A high-precision and high-efficiency resonant gyro frequency splitting measurement method and related components

Abstract

The application discloses a high-precision and high-efficiency resonant gyro frequency splitting measurement method and related components, and relates to the field of frequency splitting determination. First, the decay time constant of a resonator in a gyroscope when a damping is introduced is determined. An excitation force is applied to the resonator to control the vibration of the resonator to a preset amplitude value. According to the amplitude of the excitation force control amount corresponding to the excitation force, the angular frequency of the excitation force, the stable vibration amplitude value of the resonator and the decay time constant, the conversion coefficient between the amplitude of the excitation force control amount and the amplitude of the excitation force is determined. The gyroscope is controlled to operate in a full-angle mode, and the vibration mode of the resonator is precession around a symmetry axis. The peak-to-peak value of the quadrature control force in the precession process of the resonator is obtained. According to the peak-to-peak value of the quadrature control force, the conversion coefficient, the angular frequency of the excitation force, the stable vibration amplitude value of the resonator, and a preset frequency splitting formula, the frequency splitting of the gyroscope is determined. The method has the advantages of high precision, good reliability and fast solving speed.

Description

Technical Field

[0001] This invention relates to the field of frequency splitting determination, and in particular to a high-precision, high-efficiency resonant gyroscope frequency splitting measurement method and related components. Background Technology

[0002] When a gyroscope is working, the harmonic oscillator within it maintains a second-order vibration state. The motion of the harmonic oscillator can be understood as the superposition of two degrees of freedom resonant vibrations. In an ideal harmonic oscillator, the two degrees of freedom resonant vibrations have the same frequency, resulting in a frequency split of 0. However, in reality, due to asymmetries in materials, manufacturing processes, and assembly, the two degrees of freedom resonant vibrations of the harmonic oscillator have different eigenfrequencys, making the frequency split non-zero. The closer the eigenfrequency of the two degrees of freedom vibrations are, the smaller the frequency split of the gyroscope, and the higher its sensitivity. Therefore, frequency split is a crucial parameter for judging the performance of a gyroscope. Thus, it is essential to provide a method for quickly and accurately determining the frequency split. Summary of the Invention

[0003] The purpose of this invention is to provide a high-precision and high-efficiency method for measuring the frequency splitting of a resonant gyroscope and related components. This method can determine the frequency splitting based on the peak-to-peak value of the orthogonal control force of the gyroscope, and has the advantages of high precision, high reliability and fast solution speed.

[0004] To address the aforementioned technical problems, this invention provides a high-precision, high-efficiency method for measuring the frequency fragmentation of a resonant gyroscope, comprising:

[0005] Determine the decay time constant of the harmonic oscillator in the gyroscope when damping is introduced;

[0006] An excitation force is applied to the harmonic oscillator to control its vibration to a preset amplitude value. The conversion coefficient between the amplitude of the excitation force control quantity and the amplitude of the excitation force is determined based on the amplitude of the excitation force control quantity corresponding to the excitation force, the angular frequency of the excitation force, the stable vibration amplitude value of the harmonic oscillator, and the decay time constant.

[0007] The gyroscope is controlled to operate in full-angle mode and the vibration mode of the harmonic oscillator is precession about the axis of symmetry, and the peak-to-peak value of the orthogonal control force during the precession process of the harmonic oscillator is obtained;

[0008] The frequency split of the gyroscope is determined based on the peak-to-peak value of the orthogonal control force, the conversion coefficient, the angular frequency of the excitation force, the stable vibration amplitude of the harmonic oscillator, and a preset frequency splitting formula.

[0009] Optionally, determining the decay time constant when damping is introduced in the resonator of the gyroscope includes:

[0010] After controlling the resonator in the gyroscope to vibrate to a first preset amplitude value, the force applied to the resonator is removed to determine the amplitude decay curve of the resonator, and the amplitude decay curve is fitted to determine the decay time constant.

[0011] Optionally, removing the force applied to the resonator to determine the amplitude decay curve of the resonator, and fitting the amplitude decay curve to determine the decay time constant, includes:

[0012] The force applied to the harmonic oscillator is removed, and the first dynamic equation of the harmonic oscillator after the force is removed is determined. The first dynamic equation is: Wherein, τ is the decay time constant, ω0 is the eigenfrequency of the simple harmonic oscillator, and x represents the displacement of the harmonic oscillator;

[0013] The first dynamic equation is solved using the method of undetermined coefficients to obtain the fitting equation for the amplitude decay curve. The fitting equation for the amplitude decay curve is as follows: Where a0 is the detected initial vibration amplitude value of the harmonic oscillator, and t is time. This is the initial phase;

[0014] The decay time constant is determined based on the fitting equation of the amplitude decay curve.

[0015] Optionally, an excitation force is applied to the resonator to control its vibration to a preset amplitude value. A conversion coefficient between the amplitude of the excitation force control quantity and the amplitude of the excitation force is determined based on the amplitude of the excitation force control quantity corresponding to the excitation force, the angular frequency of the excitation force, the stable vibration amplitude value of the resonator, and the decay time constant. This includes:

[0016] The second dynamic equation corresponding to the harmonic oscillator after the excitation force is applied to the harmonic oscillator is determined, and the second dynamic equation is: Where x represents the displacement of the harmonic oscillator, τ is the decay time constant, ω0 is the eigenfrequency of the simple harmonic oscillator, f0 is the amplitude of the excitation force, and ω f The angular frequency of the excitation force;

[0017] The second dynamic equation is solved using the method of undetermined coefficients to obtain the steady-state solution of the harmonic oscillator. The steady-state solution of the harmonic oscillator is: x = a1cos(ω f t+ψ), where a1 is the detected stable vibration amplitude value of the harmonic oscillator, and ψ is the initial phase;

[0018] Substitute the steady-state solution of the vibration of the harmonic oscillator into the second dynamic equation corresponding to the harmonic oscillator to determine the correspondence between the detected stable vibration amplitude of the harmonic oscillator and the amplitude of the excitation force.

[0019] The preset conversion coefficient relationship is determined based on the correspondence between the stable vibration amplitude of the harmonic oscillator and the amplitude of the excitation force;

[0020] The amplitude of the excitation force control quantity corresponding to the excitation force, the angular frequency of the excitation force, the stable vibration amplitude of the harmonic oscillator, and the decay time constant are input into the preset conversion coefficient relationship, and the conversion coefficient is obtained through the preset conversion coefficient relationship.

[0021] Optionally, determining the correspondence between the detected stable vibration amplitude of the resonator and the amplitude of the excitation force includes:

[0022] The correspondence between the stable vibration amplitude of the harmonic oscillator and the amplitude of the excitation force is determined as follows:

[0023] Where, λ*n0=f0, a1 is the detected stable vibration amplitude value of the harmonic oscillator, λ is the conversion coefficient, n0 is the amplitude of the excitation force control quantity, τ is the decay time constant, and ω f f0 is the angular frequency of the excitation force, and f0 is the amplitude of the excitation force.

[0024] Optionally, the frequency split of the gyroscope is determined based on the peak-to-peak value of the orthogonal control force, the conversion coefficient, the angular frequency of the excitation force, the stable vibration amplitude of the resonator, and a preset frequency split formula, including:

[0025] Substitute the peak-to-peak value of the orthogonal control force, the conversion coefficient, the angular frequency of the excitation force, and the vibration amplitude value of the harmonic oscillator into the preset frequency decomposition formula, and use the solution of the preset frequency decomposition formula as the frequency decomposition of the gyroscope;

[0026] The preset frequency splitting formula is: Among them, f y -f x For the frequency splitting of the gyroscope, ω f For the purposes of this discussion, n Qpp λ is the peak-to-peak value of the orthogonal control force, λ is the conversion coefficient, and a1 is the detected stable vibration amplitude value of the harmonic oscillator.

[0027] To address the aforementioned technical problems, this application also provides a high-precision, high-efficiency resonant gyroscope frequency splitting measurement system, comprising:

[0028] The decay time constant determination unit is used to determine the decay time constant when damping is introduced into the harmonic oscillator in the gyroscope;

[0029] A conversion coefficient determination unit is used to apply an excitation force to the resonator to control the resonator to vibrate to a preset amplitude value, and to determine the conversion coefficient between the amplitude of the excitation force control quantity and the amplitude of the excitation force based on the amplitude of the excitation force control quantity corresponding to the excitation force, the angular frequency of the excitation force, the stable vibration amplitude value of the resonator, and the decay time constant.

[0030] The orthogonal control force peak-to-peak value determination unit is used to control the gyroscope to operate in full-angle mode and the vibration mode of the harmonic oscillator to precess around the axis of symmetry, and to obtain the peak-to-peak value of the orthogonal control force during the precession process of the harmonic oscillator.

[0031] The frequency splitting determination unit is used to determine the frequency splitting of the gyroscope based on the peak-to-peak value of the orthogonal control force, the conversion coefficient, the angular frequency of the excitation force, the stable vibration amplitude value of the harmonic oscillator, and a preset frequency splitting formula.

[0032] Optionally, the frequency splitting determination unit is specifically used for:

[0033] Substitute the peak-to-peak value of the orthogonal control force, the conversion coefficient, the angular frequency of the excitation force, and the stable vibration amplitude value of the harmonic oscillator into the preset frequency decomposition formula, and use the solution of the preset frequency decomposition formula as the frequency decomposition of the gyroscope;

[0034] The preset frequency splitting formula is: Among them, f y -f x For the frequency splitting of the gyroscope, ω f Let n be the angular frequency of the excitation force. Qpp λ is the peak-to-peak value of the orthogonal control force, λ is the conversion coefficient, and a1 is the detected stable vibration amplitude value of the harmonic oscillator.

[0035] To address the aforementioned technical problems, this application also provides a high-precision, high-efficiency resonant gyroscope frequency splitting measurement device, comprising:

[0036] Memory, used to store computer programs;

[0037] A processor is used to execute the computer program to implement the steps of any of the above-described high-precision and high-efficiency resonant gyroscope frequency splitting measurement methods.

[0038] To address the aforementioned technical problems, this application also provides a computer-readable storage medium storing a computer program, which, when executed by a processor, implements the steps of any of the above-described high-precision, high-efficiency resonant gyroscope frequency splitting measurement methods.

[0039] The beneficial effect of this application lies in providing a high-precision and high-efficiency frequency splitting measurement method and related components for resonant gyroscopes. First, the decay time constant of the resonator in the gyroscope when damping is introduced is determined. An excitation force is applied to the resonator to control its vibration to a preset amplitude value. Based on the amplitude of the excitation force control quantity, the angular frequency of the excitation force, the stable vibration amplitude of the resonator, and the decay time constant, the conversion coefficient between the amplitude of the excitation force control quantity and the amplitude of the excitation force is determined. The gyroscope is controlled to operate in full-angle mode with the resonator's vibration mode precessing around its axis of symmetry, and the peak-to-peak value of the orthogonal control force during the resonator's precession process is obtained. The frequency splitting of the gyroscope is determined based on the peak-to-peak value of the orthogonal control force, the conversion coefficient, the angular frequency of the excitation force, the stable vibration amplitude of the resonator, and the preset frequency splitting formula. This method has the advantages of high precision, high reliability, and fast solution speed. Attached Figure Description

[0040] To more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings used in the prior art and embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0041] Figure 1 A flowchart of a high-precision and high-efficiency resonant gyroscope frequency splitting measurement method provided by the present invention;

[0042] Figure 2 A decay amplitude curve of a harmonic oscillator for a gyroscope provided in this application;

[0043] Figure 3 A schematic diagram of a high-precision and high-efficiency resonant gyroscope frequency splitting measurement system provided by the present invention;

[0044] Figure 4 A schematic diagram of a high-precision and high-efficiency resonant gyroscope frequency splitting measurement device provided by the present invention;

[0045] Figure 5 This is a schematic diagram of the structure of a computer-readable storage medium provided by the present invention. Detailed Implementation

[0046] The core of this invention is to provide a high-precision and high-efficiency resonant gyroscope frequency splitting measurement method and related components, which can determine the frequency splitting based on the peak-to-peak value of the orthogonal control force of the gyroscope, and has the advantages of high precision, good reliability and fast solution speed.

[0047] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, 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, 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.

[0048] Please refer to Figure 1 , Figure 1 A flowchart of a high-precision, high-efficiency resonant gyroscope frequency splitting measurement method provided by the present invention is provided, the method comprising:

[0049] S1: Determine the decay time constant when damping is introduced into the harmonic oscillator in the gyroscope;

[0050] S2: Apply an excitation force to the harmonic oscillator to control its vibration to a preset amplitude value. Determine the conversion coefficient between the amplitude of the excitation force control quantity and the amplitude of the excitation force based on the amplitude of the excitation force control quantity, the angular frequency of the excitation force, the stable vibration amplitude value of the harmonic oscillator, and the decay time constant.

[0051] S3: Control the gyroscope to operate in full-angle mode and the resonator to precess around the axis of symmetry, and obtain the peak-to-peak value of the orthogonal control force during the precession of the resonator;

[0052] S4: Determine the frequency split of the gyroscope based on the peak-to-peak value of the orthogonal control force, the conversion coefficient, the angular frequency of the excitation force, the stable vibration amplitude of the harmonic oscillator, and the preset frequency split formula.

[0053] The frequency split determination method of this application differs from previous methods that obtain frequency split information from the evolution of superimposed signals. This application uses the peak-to-peak value of the orthogonal control force during control to determine the frequency split value. By controlling the resonator to vibrate to a certain amplitude value and then removing all forces, the amplitude decay curve of the resonator can be observed, and the decay time constant can be obtained by fitting the amplitude decay curve. The resonator is controlled to a specific amplitude (i.e., a preset amplitude value) to obtain the conversion coefficient between the amplitude of the excitation force control quantity and the amplitude of the excitation force. The gyroscope is controlled in full-angle mode, and the resonator vibration mode is made to precess around the axis of symmetry using a turntable or a virtual precession control method. During the precession of the resonator, the orthogonal control force changes sinusoidally. The frequency split can be obtained from the peak-to-peak value of the orthogonal control force using a preset frequency split formula, which has the advantages of high accuracy, high reliability, and fast solution speed. It should also be noted that the gyroscope in this application is a Coriolis gyroscope.

[0054] The specific process for determining the decay time constant in this application is as follows: After controlling the resonator in the gyroscope to vibrate to a first preset amplitude value, the force applied to the resonator is removed to determine the amplitude decay curve of the resonator, and the amplitude decay curve is fitted to determine the decay time constant. Specifically, damping is introduced into the simple resonator, and the damping can be described by the decay time constant τ. The first dynamic equation of the damped resonator can be expressed as: Where τ is the decay time constant, ω0 is the eigenfrequency of the simple harmonic oscillator, and x represents the displacement of the harmonic oscillator. The equation can be solved using the method of undetermined coefficients, let the solution be... Considering the orthogonality between sin and cos, we can then obtain... Where a0 is the detected initial vibration amplitude value of the harmonic oscillator, and t is time. As the initial phase, a0 and Determined by initial conditions. Please refer to... Figure 2 , Figure 2 The diagram shows the attenuation amplitude curve of a harmonic oscillator for a gyroscope provided in this application. Clearly, damping causes the vibration amplitude to decay exponentially (amplitude = ...). The decay time constant τ can be obtained based on the amplitude decay curve using an exponential fitting method.

[0055] Based on this, the specific process by which this application determines the conversion coefficient between the excitation force control quantity and the excitation force applied to the resonator is as follows: An excitation force is applied to the damped resonator to induce forced vibration. Assume the amplitude of the excitation force is f0, and the angular frequency is ω. f With the initial phase set to 0, the second dynamic equation of the harmonic oscillator becomes: The steady-state solution of the equation is obtained using the method of undetermined coefficients. Let the steady-state solution of the harmonic oscillator be x = a1cos(ω). fGiven t+ψ), and considering the orthogonality between sin and cos, the equation can be decomposed into:

[0056]

[0057] When ω0=ω f When cosψ=0, This simplified solution represents the state that needs to be controlled when controlling the resonator. Typically, phase-locked loops are used to control the phase of the excitation force to lead the signal. Then this state can be achieved.

[0058] Clearly, the stable vibration amplitude a1 of the damped resonator is proportional to the amplitude of the excitation force f0, and the stable vibration amplitude a1 of the damped resonator is proportional to the decay time constant τ. During control, a DAC outputs an analog voltage, which is then converted into electrostatic force, i.e., the excitation force, at the resonator electrodes via an analog circuit. This conversion process is relatively complex, but linear and deterministic. Therefore, this application uses a coefficient λ to replace this conversion f0 = λn0, where n0 is the amplitude value of the DAC conversion during control, i.e., the amplitude of the excitation force control quantity. Thus, we can obtain... In practice, n0 is the applied known and definite amplitude, τ can be quickly obtained by fitting the attenuation curve as shown in the previous section, and ω f This can be easily obtained from phase-locked loop, where a1 is the detected signal amplitude value. The value of the conversion coefficient λ can be obtained from the above formula.

[0059] Furthermore, a resonant gyroscope can typically be considered as the superposition of the motions of two simple harmonic oscillators vibrating along their principal axes. In reality, the intrinsic frequencies of the two harmonic oscillators along their stiffness principal axes are different; this difference is known as frequency splitting. Moreover, the damping asymmetry of a resonant gyroscope is usually small, so the damping can be considered uniform. This application further analyzes the frequency splitting in both cases where the stiffness axis and the electrode detection direction are aligned and inconsistent, as detailed below:

[0060] When the stiffness axis direction and the electrode detection direction are aligned, and when the stiffness axis direction of the resonant gyroscope is aligned with the electrode direction, the two equations corresponding to the two degrees of freedom channels of the resonator are independent:

[0061]

[0062] With uniform damping, the τ for both degrees of freedom is the same, and the eigenfrequency ω for the x-channel and y-channel are respectively... x and ω y The amplitude and angular frequency (or phase) of the vibration signals from the two channels are determined by the force F of the two channels. x and F yThe decision is made. Clearly, to maintain the two degrees of freedom of the resonant gyroscope in phase (a requirement that the resonator must meet in force balance mode or full-angle mode control), forces F from both channels are needed. x and F y Having the same frequency, and because ω x ≠ω y F x and F y They have different phases.

[0063] Assuming the harmonic oscillator is controlled at angle α, that is Substituting into the left side of the second dynamic equation, we get:

[0064]

[0065] Clearly, if the forces of the two channels are as shown on the right side of the above equation, the control requirements are met. Furthermore, in resonant gyroscope control, the amplitude control force leads the phase of the detection signal. The waveform of the amplitude control force is then: The quadrature control force is the amplitude control force plus the phase. The waveform of the orthogonal control force is obtained as follows:

[0066] Where ω f It is between ω x and ω y Between. Without loss of generality, choose ω. y >ω x Take ω y =ω x +dω, then ω f >ω x .

[0067]

[0068] In terms of control, the strategy adopted in this application is:

[0069]

[0070] By correlating the theoretical formula with the control formula, we obtain the amplitude control force as follows: As can be seen, the results are consistent with those obtained for a single-degree-of-freedom simple harmonic oscillator. Furthermore, due to the absence of damping inhomogeneity, the amplitude control force does not change with the mode shape angle α.

[0071] The equation for the orthogonal control force is obtained at the same time.

[0072] Based on the above formula, we can obtain

[0073]

[0074] F Q The angle α changes with different mode shapes. When a full-angle gyroscope is placed on a turntable and the gyroscope is rotated, or by using virtual precession to gradually change the mode shape angle (preferably along a linear shape), i.e., by gradually changing α, F can be observed. Q It varies with the sine function of α. From F Q The extreme values ​​can be obtained as a quantity proportional to the frequency split. The frequency split can be obtained by the relative magnitudes of the amplitude control force and the quadrature control force.

[0075] Considering the actual amplitude of the orthogonal control force is n Q λ=F Q F Q It is difficult to obtain in practice, while n Q The control variable added in the control process is known. Therefore, the frequency decomposition can be simply obtained as:

[0076] ω f With ω y and ω x Therefore, the preset frequency splitting formula in this application is approximately... Among them, f y -f x For the frequency splitting of the gyroscope, ω f Let n be the angular frequency of the excitation force. Qpp λ is the peak-to-peak value of the orthogonal control force, λ is the conversion coefficient, and a1 is the detected initial vibration amplitude value of the harmonic oscillator.

[0077] Furthermore, if we consider that the direction of the principal stiffness axis is not consistent with the direction of the electrode, there exists an included angle θ. ω ,θ ω The value of θ is random. ω At the same time, the above approach still holds true. The dynamic equation in this case can be expressed as:

[0078]

[0079] in Following the same control strategy as in the previous section, we can similarly derive the following:

[0080]

[0081] It can be seen that θ ω The difference only causes the orthogonal control force of the gyroscope to vary with the mode shape angle θ. ω The maximum and minimum values ​​of the translation and orthogonal control are still determined by the frequency split. Therefore, the above approach also holds true in general.

[0082] In summary, the preset frequency splitting formula is as follows: Among them, f y -f x For the frequency splitting of the gyroscope, ω f Let n be the angular frequency of the excitation force. Qpp Let λ be the peak-to-peak value of the orthogonal control force, λ be the conversion coefficient, and a1 be the detected stable vibration amplitude value of the resonator. Substituting the peak-to-peak value of the orthogonal control force, the conversion coefficient, the angular frequency of the excitation force, and the stable vibration amplitude value of the resonator into the preset frequency decomposition formula, the solution of the preset frequency decomposition formula is the frequency decomposition of the gyroscope.

[0083] It should also be noted that when the frequency fragmentation of the gyroscope is relatively small, the effects of uneven damping and environmental fluctuations on the methods used to determine the frequency fragmentation of the gyroscope in related technologies are very significant, resulting in large fluctuations and generally low reliability. In contrast, the high-precision, high-efficiency resonant gyroscope frequency fragmentation measurement method provided in this application is highly efficient, has a short waiting time, high accuracy, good reliability, is unaffected by external rotational speed, and can perform multiple measurements quickly. Furthermore, the frequency fragmentation of the gyroscope can be observed in real time while the gyroscope is operating in full-angle mode, recording whether there are changes in the frequency fragmentation, which facilitates the analysis of the gyroscope's characteristics.

[0084] In summary, this application provides a high-precision and high-efficiency method for measuring the frequency splitting of a resonant gyroscope. First, the decay time constant of the resonator in the gyroscope when damping is introduced is determined. An excitation force is applied to the resonator to control its vibration to a preset amplitude value. Based on the amplitude of the excitation force control quantity, the angular frequency of the excitation force, the stable vibration amplitude of the resonator, and the decay time constant, the conversion coefficient between the amplitude of the excitation force control quantity and the amplitude of the excitation force is determined. The gyroscope is controlled to operate in full-angle mode with the resonator's vibration mode precessing around its axis of symmetry, and the peak-to-peak value of the orthogonal control force during the resonator's precession process is obtained. The frequency splitting of the gyroscope is determined based on the peak-to-peak value of the orthogonal control force, the conversion coefficient, the angular frequency of the excitation force, the stable vibration amplitude of the resonator, and the preset frequency splitting formula. This method has the advantages of high precision, high reliability, and fast solution speed.

[0085] Based on the above embodiments:

[0086] As an optional embodiment, determining the decay time constant when damping is introduced in the resonator of the gyroscope includes:

[0087] After controlling the resonator in the gyroscope to vibrate to the first preset amplitude value, the force applied to the resonator is removed to determine the amplitude decay curve of the resonator, and the amplitude decay curve is fitted to determine the decay time constant.

[0088] Specifically, the first dynamic equation of the harmonic oscillator is determined after the force applied to it is removed. The first dynamic equation is: Where τ is the decay time constant, ω0 is the eigenfrequency of the simple harmonic oscillator, and x represents the displacement of the harmonic oscillator;

[0089] The first dynamic equation is solved using the method of undetermined coefficients to obtain the fitting equation for the amplitude decay curve. The fitting equation for the amplitude decay curve is as follows: Where a0 is the detected initial vibration amplitude of the harmonic oscillator, and t is time. This is the initial phase;

[0090] The decay time constant is determined based on the fitting equation of the amplitude decay curve.

[0091] In this embodiment, damping is introduced into the simple harmonic oscillator to determine its amplitude decay curve, and then the decay time constant is calculated. The damping is described by the time constant τ, and the dynamic equation of the damped harmonic oscillator can be expressed as:

[0092] Solve the equation using the method of undetermined coefficients, and let the solution be...

[0093]

[0094]

[0095] Considering the orthogonality between sin and cos, the equation can be decomposed into

[0096]

[0097] get then Where a0 and Determined by the initial conditions. Clearly, damping causes the vibration amplitude to decay exponentially (amplitude = ...). The presence of damping causes the damped oscillation frequency of the harmonic oscillator to decrease compared to its intrinsic oscillation frequency, ω < ω0. The damping time constant τ can be easily obtained by using an exponential fitting method to the envelope dashed line in the above figure.

[0098] As an optional embodiment, an excitation force is applied to the resonator to control its vibration to a preset amplitude value. A conversion coefficient between the amplitude of the excitation force control quantity and the amplitude of the excitation force is determined based on the amplitude of the excitation force control quantity, the angular frequency of the excitation force, the stable vibration amplitude of the resonator, and the decay time constant. This includes:

[0099] The second dynamic equation of the harmonic oscillator after applying an excitation force is determined. The second dynamic equation is: Where x represents the displacement of the harmonic oscillator, τ is the decay time constant, ω0 is the eigenfrequency of the simple harmonic oscillator, f0 is the amplitude of the excitation force, and ω f The angular frequency of the excitation force;

[0100] The steady-state solution of the harmonic oscillator is obtained by solving the second dynamic equation using the method of undetermined coefficients. The steady-state solution of the harmonic oscillator is: x = a1cos(ω f t+ψ), where a1 is the detected stable vibration amplitude of the harmonic oscillator, and ψ is the initial phase;

[0101] Substitute the steady-state solution of the harmonic oscillator into the second dynamic equation corresponding to the harmonic oscillator to determine the correspondence between the detected steady vibration amplitude of the harmonic oscillator and the amplitude of the excitation force.

[0102] The preset conversion coefficient relationship is determined based on the correspondence between the stable vibration amplitude of the harmonic oscillator and the amplitude of the excitation force;

[0103] The amplitude of the excitation force control quantity corresponding to the excitation force, the angular frequency of the excitation force, the stable vibration amplitude of the harmonic oscillator, and the decay time constant are input into the preset conversion coefficient relationship, and the conversion coefficient is obtained through the preset conversion coefficient relationship.

[0104] In this embodiment, to determine the conversion coefficient, a further excitation force is applied to the damped resonator, causing it to undergo forced vibration. Assume the amplitude of the excitation force is f0, and the angular frequency is ω. f With the initial phase set to 0, the dynamic equations become:

[0105]

[0106] The steady-state solution of the equation is obtained using the method of undetermined coefficients. Let the steady-state solution of the harmonic oscillator be x = a1cos(ω). f If t+ψ), then:

[0107]

[0108] Substituting into the dynamic equation, we get:

[0109]

[0110] Considering the orthogonality between sin and cos, the equation can be decomposed into:

[0111]

[0112] When ω0=ω f When cosψ=0, This simplified solution represents the state that needs to be controlled when controlling the resonator. Typically, phase-locked loops are used to control the phase of the excitation force to lead the signal. Then this state can be achieved.

[0113] Clearly, the stable vibration amplitude a1 of the damped resonator is proportional to the amplitude of the excitation force f0, and the stable vibration amplitude a1 of the damped resonator is proportional to the decay time constant τ. During control, a DAC outputs an analog voltage, which is then converted into electrostatic force, i.e., the excitation force, at the resonator electrodes via an analog circuit. This conversion process is relatively complex, but linear and deterministic. Therefore, this application uses a coefficient λ to replace this conversion f0 = λn0, where n0 is the amplitude value of the DAC conversion during control, i.e., the amplitude of the excitation force control quantity. Thus, we can obtain... In practice, n0 is the applied known and definite amplitude, τ can be quickly obtained by fitting the attenuation curve as shown in the previous section, and ω f The amplitude of the signal can be easily obtained from the phase-locked loop, where a1 is the detected signal amplitude value. The value of the conversion coefficient λ can be obtained from the above formula. Based on this, the frequency split of the high-precision and high-efficiency resonant gyroscope frequency split measurement gyroscope is determined according to the peak-to-peak value of the orthogonal control force, the conversion coefficient, the angular frequency of the excitation force, the stable vibration amplitude value of the resonator, and the preset frequency split formula. It has the advantages of high accuracy, good reliability, and fast solution speed.

[0114] Please refer to Figure 3 , Figure 3 This invention provides a schematic diagram of a high-precision, high-efficiency resonant gyroscope frequency splitting measurement system, which includes:

[0115] The decay time constant determination unit 11 is used to determine the decay time constant when damping is introduced into the harmonic oscillator in the gyroscope.

[0116] The conversion coefficient determination unit 12 is used to apply an excitation force to the resonator to control the resonator to vibrate to a preset amplitude value. It determines the conversion coefficient between the amplitude of the excitation force control quantity and the amplitude of the excitation force based on the amplitude of the excitation force control quantity corresponding to the excitation force, the angular frequency of the excitation force, the stable vibration amplitude value of the resonator, and the decay time constant.

[0117] The orthogonal control force peak-to-peak value determination unit 13 is used to control the gyroscope to operate in full-angle mode and the vibration mode of the harmonic oscillator to precess around the axis of symmetry, and to obtain the peak-to-peak value of the orthogonal control force during the precession process of the harmonic oscillator.

[0118] The frequency splitting determination unit 14 is used to determine the frequency splitting of the gyroscope based on the peak-to-peak value of the orthogonal control force, the conversion coefficient, the angular frequency of the excitation force, the stable vibration amplitude of the harmonic oscillator, and the preset frequency splitting formula.

[0119] For a detailed description of the high-precision and high-efficiency resonant gyroscope frequency splitting measurement system provided in this application, please refer to the embodiments of the high-precision and high-efficiency resonant gyroscope frequency splitting measurement method described above. This application will not repeat the details here.

[0120] Based on the above embodiments:

[0121] As an optional embodiment, the frequency splitting determination unit 14 is specifically used for:

[0122] Substitute the peak-to-peak value of the orthogonal control force, the conversion coefficient, the angular frequency of the excitation force, and the stable vibration amplitude of the harmonic oscillator into the preset frequency decomposition formula, and use the solution of the preset frequency decomposition formula as the frequency decomposition of the gyroscope.

[0123] The preset frequency splitting formula is as follows Among them, f y -f x For frequency decomposition of the gyroscope, ω f n is the angular frequency of the excitation force. Qpp λ is the peak-to-peak value of the orthogonal control force, λ is the conversion coefficient, and a1 is the measured stable vibration amplitude of the harmonic oscillator.

[0124] Please refer to Figure 4 , Figure 4 This invention provides a schematic diagram of a high-precision, high-efficiency resonant gyroscope frequency splitting measurement device, which includes:

[0125] Memory 21 is used to store computer programs;

[0126] The processor 22 is used to execute a computer program to implement the steps of any of the above-mentioned high-precision and high-efficiency resonant gyroscope frequency splitting measurement methods.

[0127] For a detailed description of the high-precision and high-efficiency resonant gyroscope frequency splitting measurement device provided in this application, please refer to the embodiments of the high-precision and high-efficiency resonant gyroscope frequency splitting measurement method described above. This application will not repeat the details here.

[0128] Please refer to Figure 5 , Figure 5 This is a schematic diagram of a computer-readable storage medium provided in this application. The computer-readable storage medium 31 stores a computer program, which, when executed by a processor, implements the steps of any of the above-mentioned high-precision and high-efficiency resonant gyroscope frequency splitting measurement methods.

[0129] For a detailed description of the computer-readable storage medium 31 provided in this application, please refer to the embodiments of the high-precision and high-efficiency resonant gyroscope frequency splitting measurement method described above. This application will not repeat the details here.

[0130] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the apparatus disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the description is relatively simple; relevant parts can be referred to the method section.

[0131] It should also be noted that, in this specification, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0132] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A high-precision, high-efficiency method for measuring the frequency splitting of a resonant gyroscope, characterized in that, include: Determine the decay time constant of the harmonic oscillator in the gyroscope when damping is introduced; An excitation force is applied to the harmonic oscillator to control its vibration to a preset amplitude value. The conversion coefficient between the amplitude of the excitation force control quantity and the amplitude of the excitation force is determined based on the amplitude of the excitation force control quantity corresponding to the excitation force, the angular frequency of the excitation force, the stable vibration amplitude value of the harmonic oscillator, and the decay time constant. The gyroscope is controlled to operate in full-angle mode and the vibration mode of the harmonic oscillator is precession about the axis of symmetry, and the peak-to-peak value of the orthogonal control force during the precession process of the harmonic oscillator is obtained; The frequency split of the gyroscope is determined based on the peak-to-peak value of the orthogonal control force, the conversion coefficient, the angular frequency of the excitation force, the stable vibration amplitude of the harmonic oscillator, and a preset frequency split formula. Specifically, applying an excitation force to the resonator to control its vibration to a preset amplitude value, and determining the conversion coefficient between the amplitude of the excitation force control quantity and the amplitude of the excitation force based on the amplitude of the excitation force control quantity corresponding to the excitation force, the angular frequency of the excitation force, the stable vibration amplitude value of the resonator, and the decay time constant, includes: The second dynamic equation corresponding to the harmonic oscillator after the excitation force is applied to the harmonic oscillator is determined, and the second dynamic equation is: Where x represents the displacement of the harmonic oscillator. The decay time constant is... Let be the eigenfrequency of the simple harmonic oscillator. The amplitude of the excitation force, The angular frequency of the excitation force; The second dynamic equation is solved using the method of undetermined coefficients to obtain the steady-state solution of the harmonic oscillator. The steady-state solution of the harmonic oscillator is as follows: ,in, The measured stable vibration amplitude value of the harmonic oscillator is... This refers to the steady-state vibration phase of the harmonic oscillator; Substitute the steady-state solution of the vibration of the harmonic oscillator into the second dynamic equation corresponding to the harmonic oscillator to determine the correspondence between the detected stable vibration amplitude of the harmonic oscillator and the amplitude of the excitation force. The preset conversion coefficient relationship is determined based on the correspondence between the stable vibration amplitude of the harmonic oscillator and the amplitude of the excitation force; The amplitude of the excitation force control quantity corresponding to the excitation force, the angular frequency of the excitation force, the stable vibration amplitude of the harmonic oscillator, and the decay time constant are input into the preset conversion coefficient relationship, and the conversion coefficient is obtained through the preset conversion coefficient relationship.

2. The high-precision, high-efficiency resonant gyroscope frequency splitting measurement method as described in claim 1, characterized in that, The determination of the decay time constant when damping is introduced in the harmonic oscillator of the gyroscope includes: After controlling the resonator in the gyroscope to vibrate to a first preset amplitude value, the force applied to the resonator is removed to determine the amplitude decay curve of the resonator, and the amplitude decay curve is fitted to determine the decay time constant.

3. The high-precision, high-efficiency resonant gyroscope frequency splitting measurement method as described in claim 2, characterized in that, Removing the force applied to the resonator to determine the amplitude decay curve of the resonator, and fitting the amplitude decay curve to determine the decay time constant, includes: The force applied to the harmonic oscillator is removed, and the first dynamic equation of the harmonic oscillator after the force is removed is determined. The first dynamic equation is: ,in, The decay time constant is... Let be the eigenfrequency of the simple harmonic oscillator, and x represent the displacement of the harmonic oscillator. The first dynamic equation is solved using the method of undetermined coefficients to obtain the fitting equation for the amplitude decay curve. The fitting equation for the amplitude decay curve is as follows: ,in, The initial vibration amplitude value of the harmonic oscillator is detected, where t is time. This is the initial phase of the free decaying vibration of the harmonic oscillator; The decay time constant is determined based on the fitting equation of the amplitude decay curve.

4. The high-precision, high-efficiency resonant gyroscope frequency splitting measurement method as described in claim 1, characterized in that, Determining the correspondence between the detected stable vibration amplitude of the harmonic oscillator and the amplitude of the excitation force includes: The correspondence between the stable vibration amplitude of the harmonic oscillator and the amplitude of the excitation force is determined as follows: ,in, , The measured stable vibration amplitude value of the harmonic oscillator is... The conversion coefficient is... The amplitude of the excitation force control quantity. The decay time constant is... The angular frequency of the excitation force. The amplitude of the excitation force is given.

5. The high-precision, high-efficiency resonant gyroscope frequency splitting measurement method as described in claim 1, characterized in that, The frequency split of the gyroscope is determined based on the peak-to-peak value of the orthogonal control force, the conversion coefficient, the angular frequency of the excitation force, the stable vibration amplitude of the resonator, and a preset frequency splitting formula, including: Substitute the peak-to-peak value of the orthogonal control force, the conversion coefficient, the angular frequency of the excitation force, and the stable vibration amplitude value of the harmonic oscillator into the preset frequency decomposition formula, and use the solution of the preset frequency decomposition formula as the frequency decomposition of the gyroscope; The preset frequency splitting formula is: ,in, For the frequency splitting of the gyroscope, The angular frequency of the excitation force. The peak-to-peak value of the orthogonal control force. The conversion coefficient is... The measured stable vibration amplitude value of the harmonic oscillator.

6. A high-precision, high-efficiency resonant gyroscope frequency splitting measurement system, characterized in that, include: The decay time constant determination unit is used to determine the decay time constant when damping is introduced into the harmonic oscillator in the gyroscope; A conversion coefficient determination unit is used to apply an excitation force to the resonator to control the resonator to vibrate to a preset amplitude value, and to determine the conversion coefficient between the amplitude of the excitation force control quantity and the amplitude of the excitation force based on the amplitude of the excitation force control quantity corresponding to the excitation force, the angular frequency of the excitation force, the stable vibration amplitude value of the resonator, and the decay time constant. The orthogonal control force peak-to-peak value determination unit is used to control the gyroscope to operate in full-angle mode and the vibration mode of the harmonic oscillator to precess around the axis of symmetry, and to obtain the peak-to-peak value of the orthogonal control force during the precession process of the harmonic oscillator. The frequency splitting determination unit is used to determine the frequency splitting of the gyroscope based on the peak-to-peak value of the orthogonal control force, the conversion coefficient, the angular frequency of the excitation force, the stable vibration amplitude value of the harmonic oscillator, and a preset frequency splitting formula. Specifically, applying an excitation force to the resonator to control its vibration to a preset amplitude value, and determining the conversion coefficient between the amplitude of the excitation force control quantity and the amplitude of the excitation force based on the amplitude of the excitation force control quantity corresponding to the excitation force, the angular frequency of the excitation force, the stable vibration amplitude value of the resonator, and the decay time constant, includes: The second dynamic equation corresponding to the harmonic oscillator after the excitation force is applied to the harmonic oscillator is determined, and the second dynamic equation is: Where x represents the displacement of the harmonic oscillator. The decay time constant is... Let be the eigenfrequency of the simple harmonic oscillator. The amplitude of the excitation force, The angular frequency of the excitation force; The second dynamic equation is solved using the method of undetermined coefficients to obtain the steady-state solution of the harmonic oscillator. The steady-state solution of the harmonic oscillator is as follows: ,in, The measured stable vibration amplitude value of the harmonic oscillator is... This refers to the steady-state vibration phase of the harmonic oscillator; Substitute the steady-state solution of the vibration of the harmonic oscillator into the second dynamic equation corresponding to the harmonic oscillator to determine the correspondence between the detected stable vibration amplitude of the harmonic oscillator and the amplitude of the excitation force. The preset conversion coefficient relationship is determined based on the correspondence between the stable vibration amplitude of the harmonic oscillator and the amplitude of the excitation force; The amplitude of the excitation force control quantity corresponding to the excitation force, the angular frequency of the excitation force, the stable vibration amplitude of the harmonic oscillator, and the decay time constant are input into the preset conversion coefficient relationship, and the conversion coefficient is obtained through the preset conversion coefficient relationship.

7. The high-precision, high-efficiency resonant gyroscope frequency splitting measurement system as described in claim 6, characterized in that, The frequency splitting determination unit is specifically used for: Substitute the peak-to-peak value of the orthogonal control force, the conversion coefficient, the angular frequency of the excitation force, and the stable vibration amplitude value of the harmonic oscillator into the preset frequency decomposition formula, and use the solution of the preset frequency decomposition formula as the frequency decomposition of the gyroscope; The preset frequency splitting formula is: ,in, For the frequency splitting of the gyroscope, The angular frequency of the excitation force. The peak-to-peak value of the orthogonal control force. The conversion coefficient is... The measured stable vibration amplitude value of the harmonic oscillator.

8. A high-precision, high-efficiency resonant gyroscope frequency splitting measurement device, characterized in that, include: Memory, used to store computer programs; A processor, configured to execute the computer program to implement the steps of the high-precision, high-efficiency resonant gyroscope frequency splitting measurement method as described in any one of claims 1 to 5.

9. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program that, when executed by a processor, implements the steps of the high-precision, high-efficiency resonant gyroscope frequency splitting measurement method as described in any one of claims 1 to 5.

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