A multi-degree-of-freedom motion actuator timing trajectory vibration suppression method, device, equipment and medium

Abstract

The application discloses a kind of multi-degree-of-freedom motion actuator timing trajectory vibration suppression method, device, equipment and medium, method includes: the timing high-dimensional space state physical trajectory vector of motion actuator is collected, decoupling is rigid rigid body displacement component and flexible high-frequency disturbance component.Two-way component is as the excitation input generalized dynamics equivalent multivariate second-order state space operator, mapping out initial background energy and initial vibration energy;With nonlinear overflow cross correction operator, in combination with time-varying acceleration and jerk, band leakage energy is removed, and converges to eigenvalue perturbation energy functional;Finally, through multivariate gradient threshold discriminant matrix closed loop inverse modulation time scale scaling factor, nonlinear smooth modulation is carried out.The application gradually eliminates structure physical self-vibration under the premise of ensuring system geometric profile boundary tolerance.

Description

Technical Field

[0001] This invention belongs to the field of multi-degree-of-freedom spatial precision motion control and complex trajectory interpolation dynamics planning technology. Specifically, it relates to a method, device, equipment and medium for suppressing the vibration of the temporal trajectory of a multi-degree-of-freedom motion actuator. The method is a real-time vibration suppression method for the physical trajectory vector of the temporal spatial state based on the generalized dynamic equivalent mapping of mechanical components, frequency band nonlinear overflow cross correction and adaptive dynamic feedback closed-loop adjustment of time scale scaling factor. Background Technology

[0002] In high-speed, high-acceleration nonlinear trajectory tracking or frequent direction changes, multi-degree-of-freedom high-dimensional spatial physical displacement actuators are highly susceptible to structural physical self-vibration under rigid master-controlled excitation due to the inherent flexible modes, nonlinear frictional damping, and dynamic transmission clearances of the physical system. This self-vibration causes severe time-frequency domain perturbation responses at the end of the spatial physical trajectory, thereby degrading the macroscopic profile deformation accuracy and exacerbating structural fatigue damage to the actuator.

[0003] Traditional control methods for such vibration disturbances often rely on offline open-loop time-domain shaping, such as offline truncation of the excitation signal through a pre-set specific filter response bandwidth or a specific frequency input shaper. These methods are highly dependent on static, time-invariant system dynamic parameters and lack online adaptive evolution characteristics, making them prone to failure under varying loads and unpredictable environmental disturbances. Another approach relies on online feedback compensation based on physical position or velocity characteristic deviations. However, because the evolution of high-frequency natural vibrations in the time domain is extremely drastic, by the time the physical sensor detects a significant spatial displacement deviation and triggers a servo closed-loop response, the vibration energy has already fully accumulated within the physical system, causing physical deformation. This adjustment mechanism based on "response deviation" inherently suffers from an unavoidable phase lag in its timing logic.

[0004] While state observation based on the dynamic energy method offers some trend prediction for cumulative effects, in actual high-dynamic operations, the high-order spectral components of the low-frequency signal characterizing the displacement components of a macroscopic rigid body inevitably extend into the flexible high-frequency disturbance band when experiencing abrupt changes in the first and second derivatives. Due to the limitations of the attenuation wake of the transition band of the time-domain real-time filter and the nonlinear coupling of the mechanical structure, conventional signal decoupling methods produce severe frequency band cross-coupling. This leads to some normal macroscopic rigid displacement excitation energy being incorrectly identified and superimposed into the flexible disturbance energy, forming high-frequency band energy artifacts. If these artifacts are not quantitatively stripped and dynamically corrected, the control system will experience severe false defense misjudgments, resulting in the blind suppression of the system's driving energy input even when the mechanical structure has not undergone substantial structural vibration. Consequently, without substantially improving the contour accuracy, the macroscopic operational efficiency of the actuator is greatly sacrificed. Therefore, how to accurately construct the intrinsic perturbation energy functional, quantify and subtract the frequency band nonlinear overflow term, and use this to drive the adaptive smooth mapping of the time scale scaling factor is a fundamental technical bottleneck that urgently needs to be overcome in the field of precision control engineering. Summary of the Invention

[0005] This invention provides a method, device, equipment, and medium for suppressing the temporal trajectory of a multi-degree-of-freedom motion actuator. It fully decouples the input trajectory by using a multi-dimensional modal time-frequency domain decoupling operator, constructs a generalized dynamic second-order state-space operator to realize the quadratic reproduction of energy, innovatively introduces a nonlinear overflow cross-correction operator to eliminate energy artifacts, and relies on the time scale scaling factor of the real-time inverse modulation interpolator of the multivariate gradient threshold discrimination matrix to progressively eliminate the structural physical vibration while ensuring the tolerance of the system's geometric contour boundary.

[0006] To achieve the above objectives, the technical solution of the present invention is as follows:

[0007] This invention provides a time-series trajectory vibration suppression method for multi-degree-of-freedom motion actuators based on time-varying motion state spatial energy functional adaptive correction and scale scaling, comprising the following core steps:

[0008] Step 1, temporal trajectory acquisition and multidimensional modal time-frequency domain decoupling and separation: In the set discrete sampling time slot, the temporal high-dimensional spatial state physical trajectory vector of the motion actuator is acquired in real time. The physical trajectory vector is decoupled in the time-frequency domain using an adaptive time-domain filtering operator and separated into multidimensional modal components that represent macroscopic rigid body displacement components and microscopic flexible high-frequency disturbance components.

[0009] Step 2, State-space operator dynamic energy quadratic form mapping: Construct a generalized dynamic equivalent multivariate second-order state-space operator, and inject the macroscopic rigid body displacement component and the microscopic flexible high-frequency disturbance component as external generalized non-conservative force excitation vectors into the state-space operator. The initial background excitation field energy index and the initial vibration excitation field energy index are obtained by online quantization through the construction of the state vector quadratic form.

[0010] Step 3, Nonlinear overflow cross-adaptive correction: Based on the time-varying multi-derivative motion state of the current actuator, the leakage energy term caused by non-ideal isolation of the frequency band is calculated using the nonlinear overflow cross-correction operator, and the leakage energy term is dynamically deducted from the initial vibration excitation field energy index in reverse, and the intrinsic perturbation energy functional is converged.

[0011] Step 4, Multivariate Gradient Threshold Discrimination and Time Scale Scaling Factor Feedback Control: The intrinsic perturbation energy functional is imported into a preset multivariate gradient threshold discrimination matrix for state interval comparison, a nonlinear convergence feedback law is constructed to solve the time scale scaling factor online, and the time scale scaling factor is used to adaptively and dynamically adjust the energy injection rate of the physical trajectory vector in the subsequent interpolation time slot.

[0012] Furthermore, in step one, the adaptive time-domain filtering operator is any one of the Kalman decoupling filtering operator, the adaptive center frequency Wiener filtering operator, or the dynamic time-varying band-stopping operator, and the filtering response bandwidth and cutoff frequency of the operator are dynamically reconstructed online with the spatial evolution of the time-varying physical pose or load inertia of the displacement actuator.

[0013] Furthermore, in step two, the characteristic parameters of the equivalent mass matrix, equivalent damping matrix, and equivalent stiffness matrix corresponding to the generalized dynamic equivalent multivariate second-order state-space operator are obtained by time-series updates through online recursive least squares parameter estimation methods or offline multi-frequency calibration and frequency sweep identification mechanisms.

[0014] Furthermore, in step three, the nonlinear overflow cross-correction operator is a nonlinear mapping operator constructed based on the frequency band cross-over overlap area function of macroscopic rigid body displacement components and microscopic flexible high-frequency disturbance components in the transition band of the adaptive time-domain filter operator, combined with the time-varying acceleration and the higher-order derivative vector of jerk.

[0015] Furthermore, in step four, the online calculation and adaptive closed-loop dynamic adjustment of the time scale scaling factor includes:

[0016] When the intrinsic perturbation energy functional is in the unscented stable region, the time scale scaling factor is constantly mapped to a saturated all-pass value of 1.0;

[0017] When the intrinsic perturbation energy functional is in the asymptotic perturbation region, the time scale scaling factor decreases smoothly and steadily with the increase of deformation energy flow according to the nonlinear logarithmic decay control law.

[0018] When the intrinsic perturbation energy functional is in a high-risk instability region, the time scale scaling factor is forcibly assigned a set hard-limiting penalty constant, and the interpolator is activated at the same time to reconstruct the time-series trajectory.

[0019] Furthermore, in step four, the energy injection rate of the physical trajectory vector in the subsequent interpolation time slot is adaptively and dynamically adjusted using the time scale scaling factor. This includes at least one of the following: real-time inverse modulation of the trajectory feed rate of the multi-axis interpolator, online dynamic compensation of the spatial position coordinate command of the high-dimensional physical trajectory vector, and reconstruction of the time-domain velocity curve control law of the current discrete interpolation segment.

[0020] In another aspect, the present invention provides a timing trajectory vibration suppression device for a multi-degree-of-freedom motion actuator, comprising:

[0021] Decoupling unit: used to collect the temporal high-dimensional spatial state physical trajectory vector of the motion actuator in real time within a set discrete sampling time slot, and use an adaptive time-domain filtering operator to decouple the physical trajectory vector in the time and frequency domain, separating it into multi-dimensional modal components that characterize macroscopic rigid body displacement components and microscopic flexible high-frequency disturbance components.

[0022] Energy index quantization unit: used to construct a generalized dynamic equivalent multivariate second-order state-space operator, injecting the macroscopic rigid body displacement component and the microscopic flexible high-frequency disturbance component as external generalized non-conservative force excitation vectors into the state-space operator, and obtaining the initial background excitation field energy index and the initial vibration excitation field energy index by constructing a quadratic form of the state vector for online quantization.

[0023] Energy correction unit: Based on the time-varying multi-derivative motion state of the current actuator, the leakage energy term caused by nonlinear overflow cross correction operator is calculated, and the leakage energy term is dynamically deducted from the initial vibration excitation field energy index to obtain the intrinsic perturbation energy functional.

[0024] Control unit: The intrinsic perturbation energy functional is imported into a preset multivariate gradient threshold discrimination matrix for state interval comparison, a nonlinear convergence feedback law is constructed to solve the time scale scaling factor online, and the time scale scaling factor is used to adaptively and dynamically adjust the energy injection rate of the physical trajectory vector in the subsequent interpolation time slot.

[0025] In another aspect, the present invention provides an electronic device, including a memory and a processor, wherein the memory stores a computer program, and when the computer program is called and executed by the processor, it implements the steps in the time-series trajectory vibration suppression method for multi-degree-of-freedom motion actuators as described above.

[0026] In another aspect, the present invention provides a computer-readable medium, characterized in that the computer-readable medium stores a computer program, which, when called and executed by a computer, implements the steps in the time-series trajectory vibration suppression method for multi-degree-of-freedom motion actuators as described above.

[0027] In summary, the beneficial effects of the present invention are as follows:

[0028] 1. Overcoming the bottleneck of timing phase lag: This invention breaks through the traditional passive adjustment framework based on endpoint error feedback, elevating the observation dimension to the energy space functional category of the quadratic form of the state vector. Utilizing the physical foresight of the energy accumulation process, it completes the accurate calculation of the perturbation trend before the macroscopic deformation of the displacement actuator occurs, eliminating the phase lag of the response control from its physical origin.

[0029] 2. Eliminating false vibration suppression caused by high-frequency band energy artifacts: This invention uses a nonlinear overflow cross-correction operator to accurately extract and subtract unreal high-frequency components generated in the filter transition band due to first- and second-order derivative transitions. This ensures that the system will not trigger erroneous vibration suppression and deceleration responses when experiencing extremely high geometric curvature motions such as complex acute-angle trajectories, achieving efficient and low-power trajectory tracking.

[0030] 3. Achieving an adaptive dynamic balance between geometric profile tolerance and temporal energy flow constraints: Adjusting the time scale scaling factor based on multivariate gradient thresholding and a nonlinear logarithmic convergent feedback law ensures the continuous differentiability of the control input in the time domain. The system maintains a high-throughput, full-rate energy flow injection when no signs of oscillation are observed, and smoothly limits the rate at the oscillation initiation critical point. This confines the deformation energy within a safe envelope while avoiding secondary profile overcutting caused by abrupt changes in control commands, thus synergistically ensuring both execution accuracy and operational efficiency.

[0031] 4. This invention lowers the barriers to engineering implementation and debugging costs, and possesses excellent resistance to time-varying parameter drift: Traditional vibration suppression algorithms heavily rely on precise, time-invariant physical models of mechanical components (such as accurate joint natural frequencies and damping ratios). Once the equipment experiences mechanical wear, lubrication deterioration, increased joint clearance, or sudden load changes due to long-term operation, leading to parameter drift, traditional control will fail. This invention, based on an energy quadratic trend mapping mechanism, fundamentally decouples the strong binding relationship between vibration suppression effect and the accuracy of joint model dynamic parameters. Even if there are measurement or estimation deviations within the engineering tolerance range for indicators such as resonant frequency, damping ratio, and stiffness of each joint, the closed-loop energy control strategy of this invention can always suppress the structural natural vibration energy within a safe envelope by adjusting the time scale scaling factor. This not only enables the algorithm to maintain a constant high-precision vibration suppression level throughout the entire life cycle of the actuator (accompanied by mechanical aging and parameter drift), but also eliminates the cumbersome on-site joint parameter tuning and high-precision dynamic parameter calibration process, significantly improving the usability and industrial engineering application value of precision motion control systems. Attached Figure Description

[0032] Figure 1 This is a control principle diagram of the method of the present invention;

[0033] Figure 2 This is a flowchart illustrating the execution process of the method of the present invention. Detailed Implementation

[0034] The specific embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0035] Example 1: A method for suppressing vibrations in the timing trajectory of a multi-degree-of-freedom motion actuator. This example operates within the real-time interpolation core control loop of a multi-degree-of-freedom precision CNC robotic arm or a multi-axis linkage machining system. Based on this embodiment of the invention, combined with... Figure 1 The energy flow control architecture is described. The physical trajectory vector X(t) of the high-dimensional temporal state is decoupled in the time and frequency domains through an adaptive time-domain filtering operator (Kalman filter) to extract the rigid body displacement components. With flexible high-frequency disturbance components The two components, as excitation inputs, are equivalent to a second-order multivariate state-space operator in the generalized dynamics, mapping the initial background energy. With initial vibrational energy Furthermore, a nonlinear overflow crossover correction operator is utilized, combined with time-varying acceleration. and accelerometer After eliminating band leakage energy, it converges to the intrinsic perturbation energy functional. Finally, the closed-loop inverse modulation timescale scaling factor of the multivariate gradient threshold discrimination matrix is ​​determined. .

[0036] According to the embodiments of the present invention, in conjunction with Figure 2 This section describes the specific execution logic of the algorithm in a computer or PLC control system. The detailed implementation scheme is broken down as follows:

[0037] Step 1: Decoupling and separation of time-series trajectory acquisition and multi-dimensional modal time-frequency domain.

[0038] The control system in the limited discrete sampling time slots Within, real-time capture of physical trajectory vectors in high-dimensional temporal space. An adaptive Kalman decoupling filter operator is introduced, and its natural frequency is set as the filter cutoff band based on the current structural configuration of the actuator. This decoupling operator decomposes the original trajectory vector into macroscopic rigid body displacement components. With microscopic flexible high-frequency disturbance components Furthermore, spatial streaming data always satisfies the following state conservation equation:

[0039]

[0040] Step 2: Quadratic form mapping of state-space operator dynamics energy

[0041] To transform a spatial geometric displacement sequence into measurable structural kinetic and potential energy, this invention constructs a method based on an equivalent mass matrix. Equivalent damping matrix and equivalent stiffness matrix The generalized dynamic equivalent multivariate second-order state-space operator. The generalized transport state equation of this operator is characterized as:

[0042]

[0043] in, The external generalized nonconservative force excitation vector. These are the state variables inside the operator. The decoupled variables obtained in step one are respectively... and As an external incentive By injecting this state-space operator and constructing the following quadratic form structure of the state vector, the energy index of the initial background excitation field can be reproduced online and quantized in place. Energy index of initial vibration excitation field :

[0044]

[0045]

[0046] Step 3: Adaptive Correction of Nonlinear Overflow Crossover

[0047] Because the adaptive Kalman decoupling filter operator has a non-ideal gradient transition band attenuation trail in the frequency domain, when During transient high-acceleration transitions, some normal background energy flow overflows and forms energy artifacts, which parasitize the environment. Therefore, this invention defines a nonlinear overflow crossover correction operator. This operator is derived from the time-varying acceleration vector of the current displacement axis. and the higher-order derivative vector of jerk. Dynamic control is achieved using a nonlinear multivariate function. (Leakage energy term) The operator model is defined as follows:

[0048]

[0049] in, This is the time-frequency domain cross-adjustment weighting factor. By inversely subtracting the initial energy index from the leakage energy term, the intrinsic perturbation energy functional that accurately reflects the intrinsic deformation potential of the physical structure is obtained. :

[0050]

[0051] Step 4: Multivariate gradient threshold discrimination and time scale scaling factor feedback control

[0052] The system presets a critical safety threshold. With the maximum transition danger threshold The state machine is divided into three energy state spaces, and the time scale scaling factor of the multi-axis interpolator is determined based on the multivariate gradient threshold discrimination matrix. Perform the following nonlinear smoothing modulation:

[0053]

[0054] In the formula, To control the smoothness of the logarithmic decay rate, the gain is adaptively controlled. This is achieved through real-time calculation. Acting on a multi-axis dynamic interpolator, it increases the feed rate of the originally planned temporal physical trajectory of the physical system. The trajectory feed rate of the real-time inverse modulation multi-axis interpolator is obtained by performing an adaptive unscented blanking transform using the scaling coefficients. : Because the feedback law is constructed using a logarithmically continuously differentiable curve, it can smoothly adjust the system's time base within the asymptotic perturbation region. This suppresses excitation energy and avoids geometric overcutting of the multidimensional trajectory at the spatial physical boundary, effectively synergistically combining the anti-self-vibration effect with the accuracy of dynamic geometric profile preservation.

[0055] Example 2: A vibration damping device for the timing trajectory of a multi-degree-of-freedom motion actuator, comprising:

[0056] Decoupling unit: used to collect the temporal high-dimensional spatial state physical trajectory vector of the motion actuator in real time within a set discrete sampling time slot, and use an adaptive time-domain filtering operator to decouple the physical trajectory vector in the time and frequency domain, separating it into multi-dimensional modal components that characterize macroscopic rigid body displacement components and microscopic flexible high-frequency disturbance components.

[0057] Energy index quantization unit: used to construct a generalized dynamic equivalent multivariate second-order state-space operator, injecting the macroscopic rigid body displacement component and the microscopic flexible high-frequency disturbance component as external generalized non-conservative force excitation vectors into the state-space operator, and obtaining the initial background excitation field energy index and the initial vibration excitation field energy index by constructing a quadratic form of the state vector for online quantization.

[0058] Energy correction unit: Based on the time-varying multi-derivative motion state of the current actuator, the leakage energy term caused by nonlinear overflow cross correction operator is calculated, and the leakage energy term is dynamically deducted from the initial vibration excitation field energy index to obtain the intrinsic perturbation energy functional.

[0059] Control unit: The intrinsic perturbation energy functional is imported into a preset multivariate gradient threshold discrimination matrix for state interval comparison, a nonlinear convergence feedback law is constructed to solve the time scale scaling factor online, and the time scale scaling factor is used to adaptively and dynamically adjust the energy injection rate of the physical trajectory vector in the subsequent interpolation time slot.

[0060] Example 3: An electronic device includes a memory and a processor. The memory stores a computer program. When the computer program is called and executed by the processor, it implements the steps in the timing trajectory vibration suppression method for a multi-degree-of-freedom motion actuator as described in Example 1.

[0061] Example 4: A computer-readable medium storing a computer program, which, when executed by a computer, implements the steps in the timing trajectory vibration suppression method for a multi-degree-of-freedom motion actuator as described in Example 1.

[0062] Unless otherwise specified, all embodiments of this invention are existing technologies or can be implemented using existing technologies. The above descriptions are merely preferred embodiments of this invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the inventive concept of this invention, and these modifications and improvements all fall within the protection scope of this invention.

Claims

1. A method for suppressing vibrations in the timing trajectory of a multi-degree-of-freedom motion actuator, characterized in that, Includes the following steps: Step 1: In real time, the physical trajectory vector of the motion actuator in the time sequence high-dimensional space is acquired within the set discrete sampling time slot. The physical trajectory vector is decoupled in the time and frequency domains using an adaptive time-domain filtering operator and separated into multi-dimensional modal components that represent macroscopic rigid body displacement components and microscopic flexible high-frequency disturbance components. Step 2: Construct a generalized dynamic equivalent multivariate second-order state-space operator. Inject the macroscopic rigid body displacement component and the microscopic flexible high-frequency disturbance component into the state-space operator as external generalized non-conservative force excitation vectors, respectively. Obtain the initial background excitation field energy index and the initial vibration excitation field energy index by constructing a quadratic form of the state vector and quantizing it online. Step 3: Based on the time-varying multi-derivative motion state of the current actuator, the leakage energy term caused by nonlinear overflow cross correction operator is calculated, and the leakage energy term is dynamically deducted from the initial vibration excitation field energy index to obtain the intrinsic perturbation energy functional. Step 4: Import the intrinsic perturbation energy functional into a preset multivariate gradient threshold discrimination matrix for state interval comparison, construct a nonlinear convergence feedback law to solve the time scale scaling factor online, and use the time scale scaling factor to adaptively and dynamically adjust the energy injection rate of the physical trajectory vector in the subsequent interpolation time slot.

2. The method for suppressing vibration of a multi-degree-of-freedom motion actuator's timing trajectory according to claim 1, characterized in that, In step one, the adaptive time-domain filtering operator is any one of the Kalman decoupling filtering operator, the adaptive center frequency Wiener filtering operator, or the dynamic time-varying band-stopping operator, and the filtering response bandwidth and cutoff frequency of the operator are dynamically reconstructed online with the spatial evolution of the time-varying physical pose or load inertia of the displacement actuator.

3. The method for suppressing vibrations in the timing trajectory of a multi-degree-of-freedom motion actuator according to claim 1, characterized in that, In step two, the characteristic parameters of the equivalent mass matrix, equivalent damping matrix, and equivalent stiffness matrix corresponding to the generalized dynamic equivalent multivariate second-order state-space operator are obtained by time-series updates through online recursive least squares parameter estimation methods or offline multi-frequency calibration and frequency sweep identification mechanisms.

4. The method for suppressing vibrations in the timing trajectory of a multi-degree-of-freedom motion actuator according to claim 1, characterized in that, In step three, the nonlinear overflow cross-correction operator is a nonlinear mapping operator constructed based on the frequency band cross-over overlap area function of macroscopic rigid body displacement components and microscopic flexible high-frequency disturbance components in the transition band of the adaptive time-domain filter operator, combined with the time-varying acceleration and the higher-order derivative vector of jerk.

5. The method for suppressing vibration of the timing trajectory of a multi-degree-of-freedom motion actuator according to claim 1, characterized in that, In step four, the online calculation and adaptive closed-loop dynamic adjustment of the time scale scaling factor includes: When the intrinsic perturbation energy functional is in the unscented stable region, the time scale scaling factor is constantly mapped to a saturated all-pass value of 1.0; When the intrinsic perturbation energy functional is in the asymptotic perturbation region, the time scale scaling factor decreases smoothly and steadily with the increase of deformation energy flow according to the nonlinear logarithmic decay control law. When the intrinsic perturbation energy functional is in a high-risk instability region, the time scale scaling factor is forcibly assigned a set hard-limiting penalty constant, and the interpolator is activated at the same time to reconstruct the time-series trajectory.

6. The method for suppressing vibration of the timing trajectory of a multi-degree-of-freedom motion actuator according to claim 5, characterized in that, In step four, the energy injection rate of the physical trajectory vector in the subsequent interpolation time slot is adaptively and dynamically adjusted using the time scale scaling factor. This includes at least one of the following: real-time inverse modulation of the trajectory feed rate of the multi-axis interpolator, online dynamic compensation of the spatial position coordinate command of the high-dimensional physical trajectory vector, and reconstruction of the time-domain velocity curve control law for the current discrete interpolation segment.

7. A vibration damping device for the timing trajectory of a multi-degree-of-freedom motion actuator, characterized in that, include: Decoupling unit: used to collect the temporal high-dimensional spatial state physical trajectory vector of the motion actuator in real time within a set discrete sampling time slot, and use an adaptive time-domain filtering operator to decouple the physical trajectory vector in the time and frequency domain, separating it into multi-dimensional modal components that characterize macroscopic rigid body displacement components and microscopic flexible high-frequency disturbance components. Energy index quantization unit: used to construct a generalized dynamic equivalent multivariate second-order state-space operator, injecting the macroscopic rigid body displacement component and the microscopic flexible high-frequency disturbance component as external generalized non-conservative force excitation vectors into the state-space operator, and obtaining the initial background excitation field energy index and the initial vibration excitation field energy index by constructing a quadratic form of the state vector for online quantization. Energy correction unit: Based on the time-varying multi-derivative motion state of the current actuator, the leakage energy term caused by nonlinear overflow cross correction operator is calculated, and the leakage energy term is dynamically deducted from the initial vibration excitation field energy index to obtain the intrinsic perturbation energy functional. Control unit: The intrinsic perturbation energy functional is imported into a preset multivariate gradient threshold discrimination matrix for state interval comparison, a nonlinear convergence feedback law is constructed to solve the time scale scaling factor online, and the time scale scaling factor is used to adaptively and dynamically adjust the energy injection rate of the physical trajectory vector in the subsequent interpolation time slot.

8. An electronic device, characterized in that, It includes a memory and a processor, wherein the memory stores a computer program, and when the computer program is invoked and executed by the processor, it implements the steps of the method as described in any one of claims 1-6.

9. A computer-readable medium, characterized in that, The computer-readable medium stores a computer program that, when executed by a computer, implements the steps of the method as described in any one of claims 1-6.

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