Harmonic oscillator-based nonlinear dynamic control method for vibration standing wave measurement angle

Abstract

The invention discloses a nonlinear dynamic control method for a vibration standing wave measurement angle based on a harmonic oscillator, and relates to the technical field of inertial measurement, and the method comprises the following steps: S1, system modeling and characteristic analysis; s2, determining a control target; determining expected performance indexes including stability, tracking error, response speed and anti-interference capability; s3, selecting a nonlinear control method; selecting a non-linear control method according to the non-linear degree, the real-time requirement and the robustness requirement; s4, designing a controller to meet the dynamic control target of the system; s5, verification and optimization are carried out; the performance of the controller is verified in simulation and actual environments, and control parameters are adjusted to meet performance requirements. According to the invention, through system modeling, control target determination, nonlinear control method selection, controller design and verification optimization, the accuracy and stability of the harmonic oscillator vibration standing wave measurement angle are ensured. The method can adapt to different non-linear degrees, real-time requirements and robustness requirements, and the comprehensive performance of a measurement system is improved.

Description

Technical Field

[0001] The invention relates to the technical field of inertial measurement, and in particular to a nonlinear dynamic control method for measuring angles of vibration standing waves based on a harmonic oscillator. Background Art

[0002] The hemispherical resonator gyroscope is a high-performance solid-state vibrating gyroscope with the characteristics of long life, high reliability and high precision. The vibration standing wave measurement angle of the hemispherical resonator is a technology based on the principle of resonator vibration, which is used to measure the rotation angle or angular velocity. Specifically, when a hemispherical resonator is excited to vibrate, it forms standing waves with specific antinodes and nodes. When the carrier of the hemispherical resonator does not rotate, the positions of these antinodes and nodes remain unchanged. However, once the carrier begins to rotate, the standing wave will precess, that is, the positions of the antinodes and nodes will change as the carrier rotates. There is a fixed proportional relationship between the precession angle and the rotation angle of the carrier, and this proportional relationship is called the precession factor. By measuring this precession angle, the rotation angle or angular velocity of the carrier can be calculated.

[0003] When the hemispherical resonator is measuring vibration standing waves, the damping of the hemispherical resonator and the internal defects, uneven mass distribution, residual stress, geometric dimension deviation caused by the processing process will cause the resonance frequencies of the resonator axes to be unequal, resulting in the standing wave drift of the hemispherical resonator, which greatly affects the final performance of the gyroscope. In the prior art, a mathematical model for compensating the measurement system is designed based on the characteristics of the oscillator's defects. However, the performance of the oscillator is overly dependent on the mathematical model. When nonlinear errors and interference occur, the system loses stability, causing the model to collapse. Summary of the invention

[0004] The present invention aims to provide a nonlinear dynamic control method for measuring the angle of vibration standing wave based on a resonator to solve the above problems.

[0005] The present invention is achieved through the following technical solutions: The nonlinear dynamic control method of the vibration standing wave measurement angle based on the harmonic oscillator includes the following steps: S1: System modeling and characterization analysis; Obtain the mathematical model of the resonator system and analyze the factors that affect the vibration standing wave measurement angle in the system; S2: Determine control objectives; Determine the expected performance indicators, including stability, tracking error, response speed, and anti-interference ability; S3: Nonlinear control method selection; Select the nonlinear control method based on the degree of nonlinearity, real-time requirements, and robustness requirements; S4: Controller design to meet the system dynamic control objectives; S5: Validation and Optimization; Verify controller performance in simulation and real environments and adjust control parameters to meet performance requirements.

[0006] The present invention ensures the accuracy and stability of the angle of the resonator vibration standing wave measurement through system modeling, determination of control targets, selection of nonlinear control methods, controller design and verification optimization. This method can adapt to different nonlinear degrees, real-time requirements and robustness requirements, and improves the comprehensive performance of the measurement system.

[0007] Preferably, in S1, it specifically includes the following steps: S1.1: Obtain the mathematical model of the resonator system, including the vibration equation of the resonator, the formation mechanism of standing waves and its influence on the rotation angle measurement; S1.2: Analyze the factors that affect the vibration standing wave measurement angle in the system, including the damping of the resonator, internal defects, uneven mass distribution, residual stress and geometric dimension deviation; S1.3: Establish a mathematical model of the resonant frequency of each axis of the resonator and analyze its influence on the standing wave drift.

[0008] The present invention enhances the understanding of the vibration characteristics of the system by obtaining the mathematical model of the resonator system and analyzing the influencing factors, so that the standing wave measurement angle can be controlled more accurately. Specifically, key factors such as damping and internal defects are identified, providing important references for subsequent control strategies.

[0009] Preferably, in S2, it specifically includes the following steps: S2.1: Determine the expected performance indicators, including system stability, tracking error, response speed, and anti-interference ability.

[0010] S2.2: Confirm the control objectives, which include controlling the standing wave drift error within ±0.01°, the response time not exceeding 1ms, and the anti-interference ability reaching ±100g acceleration.

[0011] The present invention clarifies the performance indicators and control objectives, so that the control method can be optimized according to specific performance requirements.

[0012] Preferably, in S3, it specifically includes the following steps: S3.1: Select appropriate nonlinear control methods, including sliding mode control methods, based on the degree of system nonlinearity, real-time requirements, and robustness requirements.

[0013] S3.2: Analyze the applicability and advantages of the selected nonlinear control method.

[0014] The present invention improves the applicability and advantages of the control strategy by selecting an appropriate nonlinear control method, such as sliding mode control. This method can adapt to the nonlinear characteristics of the system and improve the real-time and robustness of the control.

[0015] Preferably, in S4, it specifically includes the following steps: S4.1: Design nonlinear controllers to meet the system dynamic control objectives. Controller design includes controller design, parameter optimization, and algorithm implementation.

[0016] S4.2: The controller adjusts the excitation parameters of the resonator, such as the excitation frequency and amplitude, in real time to suppress the standing wave drift and improve the measurement accuracy.

[0017] The present invention realizes real-time adjustment of the resonator excitation parameters by designing a nonlinear controller, effectively suppresses standing wave drift, and improves measurement accuracy. This method optimizes the dynamic response of the system by accurately controlling the excitation frequency and amplitude.

[0018] Preferably, in S5, it specifically includes the following steps: S5.1: Verify the performance of the controller through simulation and experiments, including stability, tracking error, response speed, and anti-interference ability.

[0019] S5.2: Optimize the controller based on the verification results, such as adjusting control parameters, improving control algorithms, and optimizing system structure to further improve the performance of the controller.

[0020] The present invention ensures that the performance of the controller meets the requirements of stability, tracking error, response speed and anti-interference ability through simulation and experimental verification. The optimization step further improves the performance of the controller, making it more reliable in practical applications.

[0021] Preferably, in S4, the nonlinear controller includes a sliding mode controller, which specifically includes the following: By introducing the sliding surface equation: ; in, is the sliding surface, which is used to describe the state and control objectives of the system; is the standing wave drift error, which represents the deviation between the actual vibration of the resonator and the expected vibration; is a positive proportional coefficient, used to adjust the strength of sliding mode control; It is the integral of the error, which is used to accumulate historical error information and enhance the robustness of control; Modify the control law of the sliding mode controller, use adaptive gain, and dynamically adjust the gain according to the size of the standing wave drift error to improve the robustness and accuracy of the control; The adaptive gain adjustment formula is as follows: ; in is the dynamically adjusted gain, is the initial gain, is the gain adjustment factor, is the absolute value of the error, which is used to dynamically adjust the gain according to the error size; The performance of the sliding mode controller under different disturbance and uncertainty conditions is verified through simulation to ensure the stability and reliability of the controller in practical applications.

[0022] The present invention introduces a sliding mode controller, which enhances the robustness and accuracy of control through sliding mode surface equation and adaptive gain adjustment. This method can dynamically adjust the control accuracy, adapt to different interference and uncertain conditions, and ensure the stability and reliability of the controller.

[0023] Preferably, in S4, the nonlinear controller includes an adaptive controller, specifically including the following: By learning the parameter changes of the resonator online, the control parameters can be adjusted in real time to adapt to different working conditions.

[0024] Introducing the adaptive law: ; in Control parameters for real-time adjustment; is the initial control parameter; is the adaptive gain, used to adjust the update rate of the control parameters; is the standing wave drift error, which represents the deviation between the actual vibration of the resonator and the expected vibration; is the derivative of the control parameter, indicating the rate at which the parameter is updated; Verify the performance of the adaptive controller under different environmental conditions through experiments to ensure the adaptability and reliability of the controller under complex conditions; Nonlinear controllers also include neural network controllers, which include the following: By training the neural network model, the nonlinear dynamic characteristics of the resonator are learned to achieve precise control of the standing wave drift.

[0025] The weight update of the neural network controller is expressed as follows: ; in is the learning rate, which is used to control the step size of weight update. is the updated weight; is the gradient of the error function with respect to the weight, indicating the direction of weight update; The performance of the neural network controller under different interference conditions is verified through experiments to ensure the adaptability and reliability of the controller in practical applications.

[0026] The present invention realizes online learning of harmonic oscillator parameter changes and nonlinear dynamic characteristics through an adaptive controller and a neural network controller. This method improves the adaptability and reliability of the controller, especially under complex and changing working conditions.

[0027] Preferably, in S4, the sliding mode controller, the adaptive controller and the neural network controller are integrated by a multi-modal control method: The multi-modal control method comprises the following steps: Combining the advantages of sliding mode control, adaptive control and neural network control, the comprehensive control of the resonator is realized; Determine the multi-modal control fusion function and introduce switching logic to select the appropriate control mode according to different working conditions to improve the flexibility and robustness of control; Verify the performance of the multi-mode nonlinear controller through simulation and experiments to ensure the efficiency and reliability of the controller under different working conditions; The multi-modal control fusion function specifically includes the following: Multimodal control fusion Defined as: ; in, It is a sliding mode control strategy; It is an adaptive control strategy; It is a neural network control strategy; is the final control input; , and are the weights of sliding mode control, adaptive control and neural network control, respectively. ; The present invention integrates sliding mode control, adaptive control and neural network control through a multi-modal control method, thereby improving the flexibility and robustness of control. This method can select a suitable control mode according to different working conditions, ensuring the efficiency and reliability of the controller under different conditions.

[0028] Preferably, in S5.2, it includes: Through frequency domain analysis, the frequency domain characteristics of the resonant subsystem, including the resonant frequency and damping ratio, are identified, and the frequency domain characteristics of the controller are optimized; The formula for frequency domain analysis is expressed as: ; in, is the spectrum function after diffraction, indicating the change of the frequency domain signal after passing through the resonant subsystem, and represents the response characteristics of the resonant subsystem to different frequency components; is the original spectrum function, which represents the frequency domain signal input to the resonant subsystem and represents the frequency domain representation of the external excitation or initial condition; is the physical size or characteristic length of the resonator; The corresponding coordinate system on the frequency domain spectrum, namely the spatial frequency, represents the frequency response of the resonator system in different directions; It is the distance that the signal propagates or acts in the resonator system.

[0029] Genetic algorithm is used to optimize the controller parameters to improve the control accuracy and stability.

[0030] The performance of the frequency domain optimization controller is verified through experiments to ensure the adaptability and reliability of the controller under different frequency domain conditions.

[0031] The present invention identifies the frequency domain characteristics of the resonator system and optimizes the controller parameters through frequency domain analysis and genetic algorithm optimization. This method improves the adaptability and reliability of the controller under different frequency domain conditions and ensures the optimization of the controller performance.

[0032] Compared with the prior art, the present invention has the following advantages and beneficial effects: The present invention proposes a nonlinear dynamic control method for measuring the vibration standing wave angle of a resonator, the core of which is to achieve precise control of the vibration characteristics of the resonator through systematic steps to improve the accuracy and stability of the measurement angle. First, by obtaining the mathematical model of the resonator system and analyzing the influencing factors, the understanding of the vibration characteristics of the system is enhanced, which provides an important reference for the subsequent control strategy. Selecting an appropriate nonlinear control method, such as sliding mode control, improves the applicability and advantages of the control strategy, and enhances the real-time and robustness of the control. Designing a nonlinear controller realizes real-time adjustment of the resonator excitation parameters, effectively suppresses the standing wave drift, and improves the measurement accuracy. Through simulation and experimental verification, it is ensured that the performance of the controller meets the requirements of stability, tracking error, response speed and anti-interference ability, and further optimizes the performance of the controller, making it more reliable in practical applications. The introduction of sliding mode controller and adaptive gain adjustment enhances the robustness and accuracy of the control, and can dynamically adjust the control accuracy to adapt to different interference and uncertain conditions. Through the adaptive controller and the neural network controller, the online learning of the resonator parameter changes and the learning of nonlinear dynamic characteristics are realized, and the adaptability and reliability of the controller are improved. Finally, by integrating sliding mode control, adaptive control and neural network control through multi-modal control methods, the flexibility and robustness of control are improved, ensuring the efficiency and reliability of the controller under different conditions. Through frequency domain analysis and genetic algorithm optimization, the frequency domain characteristics of the resonator system are identified, and the controller parameters are optimized, which improves the adaptability and reliability of the controller under different frequency domain conditions. In summary, the method of this patent can ensure high-precision measurement of the resonator in complex environments, which is of great significance for improving the application scope and reliability of vibration standing wave measurement technology. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] The drawings described herein are used to provide a further understanding of the embodiments of the present invention, constitute a part of this application, and do not constitute a limitation of the embodiments of the present invention. In the drawings: Figure 1 It is a schematic diagram of the steps of the present invention. DETAILED DESCRIPTION

[0034] In order to make the purpose, technical scheme and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the embodiments and drawings. The schematic implementation modes and descriptions of the present invention are only used to explain the present invention and are not intended to limit the present invention. It should be noted that the present invention is already in the actual development and use stage.

[0035] Embodiment: like Figure 1 As shown, the nonlinear dynamic control method of the vibration standing wave measurement angle based on the resonator includes the following steps: S1: System modeling and characterization analysis; Obtain the mathematical model of the resonator system and analyze the factors that affect the vibration standing wave measurement angle in the system; S2: Determine control objectives; Determine the expected performance indicators, including stability, tracking error, response speed, and anti-interference ability; S3: Nonlinear control method selection; Select the nonlinear control method based on the degree of nonlinearity, real-time requirements, and robustness requirements; S4: Controller design to meet the system dynamic control objectives; S5: Validation and Optimization; Verify controller performance in simulation and real environments and adjust control parameters to meet performance requirements.

[0036] The present invention ensures the accuracy and stability of the angle of the resonator vibration standing wave measurement through system modeling, determination of control targets, selection of nonlinear control methods, controller design and verification optimization. This method can adapt to different nonlinear degrees, real-time requirements and robustness requirements, and improves the comprehensive performance of the measurement system.

[0037] In this embodiment, in S1, it specifically includes the following steps: S1.1: Obtain the mathematical model of the resonator system, including the vibration equation of the resonator, the formation mechanism of standing waves and its influence on the rotation angle measurement; The resonator of the present invention is a physical system that can vibrate with maximum amplitude at a specific frequency (called resonant frequency). In this embodiment, the resonator is used to measure the angle by analyzing the characteristics of its vibration standing wave. The vibration standing wave refers to a stable vibration mode formed on the resonator. This mode appears as a wave residence in space and is usually formed by the interference of two traveling waves with the same frequency and amplitude but opposite phases.

[0038] In this embodiment, obtaining the mathematical model of the resonator system refers to creating a mathematical model to describe the dynamic behavior of the system. Characteristic analysis refers to analyzing these models to identify key factors that affect system performance.

[0039] S1.2: Analyze the factors that affect the vibration standing wave measurement angle in the system, including the damping of the resonator, internal defects, uneven mass distribution, residual stress and geometric dimension deviation; S1.3: Establish a mathematical model of the resonant frequency of each axis of the resonator and analyze its influence on the standing wave drift.

[0040] The present invention enhances the understanding of the vibration characteristics of the system by obtaining the mathematical model of the resonator system and analyzing the influencing factors, so that the standing wave measurement angle can be controlled more accurately. Specifically, key factors such as damping and internal defects are identified, providing important references for subsequent control strategies.

[0041] In this embodiment, in S2, it specifically includes the following steps: S2.1: Determine the expected performance indicators, including system stability, tracking error, response speed, and anti-interference ability.

[0042] S2.2: Confirm the control objectives, which include controlling the standing wave drift error within ±0.01°, the response time not exceeding 1ms, and the anti-interference ability reaching ±100g acceleration.

[0043] The present invention clarifies the performance indicators and control objectives, so that the control method can be optimized according to specific performance requirements.

[0044] In this embodiment, in S3, it specifically includes the following steps: S3.1: Select appropriate nonlinear control methods, including sliding mode control methods, based on the degree of system nonlinearity, real-time requirements, and robustness requirements.

[0045] S3.2: Analyze the applicability and advantages of the selected nonlinear control method.

[0046] The present invention improves the applicability and advantages of the control strategy by selecting an appropriate nonlinear control method, such as sliding mode control. This method can adapt to the nonlinear characteristics of the system and improve the real-time and robustness of the control.

[0047] In this embodiment, in S4, it specifically includes the following steps: S4.1: Design nonlinear controllers to meet the system dynamic control objectives. Controller design includes controller design, parameter optimization, and algorithm implementation.

[0048] S4.2: The controller adjusts the excitation parameters of the resonator, such as the excitation frequency and amplitude, in real time to suppress the standing wave drift and improve the measurement accuracy.

[0049] The present invention realizes real-time adjustment of the resonator excitation parameters by designing a nonlinear controller, effectively suppresses standing wave drift, and improves measurement accuracy. This method optimizes the dynamic response of the system by accurately controlling the excitation frequency and amplitude.

[0050] In this embodiment, in S5, it specifically includes the following steps: S5.1: Verify the performance of the controller through simulation and experiments, including stability, tracking error, response speed, and anti-interference ability.

[0051] S5.2: Optimize the controller based on the verification results, such as adjusting control parameters, improving control algorithms, and optimizing system structure to further improve the performance of the controller.

[0052] The present invention ensures that the performance of the controller meets the requirements of stability, tracking error, response speed and anti-interference ability through simulation and experimental verification. The optimization step further improves the performance of the controller, making it more reliable in practical applications.

[0053] In this embodiment, in S4, the nonlinear controller includes a sliding mode controller, which specifically includes the following: By introducing the sliding surface equation: ; in, is the sliding surface, which is used to describe the state and control objectives of the system; is the standing wave drift error, which represents the deviation between the actual vibration of the resonator and the expected vibration; is a positive proportional coefficient, used to adjust the strength of sliding mode control; It is the integral of the error, which is used to accumulate historical error information and enhance the robustness of control; Modify the control law of the sliding mode controller, use adaptive gain, and dynamically adjust the gain according to the size of the standing wave drift error to improve the robustness and accuracy of the control; The adaptive gain adjustment formula is as follows: ; in is the dynamically adjusted gain, is the initial gain, is the gain adjustment factor, is the absolute value of the error, which is used to dynamically adjust the gain according to the error size; The performance of the sliding mode controller under different disturbance and uncertainty conditions is verified through simulation to ensure the stability and reliability of the controller in practical applications.

[0054] It can be understood that sliding mode control is a nonlinear control strategy that designs a sliding surface and a control law so that the system state can reach and slide along the sliding surface, thereby achieving the desired performance.

[0055] The present invention introduces a sliding mode controller, which enhances the robustness and accuracy of control through sliding mode surface equation and adaptive gain adjustment. This method can dynamically adjust the control accuracy, adapt to different interference and uncertain conditions, and ensure the stability and reliability of the controller.

[0056] In this embodiment, in S4, the nonlinear controller includes an adaptive controller, which specifically includes the following: By learning the parameter changes of the resonator online, the control parameters can be adjusted in real time to adapt to different working conditions.

[0057] Introducing the adaptive law: ; in Control parameters for real-time adjustment; is the initial control parameter; is the adaptive gain, used to adjust the update rate of the control parameters; is the standing wave drift error, which represents the deviation between the actual vibration of the resonator and the expected vibration; is the derivative of the control parameter, indicating the rate at which the parameter is updated; Verify the performance of the adaptive controller under different environmental conditions through experiments to ensure the adaptability and reliability of the controller under complex conditions; It can be understood that an adaptive controller is a controller that can automatically adjust control parameters according to changes in system parameters or changes in external conditions.

[0058] Nonlinear controllers also include neural network controllers, which include the following: By training the neural network model, the nonlinear dynamic characteristics of the resonator are learned to achieve precise control of the standing wave drift.

[0059] The weight update of the neural network controller is expressed as follows: ; in is the learning rate, which is used to control the step size of weight update. is the updated weight; is the gradient of the error function with respect to the weight, indicating the direction of weight update; The performance of the neural network controller under different interference conditions is verified through experiments to ensure the adaptability and reliability of the controller in practical applications.

[0060] The present invention realizes online learning of harmonic oscillator parameter changes and nonlinear dynamic characteristics through an adaptive controller and a neural network controller. This method improves the adaptability and reliability of the controller, especially under complex and changing working conditions.

[0061] The standing wave drift error refers to the deviation between the actual vibration of the resonator and the expected vibration, and this deviation may lead to inaccurate measurement of the angle.

[0062] It can be understood that a neural network controller is a controller that uses artificial neural networks to learn the dynamic characteristics of the system and make control decisions.

[0063] In this embodiment, in S4, the sliding mode controller, the adaptive controller and the neural network controller are integrated through a multi-modal control method: The multi-modal control method comprises the following steps: Combining the advantages of sliding mode control, adaptive control and neural network control, the comprehensive control of the resonator is realized; Determine the multi-modal control fusion function and introduce switching logic to select the appropriate control mode according to different working conditions to improve the flexibility and robustness of control; Verify the performance of the multi-mode nonlinear controller through simulation and experiments to ensure the efficiency and reliability of the controller under different working conditions; The multi-modal control fusion function specifically includes the following: Multimodal control fusion Defined as: ; in, It is a sliding mode control strategy; It is an adaptive control strategy; It is a neural network control strategy; is the final control input; , and are the weights of sliding mode control, adaptive control and neural network control, respectively. ; The present invention integrates sliding mode control, adaptive control and neural network control through a multi-modal control method, thereby improving the flexibility and robustness of control. This method can select a suitable control mode according to different working conditions, ensuring the efficiency and reliability of the controller under different conditions.

[0064] In this embodiment, S5.2 includes: Through frequency domain analysis, the frequency domain characteristics of the resonant subsystem, including the resonant frequency and damping ratio, are identified, and the frequency domain characteristics of the controller are optimized; The formula for frequency domain analysis is expressed as: ; in, is the spectrum function after diffraction, indicating the change of the frequency domain signal after passing through the resonant subsystem, and represents the response characteristics of the resonant subsystem to different frequency components; is the original spectrum function, which represents the frequency domain signal input to the resonant subsystem and represents the frequency domain representation of the external excitation or initial condition; is the physical size or characteristic length of the resonator; The corresponding coordinate system on the frequency domain spectrum, namely the spatial frequency, represents the frequency response of the resonator system in different directions; It is the distance that the signal propagates or acts in the resonator system.

[0065] Genetic algorithm is used to optimize the controller parameters to improve the control accuracy and stability.

[0066] The performance of the frequency domain optimization controller is verified through experiments to ensure the adaptability and reliability of the controller under different frequency domain conditions.

[0067] The present invention identifies the frequency domain characteristics of the resonator system and optimizes the controller parameters through frequency domain analysis and genetic algorithm optimization. This method improves the adaptability and reliability of the controller under different frequency domain conditions and ensures the optimization of the controller performance.

[0068] In this embodiment, the genetic algorithm is a heuristic search algorithm that imitates the process of natural selection and is used to solve optimization and search problems.

[0069] The specific implementation methods described above further illustrate the objectives, technical solutions and beneficial effects of the present invention in detail. It should be understood that the above description is only a specific implementation method of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A nonlinear dynamic control method for measuring angle of vibration standing wave based on a resonator, characterized in that: The steps include: S1: System modeling and characterization analysis; Obtain the mathematical model of the resonator system and analyze the factors that affect the vibration standing wave measurement angle in the system; S2: Determine control objectives; Determine the expected performance indicators, including stability, tracking error, response speed, and anti-interference ability; S3: Nonlinear control method selection; Select the nonlinear control method based on the degree of nonlinearity, real-time requirements, and robustness requirements; S4: Controller design to meet the system dynamic control objectives; S5: Validation and Optimization; Verify controller performance in simulation and real environments and adjust control parameters to meet performance requirements.

2. The nonlinear dynamic control method for measuring angle of vibration standing wave based on a harmonic oscillator according to claim 1, characterized in that: In S1, it specifically includes the following steps: S1.1: Obtain the mathematical model of the resonator system, including the vibration equation of the resonator, the formation mechanism of standing waves and its influence on the rotation angle measurement; S1.2: Analyze the factors that affect the vibration standing wave measurement angle in the system, including the damping of the resonator, internal defects, uneven mass distribution, residual stress and geometric dimension deviation; S1.3: Establish a mathematical model of the resonant frequency of each axis of the resonator and analyze its influence on the standing wave drift.

3. The nonlinear dynamic control method for measuring angle of vibration standing wave based on a harmonic oscillator according to claim 1, characterized in that: In S2, it specifically includes the following steps: S2.1: Determine the expected performance indicators, including system stability, tracking error, response speed and anti-interference ability; S2.2: Confirm the control objectives, which include controlling the standing wave drift error within ±0.01°, the response time not exceeding 1ms, and the anti-interference ability reaching ±100g acceleration.

4. The nonlinear dynamic control method for measuring angle of vibration standing wave based on a harmonic oscillator according to claim 1, characterized in that: In S3, it specifically includes the following steps: S3.1: Select appropriate nonlinear control methods, including sliding mode control, based on the system nonlinearity, real-time requirements, and robustness requirements; S3.2: Analyze the applicability and advantages of the selected nonlinear control method and output strategy.

5. The nonlinear dynamic control method for measuring angle of vibration standing wave based on a harmonic oscillator according to claim 1, characterized in that: In S4, it specifically includes the following steps: S4.1: Design nonlinear controllers to meet the system dynamic control objectives. Controller design includes the design of control laws, parameter optimization, and algorithm implementation. S4.2: The controller adjusts the excitation parameters of the resonator, including the excitation frequency and amplitude, in real time to suppress the standing wave drift and improve the measurement accuracy.

6. The nonlinear dynamic control method for measuring angle of vibration standing wave based on a harmonic oscillator according to claim 1, characterized in that: In S5, it specifically includes the following steps: S5.1: Verify the performance of the controller through simulation and experiments, including stability, tracking error, response speed and anti-interference ability; S5.2: Optimize the controller based on the verification results, including adjusting control parameters, improving control algorithms and optimizing system structure to further improve the performance of the controller.

7. The nonlinear dynamic control method for measuring angle of vibration standing wave based on a harmonic oscillator according to claim 5, characterized in that: In S4.1, the nonlinear controller includes a sliding mode controller, which includes the following: By introducing the sliding surface equation: ； in, is the sliding surface, which is used to describe the state and control objectives of the system; is the standing wave drift error, which represents the deviation between the actual vibration of the resonator and the expected vibration; is a positive proportional coefficient, used to adjust the strength of sliding mode control; It is the integral of the error, which is used to accumulate historical error information and enhance the robustness of control; Modify the control law of the sliding mode controller, use adaptive gain, and dynamically adjust the gain according to the size of the standing wave drift error to improve the robustness and accuracy of the control; The adaptive gain adjustment formula is as follows: ； in is the dynamically adjusted gain, is the initial gain, is the gain adjustment factor, is the absolute value of the error, which is used to dynamically adjust the gain according to the error size; The performance of the sliding mode controller under different disturbance and uncertainty conditions is verified through simulation to ensure the stability and reliability of the controller in practical applications.

8. The nonlinear dynamic control method for measuring angle of vibration standing wave based on a harmonic oscillator according to claim 7, characterized in that: In S4, the nonlinear controller includes an adaptive controller, which specifically includes the following: By learning the parameter changes of the resonator online, the control parameters can be adjusted in real time to adapt to different working conditions; Introducing the adaptive law: ； in Control parameters for real-time adjustment; is the initial control parameter; is the adaptive gain, used to adjust the update rate of the control parameters; is the standing wave drift error, which represents the deviation between the actual vibration of the resonator and the expected vibration; is the derivative of the control parameter, indicating the rate at which the parameter is updated; Verify the performance of the adaptive controller under different environmental conditions through experiments to ensure the adaptability and reliability of the controller under complex conditions; Nonlinear controllers also include neural network controllers, which include the following: By training the neural network model, the nonlinear dynamic characteristics of the resonator are learned to achieve precise control of the standing wave drift; The weight update of the neural network controller is expressed as follows: ； in is the learning rate, which is used to control the step size of weight update. is the updated weight; is the gradient of the error function with respect to the weight, indicating the direction of weight update; The performance of the neural network controller under different interference conditions is verified through experiments to ensure the adaptability and reliability of the controller in practical applications.

9. The nonlinear dynamic control method for measuring angle of vibration standing wave based on a harmonic oscillator according to claim 8, characterized in that: In S4, the sliding mode controller, adaptive controller and neural network controller are integrated through a multi-modal control method: The multi-modal control method comprises the following steps: Combining the advantages of sliding mode control, adaptive control and neural network control, the comprehensive control of the resonator is realized; Determine the multi-modal control fusion function and introduce switching logic to select the appropriate control mode according to different working conditions to improve the flexibility and robustness of control; Verify the performance of the multi-mode nonlinear controller through simulation and experiments to ensure the efficiency and reliability of the controller under different working conditions; The multi-modal control fusion function specifically includes the following: Multimodal control fusion Defined as: ； in, It is a sliding mode control strategy; It is an adaptive control strategy; It is a neural network control strategy; is the final control input; , and are the weights of sliding mode control, adaptive control and neural network control, respectively. .

10. The nonlinear dynamic control method for measuring angle of vibration standing wave based on a harmonic oscillator according to claim 6, characterized in that: In S5.2, include: Through frequency domain analysis, the frequency domain characteristics of the resonant subsystem, including the resonant frequency and damping ratio, are identified, and the frequency domain characteristics of the controller are optimized; The formula for frequency domain analysis is expressed as: ； in, is the spectrum function after diffraction, indicating the change of the frequency domain signal after passing through the resonant subsystem, and represents the response characteristics of the resonant subsystem to different frequency components; is the original spectrum function, which represents the frequency domain signal input to the resonant subsystem and represents the frequency domain representation of the external excitation or initial condition; is the physical size or characteristic length of the resonator; The corresponding coordinate system on the frequency domain spectrum, namely the spatial frequency, represents the frequency response of the resonator system in different directions; is the distance that the signal propagates or acts in the resonator system; Use genetic algorithm to optimize controller parameters; The performance of the frequency domain optimization controller is verified through experiments to ensure the adaptability and reliability of the controller under different frequency domain conditions.

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