmission characteristics of the mounting mechanism are not static. With the increase in the number of flights, the connecting parts of the mounting mechanism may experience slight wear, the vibration damping pads may age, and the bolts may loosen slightly. These changes will alter the vibration transfer function. Therefore, the vibration transfer function needs to be continuously updated. The update method is as follows: After each flight mission, the system performs a deconvolution operation on the airframe vibration spectrum Au(f,t) recorded throughout the flight and the measured vibration spectrum Ar(f,t) at the refrigeration system installation point to obtain the actual vibration transfer function Hnew(f) for the flight. Deconvolution in the frequency domain is represented by division, i.e., Hnew(f) = meant(Ar(f,t), Au(f,t), meaning that the amplitude is averaged over the entire time period at each frequency point.
[0116] Suppose that during a single flight mission, the focus is on a frequency f = 50Hz, which is close to the compressor's fundamental frequency and serves as a key frequency for assessing resonance risk. Vibration spectrum data was recorded at five moments throughout the flight. The Ar(f) / Au(f) ratios at these five moments are 0.6, 0.58, 0.63, 0.57, and 0.64, respectively. Therefore, Hnew(f) = (0.6 + 0.58 + 0.63 + 0.57 + 0.64) / 5 = 0.604. This indicates that at the 50Hz frequency, the actual vibration transfer function value measured during this flight is 0.604, meaning the vibration felt at the cooling system mounting point is approximately 60.4% of the original vibration at the UAV connection point.
[0117] During the same flight mission, the same calculation process needs to be performed on other frequencies of interest, such as 80Hz, 100Hz, and 120Hz, to obtain Hnew(f) for each frequency. The calculation results of all frequency points are then combined to form the complete spectrum of the actual vibration transfer function Hnew(f) for this flight.
[0118] After obtaining Hnew(f), it is weighted and averaged with the historical transfer function Hold(f) to obtain the weighted average value Hup(f) = a × Hold(f) + (1-a) × Hnew(f), where a is the historical weight, preferably 0.7-0.9. Hup(f) is used to update the vibration transfer function.
[0119] In this application, when the flight control system executes an emergency landing procedure, it calculates the maximum permissible horizontal acceleration ahmax based on the current health index H. The calculation formula is: ahmax = H × ahmax - r, where ahmax - r is a preset reference maximum horizontal acceleration, preferably 0.3g.
[0120] The landing path planning uses ahmax as a hard constraint. Specifically, the path is discretized into piecewise cubic Bézier curves, each defined by four control points: a starting point, two intermediate control points, and an ending point. At the boundaries of each segment, an acceleration continuity condition is enforced: the acceleration vector at the end of the previous segment equals the acceleration vector at the starting point of the next segment.
[0121] In this embodiment, the forced acceleration continuity condition is enforced by incorporating the acceleration equations at the intersections as equality constraints when optimizing the control points of each segment of the Bézier curve. The optimization objective is to minimize the total path length while satisfying the acceleration constraints. The resulting landing path exhibits a more continuous acceleration curve and avoids acceleration jumps at segment boundaries, thus preventing impact on the refrigeration system.
[0122] Suppose a drone needs to land from point A (hovering position) to point B (target landing point) on the ground. The landing path must satisfy the maximum horizontal acceleration constraint, and the acceleration curve cannot have any abrupt changes. First, the entire path can be divided into two Bézier curves, for example: the first segment from A to the midpoint M, and the second segment from M to B. Each segment is a cubic Bézier curve, defined by four control points. The control points for the first segment are P0=A, P1, P2, P3=M; the control points for the second segment are Q0=M, Q1, Q2, Q3=B.
[0123] First, we give an initial, unoptimized control point location. Assume A = ((0,0,50) (horizontal position origin, height 50 meters), B = (10,0,0) (horizontal position 10 meters, ground), and midpoint M = (5,0,25)).
[0124] The initial control points are roughly set to be evenly distributed across the segments. For example, in the first segment, P0=(0,0,50), P1=(1.67,0,37.5), P2=(3.33,0,25), and P3=(5,0,25); in the second segment, Q0=(5,0,25), Q1=(6.67,0,16.7), Q2=(8.33,0,8.3), and Q3=(10,0,0).
[0125] The second derivative (acceleration) of a cubic Bézier curve at time t is determined by the control points. For the first segment, the acceleration at the starting point (t=0) is... The acceleration at the endpoint (e.g., at t=1) is: The acceleration at the starting point of the second segment is similarly calculated: For acceleration to be continuous, the acceleration at the end of the first segment must equal the acceleration at the beginning of the second segment, that is, it must be... = Substituting M, we obtain the equality constraints. = ,Right now = Simplified to: = .
[0126] The optimization objective is to minimize the total path length or energy consumption while satisfying the above-mentioned equality constraints. The x, y, and z coordinate components of the acceleration at each control point are treated as variables, the acceleration continuity equation as a constraint, and the path length as the objective function. A sequential quadratic programming approach is used to solve this problem. The solution method is briefly described below: The variables to be optimized in the sequential quadratic programming solution are the coordinates of four control points of two Bézier curves (P1, P2, Q1, Q2, each containing three components x, y, and z, for a total of 12 variables, with P0, P3, Q0, and Q3 fixed). That is, to find a set of control point positions that minimizes the path length and satisfies the acceleration continuity condition.
[0127] The objective function is the sum of the arc lengths of the two Bézier curves, i.e., the total path length, which measures the economic efficiency of the path in location space. The constraint is the acceleration continuity equation. = That is, the accelerations of the two segments are the same at the junction M.
[0128] The first iteration is as follows: Given the initial control point positions, as described above with a coarse value given by a uniform distribution, calculate the objective function value (path length) and constraint value (acceleration difference) at that position. Approximate the objective function at the current point using a quadratic function, preferably with a second-order Taylor expansion, and approximate the constraints using a linear function, preferably with a first-order Taylor expansion. Solve this simplified quadratic programming subproblem to obtain the adjustment direction for each control point.
[0129] The second iteration then proceeds as follows: the adjustment value from the first step is added to the current control point position to obtain a new position, and the objective function and constraints are recalculated. If the constraints are still not satisfied (i.e., the acceleration difference is not zero), the quadratic and linear approximations are reconstructed using the new position to solve for a new adjustment value. Each iteration approaches the optimal point that satisfies the constraints.
[0130] Stop when the adjustment amount in each iteration is small enough, such as when the control point displacement is less than the preset accuracy of 0.01m, and the constraint is close to zero.
[0131] Finally, it should be noted that the implementation basis of the UAV-mounted cryogenic refrigeration system and its coupling control method with the flight control provided in this application is that the mass ratio of R600a, R1150, and R50 in the refrigerant mixture discharged from the compressor of the cryogenic refrigeration system in the UAV-mounted heavy-duty refrigerator is 63.59:34.91:1.50. Under this ratio, and by improving the evaporator structure, such as... Figure 3 As shown, after the copper tube 10 is flattened, it is directly bonded to the refrigerator inner liner 20 through the adhesive heat-conducting film 50. There will be no adhesive gaps, and no additional cooling capacity will be consumed due to adhesive gaps. Thus, the heat exchange temperature is precisely controlled at about 3°C. When the temperature of the refrigerant mixture reaches about -85°C, the temperature inside the refrigerator is maintained at about -82°C. Through the combined effect of controlling the suction and discharge pressure of the compressor and controlling the inner diameter of the capillary tube, the ultra-low temperature refrigeration system and the UAV are coupled and controlled by the method provided in this application. Only then can the refrigerator be kept in an ultra-low temperature environment of about -82°C during the flight of the UAV.
[0132] It should also be noted that the upper limit of the discharge pressure in the safety envelope is not arbitrarily set. It is based on the discharge pressure Pbase corresponding to the compressor operating under the above mass ratio and the evaporator inlet temperature reaching the target value of -85℃. In the experimental calibration, the corresponding discharge pressure value was recorded when the evaporator inlet temperature stabilized at -85℃±1℃. The average value of multiple experiments was taken as Pbase. Then, the upper limit of the discharge pressure was obtained by multiplying the reference pressure Pbase by the safety factor SF determined according to the condenser heat dissipation conditions. The safety factor SF increases with the increase of ambient temperature. In this application, when the ambient temperature is greater than 35℃, the safety factor SF=1.05; when 25℃<SF≤35℃, the safety factor SF=1.08; and when the ambient temperature>35℃, the safety factor SF is 1.12.
[0133] It should be stated that the above-described specific embodiments are merely preferred embodiments and technical principles applied in this application. Those skilled in the art should understand that various modifications, equivalent substitutions, and variations can be made to this application. However, such variations, as long as they do not depart from the spirit of this application, should be within the scope of protection of this application. Furthermore, some terminology used in this application's specification and claims is not limiting but merely for ease of description.
Claims
1. A UAV-mounted cryogenic refrigeration system and its coupling control method with flight control, characterized in that, include: Obtain the multiphysics state parameters of the cryogenic refrigeration system mounted on the UAV; A health index is generated based on the degree of deviation between the multiphysics state parameters and the preset safety envelope; A bidirectional data channel is dynamically established between the flight controller and the cooling system controller to transmit the health index to the flight controller and the flight attitude information of the flight controller to the cooling system controller. The flight controller adjusts the flight strategy based on the health index, and the cooling system controller adjusts the cooling parameters based on the flight attitude information. When the health index falls below the threshold or a refrigerant leak is detected, the flight controller executes an emergency landing procedure, and the refrigeration system controller simultaneously executes a safety shutdown procedure.
2. The UAV-mounted cryogenic refrigeration system and its coupling control method with flight control as described in claim 1, characterized in that, The preset security envelope is defined in the following way: During the operation of the refrigeration system, the compressor discharge pressure, the liquid level of the vapor-liquid separator, and the evaporator inlet temperature are collected synchronously. The product of the discharge pressure and the liquid level is used as the load characterization quantity, and the ratio of the evaporator inlet temperature to the discharge pressure is used as the efficiency characterization quantity. The values of each safety envelope boundary are dynamically adjusted according to the mapping relationship between the load characterization quantity and the efficiency characterization quantity.
3. The UAV-mounted cryogenic refrigeration system and its coupling control method with flight control as described in claim 1, characterized in that, The bidirectional data channel is constructed in the following manner: The health index is used as the basis for channel priority classification. When the health index is higher than the first threshold, the channel operates at the first priority and only transmits the health index and fault flags to minimize communication bandwidth usage. Channels with a health index between the first and second thresholds operate at the second priority, supplementing the transmission of multi-physics state parameters in various dimensions, enabling the flight controller to perceive the degradation trend of the cooling system; when the health index is below the second threshold, the channel operates at the third priority, supplementing the transmission of real-time decision logs of the cooling system controller, enabling the ground station to retrospectively review the control logic during emergency phases.
4. The UAV-mounted cryogenic refrigeration system and its coupling control method with flight control as described in claim 1, characterized in that, The health index is calculated as follows: the deviation of the multiphysics state parameters of each dimension from their respective safe envelope boundaries is calculated, the weighted average of the two dimensions with the largest deviation is taken as the main score, the root mean square of the sum of the squares of the deviations of the other dimensions is taken as the fluctuation penalty term, and the health index is obtained by subtracting the fluctuation penalty term from the main score.
5. The UAV-mounted cryogenic refrigeration system and its coupling control method with flight control as described in claim 1, characterized in that, The refrigeration system controller adjusts the refrigeration parameters based on the flight attitude information by: recording the refrigerant distribution recovery time after each attitude change; using the median of the recovery times as a time constant; performing linear regression on the recovery time corresponding to the same attitude change amplitude in multiple sets of historical data and the compressor speed adjustment; using the regression slope as the compensation coefficient for the attitude change amplitude range; and multiplying the current attitude change rate by the compensation coefficient for the corresponding range to obtain the compressor speed compensation.
6. The UAV-mounted cryogenic refrigeration system and its coupling control method with flight control as described in claim 1, characterized in that, The emergency landing procedure determines the landing strategy based on a combination of the health index and the refrigerant leakage concentration, using the following method: The health index is normalized to a weight coefficient between 0 and 1. The weight coefficient is multiplied by the preset maximum search radius to obtain the actual search radius. Candidate points that meet the landing conditions are searched within the actual search radius. The landing conditions are as follows: The gas concentration decay curve value at the candidate point is lower than the safety threshold, and the angle between the line connecting the candidate point and the leak source and the wind direction is greater than the first preset angle. When there is no candidate point that meets the landing conditions within the actual search radius, the safety threshold in the landing conditions is dynamically relaxed based on the health index. For every decrease of the health index by the first preset value, the safety threshold is increased by the second preset value.
7. The UAV-mounted cryogenic refrigeration system and its coupling control method with flight control as described in claim 1, characterized in that, Also includes: The vibration transfer function of the mounting mechanism is obtained. The flight controller calculates the vibration energy transmitted to the cooling system based on the convolution result of the current airframe vibration spectrum and the vibration transfer function. When the vibration energy exceeds a preset threshold, the difference between the vibration energy and the threshold is used as the adjustment amount to proportionally reduce the setpoint of the rotational speed of each propeller, so that the vibration energy transmitted to the cooling system converges to below the threshold.
8. The UAV-mounted cryogenic refrigeration system and its coupling control method with flight control as described in claim 7, characterized in that, The vibration transfer function is updated in the following way: After each flight mission, the vibration spectrum of the aircraft recorded throughout the flight is deconvolved with the actual vibration spectrum at the refrigeration system installation point to obtain the actual vibration transfer function of the flight. The actual vibration transfer function is then weighted and averaged with the historical transfer function, and the vibration transfer function is updated with the weighted result.
9. The UAV-mounted cryogenic refrigeration system and its coupling control method with flight control as described in claim 1, characterized in that, When the flight control system executes the emergency landing procedure, it calculates the maximum permissible horizontal acceleration based on the current health index. The maximum permissible horizontal acceleration is proportional to the health index. When the health index approaches "0", the maximum permissible horizontal acceleration also approaches "0". The landing path planning uses the maximum permissible horizontal acceleration as a hard constraint. By discretizing the path into piecewise Bézier curves and forcibly applying acceleration continuity conditions at the boundaries of each segment, a smooth trajectory is generated.
10. The UAV-mounted cryogenic refrigeration system and its coupling control method with flight control according to any one of claims 1-9, characterized in that, The refrigerant mixture discharged from the compressor of the cryogenic refrigeration system has a refrigerant ratio of R600a, R1150, and R50 of 63.59:34.91:1.
50. The upper limit of the discharge pressure in the safety envelope is determined by the following method: The upper limit of the exhaust pressure is obtained by multiplying the exhaust pressure by a safety factor determined based on the condenser heat dissipation conditions, whereby the exhaust pressure is the same as the reference pressure when the compressor is operating at the specified mass ratio and the evaporator inlet temperature reaches the target value. The safety factor increases with increasing ambient temperature.