Dynamic modeling and verification method and system for sailboard driving and flexible coupling

Abstract

The invention discloses a dynamic modeling and verification method and system for sailboard driving and flexible coupling, and the method comprises the steps: measuring a driving torque in a sailboard driving process under different open-loop rotation angular velocity commands of a sailboard driving mechanism, and then carrying out the calculation to obtain the angular acceleration of the rotation of a sailboard; then, obtaining a spectrogram of the sailboard driving torque and the sailboard rotation angular acceleration through fast Fourier transform, extracting the main frequency of the spectrogram, and fitting the relationship between the sailboard driving torque and the sailboard rotation angular acceleration and the open-loop rotation angular velocity command of the driving mechanism; and finally, the fitted sailboard driving torque is added to satellite rigid body attitude dynamics, the sailboard rotation angular acceleration is added to a sailboard flexible vibration equation, and the satellite attitude control angular velocity stability and the coupling vibration influence on flexible accessories are analyzed.

Description

Technical Field

[0001] The present invention belongs to the technical field of satellite dynamics, and particularly relates to a dynamic modeling and verification method and system for sailboard drive and flexible coupling. Background Art

[0002] When most satellites are in orbit, the solar sailboard needs to rotate relative to the satellite body to track the sun. Traditional sailboard drive mechanisms all use stepper motors for driving. To ensure simple and reliable driving, stepper motors are generally driven in an open-loop control manner, and this method is widely used in orbit. However, the open-loop drive of the stepper motor is controlled by PWM pulses, and its dynamic response performance is poor. Coupled with the influence of the motor's own harmonic torque and the mechanism's frictional torque, the rotational speed of the sailboard drive is unstable, directly affecting the stability of satellite attitude control.

[0003] In the traditional satellite dynamics modeling process, the influence of unstable driving torque generated during the sailboard drive process is not considered, and the coupling influence between the frequency of the sailboard drive disturbance torque and the structural frequencies of flexible attachments such as the satellite sailboard is ignored. The satellite attitude dynamics modeling is not accurate enough, resulting in the satellite attitude simulation results not being able to truly reflect the state of the actual in-orbit operation process, and there is a large difference between the ground simulation attitude stability and the in-orbit data. Summary of the Invention

[0004] The technical problem to be solved by the present invention is: The present invention provides a dynamic modeling and verification method and system for sailboard drive and flexible coupling. In order to more truly and completely reflect the influence of sailboard drive control on satellite attitude stability, the flexible coupling influence between the sailboard drive disturbance torque and the structural vibration of flexible attachments such as the satellite sailboard is verified.

[0005] The technical solution adopted by the present invention is: A dynamic modeling and verification method for sailboard drive and flexible coupling, comprising:

[0006] Obtaining the sailboard driving torque and the sailboard rotational angular acceleration corresponding to different driving mechanism open-loop rotational angular velocities ω i ;

[0007] Calculating the spectrograms of the sailboard driving torque and the sailboard rotational angular acceleration corresponding to different driving mechanism open-loop rotational angular velocities ω i ;

[0008] Fitting to obtain the relationship between the sailboard driving torque and different driving mechanism open-loop rotational angular velocities ω i and the relationship between the sailboard rotational angular acceleration and different driving mechanism open-loop rotational angular velocities ω i ;

[0009] Substituting the relationship between the sailboard driving torque and different driving mechanism open-loop rotational angular velocities ω obtained by fitting iThe relational expressions of the driving torque of the sailboard and the angular acceleration of the sailboard's rotation, and the open-loop rotational angular velocity ω of different driving mechanisms i Add the relational expressions to the satellite dynamics model to obtain an updated satellite dynamics model;

[0010] Perform satellite attitude control simulation on the updated satellite dynamics model.

[0011] Furthermore, the obtaining of the driving torque of the sailboard and the angular acceleration of the sailboard's rotation includes:

[0012] Install the sailboard simulation piece on the sailboard driving mechanism. The sailboard simulation piece has the same inertia as the sailboard. Measure the actual magnitude of the driving torque of the sailboard during the driving process of the sailboard through a six-axis force test bench at different open-loop rotational angular velocities ω of the driving mechanism i ; Calculate the curve of the angular acceleration of the sailboard's rotation changing with time according to the inertia of the sailboard simulation piece; i represents different rotational angular velocity gears.

[0013] Furthermore, the calculating of the spectrum diagrams of the driving torque of the sailboard and the angular acceleration of the sailboard's rotation corresponding to different open-loop rotational angular velocities ω of different driving mechanisms i :

[0014] Perform fast Fourier transform on the data of the driving torque of the sailboard and the angular acceleration of the sailboard's rotation corresponding to different open-loop rotational angular velocities ω of different driving mechanisms i to obtain the spectrum diagrams of the driving torque of the sailboard and the angular acceleration of the sailboard's rotation;

[0015] Extract the frequency signals f i of the driving torque of the sailboard, the amplitude A i of the driving torque of the sailboard, and the angular acceleration B i of the sailboard's rotation according to the spectrum diagrams of the driving torque of the sailboard and the angular acceleration of the sailboard's rotation.

[0016] Furthermore, the fitting of the relationship between the driving torque of the sailboard and different open-loop rotational angular velocities ω of different driving mechanisms i and the relationship between the angular acceleration of the sailboard's rotation and different open-loop rotational angular velocities ω of different driving mechanisms i includes:

[0017] Calculate the driving frequency f i of the sailboard according to the relationship between the driving frequency of the stepping motor and the open-loop rotational angular velocity ω 驱i of the driving mechanism:

[0018]

[0019] where k is the reduction ratio and θ b is the step angle of the stepping motor;

[0020] Determine the frequency signal fi With the frequency doubling relationship of the windsurfing driving frequency f 驱i and fitting to obtain the open-loop rotational angular velocity ω of different driving mechanisms i Under the condition, the amplitude A of the windsurfing driving torque i The relational expression between A and the rotational angular velocity of the windsurfing i = f(ω i ), the angular acceleration B of the windsurfing rotation i The relational expression between B and the rotational angular velocity of the windsurfing i = f(ω i );

[0021] Fitting to obtain the relational expression T of the windsurfing driving torque 驱动干扰 And the open-loop rotational angular velocity of the driving mechanism 驱动干扰 = f(ω i ), the angular acceleration of the windsurfing rotation And the relationship between the open-loop rotational angular velocity of the driving mechanism

[0022]

[0023] Furthermore, the relational expression of the windsurfing driving torque obtained by fitting with the open-loop rotational angular velocity ω of different driving mechanisms i The relational expression of the angular acceleration of the windsurfing rotation and the open-loop rotational angular velocity ω of different driving mechanisms i Adding to the satellite dynamics model, the updated satellite dynamics model includes:

[0024] Adding the fitted windsurfing driving torque T 驱动干扰 To the satellite rigid body attitude dynamics model:

[0025]

[0026] Among them, I 卫星 Represents the moment of inertia of the satellite, Represents the angular acceleration of the satellite's rotation, T 其他 Represents the torque that drives the rotation of the satellite body;

[0027] Adding the angular acceleration of the windsurfing rotation to the windsurfing flexural vibration equation to verify the change of the windsurfing flexural vibration:

[0028]

[0029] Among them, q is the vibration mode coordinate of the windsurfing, ζ is the windsurfing damping coefficient matrix, Ω is the windsurfing flexural vibration frequency matrix, B 转动 Is the coupling coefficient of the windsurfing rotation to the satellite body, b 转 Is the coupling coefficient of the windsurfing's own rotation.

[0030] Further, the satellite attitude control simulation for the updated satellite dynamics model includes:

[0031] Adding the updated dynamics model to the satellite attitude control simulation, performing simulation according to the actual operating state of the satellite, generating open-loop rotational angular velocity commands of different magnitudes for the drive mechanism according to the orbital altitude, and verifying the influence of the unstable characteristics of the driving torque of the sailboard stepping motor on the stability of the satellite attitude control angular velocity and the coupled vibration of the satellite flexible appendages.

[0032] A dynamic modeling and verification system for sailboard drive and flexible coupling includes:

[0033] The first module is used to obtain the sailboard driving torque and the sailboard rotational angular acceleration corresponding to different open-loop rotational angular velocities ω of the drive mechanism; calculate the spectrograms of the sailboard driving torque and the sailboard rotational angular acceleration corresponding to different open-loop rotational angular velocities ω of the drive mechanism; i The second module is used to fit the relationship between the sailboard driving torque and different open-loop rotational angular velocities ω of the drive mechanism, and the relationship between the sailboard rotational angular acceleration and different open-loop rotational angular velocities ω of the drive mechanism; i The third module is used to add the relationship between the sailboard driving torque and different open-loop rotational angular velocities ω of the drive mechanism, and the relationship between the sailboard rotational angular acceleration and different open-loop rotational angular velocities ω of the drive mechanism obtained by fitting to the satellite dynamics model to obtain the updated satellite dynamics model; perform satellite attitude control simulation on the updated satellite dynamics model.

[0034] The advantages of the present invention compared with the prior art are: i i i i

[0035] The method and system in the present invention can improve the authenticity of satellite dynamics modeling, establish and verify the model of the change of the driving torque of the sailboard stepping motor, extract the frequency and amplitude information of the main influence, and can verify the stability of the satellite attitude angular velocity and the influence on the coupled vibration of the flexible appendages during the satellite attitude control simulation process. i i

[0036]

[0037] The method and system of the present invention can better simulate the on-orbit operation process of the satellite, improve the authenticity of the ground simulation attitude data, and make the attitude control simulation results after ground dynamics modeling closer to the on-orbit state.

[0038]

[0039] Figure 1 Description of the Drawings

[0039] Figure 1 is the flowchart of the method of the present invention. Detailed Embodiments

[0040] The present invention will be described with reference to the accompanying drawings.

[0041] The present invention provides a dynamic modeling and verification method for sailboard drive and flexible coupling. First, install the sailboard drive mechanism with a sailboard simulation on a six-axis force test bench. Under different open-loop rotational angular velocity commands of the drive mechanism, measure the driving torque during the sailboard drive process, and then obtain the angular acceleration curve of the sailboard drive mechanism rotating with time according to the inertia of the sailboard simulation. Then, obtain the frequency spectrum diagrams of the sailboard driving torque and the sailboard rotational angular acceleration through fast Fourier transform. According to the main frequency components of the sailboard driving torque and the sailboard rotational angular acceleration, fit the relationship between the sailboard driving torque, the sailboard rotational angular acceleration, and the open-loop rotational angular velocity command of the drive mechanism. Finally, add the fitted sailboard driving torque to the satellite rigid body attitude dynamics, and add the sailboard angular acceleration to the sailboard flexible vibration equation to analyze the stability of the satellite attitude control angular velocity and the influence on the coupled vibration of the flexible appendage.

[0042] The specific steps of the present invention are as follows:

[0043] Step S1: Obtain the sailboard driving torque and the angular acceleration of the sailboard rotation.

[0044] After the design scheme of the satellite sailboard and the drive mechanism is determined, produce a sailboard simulation with the same inertia as the sailboard, install the sailboard simulation on the sailboard drive mechanism, and measure the actual magnitude of the sailboard driving torque during the sailboard drive process through a ground six-axis force test bench under different open-loop rotational angular velocities ω i (i is different rotational angular velocity gears) commands, and then calculate the time-varying curve of the sailboard rotational angular acceleration according to the inertia of the sailboard simulation.

[0045] Step S2: Obtain the frequency spectrum diagrams of the sailboard driving torque and the sailboard rotational angular acceleration through fast Fourier transform.

[0046] Perform fast Fourier transform on the sailboard driving torque and the angular acceleration data of the sailboard rotation measured and calculated under different open-loop rotational angular velocity ω i commands to obtain the frequency spectrum diagrams of the sailboard driving torque and the sailboard rotational angular acceleration, and extract the frequency signals f i (the frequency signals of the sailboard driving torque and the sailboard rotational angular acceleration are the same) and the corresponding amplitudes (the amplitude A corresponding to the sailboard driving torque i and the amplitude B of the sailboard rotational angular acceleration i ) magnitudes.

[0047] Step S3: Fit the relationship between the sailboard driving torque, the sailboard rotational angular acceleration, and the open-loop rotational angular velocity command of the drive mechanism.

[0048] Step S3-1: First, calculate the driving frequency f of the sailboard according to the relationship between the stepping motor driving frequency and the open-loop rotational angular velocity command of the driving mechanism 驱i :

[0049]

[0050] where ω i is the open-loop rotational angular velocity command of the driving mechanism, k is the reduction ratio, and θ b is the step angle of the stepping motor.

[0051] Step S3-2: Determine the multiple-frequency relationship between the main frequency signal f i extracted in Step S2 and the driving frequency f 驱i of the sailboard, and fit the relationship between the magnitude of the main frequency corresponding to different open-loop rotational angular velocity commands of the driving mechanism and the rotational angular velocity of the sailboard to obtain A i = f(ω i ) and B i = f(ω i ).

[0052] Step S3-3: Finally, obtain the relationship between the driving torque of the sailboard and the rotational angular acceleration of the sailboard and the open-loop rotational angular velocity command of the driving mechanism

[0053] Step S4: Add the driving torque of the sailboard and the rotational angular acceleration of the sailboard obtained by fitting in Step S3 to the satellite dynamics model.

[0054] Add the driving torque T 驱动干扰 of the sailboard obtained by fitting to the satellite rigid body attitude dynamics model, and rotate the satellite body together with other torques.

[0055]

[0056] where I 卫星 represents the moment of inertia of the satellite, represents the rotational angular acceleration of the satellite, and T 其他 represents the torque for driving the satellite body to rotate;

[0057] Add the angular acceleration of the sailboard rotation to the sailboard flexural vibration equation to verify the change of the sailboard flexural vibration.

[0058]

[0059] where q is the sailboard vibration mode coordinate, ζ is the sailboard damping coefficient matrix, Ω is the sailboard flexural vibration frequency matrix, B 转动 is the coupling coefficient of the sailboard rotation to the satellite body, and b 转is the coupling coefficient of the self-rotation of the sailboard.

[0060] Step S5: Update the dynamic model for satellite attitude control simulation

[0061] Add the updated dynamic model to the satellite attitude control simulation, perform simulation according to the actual operating state of the satellite, generate open-loop rotational angular velocity commands of different magnitudes for the drive mechanism according to the orbital altitude simulation, and verify the influence of the unstable characteristics of the driving torque of the sailboard stepping motor on the stability of the satellite attitude control angular velocity and the coupled vibration of the satellite flexible appendage.

[0062] A dynamic modeling and verification system for sailboard drive and flexible coupling includes:

[0063] The first module is used to obtain the driving torque of the sailboard and the angular acceleration of the sailboard rotation corresponding to different open-loop rotational angular velocities ω of the drive mechanism; calculate the spectrogram of the driving torque of the sailboard and the angular acceleration of the sailboard rotation corresponding to different open-loop rotational angular velocities ω of the drive mechanism; i The corresponding driving torque of the sailboard and the angular acceleration of the sailboard rotation; calculate the spectrogram of the driving torque of the sailboard and the angular acceleration of the sailboard rotation corresponding to different open-loop rotational angular velocities ω of the drive mechanism; i The corresponding driving torque of the sailboard and the angular acceleration of the sailboard rotation; calculate the spectrogram of the driving torque of the sailboard and the angular acceleration of the sailboard rotation corresponding to different open-loop rotational angular velocities ω of the drive mechanism;

[0064] The second module is used to fit the relationship between the driving torque of the sailboard and different open-loop rotational angular velocities ω of the drive mechanism, and the relationship between the angular acceleration of the sailboard rotation and different open-loop rotational angular velocities ω of the drive mechanism; i The relationship between the driving torque of the sailboard and different open-loop rotational angular velocities ω of the drive mechanism, and the relationship between the angular acceleration of the sailboard rotation and different open-loop rotational angular velocities ω of the drive mechanism; i The relationship between the driving torque of the sailboard and different open-loop rotational angular velocities ω of the drive mechanism, and the relationship between the angular acceleration of the sailboard rotation and different open-loop rotational angular velocities ω of the drive mechanism;

[0065] The third module is used to add the relationship between the driving torque of the sailboard and different open-loop rotational angular velocities ω of the drive mechanism, and the relationship between the angular acceleration of the sailboard rotation and different open-loop rotational angular velocities ω of the drive mechanism to the satellite dynamic model to obtain the updated satellite dynamic model; perform satellite attitude control simulation on the updated satellite dynamic model. i The relationship between the driving torque of the sailboard and different open-loop rotational angular velocities ω of the drive mechanism, and the relationship between the angular acceleration of the sailboard rotation and different open-loop rotational angular velocities ω of the drive mechanism; i The relationship between the driving torque of the sailboard and different open-loop rotational angular velocities ω of the drive mechanism, and the relationship between the angular acceleration of the sailboard rotation and different open-loop rotational angular velocities ω of the drive mechanism;

[0066] Embodiment

[0067] Taking a sun-synchronous orbit satellite with an average orbital altitude of 705 km and a local time of the ascending node of 13:30 as an example, a conventional stepping motor is used for sailboard drive to further describe the technical solution of the present invention, but the scope of protection is not limited thereto.

[0068] The specific implementation steps of the present invention are as follows:

[0069] Step S1: Obtain the driving torque of the sailboard and the angular acceleration of the sailboard rotation.

[0070] On this sun-synchronous orbit, the orbital angular velocity is ω0 = 0.0607° / s. The rotational angular velocity of the solar panel driven by the satellite in orbit for a long time varies near the orbital angular velocity. According to the design of the driving angular velocity of the stepping motor in the solar panel drive mechanism, its open-loop rotational angular velocity command increases in increments of 0.0002° / s. Therefore, five open-loop rotational angular velocity commands in the range of 0.0603 - 0.0611° / s are selected for the solar panel driving torque test.

[0071] During ground testing, a simulation component with the same inertia as the solar panel and the solar panel drive mechanism are installed on a six-axis force test bench. Under the above five open-loop rotational angular velocity commands of the drive mechanism, the magnitude of the driving torque during the solar panel drive is measured, and then, based on the inertia of the solar panel simulation component, the angular acceleration curve of the solar panel rotation is calculated.

[0072] Step S2: Obtain the spectrograms of the solar panel driving torque and the solar panel rotational angular acceleration through fast Fourier transform.

[0073] Perform fast Fourier transform on the solar panel driving torque and the angular acceleration data of the solar panel rotation measured and calculated under different open-loop rotational angular velocity ω i commands of the drive mechanism to obtain the spectrograms of the solar panel driving torque and the solar panel dynamic angular acceleration, and extract the frequency signals f i and the corresponding amplitudes (the amplitude corresponding to the solar panel driving torque is A i and the amplitude corresponding to the solar panel rotational angular acceleration is B i ).

[0074] For example, when rotating at an open-loop rotational angular velocity of 0.0607° / s, by obtaining that the magnitude of the driving torque is within the range of ±30×10 - 3 Nm, the main frequency signals among them are extracted as 1.686 Hz and 5.058 Hz through fast Fourier transform. The amplitudes corresponding to the solar panel driving torque are 1.5×10 -3 Nm and 8.5×10 -3 Nm, and the amplitudes corresponding to the solar panel rotational angular acceleration are 0.3×10 -3 ° / s 2 and 1.7×10 -3 ° / s 2 .

[0075] Step S3: Fit the relationships between the solar panel driving torque, the solar panel rotational angular acceleration, and the open-loop rotational angular velocity command of the drive mechanism.

[0076] Step S3-1: First, calculate the solar panel drive frequency f 驱 .

[0077] For example, when driving the open-loop rotational angular velocity command of the drive mechanism at 0.0607° / s,

[0078]

[0079] where ω i is the driving speed of 0.0607° / s, k is the reduction ratio of 100, and θ b is the step angle of the stepper motor of 0.9°.

[0080] Step S3-2: Analyze and obtain that the frequency signal f i extracted in step S2 is mainly the fundamental frequency and the third harmonic of the sailboard driving frequency f 驱i . According to the test results of the open-loop rotational angular velocity command of the five-speed drive mechanism, the change in the rotational angular velocity of the sailboard is not significant, the change range of the measured sailboard driving torque is basically the same, and the magnitudes of the main frequencies extracted are close. Therefore, it can be regarded as a constant value, and 1.5×10 -3 Nm and 8.5×10 -3 Nm are adopted.

[0081] Step S3-3: Finally, fit to obtain the relationship between the driving torque, angular acceleration, and angular velocity of the sailboard as follows:

[0082] T 驱动干扰 =(1.5sin(2πf 驱 t)+8.5sin(6πf 驱 t + α)) / 1000

[0083]

[0084] where α is the phase difference of different main influencing frequencies, which is set as a randomly generated phase angle in the dynamic model.

[0085] Step S4: Add the fitted sailboard driving torque and sailboard rotational angular acceleration to the satellite dynamic model.

[0086] Add the fitted sailboard driving torque T 驱动干扰 to the rigid body attitude dynamics of the satellite to rotate the satellite body together with other torques.

[0087]

[0088] Add the actual angular acceleration of the sailboard to the sailboard flexural vibration equation to verify the change in sailboard flexural vibration.

[0089]

[0090] Step S5: Update the dynamic model for satellite attitude control simulation analysis

[0091] After adding satellite attitude control simulation to the updated dynamic model after fitting and modeling the open-loop rotational angular velocity command of the five-gear drive mechanism, the sailboard rotates at 0.0607° / s for a long time.

[0092] Taking the satellite's overall inertia of 1000 kg·m 2 as an example for satellite attitude control simulation, before the satellite dynamic model is updated, the stability of the pitch-axis attitude angular velocity is about 0.0004° / s;

[0093] Adding the sailboard driving torque with a magnitude within the range of ±30 mNm from this test to the dynamic model, without updating the sailboard flexible vibration equation and setting the sailboard flexible vibration equation to be unaffected by the satellite body angular velocity, the stability of the pitch-axis attitude angular velocity is about 0.0005° / s;

[0094] Adding the sailboard driving torque and the sailboard rotational angular acceleration in the present invention to the satellite dynamic model for satellite attitude control simulation, the stability of the pitch-axis attitude angular velocity is about 0.0007° / s. This result has a significant change. After analysis, the second-order torsional frequency of the sailboard is 5.256 Hz, which is relatively close to the triple frequency of 5.058 Hz of the sailboard driving torque. Therefore, the sailboard has a large flexible oscillation, the stability of the satellite pitch-axis angular velocity changes greatly, and the satellite needs to take measures to reduce the influence of this problem.

[0095] The satellite in this example has no other flexible attachments. If there are other flexible attachments, the influence of the unstable characteristics of the sailboard stepper motor driving torque on the coupled vibration of other flexible attachments can also be verified through attitude control simulation.

[0096] Through the description of this example, the method of the present invention can improve the authenticity of satellite dynamic modeling, verify the stability of the satellite attitude angular velocity and the influence on the coupled vibration of other flexible attachments.

[0097] Although the content of the present invention has been introduced in detail through the above examples, it should be recognized that the above description should not be considered as a limitation of the present invention. After those skilled in the art have read the above content, various modifications and substitutions of the present invention will be obvious. Therefore, the protection scope of the present invention should be defined by the appended claims.

Claims

1. A dynamic modeling and verification method for sailboard drive and flexible coupling, characterized in that: include: Obtain the open-loop rotation angular velocity ω of different drive mechanisms i The corresponding sailboard driving torque and sailboard rotation angular acceleration; The open-loop rotation angular velocity ω of different drive mechanisms is calculated i The corresponding frequency spectrum of the sailboard driving torque and the sailboard rotation angular acceleration; The windsurfing driving torque and the open-loop rotation angular velocity ω of different driving mechanisms are obtained by fitting i The relationship between the angular acceleration of the sailboard and the open-loop angular velocity ω of different drive mechanisms i The relationship between The fitted sailboard driving torque and the open-loop rotation angular velocity ω of different driving mechanisms are i The relationship between the angular acceleration of the sailboard and the open-loop angular velocity ω of different drive mechanisms i The relationship of is added into the satellite dynamics model to obtain an updated satellite dynamics model; Satellite attitude control simulation is performed on the updated satellite dynamics model.

2. The method for dynamic modeling and verification of sailboard drive and flexible coupling according to claim 1, characterized in that: The obtaining of the sailboard driving torque and the sailboard rotation angular acceleration comprises: The sailboard simulation is installed on the sailboard driving mechanism. The inertia of the sailboard simulation is the same as that of the sailboard. The six-dimensional force test bench is used to test the angular velocity ω of the open loop rotation of the driving mechanism at different i Under the condition of the above, the actual size of the driving torque of the sailboard during the driving process of the sailboard is measured; according to the inertia of the sailboard simulation part, the curve of the angular acceleration of the sailboard changing with time is calculated; i is the different angular velocity gears of rotation.

3. The method for dynamic modeling and verification of sailboard drive and flexible coupling according to claim 2, characterized in that: The calculation obtains the open-loop rotation angular velocity ω of different drive mechanisms i The corresponding spectrum of the sailboard driving torque and the sailboard rotation angular acceleration: Open-loop rotation angular velocity ω for different drive mechanisms i The corresponding sailboard driving torque and sailboard rotation angular acceleration data are subjected to fast Fourier transformation to obtain a frequency spectrum of the sailboard driving torque and the sailboard rotation angular acceleration; According to the spectrum of the sailboard driving torque and the sailboard rotation angular acceleration, the frequency signal f of the sailboard driving torque and the sailboard rotation angular acceleration is extracted. i , sailboard driving torque amplitude A i and the angular acceleration of the windsurfing board B i .

4. The method for dynamic modeling and verification of sailboard drive and flexible coupling according to claim 3, characterized in that: The fitting results show that the sailboard driving torque and the open-loop rotation angular velocity ω of different driving mechanisms i The relationship between the angular acceleration of the windsurfing board and the open-loop angular velocity ω of different drive mechanisms i relationships, including: According to the stepper motor driving frequency and the open-loop rotation angular velocity ω of the driving mechanism i The relationship between the windsurfing board driving frequency f is calculated. 驱i : Where k is the reduction ratio, θ b is the step angle of the stepper motor; Determine the frequency signal f i and the windsurfing board driving frequency f 驱i The frequency-multiplication relationship is obtained by fitting the open-loop rotation angular velocity ω of different drive mechanisms. i The sailboard driving torque amplitude A i The relationship between the angular velocity of the windsurfing board and i =f(ω i ), angular acceleration of windsurfing board B i The relationship between the angular velocity of the windsurfing board and i =f(ω i ); The windsurfing driving torque T is obtained by fitting 驱动干扰 The relationship between the open-loop rotation angular velocity of the drive mechanism and T 驱动干扰 =f(ω i ), angular acceleration of windsurfing board Relationship with the open-loop angular velocity of the drive mechanism 5. The method for dynamic modeling and verification of sailboard drive and flexibility coupling according to claim 4, characterized in that: The windsurfing driving torque obtained by fitting is compared with the open-loop rotation angular velocity ω of different driving mechanisms. i The relationship between the angular acceleration of the sailboard and the open-loop angular velocity ω of different drive mechanisms i The relationship of is added to the satellite dynamics model to obtain the updated satellite dynamics model, including: The fitted sailboard driving torque T 驱动干扰 Added to the satellite rigid body attitude dynamics model: Among them, I 卫星 represents the satellite’s moment of inertia, represents the angular acceleration of the satellite, T 其他 It represents the torque that drives the satellite body to rotate; Add the angular acceleration of the sailboard's rotation to the sailboard's flexible vibration equation to verify the change in the sailboard's flexible vibration: Among them, q is the vibration modal coordinate of the sailboard, ζ is the damping coefficient matrix of the sailboard, Ω is the flexible vibration frequency matrix of the sailboard, and B 转动 is the coupling coefficient of the sailboard rotation to the satellite body, b 转 is the coupling coefficient of the windsurfing board’s own rotation.

6. The method for dynamic modeling and verification of sailboard drive and flexibility coupling according to claim 5, characterized in that: The performing satellite attitude control simulation on the updated satellite dynamics model includes: The updated dynamic model is added to the satellite attitude control simulation. The simulation is carried out according to the actual operating status of the satellite. The open-loop rotation angular velocity commands of the drive mechanism of different sizes are generated according to the orbital altitude simulation to verify the influence of the unstable characteristics of the driving torque of the sailboard stepper motor on the stability of the satellite attitude control angular velocity and the coupled vibration of the satellite flexible attachment.

7. A dynamic modeling and verification system for sailboard drive and flexible coupling, characterized in that: include: The first module is used to obtain the open-loop rotation angular velocity ω of different drive mechanisms i The corresponding sailboard driving torque and sailboard rotation angular acceleration; The open-loop rotation angular velocity ω of different drive mechanisms is calculated i The corresponding frequency spectrum of the sailboard driving torque and the sailboard rotation angular acceleration; The second module is used to fit the sailboard driving torque and the open-loop rotation angular velocity ω of different driving mechanisms i The relationship between the angular acceleration of the sailboard and the open-loop angular velocity ω of different drive mechanisms i The relationship between The third module is used to compare the fitted sailboard driving torque with the open-loop rotation angular velocity ω of different driving mechanisms i The relationship between the angular acceleration of the sailboard and the open-loop angular velocity ω of different drive mechanisms i The relationship is added to the satellite dynamics model to obtain an updated satellite dynamics model; and satellite attitude control simulation is performed on the updated satellite dynamics model.

8. The dynamic modeling and verification system for windsurfing drive and flexible coupling according to claim 7, characterized in that: The obtaining of the sailboard driving torque and the sailboard rotation angular acceleration comprises: The sailboard simulation is installed on the sailboard driving mechanism. The inertia of the sailboard simulation is the same as that of the sailboard. The six-dimensional force test bench is used to test the angular velocity ω of the open loop rotation of the driving mechanism at different i Under the condition of the windsurfing board, the actual size of the driving torque of the windsurfing board during the driving process is measured; according to the inertia of the windsurfing board simulation part, the curve of the windsurfing board rotation angular acceleration changing with time is calculated; i is the gear of different rotation angular velocity; The calculation obtains the open-loop rotation angular velocity ω of different drive mechanisms i The corresponding spectrum of the sailboard driving torque and the sailboard rotation angular acceleration: Open-loop rotation angular velocity ω for different drive mechanisms i The corresponding sailboard driving torque and sailboard rotation angular acceleration data are subjected to fast Fourier transformation to obtain a frequency spectrum of the sailboard driving torque and the sailboard rotation angular acceleration; According to the spectrum of the sailboard driving torque and the sailboard rotation angular acceleration, the frequency signal f of the sailboard driving torque and the sailboard rotation angular acceleration is extracted. i , sailboard driving torque amplitude A i and the angular acceleration of the windsurfing board B i .

9. A dynamic modeling and verification system for sailboard drive and flexible coupling according to claim 8, characterized in that: The fitting results show that the sailboard driving torque and the open-loop rotation angular velocity ω of different driving mechanisms i The relationship between the angular acceleration of the windsurfing board and the open-loop angular velocity ω of different drive mechanisms i relationships, including: According to the stepper motor driving frequency and the open-loop rotation angular velocity ω of the driving mechanism i The relationship between the windsurfing board driving frequency f is calculated. 驱i : Where k is the reduction ratio, θ b is the step angle of the stepper motor; Determine the frequency signal f i and the windsurfing board driving frequency f 驱i The frequency-multiplication relationship is obtained by fitting the open-loop rotation angular velocity ω of different drive mechanisms. i The sailboard driving torque amplitude A i The relationship between the angular velocity of the windsurfing board and i =f(ω i ), angular acceleration of windsurfing board B i The relationship between the angular velocity of the windsurfing board and i =f(ω i ); The windsurfing driving torque T is obtained by fitting 驱动干扰 The relationship between the open-loop rotation angular velocity of the drive mechanism and T 驱动干扰 =f(ω i ), angular acceleration of windsurfing board Relationship with the open-loop angular velocity of the drive mechanism 10. A windsurfing board drive and flexible coupling dynamics modeling and verification system according to claim 9, characterized in that: The windsurfing driving torque obtained by fitting is compared with the open-loop rotation angular velocity ω of different driving mechanisms. i The relationship between the angular acceleration of the sailboard and the open-loop angular velocity ω of different drive mechanisms i The relationship of is added to the satellite dynamics model to obtain the updated satellite dynamics model, including: The fitted sailboard driving torque T 驱动干扰 Added to the satellite rigid body attitude dynamics model: Among them, I 卫星 represents the satellite's moment of inertia, represents the angular acceleration of the satellite, T 其他 It represents the torque that drives the satellite body to rotate; Add the angular acceleration of the sailboard's rotation to the sailboard's flexible vibration equation to verify the change in the sailboard's flexible vibration: Among them, q is the vibration modal coordinate of the sailboard, ζ is the damping coefficient matrix of the sailboard, Ω is the flexible vibration frequency matrix of the sailboard, and B 转动 is the coupling coefficient of the sailboard rotation to the satellite body, b 转 is the coupling coefficient of the windsurfing board’s own rotation.

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