Flexible sailboard satellite active vibration control method and device for SADA disturbance

Abstract

The invention provides a flexible sailboard satellite active vibration control method and device for SADA disturbance, and belongs to the field of spacecraft attitude determination and control. The method solves the problem of stability caused by frequency drift in the prior art and the problem that the method depends on a satellite model and cannot adapt to a time-varying system. The method comprises the following steps: acquiring an SADA driving angle, an angular velocity of a fiber-optic gyroscope and voltage data of a piezoelectric sensor; performing discrete short-time Fourier transform on the voltage data to obtain an amplitude spectrum and a phase spectrum; identifying the frequency corresponding to the peak value of the amplitude according to the amplitude spectrum, and associating the SADA driving angle corresponding to the peak value with the angular velocity of the fiber-optic gyroscope; the stability of the whole satellite is judged according to the angular velocity of the fiber-optic gyroscope, and when the angular velocity exceeds a set threshold value, control parameters of the piezoelectric actuator are adjusted in a segmented mode; and iteratively executing the steps until the stability of the whole satellite meets the index requirement. The method is mainly used in satellite control field.

Description

Technical Field

[0001] This invention belongs to the field of spacecraft attitude determination and control, and in particular relates to an active vibration control method for flexible solar panel satellites to address SADA disturbances. Background Technology

[0002] With the rapid development of the satellite industry, the demand for energy supply from high-power satellite payloads is increasing, driving the need for ultra-large flexible solar panels. Compared to the satellite itself, ultra-large flexible solar panels can provide more abundant energy, but they also introduce significant stability control challenges. For example, when a satellite with a large flexible solar panel is in orbit, if the fundamental frequency of the solar panel is not clearly identified or the control strategy is inappropriate, frequent flexible vibrations may lead to structural fatigue, reduced solar panel lifespan, or even instability of the entire satellite's attitude, making it impossible to meet mission requirements in terms of stability. In more severe cases, the flywheel may overheat and be damaged due to frequent acceleration and deceleration, further shortening the overall satellite lifespan. These shortcomings have been repeatedly demonstrated in actual missions.

[0003] Existing attitude control methods for satellites with large flexible solar panels in orbit largely rely on adjusting the control bandwidth to avoid dangerous frequencies to achieve stability. Specifically, traditional controllers are designed with sufficient stability margin at the flexible modal frequencies, typically setting the control bandwidth below the first-order flexible frequency to avoid exciting vibrations. For example, some satellite systems use linear time-invariant controllers to suppress vibrations by fixing parameters, but this method has limitations when dealing with large solar panels. As the size of the solar panels increases, and the entire satellite is connected to the panels via a Solar Actuation and Control (SADA) mechanism, the rotation of the SADA orients the panels towards the sun, but also introduces complex dynamic changes. In finite element analysis, the vibration modal frequencies and mode shapes of large flexible solar panels are highly dependent on the boundary conditions of the SADA; when the SADA rotates and locks, its internal mechanical structures, such as motors, constitute specific mechanical impedances, which differ from the state of the solar panels when they are freely floating or rotating at other angles. Therefore, different rotation angles of the SADA correspond to different fixed support conditions, causing the natural frequencies of the solar panels to drift. Existing technologies cannot adapt to this drift in real time. For example, when the SADA rotates, causing the frequency to drift downward and enter the control bandwidth, the control force will instead give positive feedback to the vibration mode, causing vibration divergence.

[0004] Furthermore, traditional vibration suppression strategies, when faced with flexible structures with increasingly lower fundamental frequencies, can only continuously reduce the control bandwidth. This results in the entire satellite losing its ability to maneuver rapidly and for the solar panels to rotate quickly. For example, under certain critical energy acquisition conditions, the satellite cannot adjust its attitude in time to optimize solar orientation, thus reducing the overall efficiency of the satellite. Simultaneously, the continuous rotation process of SADA (Solar Adaptor Assistance) causes its dynamic parameters to exhibit periodic time-varying characteristics, rather than being a nonlinear time-invariant system. Nonlinear factors such as friction and gear backlash during the SADA drive process further excite vibrations in the solar panels. However, limited by ground-based testing conditions, existing technologies cannot accurately acquire or establish models of these time-varying parameters. For example, ground simulations cannot fully reproduce the SADA behavior in the space environment, leading to deviations in model parameters. Traditional controllers are mostly designed as linear time-invariant systems and lack the ability to track and adapt to time-varying dynamics. When the parameters of the time-varying system change rapidly or with sufficiently large amplitude, the stability margin of the fixed controller is quickly consumed, causing the system to become unstable at a specific operating point.

[0005] While active vibration control methods can enhance the rigidity of flexible solar panels and improve system stability through active control, existing active control methods are highly dependent on the establishment of high-precision satellite models. For example, these methods typically optimize control parameters based on model parameters from ground tests and consistently apply the same set of parameters. However, when the model parameters are inaccurate, the calculated control parameters may create positive feedback, leading to overall satellite control instability. This model dependency limits their on-orbit adaptability and makes them unable to effectively cope with dynamic changes caused by SADA rotation. Summary of the Invention

[0006] In view of this, the present invention aims to propose a method and device for active vibration control of flexible solar panels for SADA disturbances, in order to solve the stability problem caused by frequency drift in the prior art, as well as the problem that it relies on satellite models and cannot adapt to time-varying systems.

[0007] To achieve the above objectives, the present invention adopts the following technical solution: An active vibration control method for flexible solar panel satellites to address SADA disturbances, the method comprising: Step 1: Install symmetrically arranged piezoelectric sensors and piezoelectric actuators on the solar panels to collect SADA drive angles, fiber optic gyroscope angular velocities, and piezoelectric sensor voltage data under the conditions of three-axis Earth-to-ground interaction of the entire satellite body and controlled rotation of the solar panels to track the sun. Step 2: Perform discrete short-time Fourier transform on the voltage data of the piezoelectric sensor to obtain the amplitude spectrum and phase spectrum; Step 3: Identify the frequency corresponding to the amplitude peak based on the amplitude spectrum, use it as the target frequency for priority suppression in active vibration control, and associate the SADA drive angle corresponding to the peak with the angular velocity of the fiber optic gyroscope; Step 4: Determine the overall satellite stability based on the angular velocity of the fiber optic gyroscope. When the angular velocity exceeds the set threshold, adjust the control parameters of the piezoelectric actuator. The control parameters are adjusted in segments according to the SADA drive angle and angular velocity. Step 5: Iterate through steps 1 to 4 until the overall satellite stability meets the target requirements across the entire orbit.

[0008] Furthermore, a preferred embodiment is proposed, wherein the measurement equation of the piezoelectric sensor is:

[0009] in, The voltage value is obtained by measuring the piezoelectric sensor. The coefficient is related to the piezoelectric material itself. The modal derivative difference matrix is... These are modal coordinates.

[0010] Furthermore, a preferred method is proposed, wherein the calculation formula for the discrete short-time Fourier transform in step 2 is as follows:

[0011] in, Indicates the first The first time frame, the first Complex spectral values ​​at each frequency index Indicates the original signal at The sampled value at that location, Indicates the window function in The value of position, L represents the window length, i.e., the number of sampling points analyzed per frame. This represents the natural constant, which is 2.71828. Represents the imaginary unit, satisfying k represents the frequency index value. This represents the intra-frame index value, with a value range of [value range missing]. N represents the number of points in the Fourier transform. w For window functions; The amplitude spectrum and phase spectrum are calculated using the following formulas:

[0012]

[0013] in, Indicates amplitude spectrum, Represents the phase spectrum. express The real part, express The imaginary part, It represents a complex argument.

[0014] Furthermore, a preferred method is proposed, wherein the window function of the discrete short-time Fourier transform in step 2 is the Hanning window.

[0015] Furthermore, a preferred method is proposed, wherein the amplitude spectrum identification is based on the global maximum value of the amplitude spectrum, the amplitude frequency of which corresponds to the flexible mode frequency drift caused by SADA selection, and is used as the target frequency of the MPPF controller.

[0016] Furthermore, a preferred embodiment is proposed, wherein the piezoelectric actuator in step 4 is controlled by an MPPF controller, which includes a second-order compensator and a first-order compensator, specifically as follows:

[0017] in, Indicates the first The first mode in the 1st order Second derivatives of the state variables of the second-order compensator at each control node. Indicates control damping, Indicates the control frequency. Indicates the first The first mode in the 1st order The first derivative of the state variables of the second-order compensator of each control node. Indicates the first The first mode in the 1st order The state variables of the second-order compensator of each control node. Indicates the first The measured voltage value of the piezoelectric sensor at each control node. Indicates the first The first mode in the 1st order The first derivative of the state variables of the first-order compensator of each control node. Indicates the first The first mode in the 1st order The state variables of the first-order compensator of each control node. Indicates the first The first mode in the 1st order The component of the voltage applied by the actuator of each control node. and This indicates the control parameters.

[0018] Furthermore, a preferred embodiment is proposed, wherein the control frequency... Based on the peak amplitude frequency identified in step 3, the control parameters are set. and The adjustment is segmented according to the angle and angular velocity of the SADA. The segmented adjustment adopts a lookup table method. The segmented area is identified based on the out-of-tolerance area. The piezoelectric actuator control parameters are set to 0 in the non-out-of-tolerance area.

[0019] Based on the same inventive concept, this invention also proposes an active vibration control device for flexible solar panel satellites to address SADA disturbances, the device comprising: The data acquisition unit is used to acquire the SADA drive angle, fiber optic gyroscope angular velocity, and piezoelectric sensor voltage data under the following conditions: three-axis Earth-to-ground and controlled rotation of the satellite body to track the sun under on-orbit conditions. The Fourier transform unit is used to perform discrete short-time Fourier transform on the voltage data of the piezoelectric sensor to obtain the amplitude spectrum and phase spectrum. The amplitude spectrum identification unit is used to identify the frequency corresponding to the peak value of the amplitude spectrum, which is used as the target frequency for priority suppression in active vibration control, and to associate the SADA drive angle corresponding to the peak value with the angular velocity of the fiber optic gyroscope. The judgment unit is used to determine the overall satellite stability based on the angular velocity of the fiber optic gyroscope. When the angular velocity exceeds a set threshold, the control parameters of the piezoelectric actuator are adjusted in segments according to the SADA drive angle and angular velocity. The iteration unit is used to iteratively execute the process from the data acquisition unit to the judgment unit until the overall satellite stability meets the target requirements across the entire orbit.

[0020] Based on the same inventive concept, the present invention also proposes a computer device, including a memory and a processor, wherein the memory stores a computer program, and when the processor runs the computer program stored in the memory, the processor executes a flexible solar panel satellite active vibration control method for SADA disturbances as described in any of the preceding claims.

[0021] Based on the same inventive concept, the present invention also proposes a computer-readable storage medium storing a computer program that, when executed by a processor, performs the steps of a flexible solar panel satellite active vibration control method for SADA disturbances as described in any one of the above.

[0022] Compared with the prior art, the beneficial effects of the present invention are: First, existing technologies mostly employ linear time-invariant controllers, relying on fixed model parameters obtained from ground tests and setting a fixed control bandwidth to avoid dangerous frequencies. For example, traditional methods set the bandwidth below the first-order flexibility frequency, but this cannot adapt to boundary condition changes caused by SADA rotation. When SADA rotation causes the solar panel's natural frequency to drift into the control bandwidth, the fixed controller will trigger positive feedback, exacerbating vibration. This invention, however, abandons this static model dependency. It uses piezoelectric sensors to collect voltage data in real time and combines this with short-time Fourier transform for online frequency identification, directly adjusting control parameters for dynamic on-orbit conditions, thereby avoiding instability caused by frequency drift.

[0023] Secondly, existing technologies lack adaptability to time-varying systems. During the continuous rotation of the SADA (Satellite Adaptor Controller), nonlinear factors such as friction and gear backlash cause the dynamic parameters to change periodically over time. However, traditional controllers are designed as linear time-invariant systems and cannot respond quickly to parameter changes. This invention utilizes the segmented parameter adjustment mechanism of the MPPF (Multimodal Positive Position Feedback) controller, using the SADA angle and angular velocity as the segmentation basis and employing a lookup table method for nonlinear partitioning. Control parameters are set separately for out-of-tolerance regions, rather than being globally fixed, enabling the controller to adapt to the time-varying characteristics of SADA rotation and avoiding stability margin depletion. Through online identification and parameter adjustment, the overall satellite stability is improved by more than 20%.

[0024] Finally, existing technologies often sacrifice maneuverability to mitigate the risk of model inaccuracies, such as reducing control bandwidth, which prevents the entire satellite from maneuvering quickly or the solar panels from rapidly orienting themselves to the sun. This invention uses closed-loop iterative optimization to dynamically adjust parameters while ensuring stability. Initial control parameters are set to zero, and the piezoelectric actuator is activated only when the fiber optic gyroscope detects a stability deviation, achieving on-demand control and preserving the satellite's maneuverability while improving accuracy.

[0025] This invention is applied to the field of satellite control. Attached Figure Description

[0026] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an undue limitation of the invention. In the drawings: Figure 1 This is a flowchart of a flexible solar panel satellite active vibration control method for SADA disturbances as described in this invention. Figure 2 This is a schematic diagram of the satellite configuration described in this invention, wherein 1 is the solar panel, 2 is the satellite body, 3 is the A-axis of SADA, 4 is the B-axis of SADA, A1, A2, A3, A4, and A5 all represent piezoelectric actuators, and S1, S2, S3, S4, and S5 all represent piezoelectric sensors. Figure 3 This is a schematic diagram of the two-axis drive angle of the SADA system described in this invention. Figure 4 This is a schematic diagram of the SADA two-axis drive angular velocity according to the present invention; Figure 5 This is a schematic diagram of the satellite angular velocity without active control as described in this invention; Figure 6 This is a schematic diagram of the piezoelectric voltage data measured according to the present invention; Figure 7 This is the spectrum calculated using piezoelectric data within the out-of-tolerance time region described in this invention; Figure 8 This is a schematic diagram of the SADA two-axis drive angle when the angular velocity is out of tolerance, as described in this invention. AngleA represents the drive rotation angle of axis A, and AngleB represents the drive rotation angle of axis B. Figure 9 This is a schematic diagram of the SADA two-axis drive angular velocity when the angular velocity is out of tolerance, as described in this invention. In this diagram, OmgA represents the drive rotational angular velocity of axis A, and OmgB represents the drive rotational angular velocity of axis B. Figure 10 This is the spectrum diagram after modifying the piezoelectric control parameters as described in this invention; Figure 11 This is a schematic diagram of the satellite angular velocity after modifying the control parameters as described in this invention, where OmgNone represents the satellite angular velocity without active vibration control, and OmgPPF represents the satellite angular velocity after active vibration control. Detailed Implementation

[0027] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. It should be noted that, unless otherwise specified, the embodiments and features in the embodiments of the present invention can be combined with each other, and the described embodiments are only some embodiments of the present invention, not all embodiments.

[0028] Implementation Method 1, see Figure 1 This embodiment describes a method for active vibration control of flexible solar panels for SADA disturbances. This embodiment addresses the stability issues caused by frequency drift in existing technologies, as well as the inability to adapt to time-varying systems due to reliance on satellite models. The method includes: Step 1: Install symmetrically arranged piezoelectric sensors and piezoelectric actuators on the solar panels to collect SADA drive angles, fiber optic gyroscope angular velocities, and piezoelectric sensor voltage data under the conditions of three-axis Earth-to-ground interaction of the entire satellite body and controlled rotation of the solar panels to track the sun. Step 2: Perform discrete short-time Fourier transform on the voltage data of the piezoelectric sensor to obtain the amplitude spectrum and phase spectrum; Step 3: Identify the frequency corresponding to the amplitude peak based on the amplitude spectrum, use it as the target frequency for priority suppression in active vibration control, and associate the SADA drive angle corresponding to the peak with the angular velocity of the fiber optic gyroscope; Step 4: Determine the overall satellite stability based on the angular velocity of the fiber optic gyroscope. When the angular velocity exceeds the set threshold, adjust the control parameters of the piezoelectric actuator. The control parameters are adjusted in segments according to the SADA drive angle and angular velocity. Step 5: Iterate through steps 1 to 4 until the overall satellite stability meets the target requirements across the entire orbit.

[0029] The core technical principle of the method proposed in this embodiment lies in its subversion of the traditional fixed approach of modeling first and then controlling, and the proposal of an active vibration control method with online identification and segmented adaptive control. This effectively solves the core problem that traditional controllers cannot handle: the time-varying dynamic parameters of the solar panel caused by the rotation of the SADA (Solar Panel Drive Mechanism).

[0030] Existing technologies rely entirely on inaccurate, fixed model parameters obtained from ground tests to design controllers. The method proposed in this embodiment, however, abandons this dependence on inaccurate prior models. Its basic principle is to use voltage data from piezoelectric sensors operating in orbit as input variables that directly reflect the actual vibration state of the solar panel. By performing a short-time Fourier transform on the voltage signal, the actual dominant vibration frequency and amplitude of the solar panel at the current SADA angle and angular velocity can be acquired and analyzed in real time. This sensing method based on real on-orbit data achieves, for the first time, accurate and online capture of frequency drift phenomena under different SADA angles.

[0031] Traditional linear time-invariant controllers employ a uniform approach for all operating conditions, which is the fundamental reason for their failure in time-varying systems related to SADA rotation. The core principle of this implementation lies in recognizing that the SADA angle and angular velocity together define a time-varying operating point, and proposing a strategy of segmenting control parameters based on the combination of SADA angle and angular velocity. Instead of simple equal-interval segmentation, it locates the problematic operating condition region by monitoring whether the fiber optic gyroscope angular velocity exceeds tolerance, and establishes a mapping relationship between this region and the dominant frequency identified by the piezoelectric sensor. Finally, a control parameter lookup table enables the controller to proactively switch to the optimal control parameter set based on the real-time SADA motion state.

[0032] Existing technologies passively avoid flexible vibrations by limiting control bandwidth and sacrificing maneuverability. This implementation uses a multimodal positive position feedback (MPPF) controller as the active control actuator. The dominant frequency identified by the piezoelectric sensor is directly set as the core parameter of the MPPF controller. The role of the MPPF controller is no longer simply to suppress the signal, but to actively inject damping into specific vibration modes of the sail. Specifically, its second-order compensator is used to achieve precise SADA control at the target frequency, while the first-order compensator is used to broaden the damping effect near that frequency. By adjusting the parameters, precise damping matching of the vibration modes is achieved, thereby fundamentally dissipating vibration energy.

[0033] Through online identification and adaptive control, the method proposed in this embodiment can effectively suppress the vibration of the large flexible solar panel caused by SADA disturbances. After adjusting the control parameters for specific operating conditions, the previously out-of-tolerance satellite angular velocity was effectively suppressed to within the required range (less than 0.005° / s), achieving stability compliance across the entire orbital range. This method can improve the overall satellite stability by more than 20%, which is crucial for high-precision Earth observation and scientific exploration missions.

[0034] The method proposed in this embodiment directly and actively suppresses the vibration source, reducing the vibration amplitude caused by SADA interference by up to 25%. This not only reduces the interference of vibration on attitude control, but also fundamentally reduces the risk of fatigue damage to flexible structures, helping to extend the design life of the solar array and even the entire satellite, while avoiding the problem of overheating and damage to the flywheel due to frequent compensation vibration.

[0035] Because the proposed implementation method actively suppresses rather than passively avoids vibrations, there is no need to excessively sacrifice control bandwidth for stability. This allows the satellite to regain its rapid maneuverability and the ability of its solar panels to rotate quickly. In situations requiring sun orientation to obtain energy, the satellite can adjust its attitude more rapidly, ensuring energy supply efficiency and improving the overall mission performance.

[0036] The greatest advantage of the method proposed in this embodiment is that it does not rely on ground models that are difficult to obtain accurately. Through a closed-loop adaptive mechanism, it can automatically adapt to changes in dynamic parameters caused by SADA rotation, friction, gear backlash, etc., overcoming the fatal flaw of traditional fixed-parameter controllers that easily exhaust stability margin in the face of time-varying systems, and exhibiting extremely strong environmental adaptability and robustness.

[0037] Implementation Method 2, see below Figures 2 to 11 This embodiment describes a complete implementation of the active vibration control method for flexible solar panel satellites against SADA disturbances described in Embodiment 1. Specifically: An active vibration control method for flexible solar panel satellites to address SADA disturbances, the method comprising: Step 1: Install symmetrically arranged piezoelectric sensors and piezoelectric actuators on the solar panels to collect SADA drive angles, fiber optic gyroscope angular velocities, and piezoelectric sensor voltage data under the conditions of three-axis Earth-to-ground interaction of the entire satellite body and controlled rotation of the solar panels to track the sun. The satellite configuration diagram in this embodiment is as follows: Figure 2 As shown, the satellite body 2 and the solar panel 1 are connected by a solar panel drive mechanism (SADA), which includes the A-axis 3 and the B-axis 4 of the SADA; piezoelectric sensors Ai and piezoelectric actuators Si are symmetrically arranged on the solar panel 1.

[0038] Step 2: Perform discrete short-time Fourier transform on the voltage data of the piezoelectric sensor to obtain the amplitude spectrum and phase spectrum; In this embodiment, voltage data is plotted based on the measured voltage of the piezoelectric sensor. A short-time Fourier transform is then performed, dividing the long-term non-stationary signal into many shorter segments. Each segment can be approximated as stationary. The amplitude and phase of each segment are then obtained through a short-time Fourier transform, and the corresponding SADA drive angular velocity is saved. The measurement equation of the piezoelectric sensor described in this embodiment is:

[0039] in, The voltage value is obtained by measuring the piezoelectric sensor. This represents the first voltage value measured by the piezoelectric sensor. This represents the i-th voltage value measured by the piezoelectric sensor. The coefficient is related to the piezoelectric material itself. The modal derivative difference matrix is... These are modal coordinates.

[0040] The amplitude spectrum is obtained by discrete short-time Fourier transform. and phase spectrum As shown below: The formula for calculating the Discrete Short-Time Fourier Transform is: , in, Indicates the first The first time frame, the first Complex spectral values ​​at each frequency index Indicates the original signal at The sampled value at that location, Indicates the window function in The value of position, L represents the window length, i.e., the number of sampling points analyzed per frame. This represents the natural constant, 2.71828. Represents the imaginary unit, satisfying k represents the frequency index value. This represents the intra-frame index value, with a value range of [value range missing]. N represents the number of points in the Fourier transform. w For window functions; The amplitude spectrum and phase spectrum are calculated using the following formulas: , , express The real part, express The imaginary part, It represents a complex argument.

[0041] To analyze the low-frequency structural modes, the sampling frequency of the piezoelectric sensor is fs, and the expected frequency resolution is Δf. There are a total of L sampling points, where L = fs / Δf. Since the satellite structure has multiple modal responses, the Hanning window is beneficial for vibration analysis during satellite operation due to its trade-off between frequency resolution and leakage suppression. Therefore, the window function is selected as the Hanning window.

[0042] Step 3: Identify the frequency corresponding to the amplitude peak based on the amplitude spectrum, use it as the target frequency for priority suppression in active vibration control, and associate the SADA drive angle corresponding to the peak with the angular velocity of the fiber optic gyroscope; The amplitude spectrum identification described in this embodiment is based on the global maximum value of the amplitude spectrum. That is, the peak value with the highest amplitude is found according to the amplitude spectrum. This peak value is considered as the main factor causing structural vibration and affecting attitude accuracy. The frequency of this amplitude value corresponds to the flexible modal frequency drift caused by SADA selection and is used as the target frequency of the MPPF controller. This peak value should be the target that the active vibration controller prioritizes to suppress, and the angle and angular velocity of the corresponding SADA segment are obtained according to step 2.

[0043] Step 4: Determine the overall satellite stability based on the angular velocity of the fiber optic gyroscope. When the angular velocity exceeds the set threshold, adjust the control parameters of the piezoelectric actuator. The control parameters are adjusted in segments according to the SADA drive angle and angular velocity. In this embodiment, the stability of the entire satellite is determined based on the angular velocity data of the fiber optic gyroscope. When the telemetry frequency of the angular velocity is f... yc If, within a specified time period T, the angular velocity exceeds a set threshold for N frames (this threshold is determined based on the satellite platform's specifications and must meet the payload's operational requirements), the overall satellite stability is considered to be out of tolerance. When the overall satellite stability meets the requirements, the piezoelectric actuator remains inactive; when it exceeds the tolerance, the piezoelectric actuator adjusts its control voltage. Because the satellite's three-axis rotation relative to the ground is periodic, control parameters are segmented for different SADA rotation angles and angular velocities (segmentation is done using a lookup table, as the non-linear relationship between angle and angular velocity cannot be controlled at equal intervals; the main focus is on identifying and modifying parameters in the out-of-tolerance regions), corresponding to different piezoelectric actuator drive voltage control parameters.

[0044] The general form of the dynamic equations of the flexible structure (i.e., the form of the influence of the piezoelectric actuator on the modal coordinates) is: ,in, This refers to the control voltage value output by the piezoelectric actuator. The control voltage for the first control node. The control voltage for the Nth control node. The coefficient is related to the piezoelectric material itself. The second derivative of the flexible modal coordinates. Here is the damping matrix. The first derivative of the flexible modal coordinates, Here is the stiffness matrix. This is the modal shape difference matrix.

[0045] The piezoelectric actuator is controlled using an MPPF controller, which includes a second-order compensator and a first-order compensator. The second-order compensator is used to achieve precise SADA control at the target frequency, and the first-order compensator is used to increase the control parameters at the target frequency. Damping within a certain frequency range nearby. The selection is based on the frequency corresponding to the peak amplitude obtained in step 2, including:

[0046] in, Indicates the first The first mode in the 1st order Second derivatives of the state variables of the second-order compensator at each control node. Indicates control damping, Indicates the control frequency. Indicates the first The first mode in the 1st order The first derivative of the state variables of the second-order compensator of each control node. Indicates the first The first mode in the 1st order The state variables of the second-order compensator of each control node. Indicates the first The measured voltage value of the piezoelectric sensor at each control node. Indicates the first The first mode in the 1st order The first derivative of the state variables of the first-order compensator of each control node. Indicates the first The first mode in the 1st order The state variables of the first-order compensator of each control node. Indicates the first The first mode in the 1st order The component of the voltage applied by the actuator of each control node. and This indicates the control parameters.

[0047] The control frequency described in this embodiment Based on the peak amplitude frequency identified in step 3, the control parameters are set. and The adjustment is segmented according to the angle and angular velocity of the SADA. The segmented adjustment adopts a lookup table method. The segmented area is identified based on the out-of-tolerance area. The piezoelectric actuator control parameters are set to 0 in the non-out-of-tolerance area.

[0048] Step 5: Adjust the control frequency of the piezoelectric actuator And modify parameters as needed , Then, iteratively execute steps 1 to 4 until the overall satellite stability meets the target requirements across the entire orbit.

[0049] In this embodiment, the satellite's orbital altitude is set to 500km and the orbital inclination angle to 50°.

[0050] The moment of inertia of the central rigid body is set as: [155.4 2.3 20; 2.3 387.9 5.1; 20 5.1 512.3] ; The moment of inertia of the windsurfing is set as follows: [1145.9 -0.217 0.178; -0.217 40.4 -0.015; 0.178 -0.015 1170] ; The flexible coupling coefficient is: ; The first three frequencies given for the ground calculation of the solar panel are 0.082Hz, 0.131Hz, and 0.172Hz, respectively. Based on the mode shape of the solar panel, only the influence of a single frequency is considered, and the initial control parameters are... , and control frequency Set them to: =0, 0 and Set to 0Hz.

[0051] Taking a beta angle of 30 degrees as an example, the SADA two-axis angle and angular velocity drive of the windsurfing system are as follows: Figure 3 and Figure 4 As shown, by analyzing the overall satellite stability (i.e., the angular velocity exceeding the tolerance range (set to 0.005° / s) under different SADA drive angular velocities, the control parameters are modified after spectrum analysis to suppress the stability. If the stability meets the requirements, piezoelectric active control is not performed.

[0052] like Figure 5 and Figure 6 As shown, Fourier spectrum analysis was performed on the piezoelectric voltage data in the out-of-tolerance region. The Hanning window was selected as the window function, the sampling frequency was 20Hz, and the segment length was set to 1000. The results are as follows: Figure 7 The spectrum shown. Locate the corresponding drive angle and angular velocity region for the sail, such as... Figure 8and Figure 9 As shown. According to Figure 7 The frequency at which the spectrum calculation exceeds the tolerance is 0.18Hz. The piezoelectric control frequency needs to be modified. It is 0.18Hz. Set to 2. Set to 38. Analyze the spectrum after modifying the control parameters as follows: Figure 10 As shown, the peak at 0.18 Hz is weakened.

[0053] After modifying the parameters of the angular velocity in the time domain of this region, as follows: Figure 11 As shown, the previously out-of-tolerance angular velocity now meets the requirement of less than 0.005° / s, indicating that the parameter modification is effective. Save the corresponding piezoelectric control parameters for this region. When the SADA's A-axis angle is in the range of [50°~120°] and the A-axis angular velocity is in the range of [-0.05° / s~0.05° / s], and the SADA's B-axis angle is in the range of [-150°~-140°] and the B-axis angular velocity is in the range of [-0.05° / s~-0.12° / s], use these parameters for control. In the region within tolerance, set all piezoelectric control parameters to 0. Repeat steps 1 to 4 for parameter adjustment and control in all out-of-tolerance regions until the overall satellite stability meets the requirements.

[0054] This embodiment proposes an active vibration control method for satellites with large flexible solar panels to address SADA disturbances. Based on long-term on-orbit data of the satellite, flexible mode information is identified using voltage data from piezoelectric sensors. The identified mode data is then segmented for specific angles and angular velocities related to SADA, and the control parameters of the piezoelectric actuators are corrected. This reduces the vibration amplitude caused by SADA interference by 25% and improves the overall stability of the satellite by more than 20%.

[0055] Those skilled in the art will understand that embodiments of this disclosure can be provided as methods, systems, or computer program products. Therefore, this disclosure can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this disclosure can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0056] This disclosure is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this disclosure. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create a machine for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 The computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to operate in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes. These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0057] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of this disclosure and not to limit its protection scope. Although this disclosure has been described in detail with reference to the above embodiments, those skilled in the art should understand that after reading this disclosure, they can still make various changes, modifications or equivalent substitutions to the specific implementation of the invention, but these changes, modifications or equivalent substitutions are all within the protection scope of the published pending claims.

Claims

1. A flexible panel satellite active vibration control method against SADA disturbance, characterized in that, The method comprises: Step 1: install symmetrically arranged piezoelectric sensors and piezoelectric actuators on a solar panel, collect SADA driving angles, angular velocities of fiber optic gyroscope and voltage data of piezoelectric sensors under the working condition of three-axis body-to-ground and controlled rotation of the panel to track the sun in orbit; Step 2: perform discrete short-time Fourier transform on the voltage data of the piezoelectric sensor to obtain amplitude spectrum and phase spectrum; Step 3: identify the frequency corresponding to the amplitude peak value according to the amplitude spectrum as the target frequency for priority suppression of active vibration control, and associate the SADA driving angle and the angular velocity of the fiber optic gyroscope corresponding to the peak value; Step 4: determine the stability of the whole satellite according to the angular velocity of the fiber optic gyroscope, and adjust the control parameters of the piezoelectric actuator when the angular velocity exceeds the set threshold, wherein the control parameters are adjusted in sections according to the SADA driving angle and the angular velocity; Step 5: iteratively execute steps 1 to 4 until the whole satellite stability meets the index requirements throughout the orbit.

2. The active vibration control method for SADA perturbation of a flexible panel satellite according to claim 1, wherein, The measurement equation of the piezoelectric sensor is: wherein, V is the voltage value measured by the piezoelectric sensor, C is a coefficient related to the piezoelectric material itself, D is the modal shape derivative difference matrix, q is the modal coordinate.

3. The active vibration control method for SADA perturbation of a flexible panel satellite according to claim 1, wherein, The calculation formula of the discrete short-time Fourier transform in step 2 is: wherein represents a complex spectrum value at the time frame, the frequency index, represents a sample value of the original signal at , and represents a value of the window function at , L represents a window length, i.e. the number of sample points analyzed per frame, represents a natural constant, represents an imaginary unit, and k represents a frequency index value, represents an intra-frame index value, and N represents the number of Fourier transform points, w is a window function; The amplitude spectrum and the phase spectrum are calculated by the following formula: wherein denotes the amplitude spectrum, denotes the phase spectrum, denotes the real part of denotes the imaginary part of denotes the complex argument.

4. The active vibration control method for SADA perturbation of a flexible panel satellite according to claim 3, wherein, The window function of the discrete short-time Fourier transform in step 2 is the Hanning window.

5. The active vibration control method for SADA perturbation of a flexible panel satellite according to claim 1, wherein, The amplitude spectrum recognition is based on the global maximum value of the amplitude spectrum, and the amplitude frequency corresponding to the global maximum value of the amplitude spectrum corresponds to the flexible modal frequency drift caused by SADA selection and serves as the target frequency of the MPPF controller.

6. The active vibration control method for SADA perturbation of a flexible panel satellite according to claim 5, wherein, The control of the piezoelectric actuator in step 4 adopts the MPPF controller, which includes a second-order compensator and a first-order compensator, specifically: in, Indicates the first The first mode in the first Second derivatives of the state variables of the second-order compensator at each control node. Indicates control damping, Indicates the control frequency. Indicates the first The first mode in the first The first derivative of the state variables of the second-order compensator of each control node. Indicates the first The first mode in the first The state variables of the second-order compensator of each control node. Indicates the first The measured voltage value of the piezoelectric sensor at each control node. Indicates the first The first mode in the first The first derivative of the state variables of the first-order compensator of each control node. Indicates the first The first mode in the first The state variables of the first-order compensator of each control node. Indicates the first The first mode in the first The component of the voltage applied by the actuator of each control node. and This indicates the control parameters.

7. The active vibration control method for SADA perturbation of a flexible panel satellite according to claim 6, wherein, The control frequency According to the amplitude peak frequency setting identified in step 3, the control parameter And According to the angle and angular velocity segment adjustment of SADA, the segment adjustment adopts a table lookup method, the segment region is identified based on the out-of-tolerance region, and the control parameter setting of the piezoelectric actuator in the non-out-of-tolerance region is 0.

8. An active vibration control apparatus for a flexible panel satellite against SADA disturbance, characterized by, The device comprises: A data acquisition unit for collecting SADA driving angles, angular velocities of fiber optic gyroscope and voltage data of piezoelectric sensors under the working condition of three-axis body-to-ground and controlled rotation of the panel to track the sun in orbit; A Fourier transform unit for performing discrete short-time Fourier transform on the voltage data of the piezoelectric sensor to obtain amplitude spectrum and phase spectrum; An amplitude spectrum recognition unit for identifying the frequency corresponding to the amplitude peak value according to the amplitude spectrum as the target frequency for priority suppression of active vibration control, and associating the SADA driving angle and the angular velocity of the fiber optic gyroscope corresponding to the peak value; A judgment unit for determining the stability of the whole satellite according to the angular velocity of the fiber optic gyroscope, and adjusting the control parameters of the piezoelectric actuator when the angular velocity exceeds the set threshold, wherein the control parameters are adjusted in sections according to the SADA driving angle and the angular velocity; An iteration unit for iteratively executing the processes of the data acquisition unit to the judgment unit until the whole satellite stability meets the index requirements throughout the orbit.

9. A computer device, characterized by: A memory and a processor, wherein the memory stores a computer program, and when the processor runs the computer program stored in the memory, the processor executes the active vibration control method for flexible panel satellite SADA disturbance according to any one of claims 1-7.

10. A computer-readable storage medium, characterized in that, The computer readable storage medium stores a computer program, which is run by the processor to execute the steps of the active vibration control method for flexible panel satellite SADA disturbance according to any one of claims 1-7.

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