Matching design method for cable parallel robot vibration suppression device based on frequency and power

Abstract

The invention discloses a cable parallel robot vibration suppression device matching design method based on frequency and power, and the method comprises the steps: firstly obtaining the vibration energy distribution and inherent frequency characteristics of an under-constrained cable parallel robot system in a full working space through the building of a system dynamic model of the under-constrained cable parallel robot and the modal analysis; secondly, establishing an alternative device library comprising various actuators such as a flywheel, a rotor wing, a pendulum bob, a linear inertia mass block and an air injection device, and constructing a parameterized kinetic model of each device; based on a parameter matching derivation method of a physical mechanism, quantitative constraint relations among motor power, response bandwidth, geometric dimensions and system vibration frequency and energy are respectively established for different devices; and finally, based on the deduced matching criterion, determining an optimal device configuration and design parameters by using an optimization algorithm. According to the method, it can be ensured that the dynamic response capacity of the vibration suppression device is highly matched with the vibration characteristic of the robot system from the physical mechanism level, and the multi-dimensional coupling vibration problem of the under-constrained cable parallel robot is effectively solved.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of robot technology, in particular to a frequency and power based cable parallel robot vibration suppression device matching design method. BACKGROUND

[0002] Cable-driven parallel robots have wide application prospects in large radio telescope feed support, large ship spraying, high-speed warehouse logistics, etc. due to their large workspace, strong load capacity, lightweight structure and other advantages. However, the end platform of the cable parallel robot is usually driven by flexible cables, and there may be under-constrained characteristics in some degrees of freedom. This structural feature makes it prone to multi-dimensional coupled vibration during high-speed operation.

[0003] Common vibration forms include low-frequency, large-amplitude linear vibration (e.g. large swinging) in the direction without cable constraint (or weak constraint), and high-frequency, small-amplitude angular vibration (e.g. high-frequency shaking) in the direction constrained by the cable.

[0004] Existing vibration suppression techniques mainly focus on the design of control algorithms, such as PID control, sliding mode control or input shaping, etc. However, if the physical parameters of the front-end vibration suppression device itself do not match the vibration characteristics of the robot, no matter how advanced the control algorithm is, it cannot work effectively. For example: if a slow-response rotor is selected to suppress high-frequency angular vibration, it may cause reverse excitation due to thrust lag; if a flywheel with insufficient energy storage capacity is selected to suppress large-amplitude low-frequency vibration, the motor may reach saturation within half a vibration period, and cannot continuously dissipate energy.

[0005] Therefore, there is an urgent need for a systematic design method that can inversely deduce the type selection and key parameters (such as motor power, moment of inertia, rotor size, etc.) of the vibration suppression device from the physical mechanism according to the inherent vibration characteristics (frequency, energy, mode) of the cable parallel robot, in order to achieve optimal vibration suppression effect. SUMMARY

[0006] In order to solve the problems existing in the prior art, the purpose of the present application is to provide a cable parallel robot vibration suppression device optimization design method based on parameter matching. This method identifies vibration characteristics by establishing a dynamic model of the robot, and establishes a parameterized model for vibration suppression devices with different physical mechanisms such as flywheels, rotors and pendulums, and proposes dual design criteria of "power matching" and "frequency matching", thereby guiding the scientific selection and parameter optimization of the device.

[0007] In order to achieve the above purpose, the technical scheme adopted by the present application is as follows: A frequency and power based cable parallel robot vibration suppression device matching design method, comprising the following steps: Step S101: Vibration Feature Extraction: Establish a system dynamic model of the underconstrained parallel robot, introduce the Hessian matrix to characterize the nonlinear influence of the dynamic platform's attitude change on stiffness, solve for the global stiffness matrix and inertia matrix in the entire workspace, identify the dominant coupled vibration modes of the underconstrained parallel robot system, and extract the natural frequencies of each order. and the corresponding maximum vibrational energy ; Optionally, establishing the system dynamics model of the underconstrained cable parallel robot specifically includes: introducing the Hessian matrix to calculate the active stiffness matrix caused by cable force changes, and combining the passive stiffness matrix caused by cable elasticity and the underconstrained stiffness matrix caused by gravity to construct a global stiffness matrix for the entire workspace. With the inertia matrix; by solving the generalized eigenvalue problem Modal analysis was performed, in which The system quality matrix, For the natural frequency, These are vibration modes.

[0008] Step S102: Vibration damping device mechanism modeling. Establish a library of candidate active vibration damping devices, construct a parameterized dynamic model of each vibration damping device in the library, and analyze the mapping relationship between the physical mechanism of each vibration damping device generating damping force or torque and the driving parameters.

[0009] Optionally, the library of alternative active vibration damping devices includes at least one or more of the following: flywheel devices, rotor devices, pendulum devices, linear inertial mass devices, and jet devices; the modeling mechanism of the parametric dynamic model for different vibration damping devices is as follows: For the flywheel device: the motor stator is regarded as a fixed mass block and the rotor is regarded as a high-speed rotating rigid body; a dynamic model based on the inertial reaction torque generated by angular acceleration is established. Its vibration suppression mechanism is to generate an inertial torque opposite to the platform vibration by adjusting the angular acceleration, and to utilize the gyroscopic effect torque generated by high-speed rotation.

[0010] For the rotor device: the rotor device is regarded as a rigid rotor that can generate unidirectional thrust; a dynamic model based on aerodynamic principles to generate unidirectional thrust is established, and its vibration suppression mechanism is to generate tension or thrust along the direction of the rotating shaft by adjusting the motor speed, and the output force is proportional to the square of the speed.

[0011] For the pendulum device: the pendulum is simplified as a point mass rotating around a fixed axis; a nonlinear oscillation model including gravitational torque and inertial torque is established; its vibration suppression mechanism includes the gravitational restoring torque generated by the change of the pendulum angle, and the adjustment effect on the overall center of gravity position of the platform during the oscillation process.

[0012] For a linear inertial mass block device: the linear inertial mass block is regarded as a point mass that performs a single degree of freedom translation along the guide rail; a model based on the inertial reaction force generated by translational acceleration is established; its vibration suppression mechanism is to utilize the inertial reaction force generated by the accelerated motion of the linear inertial mass block.

[0013] For jet propulsion devices: the nozzle is considered as an ideal point source; a model is established based on the instantaneous thrust generated by gas recoil, ignoring the time delay effect of gas flow.

[0014] Step S103: Derive the parameter matching criterion. Based on the vibration characteristics extracted in step S101 and the parameterized dynamic models of each device in step S102, analyze the physical boundary conditions that limit the vibration suppression efficiency of each vibration suppression device, and derive and establish a dual parameter matching model that includes "power matching" and "frequency matching".

[0015] Optionally, the general parameter matching criteria established in step S103 include: (1) General power matching criteria: The rated power of the vibration damping device motor is required to be within the specified range. The following constraints must be met to ensure that the residual vibrational energy of the under-constrained parallel robot system is dissipated within a specified time: in, The vibrational energy at the maximum vibrational mode. For the set desired decay time, The overall efficiency coefficient of the vibration damping device; (2) General frequency matching criterion: The effective response bandwidth of the vibration damping device must cover all natural frequencies. Furthermore, the response time constant of the vibration damping device to generate effective vibration damping force Must meet .

[0016] The derivation process for parameter matching of the flywheel device includes: constructing a unidirectional acceleration model of the flywheel based on its natural frequencies. Derivation of the maximum effective acceleration time of the flywheel within a single half-cycle of vibration. Based on flywheel rotational inertia and the maximum torque of the motor The flywheel is driven to reach saturation speed. Theoretical time required; Establishing frequency matching criteria: requiring the flywheel system to reach maximum kinetic energy. The required time matches the half-cycle of the vibration, thus deriving the constraint relationship: in This refers to the rated power of the motor. The matching parameter reflects the frequency matching degree between the flywheel and the vibration damping system. It ranges from 1 / 3 to 3, with the optimal frequency matching degree between the flywheel and the vibration damping device being 1. This determines the optimal ratio between the flywheel moment of inertia and the motor selection.

[0017] The derivation process for parameter matching of the rotor device includes: establishing the relationship between rotor thrust, rotor speed, and rotor geometry parameters; and defining the acceleration of the rotor from rest to generate effective vibration-damping thrust based on aerodynamic principles and motor response characteristics. response time constant Based on the trapezoidal velocity curve assumption, the proportion of effective work time of the rotor within a single vibration cycle is derived. Establish frequency matching criteria: to ensure If the value is greater than a preset threshold (e.g., 35%), the response time of the rotor from acceleration from rest to generating effective vibration-damping thrust is derived. With each order of natural frequency Constraints: This criterion is used to constrain the design upper limits of rotor diameter, motor KV value, and moment of inertia in order to avoid response lag under high-frequency vibration.

[0018] The parameter matching derivation process for the pendulum device includes: constructing a nonlinear oscillation model of the pendulum in a gravitational field; defining two working modes of the pendulum: (1) Continuous rotation mode: the pendulum rotates 360 degrees around the axis of rotation, and the pendulum is regarded as an eccentric flywheel. The vibration is mainly suppressed by the inertial reaction torque generated by the change of angular velocity; (2) Interval oscillation mode: the pendulum is limited to a preset angle range (such as the initial position). The pendulum swings back and forth, primarily utilizing the periodic change in gravitational potential energy and the reaction torque generated by the swing to dampen vibrations; the energy dissipation capacity of the pendulum in continuous rotation mode is analyzed. With the ability to dissipate gravitational potential energy in the interval oscillation mode Establish mode switching and parameter matching criteria: when the natural frequencies of each order... Lower unidirectional allowable acceleration time Greater than the critical threshold When matching continuous rotation mode, the motor torque is the main design constraint; when the natural frequencies of each order... Higher unidirectional allowable acceleration time Less than or equal to the critical threshold When the matching interval swing mode is used, the length of the swing arm and the mass of the pendulum are the main design constraints, and the energy dissipation is improved by maximizing the change of gravitational potential energy.

[0019] The parameter matching derivation process for the linear inertial mass device includes: constructing an acceleration motion model of the linear inertial mass within a finite stroke; analyzing the acceleration bottleneck caused by the motor torque limitation and the speed bottleneck caused by the lead screw stroke limitation; and deriving the mass of the linear inertial mass. Energy dissipation in a single cycle The non-monotonic influence relationship is used to determine the natural frequencies at each order. The optimal quality exists below. Extreme value conditions: This serves as the basis for selecting the slider quality and the lead screw pitch.

[0020] The derivation process for parameter matching of the jet propulsion system includes: constructing a pulse modulation model of the jet propulsion system, treating thrust control as pulse width modulation of a constant recoil force; establishing a response bandwidth matching criterion: defining the minimum opening and closing response time of the jet propulsion system's solenoid valve as... To ensure that the control system can effectively modulate and track the vibration signal and avoid aliasing or control lag, the minimum response time and the natural frequencies of each order are derived. Constraints: in To control the resolution coefficient, this criterion is used to constrain the selection of jet valves, ensuring that their switching frequency is much higher than the system vibration frequency.

[0021] Step S104: Parameter optimization and configuration determination. With the objective function of maximizing the energy dissipation efficiency or motor power utilization rate per unit cycle, optimization is performed within the parameter space that satisfies the matching criteria described in step S103 to determine the specific configuration and key design parameters of the final vibration damping device.

[0022] Optionally, the parameter optimization and configuration determination specifically include: selecting a device based on the identified modal characteristics by comparing the matching results of each device, for example: when there is high-frequency angular vibration, a flywheel is preferred, and when there is low-frequency linear vibration, a rotor is preferred; using a global optimization algorithm (such as a genetic algorithm or a particle swarm optimization algorithm), under the constraint of satisfying the power matching and frequency matching criteria, the physical parameters (such as flywheel inertia and rotor diameter) and control parameters of the selected device are jointly optimized with the energy dissipation efficiency or motor power utilization rate per unit cycle as the objective function.

[0023] Compared with the prior art, the present invention has the following advantages: The frequency and power-based vibration damping device matching design method for cable-parallel robots establishes a "power-frequency" dual-parameter matching model based on physical mechanisms. It quantitatively analyzes the coupling relationship between the key design parameters of actuators such as flywheels and rotors and the vibration characteristics of the robot, ensuring the effectiveness and response speed of the vibration damping device. At the same time, it combines a global optimization algorithm to achieve lightweight and high-efficiency design of the vibration damping device, significantly improving the robot's operating accuracy and system stability.

[0024] The frequency and power-based matching design method for vibration damping devices of cable-parallel robots provides a general selection methodology covering various actuators (flywheels, rotors, pendulums, linear mass blocks, jet devices). It is not only applicable to specific configurations but can also be extended to the vibration control hardware design of various flexible drive systems, and has broad engineering application value. Attached Figure Description

[0025] Figure 1 This is a flowchart of a matching design method for a cable parallel robot vibration damping device based on frequency and power, according to an embodiment of this application. Detailed Implementation

[0026] The technical solution of the present invention will be clearly and completely described below with reference to the accompanying drawings and specific embodiments. It should be noted that the embodiments described below with reference to the accompanying drawings are exemplary and intended to explain this application, and should not be construed as limiting the present invention.

[0027] Specifically, Figure 1 This is a flowchart illustrating a matching design method for a cable parallel robot vibration damping device based on frequency and power, provided in an embodiment of this application.

[0028] like Figure 1 As shown, the matching design method for the vibration damping device of the cable-parallel robot based on frequency and power includes the following steps: In step S101, a system dynamic model of the underconstrained parallel robot is established. The Hessian matrix is ​​introduced to characterize the nonlinear influence of the dynamic platform's attitude change on stiffness. The global stiffness matrix and inertia matrix in the entire workspace are solved to identify the dominant coupled vibration modes of the underconstrained parallel robot system and extract the natural frequencies of each order. and the corresponding maximum vibrational energy .

[0029] In actual implementation, a dynamic model incorporating cable elasticity and catenary effects is established. To accurately characterize the impact of cable force variations on stiffness over long spans, the Hessian matrix is ​​introduced to calculate the active stiffness matrix. Combining the passive stiffness matrix caused by the rope's elasticity. and the underconstrained stiffness matrix caused by gravity Construct the global stiffness matrix for the entire workspace. By solving the generalized eigenvalue problem: in Here is the system inertia matrix. The natural angular frequency, This represents the vibration mode vector. Modal analysis identifies the main vibration modes in the underconstrained parallel robot system, such as low-frequency, large-amplitude linear vibrations in the underconstrained degrees of freedom and high-frequency, small-amplitude angular vibrations in the constrained degrees of freedom. Based on preset external disturbance conditions, the maximum vibration energy under each mode is calculated using the energy method. .

[0030] In step S102, a library of alternative active vibration damping devices is established, and a parameterized dynamic model of each damping device in the library is constructed. The mapping relationship between the physical mechanism of the damping force or torque generated by each device and its driving parameters is analyzed. In actual execution, the alternative device library includes one or more of the following: flywheel, rotor, pendulum, linear inertial mass block, and jet device. The following dynamic models are constructed for different devices: For the flywheel device, a dynamic equation based on angular acceleration is established. ,in, The torque output by the flywheel. Let be the moment of inertia of the flywheel. For the flywheel's angular acceleration, it is determined that the flywheel mechanism suppresses vibration through inertial reaction torque; for the rotor mechanism, a thrust-speed model is established. ,in The tensile coefficient can be obtained by fitting experimental data. The thrust output by the rotor. Given the angular velocity of the rotor rotation, we define its vibration suppression mechanism utilizing aerodynamic thrust; for the pendulum device, we establish a nonlinear oscillation model. ,in The torque output by the pendulum. Let the moment of inertia of the pendulum be... Let be the angular acceleration of the pendulum. For the mass of the pendulum, It is the acceleration due to gravity. Let be the distance from the center of mass of the pendulum to the axis of rotation. Define the rotation angle of the pendulum; clarify that the pendulum device utilizes the coupling effect of gravitational torque and inertial torque; for a linear inertial mass device, establish a translational acceleration model. ,in The thrust output by the linear inertial mass block device. The mass of the mass block. The acceleration of the mass block motion is given; it is clarified that the linear inertial mass block device uses translational inertial force to suppress vibration; for the jet device, a recoil thrust model based on the ideal point source assumption is established, ignoring the time delay effect of gas flow, and it is clarified that it uses the instantaneous recoil force generated by gas jet to suppress vibration.

[0031] In step S103, based on the vibration characteristics extracted in step S101 and the parameterized dynamic models of each device in step S102, the physical boundary conditions that limit the vibration suppression efficiency of each vibration suppression device are analyzed, and a dual parameter matching model including "power matching" and "frequency matching" is derived and established.

[0032] In actual implementation, a general power matching criterion is established: in order to achieve the desired power decay time... Internal friction dissipates the system's maximum vibrational energy. Derive the rated power required for the motor of the vibration damping device. Must meet: Derivation of frequency matching criteria for specific devices: For flywheel mechanisms, based on their natural frequencies... Derivation of the maximum effective acceleration time of the flywheel within a single half-cycle of vibration. To ensure the flywheel can keep up with the high-frequency vibrations, the flywheel system must reach its maximum kinetic energy. The required time matches the half-cycle of the vibration, i.e., satisfies: This formula is used to determine the optimal ratio between the flywheel's moment of inertia and the motor selection.

[0033] For rotorcraft, the response time of the rotor from rest to generating effective vibration-damping thrust is defined as follows: .like Beyond half the vibration half-cycle, the vibration suppression efficiency will drop sharply. Therefore, the constraint relationship is derived as follows: This guideline is used to constrain the design upper limit of rotor diameter and motor rotational inertia to avoid high-frequency lag.

[0034] For the pendulum device, based on the natural frequencies of each order... The resulting one-way allowable acceleration time With critical threshold Relationship, establish mode switching criteria: when The timing is matched with a continuous rotation mode, which maximizes kinetic energy dissipation by utilizing a long acceleration time; when The time-matched interval oscillation mode utilizes changes in gravitational potential energy to suppress vibration.

[0035] For a linear inertial mass device, the dual limitations of motor torque and lead screw stroke on the maximum unidirectional acceleration time are analyzed, and the mass of the linear inertial mass is derived. Energy dissipation in a single cycle The non-monotonic influence relationship is used to determine the natural frequencies at each order. The optimal quality exists below. Extreme value conditions: For jet propulsion systems, based on high-frequency control requirements, a response bandwidth matching criterion is established: the minimum opening and closing response time of the jet propulsion system's solenoid valve. With each order of natural frequency and control resolution coefficient Satisfy the constraints: In step S104, with the objective function of maximizing the energy dissipation efficiency or motor power utilization rate per unit cycle, optimization is performed within the parameter space that satisfies the matching criteria described in step S3 to determine the specific configuration and key design parameters of the final vibration damping device.

[0036] In actual implementation, configuration selection is first based on modal characteristics. For any identified vibration mode, its natural frequencies are determined. and maximum vibrational energy The dynamic models of the five alternative devices were sequentially substituted into the analysis. First, it was calculated whether the power of each device met the requirements, and then frequency matching calculations were performed. For the flywheel device, the calculations showed that it met the requirements. Required motor parameters to determine if overload is possible; for the rotor system, calculate the acceleration time. Determine whether it satisfies To avoid lag; for the pendulum device, determine its suitable operating mode based on the frequency; for the linear inertial mass block, calculate the optimal mass under extreme conditions. To determine if the load limit is exceeded, for jet devices, check if the required switching frequency is within the solenoid valve's response bandwidth. The optimal configuration is determined by comparing the matching degree of each device under specific modes with the engineering cost.

[0037] For the selected vibration damping device, a global optimization algorithm (such as a genetic algorithm or particle swarm optimization) is used to optimize the parameters. The objective function can be set to maximize the energy dissipation efficiency or motor power utilization rate per unit cycle, with constraints satisfying the aforementioned power matching and frequency matching criteria. Specifically, the optimization variables include the inertia and geometric parameters of the vibration damping device, as well as the rated torque and speed of each motor. Through algorithm iteration, the optimal combination of physical parameters is calculated to achieve a balance between lightweight design and high performance.

[0038] It is worth noting that although the technical solutions and embodiments of the present invention have been described in detail above with reference to the accompanying drawings, the present invention is not limited to the specific embodiments described above. The embodiments described above are merely illustrative. Those skilled in the art can make many other forms based on the inspiration of the present invention without departing from the spirit and scope of the claims, and these all fall within the scope of protection of the present invention.

Claims

1. A matching design method for a vibration damping device of a cable-parallel robot based on frequency and power, characterized in that, Includes the following steps: Step S101: Vibration Feature Extraction: Establish a system dynamic model of the underconstrained parallel robot, introduce the Hessian matrix to characterize the nonlinear influence of the dynamic platform's attitude change on stiffness, solve for the global stiffness matrix and inertia matrix in the entire workspace, identify the dominant coupled vibration modes of the underconstrained parallel robot system, and extract the natural frequencies of each order. and the corresponding maximum vibrational energy ; Step S102: Vibration damping device mechanism modeling: Establish a library of alternative active vibration damping devices, construct a parameterized dynamic model of each vibration damping device in the library, and analyze the mapping relationship between the physical mechanism of each vibration damping device generating damping force or torque and the driving parameters. Step S103: Derive the parameter matching criterion: Based on the vibration characteristics extracted in step S101 and the parameterized dynamic models of each device in step S102, analyze the physical boundary conditions that limit the vibration suppression efficiency of each vibration suppression device, and derive and establish a dual parameter matching model that includes "power matching" and "frequency matching". Step S104: Parameter optimization and configuration determination: Taking the maximization of energy dissipation efficiency or motor power utilization rate within a unit cycle as the objective function, optimization is performed within the parameter space that satisfies the matching criteria described in step S103 to determine the specific configuration and key design parameters of the final vibration damping device.

2. The method according to claim 1, characterized in that, The library of alternative active vibration damping devices established in step S102 includes one or more of the following: flywheel device, rotor device, pendulum device, linear inertial mass block device, and jet device.

3. The method according to claim 2, characterized in that, For any device in the pool of candidate active vibration damping devices, the general parameter matching criteria established in step S103 include: (1) General power matching criteria: The rated power of the vibration damping device motor is required to be within the specified range. The following constraints must be met to ensure that the residual vibrational energy of the under-constrained parallel robot system is dissipated within a specified time: in, The vibrational energy at the maximum vibrational mode. For the set desired decay time, The overall efficiency coefficient of the vibration damping device; (2) General frequency matching criterion: The effective response bandwidth of the vibration damping device must cover all natural frequencies. Furthermore, the response time constant of the vibration damping device to generate effective vibration damping force Must meet .

4. The method according to claim 3, characterized in that, The derivation process for parameter matching of the flywheel device includes: constructing a unidirectional acceleration model of the flywheel based on its natural frequencies. Derivation of the maximum effective acceleration time of the flywheel within a single half-cycle of vibration. Based on flywheel rotational inertia and the maximum torque of the motor The flywheel is driven to reach saturation speed. Theoretical time required; Establishing frequency matching criteria: requiring the flywheel system to reach maximum kinetic energy. The required time matches the half-cycle of the vibration, thus deriving the constraint relationship: in This refers to the rated power of the motor. The matching parameter reflects the frequency matching degree between the flywheel and the vibration damping system. It ranges from 1 / 3 to 3, with the optimal frequency matching degree between the flywheel and the vibration damping device being 1. This determines the optimal ratio between the flywheel moment of inertia and the motor selection.

5. The method according to claim 3, characterized in that, The derivation process for parameter matching of the rotor device includes: establishing the relationship between rotor thrust, rotor speed, and rotor geometry parameters; and defining the acceleration of the rotor from rest to generate effective vibration-damping thrust based on aerodynamic principles and motor response characteristics. response time constant Based on the trapezoidal velocity curve assumption, the proportion of effective work time of the rotor within a single vibration cycle is derived. Establish frequency matching criteria: to ensure The response time of the rotor from static acceleration to generating effective vibration-damping thrust is derived when the value exceeds a preset threshold. With each order of natural frequency Constraints: This criterion is used to constrain the design upper limits of rotor diameter, motor KV value, and moment of inertia in order to avoid response lag under high-frequency vibration.

6. The method according to claim 3, characterized in that, The derivation process for parameter matching of the pendulum device includes: constructing a nonlinear oscillation model of the pendulum in a gravitational field; defining two working modes of the pendulum: (1) continuous rotation mode: the pendulum rotates 360 degrees around the axis of rotation, and the pendulum is regarded as an eccentric flywheel, mainly using the inertial reaction torque generated by the change of angular velocity to suppress vibration; (2) interval oscillation mode: the pendulum is restricted to oscillation within a preset angle range, mainly using the periodic change of gravitational potential energy and the reaction torque generated by the oscillation to suppress vibration; analyzing the kinetic energy dissipation capability of the pendulum in the continuous rotation mode. With the ability to dissipate gravitational potential energy in the interval oscillation mode Establish mode switching and parameter matching criteria: when the natural frequencies of each order... Lower unidirectional allowable acceleration time Greater than the critical threshold When matching continuous rotation mode, the motor torque is the main design constraint; when the natural frequencies of each order... Higher unidirectional allowable acceleration time Less than or equal to the critical threshold When the matching interval swing mode is used, the length of the swing arm and the mass of the pendulum are the main design constraints, and the energy dissipation is improved by maximizing the change of gravitational potential energy.

7. The method according to claim 3, characterized in that, The parameter matching derivation process for the linear inertial mass device includes: constructing an acceleration motion model of the linear inertial mass within a finite stroke; analyzing the acceleration bottleneck caused by the motor torque limitation and the speed bottleneck caused by the lead screw stroke limitation; and deriving the mass of the linear inertial mass. Energy dissipation in a single cycle The non-monotonic influence relationship is used to determine the natural frequencies at each order. The optimal quality exists below. Extreme value conditions: This serves as the basis for selecting the slider quality and the lead screw pitch.

8. The method according to claim 3, characterized in that, The derivation process for parameter matching of the jet propulsion system includes: constructing a pulse modulation model of the jet propulsion system, treating thrust control as pulse width modulation of a constant recoil force; establishing a response bandwidth matching criterion: defining the minimum opening and closing response time of the jet propulsion system's solenoid valve as... To ensure that the control system can effectively modulate and track the vibration signal and avoid aliasing or control lag, the minimum response time and the natural frequencies of each order are derived. Constraints: in To control the resolution coefficient, this criterion is used to constrain the selection of jet valves, ensuring that their switching frequency is much higher than the system vibration frequency.

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