Two-stage negative impedance electromagnetic shunt damper optimization method and related equipment

Abstract

The embodiment of the invention discloses a two-stage negative impedance electromagnetic shunt damper optimization method and related equipment, and the method comprises the steps: building a two-degree-of-freedom linear system kinetic model and a two-degree-of-freedom linear system kinetic equation, and deducing a force transmission rate analytical expression of a two-degree-of-freedom linear system; performing parameter optimization calculation on the two-stage negative impedance electromagnetic shunt damper based on the expression to obtain optimal parameters; and designing the two-stage negative impedance electromagnetic shunt damper according to the optimal parameters. The method can solve the problems that in the design process, inductance, resistance and rigidity parameters are difficult to balance, and design efficiency is low, can be suitable for multi-objective optimization design of the negative impedance electromagnetic shunt damper, has the advantages of being high in calculation efficiency, good in convergence and uniform in solution set distribution, and has good application prospects. The damper which is low in power, simple in electronic equipment, small in mass and good in vibration isolation performance can be designed easily, and hardware support is provided for micro-vibration suppression of spacecrafts. The method is widely applied to the technical field of micro-vibration suppression of spacecrafts.

Description

Technical Field

[0001] This invention relates to the field of spacecraft micro-vibration suppression technology, and in particular to an optimization method and related equipment for a two-stage negative impedance electromagnetic shunt damper. Background Technology

[0002] As high-precision spacecraft demonstrate increasingly important application value in fields such as remote sensing, communication, and observation, the demand for improving spacecraft observation resolution and pointing stability is becoming increasingly urgent. Compared to conventional spacecraft, high-precision spacecraft, represented by high-resolution satellites, laser communication satellites, and space telescopes, require "ultra-stable" attitude and "ultra-precise" pointing. However, micro-vibrations caused by satellite platform jitter can severely affect the stability of sensitive payloads, significantly hindering the improvement of these key performance characteristics. Therefore, suppressing micro-vibrations in spacecraft is crucial.

[0003] Micro-vibrations in spacecraft are mainly caused by rotating components such as momentum wheels, reaction wheels, control moment gyroscopes, and cryogenic coolers. Due to factors such as mass imbalance in these rotating components, when the rotor rotates at high speed, these factors will generate disturbance forces and torques of various frequencies, which will act on the spacecraft platform and cause micro-vibrations in the spacecraft.

[0004] Currently, micro-vibration suppression can be achieved by isolating sensitive targets from vibration sources, suppressing vibration sources, or optimizing vibration transmission paths through spacecraft structures. Installing vibration isolation devices effectively suppresses vibration transmission to satellite platforms and has become the mainstream method for suppressing micro-vibrations. Damping vibration isolation devices can be classified into passive, active, and hybrid types according to whether a control strategy is required. From the perspective of cost and complexity, passive devices are more advantageous, but their adaptability to unknown and variable excitations is limited, and they lack compensation mechanisms. Although active devices can effectively compensate for low-frequency resonance attenuation and improve vibration isolation performance across the entire frequency band, the control force and feedback signal require external sensors and actuators, leading to high power consumption and more complex designs. Hybrid devices combine active and passive devices, such as placing a voice coil actuator in parallel with a D-shaped strut. Although the reliability is higher, it does not overcome the core limitations of purely active devices. Therefore, developing dampers with low power, simple electronic equipment, small device mass, and good vibration isolation performance is of great significance for the suppression of micro-vibrations in spacecraft.

[0005] However, the current design process of spacecraft micro-vibration suppression dampers mainly relies on manual operation and experience-based judgment, and their efficiency and reliability have become bottlenecks restricting further performance optimization. Summary of the Invention

[0006] To address at least one of the aforementioned technical problems, the present invention aims to provide an optimization method and related equipment for a two-stage negative impedance electromagnetic shunt damper.

[0007] On one hand, embodiments of the present invention include an optimization method for a two-stage negative impedance electromagnetic shunt damper, the optimization method comprising the following steps: Establish a dynamic model of a two-degree-of-freedom linear system including a negative impedance electromagnetic shunt damper; Based on the dynamic model of a two-degree-of-freedom linear system, the dynamic equations of the two-degree-of-freedom linear system are established, and the analytical expression of the force transmissibility of the dynamic model of the two-degree-of-freedom linear system is derived. Based on the analytical expression of force transmissibility, the parameters of the negative impedance electromagnetic shunt damper are optimized to obtain the optimal parameters. Based on the optimal parameters, a two-stage negative impedance electromagnetic shunt damper is designed.

[0008] Furthermore, a dynamic model of a two-degree-of-freedom linear system including a negative impedance electromagnetic shunt damper is established, including: Establish a reaction flywheel model, a first structural model, a magnet model, a second structural model, and a base model; the first structural model and the second structural model respectively include a spring plate model connected in parallel and a negative impedance electromagnetic shunt damper model; By sequentially connecting the reaction flywheel model, the first structural model, the magnet model, the second structural model, and the base model, a dynamic model of a two-degree-of-freedom linear system is obtained.

[0009] Furthermore, the negative impedance electromagnetic shunt damper model includes a coil model, an inductor model, and a negative impedance circuit model connected in series.

[0010] Furthermore, the negative impedance circuit model includes an operational amplifier model, a first resistor model, a second resistor model, and a third resistor model. The inverting input terminal of the operational amplifier model serves as the input terminal of the negative impedance circuit model. The output terminal of the operational amplifier model is connected to the inverting input terminal through the first resistor model. The output terminal of the operational amplifier model is connected to the non-inverting input terminal of the operational amplifier model through the second resistor model. The non-inverting input terminal forms the output terminal of the negative impedance circuit model through the third resistor model.

[0011] Furthermore, based on the dynamic model of a two-degree-of-freedom linear system, the dynamic equations of the two-degree-of-freedom linear system are established, and the analytical expression for the force transmissibility of the dynamic model of the two-degree-of-freedom linear system is derived, including: Based on the dynamic equations of a two-degree-of-freedom linear system, an analytical expression for the force transmissibility is derived.

[0012] in, / , Indicates the mass of the magnet model Mass of the reaction flywheel model The mass ratio, , This represents the total resistance of the negative impedance electromagnetic shunt damper model. With total inductance The ratio, , Indicates the stiffness of the spring sheet model Mass of the reaction flywheel model Specific stiffness; , The electromechanical transducer coefficients are determined by the inherent properties of the coil and magnet models. Represents the coupling coefficient; , , , , , , , .

[0013] Furthermore, based on the analytical expression for force transmissibility, parameter optimization calculations are performed on the negative impedance electromagnetic shunt damper to obtain the optimal parameters, including: Define the objective function; the objective function includes the first-order resonant amplification factor function and the high-frequency attenuation rate function, which are expressed in terms of the total resistance. Total inductance and stiffness As a variable; A fast non-dominated sorting genetic algorithm is executed to perform multi-objective optimization of the objective function, obtaining an initial Pareto solution set and a Pareto front. The initial Pareto solution set includes multiple sets of solutions, each containing the total resistance. Total inductance and stiffness The specific value; The solutions in the initial Pareto solution set are filtered to obtain the filtered Pareto solution set; Select a set of solutions from the Pareto solution set as the optimal parameters.

[0014] Furthermore, the solutions in the initial Pareto solution set are filtered to obtain a filtered Pareto solution set, including: Based on the first-order resonant amplification factor and high-frequency attenuation rate given by the Pareto front, solutions that meet the requirements in the initial Pareto solution set are retained, while solutions that do not meet the requirements are filtered out to obtain a filtered Pareto solution set. The requirements include that the corresponding first-order resonant amplification factor is less than 3dB and the corresponding high-frequency attenuation rate is less than -40dB at 100 Hz.

[0015] Furthermore, a set of solutions is determined from the Pareto solution set as optimal parameters, including: Calculate the ratio of total inductance to total resistance for each solution in the Pareto solution set; Choose the set of solutions with the minimum ratio of total inductance to total resistance as the optimal parameters.

[0016] On the other hand, embodiments of the present invention also include a computer device including a memory and a processor, the memory for storing at least one program and the processor for loading at least one program to execute the two-stage negative impedance electromagnetic shunt damper optimization method of the embodiments.

[0017] On the other hand, embodiments of the present invention also include a computer program product, comprising a computer program that, when executed by a processor, implements the two-stage negative impedance electromagnetic shunt damper optimization method of the embodiments.

[0018] The beneficial effects of the embodiments of the present invention are as follows: The optimization method for the two-stage negative impedance electromagnetic shunt damper in the embodiments can overcome the problems of difficulty in balancing inductance, resistance and stiffness parameters and low design efficiency in the design process of two-stage negative impedance electromagnetic shunt dampers. It can be applied to the multi-objective optimization design of negative impedance electromagnetic shunt dampers, and has the characteristics of high computational efficiency, good convergence and uniform solution distribution. It can improve the design efficiency and accuracy of two-stage negative impedance electromagnetic shunt dampers, and is conducive to designing dampers with low power, simple electronic equipment, small mass and good vibration isolation performance, providing hardware support for the suppression of micro-vibrations in spacecraft. Attached Figure Description

[0019] Figure 1 This is a schematic diagram illustrating the steps of the optimization method for the two-stage negative impedance electromagnetic shunt damper in the embodiment; Figure 2 This is a schematic diagram of the dynamics model of a two-degree-of-freedom linear system in the embodiment; Figure 3 This is a schematic diagram of the negative impedance electromagnetic shunt damper model in the embodiment; Figure 4 This is a schematic diagram of the Pareto fronts obtained by the NSGA-II algorithm for two objective functions in the embodiment; Figure 5This is a schematic diagram illustrating the Pareto set (initial Pareto solution set) corresponding to the Pareto fronts obtained by the NSGA-II algorithm for the two objective functions in the embodiment. Figure 6 This is a schematic diagram of the Pareto set (the Pareto solution set) after filtering according to the indicator requirements in the example; Figure 7 This is a schematic diagram of the vibration isolation performance of a two-stage negative impedance electromagnetic shunt damper system based on the Pareto solution set in the embodiment. Figure 8 This is a schematic diagram of the force transmissibility curve of the two-stage negative impedance electromagnetic shunt damper system after optimization design in the embodiment. Detailed Implementation

[0020] Semi-active vibration isolation falls under the category of active vibration isolation, with performance approaching that of active systems. It typically requires fewer auxiliary devices (such as sensors and actuators) and consumes less energy. Its stiffness or damping can be actively adjusted. Connecting a negative impedance circuit to an electromagnetic shunt damper (EMSD) improves the EMSD's vibration isolation performance. Compared to the complex control circuitry of active systems, the negative impedance circuit has simpler electronics, offering advantages such as lower power consumption and higher reliability. Since the negative impedance circuit requires no control algorithm, and some of the energy required by the device is provided by the relative motion between the magnet and the coil, this type of EMSD can be classified as a semi-active device. Stabile A. et al. at the Surrey Space Center conducted extensive ground tests on this damper, confirming its excellent vibration isolation performance. The related technology has gained recognition in the field of spacecraft micro-vibration suppression.

[0021] Based on the above principles, a two-stage negative impedance electromagnetic shunt damper can be designed and its parameters optimized to meet the requirements of spacecraft micro-vibration suppression for vibration isolation performance, design efficiency, and accuracy.

[0022] In this embodiment, to design a damper that meets the requirements, an optimization method for a two-stage negative impedance electromagnetic shunt damper is provided. (Refer to...) Figure 1 The optimization method for a two-stage negative impedance electromagnetic shunt damper includes the following steps: S1. Establish a dynamic model of a two-degree-of-freedom linear system including a negative impedance electromagnetic shunt damper; S2. Based on the dynamic model of a two-degree-of-freedom linear system, establish the dynamic equations of the two-degree-of-freedom linear system and derive the analytical expression of the force transmissibility of the dynamic model of the two-degree-of-freedom linear system; S3. Based on the analytical expression of force transmissibility, perform parameter optimization calculations on the negative impedance electromagnetic shunt damper to obtain the optimal parameters; S4. Based on the optimal parameters, design a two-stage negative impedance electromagnetic shunt damper.

[0023] In this embodiment, a computer can be used to perform steps S1-S4.

[0024] When performing step S1, which is to establish a dynamic model of a two-degree-of-freedom linear system including a negative impedance electromagnetic shunt damper, the following steps can be performed: S101. Establish the reaction flywheel model, the first structure model, the magnet model, the second structure model, and the base model; S102. By sequentially connecting the reaction flywheel model, the first structural model, the magnet model, the second structural model, and the base model in series, a dynamic model of a two-degree-of-freedom linear system is obtained.

[0025] The reaction flywheel model in step S101 can be a data model capable of simulating a physical reaction flywheel, or it can be a physical reaction flywheel. In this embodiment, a data model is used as an example for explanation.

[0026] The structure of the two-degree-of-freedom linear system dynamics model obtained by executing steps S101-S102 is as follows: Figure 2 As shown. (Refer to...) Figure 2 The mass of the reaction flywheel model is The mass of the magnet model is The first and second structural models have the same structure, each including a spring plate model connected in parallel and a negative impedance electromagnetic shunt damper model, respectively. The stiffness coefficient of the spring plate model in the first structural model is... The stiffness coefficient of the spring sheet model in the second structural model is In this embodiment, the stiffness coefficients of the two spring sheet models are equal, that is... = = Unlike traditional tuned mass dampers, Figure 2 The dynamic model of the two-degree-of-freedom linear system shown has a mass of The magnet model is inserted into a mass of The reaction flywheel model and the base model (first structural model and second structural model) are related.

[0027] Figure 2 In the dynamic model of the two-degree-of-freedom linear system shown, the first structural model includes a negative impedance electromagnetic shunt damper model EMSD1, and the second structural model includes a negative impedance electromagnetic shunt damper model EMSD2. Both of them have... Figure 3The structures shown are identical for the two negative impedance electromagnetic shunt damper models. One of the negative impedance electromagnetic shunt damper models will be used as an example for explanation.

[0028] Reference Figure 3 The negative impedance electromagnetic shunt damper model includes a coil model, an inductor model, and a negative impedance circuit model, which are connected in series. The resistance value of the coil model is... The inductance value of the coil model is The induced voltage generated when the coil model is working is The resistance value of the inductor model connected in series with the coil model is... Inductance value The inductance value can be changed by altering the inductor model. This is used to adjust the resistance to inductance ratio of the entire closed loop in the negative impedance electromagnetic shunt damper model.

[0029] Reference Figure 3 The negative impedance circuit consists of an operational amplifier model and a first resistor model (resistance value is...). ), second resistor model (resistance value) ) and the third resistor model (resistance value is The circuit consists of three resistors: an operational amplifier model and a negative impedance circuit model. The inverting input of the operational amplifier model serves as the input of the negative impedance circuit model. The output of the operational amplifier model is connected to the inverting input through the first resistor model. The output of the operational amplifier model is connected to the non-inverting input through the second resistor model. The non-inverting input is connected to the output of the negative impedance circuit model through the third resistor model. The output of the negative impedance circuit model is grounded.

[0030] The equivalent resistance of the entire negative impedance circuit, that is, the resistance between the input and output terminals of the negative impedance circuit, is:

[0031] when When a negative impedance circuit produces a negative resistance. The total resistance of a closed circuit .definition This is the electromechanical transducer coefficient, which quantifies the coupling relationship between the conductive material and the magnetic field. The size is determined by the inherent properties of the coil model and the magnet model.

[0032] In step S2, for Figure 2The dynamic model of the two-degree-of-freedom linear system shown can be used to establish the dynamic equations of a two-stage negative impedance electromagnetic shunt damper, and derive the analytical expression for the force transmissibility of the system in the frequency domain. Specifically, firstly, based on the principles of structural dynamics, Faraday's law of electromagnetic induction, Kirchhoff's voltage law and Lorentz force law related to negative impedance circuits, a force analysis is performed on the dynamic model of the two-degree-of-freedom linear system. Through this force analysis, the dynamic equations of the two-degree-of-freedom linear system consist of the following eight equations:

[0033] In formula (2), The displacement of the reaction flywheel model relative to the base model. This represents the displacement of the magnet model relative to the base model. It is the speed of the reaction flywheel model. It is the acceleration of the reaction flywheel model. It is the speed of the magnet model. It is the acceleration of the magnet model.

[0034] In formula (2), , and They are respectively Figure 3 The negative impedance electromagnetic shunt damper model shown represents the total resistance, total inductance, and current of a closed loop. , and The negative impedance electromagnetic shunt damper model in the second structural model is taken as... Figure 3 The total resistance, total inductance, and current of the closed loop shown.

[0035] In formula (2), The induced voltage generated when the negative impedance electromagnetic shunt damper model in the first structural model is working; This refers to the induced voltage generated when the negative impedance electromagnetic shunt damper model in the second structural model is working. The electromagnetic force generated by the interaction between the negative impedance electromagnetic shunt damper model and the magnet model when the first structural model is working. The electromagnetic force generated by the interaction between the negative impedance electromagnetic shunt damper model and the magnet model when the second structural model is working.

[0036] In formula (2), The input force represents the force transmitted from the micro-vibrations caused by the reaction wheel model. The force transmitted to the base can be expressed as...

[0037] Converting this single-input single-output system to the frequency domain, in this embodiment, since the structure and device parameters of the first and second structural models are the same, it can be simplified to... , , By performing a Laplace transform on equations (2) and (3) and simultaneously solving the two equations, we can obtain the analytical expression for the force transmissibility of a two-degree-of-freedom linear system in the frequency domain.

[0038] In formula (4), / , Indicates the mass of the magnet model Mass of the reaction flywheel model The mass ratio, , This represents the total resistance of the negative impedance electromagnetic shunt damper model. With total inductance The ratio, , Indicates the stiffness of the spring sheet model Mass of the reaction flywheel model Specific stiffness; , The electromechanical transducer coefficients are determined by the inherent properties of the coil and magnet models. Represents the coupling coefficient; , , , , , , , .

[0039] In step S3, the parameters of the two-stage negative impedance electromagnetic shunt damper are optimized according to the analytical expression of the two-degree-of-freedom force transmissivity shown in formula (4) to obtain the optimal parameters.

[0040] Specifically, when performing step S3, which is to perform parameter optimization calculations on the two-stage negative impedance electromagnetic shunt damper to obtain the optimal parameters, the following steps can be performed: S301. Define the objective function; S302. Execute the fast non-dominated sorting genetic algorithm to perform multi-objective optimization of the objective function and obtain the initial Pareto solution set; S303. Filter the solutions in the initial Pareto solution set to obtain the filtered Pareto solution set; S304. Select a set of solutions from the Pareto solution set as the optimal parameters.

[0041] In steps S301-S303, the fast non-dominated sorting genetic algorithm (NSGA-II) with an elite strategy is used to perform parameter optimization calculations on the two-stage negative impedance electromagnetic shunt damper.

[0042] In step S301, since the two-degree-of-freedom vibration isolation system subjected to sinusoidal excitation has two performance indicators, namely the first-order resonance amplification function of the two-degree-of-freedom linear system... and high-frequency attenuation function Therefore, these two functions are used as the objective functions.

[0043] Due to the first-order resonance amplification function The first-order resonant amplification factor and high-frequency attenuation rate function represent There is a certain conflict between the indicated high-frequency attenuation performance, therefore a multi-objective optimization algorithm is needed to optimize the three parameters of the two-stage negative impedance electromagnetic shunt damper. , and Optimization is performed to simultaneously minimize the system's resonant amplification factor and maximize the high-frequency attenuation rate. Specifically, in step S302, a fast non-dominated sorting genetic algorithm (NSGA-II) with an elitist strategy is run to perform multi-objective optimization of the objective function. Specifically, the mass of the reaction flywheel model can be set. The mass of the magnet model is 5 kg. The weight is 0.18 kg, and the electromechanical transducer coefficient is... Take 10.79 The two objective functions are the first-order resonance amplification factor function. and high-frequency attenuation function When using NSGA-II for computation, the population size was set to 100; the optimal front-end individual coefficient was 0.3; the maximum number of generations and the stopping generation were both 200; and the fitness function bias was 1e-100. During optimization, the stiffness was determined based on the actual engineering requirements. ,resistance and inductor The scope, for , , Perform parameter optimization.

[0044] By executing step S302, we can obtain Figure 4 The results are shown. Figure 4 The Pareto fronts obtained by the NSGA-II algorithm for two objective functions when designing a two-stage negative impedance electromagnetic shunt damper are plotted. The horizontal axis represents the first-order resonant amplification factor, and the vertical axis represents the attenuation rate at 100 Hz. A total of 30 sets of data were obtained, each corresponding to a set of total resistance. Total inductance and stiffness The specific value of is equivalent to a solution, thus forming . Figure 5 The initial Pareto solution set shown can be used to select design parameters that meet the requirements. Figure 5 In the initial Pareto solution set, the stiffness represented by each set of solutions is... ,resistance and inductor Distributed within the following range:

[0045] for Figure 5 The initial Pareto solution set shown can be processed by step S303, which involves selecting parameters from the initial Pareto solution set that meet the specified criteria to form a filtered Pareto solution set. In this embodiment, the following criteria can be set: the corresponding first-order resonant amplification factor is less than 3 dB, and the corresponding high-frequency attenuation rate is less than -40 dB at 100 Hz. Based on these criteria, the solutions in the initial Pareto solution set are filtered, with solutions that meet the criteria retained and those that do not. The retained solutions form the filtered Pareto solution set. The first-order resonant amplification factor and high-frequency attenuation rate can be obtained from the Pareto front corresponding to the initial Pareto solution set.

[0046] In this embodiment, by executing step S303, the following can be obtained: Figure 6 The filtered Pareto solution set shown contains 14 solutions. Figure 7 The vibration isolation performance of a two-stage negative impedance electromagnetic shunt damper system based on the screening of Pareto solutions is presented.

[0047] Considering the total resistance of the circuit Total inductance and frequency The additional leading phase angle caused by the combination

[0048]

[0049] Additional leading phase angle This will cause the phase difference between the voltage across the negative resistor and the input voltage to be greater than [the phase difference is missing from the original text]. This prevents the electromagnetic damping force from being applied at the peak of the structural vibration velocity, weakening the damping energy dissipation effect and reducing vibration isolation performance. Therefore, it can be seen that if a solution corresponds to a total inductance... and total resistance The ratio is The smaller the value, the better the energy dissipation effect of electromagnetic damping, and the better the vibration isolation performance of the device. Therefore, when designing the parameters of a two-stage negative impedance electromagnetic shunt damper, the total inductance can be searched. and total resistance The solution that minimizes the ratio.

[0050] Based on the above principle, step S304 is executed, selecting from the 14 sets of solutions in the Pareto solution set. The smallest set of data, i.e. Figure 6 In =0.93 Ω, =5.78 mH, The solution of 1186 N / m is used as the optimal parameter obtained by performing step S3 to design a two-stage negative impedance electromagnetic shunt damper.

[0051] Figure 8 The force transmissibility curves of a two-stage negative impedance electromagnetic shunt damper system after applying optimal parameters are presented. Based on... Figure 8 It can be seen that if a two-stage negative impedance electromagnetic shunt damper with such optimal parameters is used, the micro-vibrations of the spacecraft can be effectively suppressed.

[0052] In this embodiment, by implementing a two-stage negative impedance electromagnetic shunt damper optimization method, the problem of difficulty in coordinating the balance of inductance, resistance, and stiffness parameters in the design process of two-stage negative impedance electromagnetic shunt dampers is effectively solved, significantly improving design efficiency. The NSGA-II algorithm used in the two-stage negative impedance electromagnetic shunt damper optimization method has good convergence performance and can quickly approximate the Pareto optimal solution set, ensuring the validity of the optimization results. The solution set obtained by the two-stage negative impedance electromagnetic shunt damper optimization method is uniformly distributed, achieving a good balance between convergence and diversity, providing a basis for engineering decision-making. This method offers multiple feasible solutions and provides optimal parameters to guide the design of two-stage negative impedance electromagnetic shunt dampers. The optimization method for two-stage negative impedance electromagnetic shunt dampers can minimize the first-order resonance amplification factor and maximize the high-frequency attenuation rate. Since the optimization method is easily implemented via computer, it can improve the design efficiency and accuracy of two-stage negative impedance electromagnetic shunt dampers, facilitating the design of dampers with low power, simple electronic equipment, small mass, and good vibration isolation performance, thus providing hardware support for the suppression of micro-vibrations in spacecraft.

[0053] In this embodiment, a computer device can be used, including a memory and a processor. The memory is used to store at least one program, and the processor is used to load at least one program to execute the two-stage negative impedance electromagnetic shunt damper optimization method, thereby obtaining the effect of the two-stage negative impedance electromagnetic shunt damper optimization method.

[0054] In this embodiment, a computer program product, including a computer program, can be used to implement the two-stage negative impedance electromagnetic shunt damper optimization method in the embodiment when the computer program is executed by a processor.

[0055] It should be noted that, unless otherwise specified, when a feature is referred to as "fixed" or "connected" to another feature, it can be directly fixed or connected to the other feature, or indirectly fixed or connected to the other feature. Furthermore, the descriptions of "upper," "lower," "left," and "right" used in this disclosure are only relative to the relative positional relationships of the components of this disclosure in the accompanying drawings. The singular forms "a" and "the" used in this disclosure are also intended to include the plural forms, unless the context clearly indicates otherwise. Moreover, unless otherwise defined, all technical and scientific terms used in this embodiment have the same meaning as commonly understood by one of ordinary skill in the art. The terminology used in this embodiment specification is only for describing specific embodiments and is not intended to limit the embodiments of the invention. The term "and / or" as used in this embodiment includes any combination of one or more of the associated listed items.

[0056] It should be understood that although the terms first, second, third, etc., may be used to describe various elements in this disclosure, these elements should not be limited to these terms. These terms are only used to distinguish elements of the same type from each other. For example, a first element may also be referred to as a second element without departing from the scope of this disclosure, and similarly, a second element may also be referred to as a first element. The use of any and all instances or exemplary language (“e.g.,” “such as,” etc.) provided in this embodiment is intended only to better illustrate embodiments of the invention and, unless otherwise required, does not impose a limitation on the scope of embodiments of the invention.

[0057] It should be recognized that embodiments of the present invention can be implemented or carried out by computer hardware, a combination of hardware and software, or by computer instructions stored in a non-transitory computer-readable storage medium. The method can be implemented using standard programming techniques—including a non-transitory computer-readable storage medium configured with a computer program, wherein such a storage medium causes the computer to operate in a specific and predefined manner—according to the methods and drawings described in the specific embodiments. Each program can be implemented in a high-level procedural or object-oriented programming language to communicate with the computer system. However, if desired, the program can be implemented in assembly or machine language. In any case, the language can be a compiled or interpreted language. Furthermore, for this purpose, the program can run on a programmed application-specific integrated circuit (ASIC).

[0058] Furthermore, the procedures described in this embodiment can be performed in any suitable order unless otherwise indicated by this embodiment or otherwise obviously contradict the context. The procedures (or variations and / or combinations thereof) described in this embodiment can be executed under the control of one or more computer systems configured with executable instructions, and can be implemented by hardware or a combination thereof as code (e.g., executable instructions, one or more computer programs, or one or more applications) that commonly executes on one or more processors. A computer program includes a plurality of instructions executable by one or more processors.

[0059] Furthermore, the method can be implemented in any suitable type of computing platform, including but not limited to personal computers, minicomputers, mainframes, workstations, networked or distributed computing environments, standalone or integrated computer platforms, or in communication with charged particle tools or other imaging devices, etc. Aspects of embodiments of the invention can be implemented as machine-readable code stored on a non-transitory storage medium or device, whether removable or integrated into a computing platform, such as a hard disk, optical read and / or write storage medium, RAM, ROM, etc., such that it is readable by a programmable computer, and when the storage medium or device is read by the computer, it can be used to configure and operate the computer to perform the processes described herein. Furthermore, the machine-readable code, or portions thereof, can be transmitted via wired or wireless networks. The invention of this embodiment includes these and other different types of non-transitory computer-readable storage media when such media comprises instructions or programs that implement the steps above in conjunction with a microprocessor or other data processor. Embodiments of the invention also include the computer itself when programmed according to the methods and techniques of embodiments of the invention.

[0060] A computer program can be applied to input data to perform the functions of this embodiment, thereby transforming the input data to generate output data stored in non-volatile memory. The output information can also be applied to one or more output devices, such as a display. In a preferred embodiment of the invention, the transformed data represents physical and tangible objects, including a specific visual depiction of physical and tangible objects generated on the display.

[0061] The above are merely preferred embodiments of the present invention. The embodiments of the present invention are not limited to the above-described implementations. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of the embodiments of the present invention, as long as they achieve the same technical effects, should be included within the scope of protection of the embodiments of the present invention. Within the scope of protection of the embodiments of the present invention, the technical solutions and / or implementation methods can have various modifications and variations.

Claims

1. An optimization method for a two-stage negative impedance electromagnetic shunt damper, characterized in that, The optimization method for the two-stage negative impedance electromagnetic shunt damper includes: Establish a dynamic model of a two-degree-of-freedom linear system including a negative impedance electromagnetic shunt damper; Based on the dynamic model of the two-degree-of-freedom linear system, the dynamic equation of the two-degree-of-freedom linear system is established, and the analytical expression of the force transmissibility of the dynamic model of the two-degree-of-freedom linear system is derived. Based on the analytical expression of force transmissibility, the parameters of the negative impedance electromagnetic shunt damper are optimized to obtain the optimal parameters. Based on the optimal parameters, a two-stage negative impedance electromagnetic shunt damper is designed.

2. The optimization method for a two-stage negative impedance electromagnetic shunt damper according to claim 1, characterized in that, The establishment of a two-degree-of-freedom linear system dynamic model including a negative impedance electromagnetic shunt damper includes: Establish a reaction flywheel model, a first structural model, a magnet model, a second structural model, and a base model; the first structural model and the second structural model respectively include a spring plate model connected in parallel and a negative impedance electromagnetic shunt damper model; The reaction flywheel model, the first structural model, the magnet model, the second structural model, and the base model are connected in series to obtain the dynamic model of the two-degree-of-freedom linear system.

3. The optimization method for a two-stage negative impedance electromagnetic shunt damper according to claim 2, characterized in that, The negative impedance electromagnetic shunt damper model includes a coil model, an inductor model, and a negative impedance circuit model connected in series.

4. The optimization method for a two-stage negative impedance electromagnetic shunt damper according to claim 3, characterized in that, The negative impedance circuit model includes an operational amplifier model, a first resistor model, a second resistor model, and a third resistor model. The inverting input terminal of the operational amplifier model serves as the input terminal of the negative impedance circuit model. The output terminal of the operational amplifier model is connected to the inverting input terminal through the first resistor model. The output terminal of the operational amplifier model is connected to the non-inverting input terminal of the operational amplifier model through the second resistor model. The non-inverting input terminal forms the output terminal of the negative impedance circuit model through the third resistor model.

5. The optimization method for a two-stage negative impedance electromagnetic shunt damper according to any one of claims 2-4, characterized in that, The step of establishing the dynamic equations of the two-degree-of-freedom linear system based on the dynamic model of the two-degree-of-freedom linear system, and deriving the analytical expression for the force transmissibility of the dynamic model of the two-degree-of-freedom linear system, includes: Based on the dynamic equations of the two-degree-of-freedom linear system, the analytical expression for the force transmissibility is derived. in, / , Indicates the mass of the magnet model With respect to the mass of the reaction flywheel model The mass ratio, , This represents the total resistance of the negative impedance electromagnetic shunt damper model. With total inductance The ratio, , This indicates the stiffness of the spring sheet model. With respect to the mass of the reaction flywheel model Specific stiffness; , The electromechanical transducer coefficients are determined by the inherent properties of the coil model and the magnet model. Represents the coupling coefficient; , , , , , , , .

6. The optimization method for a two-stage negative impedance electromagnetic shunt damper according to claim 5, characterized in that, The step of performing parameter optimization calculations on the negative impedance electromagnetic shunt damper based on the analytical expression of the force transmissibility to obtain optimal parameters includes: Define an objective function; the objective function includes the first-order resonant amplification factor function and the high-frequency attenuation rate function of the force transmissibility analytical expression, wherein the first-order resonant amplification factor function and the high-frequency attenuation rate function are respectively expressed in terms of the total resistance. Total inductance and stiffness As a variable; A fast non-dominated sorting genetic algorithm is executed to perform multi-objective optimization on the objective function, obtaining an initial Pareto solution set and a Pareto front; the initial Pareto solution set includes multiple sets of solutions, each set including the total resistance. Total inductance and stiffness The specific value; The solutions in the initial Pareto solution set are filtered to obtain the filtered Pareto solution set; A set of solutions is selected from the selected Pareto solution set as the optimal parameters.

7. The optimization method for a two-stage negative impedance electromagnetic shunt damper according to claim 6, characterized in that, The step of filtering the solutions in the initial Pareto solution set to obtain a filtered Pareto solution set includes: Based on the first-order resonant amplification factor and high-frequency attenuation rate given by the Pareto front, solutions that meet the index requirements in the initial Pareto solution set are retained, and solutions that do not meet the index requirements are filtered out to obtain the filtered Pareto solution set; the index requirements include a first-order resonant amplification factor of less than 3dB and a high-frequency attenuation rate of less than -40dB at 100 Hz.

8. The optimization method for a two-stage negative impedance electromagnetic shunt damper according to claim 6, characterized in that, The step of determining a set of solutions from the selected Pareto solution set as the optimal parameters includes: Calculate the ratio of total inductance to total resistance for each solution in the Pareto solution set. The set of solutions with the minimum ratio of total inductance to total resistance is selected as the optimal parameters.

9. A computer device, characterized in that, It includes a memory and a processor, the memory being used to store at least one program, and the processor being used to load at least one program to execute the two-stage negative impedance electromagnetic shunt damper optimization method according to any one of claims 1-8.

10. A computer program product, comprising a computer program, characterized in that, When the computer program is executed by the processor, it implements the optimization method for the two-stage negative impedance electromagnetic shunt damper as described in any one of claims 1-8.

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