A fully digital autonomous frequency control method for a hemispherical resonant gyroscope

Abstract

This invention discloses a fully digital autonomous frequency control method for a hemispherical resonator gyroscope, belonging to the field of inertial instrument control technology. The method first performs autonomous frequency identification of the hemispherical resonator gyroscope, and then performs fully digital closed-loop control of the hemispherical resonator gyroscope. The autonomous frequency identification of the hemispherical resonator gyroscope is achieved through active excitation and signal frequency identification. The fully digital closed-loop control of the hemispherical resonator gyroscope includes digital frequency and phase discrimination, digital loop filtering, CNC oscillator processing, and digital reference signal source output. This method can achieve autonomous initial frequency identification of the hemispherical resonator gyroscope and high-stability, high-precision frequency closed-loop control, effectively improving the production efficiency and performance indicators of hemispherical resonator gyroscope products.

Description

Technical Field

[0001] This invention relates to a fully digital autonomous frequency control method for a hemispherical resonant gyroscope, belonging to the field of inertial instrument control technology. Background Technology

[0002] Hemispherical resonator (BR) gyroscope control is generally divided into frequency control, amplitude control, quadrature control, and force balance control. Frequency control is the core and foundation of BR gyroscope control, providing the synchronization frequency and phase reference for amplitude control, quadrature control, and force balance control. To address the control problems of BR gyroscopes, a frequency control method adapted to analog control mode has been developed and applied to some products, solving the frequency control problem of first-generation BR gyroscopes. However, with the development of BR gyroscope technology and the need for product upgrades, BR gyroscope control has evolved from analog control mode to fully digital control mode. The previously proposed frequency control method is no longer applicable, requiring a new frequency control method. Simultaneously, the increasing demand for large-scale production places higher demands on the production efficiency of BR gyroscope products. As the core component of BR gyroscope control, frequency control must meet the requirements of large-scale production, and its operation must be fully autonomous to improve the production efficiency of BR gyroscope products. Summary of the Invention

[0003] The technical problem solved by this invention is to overcome the shortcomings of the prior art and propose a fully digital autonomous frequency control method for hemispherical resonant gyroscopes. It adopts fully digital closed-loop control, and the generated reference signal can be used as a digital reference signal to provide amplitude control, orthogonal control and force balance control links, so as to achieve stable, accurate and environmentally adaptable frequency control and phase control.

[0004] The technical solution of this invention is:

[0005] A fully digital autonomous frequency control method for a hemispherical resonant gyroscope includes:

[0006] After performing ADC conversion on the output signal of the hemispherical resonant gyroscope, the frequency of the hemispherical resonant gyroscope is identified and used as the initial value for frequency control of the hemispherical resonant gyroscope.

[0007] The signal converted by the ADC is then subjected to frequency and phase discrimination processing. The output signal is compared with the reference signal in terms of frequency and phase to obtain the phase difference signal.

[0008] The phase difference signal is digitally loop filtered to obtain the filtered voltage signal.

[0009] The initial value of the hemispherical resonant gyroscope frequency control is used as the initial frequency of the numerically controlled oscillator, and the voltage signal is used as the input and the frequency signal is output.

[0010] The frequency signal is input into the digital reference source to generate a reference signal, which is then input into the frequency and phase detector to achieve closed-loop control of the frequency of the hemispherical resonant gyroscope. The reference signal after closed-loop control is then extracted and applied to the amplitude control, quadrature control, and force balance control of the hemispherical resonant gyroscope.

[0011] Furthermore, methods for identifying the frequency of a hemispherical resonant gyroscope include:

[0012] S1: Perform ADC sampling on the output signal of the hemispherical resonant gyroscope. In one second, count the number of zero crossings of the sampled data in two adjacent seconds. The count value is the identification frequency value.

[0013] S2: Perform a correctness check on the two initial frequency values:

[0014] f min ≤f1≤f max And f min ≤f2≤f max And -Δf if ≤f1-f2≤+Δf if

[0015] In the formula, f min and f max These represent the minimum and maximum values ​​of the frequency, respectively, and f1 and f2 are the frequency values ​​of two consecutive identifications, respectively. Δf if This is the threshold for determining the difference;

[0016] If the determination passes, execute S3; if the determination fails, actively excite the hemispherical resonator gyroscope. When the amplitude of the hemispherical resonator gyroscope output signal is greater than the set threshold value, stop the excitation, and then execute S1 and S3 in sequence.

[0017] S3: Calculate the average of two consecutive identified frequency values ​​and use the average value as the frequency of the hemispherical resonant gyroscope.

[0018] Furthermore, if the test fails, the hemispherical resonant gyroscope is actively excited. The method of active excitation is as follows:

[0019] The hemispherical resonant gyroscope is excited by a sinusoidal signal with a variable frequency. The frequency of the sinusoidal signal starts from the initial value f. min Gradually increase to the final frequency value f max ;

[0020] An active excitation circuit is constructed, including an ADC circuit, a DAC circuit, and a digital processing unit. The ADC circuit samples the output signal of the hemispherical resonant gyroscope, and the sampled digital signal serves as the input to the digital processing unit. The output of the digital processing unit is converted by the DAC circuit and then input back to the hemispherical resonant gyroscope to form a loop. The digital processing unit is used to set the phase and gain. By setting the gain and phase, the loop gain is ensured to be no less than 1, and the phase satisfies 2kπ, where k is a non-negative integer, making the loop a positive feedback loop. When the amplitude of the hemispherical resonant gyroscope output signal sampled by the ADC current exceeds a set threshold value, the excitation is stopped.

[0021] Furthermore, for a sinusoidal signal with variable frequency, the step frequency of the frequency change is determined by the quality factor of the hemispherical resonant gyroscope, and the step time is determined by the resonant frequency of the hemispherical resonant gyroscope.

[0022] Furthermore, based on a mathematical model for frequency and phase detection, frequency and phase detection processing is performed on the output signal of the hemispherical resonant gyroscope; the mathematical model is as follows:

[0023] x(k+1)=Φx(k)+w(k)

[0024] z(k)=r T (k)x(k)+v(k) r(k) = [sinωt cosωt] T

[0025] In the formula, z(k) represents the state observation; r(k) represents the reference signal used for frequency and phase discrimination, and the initial state is the identified hemispherical resonant gyroscope frequency; w(k) represents white noise, v(k) represents the observed white noise; A1(k) represents the amplitude of the hemispherical resonant gyroscope output signal relative to the reference signal, and A2(k) represents the phase difference of the hemispherical resonant gyroscope signal relative to the reference signal.

[0026] Furthermore, based on the mathematical model, the phase difference A2(k) between the output signal of the hemispherical resonant gyroscope and the reference signal is obtained through recursive calculation, specifically:

[0027]

[0028] K(k)=P(k / k-1)r(k)(r T (k)P(k / k-1)r(k+R(k)) -1

[0029] P(k / k-1)=ΦP(k-1)Φ T +Q(k-1)

[0030] P(k)=[IK(k)r T (k)]P(k / k-1)[IKk r T (k)] T +K(k)R(k)K(k) T

[0031] In the formula, Let x(k) represent the estimated value at time k. Let x(k-1) be the estimated value of x(k-1) at time k at time k-1, K(k) and P(k) be the intermediate variables at time k, P(k / k-1) be the estimated value of P(k) at time k at time k-1, and Q(k) and R(k) be the covariance matrices of w(k) and v(k).

[0032] Furthermore, the phase difference signal is subjected to digital loop filtering, as shown below:

[0033] Δu(k)=(K p +K i )·e(k)-K p ·e(k-1)

[0034] In the formula, K p K is the gain parameter. i Here, e(k) is the phase difference signal between the hemispherical resonant gyroscope signal and the reference signal at time k, and Δu(k) is the output signal obtained by digital loop filtering at time k.

[0035] Furthermore, using the frequency of the hemispherical resonant gyroscope as the initial frequency of the numerically controlled oscillator, and taking the voltage signal as the input, the output frequency signal f is:

[0036]

[0037] In the formula, K is the filtered voltage signal, N represents the number of binary bits required for the numerically controlled oscillator to achieve the desired result, and f sys f0 is the fundamental frequency of the numerically controlled oscillator and f0 is the initial frequency of the numerically controlled oscillator.

[0038] Furthermore, the digital reference signal source is implemented using the CORDIC algorithm to generate a waveform signal of the output frequency signal of the numerically controlled oscillator, which serves as a reference signal.

[0039] The advantages of this invention compared to the prior art are:

[0040] (1) The frequency autonomous identification method proposed in this invention achieves autonomous identification of the frequency of hemispherical resonant gyroscope by active excitation and timed zero-crossing sampling every second. This method is an online frequency identification method that does not require offline measurement of the resonant frequency of the hemispherical resonant gyroscope, which significantly improves the debugging and production efficiency of hemispherical resonant gyroscope products.

[0041] (2) The all-digital frequency control method proposed in this invention uses an all-digital frequency and phase discrimination algorithm to recursively calculate the amplitude and phase of the gyroscope signal, and uses the phase information for frequency control. This method implements all-digital frequency closed-loop control in software, and is not easily affected by factors such as parameter aging and drift of electronic devices on the frequency closed-loop control effect. Attached Figure Description

[0042] Various other advantages and benefits will become apparent to those skilled in the art upon reading the following detailed description of preferred embodiments. The accompanying drawings are for illustrative purposes only and are not intended to limit the invention. Furthermore, the same reference numerals denote the same parts throughout the drawings. In the drawings:

[0043] Figure 1 This is a flowchart of the fully digital autonomous frequency control method for a hemispherical resonant gyroscope according to an embodiment of the present invention;

[0044] Figure 2 This is a block diagram illustrating the active excitation principle in frequency autonomous identification according to an embodiment of the present invention.

[0045] Figure 3 This is a block diagram illustrating the frequency closed-loop control principle in the frequency control of an embodiment of the present invention. Detailed Implementation

[0046] Exemplary embodiments of the present disclosure will now be described in more detail with reference to the accompanying drawings. While exemplary embodiments of the present disclosure are shown in the drawings, it should be understood that the present disclosure may be implemented in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the disclosure to those skilled in the art.

[0047] To address the issues of insufficient automation and low frequency control accuracy in hemispherical resonator gyroscope tuning, this invention proposes a fully digital autonomous frequency control method for hemispherical resonator gyroscopes, such as... Figure 1 As shown, it specifically includes:

[0048] S1: Autonomous frequency identification of the hemispherical resonant gyroscope

[0049] S1.1: Frequency Identification

[0050] The sensitive signal from a hemispherical resonator gyroscope, after processing by a preamplifier circuit, is generally a sinusoidal signal. Frequency identification of the hemispherical resonator gyroscope involves identifying the sinusoidal signal it is sensitive to. Typically, the frequency of a hemispherical resonator gyroscope is between 4500Hz and 5500Hz. Frequency identification first involves sampling the sinusoidal electrical signal detected by the hemispherical resonator using an ADC. The sampling frequency is determined according to the Nyquist sampling theorem, and a sampling rate of 10 times is generally preferred; in this embodiment, a sampling frequency of 5MHz is selected. Then, the number of zero-crossings of the sampled data is counted per second, and the count value is the identified frequency value. The identified frequency value is then transmitted to S1.2 for frequency accuracy determination.

[0051] S1.2: Frequency Correctness Determination

[0052] The frequency accuracy determination is to eliminate outliers generated in the S1.1 frequency identification process and ensure the accuracy of the identified frequency.

[0053] The frequency correctness determination first checks whether the frequency value f identified by the frequency identification satisfies the following:

[0054] f min ≤f≤f max

[0055] Among them, the minimum value of the determination frequency f min and maximum value f max Based on the structural dimensions and manufacturing process of the hemispherical resonator in a hemispherical gyroscope, the frequency range of a typical 30mm hemispherical resonator is 4500Hz to 5500Hz. Therefore, the minimum value f min The frequency is 4500Hz, and the maximum value is f. max The frequency is 5500Hz, which is the frequency value determined in the example to meet the following criteria:

[0056] 4500Hz≤f≤5500Hz

[0057] To ensure the effectiveness of outlier removal, the difference Δf between two consecutive identified frequency values ​​in S1.1 is re-evaluated to determine whether the difference between two consecutive frequency identification values ​​satisfies the following:

[0058] -Δf if ≤Δf≤+Δf if

[0059] Among them, the threshold for determining the difference is Δf if Determined by the resolution of frequency identification in S1.1, this embodiment uses a one-second timing for zero-crossing sampling and counting, with a resolution of ±1Hz. Considering the margin for signal detection, the threshold Δf is determined. if 2Hz was selected.

[0060] If all of the following conditions are met, the test is "passed"; otherwise, the test is "failed".

[0061] 4500Hz≤f≤5500Hz and -2Hz≤Δf≤+2Hz

[0062] If the result is "passed", the process proceeds to S1.4 for final frequency determination. If the result is "failed", the process proceeds to S1.3 for active excitation of the hemispherical resonator gyroscope.

[0063] S1.3: If S1.2 fails, then perform active excitation of the hemispherical resonant gyroscope.

[0064] S1.3.1: First, a sinusoidal signal with a variable frequency is used to excite the hemispherical resonant gyroscope. The frequency of the sinusoidal signal changes according to a certain step frequency Δf. step A certain step time ΔT step From the initial value of frequency f min Gradually increase to the final frequency value f max The stepping frequency is determined by the quality factor of the hemispherical resonator gyroscope, the stepping time is determined by the resonant frequency of the hemispherical resonator gyroscope, and the initial and final frequency values ​​are determined by the structural dimensions and manufacturing process of the hemispherical resonator. In this embodiment, the quality factor of the hemispherical resonator gyroscope is 5 million, the resonant frequency is 5000Hz, the stepping frequency can be determined by the empirical formula (50~100)*5000Hz / 5000000, and the stepping frequency is taken as 0.25Hz; the stepping time can be determined by the empirical formula (10~20)*1 / 5000, and is taken as 2ms. Typically, the frequency range of a 30mm hemispherical resonator is 4500Hz~5500Hz, therefore the initial frequency value (also called the minimum value in S1.2) f min The final frequency value (also referred to as the maximum value in S1.2) is 4500Hz. max It is 5500Hz.

[0065] S1.3.2: Construction Figure 2 The active excitation circuit shown includes an ADC (Analog-to-Digital Converter), a DAC (Digital-to-Analog Converter), and a dashed box representing a digital processing unit, typically an FPGA or DSP circuit. It includes at least gain and phase setting stages. By setting the gain and phase, the loop gain is ensured to be no less than 1, and the phase satisfies 2kπ, k = 0, 1, 2… According to automatic control theory, under these conditions, a positive feedback loop will be formed, and the hemispherical resonator gyroscope will be actively excited. When the ADC samples a sinusoidal signal amplitude from the hemispherical resonator gyroscope that exceeds a threshold value, the excitation will stop, and the process will proceed to S1.1, continuing with subsequent stages. In this embodiment, the gain is set to 10, the phase to 0, and the threshold value is set to 0.5V based on empirical values.

[0066] S1.4: If S1.2 passes the judgment, the average of two adjacent identification frequency values ​​in S1.2 will be calculated. The average of the two adjacent identification frequency values ​​will be used as the final determined frequency value and passed to S4 as the initial value for the calculation.

[0067] S2: The purpose of frequency control of hemispherical resonant gyroscope is to synchronously track the frequency and phase of hemispherical resonant gyroscope in real time. In order to achieve the above purpose, a frequency closed-loop control loop needs to be designed to control the frequency and phase of hemispherical resonant gyroscope in a closed loop. Figure 3 This is a block diagram of the frequency control loop of a hemispherical resonant gyroscope. The ADC is an analog-to-digital converter circuit, and the dashed box represents the digital processing unit, which is usually an FPGA or DSP circuit. For closed-loop frequency control, it needs to include a frequency and phase detection stage, a digital loop filtering stage, a digitally controlled oscillator stage, and a digital reference signal source stage.

[0068] The function of frequency and phase detection is to compare the sinusoidal signal from the hemispherical resonator gyroscope with the reference signal generated by the frequency closed-loop control, based on the difference in frequency and phase. The purpose of the frequency closed-loop control loop is to control the sinusoidal signal from the hemispherical resonator gyroscope to have the same phase and frequency as the reference signal generated by the frequency closed-loop control. The frequency difference between the two sinusoidal signals is essentially a phase difference; therefore, frequency and phase detection essentially involves calculating the phase difference between the two sinusoidal signals.

[0069] To calculate the phase difference, a mathematical model for frequency and phase detection must first be established:

[0070] x(k+1)=Φx(k)+w(k)

[0071] z(k)=r T (k)x(k)+v(k) r(k) = [sinωt cosωt] T

[0072] Where A1(k) represents the calculated amplitude of the hemispherical resonant gyroscope signal relative to the reference signal, A2(k) represents the calculated phase of the hemispherical resonant gyroscope signal relative to the reference signal, z(k) represents the state observation, r(k) represents the frequency and phase discrimination reference signal, the sine and cosine signals generated from S5, w(k) represents white noise, and v(k) represents the observed white noise.

[0073] To calculate the phase of the hemispherical resonant gyroscope signal relative to the reference signal, the following mathematical recursive formula is required:

[0074]

[0075] K(k)=P(k / k-1)r(k)(r T (k)P(k / k-1)r(k+R(k))-1

[0076] P(k / k-1)=ΦP(k-1)Φ T +Q(k-1)

[0077] P(k)=[IK(k)r T (k)]P(k / k-1)[IK k r T (k)] T +K(k)R(k)K(k) T

[0078] in, Let x(k) represent the estimated value at time k. Let represent the estimated value of x(k-1) at time k based on time k-1, K(k) and P(k) be intermediate variables at time k, P(k / k-1) represent the estimated value of P(k) at time k based on time k-1, and Q(k) and R(k) be the covariance matrices of w(k) and v(k), determined based on empirical values. In this embodiment, Q is determined to be [0.001, 0.001]. T R = 0.001.

[0079] The recursive solution A2(k) is the output of frequency and phase detection, which is passed to the S3 stage.

[0080] S3: Digital loop filtering is essentially a control and regulation process, which can be expressed by the formula:

[0081] Δu(k)=(K p +K i )·e(k)-K p ·e(k-1)

[0082] Among them, K p K is the gain parameter. i Let e(k) be the integration parameter, A2(k) be the output of stage S2 at time k, and Δu(k) be the output of the digital loop filter stage at time k, which is then passed to S4. The gain parameter K... p and integration parameter K i K was obtained through experimental debugging; in this embodiment, it is... p =1,K i =0.0028.

[0083] S4: The numerically controlled oscillator is used to generate the frequency of a specified signal, which can be expressed by the formula:

[0084]

[0085] Where K is the output Δu(k) of S3, N represents the number of binary bits required for the numerically controlled oscillator to achieve the desired signal frequency resolution, and f sys f0 is the fundamental frequency of the numerically controlled oscillator, and f0 is the initial frequency of the numerically controlled oscillator, which is the frequency determination value from S1.4.

[0086] In this embodiment, N = 40, f sys =500kHz, achieving a frequency resolution of 4.55E-7Hz for the numerically controlled oscillator.

[0087] S5: The digital reference signal source is implemented using the CORDIC algorithm to generate waveform signals of a specified frequency. The digital reference source receives the frequency signal f generated from S4 and uses the CORDIC algorithm to generate the reference signals sinωt and cosωt required by S2.

[0088] The embodiments described above are merely preferred embodiments of the present invention. Ordinary variations and substitutions made by those skilled in the art within the scope of the technical solution of the present invention should be included within the protection scope of the present invention.

Claims

1. A fully digital autonomous frequency control method for a hemispherical resonant gyroscope, characterized in that, include: After performing ADC conversion on the output signal of the hemispherical resonant gyroscope, the frequency of the hemispherical resonant gyroscope is identified and used as the initial value for frequency control of the hemispherical resonant gyroscope. The signal converted by the ADC is then subjected to frequency and phase discrimination processing. The output signal is compared with the reference signal in terms of frequency and phase to obtain the phase difference signal. The phase difference signal is digitally loop filtered to obtain the filtered voltage signal. The initial value of the hemispherical resonant gyroscope frequency control is used as the initial frequency of the numerically controlled oscillator, and the voltage signal is used as the input and the frequency signal is output. The frequency signal is input into the digital reference source to generate a reference signal, which is then input into the frequency and phase detector to achieve closed-loop control of the frequency of the hemispherical resonant gyroscope. The reference signal after closed-loop control is then extracted and applied to the amplitude control, quadrature control, and force balance control of the hemispherical resonant gyroscope. Methods for identifying the frequency of a hemispherical resonant gyroscope include: S1: Perform ADC sampling on the output signal of the hemispherical resonant gyroscope. In one second, count the number of zero crossings of the sampled data in two adjacent seconds. The count value is the identification frequency value. S2: Perform a correctness check on the two initial frequency values: f min ≤f1≤f max And f min ≤f2≤f max And -Δf if ≤f1-f2≤+Δf if In the formula, f min and f max These represent the minimum and maximum values ​​of the frequency, respectively, and f1 and f2 are the frequency values ​​of two consecutive identifications, respectively. Δf if This is the threshold for determining the difference; If the determination passes, execute S3; if the determination fails, actively excite the hemispherical resonator gyroscope. When the amplitude of the hemispherical resonator gyroscope output signal is greater than the set threshold value, stop the excitation, and then execute S1 and S3 in sequence. S3: Calculate the average of two consecutive identified frequency values ​​and use the average value as the frequency of the hemispherical resonant gyroscope.

2. The fully digital autonomous frequency control method for a hemispherical resonant gyroscope according to claim 1, characterized in that, If the determination fails, the hemispherical resonant gyroscope is actively excited. The method of active excitation is as follows: The hemispherical resonant gyroscope is excited by a sinusoidal signal with a variable frequency. The frequency of the sinusoidal signal starts from the initial value f. min Gradually increasing to the final frequency value f max ; An active excitation circuit is constructed, including an ADC circuit, a DAC circuit, and a digital processing unit. The ADC circuit samples the output signal of the hemispherical resonant gyroscope, and the sampled digital signal serves as the input to the digital processing unit. The output of the digital processing unit is converted by the DAC circuit and then input back to the hemispherical resonant gyroscope to form a loop. The digital processing unit is used to set the phase and gain. By setting the gain and phase, the loop gain is ensured to be no less than 1, and the phase satisfies 2kπ, where k is a non-negative integer, making the loop a positive feedback loop. When the amplitude of the hemispherical resonant gyroscope output signal sampled by the ADC current exceeds a set threshold value, the excitation is stopped.

3. The fully digital autonomous frequency control method for a hemispherical resonant gyroscope according to claim 2, characterized in that, For a sinusoidal signal with variable frequency, the step frequency of the frequency change is determined by the quality factor of the hemispherical resonant gyroscope, and the step time is determined by the resonant frequency of the hemispherical resonant gyroscope.

4. The fully digital autonomous frequency control method for a hemispherical resonant gyroscope according to claim 1, characterized in that, Based on a mathematical model for frequency and phase discrimination, frequency and phase discrimination processing is performed on the output signal of a hemispherical resonant gyroscope; the mathematical model is as follows: x(k+1)=Φx(k)+w(k) z(k)=r T (k)x(k)+v(k) In the formula, z(k) represents the state observation; r(k) represents the reference signal used for frequency and phase discrimination, and the initial state is the reference signal generated by the identified hemispherical resonant gyroscope frequency; w(k) represents white noise, v(k) represents the observed white noise; A1(k) represents the amplitude of the hemispherical resonant gyroscope output signal relative to the reference signal, and A2(k) represents the phase difference between the hemispherical resonant gyroscope signal and the reference signal.

5. The fully digital autonomous frequency control method for a hemispherical resonant gyroscope according to claim 4, characterized in that, Based on the mathematical model, the phase difference A2(k) between the output signal of the hemispherical resonant gyroscope and the reference signal is obtained through recursive calculation, specifically: Where, Let x(k) represent the estimated value at time k. Let x(k-1) be the estimated value of x(k-1) at time k at time k-1, K(k) and P(k) be the intermediate variables at time k, P(k / k-1) be the estimated value of P(k) at time k at time k-1, and Q(k) and R(k) be the covariance matrices of w(k) and v(k).

6. The fully digital autonomous frequency control method for a hemispherical resonant gyroscope according to claim 1, characterized in that, Digital loop filtering of the phase difference signal is expressed as: Δu(k)=(K p +K i )·e(k)-K p e(k-1) In the formula, K p K is the gain parameter. i Here, e(k) is the phase difference signal between the hemispherical resonant gyroscope signal and the reference signal at time k, and Δu(k) is the output signal obtained by digital loop filtering at time k.

7. The fully digital autonomous frequency control method for a hemispherical resonant gyroscope according to claim 1, characterized in that, Using the frequency of the hemispherical resonant gyroscope as the initial frequency of the numerically controlled oscillator, and taking the voltage signal as the input, the output frequency signal f is: In the formula, K is the filtered voltage signal, N represents the number of binary bits required for the numerically controlled oscillator to achieve the desired result, and f sys f0 is the fundamental frequency of the numerically controlled oscillator and f0 is the initial frequency of the numerically controlled oscillator.

8. The fully digital autonomous frequency control method for a hemispherical resonant gyroscope according to claim 1, characterized in that, The digital reference signal source is implemented using the CORDIC algorithm to generate the waveform signal of the output frequency signal of the numerically controlled oscillator, which serves as the reference signal.

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