A test system and method for key parameters of a turbojet engine

Abstract

This invention relates to a key parameter testing system and method for turbojet engines, belonging to the field of unmanned aerial vehicle (UAV) technology. It enables the measurement of key parameters and identification of dynamic characteristics of turbojet engines, providing prerequisite input conditions for the design and simulation of flight control laws and effectively reducing experimental risks. The system includes a mounting bracket, engine working components, a main control module, a thrust sensor, and an environmental measurement sensor. The mounting bracket is used to fix the turbojet engine under test. The engine working components are connected to the turbojet engine under test to ensure its normal operation. The main control module is connected to the turbojet engine under test and the environmental measurement sensor to control the actions of the turbojet engine under test according to test requirements and environmental data monitored by the environmental measurement sensor. The thrust sensor is located between the engine mounting bracket and the turbojet engine under test and is connected to the main control module to measure the thrust of the turbojet engine under test.

Description

Technical Field

[0001] This invention relates to the field of unmanned aerial vehicle (UAV) technology, and in particular to a test system and method for testing key parameters of turbojet engines. Background Technology

[0002] The measurement of key engine parameters and the identification of dynamic characteristics are crucial for the performance evaluation and flight control law design of the entire UAV. During the procurement of many imported aero engines, manufacturers often fail to provide accurate mathematical models, severely impacting the overall design of the UAV. Therefore, purchased aero engines typically require extensive ground testing before installation and use to confirm their operating parameters and identify their mathematical models.

[0003] Turbojet engines have high impeller rotation speeds and high exhaust gas temperatures. To ensure a long engine lifespan, their dynamic adjustment process is typically slow, which significantly impacts the flight control of high-speed unmanned aerial vehicles (UAVs). Currently, ground-based engine test benches often suffer from poor real-time data measurement and low sampling frequency. While integrating the engine onto a UAV can solve the real-time data problem, the accuracy of the collected data is often insufficient, and some data may even be unavailable, failing to meet the requirements for identifying the dynamic characteristics of turbojet engines. Furthermore, the full-damper control process of turbojet engines exhibits significant nonlinear characteristics, necessitating the use of first-order inertial and proportional elements. The dynamic characteristics have a large error when performing identification, making it unsuitable for high-speed drones.

[0004] Patent CN 105510035 A discloses a piston-type aero-engine testing system that stores test data on an industrial computer, resulting in poor data real-time performance and low sampling frequency. While integrating the engine onto a UAV can solve the real-time data sampling problem, the accuracy of the collected data is often insufficient, and some data may even be unavailable. Patent CN110889239 A discloses an aero-gas turbine engine modeling method based on flight parameter data identification, providing a method for identifying engine damper to speed. However, its engine model uses first-order integral, proportional, and additive components, i.e. The model identified by this method deviates significantly from the actual dynamic process of the engine and cannot reflect the changes in engine damper and thrust, so it cannot be used directly in the design of control laws.

[0005] Therefore, it is necessary to study a test system and test method for key parameters of turbojet engines to address the shortcomings of existing technologies and solve or mitigate one or more of the above-mentioned problems. Summary of the Invention

[0006] In view of this, the present invention provides a key parameter testing system and method for turbojet engines, which can realize the measurement of key parameters and identification of dynamic characteristics of turbojet engines, provide prerequisite input conditions for the design and simulation of flight control laws, and effectively reduce experimental risks.

[0007] This invention provides a key parameter testing system for a turbojet engine, characterized in that the system includes: an engine mounting bracket, engine working parts, a main control module, a thrust sensor, and an environmental measurement sensor;

[0008] The engine mounting bracket is used to fix the turbojet engine under test.

[0009] The engine working parts are connected to the turbojet engine under test to ensure the normal operation of the turbojet engine under test.

[0010] The main control module is connected to the turbojet engine under test and the environmental measurement sensor, and is used to control the action of the turbojet engine under test according to the test requirements and the environmental data monitored by the environmental measurement sensor.

[0011] The thrust sensor is positioned between the engine mounting bracket and the turbojet engine under test, and is connected to the main control module to measure the thrust of the turbojet engine under test.

[0012] In addition to the aspects and any possible implementations described above, a further implementation is provided in which the main control module includes an airborne flight control computer, a monitoring computer, and a parameter recorder; the monitoring computer, the airborne flight control computer, and the turbojet engine under test are connected in sequence.

[0013] The environmental measurement sensor is connected to the monitoring computer;

[0014] Both the parameter recorder and the thrust sensor are connected to the airborne flight control computer.

[0015] The airborne flight control computer is used to receive instructions from the monitoring computer to control the operation of the turbojet engine under test, and to collect the operating parameters of the turbojet engine under test and transmit them to the parameter recorder for recording.

[0016] In addition to the aspects described above and any possible implementations, a further implementation is provided in which the system further includes an engine mounting stand, on which the engine mounting bracket and the engine working accessory are both fixed.

[0017] In addition to the aspects and any possible implementations described above, a further implementation is provided in which the engine working accessories include an intake manifold, fuel and starting system accessories that are compatible with the turbojet engine under test.

[0018] In addition to the aspects described above and any possible implementations, a further implementation is provided in which the environmental data monitored by the environmental measurement sensor includes the temperature, humidity, and atmospheric pressure of the test environment.

[0019] On the other hand, the present invention provides a method for testing key parameters of a turbojet engine, wherein the testing method is implemented using any of the testing systems described above; the steps of the method include:

[0020] S1. Select several typical damper test points within the entire damper range;

[0021] S2. The main control module controls the turbojet engine under test to work at each typical damper test point and maintain the preset time according to the selected typical damper test points.

[0022] S3. The main control module collects and stores the key parameters of the turbojet engine under test under each typical damper test point condition; the key parameters include damper data, speed data and thrust data.

[0023] S4. Read the key parameters stored, analyze them using MATLAB, and determine the static gain of the engine model and each typical damper test point under balanced conditions.

[0024] S5. Use Simulink to perform linear simulations of key parameters to identify other parameters besides static gain under the equilibrium state of different typical damper test points, including inertial time constant and time delay.

[0025] S6. Based on the results of S4 and S5, obtain the engine model under a certain equilibrium condition;

[0026] S7. Use Simulink to perform a nonlinear full simulation of the engine model obtained in S6.

[0027] S8. Compare the simulation results of S7 with the key parameter data obtained from the test to analyze whether the thrust error meets the tolerance requirements.

[0028] If the conditions are met, the engine model obtained in step S6 is determined to be real and valid, and can be used for the design and simulation of the control law; otherwise, repeat steps S6-S8 until the above tolerance requirements are met.

[0029] In addition to the aspects and any possible implementations described above, a further implementation is provided in which the tolerance requirement in step S8 is specifically: thrust error ≤ 10%.

[0030] In addition to the aspects and any possible implementations described above, a further implementation is provided in which the selection of typical damper test points in step S1 is specifically as follows: test points are selected in 5% increments within the 50% to 100% damper range.

[0031] In addition to the aspects and any possible implementations described above, an implementation is further provided in which test points are selected in 5% increments within the 50% to 100% damper range, specifically including: increasing from 50% to 100% and decreasing from 100% to 50%.

[0032] In addition to the aspects and any possible implementations described above, a further implementation is provided, wherein step S4 includes:

[0033] S41. Plot the curves of the damper data, speed data, and thrust data over time. Analyze the data in conjunction with the actual test process to see if there are any missing frames or data jumps, and remove the failed data.

[0034] S42. Plot the engine's throttle-thrust variation curve, and determine the engine model based on this curve;

[0035] S43. Using MATLAB to perform curve fitting on the damper and thrust, the full expressions for the damper and thrust are obtained:

[0036] S44. Differentiate the full expression of damper and thrust to obtain the relationship between static gain and damper under equilibrium state, thereby determining static gain.

[0037] Compared with the prior art, one of the above technical solutions has the following advantages or beneficial effects: The test system of the present invention has the characteristics of simple structure and high real-time measurement data. Using the present invention, the key parameters of turbojet engines can be measured and dynamic characteristics identified, providing the prerequisite input conditions for the design and simulation of flight control laws, and effectively reducing the test risk.

[0038] Of course, any product implementing this invention does not necessarily need to achieve all of the technical effects described above at the same time. Attached Figure Description

[0039] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0040] Figure 1 This is a connection diagram of a drone turbojet engine testing system provided in one embodiment of the present invention.

[0041] In the figure:

[0042] 1. Engine mounting stand; 2. Fuel and starting system accessories of the engine under test; 3. Turbojet engine under test; 4. Air intake; 5. Thrust sensor; 6. Engine mounting bracket; 7. Cables; 8. DC regulated power supply; 9. Parameter recorder; 10. Airborne flight control computer; 11. Monitoring computer; 12. Environmental measurement sensor. Detailed Implementation

[0043] To better understand the technical solution of the present invention, the embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0044] It should be understood that the described embodiments are merely some, not all, of the embodiments of the present invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

[0045] To address the shortcomings of existing technologies, this invention provides a key parameter testing system and dynamic characteristic identification method for turbojet engines. Wherein:

[0046] Turbojet engine key parameter testing system, such as Figure 1 As shown, it includes:

[0047] An engine mounting stand is equipped with an engine mounting bracket and accessories for the engine under test, including the air intake, fuel, and starting system. It is used to fix the turbojet engine under test and ensure its normal operation. A force sensor is mounted on the engine mounting stand. The force sensor is installed between the engine mounting bracket and the turbojet engine under test and is used to measure the engine thrust in real time.

[0048] The monitoring computer is equipped with engine control software, allowing test personnel to control and monitor the engine in real time during the test.

[0049] A thrust sensor with an installation interface compatible with the turbojet engine under test and the engine mounting stand, is used to measure the thrust generated by the turbojet engine in real time during operation.

[0050] The airborne flight control computer has multiple communication interfaces such as CAN, RS422, and USB. It can be connected to the turbojet engine under test, the thrust sensor, the parameter recorder, the monitoring computer, and other equipment. It is used to receive instructions generated by the monitoring computer to control the engine operation. On the other hand, it collects information such as engine speed and thrust output by the engine fixed test bench and sends it to the parameter recorder.

[0051] The parameter recorder can receive and store key status parameters sent by the airborne flight control computer in real time, providing a basis for identifying the dynamic characteristics of the engine;

[0052] The DC regulated power supply has two independent DC power outputs, which can provide power to the engine under test and the airborne flight control computer, respectively.

[0053] This temperature, humidity, and atmospheric pressure sensor can measure the temperature, humidity, and atmospheric pressure of the test environment in real time and transmit the data to a monitoring computer via a digital interface.

[0054] The method for measuring key parameters and identifying dynamic characteristics using the aforementioned turbojet engine testing system provided by this invention includes:

[0055] First, typical test points are selected within the entire damper range. Key parameters such as damper setpoint, engine speed, and thrust at these typical test points are measured and recorded using the aforementioned testing system. Then, the nonlinear response characteristics of the engine within the entire damper range are obtained through parameter identification methods. Specifically, the following steps are included:

[0056] Step 1: After the engine starts, select several typical test points in the full choke range (idle speed -> vehicle speed -> idle speed) at 5% choke increments.

[0057] Step 2: After the speed stabilizes at a typical test point, adjust the damper position via the monitoring computer to proceed to the next test point;

[0058] Step 3: During the test, data such as throttle input, engine speed, and thrust are stored in the parameter recorder at a data refresh rate of no less than 20Hz.

[0059] Step 4: After the test, read and analyze the key parameters such as engine throttle setpoint, speed, and thrust, use MATLAB to plot the corresponding curves and determine their rationality in combination with the actual test situation;

[0060] Step 5: Use MATLAB to plot the variation curve with the throttle command as input and the thrust magnitude as output, and fit the nonlinear expression of the throttle command and thrust. Observe the curve to approximately determine the engine model.

[0061] Step 6: Linearize the nonlinear expressions of damper command and thrust at each typical test point to determine the static gain under equilibrium conditions at that point.

[0062] Step 7: Use the Parameter Estimation toolbox in Simulink to perform linear simulation and identify the inertial time constant T and time delay τ at different test points under equilibrium conditions.

[0063] Step 8: Based on the models under equilibrium conditions at different typical test points, calculate the model under any equilibrium condition;

[0064] Step 9: Using the calculated model, perform a nonlinear full-scale simulation in Simulink. Compare the full-scale simulation results with the damper command-thrust curve obtained from the experiment to analyze whether the thrust error meets the tolerance requirements.

[0065] The tolerance threshold value ranges from ≤10%.

[0066] If the thrust obtained from the nonlinear simulation is within the above tolerance threshold range, it indicates that the engine thrust mathematical model identified through the above steps is true and effective, and can be used for control law design and simulation. Otherwise, repeat step 8. Based on the model under equilibrium conditions at different typical test points, establish a nonlinear model under any equilibrium condition for the data characteristics of the throttle rising and falling phases respectively, and repeat step 9 until the nonlinear thrust error of the entire throttle meets the requirements.

[0067] Example 1

[0068] like Figure 1 As shown, this invention discloses a key parameter testing system for a UAV turbojet engine, mainly comprising an engine mounting stand 1, a thrust sensor 5, an engine mounting bracket 6, cables for power supply and communication to the engine mounting stand 7, a DC regulated power supply 8, a parameter recorder 9, an onboard flight control computer 10, a monitoring computer 11, and an environmental measurement sensor combining temperature, humidity, and atmospheric pressure 12. In the figure, 3 represents the turbojet engine under test, 4 represents the engine's air intake, and 2 represents the fuel and starting system accessories of the engine under test.

[0069] Among them, the engine fuel and starting system accessory 2 includes an oil tank, solenoid valve, igniter, starter battery, etc., which are fixed to the engine mounting frame 1 by cable ties, clamps, etc.

[0070] The air intake duct 4 of the engine is sealed to the air intake of the turbojet engine 3 by tape.

[0071] The thrust sensor 5 is a cylindrical tension and compression type force sensor that is installed between the turbojet engine 3 under test and the engine mounting bracket 6 via an M12 threaded rod.

[0072] The DC regulated power supply 8 supplies power to the ECU of the turbojet engine 3 under test and the airborne flight control computer 10 through two independent power supply cables.

[0073] The airborne flight control computer 10 controls the operation of the turbojet engine 3 under test through the CAN interface and collects its status data in real time at a frequency of not less than 20Hz; at the same time, the airborne flight control computer 10 writes the key status data collected in real time to the parameter recorder 9 through the USB interface.

[0074] The monitoring computer 11 sends engine control commands to the airborne flight control computer 10 via RS422 and receives the status data returned by it; at the same time, it receives test environment data sent by the temperature, humidity and atmospheric pressure combined environmental measurement sensor 12 via RS485.

[0075] The specific methods and steps for measuring key parameters and identifying dynamic characteristics of a certain UAV turbojet engine are as follows:

[0076] 1) Select measurement points in 5% increments within the 50% to 100% damper range. The measurement points recorded when increasing from 50% to 100% are marked as N. 50+ N 55+ ...N 95+ The measurement points recorded when the percentage decreases from 100% to 50% are marked as N. 100- N 95- N 90- ...N 55- ;

[0077] 2) The engine should run stably for more than 3 minutes at each measurement point to ensure that the dynamic adjustment process is completely transitioned to a steady state;

[0078] 3) Set the engine choke to δ p The rotational speed n and thrust P are recorded in real time in the parameter recorder 9, with a data storage period of 50ms.

[0079] 4) After the experiment, analyze and plot the damper setpoint δ p The curves of the changes of speed n, thrust P and time are analyzed in conjunction with the actual test process to determine whether there are any frame drops, data jumps or other issues.

[0080] 5) After confirming the validity of the recorded data, draw the engine choke command δ. p —Thrust change P-curve. Observing the curve, it can be seen that the dynamic characteristic of thrust change from throttle command to thrust can be approximated as a first-order inertial element with a certain time delay. Therefore, the engine model is determined as follows: The form;

[0081] 6) Using MATLAB to control the damper command δ p By performing curve fitting with the thrust P, the relationship between P and δ can be obtained. p The full expression:

[0082]

[0083] The maximum relative error of the fit is 2.758%, which meets the requirements.

[0084] 7) For P(δ) p Differentiating the expression yields the static gain K as a function of the damper command δ under equilibrium conditions. pss The relationship between the changes is as follows:

[0085]

[0086] The damper command δ will be transferred separately. pss Substituting 50%, 55%, ..., 100% into the above formula yields the static gain K' under different equilibrium conditions, denoted as K'. 50 K' 55 ...K' 100 ;

[0087] 8) Using the Parameter Estimation toolbox built into Simulink, identify the static gain K, inertial time constant T, and time delay τ under this condition at different test points through step response, and label them as K. 50+ K 55+ ...K 100- K 95- ...K 55- T 50+ T 55+ ...T 100- T 95- ...T 55- , τ 50+ τ 55+ ...τ 100- τ 95- ...τ 55- ;

[0088] 10) The experimental results obtained from identifying two dynamic processes—one increasing and one decreasing—at the same given damper location are averaged, i.e., K 50 =K 50+ K 55 =(K 55+ +K 55- ) / 2……K 95 =(K 95+ +K 95- ) / 2、K 100 =K 100- Thus, the linearized model for small perturbations at damper commands of 50%, 55%, ..., 100% can be determined;

[0089] 11) Comparing the static gain K obtained through parameter estimation with the theoretically calculated static gain K', it was found that the two sets of data are basically consistent. Therefore, the theoretical calculation formula for the static gain is adopted. As the final identification result;

[0090] 12) Analysis of the identification results revealed significant differences in the time constants of the inertial elements identified during the rising and falling phases of the damper command. To address this issue, firstly, the experimental data from the rising, falling, and entire change phases of the damper command were averaged to determine the model under arbitrary equilibrium conditions. Secondly, nonlinear full-scale simulations were performed on the three models to comprehensively select the model with the best performance.

[0091] 13) By comparing the nonlinear simulation results under three different models, it was found that the model response obtained after averaging the experimental data throughout the entire change phase has the smallest relative thrust error compared to the actual test data, and also exhibits better dynamic characteristics throughout the flight. Therefore, the calculations for the inertial time constant T and time delay τ can be determined as follows:

[0092] T = (T 50+ +T 55+ +...+T 95+ +T 100- +T 95- +...T 55- ) / 20;

[0093] τ=(τ 50+ +τ 55+ +...+τ 95+ +τ 100- +τ 95- +...τ 55- ) / 20;

[0094] 14) From step 13), the dynamic response characteristics of this type of turbojet engine under any equilibrium condition can be finally determined as follows:

[0095]

[0096] in:

[0097] The foregoing has provided a detailed description of a key parameter testing system and method for a turbojet engine provided in the embodiments of this application. The descriptions of the embodiments above are merely for the purpose of helping to understand the method and its core ideas; furthermore, those skilled in the art will recognize that, based on the ideas of this application, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of this application.

[0098] It should also be noted that the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a product or system comprising a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a product or system. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the product or system including said element. "Substantially" means within an acceptable margin of error, indicating that a person skilled in the art can resolve the technical problem and substantially achieve the technical effect within a certain margin of error.

[0099] The terminology used in the embodiments of this invention is for the purpose of describing particular embodiments only and is not intended to limit the invention. The singular forms “a,” “the,” and “the” used in the embodiments of this invention and the appended claims are also intended to include the plural forms unless the context clearly indicates otherwise. In the above embodiments, implementation may be achieved wholly or partially by software, hardware, firmware, or any combination thereof. When implemented in the form of a computer program product, which includes one or more computer instructions, when loaded or executed on a computer, all or part of the processes or functions described in the embodiments of this invention are generated. The computer may be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions may be stored in a computer-readable storage medium or transmitted from one computer-readable storage medium to another, for example, the computer instructions may be transmitted from one website, computer, server, or data center to another via wired (e.g., coaxial cable, fiber optic, digital subscriber line (DSL) or wireless (e.g., infrared, wireless, microwave, etc.) means). The computer-readable storage medium may be any available medium accessible to a computer or a data storage device such as a server or data center that integrates one or more available media. The available media may be magnetic media (e.g., floppy disks, hard disks, magnetic tapes), optical media (e.g., DVDs), or semiconductor media (e.g., solid state disks (SSDs)).

Claims

1. A method for testing key parameters of a turbojet engine, characterized in that, The steps of the method include: S1. Select several typical damper test points within the entire damper range; S2. The main control module controls the turbojet engine under test to work at each typical damper test point and maintain the preset time according to the selected typical damper test points. S3. The main control module collects and stores the key parameters of the turbojet engine under test under each typical damper test point condition; the key parameters include damper data, speed data and thrust data. S4. Read the key parameters stored, analyze them using MATLAB, and determine the static gain of the engine model and each typical damper test point under balanced conditions. S5. Use Simulink to perform linear simulations of key parameters to identify other parameters besides static gain under the equilibrium state of different typical damper test points, including inertial time constant and time delay. S6. Based on the results of S4 and S5, obtain the engine model under a certain equilibrium condition; S7. Use Simulink to perform a nonlinear full simulation of the engine model obtained in S6. S8. Compare the simulation results of S7 with the key parameter data obtained from the test to analyze whether the thrust error meets the tolerance requirements. If the conditions are met, the engine model obtained in step S6 is determined to be real and valid, and can be used for the design and simulation of the control law; otherwise, repeat steps S6-S8 until the above tolerance requirements are met. The key parameter testing system for turbojet engines used to implement the method includes: an engine mounting bracket, engine working parts, a main control module, a thrust sensor, and an environmental measurement sensor. The engine mounting bracket is used to fix the turbojet engine under test. The engine working parts are connected to the turbojet engine under test to ensure the normal operation of the turbojet engine under test. The main control module is connected to the turbojet engine under test and the environmental measurement sensor, and is used to control the action of the turbojet engine under test according to the test requirements and the environmental data monitored by the environmental measurement sensor. The thrust sensor is positioned between the engine mounting bracket and the turbojet engine under test, and is connected to the main control module to measure the thrust of the turbojet engine under test.

2. The method for testing key parameters of a turbojet engine according to claim 1, characterized in that, The main control module includes an airborne flight control computer, a monitoring computer, and a parameter recorder; the monitoring computer, the airborne flight control computer, and the turbojet engine under test are connected in sequence. The environmental measurement sensor is connected to the monitoring computer; Both the parameter recorder and the thrust sensor are connected to the airborne flight control computer. The airborne flight control computer is used to receive instructions from the monitoring computer to control the operation of the turbojet engine under test, and to collect the operating parameters of the turbojet engine under test and transmit them to the parameter recorder for recording.

3. The method for testing key parameters of a turbojet engine according to claim 1, characterized in that, The system also includes an engine mounting stand, on which the engine mounting bracket and the engine working parts are fixed.

4. The method for testing key parameters of a turbojet engine according to claim 1, characterized in that, The engine working accessories include the intake manifold, fuel system, and starting system accessories that are compatible with the turbojet engine under test.

5. The method for testing key parameters of a turbojet engine according to claim 1, characterized in that, The environmental data monitored by the environmental measurement sensor includes the temperature, humidity, and atmospheric pressure of the test environment.

6. The method for testing key parameters of a turbojet engine according to claim 1, characterized in that, The tolerance requirement in step S8 is specifically: thrust error ≤ 10%.

7. The method for testing key parameters of a turbojet engine according to claim 1, characterized in that, The selection of typical damper test points in step S1 is as follows: test points are selected in 5% increments within the 50%~100% damper range.

8. The method for testing key parameters of a turbojet engine according to claim 7, characterized in that, Test points were selected in 5% increments within the 50%~100% damper range, specifically from 50% to 100% and from 100% to 50%.

9. The method for testing key parameters of a turbojet engine according to claim 1, characterized in that, Step S4 includes: S41. Plot the curves of the damper data, speed data, and thrust data over time. Analyze the data in conjunction with the actual test process to see if there are any missing frames or data jumps, and remove the failed data. S42. Plot the engine's throttle-thrust variation curve, and determine the engine model based on this curve; S43. Using MATLAB to perform curve fitting on the damper and thrust, the full expressions for the damper and thrust are obtained: S44. Differentiate the full expression of damper and thrust to obtain the relationship between static gain and damper under equilibrium state, thereby determining static gain.

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