A method for correcting measurement error of a vehicle-mounted pressure sensor

CN122961525APending Publication Date: 2026-10-23刘佳
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Patent Information

Application Number
CN202611006653.X
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2026-07-07
Publication Date
2026-10-23

AI Technical Summary

Technical Problem

[0006]本发明的目的在于提供一种车载压力传感器测量误差修正方法,用于解决现有压力传感器补偿方法难以区分真实压力动态变化与传感器测量误差、难以适应慢变漂移和温度漂移、以及异常故障场景下容易过度修正的问题

Benefits of technology

[0014]与现有技术相比,本发明至少具有如下有益效果:第一,本发明通过可信稳态窗口限制误差更新时机,能够避免在压力快速动态变化时将系统真实压力变化误判为传感器误差;第二,本发明通过温度压力关系和执行部件状态构建参考压力,使补偿过程具有物理含义和可解释性;第三,本发明通过稳态门控、温度分区、限幅保护和异常诊断的组合,提高了压力修正结果的稳定性;第四,本发明能够适用于固定零点偏移、慢变漂移、温度漂移和比例误差等多类传感器误差场景。

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Abstract

The application discloses a kind of vehicle-mounted pressure sensor measurement error correction methods, belong to vehicle sensor measurement calibration and vehicle-mounted heat management control technical field.The method obtains the pressure observation value of vehicle-mounted pressure sensor and vehicle speed, environmental temperature, pipeline temperature, compressor state and compressor speed and other vehicle operating parameters, whether current sampling time is in credible steady state window based on pressure change rate, temperature change rate and executing component state change rate determination;In credible steady state window, according to temperature pressure relationship, compressor operating state and historical effective state, reference pressure is constructed, pressure observation deviation is calculated, and error estimate is updated by steady state gate;Error estimate is frozen under dynamic condition or abnormal condition, and only existing credible correction amount is used for pressure correction;At the same time, abnormal diagnosis is carried out through correction limiting and continuous deviation detection.The method can reduce the influence of pressure sensor zero point deviation, slow drift, temperature drift and proportional error on vehicle-mounted pressure measurement without relying on offline disassembly and manual calibration, improve the availability of pressure measurement results in vehicle control, fault diagnosis and heat management strategy.
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Description

Technical Field

[0001] This invention belongs to the field of vehicle sensor measurement calibration and vehicle thermal management control technology, and particularly relates to a method for correcting measurement errors of vehicle pressure sensors, which can be used for online error compensation of pressure sensors in vehicle air conditioning systems, thermal management systems, braking pressure systems, fuel evaporation pressure systems or hydraulic actuator systems. Background Technology

[0002] Onboard pressure sensors are widely used in vehicle air conditioning, thermal management, braking, fuel, and hydraulic actuator systems. Their output directly participates in closed-loop control, protection control, and fault diagnosis. For example, in onboard air conditioning and thermal management systems, pressure sensors can be used to determine the refrigerant circuit pressure status, compressor operating safety boundaries, condenser heat exchange status, and system leakage risk. When pressure measurement results are offset or drift, the controller may misjudge the system status, leading to false triggering of compressor protection strategies, decreased heat exchange control accuracy, or false fault diagnosis.

[0003] During long-term vehicle operation, pressure sensors are susceptible to factors such as component aging, temperature changes, installation stress, wiring misalignment, and power fluctuations, resulting in fixed zero-point offset, slow drift, temperature-dependent drift, or proportional error. Traditional solutions typically rely on factory calibration, offline calibration during maintenance, or simple fixed compensation, which are insufficient to adapt to sensor error variations throughout the vehicle's entire lifecycle.

[0004] Existing online compensation methods, if they do not distinguish between the steady-state and dynamic states of a vehicle system, can easily misinterpret actual pressure changes as sensor errors. For example, when a compressor starts, valve opening changes abruptly, or the vehicle's thermal load changes rapidly, the pressure change mainly comes from the evolution of the system's physical state, rather than sensor offset. Directly updating the error compensation amount at this time may lead to incorrect corrections and divergent correction values. On the other hand, when a sensor experiences an abnormally large offset or jamming fault, continuing compensation may mask the true fault, affecting vehicle safety protection and fault location.

[0005] Therefore, there is a need for an on-board pressure sensor measurement error correction method that can combine vehicle operating conditions, reference pressure, and a reliable steady-state window. This method can estimate sensor errors online under reliable conditions and avoid erroneous updates under dynamic and abnormal conditions, thereby improving the accuracy, stability, and engineering interpretability of pressure measurement results. Summary of the Invention

[0006] The purpose of this invention is to provide a method for correcting measurement errors of vehicle-mounted pressure sensors, which solves the problems of existing pressure sensor compensation methods, such as difficulty in distinguishing between real dynamic pressure changes and sensor measurement errors, difficulty in adapting to slow drift and temperature drift, and easy over-correction under abnormal fault scenarios.

[0007] To achieve the above objectives, the present invention provides the following technical solution: a method for correcting measurement errors of an on-board pressure sensor, comprising the following steps: Step 1: Obtain the pressure readings from the vehicle pressure sensor and the corresponding vehicle operating parameters.

[0008] Step 2: Based on the pressure observation value and the vehicle operating condition parameters, determine whether the current sampling time belongs to the correctable state and obtain the steady-state gating flag.

[0009] Step 3: Under correctable conditions, construct a reference pressure based on the temperature-pressure relationship, the status of the actuators, and historical effective conditions.

[0010] Step 4: Calculate the pressure observation deviation based on the pressure observation value and the reference pressure.

[0011] Step 5: Based on the steady-state gating flag, the pressure observation deviation is updated by gating to obtain the pressure sensor measurement error estimate.

[0012] Step 6: Correct the pressure observation value based on the estimated measurement error of the pressure sensor, and limit the correction amount.

[0013] Step 7: Output the corrected pressure value and generate anomaly diagnostic indicators based on the pressure observation deviation and correction amount.

[0014] Compared with existing technologies, the present invention has at least the following beneficial effects: First, the present invention limits the timing of error updates through a reliable steady-state window, which can avoid misjudging the actual pressure change of the system as a sensor error when the pressure changes rapidly and dynamically; Second, the present invention constructs a reference pressure by using the temperature-pressure relationship and the state of the actuator, making the compensation process physically meaningful and interpretable; Third, the present invention improves the stability of the pressure correction results through a combination of steady-state gating, temperature partitioning, amplitude limiting protection, and anomaly diagnosis; Fourth, the present invention is applicable to various sensor error scenarios such as fixed zero-point offset, slow drift, temperature drift, and proportional error. Attached Figure Description

[0015] Figure 1 This is an overall flowchart of the vehicle-mounted pressure sensor measurement error correction method of the present invention.

[0016] Figure 2 This is a comparison chart of the pressure curves before and after correction in a simulation embodiment of the present invention.

[0017] Figure 3 The diagram shows the error estimation and steady-state gating results in the simulation embodiment of this invention.

[0018] Figure 4 This is a comparison chart of RMSE results for different working conditions and methods in the simulation embodiments of the present invention.

[0019] Figure 5 This is a diagram showing the steady-state gating update result under dynamic operating conditions in the simulation embodiment of the present invention.

[0020] Figure 6 This is a diagram showing the abnormal diagnosis results in a simulation embodiment of the present invention. Detailed Implementation

[0021] The present invention will be further described below with reference to the accompanying drawings and specific embodiments. It should be understood that the following embodiments are for illustrative purposes only and are not intended to limit the scope of protection of the present invention. Where there is no conflict, features in the embodiments of the present invention can be combined with each other.

[0022] This embodiment uses a pressure sensor in an onboard air conditioning or thermal management system as an example. The pressure sensor can be installed on the high-pressure side, low-pressure side of the refrigerant, or in the thermal management circuit piping. The method can also be applied to scenarios such as vehicle braking pressure, fuel evaporation pressure, or hydraulic actuation pressure, simply by replacing the reference pressure model with the corresponding system's pressure state model.

[0023] like Figure 1 As shown, the overall process of this invention includes data acquisition, reliable steady-state identification, reference pressure construction, error estimation, pressure correction, and anomaly diagnosis. Figure 1 In the process, pressure observations and on-board operating parameters first enter the steady-state identification module, which outputs a steady-state gating flag; the reference pressure construction module generates a reference pressure based on temperature and the status of the actuators; the error estimation module updates the pressure sensor measurement error estimate only when the steady-state gating is effective; the pressure correction module outputs the corrected pressure; and the anomaly diagnosis module outputs a diagnostic flag when the deviation is continuously abnormal or the pressure is stuck.

[0024] Step 1: Obtain pressure observations and on-board operating parameters 101. At each sampling moment, the controller acquires the pressure observation value output by the pressure sensor. The pressure observation value can be obtained from an analog voltage signal, a digital bus signal, or a conversion result internally calculated by the on-board controller.

[0025] 102. The controller synchronously acquires the vehicle operating condition parameters corresponding to the pressure observation value. The vehicle operating condition parameters include at least one of vehicle speed, ambient temperature, pipeline temperature, refrigerant temperature, compressor start / stop status, compressor speed, fan speed, and valve opening. In embodiments of the vehicle air conditioning or thermal management system, the reference pressure is preferably constructed using pipeline temperature, ambient temperature, compressor start / stop status, and compressor speed.

[0026] 103. To describe the measurement error of the pressure sensor, the sensor observation model is defined as follows: Where represents the observed pressure value at the i-th sampling time, represents the true pressure, represents the proportional error coefficient, represents the zero-point offset, and represents the measurement noise. This model is used to illustrate that the sources of error in a pressure sensor can simultaneously include proportional error, zero-point offset, and random noise.

[0027] 104. During long-term operation, the zero-point offset of a pressure sensor can be composed of fixed offset, slow-varying drift, and temperature-dependent drift. One way to express this is as follows: Where represents the initial offset, represents the drift rate that varies with the sampling sequence number, represents the temperature drift coefficient, represents the current temperature, and represents the reference temperature.

[0028] 105. The controller performs time alignment and validity checks on the acquired data. If pressure observations or key operating parameters are missing, out of bounds, or communication is abnormal, the current sampling time is marked as uncorrectable, and the sampling point is not used to update the error estimate.

[0029] Step 2: Determine the reliable steady-state window 201. The controller calculates the sliding window rate of change based on pressure observations and on-board operating parameters. For any detected variable, the rate of change is defined as: Where represents the sliding window length and represents the sampling period. Variables can be pressure observations, pipeline temperature, compressor speed, or vehicle speed.

[0030] 202. When the pressure change rate is less than the pressure change rate threshold, the temperature change rate is less than the temperature change rate threshold, the compressor speed change rate is less than the speed change rate threshold, and the vehicle speed change rate is less than the speed change rate threshold, and the duration of the above conditions is not less than the preset minimum stabilization time, the controller determines that the current sampling time is in a reliable steady-state window.

[0031] 203. The controller generates a steady-state gating flag based on the reliable steady-state window. When the current sampling time is within the reliable steady-state window and no abnormal diagnosis is triggered, set the flag accordingly; when the controller is in a state such as compressor start-up, compressor speed step change, rapid valve change, rapid pressure rise or fall, communication abnormality, or suspected sensor failure, set the flag accordingly.

[0032] 204. The steady-state gating flag is used to control whether the error estimate is updated. The purpose of this design is to ensure that the error estimate relies only on a reliable pressure reference and steady-state operating data, avoiding the misinterpretation of actual pressure changes under dynamic operating conditions as sensor drift.

[0033] 205. In one embodiment, the steady-state determination threshold may include: a pressure change rate threshold, a compressor speed change rate threshold, a temperature change rate threshold, a vehicle speed change rate threshold, and a minimum stable duration. These thresholds can be pre-calibrated based on the system model, sensor sampling period, and controller computing resources.

[0034] Step 3, construct reference pressure 301. At the sampling moment when the steady-state gating flag is valid or the reference model is reliable, the controller constructs a reference pressure based on the temperature-pressure relationship and the state of the actuators. The reference pressure is used to represent the pressure level that the pressure sensor should theoretically output under the current vehicle operating conditions.

[0035] 302. In an embodiment of an in-vehicle air conditioning or thermal management system, when the pressure is mainly determined by temperature and compressor speed, the reference pressure can be expressed as: Where, , and represent temperature-pressure relationship parameters, represent compressor speed correction coefficient, represent compressor speed, and represent maximum reference speed.

[0036] 303. When the compressor is off or the system is in a pressure equilibrium state, the reference pressure can be set to the temperature-pressure relationship term. When the compressor is running stably, the reference pressure is determined by the temperature-pressure relationship term and the compressor speed correction term.

[0037] 304. To describe the dynamic response of pressure to the target pressure, a first-order dynamic response model can be used: Where represents the target pressure under the current operating conditions, and represents the pressure response time constant. This model is used to construct simulation data and explain the necessity of updating the freeze error under dynamic operating conditions.

[0038] 305. In another embodiment, the reference pressure can be obtained using a temperature-pressure lookup table model. The controller interpolates the current temperature into a preset temperature-pressure table to obtain the equilibrium pressure, and then corrects it based on the compressor speed, fan speed, or valve opening.

[0039] 306. In another implementation, the reference pressure can be generated from historical normal operating condition data. The controller selects historical sampling points that have not experienced faults and are within a reliable steady-state window, and establishes a mapping relationship between temperature, actuator status, and pressure for subsequent online reference pressure construction.

[0040] Step 4: Calculate the pressure observation deviation 401. The controller calculates the pressure observation deviation based on the observed pressure value and the reference pressure: 402. When positive, it indicates that the observed pressure is higher than the reference pressure; when negative, it indicates that the observed pressure is lower than the reference pressure. If the reference pressure is reliable, it can be used as an instantaneous observation of the pressure sensor's measurement error.

[0041] 403. To reduce the impact of noise on error estimation, the controller does not directly use a single sampling point as a correction value, but instead inputs it into the error estimation module to obtain a stable error estimate through smoothing, filtering, or partitioning updates.

[0042] 404. When the current sampling point does not meet the reliable steady-state condition, the controller can still calculate for monitoring, but will not use this deviation to update the error estimate. This strategy can distinguish between "observable deviation" and "updateable deviation," thereby avoiding erroneous corrections.

[0043] Step 5: Perform steady-state gating error estimation 501. The controller updates the pressure sensor measurement error estimate based on the steady-state gating flag. In a preferred embodiment, a steady-state gating exponential smoothing update is used: Where represents the smoothing update coefficient. When , the error estimate is updated based on the current bias and the estimate at the previous time step; when , the error estimate retains the previous confidence value.

[0044] 502. The above update method allows the error estimate to gradually approach the sensor offset under steady-state conditions and remains frozen under dynamic conditions. Therefore, even if the compressor starts or the system thermal load changes, causing a rapid pressure change, the error estimate will not mistake this pressure dynamic for a sensor error.

[0045] 503. For pressure sensors with significant temperature drift, the controller can divide the temperature range into multiple temperature intervals and maintain an error estimate for each interval. When the current temperature is in the *i*th temperature interval, the error estimate is updated as follows: 504. Temperature zone updates enable independent correction values ​​for different temperature ranges, thereby reducing compensation errors caused by a single global correction value operating over a wide temperature range. For vehicle air conditioning systems, this method is particularly suitable for scenarios with large variations in ambient and pipeline temperatures.

[0046] 505. In another implementation, the error estimate can be obtained using a one-dimensional Kalman filter. In this case, the pressure sensor offset is treated as a slowly varying state, and the offset is considered an observation. Filter updates are performed only when the steady-state gating flag is valid, and prediction or hold is performed under dynamic conditions.

[0047] 506. When the pressure sensor has both proportional error and zero-point offset, the controller can use the recursive least squares method to estimate the linear correction parameter online, and express the correction pressure as: Here, and are the linear correction parameters obtained through recursive updating. This implementation is applicable to scenarios where the slope of the pressure sensor output changes.

[0048] Step 6: Perform pressure correction and limit protection. 601. The controller corrects the pressure observation value based on the estimated measurement error of the pressure sensor. When using offset compensation, the corrected pressure is defined as: Where represents the corrected pressure value, represents the maximum allowable correction amplitude, and represents the limiting function.

[0049] 602. Limiting protection is used to prevent excessive correction due to sensor malfunction, reference model malfunction, or system failure. When the preset maximum correction amplitude is exceeded, the controller can either use the limited correction amount or prevent the correction amount from being updated and trigger a diagnostic check.

[0050] 603. Under dynamic operating conditions, the controller is not updated, but the pressure observation can still be corrected using the previous reliable error estimate. Therefore, this invention does not only output corrected pressure under steady-state conditions, but learns the correction amount under steady-state conditions and uses the learned correction amount cautiously under dynamic operating conditions.

[0051] 604. When the pressure observation value, reference pressure, or key operating condition parameter exceeds the limit, is missing, or communication is abnormal, the controller can output the original pressure observation value, the previous effective correction pressure, or the downgraded correction pressure, and mark the current sampling point as unusable for error update.

[0052] Step 7: Output corrected pressure and generate abnormal diagnostic indicators. 701. The controller outputs a corrected pressure, which is used for vehicle thermal management control, compressor protection control, system state estimation, or fault diagnosis. The corrected pressure can replace the original pressure observation in the upper-level control strategy, or it can be saved simultaneously with the original pressure observation for diagnostic purposes.

[0053] 702. The controller determines whether there is a sensor malfunction or system malfunction based on the pressure observation deviation. In one implementation, an malfunction diagnosis flag is triggered when the following conditions are continuously met at a certain number of sampling points: Wherein, represents the fault judgment threshold, and represents the number of continuous fault sampling points.

[0054] 703. For stuck faults, if the pressure observation value remains approximately unchanged within the preset time window, while the reference pressure, compressor status, or compressor speed changes significantly, the controller determines that the pressure sensor is suspected to be stuck and triggers the abnormal diagnosis flag.

[0055] 704. When an abnormal diagnostic flag is triggered, the controller stops using the current abnormal deviation to update the error estimate, avoiding masking the true fault through overcorrection. Simultaneously, the controller can output fault codes, freeze frame data, or diagnostic status for vehicle maintenance and fault location.

[0056] Simulation Examples To verify the effectiveness of the method of the present invention, a simulation embodiment of the pressure sensor of an on-board air conditioning or thermal management system was constructed. The simulation data was generated with a sampling period, and the duration of a single simulation was [duration missing]. The true pressure value was generated by the temperature-pressure relationship and the compressor speed correction term, and a first-order dynamic response was added; the pressure observation value was based on the true pressure value with fixed offset, slow drift, temperature drift, proportional error, and random noise added.

[0057] Table 1 lists the main parameters used in the simulation embodiments. This table is only used to illustrate one embodiment of the present invention and does not constitute a limitation on the scope of protection.

[0058]

[0059] The simulation implementation example is set up to include a comprehensive operating condition including fixed zero-point offset, slow drift, temperature-dependent drift, proportional error, compressor dynamic switching, and fault offset injection. Figure 2 The comparison results of the true pressure value, the original pressure observation value, and the corrected pressure under this combined operating condition are shown. It can be seen that the original pressure observation value deviates significantly from the true pressure value, while after steady-state gating error estimation and online correction, the corrected pressure is closer to the true pressure value.

[0060] Figure 3 The results of error estimation and steady-state gating are shown. The period during which the steady-state gating flag is valid is used to update the error estimate. Under dynamic operating conditions, the error estimate remains frozen, thereby avoiding erroneous updates when the compressor starts or the pressure changes rapidly.

[0061] Figure 4 The comparison results of RMSE under different error conditions are shown. The evaluation index is the root mean square error of the corrected pressure relative to the true pressure: Table 2 lists the comparison results of the correction accuracy of the patent-supported simulation experiments. The RMSE statistical interval in the table represents the normal operating range before fault injection; the data after fault injection is used to separately evaluate the anomaly diagnosis capability. It can be seen that both the steady-state gated exponential smoothing and steady-state gated temperature partitioning methods are significantly better than the original observations and the full-time update method, indicating that the reliable steady-state window can effectively suppress erroneous updates under dynamic operating conditions.

[0062]

[0063] As shown in Table 2, under comprehensive operating conditions, the steady-state gated exponential smoothing update strategy reduced the RMSE from [value missing] to [value missing], with an improvement rate of [percentage missing]; the RMSE of the full-time update exponential smoothing method was [value missing], with an improvement rate of [percentage missing]. This indicates that the present invention, by controlling the error update timing through a reliable steady-state window, can effectively reduce the risk of erroneous corrections under dynamic operating conditions.

[0064] Figure 5 The steady-state gating update results under dynamic operating conditions are further illustrated. The steady-state gating strategy freezes the error estimate during periods of rapid pressure change and resumes updating after the pressure stabilizes, thus ensuring good stability of the corrected pressure throughout the entire time period.

[0065] Figure 6The simulation results of the anomaly diagnosis are shown. After the injection offset jump fault, the deviation between the pressure observation value and the reference pressure continues to exceed the fault threshold. The controller triggers the anomaly diagnosis flag after a preset number of continuous sampling points and uses amplitude limiting protection to prevent the abnormally large deviation from being completely absorbed into the correction amount.

[0066] In summary, this invention achieves online measurement error correction for vehicle-mounted pressure sensors by combining reliable steady-state identification, reference pressure construction, steady-state gating error estimation, pressure correction and amplitude limiting protection, and anomaly diagnosis. This method can improve pressure measurement accuracy without adding extra hardware and has good engineering interpretability and feasibility for vehicle controller deployment.

Claims

1. A method for correcting measurement errors of an on-board pressure sensor, characterized in that, Includes the following steps: Step 1: Obtain the pressure observation value of the vehicle pressure sensor and the corresponding vehicle operating condition parameters; Step 2: Based on the pressure observation value and the vehicle operating condition parameters, determine whether the current sampling time belongs to a correctable state, and obtain the steady-state gating flag; Step 3: In the correctable state, a reference pressure is constructed based on the temperature-pressure relationship, the state of the actuator, and historical effective states; Step 4: Calculate the pressure observation deviation based on the observed pressure value and the reference pressure; Step 5: Gating update the pressure observation deviation according to the steady-state gating flag to obtain the pressure sensor measurement error estimate; Step 6: Correct the pressure observation value based on the estimated measurement error of the pressure sensor, and limit the correction amount. Step 7: Output the corrected pressure value and generate an anomaly diagnostic flag based on the pressure observation deviation and the correction amount.

2. The method according to claim 1, characterized in that, The vehicle operating parameters include at least one of the following: vehicle speed, ambient temperature, pipeline temperature, refrigerant temperature, compressor start / stop status, compressor speed, fan speed, and valve opening.

3. The method according to claim 1, characterized in that, The correctable state refers to a state in which at least one of the pressure change rate, temperature change rate, vehicle speed change rate, and actuator state change rate is less than the corresponding threshold, and the duration of the state is not less than the preset minimum stabilization time.

4. The method according to claim 1, characterized in that, The reference pressure is constructed from at least one of the following: a temperature-pressure analytical model, a temperature-pressure lookup table model, a historical normal operating condition data model, and a target control pressure model; wherein, in an on-board air conditioning system or a vehicle thermal management system, the reference pressure is constructed based on at least one of the following: pipe temperature, refrigerant temperature, compressor speed, fan speed, and valve opening.

5. The method according to claim 1, characterized in that, The pressure sensor measurement error estimate is updated only when the steady-state gating flag is valid, and retains the error estimate from the previous reliable state under dynamic or abnormal operating conditions.

6. The method according to claim 1, characterized in that, The pressure sensor measurement error estimate is obtained using at least one of the following methods: exponential smoothing, moving average, one-dimensional Kalman filtering, temperature partitioning update, or recursive least squares.

7. The method according to claim 6, characterized in that, When the temperature is in different temperature ranges, the error estimate for the corresponding temperature range is maintained to compensate for the temperature-related drift of the pressure sensor; and / or, when the pressure sensor has both proportional error and zero-point offset, the linear correction parameter is estimated online using the recursive least squares method, and the corrected pressure is output according to the linear correction parameter.

8. The method according to claim 1, characterized in that, The amplitude limiting protection restricts the estimated measurement error of the pressure sensor to a preset maximum correction amplitude range. When the estimated value exceeds the preset maximum correction amplitude range, the use of a correction value exceeding the preset maximum correction amplitude range is prohibited.

9. The method according to claim 1, characterized in that, The abnormal diagnostic flag is triggered when the number of sampling points where the deviation between the pressure observation value and the reference pressure continuously exceeds the fault threshold reaches a preset number; and / or, the abnormal diagnostic flag is triggered based on the condition that the pressure observation value remains approximately unchanged within a preset time window while the reference pressure or the state of the actuator changes significantly, in order to identify a pressure sensor jamming fault.

10. A vehicle controller, characterized in that, The method includes a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement the method according to any one of claims 1 to 9.