A method and system for designing a dynamic vibration absorber

Abstract

This invention relates to the field of intelligent manufacturing technology, and more particularly to a design method and system for a dynamic vibration absorber in the field of vibration control. The invention establishes a two-degree-of-freedom nonlinear dynamic vibration absorber system, and optimizes a passive mechanical network of biquadratic optimal form based on the linearized model fitted from this system model. Based on the system model combined with the passive mechanical network, a fractional-order integral sliding mode controller based on a disturbance observer is designed. The fractional-order switching disturbance observer can estimate and supplement various unknown factors in the system, and outputs the optimal control force through fractional-order integral sliding mode control. Finally, a semi-active capacitive control law is designed, and a suboptimal control force is obtained through force tracking to achieve vibration reduction control. This invention effectively improves the control accuracy of the dynamic vibration absorber.

Description

Technical Field

[0001] This invention relates to the field of intelligent manufacturing technology, and in particular to a design method and system for a dynamic vibration absorber. Background Technology

[0002] As industrial intelligent manufacturing technology continues to develop towards higher precision, higher efficiency, and greater intelligence, it places extreme demands on the dynamic stability of manufacturing equipment. In complex industrial environments, equipment is inevitably subjected to various vibration excitations from internal moving parts or the external environment. These vibrations can lead to deterioration of the surface quality of processed workpieces, reduced dimensional accuracy, and in severe cases, even equipment failure. Therefore, in the field of intelligent manufacturing, vibration has become a key bottleneck restricting process limits and improving product yield. Dynamic vibration absorbers are a commonly used vibration reduction technology. Control methods include passive control, active control, and semi-active control. The focus is on eliminating or minimizing vibration energy by installing dynamic vibration absorbers on the main structure. In precision machining and machine tools, ring-shaped or built-in dynamic vibration absorbers are typically installed inside or at the rear end of the spindle housing, designed specifically for the main resonant frequencies. In industrial robotics and automation, compact dynamic vibration absorbers are often installed on the end effector or the wrist of the robot's last joint, often employing piezoelectric or electromagnetic active or semi-active vibration absorbers to adapt to different loads and speeds. In semiconductor and electronics manufacturing, numerous highly optimized and tuned miniature dynamic vibration absorbers are integrated into substructures or within the structures supporting these ultra-precision components; these are often used in conjunction with active vibration control systems. In addition, dynamic vibration absorption is also applied to building, suspension, and fan systems.

[0003] With the development of the mechanical field, new mechanical component concepts are constantly being proposed and successfully constructed in reality through physical means, leading to a gradual increase in the complexity of the components in the vibration absorption network of dynamic vibration absorbers. One study proposed a passive mechanical component with two ends called inertial capacitance, improving the physical realization of passive mechanical systems. Another study designed a dynamic vibration absorber based on inertial capacitance, applying inertial capacitance, springs, and damping to the absorber network. Adding inertial capacitance elements to traditional dynamic vibration absorbers gradually improves their vibration reduction performance and widens the vibration reduction range. Further research has designed a dynamic vibration absorber design method incorporating inertial capacitance and negative stiffness elements, significantly reducing the amplitude of the system when subjected to external disturbances. In addition, research has proposed a system that simultaneously optimizes the coupling of multiple absorbers, solving the problem of neglecting synergistic effects and modal shifts in the original design. The aforementioned passive mechanical structure takes external vibration disturbance as input and dissipates or transfers energy through the preset structural parameters and mechanical characteristics of passive components such as springs, dampers, and inertial capacitance. It can output vibration reduction effect to suppress the vibration of the main system without additional energy input. However, this control method relies on the inherent characteristics of the components, the parameters are fixed and cannot be dynamically adjusted according to real-time vibration conditions. When the frequency and amplitude of the external disturbance exceed the preset adaptation range, the vibration reduction effect will decrease sharply. It is difficult to meet the requirements in complex scenarios with high requirements for vibration reduction accuracy and response speed.

[0004] Therefore, active control has gradually become a hot topic of discussion, and more and more active control methods based on dynamic vibration absorbers have been designed and proposed. Active control uses the vibration signals of the main system (such as displacement, velocity, and acceleration) in real time as input. The sliding mode controller calculates the optimal active control force in real time according to a preset control algorithm, and then drives the actuator to output the control force to act on the vibration system, thereby achieving precise vibration reduction. However, although active control can achieve control effects that passive mechanical structures cannot, it requires a large amount of energy to be continuously supplied to the actuator to output the active control force. Moreover, the configuration cost of high-precision sensors, high-performance actuators, and complex controllers is high, resulting in problems such as excessive energy consumption and high cost, which often prevents it from being considered in most cases. Based on this phenomenon, some semi-active controllers have been proposed. Semi-active control does not require the actuator to output active control force. Instead, it uses the vibration signals collected by the sensor and the optimal control force calculated by the controller as references, and tracks the effect of the optimal control force by adjusting the parameters of the semi-active components (such as adjustable damping and adjustable stiffness components).

[0005] For example, some studies have proposed semi-active springs; others have proposed semi-active damping; and still others have designed a controllable inertial flywheel. Semi-active controllers are generally composed of semi-active elements. These elements can track the optimal control force calculated by the computer using the system's feedforward and feedback information. Some studies have used semi-active damping and semi-active capacitive inertia combined with a linear quadratic regulator (LQR) and force tracking to output a suboptimal control force, further improving system performance. Semi-active control not only offers better control performance than passive control but is also less expensive than active control.

[0006] However, semi-active control relies on the real-time calculation and tracking of active control force. Typically, it requires calculating the optimal active control force under the current operating condition through a sliding mode controller, and then generating the control parameters of the semi-active element through force tracking logic. However, the existing sliding mode controllers for calculating active control force are designed based on integer order. The core of the design of integer order sliding mode controllers is based on constructing sliding surfaces and control laws using integer order calculus operators. Its theoretical basis is based on the assumption of linear or weakly nonlinear systems, which makes it difficult to adapt to the dynamic characteristics of complex nonlinear vibration systems. This makes the calculation accuracy of active control force susceptible to interference from nonlinear coupling of the system, thus affecting the tracking effect of semi-active control and greatly reducing the vibration reduction effect of the dynamic vibration absorber. Summary of the Invention

[0007] Therefore, the technical problem to be solved by the present invention is to overcome the shortcomings of existing sliding mode controllers that calculate active control force, whose design concept is limited to integer order, making it difficult to adapt to the dynamic characteristics of complex nonlinear vibration systems. This results in poor calculation accuracy of active control force, which in turn reduces the tracking effect of semi-active control and leads to poor vibration reduction effect of dynamic vibration absorbers.

[0008] To solve the above-mentioned technical problems, the present invention provides a design method for a dynamic vibration absorber, comprising:

[0009] Based on a two-degree-of-freedom nonlinear dynamic vibration absorber system, a state vector is obtained; the state vector includes: principal mass displacement, dynamic vibration absorber mass displacement, principal mass velocity, and dynamic vibration absorber mass velocity;

[0010] Based on the relative velocity between the main mass and the mass of the dynamic vibration absorber, a passive mechanical network controller is designed to obtain the passive control force.

[0011] Based on the mass velocity and fractional calculus of the dynamic vibration absorber, a sliding mode surface of the mass subsystem of the dynamic vibration absorber is constructed.

[0012] Based on the sliding surface, principal mass velocity, boundary threshold, and upper limit of amplitude of the dynamic vibration absorber mass subsystem, the influence parameters of the sliding surface of the dynamic vibration absorber mass subsystem on the sliding surface of the principal mass subsystem are obtained.

[0013] Based on the influence parameters of the principal mass velocity, the sliding surface of the dynamic vibration absorber mass subsystem on the principal mass subsystem sliding surface, and fractional calculus, the sliding surface of the principal mass subsystem is constructed.

[0014] Based on the principal mass velocity, the external disturbance estimate is obtained; based on the external disturbance estimate, passive control force, and sliding surface of the principal mass subsystem, a fractional-order integral decoupled sliding mode controller is designed to obtain the active control force.

[0015] The active control force is used to generate semi-active inertial capacity control parameters through force tracking logic;

[0016] By using the semi-active inertial capacitance control parameters and the relative acceleration between the main mass and the mass of the dynamic vibration absorber, a semi-active control force is generated, thus completing the design of the semi-active control force for the two-degree-of-freedom nonlinear dynamic vibration absorber system.

[0017] Preferably, the sliding surface of the dynamic vibration absorber mass subsystem, constructed based on the mass velocity and fractional calculus of the dynamic vibration absorber, is as follows:

[0018] ,

[0019] in, For the sliding surface of the mass subsystem of the dynamic vibration absorber, For the mass velocity of the dynamic vibration absorber, This is the second convergence gain. , This is the symbol for fractional calculus. For the second-order parameter, .

[0020] Preferably, the formula for calculating the influence parameters of the sliding surface of the dynamic vibration absorber mass subsystem on the sliding surface of the main mass subsystem based on the sliding surface of the dynamic vibration absorber mass subsystem, the principal mass velocity, the boundary threshold, and the upper limit of the amplitude is as follows:

[0021] ,

[0022] in, The parameters representing the influence of the sliding surface of the dynamic vibration absorber mass subsystem on the sliding surface of the main mass subsystem are: The upper limit of amplitude, For boundary thresholds, For symbolic functions, For the sliding surface of the mass subsystem of the dynamic vibration absorber, It is a saturation function.

[0023] Preferably, the sliding surface of the main mass subsystem is constructed based on the influence parameters of the main mass velocity, the sliding surface of the dynamic vibration absorber mass subsystem on the main mass subsystem sliding surface, and fractional calculus, as follows:

[0024] ,

[0025] in, The sliding surface of the main mass subsystem. Main mass velocity, The first convergence gain, , The symbol for fractional integrals is . For the first-order parameter, , The parameters representing the influence of the sliding surface of the mass subsystem of the dynamic vibration absorber on the sliding surface of the main mass subsystem are given.

[0026] Preferably, the fractional-order integral decoupling sliding mode controller is designed based on the external disturbance estimate, passive control force, and sliding mode surface of the main mass subsystem. The fractional-order integral decoupling sliding mode controller is as follows:

[0027] ,

[0028] ,

[0029] ,

[0030] in, For active control, The equivalent control force for sliding mode control. For switching rate, The quality of the main quality, , and Nonlinear spring stiffness of principal mass The coefficients of the linear, quadratic, and cubic terms, For passive control force, This is an estimate of external disturbances. The main mass displacement. This refers to the mass displacement of the dynamic vibration absorber. For fractional differential operators, For fractional order, Main mass velocity, The parameters representing the influence of the sliding surface of the dynamic vibration absorber mass subsystem on the sliding surface of the main mass subsystem are: The first convergence gain, , This is the switching rate gain coefficient. For the tanh function, The sliding surface of the main mass subsystem.

[0031] Preferably, the method for obtaining the external disturbance estimate based on the principal mass velocity includes:

[0032] The difference between the principal mass velocity and the estimated principal mass velocity is taken as the principal mass velocity estimation error;

[0033] Based on the absolute value of the principal mass velocity estimation error and the magnitude of the order switching threshold, the order of the fractional-order order switching interference observer is determined, the fractional-order order switching interference observer is constructed, and the external interference estimate is calculated.

[0034] Preferably, the fractional-order switching interference observer is:

[0035] ,

[0036] in, This is an estimate of external disturbances. , , The gain coefficient of the fractional-order switching interference observer. Main mass velocity estimation error, , Main mass velocity, Main mass velocity estimate, , , and Nonlinear spring stiffness of principal mass The coefficients of the linear, quadratic, and cubic terms, The main mass displacement. For passive control force, For active control, , To switch the order parameters of the interference observer for fractional-order orders, , For symbolic functions, To switch the order of the interference observer for fractional-order orders, These are the initial parameters. , For fractional differential operators, The quality of the main quality.

[0037] Preferably, the method for determining the order of the fractional-order order-switching interference observer by comparing the absolute value of the principal mass velocity estimation error with the order switching threshold includes:

[0038] Determine whether the absolute value of the principal mass velocity estimation error is less than or equal to the order switching threshold. If it is less than or equal to, then let the fractional order of the switching interference observer be . If it is greater than 1, then let the fractional order of the switching interference observer be 1. ;in, For the first order, For the second order, , The threshold for order switching. .

[0039] Preferably, the design method of the passive mechanical network controller includes:

[0040] Set the semi-active control input matrix and semi-active control force in the two-degree-of-freedom nonlinear dynamic vibration absorber system to 0, and replace the nonlinear spring stiffness of the principal mass with the linear spring stiffness of the principal mass to obtain the state vector of the two-degree-of-freedom nonlinear dynamic vibration absorber system.

[0041] The difference between the state vector of the two-degree-of-freedom nonlinear dynamic vibration absorber system and the linearized state vector is used as the error vector;

[0042] Based on the error vector, weight matrix, and simulation time setting, a linear optimization objective function is constructed.

[0043] The linear spring stiffness of the principal mass is optimized based on the linearization optimization objective function to obtain the linearized principal mass spring stiffness.

[0044] The admittance of the passive mechanical network controller of the two-degree-of-freedom nonlinear dynamic vibration absorber system is set as a double quadratic positive real function. The coefficient parameters of the double quadratic positive real function are obtained by using the linearized principal mass spring stiffness.

[0045] The biquadratic positive real functions are transformed into the topology and component parameters of a passive mechanical network controller.

[0046] The present invention also provides a dynamic vibration absorber design system, comprising:

[0047] The system modeling module is used to obtain the state vector based on the two-degree-of-freedom nonlinear dynamic vibration absorber system; the state vector includes: principal mass displacement, dynamic vibration absorber mass displacement, principal mass velocity, and dynamic vibration absorber mass velocity;

[0048] The passive control module is used to design a passive mechanical network controller based on the relative velocity between the main mass and the mass of the dynamic vibration absorber, so as to obtain the passive control force.

[0049] The first sliding surface construction module is used to construct the sliding surface of the mass subsystem of the dynamic vibration absorber based on the mass velocity and fractional calculus of the dynamic vibration absorber.

[0050] The influence parameter acquisition module is used to obtain the influence parameters of the sliding surface of the dynamic vibration absorber mass subsystem on the sliding surface of the main mass subsystem based on the sliding surface of the dynamic vibration absorber mass subsystem, the main mass velocity, the boundary threshold, and the upper limit of the amplitude of the dynamic vibration absorber mass subsystem.

[0051] The second sliding surface construction module is used to construct the sliding surface of the main mass subsystem based on the influence parameters of the main mass velocity and the sliding surface of the dynamic vibration absorber mass subsystem on the main mass subsystem sliding surface.

[0052] The sliding mode controller construction module is used to construct a fractional-order integral decoupled sliding mode controller based on the sliding surfaces of the main mass subsystem and the dynamic vibration absorber mass subsystem.

[0053] The external disturbance estimation calculation module is used to calculate the external disturbance estimate based on the master mass velocity.

[0054] The active control force calculation module is used to design a fractional-order integral decoupled sliding mode controller based on external disturbance estimates, passive control force, and the sliding mode surface of the master mass subsystem, and to obtain the active control force.

[0055] The control parameter acquisition module is used to generate semi-active inertial capacity control parameters by passing the active control force through force tracking logic;

[0056] The semi-active control force acquisition module is used to generate a semi-active control force by using the control parameters of the semi-active inertial capacitance and the relative acceleration between the main mass and the mass of the dynamic vibration absorber, thereby completing the design of the semi-active control force for the two-degree-of-freedom nonlinear dynamic vibration absorber system.

[0057] Compared with the prior art, the above-described technical solution of the present invention has the following advantages:

[0058] This invention discloses a design method and system for a dynamic vibration absorber. It employs fractional-order calculus to construct the basic logic of sliding mode control. Utilizing the nonlocal and genetic properties of fractional-order calculus, it accurately characterizes the complex characteristics of a two-degree-of-freedom nonlinear dynamic vibration absorber system, such as nonlinear stiffness and subsystem coupling. Compared to integer-order sliding mode controllers, this significantly improves the adaptability to nonlinear systems, laying the foundation for accurate calculation of active control forces. Furthermore, this invention addresses the issue that simple fractional-order sliding mode control can only focus on a single primary control objective and cannot simultaneously address the coordinated vibration reduction requirements of the primary and secondary mass subsystems. Therefore, it introduces an influence parameter between the sliding surface of the dynamic vibration absorber's mass subsystem and the sliding surface of the primary mass subsystem. This parameter establishes a correlation mechanism between the sliding surfaces of the two subsystems, achieving coordinated optimization of the core vibration reduction objective of the primary mass and the steady-state performance of the absorber's mass. Considering that directly introducing the correlation parameter may lead to increased coupling interference between subsystems and decreased control robustness, this invention further dynamically adjusts the influence parameter through adjustable parameters such as boundary thresholds and amplitude upper limits. This allows for flexible adjustment of the influence degree of the secondary subsystem on the primary subsystem according to actual vibration conditions, avoiding the limitations of single-parameter control. The fractional-order integral decoupled sliding mode controller constructed in this invention not only breaks through the nonlinear adaptation bottleneck of integer-order sliding mode controllers, but also solves the multi-objective balance defect of simple fractional-order control. The output active control force accurately matches the dynamic requirements of the nonlinear vibration system, effectively improving the force tracking effect of semi-active control, and ensuring that the suboptimal control force output by semi-active inertial capacitance can accurately suppress the vibration of the two-degree-of-freedom nonlinear dynamic vibration absorber system.

[0059] Furthermore, to address the shortcomings of existing interference observers in calculating external interference estimates—namely, insufficient adaptability to different types of interference and difficulty in balancing estimation speed and accuracy—this invention achieves precise optimization of interference estimation performance through a dynamically adjusted fractional order design. The invention adaptively determines the fractional order based on the system's state error value. Utilizing a multi-order switching mechanism, under conditions of large system state error and drastic interference changes, the adapted fractional order enhances the response speed of interference estimation, rapidly tracking dynamic changes in interference. Conversely, under conditions of small system state error and relatively stable interference, switching to another fractional order enhances the steady-state accuracy of the estimation, preventing fluctuations in the estimated value. This fractional-order switching design based on state error breaks through the limitation of fixed order in existing disturbance observers. It solves the problem of estimation lag of single-order observers under rapid time-varying disturbances and avoids the defect of insufficient accuracy under steady-state disturbances. It ensures that the fractional-order disturbance observer can maintain high estimation accuracy in different types of disturbance scenarios, providing reliable disturbance information support for the subsequent sliding mode controller to output accurate active control force, thereby improving the vibration control accuracy of the two-degree-of-freedom nonlinear dynamic vibration absorber system. Attached Figure Description

[0060] To make the content of this invention easier to understand, the invention will be further described in detail below with reference to specific embodiments and accompanying drawings, wherein:

[0061] Figure 1 This is a flowchart illustrating a dynamic vibration absorber design method according to the present invention.

[0062] Figure 2 This is a general block diagram of a dynamic vibration absorber design method according to the present invention.

[0063] Figure 3 This is a structural diagram of a two-degree-of-freedom nonlinear dynamic vibration absorber system.

[0064] Figure 4 This is the structure diagram of the passive mechanical network corresponding to the optimized double quadratic admittance function.

[0065] Figure 5 These are the external disturbance values ​​and the estimated values ​​of the fractional-order switching disturbance observer.

[0066] Figure 6 The tracking performance of a fractional integral decoupled sliding mode controller for semi-active capacitive tracking.

[0067] Figure 7 The graph shows a comparison of the effects of the present invention and different active control methods on the main mass displacement.

[0068] Figure 8 The graph shows a comparison of the effects of the present invention and different semi-active control methods on the main mass displacement.

[0069] Figure 9 This is a comparison diagram showing the effect of the relative displacement of two mass blocks under the present invention and different active control methods.

[0070] Figure 10 This is a comparison chart showing the effect of the relative displacement of two mass blocks under the present invention and different semi-active control methods. Detailed Implementation

[0071] The present invention will be further described below with reference to the accompanying drawings and specific embodiments, so that those skilled in the art can better understand and implement the present invention. However, the embodiments described are not intended to limit the present invention.

[0072] Reference Figure 1 As shown, this embodiment provides a design method for a dynamic vibration absorber, including:

[0073] like Figure 2 As shown, Figure 2 This is a general block diagram of a dynamic vibration absorber design method according to the present invention.

[0074] Step S1: Based on the two-degree-of-freedom nonlinear dynamic vibration absorber system, obtain the state vector; the state vector includes: principal mass displacement, dynamic vibration absorber mass displacement, principal mass velocity, and dynamic vibration absorber mass velocity; wherein, the two-degree-of-freedom nonlinear dynamic vibration absorber system includes a principal mass subsystem and a dynamic vibration absorber mass subsystem;

[0075] like Figure 3 As shown, Figure 3 This is a structural diagram of a two-degree-of-freedom nonlinear dynamic vibration absorber system.

[0076] Based on the nonlinearity of the spring in a two-degree-of-freedom nonlinear dynamic vibration absorber system, the dynamic equation of the two-degree-of-freedom nonlinear dynamic vibration absorber system is constructed as follows:

[0077] ,

[0078] in, Here is the mass matrix of the two-degree-of-freedom nonlinear dynamic vibration absorber system. , and These are the masses of the main mass and the dynamic vibration absorber, respectively. Let be the displacement vector of each degree of freedom of the two-degree-of-freedom nonlinear dynamic vibration absorber system. for The derivative, The displacement of the main mass The displacement of the mass of the dynamic vibration absorber. For passive control force, It is a semi-active control force. External interference Here is the damping matrix. , Here is the stiffness matrix. , For the mass spring stiffness of the dynamic vibration absorber, It is a nonlinear state. , For passive control input matrix, , For semi-active control input matrix, , The external interference input matrix, , The main mass damping value, This represents the mass damping value of the dynamic vibration absorber. , These are the main mass spring stiffness The coefficients of the first term and the coefficients of the second term.

[0079] Based on the dynamic equations of the two-degree-of-freedom nonlinear dynamic vibration absorber system, the state-space equations of the two-degree-of-freedom nonlinear dynamic vibration absorber system are established as follows:

[0080] ,

[0081] in, For system status, Let be the displacement vector of each degree of freedom of the two-degree-of-freedom nonlinear dynamic vibration absorber system. for The derivative, The displacement of the main mass The displacement of the mass of the dynamic vibration absorber. For passive control force, It is a semi-active control force. External interference For system output, and , , , , , , Indicates transpose. for The derivative, Let be the state matrix of the system. It is a 2×2 identity matrix. It is a 2×2 zero matrix. Here is the nonlinear state matrix of the system. for Among them Replace with the corresponding state variables , for The input matrix, It is a 2×1 zero matrix. for The input matrix, for The input matrix, This is the system's output matrix.

[0082] As shown in Table 1, Table 1 contains the system parameters of a nonlinear two-degree-of-freedom dynamic vibration absorber.

[0083] Table 1

[0084]

[0085] Based on the output of the two-degree-of-freedom nonlinear dynamic vibration absorber system in the state-space equations:

[0086] ,

[0087] Define the following two performance metrics:

[0088] ,

[0089] ,

[0090] in, To evaluate the performance index of the principal mass displacement of a two-degree-of-freedom nonlinear dynamic vibration absorber system, and to design and optimize the passive network controller of the two-degree-of-freedom nonlinear dynamic vibration absorber system, To evaluate the performance of the relative stroke of a two-degree-of-freedom nonlinear dynamic vibration absorber system, an active controller for the system is designed to ensure that the performance index of the two-degree-of-freedom nonlinear dynamic vibration absorber system is minimized. For simulation time, Indicates time, This represents the root mean square.

[0091] Step S2: Based on the relative velocity between the main mass and the mass of the dynamic vibration absorber, design a passive mechanical network controller to obtain the passive control force;

[0092] In this embodiment, the design method of the passive mechanical network controller includes: linearizing the nonlinear spring stiffness of the main mass based on the state space equation of the dynamic vibration absorber system; and using the linearized main mass spring stiffness, optimizing the passive mechanical network controller of the two-degree-of-freedom nonlinear dynamic vibration absorber system in the frequency domain according to the linearization optimization objective function.

[0093] Set the semi-active control input matrix and semi-active control force in the two-degree-of-freedom nonlinear dynamic vibration absorber system to 0, and replace the nonlinear spring stiffness of the principal mass with the linear spring stiffness of the principal mass to obtain the state vector of the dynamic vibration absorber system.

[0094] The difference between the state vector of the two-degree-of-freedom nonlinear dynamic vibration absorber system and the linearized state vector is used as the error vector;

[0095] Based on the error vector, weight matrix, and simulation time setting, a linear optimization objective function is constructed.

[0096] The linear spring stiffness of the principal mass is optimized based on the linearization optimization objective function to obtain the linearized principal mass spring stiffness.

[0097] The admittance of the passive mechanical network controller of the two-degree-of-freedom nonlinear dynamic vibration absorber system is set as a biquadratic positive real function, which is:

[0098] ,

[0099] in, , , , , , The parameters are biquadratic positive real functions, and all are greater than 0. For complex frequency domain variables, It is a biquadratic positive real function, and its necessary and sufficient condition is: Using passive network synthesis algorithms such as Bott-Duffin, any biquadratic positive real function... It can be implemented as a passive mechanical network containing no more than 9 components, of which the network contains only 3 types of passive mechanical components: dampers, springs, and inertial capacitance.

[0100] Using the linearized principal mass spring stiffness, the coefficient parameters of the biquadratic positive real function are obtained;

[0101] The biquadratic positive real functions are transformed into the topology and component parameters of a passive mechanical network controller.

[0102] In this embodiment, based on the passive mechanical network controller Input and its output ,in, The constructed state space is implemented as follows:

[0103] ,

[0104] in, , for The derivative, Passive mechanical network controller Input, , , , , , , , , and Passive mechanical network controller The obtained minimum state space model contains the state matrix, input matrix, output matrix, and direct transfer matrix.

[0105] Therefore, the state-space equation of the system containing the passive mechanical network controller can be obtained as follows:

[0106] ,

[0107] in, The state vector of a nonlinear two-degree-of-freedom dynamic vibration absorber system containing a passive mechanical network controller is given. It is a semi-active control force. External interference The system output, and the state matrix. Nonlinear state matrix , input matrix , input matrix Output matrix satisfy:

[0108] , , , , ,

[0109] in, Let be the state matrix of the system. Here is the nonlinear state matrix of the system. for The input matrix, for The input matrix, for The input matrix, .

[0110] To facilitate the optimization of the parameters of the passive mechanical network controller in the frequency domain, the nonlinear spring in the two-degree-of-freedom nonlinear dynamic vibration absorber system is linearized.

[0111] Specifically, let Select appropriate external disturbance input During simulation time Solve the following optimization problem:

[0112] ,

[0113] in, To optimize the objective function of the passive mechanical network controller parameters, The main mass spring stiffness, Indicates time, This represents the error between the corresponding states in the nonlinear model and the linear model. , and These are the state vectors of the nonlinear system and the linearized system, respectively. To linearize the state vector of the two-degree-of-freedom nonlinear dynamic vibration absorber system, , , , For weighting coefficients, when Select external disturbance input:

[0114] ,

[0115] in, Indicates time.

[0116] In this embodiment, a weighting coefficient is selected. , , and The optimized principal mass linear spring stiffness It is 1960 N / m.

[0117] Based on the linearized result, external disturbances To output transfer function satisfy:

[0118] ,

[0119] in, For matrix The first line, It is the identity matrix. This is the state matrix after linearization. For complex frequency variables, .

[0120] Therefore, the following optimization problem is solved:

[0121] ,

[0122] in, Let the objective function of the optimization problem be... For external disturbances To output The transfer function, for The H2 norm of the variable, st, indicates that it is constrained by a certain condition or constraint. ( ) is a biquadratic admittance function The coefficient.

[0123] Using the fmincon algorithm toolbox in MATLAB, the optimal biquadratic positive real function can be obtained as follows:

[0124] ,

[0125] The parameters of the optimal biquadratic positive real functions are obtained by using a passive network synthesis algorithm such as the Bott-Duffin algorithm. Figure 4 The 9-element passive mechanical network shown has element values ​​that satisfy... , , , , , , , , , , , They are respectively Figure 4 The stiffness of the three springs in the 9-element passive mechanical network shown. , , They are respectively Figure 4 The damping values ​​of the three dampers in the 9-element passive mechanical network shown are: , , They are respectively Figure 4 The inertial capacitance values ​​of the three inertial capacities in the 9-element passive mechanical network shown.

[0126] For the state-space equations of the nonlinear suspension system containing a passive mechanical network controller in S2, based on the inputs of the fractional-order disturbance observer and the fractional-order integral decoupled sliding mode controller... ;

[0127] ,

[0128] in, , For system status, For the state variables of a passive mechanical network, the minimum state space is used to realize them. Main mass velocity, The mass velocity of the dynamic vibration absorber is considered. The disturbance observer and active controller are designed sequentially, and the parameters of the active controller are optimized. The overall block diagram of the control system is shown below. Figure 2 As shown.

[0129] Step S3: Based on the mass velocity of the dynamic vibration absorber and fractional calculus, construct the sliding surface of the mass subsystem of the dynamic vibration absorber, expressed as:

[0130] ,

[0131] in, For the sliding surface of the mass subsystem of the dynamic vibration absorber, For the mass velocity of the dynamic vibration absorber, This is the second convergence gain. , The symbol for fractional integrals is . For the second-order parameter, .

[0132] Step S4: Based on the sliding surface, principal mass velocity, boundary threshold, and upper amplitude limit of the dynamic vibration absorber mass subsystem, the formula for the influence parameters of the sliding surface of the dynamic vibration absorber mass subsystem on the sliding surface of the principal mass subsystem is as follows:

[0133] ,

[0134] in, The parameters representing the influence of the sliding surface of the dynamic vibration absorber mass subsystem on the sliding surface of the main mass subsystem are: The upper limit of amplitude, For boundary thresholds, For symbolic functions, For the sliding surface of the mass subsystem of the dynamic vibration absorber, It is a saturation function.

[0135] Step S5: Based on the influence parameters of the principal mass velocity, the sliding surface of the dynamic vibration absorber mass subsystem on the principal mass subsystem sliding surface, and fractional calculus, construct the sliding surface of the principal mass subsystem as follows:

[0136] ,

[0137] in, The sliding surface of the main mass subsystem. Main mass velocity, The first convergence gain, , The symbol for fractional integrals is . For the first-order parameter, , The parameters representing the influence of the sliding surface of the mass subsystem of the dynamic vibration absorber on the sliding surface of the main mass subsystem are given.

[0138] Fractional integrals (e.g.) Fractional operators are continuous, non-integer-order mathematical operations. However, in practical engineering, controllers (such as hardware circuits and embedded chips) can only perform integer-order arithmetic operations or difference operations, and cannot directly implement fractional-order operators. Therefore, for engineering feasibility, an Oustaloup filter is used to approximate the fractional-order operator as an integer-order rational polynomial. In this way, the hardware / software in the engineering can indirectly complete the function of the fractional-order operator by implementing this rational polynomial. Its specific form is as follows:

[0139] ,

[0140] in, For the approximate integer-order transfer function, For fractional operators, For Laplace variables, Let the order of the fractional operator be denoted as . , , , , , and These represent the upper frequency limit, lower frequency limit, and approximate order required for the design. This invention selects... , and As filter parameters, based on these parameters, the solver's fixed step size only needs to be set to 0.01 to achieve a solution, meeting the requirements for engineering feasibility. The sum of several external harmonics is selected as the external input force. The tracking effect of the interference estimate of the present invention is as follows: Figure 5 As shown.

[0141] This invention uses intermediate variables Designing the main sliding surface At that time, it was introduced The subsystem indirectly controls the vibration absorber mass subsystem while controlling the main mass subsystem. Among them, It is a positive number less than 1, used to limit the influence of the vibration absorber mass subsystem on the main mass subsystem. The disturbance estimate is obtained from a fractional-order switching disturbance observer. The introduction of fractional calculus extends the sliding surface design from integer to fractional order, better considering the system's historical dynamic information. Using a hyperbolic tangent function instead of the traditional sign function for the switching rate effectively reduces chattering in sliding mode control. To make it practically feasible, the fractional order in the sliding mode controller is also approximated using an Oustaloup filter. , and These are the filter parameters.

[0142] Influencing parameters of this invention The addition of [the company] has increased [its influence]. The subsystem represented by the sliding surface The influence of the subsystem represented by the sliding surface can improve other performance indicators while simultaneously improving the main performance indicators, which is something that fractional-order sliding mode control algorithms cannot achieve. Furthermore, it performs better than decoupled sliding mode control because it introduces multiple designable parameter values; for example, these can be adjusted... , The value is used to change the magnitude of the influence, and to change , To adjust the overall control performance.

[0143] Fractional integrals The introduction of this allows the system to be in the sliding surface from the initial moment. superior, The sliding surface is represented by a fractional-order calculus term, completely eliminating the process of the system state approaching the sliding surface from the initial position in traditional sliding mode control. The fractional-order calculus term possesses global memory and inheritance properties, providing a large integral compensation force to accelerate convergence in the initial stage. Subsequently, the integral effect gradually weakens, naturally smoothing the release of control energy. It significantly reduces chattering amplitude without the need for excessively large boundary layers or additional filters. Compared to traditional methods, chattering suppression is more natural and effective, suitable for practical actuator applications. Furthermore, the introduction of adjustable parameters (fractional order) provides greater design freedom. The nonlocality of the fractional-order operator combined with the global robustness of integral sliding mode enables the controller to have better compensation for strongly nonlinear terms (such as nonlinear stiffness). While addressing multiple performance trade-offs, it can better handle nonlinear factors, solving key drawbacks such as incomplete decoupling, weak robustness in the arrival stage, large chattering, and insufficient steady-state accuracy. High-performance control can be achieved without an exact model.

[0144] Step S6: Based on the principal mass velocity, obtain the estimated value of external disturbance; based on the estimated value of external disturbance, passive control force, and sliding surface of the principal mass subsystem, design a fractional-order integral decoupled sliding mode controller to obtain the active control force;

[0145] In this embodiment, preferably, the fractional-order integral decoupling sliding mode controller is:

[0146] ,

[0147] ,

[0148] ,

[0149] in, For active control, The equivalent control force for sliding mode control. For switching rate, The quality of the main quality, , and Nonlinear spring stiffness of principal mass The coefficients of the linear, quadratic, and cubic terms, For passive control force, This is an estimate of external disturbances. The main mass displacement. This refers to the mass displacement of the dynamic vibration absorber. For fractional differential operators, For fractional order, Main mass velocity, The parameters representing the influence of the sliding surface of the dynamic vibration absorber mass subsystem on the sliding surface of the main mass subsystem are: The first convergence gain, , This is the switching rate gain coefficient. This refers to the tanh function.

[0150] In this embodiment, the method for obtaining the external disturbance estimate of the main mass velocity includes:

[0151] The difference between the principal mass velocity and the estimated principal mass velocity is taken as the principal mass velocity estimation error;

[0152] Based on the absolute value of the principal mass velocity estimation error and the magnitude of the order switching threshold, the order of the fractional-order order switching interference observer is determined, the fractional-order order switching interference observer is constructed, and the external interference estimate is calculated.

[0153] Considering external interference The impact caused by external interference, this invention is effective against external interference. Observations are conducted. This invention is based on the system's state error value. Fractional order adjustment is performed, using two fractional orders to ensure the estimation accuracy of the fractional-order disturbance observer under different types of disturbances. The specific form is as follows:

[0154] The fractional-order order switching interference observer is:

[0155] ,

[0156] in, This is an estimate of external disturbances. , , The gain coefficient of the fractional-order switching interference observer. Main mass velocity estimation error, , Main mass velocity, Main mass velocity estimate, , , and Nonlinear spring stiffness of principal mass The coefficients of the linear, quadratic, and cubic terms, The main mass displacement. For passive control force, For active control, , To switch the order parameters of the interference observer for fractional-order orders, , For symbolic functions, To switch the order of the interference observer for fractional-order orders, These are the initial parameters. , For fractional differential operators, The quality of the main quality.

[0157] In this embodiment, preferably, the method for determining the order of the fractional-order order-switching interference observer by comparing the absolute value of the principal mass velocity estimation error with the order switching threshold includes:

[0158] Determine the absolute value of the main mass velocity estimation error Is it less than or equal to the order switching threshold? If it is less than or equal to, then let the fractional order of the switching interference observer be . If it is greater than 1, then let the fractional order of the switching interference observer be 1. ;in, For the first order, For the second order, , The threshold for order switching. .

[0159] For fractional-order order switching of the interference observer It can be expressed by the formula:

[0160] .

[0161] This invention achieves a main mass velocity estimation error with an absolute value less than [a certain value]. When the fractional order is fixed as When the estimation error is greater than At that time, the order of the fractional order is switched to [order]. This operation can effectively maintain the estimation accuracy of the interference observer.

[0162] As shown in Table 2, Table 2 contains the parameters of the fractional-order switching interference observer.

[0163] Table 2

[0164]

[0165] In this embodiment, preferably, performance indicators are used. and Mixed Indicators Optimize the parameters of the fractional-order integral decoupled sliding mode controller (active controller):

[0166] ,

[0167] in, and This refers to the baseline performance index value when the passive network is a single damper. In this case, the selected damping value for the dynamic vibration absorber is... , and These are weighting coefficients; choose... As an external input force, simulation time The particle swarm optimization algorithm is used to solve the following objective function, optimizing the parameters in the active controller to improve performance metrics. Optimal:

[0168] ,

[0169] in, The first convergence gain, This is the second convergence gain. For fractional order, For the second-order parameter, The upper limit of amplitude, For boundary thresholds, , This is the switching rate gain coefficient.

[0170] The present invention selects the following weighting coefficients as follows: and The optimal value of the mixed index obtained is The optimized parameters are shown in Table 3, which contains the parameters of the fractional-order integral decoupled sliding mode controller based on the disturbance observer.

[0171] Table 3

[0172]

[0173] Step S7: Generate semi-active inertial control parameters by passing the active control force through force tracking logic;

[0174] Step S8: The control parameters of the semi-active inertial capacitance, the relative acceleration of the main mass and the mass of the dynamic vibration absorber are used to generate a semi-active control force through the semi-active inertial capacitance, thus completing the design of the semi-active control force for the two-degree-of-freedom nonlinear dynamic vibration absorber system.

[0175] like Figure 6 As shown, Figure 6 The tracking performance of a fractional integral decoupled sliding mode controller for semi-active capacitive tracking.

[0176] The inertia capacity of a semi-active inertial capacitance satisfies the following control law:

[0177] ,

[0178] in, The inertial capacity of a semi-active inertial capacitor. For active control, The relative acceleration between the main mass and the mass of the dynamic vibration absorber. This is the upper limit of inertia capacity. This is the lower limit of inertia capacity. The acceleration of the main mass.

[0179] The semi-active control force generated by semi-active inertial capacitance is .

[0180] In this embodiment, the passive mechanical network controller, disturbance observer, active controller, and semi-active controller designed and optimized according to the present invention are used to perform performance analysis and comparison of the control system, including:

[0181] The sum of several harmonic functions was selected as the external disturbance force and some uncertain disturbances existing in the system to perform time-domain simulation of the dynamic vibration absorber control system, with the total simulation time set to 10s. The simulation was compared with several other control methods, including: 1. Passive network control only; 2. Linearization of the model followed by control using a linear quadratic regulator (LQR) (Nagarkar et al., Procedia manufacturing, 2018) combined with a passive network; 3. Decoupled sliding mode control combined with a disturbance observer, which introduces an unsprung mass subsystem for control when designing the controller switching rate (Peng et al., Control Theory and Technology, 2025). This invention uses the above control methods and simultaneously compares the effects of active control and the effects of various active control forces using semi-active capacitive tracking. The comparison results are as follows: Figure 7 , Figure 8 , Figure 9 , Figure 10 As shown. This invention also compares the proposed method with other methods using selected performance indicators, demonstrating the superiority of this invention.

[0182] As shown in Table 4, Table 4 compares the effects of passive control, active control, and semi-active control.

[0183] Table 4

[0184]

[0185] As shown in Table 4, it can be seen that the passive network designed in this invention, combined with fractional-order integral decoupled sliding mode control based on an interference observer, improves the principal mass displacement by 72.51% compared to no control. When using semi-active capacitive tracking of the optimal control force, the principal mass displacement is improved by 47.46%. Since the function of the dynamic vibration absorber is to sacrifice its own vibration to suppress the vibration of the principal mass, there will be a sacrifice in the relative displacement between the two mass blocks. The active control algorithm designed in this invention, while improving the principal mass displacement performance, still outperforms the decoupled sliding mode control in terms of the relative displacement between the mass blocks. Although using LQR can improve the relative displacement performance, it cannot further optimize the principal mass displacement, and its maximum relative displacement value is still too large, which may cause mechanical collisions and other problems. In addition, under semi-active capacitive tracking, this invention still improves the principal mass displacement by 47.46% compared to no control, and the RMS value of the relative displacement is also the best among the three semi-active tracking methods.

[0186] This invention proposes a design method for a dynamic vibration absorber. First, a nonlinear dynamic vibration absorber system is established. Based on the linearized model fitted from this system model, a passive mechanical network with a biquadratic optimal form is obtained through optimization. Then, based on the system model combined with the passive mechanical network, a fractional-order integral sliding mode controller based on a disturbance observer is designed. The fractional-order switching disturbance observer can estimate and supplement various unknown factors in the system and output the optimal control force through fractional-order integral sliding mode control. Finally, a semi-active capacitive control law is designed, and a suboptimal control force is obtained through force tracking for vibration reduction control. This invention utilizes the fractional-order concept, overcoming the order limitation in sliding mode controller design. It can better handle nonlinear factors in the system than integer-order controllers, and the fractional-order integral can effectively reduce chattering and improve global robustness in sliding mode control. Furthermore, this invention utilizes the idea of ​​decoupled sliding mode control, considering secondary performance indicators while improving primary performance indicators. Experimental results show that the active control algorithm designed in this invention has better vibration reduction effects than other active methods, and also outperforms other active methods in handling conflict performance indicators. Moreover, the suboptimal control force obtained by semi-active capacitive tracking can achieve control effects that passive mechanical networks cannot achieve.

[0187] This second embodiment provides a dynamic vibration absorber design system, including:

[0188] The system modeling module is used to obtain the state vector based on the two-degree-of-freedom nonlinear dynamic vibration absorber system; the state vector includes: principal mass displacement, dynamic vibration absorber mass displacement, principal mass velocity, and dynamic vibration absorber mass velocity;

[0189] The passive control module is used to design a passive mechanical network controller based on the relative velocity between the main mass and the mass of the dynamic vibration absorber, so as to obtain the passive control force.

[0190] The first sliding surface construction module is used to construct the sliding surface of the mass subsystem of the dynamic vibration absorber based on the mass velocity and fractional calculus of the dynamic vibration absorber.

[0191] The influence parameter acquisition module is used to obtain the influence parameters of the sliding surface of the dynamic vibration absorber mass subsystem on the sliding surface of the main mass subsystem based on the sliding surface of the dynamic vibration absorber mass subsystem, the main mass velocity, the boundary threshold, and the upper limit of the amplitude of the dynamic vibration absorber mass subsystem.

[0192] The second sliding surface construction module is used to construct the sliding surface of the main mass subsystem based on the influence parameters of the main mass velocity and the sliding surface of the dynamic vibration absorber mass subsystem on the main mass subsystem sliding surface.

[0193] The sliding mode controller construction module is used to construct a fractional-order integral decoupled sliding mode controller based on the sliding surfaces of the main mass subsystem and the dynamic vibration absorber mass subsystem.

[0194] The external disturbance estimation calculation module is used to calculate the external disturbance estimate based on the master mass velocity.

[0195] The active control force calculation module is used to design a fractional-order integral decoupled sliding mode controller based on external disturbance estimates, passive control force, and the sliding mode surface of the master mass subsystem, and to obtain the active control force.

[0196] The control parameter acquisition module is used to generate semi-active inertial capacity control parameters by passing the active control force through force tracking logic;

[0197] The semi-active control force acquisition module is used to generate a semi-active control force by using the control parameters of the semi-active inertial capacitance and the relative acceleration between the main mass and the mass of the dynamic vibration absorber, thereby completing the design of the semi-active control force for the two-degree-of-freedom nonlinear dynamic vibration absorber system.

[0198] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0199] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0200] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0201] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0202] Obviously, the above embodiments are merely illustrative examples for clear explanation and are not intended to limit the implementation. Those skilled in the art will recognize that other variations or modifications can be made based on the above description. It is neither necessary nor possible to exhaustively list all possible implementations here. However, obvious variations or modifications derived therefrom are still within the scope of protection of this invention.

Claims

1. A design method for a dynamic vibration absorber, characterized in that, include: Based on a two-degree-of-freedom nonlinear dynamic vibration absorber system, the state vector is obtained; The state vector includes: principal mass displacement, dynamic vibration absorber mass displacement, principal mass velocity, and dynamic vibration absorber mass velocity; Based on the relative velocity between the main mass and the mass of the dynamic vibration absorber, a passive mechanical network controller is designed to obtain the passive control force. Based on the mass velocity of the dynamic vibration absorber and fractional calculus, the sliding surface of the mass subsystem of the dynamic vibration absorber is constructed. The sliding surface of the mass subsystem of the dynamic vibration absorber is as follows: ， in, For the sliding surface of the mass subsystem of the dynamic vibration absorber, For the mass velocity of the dynamic vibration absorber, This is the second convergence gain. , This is the symbol for fractional calculus. For the second-order parameter, ; Based on the sliding surface, principal mass velocity, boundary threshold, and upper amplitude limit of the dynamic vibration absorber mass subsystem, the influence parameters of the sliding surface of the dynamic vibration absorber mass subsystem on the sliding surface of the principal mass subsystem are obtained, and the formula is as follows: ， in, The parameters representing the influence of the sliding surface of the dynamic vibration absorber mass subsystem on the sliding surface of the main mass subsystem are: The upper limit of amplitude, For boundary thresholds, For symbolic functions, For the sliding surface of the mass subsystem of the dynamic vibration absorber, It is a saturation function; Based on the influence parameters of the principal mass velocity, the sliding surface of the dynamic vibration absorber mass subsystem on the principal mass subsystem sliding surface, and fractional calculus, the sliding surface of the principal mass subsystem is constructed as follows: ， in, The sliding surface of the main mass subsystem. Main mass velocity, The first convergence gain, , It is the symbol for fractional integral. For the first-order parameter, , The influence parameters of the sliding surface of the dynamic vibration absorber mass subsystem on the sliding surface of the main mass subsystem; Based on the principal mass velocity, the external disturbance is estimated; based on the external disturbance estimate, passive control force, and sliding surface of the principal mass subsystem, a fractional-order integral decoupled sliding mode controller is designed to obtain the active control force. The active control force is used to generate semi-active inertial capacity control parameters through force tracking logic; By using the semi-active inertial capacitance control parameters and the relative acceleration between the main mass and the mass of the dynamic vibration absorber, a semi-active control force is generated, thus completing the design of the semi-active control force for the two-degree-of-freedom nonlinear dynamic vibration absorber system.

2. The design method for a dynamic vibration absorber according to claim 1, characterized in that, Based on the external disturbance estimate, passive control force, and sliding surface of the main mass subsystem, a fractional-order integral decoupled sliding mode controller is designed. The fractional-order integral decoupled sliding mode controller is as follows: ， ， ， in, For active control, The equivalent control force for sliding mode control. For switching rate, The quality of the main quality, , and Nonlinear spring stiffness of principal mass The coefficients of the linear, quadratic, and cubic terms, For passive control force, This is an estimate of external disturbances. The main mass displacement. This refers to the mass displacement of the dynamic vibration absorber. For fractional differential operators, For fractional order, Main mass velocity, The parameters representing the influence of the sliding surface of the dynamic vibration absorber mass subsystem on the sliding surface of the main mass subsystem are: The first convergence gain, , This is the switching rate gain coefficient. For the tanh function, The sliding surface of the main mass subsystem.

3. The design method for a dynamic vibration absorber according to claim 1, characterized in that, The method for obtaining external disturbance estimates based on the main mass velocity includes: The difference between the principal mass velocity and the estimated principal mass velocity is taken as the principal mass velocity estimation error; Based on the absolute value of the principal mass velocity estimation error and the magnitude of the order switching threshold, the order of the fractional-order order switching interference observer is determined, the fractional-order order switching interference observer is constructed, and the external interference estimate is calculated.

4. The design method for a dynamic vibration absorber according to claim 3, characterized in that, The fractional-order order switching interference observer is: ， in, This is an estimate of external disturbances. , , The gain coefficient of the fractional-order switching interference observer. Main mass velocity estimation error, , Main mass velocity, Main mass velocity estimate, , , and Nonlinear spring stiffness of principal mass The coefficients of the linear, quadratic, and cubic terms, The main mass displacement. For passive control force, For active control, , To switch the order parameters of the interference observer for fractional-order orders, , For symbolic functions, To switch the order of the interference observer for fractional-order orders, These are the initial parameters. , For fractional differential operators, The quality of the main quality.

5. The design method for a dynamic vibration absorber according to claim 3, characterized in that, The method for determining the order of the fractional-order order-switching interference observer based on the absolute value of the principal mass velocity estimation error and the magnitude of the order switching threshold includes: Determine whether the absolute value of the principal mass velocity estimation error is less than or equal to the order switching threshold. If it is less than or equal to, then let the fractional order of the switching interference observer be . If it is greater than 1, then let the fractional order of the switching interference observer be 1. ;in, For the first order, For the second order, , The threshold for order switching. .

6. The design method for a dynamic vibration absorber according to claim 1, characterized in that, The design methods for passive mechanical network controllers include: Set the semi-active control input matrix and semi-active control force in the two-degree-of-freedom nonlinear dynamic vibration absorber system to 0, and replace the nonlinear spring stiffness of the principal mass with the linear spring stiffness of the principal mass to obtain the state vector of the two-degree-of-freedom nonlinear dynamic vibration absorber system. The difference between the state vector of the two-degree-of-freedom nonlinear dynamic vibration absorber system and the linearized state vector is used as the error vector; Based on the error vector, weight matrix, and simulation time setting, a linear optimization objective function is constructed. The linear spring stiffness of the principal mass is optimized based on the linearization optimization objective function to obtain the linearized principal mass spring stiffness. The admittance of the passive mechanical network controller of the two-degree-of-freedom nonlinear dynamic vibration absorber system is set as a double quadratic positive real function. The coefficient parameters of the double quadratic positive real function are obtained by using the linearized principal mass spring stiffness. The biquadratic positive real functions are transformed into the topology and component parameters of a passive mechanical network controller.

7. A dynamic vibration absorber design system based on the dynamic vibration absorber design method according to any one of claims 1 to 6, characterized in that, include: The system modeling module is used to obtain the state vector based on a two-degree-of-freedom nonlinear dynamic vibration absorber system. The state vector includes: principal mass displacement, dynamic vibration absorber mass displacement, principal mass velocity, and dynamic vibration absorber mass velocity; The passive control module is used to design a passive mechanical network controller based on the relative velocity between the main mass and the mass of the dynamic vibration absorber, so as to obtain the passive control force. The first sliding surface construction module is used to construct the sliding surface of the dynamic vibration absorber mass subsystem based on the mass velocity and fractional calculus of the dynamic vibration absorber. The sliding surface of the dynamic vibration absorber mass subsystem is as follows: ， in, For the sliding surface of the mass subsystem of the dynamic vibration absorber, For the mass velocity of the dynamic vibration absorber, This is the second convergence gain. , This is the symbol for fractional calculus. For the second-order parameter, ; The influence parameter acquisition module is used to obtain the influence parameters of the sliding surface of the dynamic vibration absorber mass subsystem on the sliding surface of the main mass subsystem, based on the sliding surface, main mass velocity, boundary threshold, and upper amplitude limit of the dynamic vibration absorber mass subsystem. The formula is as follows: ， in, The parameters representing the influence of the sliding surface of the dynamic vibration absorber mass subsystem on the sliding surface of the main mass subsystem are: The upper limit of amplitude, For boundary thresholds, For symbolic functions, For the sliding surface of the mass subsystem of the dynamic vibration absorber, It is a saturation function; The second sliding surface construction module is used to construct the sliding surface of the main mass subsystem based on the main mass velocity, the influence parameters of the sliding surface of the dynamic vibration absorber mass subsystem on the main mass subsystem sliding surface, and fractional calculus. The sliding surface of the main mass subsystem is as follows: ， in, The sliding surface of the main mass subsystem. Main mass velocity, The first convergence gain, , It is the symbol for fractional integral. For the first-order parameter, , The influence parameters of the sliding surface of the dynamic vibration absorber mass subsystem on the sliding surface of the main mass subsystem; The sliding mode controller construction module is used to construct a fractional-order integral decoupled sliding mode controller based on the sliding surfaces of the main mass subsystem and the dynamic vibration absorber mass subsystem. The external disturbance estimation calculation module is used to calculate the external disturbance estimate based on the master mass velocity. The active control force calculation module is used to design a fractional-order integral decoupled sliding mode controller based on external disturbance estimates, passive control force, and the sliding mode surface of the master mass subsystem, and to obtain the active control force. The control parameter acquisition module is used to generate semi-active inertial capacity control parameters by passing the active control force through force tracking logic; The semi-active control force acquisition module is used to generate a semi-active control force by using the control parameters of the semi-active inertial capacitance and the relative acceleration between the main mass and the mass of the dynamic vibration absorber, thereby completing the design of the semi-active control force for the two-degree-of-freedom nonlinear dynamic vibration absorber system.

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