Data-driven subsonic Mach number control method for transient wind tunnels

By combining static pressure and total pressure control algorithms in the subsonic and transonic continuous aerodynamic measurement experiment, the grating finger displacement was adjusted in real time, which solved the problem of insufficient Mach number control accuracy and achieved efficient and accurate Mach number control, meeting the requirements of experimental agility and high efficiency.

CN121521404BActive Publication Date: 2026-04-03INST OF HIGH SPEED AERODYNAMICS OF CHINA AERODYNAMICS RES & DEV CENT
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Patent Information

Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
Filing Date
2026-01-14
Publication Date
2026-04-03

AI Technical Summary

Technical Problem

In subsonic and transonic continuous aerodynamic measurement tests in ejector semi-recirculating transient wind tunnels, the existing technology cannot meet the given control accuracy requirements for Mach number control, nor can it meet the requirements for test agility and high efficiency.

Method used

A combined approach of data-driven static pressure control algorithm and total pressure control algorithm is adopted. By using a static pressure reference model and a real-time data-driven model, the grid finger displacement is adjusted in real time to achieve precise control of Mach number. The total pressure control is then performed using a PID control method.

Benefits of technology

This achieved a Mach number control accuracy better than ±0.002 during continuous changes in the model's angle of attack, improving test efficiency and meeting the requirements for test agility and high efficiency.

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Abstract

This invention discloses a data-driven subsonic and transonic Mach number control method for transient wind tunnels, relating to the field of aerospace wind tunnel testing. In subsonic and transonic continuous aerodynamic measurement tests, real-time Mach number control is achieved through a combination of total pressure control and static pressure control algorithms. This invention analyzes existing historical data from step-by-step tests to obtain Mach number control parameters, achieving a Mach number control accuracy consistently better than ±0.002 during continuous changes in the model's angle of attack. Furthermore, the Mach number control parameters in this invention do not require identification through unplanned step tests, effectively improving test efficiency. Additionally, by analyzing the test data from the latest test, relevant control parameters can be iteratively optimized.
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Description

Technical Field

[0001] This invention relates to the field of aerospace wind tunnel testing. More specifically, this invention relates to a data-driven method for controlling the subsonic Mach number of a transient wind tunnel for continuous subsonic aerodynamic testing of a certain ejector semi-return transient wind tunnel. Background Technology

[0002] Continuous aerodynamic measurement tests require maintaining the test Mach number control accuracy within a given range during continuous changes in the model's angle of attack in order to obtain valid test data that meets the requirements. This is based on the subsonic and transonic Mach number in the wind tunnel. Ma Calculation formula:

[0003] (1)

[0004] In the above formula, P 0 This represents the total pressure value during the steady-state phase. P s The static pressure value of the test section's sump chamber can be obtained from the formula. Ma The Mach number is determined by the ratio of total pressure to static pressure. A certain ejector semi-return transient wind tunnel controls the total pressure by adjusting the incoming airflow pressure through a pressure regulating valve, and controls the static pressure in the stagnation chamber by adjusting the throttling of the two throats through a grid finger, ultimately achieving precise Mach number control. This type of wind tunnel exhibits strong time delay and nonlinear characteristics in its flow field. Typically, Mach number control in this type of wind tunnel uses PID control, meaning both total pressure and static pressure are controlled using PID. During continuous aerodynamic measurement experiments, the total pressure control accuracy can be maintained within 0.1% throughout the Mach number adjustment process. However, in the static pressure control section, due to the continuous disturbance to the static pressure caused by the model's angle of attack and the inherent adjustment lag of the PID algorithm, the grid finger adjustment of static pressure exhibits lag, causing the Mach number control accuracy to exceed the given accuracy range, making it impossible to obtain effective experimental data.

[0005] To address this issue, patent application CN202110146655.X proposes a subsonic and transonic hydrostatic control method suitable for transient high-speed wind tunnels. Based on model predictive control, it proposes a Mach number control method that can guarantee Mach number control accuracy within ±0.003. However, this method requires grating finger step tests and model angle-of-attack step tests before continuous aerodynamic measurement experiments to identify model parameters and configure control parameters, which is insufficient to meet the current requirements for experimental agility and efficiency. Furthermore, this control method only partially achieves Mach number control accuracy of ±0.002, with the remaining portion only reaching ±0.003.

[0006] Furthermore, the subsonic static pressure control method for an ejector semi-return transient wind tunnel, patent application number CN202411278284.0, uses a grating finger control drive system that controls the grating finger to operate in position based on the grating finger displacement command obtained from the static pressure control algorithm. This allows for the adjustment of static pressure disturbances through changes in grating finger displacement, thereby shortening the time for the grating finger to adjust the static pressure disturbances, reducing the time to complete one test, and decreasing energy consumption. The grating finger displacement value in this method... cf This mainly includes: static pressure disturbance correction function f ( α The current time's gate finger displacement correction amount I is calculated based on the gate finger. f (∆ cf The correction amount II of the grid finger displacement at the current moment, calculated based on hydrostatic pressure. f (∆ P s The method consists of three parts: controlling the displacement of the grating finger to eliminate the delay caused by the static pressure disturbance of the grating finger adjustment. However, the problem is that during the model's angle of attack operation, the Mach number control accuracy will exceed the given control accuracy range. After the model stops at the angle of attack, the Mach number can only meet the given range requirements after the control accuracy is adjusted. This control method is only suitable for subsonic and transonic step-by-step tests and cannot meet the Mach number control accuracy requirements of subsonic and transonic continuous aerodynamic measurement tests.

[0007] Therefore, in order to address the urgent requirement that the Mach number control accuracy must always meet the given control accuracy and satisfy the requirements of test agility and high efficiency in a certain ejector semi-return transient wind tunnel subsonic continuous aerodynamic measurement test, it is necessary to carry out research on new Mach number control methods. Summary of the Invention

[0008] One object of the present invention is to solve at least the above-mentioned problems and / or defects, and to provide at least the advantages described below.

[0009] To achieve these objectives and other advantages of the present invention, a data-driven subsonic and transonic Mach number control method for transient wind tunnels is provided. In subsonic and transonic continuous aerodynamic measurement experiments, real-time Mach number control of the wind tunnel is achieved by combining the total pressure control algorithm and the static pressure control algorithm.

[0010] The static pressure control algorithm obtains the gate finger output displacement value Sz using the following formula:

[0011] Sz = f ( α k )+ f ( Sz k , Ma k )

[0012] In the above formula, k This refers to the current moment in the control cycle. f ( α k )for k The grid finger displacement value output by the static pressure reference model at any given time. f ( Sz k , Ma k )for k Real-time data drives the grid finger correction displacement of the model output;

[0013] The grating finger control system adjusts the grating finger to Sz to achieve real-time control of the Mach number.

[0014] Preferably, the total pressure control algorithm is based on the total pressure setpoint and the actual total pressure collected and fed back in real time, and achieves total pressure control through the PID control method.

[0015] Preferably, the gate finger correction displacement is driven by real-time data in the model output. f ( Sz k , Ma k It is characterized by the following formula:

[0016]

[0017] In the above formula, f ( Sz k , Ma k The shift is the gate finger correction displacement output by the real-time data-driven model. j For gate finger coefficient, T To control the cycle, f ( α k , -Va*T ) represents the grid finger displacement value output by the static pressure reference model for the previous control cycle. α k The actual model angle of attack for the current control cycle. Va The model's angle of attack is the constant speed. Sz k This represents the actual displacement of the gate finger during the current control cycle. k pM and k iM The Mach number coefficients, Ma k This represents the actual Mach number for the current control cycle. Ma g Set a value for the Mach number. Ma k-TThis is the actual Mach number of the previous control cycle.

[0018] Preferably, the grid finger displacement value output by the hydrostatic reference model is... f ( α k It is characterized by the following formula:

[0019]

[0020] In the above formula, α For the model's angle of attack, a, b, c, d, e, g, h These are the coefficients of the static pressure reference model, which are obtained by polynomial regression processing based on historical test data from the stepped test and the actual grid finger displacement and actual angle of attack.

[0021] Preferably, the subsonic and transonic continuous aerodynamic measurement test procedure includes the following steps:

[0022] Step 1: Given the experimental parameters, including the target Mach number. Ma g Total target pressure P 0 Model angle of attack running sequence [ α 1 , α 2 Mach number given control accuracy Δ Ma Control cycle T The model's angle of attack and constant speed Va Determine stability delay ST Return to zero latency ST 0 ;

[0023] Step 2: Run the model to the initial angle of attack. α 0 And remain unchanged, the static pressure control algorithm calculates the output displacement of the gate fingers. Sz 0 = f ( α 0), the gate finger control system moves the gate finger to the gate finger output displacement value. Sz 0 Place;

[0024] Step 3: Start the wind tunnel; the total pressure control algorithm outputs the pressure regulating valve displacement. f (△ P 0 Control the total pressure, adjusting the total pressure control accuracy to within 0.1%, and maintaining this accuracy throughout subsequent tests;

[0025] Step 4: Enter the real-time Mach number adjustment stage, where the static pressure control algorithm calculates the grid finger output displacement value. SzThe gate finger control system will operate the gate fingers to... Sz Adjust the Mach number;

[0026] Step 5: Real-time determination of whether the Mach number control accuracy is less than Δ Ma When less than △ Ma At that time, the model's angle of attack was changed from the initial angle of attack. α 0 Run at a constant speed until α 1 Otherwise, it will be a constant k Assigned value k + T Then proceed to the next control cycle and return to step 4;

[0027] Step 6: Run the model at the angle of attack to... α 1 And while maintaining this, determine whether the Mach number control accuracy is always less than Δ. Ma and maintain ST If the time is specified in seconds, then begin data acquisition for the experiment.

[0028] Step 7: Adjust the model's angle of attack from α1 to... Va The system operates at a constant speed up to α2. During this period, the grating finger control system controls the grating fingers in real time based on a hydrostatic control algorithm to ensure that the Mach number control accuracy is always less than Δ. Ma ;

[0029] Step 8: When the model's angle of attack reaches... α 2 After that, wait ST 0 After a few seconds, the test data acquisition ends, the Mach number adjustment stops, and the test is terminated by returning to zero and shutting off the engine.

[0030] The present invention has at least the following beneficial effects:

[0031] Firstly, this invention analyzes existing historical data from step-by-step tests to obtain Mach number control parameters (Mach number control parameters are the hydrostatic reference model coefficients), thereby achieving the goal of ensuring that the Mach number control accuracy is always better than ±0.002 during the continuous change of the model's angle of attack.

[0032] Secondly, the Mach number control parameters of this method do not need to be obtained through step tests, which effectively improves the test efficiency. At the same time, the Mach number control parameters are iteratively optimized by analyzing the test data of the latest train.

[0033] Other advantages, objectives and features of the present invention will become apparent in part from the following description, and in part from those skilled in the art through study and practice of the invention. Attached Figure Description

[0034] Figure 1 This is a schematic diagram of the Mach number control method of the present invention;

[0035] Figure 2 This is a flowchart of the upper part of the continuous aerodynamic measurement experiment in an embodiment of the present invention;

[0036] Figure 3 This is a flowchart of the second half of the continuous aerodynamic measurement experiment in an embodiment of the present invention;

[0037] Figure 4 This is a schematic diagram of the Mach number adjustment process in an embodiment of the present invention;

[0038] Figure 5 The test results are for prior art 1;

[0039] Figure 6 The test results are for prior art 2;

[0040] Figure 7 The results are experimental findings of the data-driven subsonic transonic Mach number control method for transient wind tunnels based on this invention. Detailed Implementation

[0041] The present invention will now be described in further detail with reference to the accompanying drawings, so that those skilled in the art can implement it based on the description.

[0042] This invention addresses a subsonic transonic continuous aerodynamic measurement test in a semi-returning, ejector-type wind tunnel. It proposes a Mach number control method based on data-driven optimization iteration. The core idea is as follows: the total pressure control section utilizes the PID control method, maintaining total pressure control accuracy within 0.1% throughout the test; for the static pressure control section, an innovative static pressure control algorithm is established based on the static pressure control benchmark model and a real-time data-driven model, obtaining Mach number control parameters through existing step-by-step test historical data.

[0043] Specifically, such as Figure 1 As shown, the total pressure control algorithm of the total pressure control section of this invention is based on the total pressure setpoint and the actual total pressure collected and fed back in real time, that is, the total pressure control is achieved through the PID control method of the following formula:

[0044]

[0045] In the above formula, △ P 0 ( k ) represents the difference between the actual total pressure and the set total pressure at the current moment, Δ P 0 ( k- 1) is the difference between the actual total pressure and the total pressure set value at the previous moment. k p0 and k i0 This is the total pressure deviation correction factor.f (△ P 0 ) represents the displacement output value of the pressure regulating valve.

[0046] The static pressure control algorithm of this invention comprises two parts: a static pressure reference model and a real-time data-driven model fusion processing. Specifically, the static pressure control algorithm is characterized by the following formula:

[0047] Sz = f ( α )+ f ( Sz, Ma )

[0048] In the above formula, Sz The grid finger output displacement value calculated by the final static pressure control algorithm. f ( α () represents the grid finger reference displacement value output by the static pressure reference model. f ( Sz, Ma The ) is the gate finger correction displacement value output by the real-time data-driven model, that is, the final gate finger output displacement value is obtained by adding the gate finger reference displacement value and the gate finger correction displacement value;

[0049] The static pressure reference model outputs the reference displacement of the grating finger at the current moment and the reference displacement of the grating finger at the previous moment based on the model angle of attack, as shown in the following formula:

[0050]

[0051] In the above formula, a, b, c, d, e, g, h These are the coefficients of the static pressure reference model. α For the model's angle of attack, f ( α ) represents the grid finger displacement value output by the static pressure reference model. The coefficients of the static pressure reference model can be obtained through polynomial regression based on the correspondence between the actual grid finger displacement and the actual angle of attack in the stepped test data (and each regression is an iterative optimization of the static pressure reference model coefficients).

[0052] The real-time data-driven model outputs the corrected displacement of the grating finger at the current moment, based on the Mach number setpoint, the actual Mach number of the wind tunnel at the current moment, and the actual displacement of the grating finger. The real-time data-driven model is characterized by the following formula:

[0053]

[0054] In the above formula, j For gate finger coefficient, T To control the cycle, f ( α - Va*T ) represents the grid finger displacement value output by the static pressure reference model for the previous control cycle. αThe actual model angle of attack for the current control cycle. Va The model's angle of attack is the constant speed. Sz This represents the actual displacement of the gate finger during the current control cycle. k pM and k iM The Mach number coefficients, Ma This represents the actual Mach number for the current control cycle. Ma g Set a value for the Mach number. Ma -T This is the actual Mach number of the previous control cycle.

[0055] Example 1

[0056] like Figure 2 - Figure 3 As shown, the experimental procedure for subsonic and transonic continuous aerodynamic force measurement includes the following steps:

[0057] Step 1: Given the experimental parameters, including the target Mach number. Ma g Total target pressure P 0 Model angle of attack running sequence [ α 1 , α 2 Mach number given control accuracy Δ Ma Control cycle T The model's angle of attack and constant speed Va Determine stability delay ST Return to zero latency ST 0 .

[0058] Step 2: Based on historical test data from the stepped advance test, polynomial regression processing is performed using actual grid finger displacement and actual angle of attack to obtain the static pressure reference model coefficients. a, b, c, d, e, g, h .

[0059] Step 3: Run the model to the initial angle of attack. α 0 And remain unchanged, the static pressure control algorithm calculates the output displacement of the gate fingers. Sz 0 = f ( α 0), the gate finger control system moves the gate finger to the gate finger output displacement value. [[ID=6 cuatro]]Sz 0 .

[0060] Step 4: Start the wind tunnel; the total pressure control algorithm outputs the pressure regulating valve displacement. f (△ P 0Control the total pressure, adjust the total pressure control accuracy to within 0.1%, and maintain it throughout the subsequent test.

[0061] Step 5: Enter the Mach number adjustment stage, begin adjusting the Mach number, and continue adjusting the Mach number throughout the subsequent experiments.

[0062] Step 6: The static pressure control algorithm calculates the output displacement value of the grid fingers. Sz and run the gate fingers to Sz Adjust the Mach number.

[0063] Step 7: Real-time determination of whether the Mach number control accuracy is less than Δ Ma When less than △ Ma At that time, the model's angle of attack was changed from the initial angle of attack. α 0 Run at a constant speed until α 1 During this process, it is not required that the Mach number control accuracy is always less than Δ. Ma .

[0064] Step 8: When the model's angle of attack reaches... α 1 Afterwards, the model's angle of attack remained. α 1 The time delay for stability determination begins, and the Mach number control accuracy remains constant at Δ. Ma and maintain ST After a few seconds, the data acquisition phase begins, and experimental data is collected continuously throughout the subsequent process. During the data acquisition phase, it is crucial to ensure that the Mach number control accuracy remains consistently less than Δ. Ma .

[0065] Step 9: The model's angle of attack changes from α1 to the velocity... Va During the constant speed operation to α2, the static pressure control algorithm calculates the output displacement value of the grating finger in real time, controls the grating finger adjustment Mach number, and ensures that the Mach number control accuracy is always less than Δ. Ma .

[0066] Step 10: When the model's angle of attack reaches... α 2 After that, wait ST 0 After a few seconds, the test data acquisition will stop, Mach number adjustment will cease, the engine will be shut down and returned to zero, and the model's angle of attack will be moved to the initial angle of attack. α 0 Then turn off the engine and end the test.

[0067] Example 2

[0068] like Figure 4 As shown, the Mach number adjustment process in the Mach number adjustment stage of the continuous aerodynamic measurement test procedure includes the following steps:

[0069] Step 1: Record the current control cycle time as k Collect the actual angle of attack of the model during the current control cycle. α k Actual Mach number Ma k Actual grid finger displacement Sz k .

[0070] Step 2: Calculate the grid finger displacement value from the hydrostatic reference model. f ( α k ):

[0071] The gate finger correction displacement is calculated by a model driven by real-time data. f ( Sz k , Ma k ):

[0072] Step 3: Calculate the output displacement value of the gate finger Sz :

[0073] Sz = f ( α k )+ f ( Sz k , Ma k ).

[0074] Step 4: Adjust the grid fingers of the grid finger control system to... Sz Adjust the Mach number at that point.

[0075] Step 5: Determine whether to stop Mach number adjustment. If stopped, stop calculating the grid finger output displacement value and maintain the grid finger displacement at the current position; if not stopped, then... k Assigned value k + T Then proceed to the next control cycle and repeat steps 1 to 5.

[0076] Verification example:

[0077] This verification example compares the test results of two prior art technologies with those of the present invention (both prior art technologies and the present invention were tested under the condition of Mach number 1.15) to illustrate the effectiveness of the present invention.

[0078] Prior art 1 (i.e., a subsonic and transonic static pressure control method applicable to transient high-speed wind tunnels, patent application number CN202110146655.X) requires, firstly, a grid finger step test and a model angle-of-attack step test to identify model parameters and configure control parameters for a single effective continuous aerodynamic measurement test in order to obtain effective continuous aerodynamic measurement test data; only then can a continuous aerodynamic measurement test under that condition be carried out. Therefore, based on this control method, two unplanned step tests are required before a single effective continuous aerodynamic measurement test can be conducted, which fails to meet the test agility requirements; and from... Figure 5 As can be seen, during the model's angle of attack operation, the Mach number control accuracy can only meet the control accuracy requirement of ±0.003, which cannot meet the requirement that the Mach number control accuracy is always better than ±0.002.

[0079] Prior art 2 (i.e., the subsonic static pressure control method for an ejector semi-return transient wind tunnel with patent application number CN202411278284.0), from Figure 6 As can be seen, during the operation of the model at certain angles of attack, the Mach number control accuracy will exceed the given control accuracy range of ±0.002. When the model stops at the target angle of attack, the Mach number control accuracy can only meet the requirement of ±0.002 after adjustment. This method cannot meet the requirement that the Mach number control accuracy is always better than ±0.002 during the operation of the model at the angle of attack. This control method is only suitable for subsonic and transonic step test.

[0080] Based on the control method described in this invention, compared to prior art 1, this invention analyzes existing historical data from stepped step tests to obtain control parameters before the test, allowing for continuous aerodynamic measurement tests to be conducted without the need for two unplanned step tests, thus meeting the test agility requirements; simultaneously, from Figure 7 As can be seen, compared with the prior art 2, the present invention maintains the Mach number control accuracy within ±0.002 during the continuous variable angle of attack test, which meets the Mach number control accuracy requirements.

[0081] The above solution is merely an illustration of a preferred example and is not limited thereto. When implementing this invention, appropriate substitutions and / or modifications can be made according to the user's needs.

[0082] Although embodiments of the present invention have been disclosed above, they are not limited to the applications listed in the specification and embodiments. It can be applied to various fields suitable for the present invention. Other modifications can be readily made by those skilled in the art. Therefore, without departing from the general concept defined by the claims and their equivalents, the present invention is not limited to the specific details and examples shown and described herein.

Claims

1. A data-driven method for controlling the subsonic transonic Mach number in a transient wind tunnel, characterized in that, In the subsonic and transonic continuous aerodynamic measurement test, the real-time Mach number control of the wind tunnel is achieved by combining the total pressure control algorithm and the static pressure control algorithm. The static pressure control algorithm obtains the gate finger output displacement value Sz using the following formula: Sz = f ( α k )+ f ( Sz k Ma k ) In the above formula, k This refers to the current time in the control cycle. f ( α k )for k The grid finger displacement value output by the static pressure reference model at any given time. f ( Sz k Ma k )for k Real-time data drives the grid finger correction displacement of the model output; The grating finger control system adjusts the grating finger to Sz to achieve real-time control of the Mach number; The total pressure control algorithm is based on the total pressure setpoint and the actual total pressure collected and fed back in real time, and achieves total pressure control through the PID control method. k Real-time data drives the grid finger correction displacement of the model output. f ( Sz k Ma k It is characterized by the following formula: In the above formula, f ( Sz k Ma k )for k Real-time data drives the grid finger displacement correction of the model output. j For gate finger coefficients, T To control the cycle, f ( α k -Va*T ) represents the grid finger displacement value output by the static pressure reference model for the previous control cycle. α k The actual model angle of attack for the current control cycle. Va The model's angle of attack is the constant speed. Sz k This represents the actual gate finger displacement during the current control cycle. k pM and k iM The Mach number coefficients, Ma k This represents the actual Mach number for the current control cycle. Ma g Set a value for the Mach number. Ma k-T This is the actual Mach number of the previous control cycle; k The grid finger displacement value output by the static pressure reference model at any time f ( α k It is characterized by the following formula: In the above formula, α For the model's angle of attack, a,b,c,d,e,g,h These are the static pressure reference model coefficients, which are obtained by polynomial regression processing based on historical test data from the stepped step test and the actual grid finger displacement and the actual model angle of attack. The experimental procedure for continuous subsonic and transonic aerodynamic measurement includes the following steps: Step 1: Specify the experimental parameters, including the Mach number setpoint. Ma g Total target pressure P 0 Model angle of attack running sequence [ α 1 , α 2 Mach number given control accuracy Δ Ma Control cycle T The model's angle of attack and constant speed Va Determine stability delay ST Return to zero latency ST 0 ; Step 2: Run the model to the initial angle of attack. α 0 And remain unchanged, the static pressure control algorithm calculates the output displacement value of the gate finger. Sz 0 = f ( α 0), the gate finger control system moves the gate finger to the gate finger output displacement value. Sz 0 Place; Step 3: Start the wind tunnel; the total pressure control algorithm outputs the pressure regulating valve displacement. f (△ P 0 Control the total pressure, adjusting the total pressure control accuracy to within 0.1%, and maintaining this accuracy throughout subsequent tests; Step 4: Enter the real-time Mach number adjustment stage, and the static pressure control algorithm calculates the grid finger output displacement value. Sz The gate finger control system will operate the gate fingers to... Sz Adjust the Mach number; Step 5: Real-time determination of whether the Mach number control accuracy is less than Δ Ma When less than △ Ma At that time, the model's angle of attack was changed from the initial angle of attack. α 0 Run at a constant speed until α 1 Otherwise, it will be a constant k Assigned value k+T Then proceed to the next control cycle and return to step 4; Step 6: Run the model at the angle of attack to... α 1 And while maintaining this, determine whether the Mach number control accuracy is always less than Δ. Ma and maintain ST If the time is specified in seconds, then begin data acquisition for the experiment. Step 7: Adjust the model's angle of attack from α1 to... Va During the constant-speed operation to α2, the grating finger control system controls the grating fingers in real time based on a hydrostatic control algorithm to ensure that the Mach number control accuracy is always less than Δ. Ma ; Step 8: When the model's angle of attack reaches... α 2 After that, wait ST 0 After a few seconds, the test data acquisition ends, the Mach number adjustment stops, and the test is terminated by returning to zero and shutting off the engine.

Citation Information

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