Truss vibration control method fusing virtual vibration absorber and notch filter

Abstract

The invention relates to the technical field of vibration control, in particular to a truss vibration control method fusing a virtual vibration absorber and a notch filter, and the method comprises the steps: building a dynamic model of a truss, carrying out the modal identification of the dynamic model, obtaining the modal parameters of the truss, determining the positions of the truss where vibration exciters are installed according to the modal parameters, and carrying out the vibration control of the truss. And after the position of the vibration exciter is confirmed, a controller is established in combination with the virtual vibration absorber and the notch filter, an output value of the controller serves as a control value of the vibration exciter and is input into the vibration exciter, and the vibration exciter is controlled to suppress truss vibration at the position of the vibration exciter. According to the method disclosed by the embodiment of the invention, the fixed-frequency disturbance is provided by using the inertial exciter, the active cancellation of the fixed-frequency disturbance on the truss is realized, and the harmonic vibration of the truss can be efficiently, accurately and stably inhibited in a complex space environment.

Description

Technical Field

[0001] The present invention relates to the field of vibration control technology, and specifically provides a truss vibration control method integrating a virtual vibration absorber and a notch filter. Background Art

[0002] With the rapid development of aerospace technology, especially the continuous advancement of on-orbit assembly technology, ultra-large aperture space telescopes and other large space structures have become important tools for cutting-edge scientific research. The realization of these large structures usually relies on deployable space truss structures, which have the advantages of light weight, large unfolding and folding volume ratio, and can support and stabilize on-orbit equipment. However, due to the low damping and dense modal characteristics of space truss structures in space, once disturbed, its vibration is difficult to decay quickly, which may have a serious impact on the precision instruments and payloads on the truss, especially for equipment such as telescopes that require extremely high pointing accuracy.

[0003] In the space environment, the vibration sources of the truss structure are diverse, including harmonic excitations generated by the internal equipment of the spacecraft, such as reaction flywheels, refrigerators, etc., as well as interference from the external environment, such as temperature changes, collisions with space debris, etc. These vibrations not only affect the stability of the structure, but may also cause a decrease in the imaging quality of the telescope.

[0004] In current research and applications, the vibration suppression methods for large space flexible trusses are mainly divided into three categories: passive control, semi-active control and active control. The passive control method is to use viscous dampers (VEDs) and dry friction dampers for vibration control. These methods reduce the amplitude of vibration by increasing structural damping. They are usually designed for broad-spectrum vibrations, but have limited effects when dealing with harmonic vibrations of specific frequencies. Passive controllers usually cannot flexibly adjust their operating frequencies, so it is difficult to achieve the best vibration suppression effect in multi-frequency vibration scenarios. Viscous dampers can effectively absorb vibration energy, while dry friction dampers consume energy through friction. However, these methods may cause vibration amplification during low-frequency vibrations, and once the passively controlled structure is designed and manufactured, its performance cannot be changed and cannot adapt to changing external disturbances or new requirements. For the complex space environment, this lack of adaptability is powerless in the face of diverse disturbances. Although the semi-active control method adds an adjustment mechanism, it is still limited by the frequency characteristics of the structure itself and cannot effectively and accurately control disturbances of different frequencies. Semi-active control methods are still limited in vibration adjustment range and frequency, and cannot meet the needs of real-time and efficient control of changing disturbances. The semi-active control method is to use tuned mass dampers for control: tuned mass dampers (TMDs) change the vibration characteristics of the structure by adjusting the additional mass and spring stiffness, so that the system resonates with vibrations of a specific frequency, thereby dissipating vibration energy. However, the tuning effect of tuned mass dampers depends on accurate system modeling, and once the design is completed, the tuning frequency cannot be flexibly adjusted. Active control methods are: actively applying control forces to suppress vibrations through methods such as piezoelectric actuators. For example, piezoelectric actuators can cause deformation by applying voltage, thereby generating control forces. This method has limited control effects on vibrations of specific frequencies and cannot effectively suppress multi-frequency harmonic excitations. Another active vibration control method based on inertial actuators provides reverse acceleration through inertial actuators to offset the vibration of the structure, with fast response and wide control bandwidth. Although active control methods have high control accuracy and response speed, they have some inherent defects. The hysteresis of piezoelectric actuators increases the complexity and instability of the system in high-precision control. In addition, existing active control methods are mostly aimed at suppressing broad-spectrum vibrations and lack the ability to accurately suppress vibrations of specific frequencies, resulting in poor control effects in multi-frequency harmonic vibration scenarios. Although some active control methods have solved the vibration problem to a certain extent, due to their complex energy supply and control systems, they are difficult to operate stably in space environments with long-term and high-reliability requirements. In addition, since these methods rely on accurate dynamic models, any inaccuracy in the model will directly affect the control effect, increasing the design complexity and uncertainty of the system.In some studies, inertial actuators have been used for vibration control of spatial truss structures. However, traditional inertial actuator control methods mainly target broad-spectrum vibrations and lack precise suppression of harmonic vibrations of specific frequencies, which easily leads to an overly wide control bandwidth and an inaccurate vibration suppression effect.

[0005] The Chinese patent publication number is CN116124394A, the publication date is May 16, 2023, and the invention patent application with the patent name "Vibration control experimental system of space flexible truss based on hydraulic-electric hybrid actuator" discloses a vibration control experimental system of space flexible truss based on hydraulic-electric hybrid actuator, including: a single-machine performance test platform of hydraulic-electric hybrid actuator, used to verify the static output force characteristics, positioning characteristics and driving frequency response characteristics of the hydraulic-electric hybrid actuator under open-loop no-load conditions, a one-dimensional vibration isolation test platform of hydraulic-electric hybrid actuator, used to verify the active and passive integrated one-dimensional broadband vibration isolation effect of the hydraulic-electric hybrid actuator under variable load mass, and a flexible truss vibration control ground experimental platform based on hydraulic-electric hybrid actuator, used to measure the influence law of the dynamic response of the flexible truss, and control the output of the hydraulic-electric hybrid actuator. However, hydraulic-electric hybrid is not suitable for space applications and there is a risk of leakage. Summary of the invention

[0006] In order to solve the above problems, the present invention provides a vibration controller designed by the method, which integrates a virtual vibration absorber and a notch filter, can actively suppress the vibration of the truss, thereby improving the vibration suppression efficiency. The truss vibration control method integrating a virtual vibration absorber and a notch filter provided by the present invention comprises: S1: Establish a dynamic model of the truss, perform modal identification on the dynamic model, and obtain the modal parameters of the truss; S2: According to the modal parameters, the exciter is set on the truss; S3: Establish a virtual vibration absorber and a notch filter, and establish a controller based on the virtual vibration absorber and the notch filter: ; in, Represents the controller output value, represents the virtual absorber gain, represents the mass of the virtual vibration absorber, represents the damping of the virtual vibration absorber, represents the stiffness of the virtual vibration absorber, represents the Laplace operator, represents the natural frequency of the truss to be suppressed, Indicates the acceleration value of the installation point of the actuator feedback, represents the first damping ratio of the truss, represents the second damping ratio of the truss, represents the gain matrix, represents the frequency response function, Represents the truss measurement output; S4: Send the controller output value to the shaker to suppress the truss vibration.

[0007] Preferably, the kinetic model is: ; in, represents the displacement vector, Indicates quality, represents damping, represents the stiffness matrix, represents the external disturbance vector, represents the control matrix, Indicates control input.

[0008] Preferably, the modal identification method is: A known excitation is applied to the truss, and the response data of the truss is recorded. The frequency response function is calculated based on the response data. Based on the frequency response function, the modal parameters of the truss are extracted by the least squares method.

[0009] Preferably, the frequency response function is: ; in, Indicates the system response, represents the known excitation applied to the truss.

[0010] Preferably, the dynamic equation of the virtual vibration absorber is: ; in, Represents the control input of the virtual vibration absorber.

[0011] Preferably, the notch filter is: ; in, represents the notch transfer function.

[0012] Preferably, the method further includes verifying the performance of the controller, wherein the verification indicators include vibration suppression efficiency and stability.

[0013] Preferably, it also includes optimizing the gain matrix by a linear quadratic regulator method : , where it represents the weight matrix of the control input, represents the matrix obtained by solving the Lyapunov equation.

[0014] Compared with the prior art, the present invention can achieve the following beneficial effects: The present invention adopts a method of integrating a virtual controller and a notch filter to actively suppress truss vibration. Through precise modeling, modal parameter extraction, flexible controller design and optimization of feedback mechanism, the system can effectively improve the ability to suppress disturbances of specific frequencies, thereby enhancing the stability and reliability of the system. Compared with passive suppression or a single suppression method, the vibration suppression efficiency is greatly improved. The notch filter is integrated in the controller so that the controller can suppress vibrations of specific frequencies, further enabling the control system to dynamically adapt to different disturbance frequencies, thereby improving the robustness and adaptability of the system. The use of a virtual controller can simplify the design process. Compared with traditional control methods, the design process is more intuitive and efficient. Combined with modal identification technology, the dynamic characteristics of the truss structure can be monitored and identified in real time, the control strategy can be optimized, and the controller performance can be flexibly adjusted by adjusting the virtual mass, damping and stiffness parameters, thereby enhancing the adaptability of the control system and being able to cope with changes in dynamic characteristics caused by environmental changes or structural aging. The embodiment of the present invention also optimizes the gain matrix by a linear quadratic regulator method, thereby improving the stability of the system, ensuring that the truss structure can quickly return to a steady state when subjected to external disturbances, and reducing the impact of vibration on the payload.

[0015] When controlling truss vibration, the embodiment of the present invention uses an exciter to complete the control, and uses an inertial exciter to provide a fixed-frequency disturbance to achieve active cancellation of the fixed-frequency disturbance on the truss. It can efficiently, accurately and stably suppress the harmonic vibration of the truss in a complex spatial environment. The energy consumption of the inertial actuator on the exciter is significantly reduced. Compared with traditional control methods, it can reduce power consumption and reduce system operating costs under the same control effect. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] Figure 1 is a flow chart of a truss vibration control method provided according to an embodiment of the present invention; Figure 2 is a schematic diagram of the installation points of the vibration exciter provided in an embodiment of the present invention; Figure 3 is a transfer function between the motor output force and the inertial actuator interface output force provided in an embodiment of the present invention; Figure 4 This is a diagram showing the effect of a simulation experiment on truss vibration control under 100 Hz single-frequency vibration provided by an embodiment of the present invention; Figure 5 It is a rendering of a simulation experiment of truss vibration control under 150 Hz multi-frequency vibration provided in accordance with an embodiment of the present invention. DETAILED DESCRIPTION

[0017] Hereinafter, embodiments of the present invention will be described with reference to the accompanying drawings. In the following description, the same modules are represented by the same reference numerals. In the case of the same reference numerals, their names and functions are also the same. Therefore, the detailed description thereof will not be repeated.

[0018] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and do not constitute a limitation of the present invention.

[0019] like Figure 1 As shown, an embodiment of the present invention provides a truss vibration control method integrating a virtual vibration absorber and a notch filter, which is specifically as follows: The truss vibration control method provided in the embodiment of the present invention belongs to active control, which uses the mechanical vibration of the exciter to make the truss obtain a certain form and magnitude of vibration, thereby resisting the vibration of the truss itself and achieving vibration suppression. Before performing truss vibration control, the exciter needs to be installed at a fixed position of the truss.

[0020] S1: Establish a dynamic model of the truss and describe the dynamic behavior of the truss by a second-order ordinary differential equation. The expression of the dynamic model is as follows: ; in, represents the displacement vector, Indicates quality, represents damping, represents the stiffness matrix, represents the external disturbance vector, represents the control matrix, Indicates control input.

[0021] The established truss dynamic model is subjected to modal identification. Modal identification is to identify the dynamic characteristics of the truss through the experimental data obtained by modal experiments on the truss dynamic model. The frequency domain analysis method is usually used to obtain the modal parameters of the truss. The specific identification process is as follows: Apply known excitation to the truss. The excitation type can be pulse excitation or swept frequency excitation. Pulse excitation is a short and intense energy input that can excite all modes of the truss in a very short time.

[0022] The advantage of pulse excitation is that it is simple and direct, and can quickly obtain the overall response of the truss. However, it may not provide detailed information about the response of the truss at different frequencies. In actual operation, pulse excitation can be applied to the truss through an exciter, and a more accurate pulse excitation can be generated by controlling the output signal of the exciter. Sweep frequency excitation is an excitation method that continuously changes the frequency over a period of time. It can start from a low frequency and gradually increase to a high frequency, or start from a high frequency and gradually decrease to a low frequency. The advantage of swept frequency excitation is that it can understand the response of the truss at different frequencies in detail, so as to more accurately extract the modal parameters. In actual operation, swept frequency excitation is usually achieved by controlling the exciter with a signal generator. The signal generator can generate a frequency signal that changes with time, and the exciter generates corresponding vibrations based on this signal. The specific type of excitation to be used can be selected according to the actual situation.

[0023] After applying a known excitation to the truss, the response data of the truss under the known excitation is recorded. The response data includes the velocity, acceleration and displacement of the truss.

[0024] Usually, the response data obtained needs to be preprocessed, such as denoising, filtering, etc., and the frequency response function is calculated based on the response data. The frequency response function is the ratio of response to excitation, that is: ; in, represents the response of the system to a known stimulus applied, represents the known excitation applied to the truss.

[0025] According to the frequency response function, the modal parameters are extracted, and the modal parameters include the natural frequency, damping ratio and mode vibration shape. There is no unique method for extracting modal parameters. The embodiment of the present invention selects the least square method to extract modal parameters, that is, to estimate the natural frequency of the truss. , Damping ratio and mode shapes, where the mode shape refers to the vibration form of the truss under a known excitation, and the natural frequency and damping ratio for: , .

[0026] S2: Based on the natural frequency, the self-disturbance frequency of the truss structure during free vibration can be obtained. The vibration strength of each part of the truss can be obtained by analyzing the modal vibration type. The damping ratio can help understand the vibration attenuation speed. Therefore, after obtaining the modal parameters, it is possible to determine the positions of the truss where the exciter should be set based on the modal parameters, that is, to obtain the installation points of the exciter, such as Figure 2 As shown, for vibration suppression.

[0027] Normally, the exciter is installed at the node with the largest displacement among all the nodes of the truss. These nodes respond most significantly to the known excitation. However, since the stroke and speed of the exciter are limited, it is necessary to avoid placing the exciter in a position where the response is too large to avoid impedance mismatch. At the same time, when setting the position of the exciter, it is necessary to consider the overall response of the truss structure to ensure that the exciter can output a stable suppression force as a whole.

[0028] S3: When suppressing truss vibration, the natural frequency of the truss needs to be combined with the control of the exciter to emit the corresponding vibration suppression force. If the natural frequency of the exciter is set to 40Hz, then in the range where the natural frequency of the truss is lower than 40Hz (the mass of the inertial actuator is set to 1kg), the efficiency of the exciter outputting the vibration suppression force is very low, which means that in the frequency range below 40Hz, the exciter cannot effectively transmit or respond to the vibration suppression force output by the controller; in the range where the natural frequency of the truss is higher than 90Hz, the vibration suppression force input to the exciter and the vibration suppression force actually output by the exciter can achieve approximately 1:1, that is, the linear relationship between input and output is better.

[0029] A virtual vibration absorber is created to "absorb" the vibration of the truss, thereby achieving the effect of suppressing the vibration of the truss. When the actuator of the exciter works in a stable frequency range, its dynamic characteristics are usually relatively stable. Therefore, when creating a virtual vibration absorber, it is not necessary to consider the dynamic characteristics of the actuator itself. Figure 3 As shown in the figure, at the natural frequency far away from the exciter, the active output force of the motor of the exciter is linearly related to the overall output force of the inertial actuator. The virtual "vibration absorption" can be realized by using the exciter to provide active control force to suppress the vibration of the truss, that is, a virtual vibration absorber that "absorbs vibration" can be created by creating a virtual mass, damping and stiffness corresponding to the natural frequency of the truss system to suppress the vibration of the specific frequency of the truss.

[0030] In the embodiment of the present invention, the dynamic equation of the virtual vibration absorber is expressed as: ; in, represents the control input of the virtual vibration absorber, represents the virtual absorber gain, represents the mass of the virtual vibration absorber, represents the damping of the virtual vibration absorber, represents the stiffness of the virtual vibration absorber, represents the Laplace operator, Indicates the acceleration value fed back from the actuator installation point, represents the truss displacement.

[0031] In order to suppress the vibration of a specific frequency of the truss, the vibration suppression controller of the embodiment of the present invention is combined with a notch filter on the basis of the virtual vibration absorber. The notch filter is designed as follows: ; in, represents the notch transfer function, represents the natural frequency of the truss to be suppressed, represents the first damping ratio of the truss, Represents the second damping ratio of the truss.

[0032] On the basis of modal identification, the virtual vibration absorber and notch filter are combined to achieve coupling and design a controller to form a closed-loop control system to actively control the vibration of the truss. The established controller can be expressed in the following form: ; in, Represents the controller output value, represents the gain matrix, represents the frequency response function, Represents truss measurement output.

[0033] Design gain matrix The modal analysis results of the truss dynamic model need to be referred to to ensure that the active control force of the exciter does not cause resonance.

[0034] The embodiment of the present invention verifies the performance of the controller through simulation or experiment. The specific evaluation indexes include the vibration suppression efficiency of the controller and the stability of the control system of the controller. Characterizes the controller control system's ability to suppress external disturbances. Good stability of the controller control system can ensure that the control system works normally within the design range.

[0035] Optimizing the Gain Matrix by the Linear Quadratic Regulator Method : , where it represents the weight matrix of the control input, It represents the matrix obtained by solving the Lyapunov equation. By optimizing the gain matrix, the position relationship of the inertial actuator relative to the exciter can be clarified.

[0036] S4: The controller output value The vibrations of the truss are suppressed by the shaker.

[0037] like Figure 4 and Figure 5 As shown, the present invention also verifies the control effect through simulation and experiment, as follows: Compare the damping effect of the inertial actuator of the exciter on 100Hz single-frequency vibration under different control schemes: Without truss vibration control, the RMS value of the truss system is 2.9425 , while the RMS value of the truss system under virtual vibration absorber control is 0.4933 The vibration attenuation rate is 83.24%. When the virtual vibration absorber is combined with the notch filter to control the truss vibration, the root mean square value of the truss system is 0.2261 , the controlled vibration attenuation rate is 92.32%.

[0038] Figure 4 and Figure 5 The damping effect of the inertial actuator on 100Hz and 150Hz multi-frequency vibrations under different control schemes is also demonstrated. In the figure, without control means no truss vibration control, DVA means truss vibration control using virtual vibration absorbers, and DVA+Notch means truss vibration control using virtual vibration absorbers combined with notch filters. The root mean square value of the uncontrolled truss system is 2.3425m / s², while the root mean square value of the truss system under virtual vibration absorber control is 1.9560m / s², and the vibration attenuation rate is 16.5%. After the virtual vibration absorber is combined with the notch method for vibration control, the root mean square value of the truss system is 0.2612m / s², and the vibration attenuation rate is 88.85%.

[0039] From the above data, it can be seen that compared with a single vibration absorber, the effect of using a virtual vibration absorber for single-frequency vibration control is more significant, but the effect is reduced in multi-frequency vibration control. However, after integrating the notch filter into the vibration absorber system, multi-frequency interference can be effectively controlled.

[0040] The present invention can also be adjusted according to different application requirements, and the design can be changed to obtain alternative solutions to adapt to more usage scenarios and improve the applicability of the system. The following are some possible design changes and other uses: 1. Expanding the control dimension: Existing designs are mainly aimed at suppressing harmonic vibrations in single-degree-of-freedom or multi-degree-of-freedom systems. To adapt to a wider range of application scenarios, the controller design can be expanded to enable it to cope with more complex multiple-input multiple-output (MIMO) systems.

[0041] 2. Integrated smart materials: Consider integrating smart materials (such as piezoelectric materials or shape memory alloys) into the system and use the active control capabilities of these materials to further improve the vibration suppression effect.

[0042] 3. Optimize the layout of sensors and actuators: According to different truss structures and vibration characteristics, the control effect of the system can be optimized by adjusting the layout of sensors and inertial actuators.

[0043] Through these design changes and application expansions, the present invention can be more widely applied to various different fields, and can be optimized according to specific needs, thereby providing a more effective vibration suppression solution.

[0044] Although the embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and cannot be understood as limiting the present invention. Those skilled in the art may change, modify, replace and modify the above embodiments within the scope of the present invention.

[0045] The above specific implementations of the present invention do not constitute a limitation on the protection scope of the present invention. Any other corresponding changes and modifications made based on the technical concept of the present invention should be included in the protection scope of the claims of the present invention.

Claims

1. A truss vibration control method integrating a virtual vibration absorber and a notch filter, characterized in that: include: S1: establishing a dynamic model of the truss, performing modal identification on the dynamic model, and obtaining modal parameters of the truss; S2: According to the modal parameters, a vibration exciter is arranged on the truss; S3: Establish a virtual vibration absorber and a notch filter, and establish a controller based on the virtual vibration absorber and the notch filter: ； in, Represents the controller output value, represents the virtual absorber gain, represents the mass of the virtual vibration absorber, represents the damping of the virtual vibration absorber, represents the stiffness of the virtual vibration absorber, represents the Laplace operator, represents the natural frequency of the truss to be suppressed, Indicates the acceleration value fed back from the actuator installation point, represents the first damping ratio of the truss, represents the second damping ratio of the truss, represents the gain matrix, represents the frequency response function, Represents the truss measurement output; S4: Sending the controller output value to the vibration exciter to suppress the truss vibration.

2. The truss vibration control method integrating virtual vibration absorber and notch filter as claimed in claim 1, characterized in that: The kinetic model is: ； in, represents the displacement vector, Indicates quality, represents damping, represents the stiffness matrix, represents the external disturbance vector, represents the control matrix, Indicates control input.

3. The truss vibration control method integrating virtual vibration absorber and notch filter as claimed in claim 1, characterized in that: The modal identification method is: A known excitation is applied to the truss, and response data of the truss is recorded. A frequency response function is calculated based on the response data. Based on the frequency response function, modal parameters of the truss are extracted by a least square method.

4. The truss vibration control method integrating virtual vibration absorber and notch filter as claimed in claim 3, characterized in that: The frequency response function is: ； in, Indicates the system response, represents the known excitation applied to the truss.

5. The truss vibration control method integrating virtual vibration absorber and notch filter as claimed in claim 1, characterized in that: The dynamic equation of the virtual vibration absorber is: ； in, Represents the control input of the virtual vibration absorber.

6. The truss vibration control method integrating virtual vibration absorber and notch filter as claimed in claim 1, characterized in that: The notch filter is: ； in, represents the notch transfer function.

7. The truss vibration control method integrating virtual vibration absorber and notch filter as claimed in claim 1, characterized in that: The method also includes verifying the performance of the controller, wherein the verification indicators include vibration suppression efficiency and stability.

8. The truss vibration control method integrating virtual vibration absorber and notch filter as claimed in claim 1, characterized in that: Also includes optimizing the gain matrix by a linear quadratic regulator method : , where it represents the weight matrix of the control input, represents the matrix obtained by solving the Lyapunov equation.

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