Signal processing method for force balance mode hemispherical resonator gyro based on vibration resonance

Abstract

This invention discloses a signal processing method for hemispherical resonant gyroscopes based on vibration resonance and force balance mode, belonging to the field of gyroscope signal processing technology. The invention addresses the problem of preserving useful signals while achieving filtering effects in the processing of angular rate signals from hemispherical resonant gyroscopes. The method includes: constructing a continuous overdamped bistable vibration resonance system based on a continuous original input signal and a set continuous high-frequency drive signal; determining the system parameters and the parameters of the high-frequency drive signal; transforming the continuous overdamped bistable vibration resonance system into a discrete overdamped bistable vibration resonance system; calculating the four intermediate slopes of the fourth-order Runge-Kutta method based on the current discrete mixed signal and the discrete output signal of the system at the adjacent previous time step, and then calculating the discrete output signal of the system at the current time step; and calculating the discrete angular rate after vibration resonance processing based on the discrete output signal of the system at the current time step. This invention improves the signal-to-noise ratio of the signal.

Description

Technical Field

[0001] This invention relates to a signal processing method for hemispherical resonant gyroscopes based on vibration resonance and force balance mode, belonging to the field of gyroscope signal processing technology. Background Technology

[0002] With the development of aerospace technology, force-balanced hemispherical resonator gyroscopes are increasingly being used for attitude measurement in spacecraft such as satellites and space stations. The high precision, high reliability, strong radiation resistance, and miniaturization of hemispherical resonator gyroscopes have led to their growing importance in spacecraft missions. A hemispherical resonator gyroscope mainly consists of a vacuum chamber, a resonator, and planar electrodes. Based on its working principle, hemispherical resonator gyroscopes can be divided into two operating modes: full-angle mode and force-balanced mode. The force-balanced mode, with its low dynamic range and high precision, better meets the requirements of spacecraft.

[0003] The working principle of a force-balanced mode hemispherical resonant gyroscope is as follows: An alternating voltage with a frequency equal to the second-order natural resonant frequency of the resonator is applied to the electrodes. When the resonator operates in second-order resonance, the standing wave at the lip of its hemispherical shell exhibits a four-antinode form. When an angular velocity is applied to the resonator, the mode shape of the resonator precesses relative to its initial position. Figure 1 As shown, at this time, the hemispherical resonator gyroscope will apply electrostatic force to the resonator through the control loop (force balance control loop) to prevent the mode shape from precessing, and obtain the external input angular rate information by solving the applied electrostatic force.

[0004] In practical applications, the angular velocity signal ultimately obtained from the force balance control loop is often mixed with noise. To improve the signal-to-noise ratio and thus obtain higher signal accuracy, this signal needs to be processed. Currently, the Extended Kalman Filter (EKF) or Forward Linear Predictive Filter (FLP) algorithm is mainly used to suppress noise. However, the EKF algorithm often relies on an accurate noise model. Due to the difficulty in establishing an accurate noise model, simplified noise models are usually used in practical applications. However, such simplified noise models often lead to system divergence, making it difficult to achieve the desired filtering effect. The FLP algorithm is sensitive to the model order. It requires theoretical analysis and repeated experiments to determine the optimal model order. If the order is too low, it will be difficult to suppress noise in the signal, thus failing to achieve the filtering effect. If the order is too high, although it can suppress noise to some extent, it will also lose useful signal. Furthermore, the FLP is mainly for predictable and coherent noise, and its prediction effect on random white noise is very poor, so this method is also difficult to achieve the desired filtering effect. Therefore, it is necessary to design a signal processing method that can achieve both filtering effect and preservation of useful signal. Summary of the Invention

[0005] To address the challenge of preserving useful signals while achieving filtering effects in the processing of hemispherical resonant gyroscope angular rate signals, this invention provides a hemispherical resonant gyroscope signal processing method based on a force balance mode of vibration resonance.

[0006] The present invention provides a signal processing method for a force balance mode hemispherical resonator gyroscope based on vibration resonance, comprising:

[0007] A continuous overdamped bistable vibration resonance system is constructed based on the continuous original input signal and the set continuous high-frequency drive signal; and the system parameters and high-frequency drive signal parameters of the continuous overdamped bistable vibration resonance system are determined according to the principle of vibration resonance.

[0008] The continuous overdamped bistable vibration resonance system is transformed into a discrete overdamped bistable vibration resonance system. The discrete mixed signal obtained from the collected discrete original input signal and the set discrete high-frequency drive signal is used as the input signal of the discrete overdamped bistable vibration resonance system. The discrete mixed signal at the initial time is set as the discrete output signal of the system at the initial time.

[0009] The four intermediate slopes of the fourth-order Runge-Kutta method are calculated based on the discrete mixed signal at the current time and the discrete output signal of the system at the adjacent previous time, and then the discrete output signal of the system at the current time is calculated.

[0010] The discrete angular rate after vibration resonance processing is calculated based on the discrete output signal of the system at the current moment.

[0011] According to the force balance mode hemispherical resonator gyroscope signal processing method based on vibration resonance of the present invention, the continuous original input signal is represented as... :

[0012] ,

[0013] In the formula For time, The amplitude of the continuous raw input signal. The angular frequency of the continuous original input signal. This is a noise signal;

[0014] Set the continuous high-frequency drive signal to In the formula The amplitude of the continuous high-frequency drive signal. For continuous high-frequency drive signal angular frequency, .

[0015] According to the force balance mode hemispherical resonator gyroscope signal processing method based on vibration resonance of the present invention, the dynamic equation of the continuously overdamped bistable vibration resonance system is as follows:

[0016] ,

[0017] In the formula The output signal of a continuously overdamped bistable resonant vibration system. Let be the potential function of a continuously overdamped bistable resonant vibration system. It is a continuous mixed signal;

[0018] .

[0019] According to the signal processing method of the force balance mode hemispherical resonator gyroscope based on vibration resonance of the present invention, the potential function of the continuously overdamped bistable vibration resonance system is... for:

[0020] ,

[0021] In the formula , Here are system parameters, where The coefficient of the quadratic term, The coefficient of the fourth term, .

[0022] According to the force balance mode hemispherical resonator gyroscope signal processing method based on vibration resonance of the present invention, the output signal of the continuously overdamped bistable vibration resonance system is obtained by using the fast and slow variable method. Approximate solution:

[0023] ,

[0024] In the formula The output signal of a continuously overdamped bistable vibration resonance system Low-frequency, slowly changing signals in the middle. The output signal of a continuously overdamped bistable vibration resonance system High-frequency, rapidly changing signals.

[0025] According to the vibration resonance-based force balance mode hemispherical resonator gyroscope signal processing method of the present invention, the method for determining the system parameters and high-frequency drive signal parameters of a continuously overdamped bistable vibration resonance system is as follows:

[0026] Output signal Substituting the approximate solution expression into the dynamic equation, we obtain:

[0027] ,

[0028] In the formula As an intermediate variable;

[0029] ;

[0030] when satisfy At that time, the system vibrates and resonates.

[0031] According to the force balance mode hemispherical resonator gyroscope signal processing method based on vibration resonance of the present invention, the continuous overdamped bistable vibration resonance system is transformed into a discrete overdamped bistable vibration resonance system, and the dynamic equation of the discrete overdamped bistable vibration resonance system is obtained as follows:

[0032] ,

[0033] In the formula To and The corresponding number Discrete output signal at time t, For discrete original input signals, For the first Discrete high-frequency driving signals at time points. For the first Discrete mixed signals at time points, Let be the potential function of a discrete overdamped bistable resonant vibration system.

[0034] According to the force balance mode hemispherical resonator gyroscope signal processing method based on vibration resonance of the present invention, when At that time, ;

[0035] when At that time, according to the first Discrete mixed signal at time step and the Discrete output signal at time 1 Calculate the four intermediate slopes of the fourth-order Runge-Kutta method:

[0036] ,

[0037] In the formula The first intermediate slope, The second intermediate slope, The third intermediate slope, This is the fourth intermediate slope.

[0038] According to the force balance mode hemispherical resonator gyroscope signal processing method based on vibration resonance of the present invention, when When, calculate the first Discrete output signal at time 1 :

[0039] ,

[0040] In the formula This represents the discrete sampling time interval.

[0041] According to the force balance mode hemispherical resonator gyroscope signal processing method based on vibration resonance of the present invention, the discrete angular rate after vibration resonance processing for:

[0042] ,

[0043] In the formula For about A cubic polynomial;

[0044] ,

[0045] In the formula The coefficients of the cubic term in the polynomial are... The coefficients of the quadratic term in the polynomial. coefficients of the linear term in a polynomial, It is a constant.

[0046] The beneficial effects of this invention are as follows: From the perspective of energy transfer, this method utilizes the dynamic characteristics of nonlinear systems to concentrate energy and transfer it to a desired specific frequency band through the action of high-frequency signals. This reduces the influence of signals from other frequency bands on the desired frequency band, thus improving the signal-to-noise ratio and exhibiting excellent filtering performance. Furthermore, a precise mathematical model of the vibration and resonance system can be established for the desired specific frequency band to achieve the filtering purpose, thus possessing advantages such as good stability and low likelihood of divergence.

[0047] The method of this invention transfers the energy of noise to the useful signal: reducing noise and enhancing the useful signal, thus effectively improving the signal-to-noise ratio while retaining the useful signal; because the method of this invention can accurately establish a mathematical model of the vibration resonance system, the system output at any time can be accurately calculated using this model, thereby accurately calculating the angular rate at any time, thus exhibiting good stability and being less prone to divergence. Attached Figure Description

[0048] Figure 1 This is a schematic diagram illustrating the working principle of a hemispherical resonant gyroscope.

[0049] Figure 2 This is a schematic diagram illustrating the physical meaning of the potential function.

[0050] Figure 3 This is a flowchart of the force balance mode hemispherical resonator gyroscope signal processing method based on vibration resonance described in this invention;

[0051] Figure 4 This is a schematic diagram comparing the original signal of the gyroscope with the signal-to-noise ratio (SNR) signal after vibration resonance processing.

[0052] Figure 5 This is a schematic diagram illustrating the comparative analysis of the original signal of the gyroscope and the signal after vibration resonance processing using the Allan variance method.

[0053] Figure 6 This is a flowchart illustrating the implementation of the method of the present invention using VHDL in the embodiments;

[0054] Figure 7 This is a schematic diagram comparing the original signal of the gyroscope and the signal after vibration resonance processing in the embodiment. Detailed Implementation

[0055] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0056] Specific Implementation Method 1: Combination Figure 2 and Figure 3 As shown, this invention provides a signal processing method for a force-balanced mode hemispherical resonator gyroscope based on vibration resonance, comprising:

[0057] A continuous overdamped bistable vibration resonance system is constructed based on the continuous original input signal and the set continuous high-frequency drive signal; and the system parameters and high-frequency drive signal parameters of the continuous overdamped bistable vibration resonance system are determined according to the principle of vibration resonance.

[0058] The continuous overdamped bistable vibration resonance system is transformed into a discrete overdamped bistable vibration resonance system. The discrete mixed signal obtained from the collected discrete original input signal and the set discrete high-frequency drive signal is used as the input signal of the discrete overdamped bistable vibration resonance system. The discrete mixed signal at the initial time is set as the discrete output signal of the system at the initial time.

[0059] The four intermediate slopes of the fourth-order Runge-Kutta method are calculated based on the discrete mixed signal at the current time and the discrete output signal of the system at the adjacent previous time, and then the discrete output signal of the system at the current time is calculated.

[0060] The discrete angular rate after vibration resonance processing is calculated based on the discrete output signal of the system at the current moment.

[0061] Furthermore, the continuous raw input signal is represented as Its mathematical model is as follows:

[0062] (1),

[0063] In the formula For time, The amplitude of the continuous raw input signal. The angular frequency of the continuous original input signal. This is a noise signal;

[0064] Utilizing the principle of vibration resonance systems, a continuous high-frequency drive signal can be added. This continuous high-frequency drive signal is set to... In the formula The amplitude of the continuous high-frequency drive signal. For continuous high-frequency drive signal angular frequency, .

[0065] A continuous high-frequency driving signal is mixed with a continuous original input signal and input to a continuously overdamped bistable vibration resonance system. The dynamic equation of the continuously overdamped bistable vibration resonance system is:

[0066] (2),

[0067] In the formula The output signal of a continuously overdamped bistable resonant vibration system is about The function; Let be the potential function of a continuously overdamped bistable resonant vibration system. It is a continuous mixed signal;

[0068] (3).

[0069] The potential function of a continuously overdamped bistable resonant vibration system takes the form of two symmetrical potential wells and an intermediate potential barrier.

[0070] Potential function of a continuously overdamped bistable resonant vibration system for:

[0071] (4),

[0072] In the formula , Here are system parameters, where The coefficient of the quadratic term, The coefficient of the fourth term, .

[0073] Potential function The physical meaning of the characterization, such as Figure 2 As shown.

[0074] At this point, the system is simultaneously affected by both fast and slow time scales. Using the fast-slow variable method, the output signal of the continuously overdamped bistable vibration resonance system can be obtained. Approximate solution:

[0075] (5),

[0076] In the formula The output signal of a continuously overdamped bistable vibration resonance system Low-frequency, slowly changing signals in the middle. The output signal of a continuously overdamped bistable vibration resonance system High-frequency, rapidly changing signals.

[0077] gyroscope output angular rate Output signal of a continuously overdamped bistable vibration resonance system The mathematical model is as follows:

[0078] (6),

[0079] In the formula It's about time. A cubic polynomial.

[0080] The method for determining the system parameters and high-frequency drive signal parameters of a continuously overdamped bistable vibration resonance system is as follows:

[0081] Output signal Substituting the approximate solution expression into the dynamic equation, we obtain:

[0082] (7),

[0083] In the formula As an intermediate variable;

[0084] (8),

[0085] when satisfy At that time, the system vibrates and resonates.

[0086] Analysis of formulas (7) and (8) shows that the dynamic characteristics of the system change when it is simultaneously subjected to both low-frequency and high-frequency signals. In this case, the overdamped particle exhibits a transition between two potential wells by overcoming the potential barrier under the combined influence of the two signals. satisfy At this time, the system vibrates and resonates, transferring the energy of the high-frequency driving signal and noise signal to the low-frequency signal by adjusting the degree of particle motion, thereby improving the signal-to-noise ratio. This effect is affected by parameters. The combined influence of these factors manifests as an effect on parameters. The nonlinear response.

[0087] Furthermore, since the actual system is a discrete system, it needs to be discretized. Transforming the continuous overdamped bistable vibration resonance system into a discrete overdamped bistable vibration resonance system yields the following dynamic equations for the discrete overdamped bistable vibration resonance system:

[0088] (9),

[0089] In the formula To and The corresponding number Discrete output signal at time t, For discrete original input signals, For the first Discrete high-frequency driving signals at time points. For the first Discrete mixed signals at time points, and correspond; Let be the potential function of a discrete overdamped bistable resonant vibration system.

[0090] when At that time, ;

[0091] when At that time, according to the first Discrete mixed signal at time step and the Discrete output signal at time 1 Calculate the four intermediate slopes of the fourth-order Runge-Kutta method:

[0092] (10)

[0093] In the formula The first intermediate slope, The second intermediate slope, The third intermediate slope, This is the fourth intermediate slope.

[0094] when When, calculate the first Discrete output signal at time 1 :

[0095] (11),

[0096] In the formula This represents the discrete sampling time interval.

[0097] Finally, the discrete angular rate after vibration resonance treatment for:

[0098] (12)

[0099] In the formula For about A cubic polynomial;

[0100] (13)

[0101] In the formula The coefficients of the cubic term in the polynomial are... The coefficients of the quadratic term in the polynomial. coefficients of the linear term in a polynomial, It is a constant. Discrete angular rate With the output angular rate of the gyroscope correspond.

[0102] The execution steps of this embodiment are as follows:

[0103] 1. The signal is collected from the force balance control loop as the discrete raw input signal; the parameters of the high-frequency signal are calculated using formula (8). Parameters of the vibration resonance system Configure settings;

[0104] 2. The acquired signal is mixed with the modulated discrete high-frequency signal to obtain a discrete mixed signal. Then input it into the already constructed discrete overdamped bistable vibration resonance system;

[0105] 3. If it is the initial moment, i.e. Calculate the vibration resonance output at the current moment. ;

[0106] 4. If it is not the initial moment, i.e. When setting the discrete sampling time interval (i.e., sampling period), utilizing the vibration resonance system output from the previous moment. and the discrete mixed signal at the current moment calculate Then use the calculation results ,calculate To obtain the output of the vibration resonance system at the current moment. .

[0107] 5. Calculate the output discrete angular rate signal using formulas (12) and (13). .

[0108] The flowchart of the force balance mode hemispherical resonator gyroscope signal processing method based on vibration resonance is as follows: Figure 3 As shown.

[0109] Verification experiment: A certain model of hemispherical resonator gyroscope was selected, and the working mode of the gyroscope was set to force balance mode. The experiment was carried out on an angular vibration turntable.

[0110] The signal sampling frequency is set to 100Hz, which is the sampling time interval. Set to 0.01s, the vibration resonance system parameters and high-frequency signal parameters are set as follows:

[0111] ;

[0112] The formula for calculating the relationship between the output and angular rate of a vibration resonance system is as follows:

[0113] ;

[0114] The output signal of the force balance control loop was selected when the turntable angular rate was set to 0° / s (i.e., the turntable was stationary). The original gyroscope signal and the signal after vibration resonance processing were compared using both signal-to-noise ratio and Allan variance methods. For example... Figure 4 and Figure 5 As shown.

[0115] 1. Signal-to-noise ratio:

[0116] Table 1 Signal-to-noise ratio

[0117]

[0118] Vibration resonance processing can transfer the energy of noise in a signal to the useful signal, thus reducing signal noise. Figure 4 It can be seen from this that the noise amplitude of the original signal reached ° / s, the noise amplitude of the signal after vibration resonance processing was reduced to ° / s; At the same time, the signal-to-noise ratio of the signal is effectively improved while retaining the useful signal through vibration resonance processing. As can be seen from Table 1, the signal-to-noise ratio of the original signal is -41.4747dB, and the signal-to-noise ratio of the signal after vibration resonance processing is -25.1372dB, so the signal-to-noise ratio is improved by 16.3375dB.

[0119] 2. Allan variance:

[0120] The angle random walk noise of the signal is calculated as shown in the table below:

[0121] Table 2. Angle Random Walk Noise of Signals

[0122]

[0123] Combination Figure 5As shown, the angular random walk noise is generated by the accumulation of white noise in the gyroscope over time. By processing the original signal through vibration resonance, the energy of the noise can be transferred to the useful signal, and the angular random walk noise can be further reduced. As can be seen from Table 2, the angular random walk noise of the original signal is 0.1536° / h, and the angular random walk noise of the signal after vibration resonance processing is 0.0829° / h. Therefore, the angular random walk noise is reduced by 0.0707° / h.

[0124] Example:

[0125] The method of this invention is implemented using the VHDL language, and the flowchart is as follows. Figure 6 As shown, Figure 6 The right side of the image shows the VHDL functions used.

[0126] The signal sampling frequency is set to 100Hz, which is the sampling time interval. Set to 0.01s, the vibration resonance system parameters and high-frequency signal parameters are set as follows:

[0127] ;

[0128] The formula for calculating the relationship between the output and angular rate of a vibration resonance system is as follows:

[0129] ;

[0130] The original input signal is obtained by acquiring the output signal of the force balance control loop when the turntable angular rate is set to 1° / s. Then, the signal processing method of the hemispherical resonant gyroscope based on vibration resonance is implemented using VHDL to obtain the signal after vibration resonance processing.

[0131] The original signal and the signal after vibration resonance processing are as follows: Figure 7 As shown.

[0132] While the invention has been described herein with reference to specific embodiments, it should be understood that these embodiments are merely examples of the principles and applications of the invention. Therefore, it should be understood that many modifications can be made to the exemplary embodiments, and other arrangements can be designed without departing from the spirit and scope of the invention as defined by the appended claims. It should be understood that different dependent claims and features described herein can be combined in ways different from those described in the original claims. It is also understood that features described in conjunction with individual embodiments can be used in other described embodiments.

Claims

1. A signal processing method for a vibration resonance based force-rebalance mode hemispherical resonator gyroscope, characterized in that include: A continuous overdamped bistable vibration resonance system was constructed based on continuous original input signals and a set continuous high-frequency drive signal. Based on the principle of vibration resonance, the system parameters and high-frequency drive signal parameters of the continuous overdamped bistable vibration resonance system are determined; the continuous overdamped bistable vibration resonance system is transformed into a discrete overdamped bistable vibration resonance system; a discrete mixed signal is obtained from the collected discrete original input signal and the set discrete high-frequency drive signal as the input signal of the discrete overdamped bistable vibration resonance system, and the discrete mixed signal at the initial moment is set as the discrete output signal of the system at the initial moment; The four intermediate slopes of the fourth-order Runge-Kutta method are calculated based on the discrete mixed signal at the current time and the discrete output signal of the system at the adjacent previous time, and then the discrete output signal of the system at the current time is calculated. The discrete angular rate after vibration resonance processing is calculated based on the discrete output signal of the system at the current moment.

2. The signal processing method of the vibration resonance-based force balance mode hemispherical resonator gyroscope according to claim 1, characterized in that, The continuous raw input signal is represented as : ， In the formula For time, The amplitude of the continuous original input signal. The angular frequency of the continuous original input signal. This is a noise signal; Set the continuous high-frequency drive signal to In the formula The amplitude of the continuous high-frequency drive signal. For continuous high-frequency drive signal angular frequency, .

3. The signal processing method for a hemispherical resonator gyroscope based on vibration resonance and force balance mode according to claim 2, characterized in that, The dynamic equation of a continuously overdamped bistable resonant vibration system is: ， In the formula The output signal of a continuously overdamped bistable resonant vibration system. Let be the potential function of a continuously overdamped bistable resonant vibration system. It is a continuous mixed signal; 。 4. The signal processing method for a hemispherical resonator gyroscope based on vibration resonance and force balance mode according to claim 3, characterized in that, Potential function of a continuously overdamped bistable resonant vibration system for: ， In the formula , Here are system parameters, where The coefficient of the quadratic term, The coefficient of the fourth term, .

5. The signal processing method for a force-balanced hemispherical resonator gyroscope based on vibration resonance according to claim 4, characterized in that, The output signal of a continuously overdamped bistable resonant vibration system is obtained using the fast-slow variable method. Approximate solution: ， In the formula The output signal of a continuously overdamped bistable vibration resonance system Low-frequency, slowly changing signals in the middle. The output signal of a continuously overdamped bistable vibration resonance system High-frequency, rapidly changing signals.

6. The signal processing method for a force-balanced hemispherical resonator gyroscope based on vibration resonance according to claim 5, characterized in that, The method for determining the system parameters and high-frequency drive signal parameters of a continuously overdamped bistable vibration resonance system is as follows: Output signal Substituting the approximate solution expression into the dynamic equation, we obtain: ， In the formulae is an intermediate variable; ， When satisfies the system vibrates in resonance.

7. The signal processing method of the vibration resonance-based force balance mode hemispherical resonator gyroscope according to claim 6, characterized in that, Transforming the continuous overdamped bistable vibration resonance system into a discrete overdamped bistable vibration resonance system yields the following dynamic equations for the discrete overdamped bistable vibration resonance system: ， In the formula To and The corresponding number Discrete output signal at time t, For discrete original input signals, For the first Discrete high-frequency driving signals at time points. For the first Discrete mixed signals at time points, Let be the potential function of a discrete overdamped bistable resonant vibration system.

8. The signal processing method for a force-balanced hemispherical resonator gyroscope based on vibration resonance according to claim 7, characterized in that, When time, the ; when At that time, according to the first Discrete mixed signal at time step and the Discrete output signal at time 1 Calculate the four intermediate slopes of the fourth-order Runge-Kutta method: ， In the formula The first intermediate slope, The second intermediate slope, The third intermediate slope, This is the fourth intermediate slope.

9. The signal processing method for a force-balanced hemispherical resonator gyroscope based on vibration resonance according to claim 8, characterized in that, when When, calculate the first Discrete output signal at time 1 : ， In the formula is a discrete sampling time interval.

10. The signal processing method for a force-balanced hemispherical resonator gyroscope based on vibration resonance according to claim 9, characterized in that, Discrete angular velocity subjected to vibratory resonance treatment is: ， wherein is a 3rd order polynomial in ; ， In the formula The coefficients of the cubic term in the polynomial are... The coefficients of the quadratic term in the polynomial. coefficients of the linear term in a polynomial, It is a constant.

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