Error identification and compensation method for hemispherical resonator gyro based on sinusoidal virtual rotation

Abstract

A kind of error identification compensation method of hemispherical resonator gyro based on sinusoidal virtual rotation, including phase error correlation signal modulation, phase error demodulation, phase error closed-loop compensation, gain error identification compensation etc., can realize high-precision online identification and compensation of phase error and gain error under the premise of reducing debugging difficulty and guaranteeing stable operation, effectively improve the scale factor and detection precision of hemispherical resonator gyro related indicators, improve overall performance, enhance system engineering practicability and reliability.

Description

Technical Field

[0001] This invention relates to the field of control measurement, and specifically to an error identification and compensation method for a hemispherical resonator gyroscope based on sinusoidal virtual rotation. Background Technology

[0002] A hemispherical resonant gyroscope is a type of vibration gyroscope that senses the angular motion of a carrier based on the circumferential precession effect of the standing wave along the lip of a hemispherical harmonic oscillator. Compared to traditional gyroscope devices, this type of gyroscope has advantages such as simple structure, high reliability, good stability, wide measurement range, and long service life, and has been widely used in aerospace, navigation and guidance, and underwater navigation fields.

[0003] Depending on the control and detection methods, hemispherical resonator gyroscopes mainly include force-balanced mode and full-angle mode. Force-balanced mode is limited by its dynamic range, making it difficult to meet the demands for large-range, high-bandwidth measurements in complex application environments. Full-angle mode, due to its larger measurement range and bandwidth, is gradually becoming an important development direction for this type of gyroscope. Full-angle mode hemispherical resonator gyroscopes mainly include continuous control schemes and time-division multiplexing control schemes. In particular, the time-division multiplexing control scheme can theoretically avoid the imbalance between drive and detection in the continuous control scheme, resulting in higher accuracy and better application prospects.

[0004] In practical applications, phase and gain errors are common in hemispherical resonator gyroscope systems. These errors directly reduce the driving efficiency of the resonator's standing wave, increase the system's energy maintenance requirements, reduce the accuracy of angular velocity detection, affect the stability of the system's scaling factor, and further weaken the stability of the closed-loop control system. They also interfere with the accuracy of identifying and compensating for manufacturing imbalances and assembly errors in the resonator. Therefore, the identification and compensation of phase and gain errors are crucial to determining the detection accuracy and long-term operational stability of hemispherical resonator gyroscopes, and have become urgent technical problems to be solved.

[0005] However, existing methods for identifying and compensating phase and gain errors, including voltage detection, amplitude control force, forgetting filter, and virtual precession, suffer from several problems. These include an inherent time delay due to the trade-off between identification accuracy and traversal efficiency, the inability to perform online real-time identification and compensation during operation, sensitivity to system parameter changes leading to poor stability and feasibility in practical engineering applications, and the presence of unexplained residual errors that may introduce short-term vibrations during identification, adversely affecting the stable operation of the system. Consequently, these methods cannot simultaneously meet the application requirements of high precision, online operation, low complexity, and no disturbance to the system. Summary of the Invention

[0006] The purpose of this invention is to overcome the shortcomings of the prior art and provide an error identification and compensation method for a hemispherical resonator gyroscope based on sinusoidal virtual rotation. This method can achieve high-precision online identification and compensation of phase error and gain error while reducing debugging difficulty and ensuring stable operation. It effectively improves the scaling factor and detection accuracy of the hemispherical resonator gyroscope, enhances overall performance, and improves the practicality and reliability of the system engineering. This invention also solves the problems of existing methods in terms of detection accuracy, working mode, debugging difficulty, and stable operation.

[0007] This invention provides a method for error identification and compensation of a hemispherical resonator gyroscope based on sinusoidal virtual rotation, comprising the following steps: (1) Based on the state equations of the hemispherical resonant gyroscope under ideal and phase error conditions, phase error correlation signal modulation is performed; (2) For the quadrature control force modulated by the phase error correlation signal, the amplitude of the sinusoidal excitation signal in the quadrature control force is obtained by multiplying and demodulating it using the known virtual rotation angular velocity and removing the high-frequency interference term by a low-pass filter. (3) Using the amplitude of the sinusoidal excitation signal as the input signal of the PID controller, the amplitude changes are tracked and the phase of the reference signal is adjusted in real time to control the amplitude of the sinusoidal excitation signal to zero, and the output value of the PID controller is fed back to the internal closed-loop control system of the hemispherical resonant gyroscope for phase error closed-loop compensation. (4) Based on the phase error identification and compensation, compare the actual detected angular velocity of the hemispherical resonant gyroscope and the applied sinusoidal virtual angular velocity to obtain a fixed proportional relationship in which the two are in phase and have the same amplitude. Then, the proportional factor compensation of the fixed proportional relationship is entered into the gyroscope's drive system to identify and compensate for the gain error.

[0008] Specifically, step (1) includes: (1.1) Based on the state equations of the hemispherical resonant gyroscope under ideal and phase error conditions, the corresponding relationships between the various control forces in the two cases are obtained respectively: (1) in, , and These represent the amplitude control force, quadrature control force, and virtual rotational force, respectively, in the presence of phase error. , and These correspond to the various control forces under ideal conditions. This represents the phase error of the hemispherical resonant gyroscope. (1.2) Set the virtual rotational angular velocity introduced by the virtual rotational force at this time. The expression is: (2) in Amplitude, Given the frequency, and combining it with the state equation of the hemispherical resonant gyroscope, the orthogonal control force at this time is obtained as: (3) in The frequency of the hemispherical harmonic oscillator is non-uniform. The resonant frequency, The resonance amplitude, Let be the angle between the stiffness axis of the harmonic oscillator and the electrode axis. , where are the scale factors of the harmonic oscillator, and are all constants.

[0009] Specifically, step (2) includes: After multiplication and demodulation using the quadrature control force modulated by the known virtual rotational angular velocity and phase error correlation signal, followed by low-pass filtering, the demodulated equation containing phase error information is obtained: (4).

[0010] Specifically, step (3) includes: (3.1) The amplitude of the sinusoidal excitation signal obtained from the demodulated equation containing phase error information is used as the input of the PID, and the amplitude control target is zero; (3.2) Utilizing the compensated phase output of the PID controller after amplitude control adjustment The initial phase of the reference signal is adjusted in real time. (3.3) Compensate phase Compensating the hemispherical resonant gyroscope system internally, we obtain the compensated equations: (5).

[0011] Specifically, step (4) includes: (4.1) The actual angular velocity detected by the hemispherical resonant gyroscope is: (6) (4.2) Combining the applied sinusoidal virtual angular velocity and the actual detected angular velocity of the hemispherical resonant gyroscope, the scaling factor is obtained: (7) (4.3) The gain error is identified and compensated during the driving process of the hemispherical resonant gyroscope by compensating the scaling factor.

[0012] Step (2) further includes detecting and controlling the amplitude of the sinusoidal excitation signal and identifying and compensating for phase errors.

[0013] In step (4), the fixed ratio of the same frequency and phase and the existence of amplitude is the magnitude of the system gain error.

[0014] The error identification and compensation method for hemispherical resonator gyroscopes based on sinusoidal virtual rotation of the present invention can achieve: 1) The method of indirectly detecting the phase error by detecting the amplitude of the sinusoidal excitation signal does not require calculating the specific value of the phase error. The amplitude of the sinusoidal excitation signal is used as the input of the PID controller, which simplifies the control process, reduces complexity, and is suitable for engineering applications.

[0015] 2) The initial phase of the reference signal is dynamically adjusted by the PID controller, resulting in a smooth control without drastic fluctuations. It can accurately identify and compensate for phase errors, effectively ensuring the detection accuracy and operational stability of the hemispherical resonator gyroscope. Through the closed-loop control circuit, the phase error can be fed back to the system in real time to achieve dynamic compensation. It can continuously track changes in phase error and has obvious advantages in online identification.

[0016] 3) It effectively avoids the problems of poor accuracy and low efficiency of the traversal optimization phase error identification method, and can take into account both high accuracy and high efficiency of detection. It also has excellent dynamic tracking characteristics. At the same time, it clarifies the necessity and practical significance of the identification and compensation order of phase error first and then phase error, which has important guiding value for practical engineering applications.

[0017] 4) The gain error of the hemispherical resonant gyroscope system driving process is obtained by quickly demodulating the virtual rotation angular velocity and then compensated for. This improves the utilization rate of the sinusoidal virtual rotation and also improves the accuracy of the gyroscope detection results, thus ensuring the stable operation of the gyroscope.

[0018] 5) No additional hardware components were added during the entire process of identifying and compensating phase error and gain error. Relying on the existing control signals and PID controller, the stability of system operation was ensured, and the implementation cost and debugging difficulty were reduced, which has high application value. Attached Figure Description

[0019] Figure 1 A schematic block diagram of an error identification and compensation method for a hemispherical resonator gyroscope based on sinusoidal virtual rotation; Figure 2 A schematic diagram of the simulation results corresponding to the constructed hemispherical resonant gyroscope model; Figure 3 This is a schematic diagram of the phase error identification and compensation results from an actual experiment. Figure 4 This is a schematic diagram of the phase error identification results after the actual phase error was artificially altered in an actual experiment. Figure 5 This is a schematic diagram comparing the simulation results of angular velocity. Figure 6 A schematic diagram of the simulation results obtained for identifying the gain error. Detailed Implementation

[0020] The specific implementation of the present invention will be described in detail below. It should be noted that the following implementation is only for further illustration of the present invention and should not be construed as a limitation on the scope of protection of the present invention. Some non-essential improvements and adjustments made to the present invention by those skilled in the art based on the above description of the present invention still fall within the scope of protection of the present invention.

[0021] This invention provides a method for error identification and compensation of a hemispherical resonator gyroscope based on sinusoidal virtual rotation, the implementation process of which is shown in the appendix. Figure 1 As shown, attached Figure 2-6 The following is a schematic diagram of the simulation / actual experimental results, followed by a detailed explanation.

[0022] Within a hemispherical resonant gyroscope system, phase error and gain error coexist and are interrelated. Phase error reduces system driving efficiency, directly causing fluctuations in the gyroscope's gain error. The accuracy of gain error identification directly depends on the accurate measurement of angular velocity. However, the presence of phase error reduces the accuracy of angular velocity detection, thus affecting the accurate identification of gain error. Therefore, it is essential to follow the order of phase error identification and compensation first, followed by gain error, to ensure the correctness of the error identification results and the normal operation of the system. Based on this, this invention provides an error identification and compensation method for a hemispherical resonant gyroscope based on sinusoidal virtual rotation, the process of which is shown in the attached figure. Figure 1 As shown, the specific steps include the following: The first step involves modulating the phase error-correlated signal based on the state equations of the hemispherical resonant gyroscope under ideal and phase error conditions. The state equations clearly demonstrate the excitation effect of the virtual rotational force on the orthogonal control force when a phase error exists. When a sinusoidally modulated virtual rotational angular velocity is introduced into the system through the virtual rotational force, this force will also excite a sinusoidal signal component with the same frequency as the virtual rotational angular velocity within the orthogonal control force. The amplitude of this sinusoidal signal is directly proportional to the phase error (proportionality coefficient less than 0). Specifically, based on the state equations of the hemispherical resonant gyroscope under ideal and phase error conditions, phase error-correlated signal modulation is performed, including the following steps: First, based on the state equations of the hemispherical resonant gyroscope under ideal and phase error conditions, the corresponding relationships between the various control forces in the two cases are obtained: (1) in, , and These represent the amplitude control force, quadrature control force, and virtual rotational force, respectively, in the presence of phase error. , and These correspond to the various control forces under ideal conditions. δφ Let be the phase error of the hemispherical resonant gyroscope; as can be seen from equation (1), when there is a phase error, the virtual rotational force will generate additional excitation in the orthogonal control force.

[0023] Second, set the virtual rotational angular velocity introduced by the virtual rotational force at this time. The expression is: (2) in Amplitude, Given the frequency, and combining it with the state equation of the hemispherical resonant gyroscope, the orthogonal control force at this time can be obtained as: (3) in The frequency of the hemispherical harmonic oscillator is non-uniform. The resonant frequency, The resonance amplitude, Let be the angle between the stiffness axis of the harmonic oscillator and the electrode axis. , where is the scale factor of the harmonic oscillator, and both are constant values. From equation (3), it can be seen that the excitation in the orthogonal control force generates a sinusoidal signal component with the same frequency as the virtual rotational angular velocity, and its amplitude is directly proportional to the phase error.

[0024] The second step involves modulating the quadrature control force using the phase error-correlated signal. This is done by multiplying and demodulating the signal using a known virtual rotational angular velocity, followed by a low-pass filter to remove high-frequency interference, yielding the amplitude of the sinusoidal excitation signal in the quadrature control force. Since the amplitude of the sinusoidal signal is directly proportional to the magnitude of the phase error, there is no need to calculate the specific value of the phase error. The amplitude indirectly reflects the change in phase error, greatly simplifying the demodulation process without interfering with the normal operation of the system.

[0025] Specifically, the phase error demodulation method includes the following steps: After multiplication and demodulation using the quadrature control force modulated by the known virtual rotational angular velocity and phase error correlation signal, followed by low-pass filtering, the demodulated equation containing phase error information is obtained: (4) It is evident that the amplitude of the demodulated excitation sinusoidal signal indirectly reflects the phase error. δφ The magnitude of the amplitude signal can be detected and controlled to identify and compensate for phase error. This method does not require additional control force in the system, nor is it subject to interference from other signals. It also simplifies the demodulation process and is suitable for practical applications.

[0026] The third step involves using the amplitude of the sinusoidal excitation signal as the input signal to the PID controller. The controller tracks amplitude changes and adjusts the phase of the reference signal in real time to control the amplitude of the sinusoidal excitation signal to zero. The output value of the PID controller is then fed back to the internal closed-loop control system of the hemispherical resonator gyroscope for phase error closed-loop compensation. It should be noted that the "modulation + demodulation + compensation" closed-loop control loop has a simple control process and can achieve high-precision online identification and compensation of phase errors. The output value of the PID controller represents the magnitude of the phase error.

[0027] Specifically, the phase error closed-loop compensation method includes the following steps: First, the amplitude of the sinusoidal excitation signal obtained from the demodulated equation containing phase error information is used as the input of the PID controller, with the amplitude control target being zero. Second, the compensated phase output of the PID controller, adjusted by amplitude control, is utilized. The initial phase of the reference signal is adjusted in real time. Thus, by changing the amplitude of the sinusoidal excitation signal, when the amplitude is controlled to zero, the phase is compensated. This is the phase error. δφ Size.

[0028] Third, compensate phase Compensating the hemispherical resonant gyroscope system internally, we obtain the compensated equations: (5) As can be seen, this method does not require direct calculation of the phase error. By adjusting the amplitude of the sinusoidal excitation signal to zero, the output of the PID controller is the magnitude of the phase error, thus achieving real-time online measurement of the phase error. This method is highly accurate, has a simple control process, and does not affect system stability.

[0029] The fourth step, based on phase error identification and compensation, involves comparing the actual detected angular velocity of the hemispherical resonant gyroscope with the applied sinusoidal virtual angular velocity to obtain a fixed proportional relationship where the two are in phase and frequency and have the same amplitude. This fixed proportional relationship is then compensated by a scaling factor (ratio) and fed into the gyroscope's drive system for gain error identification and compensation. It should be noted that this fixed proportional relationship of in phase and frequency and having the same amplitude represents the magnitude of the system gain error.

[0030] Specifically, the identification and compensation of gain error includes the following steps: First, the actual angular velocity detected by the hemispherical resonant gyroscope is: (6) Second, by combining the applied sinusoidal virtual angular velocity and the actual detected angular velocity of the hemispherical resonant gyroscope, the scaling factor is obtained: (7) It should be noted that after the phase error is accurately identified and compensated, the virtual rotational angular velocity to be applied inside the system is as shown in equation (2). However, inside the gyroscope system, due to the installation problem of the resonator and the manufacturing errors of the driving electrodes and various components, a gain error will be introduced during the driving process. Its existence will directly affect the magnitude of the virtual rotational force, and thus affect the actual measured angular velocity. The gain error changes the magnitude of the actual virtual angular velocity and introduces a scaling factor. K The value of represents the magnitude of the gain error, and the gain error of the system can be identified by equation (7).

[0031] Third, during the driving process of the hemispherical resonant gyroscope, the scaling factor is compensated to identify and compensate for the gain error.

[0032] To verify the effectiveness of the proposed method for error identification and compensation of hemispherical resonant gyroscope based on sinusoidal virtual rotation, simulations and experiments were conducted.

[0033] Example: Build a hemispherical resonant gyroscope model (e.g., using Matlab (Simulink)), and set the frequency non-uniformity in the model. The resonant frequency is 3000Hz. 8000×2 π resonance amplitude 6 µm included angle 5°, scale factor The phase error in the hemispherical resonant gyroscope model is set to 0.3. δφ The frequency of the virtual rotational angular velocity introduced by the virtual rotational force is 1.08°. It is 5 × 2π, amplitude The speed is 5° / s. Simulation experiments were conducted based on the above parameters.

[0034] The virtual rotational angular velocity in the system is set to be consistent with that in the model. Related experiments are carried out to verify the correctness of the online identification and compensation method for phase error based on orthogonal control force.

[0035] Model-based simulation results are as follows Figure 2 As shown, after the identification process begins (at the 5th second), the closed-loop system can accurately identify and compensate for the phase error of the hemispherical resonant gyroscope, achieving high precision and speed. The phase error identification and compensation results from the actual experiment are shown below. Figure 3As shown, the demodulation system can identify phase errors within 100 seconds without overshoot, and accurately compensate for the phase errors. The average compensation result is 1.7871°, consistent with the offline identification result, proving the correctness of the demodulation result. Furthermore, the fluctuation characteristics of the demodulated phase error value are evaluated. The standard deviation is 0.0031°, indicating extremely low random fluctuation and high stability of the compensation result. The range is 0.0159°, indicating a small maximum fluctuation range during the identification process, ensuring the accuracy of phase error compensation. δφ Accurate control.

[0036] To verify the dynamic characteristics of the identification system, the phase error within the system was artificially altered in an actual experiment by adjusting the phase of the signal. The phase error identification results are as follows: Figure 4 As shown in the results, the demodulation system can quickly respond to changes in phase error and accurately compensate for them. The identification results are consistent with the phase error, proving the stability and good dynamic characteristics of the demodulation system.

[0037] Combined with appendix Figure 5 Based on phase error identification and compensation, the gain error present in the system drive process is artificially set in the model. K =0.6, the simulation results comparing the actual measured sinusoidal virtual rotational angular velocity and the applied sinusoidal virtual angular velocity are shown in the figure below. Figure 5 As shown, when a gain error is added (around 2.4s), the measured sinusoidal virtual angular velocity will show a significant proportional change, while still maintaining the same frequency and phase as the applied virtual rotational angular velocity, which is consistent with the expected analysis results.

[0038] Furthermore, in combination Figure 5 The simulation results and the identified gain error simulation results are as follows: Figure 6 As shown, the system gain error can be accurately identified and compensated.

[0039] Simulation and experimental results show that the proposed method for identifying and compensating phase and gain errors of a hemispherical resonant gyroscope based on sinusoidal virtual rotation can effectively achieve high-precision identification and dynamic tracking compensation of phase and gain errors. At the same time, it clarifies the identification and compensation order of phase and gain errors, ensuring the normal operation of the hemispherical resonant gyroscope system. Figure 3 and Figure 6The identification and compensation results for phase error and gain error in the actual system are presented separately. These results are consistent with the offline identification results and preset values, indicating that the proposed method has excellent identification and compensation accuracy. Furthermore, the compensation curve changes smoothly without drastic fluctuations, making it suitable for engineering applications. The results also show that the designed identification and compensation system has good dynamic response characteristics, capable of real-time adaptive tracking and compensation for changes in phase error and gain error caused by external environmental disturbances and internal system factors, ensuring the stability of system operation.

[0040] Although exemplary embodiments of the invention have been described for illustrative purposes, those skilled in the art will understand that various modifications, additions, and substitutions in form and detail may be made without departing from the scope and spirit of the invention disclosed in the appended claims, and all such modifications and substitutions should fall within the scope of protection of the appended claims. Furthermore, the various parts of the product and the various steps of the method claimed in this invention can be combined in any combination. Therefore, the description of the embodiments disclosed in this invention is not intended to limit the scope of the invention, but rather to describe the invention. Accordingly, the scope of the invention is not limited by the above embodiments, but is defined by the claims or their equivalents.

Claims

1. A method for error identification and compensation of a hemispherical resonator gyroscope based on sinusoidal virtual rotation, characterized in that, Includes the following steps: (1) Based on the state equations of the hemispherical resonant gyroscope under ideal and phase error conditions, phase error correlation signal modulation is performed; (2) For the quadrature control force modulated by the phase error correlation signal, the amplitude of the sinusoidal excitation signal in the quadrature control force is obtained by multiplying and demodulating it using the known virtual rotation angular velocity and removing the high-frequency interference term by a low-pass filter. (3) Using the amplitude of the sinusoidal excitation signal as the input signal of the PID controller, the amplitude changes are tracked and the phase of the reference signal is adjusted in real time to control the amplitude of the sinusoidal excitation signal to zero, and the output value of the PID controller is fed back to the internal closed-loop control system of the hemispherical resonant gyroscope for phase error closed-loop compensation. (4) Based on the phase error identification and compensation, compare the actual detected angular velocity of the hemispherical resonant gyroscope and the applied sinusoidal virtual angular velocity to obtain a fixed proportional relationship in which the two are in phase and have the same amplitude. Then, the proportional factor compensation of the fixed proportional relationship is entered into the gyroscope's drive system to identify and compensate for the gain error.

2. The method as described in claim 1, characterized in that, Step (1) specifically includes: (1.1) Based on the state equations of the hemispherical resonant gyroscope under ideal and phase error conditions, the corresponding relationships between the various control forces in the two cases are obtained respectively: (1) in, , and These represent the amplitude control force, quadrature control force, and virtual rotational force, respectively, in the presence of phase error. , and These correspond to the various control forces under ideal conditions. This represents the phase error of the hemispherical resonant gyroscope. (1.2) Set the virtual rotational angular velocity introduced by the virtual rotational force at this time. The expression is: (2) in Amplitude, Given the frequency, and combining it with the state equation of the hemispherical resonant gyroscope, the orthogonal control force at this time is obtained as: (3) in The frequency of the hemispherical harmonic oscillator is non-uniform. The resonant frequency, The resonance amplitude, Let be the angle between the stiffness axis of the harmonic oscillator and the electrode axis. , where are the scale factors of the harmonic oscillator, and are all constants.

3. The method as described in claim 2, characterized in that, Step (2) specifically includes: After multiplication and demodulation using the quadrature control force modulated by the known virtual rotational angular velocity and phase error correlation signal, followed by low-pass filtering, the demodulated equation containing phase error information is obtained: (4)。 4. The method as described in claim 3, characterized in that, Step (3) specifically includes: (3.1) The amplitude of the sinusoidal excitation signal obtained from the demodulated equation containing phase error information is used as the input of the PID, and the amplitude control target is zero; (3.2) Utilizing the compensated phase output of the PID controller after amplitude control adjustment δ PID The initial phase of the reference signal is adjusted in real time. (3.3) Compensate phase δ PID Compensating the hemispherical resonant gyroscope system internally, we obtain the compensated equations: (5)。 5. The method as described in claim 4, characterized in that, Step (4) specifically includes: (4.1) The actual angular velocity detected by the hemispherical resonant gyroscope is: (6) (4.2) Combining the applied sinusoidal virtual angular velocity and the actual detected angular velocity of the hemispherical resonant gyroscope, the scaling factor is obtained: (7) (4.3) The gain error is identified and compensated during the driving process of the hemispherical resonant gyroscope by compensating the scaling factor.

6. The method as described in claim 3, characterized in that, Step (2) further includes detecting and controlling the amplitude of the sinusoidal excitation signal and identifying and compensating for phase errors.

7. The method as described in claim 5, characterized in that, In step (4), the fixed proportional relationship between the same frequency and phase and the existence of amplitude is the magnitude of the system gain error.

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