Sapphire pendulum of accelerometer and accelerometer

Abstract

This application discloses a sapphire pendulum for an accelerometer and an accelerometer. The sapphire pendulum comprises: a circular disc connected to a fixed ring on the outer ring of the disc via multiple flexible flat beams; multiple flexible flat beams, each of which flexes in the direction of the acceleration input axis of the accelerometer, and each of which is made of a flexible material in the direction close to the acceleration input axis and a rigid material in the direction away from the acceleration input axis; and an outer ring with equally spaced raised structures for mounting gaskets to support the sapphire pendulum. This application solves the technical problem of inaccurate accelerometer measurements.

Description

Technical Field

[0001] The present application relates to the field of electronic devices, and in particular to a sapphire pendulum of an accelerometer and an accelerometer. Background Art

[0002] Accelerometers are key components for measuring the angular rate of a target. In fields such as tunneling, mining, smart transportation, defense equipment, and aerospace, targets (drilling mechanisms, vehicles, drones, personnel, guided munitions, etc.) are subject to long, high-speed, and high-overload conditions during motion. Consequently, there is an urgent need for an accelerometer that is resistant to high overloads, offers high precision, is adaptable to harsh environments, and requires no calibration over a long period of time.

[0003] Existing accelerometers are primarily categorized into liquid-floating pendulum accelerometers, vibrating string accelerometers, vibration inertial accelerometers, vibrating beam accelerometers, micromachined accelerometers, and quartz flexure accelerometers. Quartz flexure accelerometers, based on the principle of servo closed-loop torque balance, offer superior measurement accuracy, linearity, long-term stability, and dynamic characteristics, earning them considerable attention from researchers and scholars both domestically and internationally. They are widely used in fields such as inertial navigation and guidance, as well as in low-frequency vibration calibration, active negative stiffness vibration isolation, and microgravity life and physics research.

[0004] However, due to the limitations of the quartz crystal material itself, the current mass-produced quartz flexible accelerometer has a maximum resolution of 1μg, which is difficult to further improve, and its overload resistance is low.

[0005] To address the above-mentioned problems, no effective solutions have been proposed so far. Summary of the Invention

[0006] The embodiments of the present application provide a sapphire pendulum of an accelerometer and an accelerometer, so as to at least solve the technical problem of inaccurate accelerometer measurement.

[0007] According to one aspect of an embodiment of the present application, a sapphire pendulum of an accelerometer is provided, comprising: a circular disk connected to a fixed ring on the outer ring of the circular disk through a plurality of flexible flat beams; a plurality of flexible flat beams, each of the flexible flat beams being bent in the direction of an acceleration input axis of the accelerometer, and each of the flexible flat beams being made of a flexible material in a direction close to the acceleration input axis and being made of a rigid material in a direction away from the acceleration input axis; and a fixed ring having raised structures distributed at equal intervals for mounting gaskets to support the sapphire pendulum.

[0008] According to another aspect of an embodiment of the present application, an accelerometer is also provided, including a mechanical head and a servo circuit, wherein the mechanical head includes the sapphire pendulum as described above; the servo circuit is used to obtain a measurement value representing acceleration information based on the vibration of the sapphire pendulum.

[0009] In one example, the servo loop includes: a pendulum deflection angle detection module, including a differential capacitance detection circuit, the differential capacitance detection circuit including: two completely symmetrical current detection circuits, configured to use a differential unbalanced bridge detection method to detect the capacitance signal output by the accelerometer head; a differential amplification circuit, configured to load the capacitance signal onto a sinusoidal carrier signal having a frequency greater than a preset frequency threshold; wherein the pendulum deflection angle detection module is further configured to modulate the sinusoidal carrier signal; a signal processing module, configured to demodulate the modulated sinusoidal carrier signal, filter out components in the modulated sinusoidal carrier signal greater than a preset frequency threshold and noise greater than a preset noise threshold, and obtain a measurement value representing acceleration information.

[0010] In one example, the differential capacitance detection circuit further includes two feedback resistors respectively connected between the two completely symmetrical current detection circuits and the differential capacitor, and the accuracy of each feedback resistor is greater than a preset accuracy and the temperature drift is less than a preset temperature drift.

[0011] In one example, the signal processing module includes: a multiplier phase-sensitive demodulation circuit, configured to multiply the modulated sinusoidal carrier signal with a sinusoidal reference signal of the same frequency to obtain a multiplied signal, wherein the multiplied signal includes a component with a frequency lower than a preset frequency threshold and two components with a frequency higher than a preset frequency threshold; a low-pass filter, configured to filter out components with a frequency higher than the preset frequency threshold and separate components with a frequency lower than the preset frequency threshold.

[0012] In one example, a hysteresis phase shift circuit is connected in series to the input end of the same-frequency sinusoidal reference signal, and the hysteresis phase shift circuit is used to adjust the phase difference between the same-frequency sinusoidal reference signal and the modulated sinusoidal carrier signal so that the phase difference meets a preset condition.

[0013] In one example, the signal processing module is further configured to: obtain the transfer function of the pendulum in the acceleration meter header by using open-loop model identification; determine the parameters of the digital controller in the signal processing module based on the transfer function; and compensate the meter header model of the accelerometer based on the parameters of the digital controller.

[0014] In one example, the signal processing module is further configured to: when there is no external input acceleration and the pendulum is in a naturally drooping state, disconnect the digital controller, output an excitation signal through the FPGA to drive the torquer, obtain a response curve, and obtain the transfer function.

[0015] In one example, the signal processing module is further configured to: cancel the integral effect when the controlled quantity of the accelerometer head deviates greatly from the set value; and introduce integral control to eliminate static error when the controlled quantity is close to the set value.

[0016] In one example, the signal processing module further includes an estimator, which is configured to: reflect the delayed controlled variable to the input end of the digital controller in advance to remove pure lag interference.

[0017] In one example, the transfer function is determined based on the rotation angle of the proof mass relative to a zero position, the moment of inertia of the proof mass, the air damping coefficient, the spring constant of the proof mass, the applied torque, the pendulum property, the natural angular frequency of the proof mass, and the damping coefficient of the proof mass.

[0018] The sapphire pendulum in the embodiment of the present application is implemented using the above structure, which solves the technical problem of inaccurate accelerometer measurement. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] The drawings described herein are used to provide a further understanding of the present application and constitute a part of the present application. The illustrative embodiments of the present application and their descriptions are used to explain the present application and do not constitute an improper limitation on the present application. In the drawings:

[0020] Figure 1A 1 is a schematic structural diagram of a multi-beam single-island complementary sapphire flexible digital accelerometer system according to an embodiment of the present application;

[0021] Figure 1B is a schematic cross-sectional structure diagram of a mechanical meter head of an accelerometer according to an embodiment of the present application;

[0022] Figure 2 1 is a schematic diagram of the three-dimensional structure of a sapphire pendulum according to an embodiment of the present application;

[0023] Figure 2A 1 is a front view of a sapphire pendulum according to an embodiment of the present application;

[0024] Figure 2B This is a sapphire pendulum cantilever beam model according to an embodiment of the present application;

[0025] Figure 2C is the first-order mode of the sapphire pendulum according to the embodiment of the present application;

[0026] Figure 2D is the second-order mode of the sapphire pendulum according to the embodiment of the present application;

[0027] Figure 3 is a schematic structural diagram of a servo loop of an accelerometer according to an embodiment of the present application;

[0028] Figure 4 is a structural diagram of a differential capacitance detection circuit according to an embodiment of the present application;

[0029] Figure 5 is a schematic structural diagram of a power amplifier circuit according to an embodiment of the present application;

[0030] Figure 6 1 is a structural diagram of a phase-sensitive demodulation circuit of a multiplier according to an embodiment of the present application;

[0031] Figure 7 is a system open-loop model identification block diagram according to an embodiment of the present application;

[0032] Figure 8 2 is a schematic diagram of a circuit structure using Smith predictive control according to an embodiment of the present application;

[0033] Figure 9 is a flowchart of an error compensation method according to an embodiment of the present application. DETAILED DESCRIPTION

[0034] In order to enable those skilled in the art to better understand the present invention, the following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments in the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts should fall within the scope of protection of this application.

[0035] It should be noted that the terms "first", "second", etc. in the specification and claims of the present application and the above-mentioned drawings are used to distinguish similar objects and are not necessarily used to describe a specific order or sequential order. It should be understood that the data used in this way can be interchangeable where appropriate, so that the embodiments of the present application described herein can be implemented in a sequence other than those illustrated or described herein. In addition, the terms "including" and "having" and any of their variations are intended to cover non-exclusive inclusions, for example, a process, method, system, product or device comprising a series of steps or units is not necessarily limited to those steps or units clearly listed, but may include other steps or units that are not clearly listed or inherent to these processes, methods, products or devices.

[0036] Example 1

[0037] According to an embodiment of the present application, an accelerometer is provided, specifically a sapphire flexible digital accelerometer. Figure 1A FIG is a structural diagram of a multi-beam single-island complementary sapphire flexible digital accelerometer according to an embodiment of the present application, as shown in FIG. Figure 1A As shown, the sapphire flexible digital accelerometer includes a mechanical head 10 and a servo loop 20 .

[0038] refer to Figure 1A and Figure 1B The mechanical meter head 10 mainly includes a sapphire pendulum 11, a torque coil 12, a permanent magnet 13, and a differential capacitor fixed plate 14. The sapphire pendulum 11 and the torque coil 12 are used together for mass detection. The gold-plated surfaces on both sides of the sapphire pendulum 11 serve as the moving plate, which together with the differential capacitor fixed plate 14 form a differential capacitance sensor. The torque coil 12 and the permanent magnet 13 serve as the actuator.

[0039] The servo loop 20 primarily consists of a pendulum deflection angle detection circuit 23, a signal processing module 22, and a feedback drive module 21. The sapphire pendulum senses input acceleration and deflects, causing a corresponding change in the capacitance of the differential capacitor sensor. The servo loop 20 calculates the pendulum deflection angle by detecting this change in differential capacitance. The signal processing module 22 then uses this deflection angle to calculate the feedback value and drives the feedback drive module 21 to force the sapphire pendulum back to its equilibrium position, achieving closed-loop control of the accelerometer. The feedback value calculated by the signal processing module 22 represents the measured acceleration.

[0040] When acceleration a is applied to the accelerometer, an inertia moment is generated at the root of the sapphire flexible flat beam. This inertia moment can be expressed as:

[0041] M a =Pa=mLa

[0042] Among them, M a represents the acceleration torque, P represents the pendulum of the sapphire flexible accelerometer pendulum, m represents the detection mass, and L represents the distance from the center of gravity of the detection mass to the support axis.

[0043] Under the action of the inertial torque, the detection mass deviates from its original equilibrium position, and the capacitance of the two sensing capacitors changes. The servo loop detects the change in capacitance and generates a feedback voltage that is loaded on the torquer coil. The current flowing through the torquer coil wire can be expressed as:

[0044]

[0045] Where, v represents the feedback voltage; R l represents the resistance of the torquer coil; i represents the current flowing through the torquer coil.

[0046] The energized torque coil is acted upon by the Lorentz force in the magnetic field, generating a restoring torque in the opposite direction of the acceleration:

[0047] M=Fl=B δ il a l

[0048] Where M is the restoring torque; F is the Lorentz force; l is the distance from the center of the torquer coil to the support axis; B δ Indicates the magnetic induction intensity of the working air gap; l a Indicates the length of the torquer coil wire.

[0049] The restoring torque drives the detection mass to move in the direction opposite to the acceleration. When the acceleration torque and the restoring torque are equal, the detection mass returns to the equilibrium position. The feedback voltage loaded on the torque coil represents the acceleration information. The relationship between the feedback voltage and the acceleration is:

[0050]

[0051] The servo loop in this embodiment will be described in detail in the following embodiments, and therefore will not be described again here.

[0052] Example 2

[0053] Figure 2 : is a schematic diagram of the three-dimensional structure of a sapphire pendulum according to an embodiment of the present application, Figure 2A : is a front view of a sapphire pendulum according to an embodiment of the present application, as shown in FIG. Figure 2 and 2A As shown, the central disk 111 of the sapphire pendulum and the torquer coil together constitute the detection mass, which serves as an acceleration sensitive element. The conductive layer of the central disk 111 of the sapphire pendulum and the torquer yoke serve as the moving electrode and fixed electrode of the differential capacitor respectively.

[0054] The center disk 111 (independent island) is connected to the outer ring's fixed ring 112 via multiple flexible flat beams 113. These flexible flat beams 113 can flex along the acceleration input axis, exhibiting high flexibility in this direction and rigidity in other directions. The outer ring serves as the supporting structure for the sapphire pendulum, with evenly spaced protrusions for mounting gaskets. Using vacuum deposition of metal thin films, semicircular conductive layers are formed on the upper and lower surfaces of the center disk 111, serving as electrode plates for the differential capacitance sensor. The same method is used to form the guide lines for the differential capacitance sensor signal and the torquer coil drive current on the two flexible flat beams 113.

[0055] refer to Figure 2BThe test mass is fixed to the fixed ring of the outer ring of the sapphire pendulum through two flexible flat beams 113. Since the test mass is highly flexible in the acceleration input direction and rigid in other directions, the sapphire pendulum can be regarded as a cantilever beam model, and each flexible flat beam 113 is treated as a beam with a uniform cross-section, as shown in Figure 2B. Assuming that the two flexible flat beams 113 are completely symmetrical, the single-arm stiffness of each flexible flat beam 113 is analyzed. The relationship between the rotation angle of any cross section on the beam and the deflection at that cross section is:

[0056]

[0057] When the deformation of the flexible flat beam 113 is very small, tanθ≈θ, and the rotation angle of any cross section on the flexible flat beam 113 is equal to the first-order derivative of the deflection at the cross section with respect to the x-coordinate.

[0058]

[0059] When there is acceleration along the input axis of the accelerometer, it is equivalent to an inertial force acting on the center of mass of the detection mass, and the flexible flat beam 113 is bent. The deflection curve equation of the sapphire pendulum should be divided into two sections AB and BC, with a total of four integral constants. The boundary conditions are x = 0, v A =0,θ A =0, the continuity condition is x=L, v B1 =v B2 ,θ B1 =θ B2 .

[0060] The bending moment equation of the flexible flat beam section is:

[0061] M(x)=-F(L+lx)

[0062] The approximate differential equation of the deflection curve of a flexible flat beam is:

[0063]

[0064] The rotation equation of the flexible flat beam is:

[0065]

[0066] According to the boundary conditions x=0,v A =0,θ A =0, we get The rotation equation of the flexible flat beam can be expressed as:

[0067]

[0068] The deflection equation of a flexible flat beam is:

[0069]

[0070] According to the boundary conditions x=0,v A =0,θ A =0, we get Substitute into the above equation. Finally, the deflection equation of the flexible flat beam 113 is obtained as follows:

[0071]

[0072] The angular displacement of the flexible flat beam 113 is the largest at point B, and the corresponding maximum deflection is:

[0073]

[0074] The single-arm stiffness of the flexible flat beam 113 can be expressed as:

[0075]

[0076] Since the two flexible flat beams 113 are completely symmetrical, the combined stiffness of the flexible flat beams 113 is twice the stiffness of a single arm of the flexible flat beam 113:

[0077]

[0078] The cross section of the flexible flat beam 113 is rectangular, and its moment of inertia I is a constant. The relationship between the structure of the flexible flat beam 113 can be expressed as:

[0079]

[0080] Here, b represents the width of the flexible flat beam 113 , and h represents the thickness of the flexible flat beam 113 .

[0081] The stiffness K of the flexible flat beam 113 is proportional to the width b and thickness h of the flexible flat beam 113, and inversely proportional to the length L of the flexible flat beam 113. The greater the stiffness of the flexible flat beam 113, the stronger the impact resistance of the sapphire pendulum and the greater the natural frequency. The maximum deflection v of the flexible flat beam 113 is max The maximum deflection v of the flexible flat beam 113 is proportional to the length L of the flexible flat beam 113. max The larger it is, the higher the sensitivity and resolution of the accelerometer.

[0082] Because the sensitivity and resolution of an accelerometer are inversely proportional to the natural frequency of the sapphire pendulum, this embodiment improves the sensitivity and resolution of the accelerometer by reducing the natural frequency of the sapphire pendulum while meeting the stiffness requirements of the sapphire pendulum. To improve the stability of the accelerometer, this embodiment increases the second-order torsional frequency of the sapphire pendulum, ensuring sufficient stiffness of the flexible flat beam 113 in other directions, thereby improving the ability to resist cross-interference.

[0083] The sapphire pendulum has only one degree of freedom in one direction, but it will still twist in other directions under non-ideal working conditions, affecting the stability of the accelerometer. Therefore, the frequency characteristics of the sapphire pendulum need to be designed. This embodiment uses the modal simulation in ANSYS software to simulate and optimize the vibration mode of the sapphire pendulum. By reducing the first-order natural frequency of the sapphire pendulum, the resolution of the accelerometer is improved. By increasing the second-order torsional frequency of the sapphire pendulum, cross interference is reduced and the stability of the accelerometer is improved. Among them, the first-order mode and second-order mode of the sapphire pendulum are as follows: Figure 2C and 2D shown.

[0084] By selecting the basic size constraints of the sapphire pendulum, setting different constraints, formulating selection criteria, and using orthogonal experimental method and deep learning optimization method, comprehensive optimization is performed to obtain the final structural dimensions of the sapphire pendulum.

[0085] Example 3

[0086] According to an embodiment of the present application, a servo loop is provided, such as Figure 3 As shown, the servo loop may include a pendulum deflection angle detection module 23 , a signal processing module, a power amplifier circuit 210 , and a carrier signal generation module 206 , wherein the signal processing module includes a phase-sensitive demodulation unit 221 and a digital control unit 222 .

[0087] Because the differential capacitor within the accelerometer's head has a capacitance of only tens of picofarads, capacitance variations can reach femtofarads, making it highly susceptible to parasitic capacitance, resulting in a very low signal-to-noise ratio (SNR) for the output signal. To address this issue, the capacitance detection circuit in the servo loop of this embodiment employs a differential unbalanced bridge detection method. Using a DDS algorithm, an FPGA generates a high-frequency sinusoidal carrier signal, which is then loaded onto the high-frequency carrier and modulated to measure the weak capacitance signal. This differential approach reduces the influence of common-mode noise and parasitic capacitance. A phase-sensitive demodulation circuit with a multiplier demodulates the modulated signal, filtering out high-frequency components and high-frequency noise, and separating the low-frequency component representing acceleration information. By adding high-precision AD and DA components, the traditional analog control module is digitized, and the measured values ​​are directly output via a digital communication interface, enabling direct application in digital measurement systems. Finally, a power amplifier circuit enhances the driving capability of the feedback voltage signal, enabling closed-loop feedback control of the accelerometer servo system.

[0088] 1) Pendulum deflection angle detection module.

[0089] The pendulum deflection angle detection module 23 includes a differential capacitance detection circuit. Dual-carrier detection requires that the two carriers are highly symmetrical, which is difficult to implement. Therefore, in this embodiment, a differential capacitance detection circuit is designed based on a single-carrier bridge modulation and demodulation method. The principle of the differential capacitance detection circuit is as follows: Figure 4 As shown, the circuit includes a signal source that generates a high-frequency carrier, two fully symmetrical current-sensing circuits, and a differential amplifier circuit to achieve amplitude modulation of the differential capacitance signal. The differential capacitance detection circuit in this embodiment uses an AC bridge modulation and demodulation capacitance detection circuit, which has high accuracy and a high signal-to-noise ratio.

[0090] A high-frequency carrier voltage V is applied to the moving plate of the differential capacitor. c Since the spectrum of the sine wave is single, it is not easy to introduce other spectrum signals during the signal modulation and demodulation process. Therefore, the carrier signal generation module 206 uses FPGA to implement DDS to generate a high-frequency signal, which is modulated into a sine wave as the carrier signal of the differential capacitor signal. The carrier frequency is f c , the carrier amplitude is The two fixed plates of the differential capacitor are connected to the input terminals of the two current detectors respectively.

[0091] In order to improve the accuracy and signal-to-noise ratio of the circuit, a low-noise, low-drift precision operational amplifier is selected in this embodiment; at the same time, in order to suppress the thermal noise of the resistor, a high-precision, low-temperature drift feedback resistor is selected to reduce the noise voltage introduced by it. f Introduce DC current to the negative input terminal of the op amp to ensure the normal operation of the op amp. f and feedback capacitor C f Together they form a high-pass filter. Therefore, the frequency of the high-frequency carrier must satisfy:

[0092]

[0093] The parasitic capacitance and parasitic resistance model analysis of the sensor capacitor shows that the sensor capacitor C x , parasitic capacitance C p3 and the parallel parasitic resistance R pp A high-pass filter is formed, and the sensing capacitor C x , parasitic capacitance C p3 and the parallel parasitic resistance R pp and the series parasitic resistance R ps Together they form a low-pass filter. Therefore, the frequency of the carrier must also satisfy the following two formulas:

[0094]

[0095]

[0096] The relationship between the voltage at the non-inverting input of the differential amplifier and the carrier is:

[0097]

[0098] The above formula can be simplified into the following form, and the carrier frequency f is finally determined c The order of magnitude should be in kHz:

[0099]

[0100] Among them, the sensing capacitor C x The change of can be expressed as a low-frequency signal C x =C x0 +ΔC x sinω s t, can be further written as:

[0101]

[0102] Since two completely symmetrical current detectors are used in this embodiment, the signal V B With the same phase as the differential amplifier input signal V A The same form, signal V B The expression is:

[0103]

[0104] Signal V A and V B Both are modulated signals. After passing through the differential amplifier circuit, the output signal V x Eliminates common mode interference and parasitic capacitance C p3 The influence of signal V x The expression is:

[0105]

[0106] In this embodiment, two fully symmetrical current detectors and a differential amplifier circuit are used to eliminate the effects of common-mode interference and parasitic capacitance, resulting in more accurate detected signals. Furthermore, in this embodiment, a high-precision, low-temperature drift feedback resistor is used to filter out noise and improve the accuracy of the detected signal.

[0107] 2) Power amplifier circuit

[0108] The acceleration voltage feedback signal output by the DA is loaded on the torque coil and converted into a current in the torque coil. The torque coil is located in a uniform magnetic field within the working air gap of the torquer. Under the action of the magnetic field, the energized torque coil is subjected to the Lorentz force:

[0109] F=Bδ il a

[0110] Where B δ represents the magnetic induction intensity of the working air gap; i represents the current flowing through the torque coil wire; l a Indicates the length of the torque coil wire.

[0111] The Lorentz force on the torque coil will generate a restoring torque at the end of the flexible flat beam 113 in the opposite direction to the acceleration:

[0112] M=Fl=B δ il a l

[0113] Where l represents the distance from the center of the torque coil to the support axis. The restoring torque drives the detection mass back to the equilibrium position. The magnitude of the restoring torque is proportional to the current i flowing through the torque coil wire. In order to ensure that the acceleration voltage feedback signal loaded on both ends of the coil can generate a sufficiently large current, a power amplifier circuit is added to the DA output end to improve the driving ability of the acceleration voltage feedback signal. The principle of the power amplifier circuit is as follows: Figure 5 shown.

[0114] Among them, the output voltage of the power amplifier of the negative feedback amplifier circuit can be expressed as:

[0115]

[0116] In order to avoid the self-oscillation of the op amp, it is necessary to meet The final current acting on the torque coil is:

[0117]

[0118] Where R l Represents the resistance of the torque coil wire.

[0119] The restoring moment acting on the root of the flexible flat beam 113 can be expressed as:

[0120]

[0121] The magnitude of the restoring torque is proportional to the acceleration voltage feedback signal, and the direction of the restoring torque is related to the polarity of the acceleration voltage feedback signal.

[0122] 3) Signal processing module.

[0123] The signal processing module includes a phase-sensitive adjustment unit 221 and a digital control unit 222 .

[0124] The signal V modulated by the differential capacitance detection circuit xis a double-sideband amplitude modulated signal, whose amplitude reflects the change of the measured value. x The acceleration measurement information obtained from the phase-sensitive demodulation needs to be further demodulated. Phase-sensitive demodulation has strong anti-interference ability and is very suitable for weak signal detection.

[0125] The phase-sensitive adjustment unit 221 of this embodiment uses a multiplier detector to demodulate the signal. The schematic diagram of the multiplier phase-sensitive demodulation circuit is as follows: Figure 6 shown.

[0126] The multiplier phase-sensitive demodulation is to convert the sinusoidal modulated signal With the same frequency sinusoidal reference signal Multiply, the multiplied signal is as follows:

[0127]

[0128] From the above formula, we can see that the multiplied signal V Z There are three frequency components, one of which is ω s The low-frequency component, and the two frequencies are 2ω c +ω s , 2ω c -ω s Therefore, the high-frequency component is further eliminated through the low-pass filter circuit to separate the low-frequency component. The magnitude of its amplitude reflects the change in the sensing capacitance ΔC x , that is, the change in acceleration.

[0129] In addition, the absolute value of the low-frequency component is also related to the phase difference between the modulation signal and the same-frequency reference signal. Therefore, a hysteresis phase shift network is connected in series at the input end of the same-frequency reference signal to adjust the phase difference between the same-frequency reference signal and the modulation signal to satisfy Or 180°, that is, to ensure that the modulated signal and the reference signal of the same frequency are in phase or anti-phase. At this time, the absolute value of the separated low-frequency signal is the largest and has the best signal-to-noise ratio.

[0130] The digital control unit 222 includes components such as a digital-analog (DA) unit, an analog-analog (AD) unit, and a digital controller. The specific bit count and performance of the DA and AD units are determined based on specific requirements. A single-chip FPGA can be used to implement the overall control solution. The FPGA serves as the core controller of the digital signal processing module, executing complex control algorithms and communicating with the navigation computer.

[0131] The digital controller requires a clear understanding of the model's specific mathematical expression to design appropriate controller parameters based on the meter's characteristics and compensate for the meter model. In an accelerometer's closed-loop system, all links except the mechanical meter and digital controller are proportional and do not affect the system order. Therefore, the accuracy of the meter model is crucial to the design of the digital controller.

[0132] Based on the sapphire rotor transfer function, the transfer function H(s) can be calculated if information such as the rotor material and dimensions is known. However, obtaining relevant parameters for actual rotors is difficult, and the actual parameters of each meter head can differ from the theoretical values ​​due to component manufacturing and installation errors. Since the model structure and order are already determined, open-loop model identification can be used to obtain the rotor transfer function.

[0133] When there is no external acceleration input and the sapphire pendulum is in a naturally drooping state, the digital controller is disconnected and the excitation signal is output through the FPGA to drive the torquer. After passing through the drive module, the header component, and the acquisition module, the response curve is obtained. The system open-loop model identification block diagram is shown below. Figure 7 shown.

[0134] In order to ensure that the pendulum deflects slightly near the equilibrium position, the intensity of the excitation signal cannot be too large, but this also makes the response signal easily obliterated by noise. In order to improve the accuracy of model identification, the random error of the response signal is reduced by taking the average of multiple repeated tests. The excitation signal x(t) and response signal y(t) obtained from the repeated tests are uploaded to the host computer. In this embodiment, it can be seen from the analysis that the pure delay of the system at a sampling rate of 100kHz is 24 sampling beats, and the open-loop system transfer function can be obtained through the MATLAB system identification toolbox.

[0135] The generalized meter is in an overdamped state, and the open-loop response is slow. It is necessary to design a controller to compensate the meter, so that the closed-loop system is in a critical damped state and the system bandwidth is increased. After the bandwidth is increased, the integral upper limit of the noise also increases, and the system stability is reduced. Therefore, the digital controller in this embodiment is conducive to ensuring the stability of the system while increasing the bandwidth. The proportional integral differential control algorithm is the most widely used control algorithm in actual engineering. It has a simple structure, good stability, and easy adjustment, which meets the use scenario requirements of this embodiment.

[0136] The current output of a positional PID controller is dependent on all past errors, requiring extensive calculations. If the computer fails, the accumulated errors can cause the system to crash. Incremental PID outputs increments of the controlled variable. Because the current output depends only on the three most recent error values, calculations are simplified and the accumulated error is minimal, making it a more suitable discrete controller for this application.

[0137] When the system's setpoint fluctuates significantly, resulting in excessive deviation within a short period of time, the integral effect causes the calculated result to continuously increase or decrease, leading to integral accumulation. This can cause the controlled variable to exceed the actuator's maximum control range, resulting in significant overshoot and prolonged oscillation. To overcome this problem, this embodiment introduces integral separation. When the controlled variable deviates significantly from the setpoint, the integral effect is canceled; when the controlled variable approaches the setpoint, integral control is introduced to eliminate static error and improve accuracy.

[0138] During the open-loop model identification, it was found that the control system has pure hysteresis in the signal transmission process. The pure hysteresis characteristic causes the measurement signal to fail to reflect the system disturbance in time, which reduces the system stability and deteriorates the dynamic characteristics, which may cause overshoot and oscillation. Figure 8 The Smith predictor control is shown in the figure. By introducing the Smith predictor to compensate for the pure lag characteristics of the large delay object, the controlled quantity after delay is reflected to the controller input in advance, the pure lag interference is removed, and the stability and dynamic characteristics of the system are improved.

[0139] This application aims to meet the future development needs of accelerometers for high precision, high reliability and calibration-free. It breaks through key technologies such as the configuration of multi-beam single-island sapphire pendulum, the design of complementary all-digital high-resolution acceleration signal analysis circuit, and high-precision error compensation, and develops a multi-beam single-island complementary high-precision flexible digital accelerometer prototype. The technology maturity level has reached 5, the resolution is better than 1μg, and the highest resolution is better than 0.5μg, providing technical support for achieving high-precision inertial navigation and guidance.

[0140] Example 4

[0141] This embodiment will describe in detail the error compensation method performed by the signal processing module in the servo loop. Figure 9 Flowchart of the error compensation method of the header model according to the embodiment of the present application. Figure 9 As shown, the method includes the following steps:

[0142] Step S902: Determine the static characteristics of the accelerometer.

[0143] For the sapphire flexible accelerometer, the input reference axis (IA), pendulum reference axis (PA) and output reference axis (OA) are used to represent the three orthogonal directions of the accelerometer. The direction relationship of the reference axis is determined by the right-hand rule and can be expressed in vector form as follows:

[0144] The static mathematical model between the output E of the sapphire flexible accelerometer and the acceleration acting along the accelerometer reference axis can be expressed as follows:

[0145]

[0146] Where A ind Indicates the indicated acceleration value; a i Indicates the acceleration acting in the direction of the accelerometer input reference axis; a o Indicates the acceleration acting in the direction of the accelerometer output reference axis; a p represents the acceleration acting on the reference axis of the accelerometer; E represents the output of the accelerometer; K0 represents the bias value; K1 represents the calibration factor; K2 represents the second-order nonlinear coefficient; K3 represents the third-order nonlinear coefficient; K ip , K io represents the cross-coupling coefficient; δ o , δ p They represent the misalignment angles of the input shaft relative to the input reference axis around the output shaft and the pendulum axis respectively.

[0147] The simplified static mathematical model of the accelerometer is:

[0148]

[0149] The coefficients of the static mathematical model of the accelerometer can be obtained by multi-point tumbling experiments in a gravity field. The accelerometer is mounted on a precision electronically controlled rotating table with the rotating axis horizontal and at 0°. The accelerometer is powered on and preheated. After the output stabilizes, its output value is recorded. The precision electronically controlled rotating table is rotated in increments of θ. n =360° / n rotation, each angle is θ n , 2 θ ,…k θ ,…(n-1)θ n , record the output value of the accelerometer at each angular position. After the turntable rotates to 360°, rotate the turntable in the opposite direction and adjust the value by the angle increment θ n The value of the accelerometer output is recorded at each angular position. The average value E of the accelerometer output value at each point when the rotating platform is in forward and reverse rotation is k (k=0, 1, 2, ..., n-1), the solution formula for each order coefficient of the accelerometer model equation is as follows.

[0150] Scaling factor:

[0151]

[0152] Bias:

[0153]

[0154] Second-order nonlinear coefficient:

[0155]

[0156] Misalignment angle of the input shaft relative to the input reference axis around the output shaft:

[0157]

[0158] Misalignment angle of the input shaft relative to the input reference axis around the pendulum axis:

[0159]

[0160] Step S904: determining the dynamic characteristics of the accelerometer.

[0161] The sapphire flexible accelerometer head senses external acceleration through the detection mass. Under the action of inertial force, a certain deflection angular displacement is generated. This angular displacement is related to the input acceleration. The physical model equation can be described as:

[0162]

[0163] The transfer function obtained by Laplace transform is:

[0164]

[0165] Where α is the rotation angle of the test mass relative to the zero position; J is the moment of inertia of the test mass; C is the air damping coefficient; K is the elastic coefficient of the test mass; M is the applied torque; mL is the pendulum; ω n It represents the natural angular frequency of the detection mass; ξ represents the damping coefficient of the detection mass.

[0166] Analyzing the impact of different frequency signals on the accelerometer, the amplitude-frequency characteristics of the accelerometer head can be expressed as:

[0167]

[0168] The phase-frequency characteristic is:

[0169]

[0170] According to the transfer function, the accelerometer head is a typical second-order system. The resonant frequency, resonant peak and cutoff frequency of the accelerometer head are:

[0171]

[0172] The natural angular frequency and damping coefficient of the detection mass determine the resonant frequency, resonant peak and cutoff frequency of the accelerometer head, and directly affect the dynamic performance of the sapphire flexible accelerometer, such as overshoot and measurement bandwidth.

[0173] Step S906: Determine appropriate controller parameters and perform error compensation on the header model.

[0174] In order to distinguish the performance of the new multi-beam single-island complementary high-precision flexible digital accelerometer, it is usually necessary to judge it based on several parameters such as scale factor, zero bias stability and temperature drift.

[0175] (1) Scale factor

[0176] The acceleration scale factor is the ratio of the accelerometer output to the input acceleration. This ratio is the slope of a straight line obtained by least squares fitting the input and output data measured over the entire input acceleration range.

[0177] Establish a linear model of the input-output relationship of the accelerometer:

[0178] F j =KΩ ij +F0+v j

[0179] Where: F j represents the output value of the accelerometer when the jth input acceleration occurs; K represents the scale factor; F0 represents the fitting zero position; v j represents the fitting error.

[0180] K and F0 can be obtained by the least squares method, and the calculation formula is as follows:

[0181]

[0182]

[0183] (2) Bias / Bias Stability

[0184] Zero bias refers to the output of the accelerometer in the zero input state, which is expressed by converting the average output over a longer period of time into the equivalent input acceleration.

[0185] Zero bias stability is the mean square error of the output acceleration under long-term zero input conditions, which characterizes the degree of dispersion of the observed values ​​around the zero bias.

[0186]

[0187] Indicates the average output value obtained by collection;

[0188] (3) Input axis misalignment angle / cross-coupling coefficient

[0189] The input misalignment angle is the angle between the input axis and the corresponding input reference axis when the accelerometer is at its zero position. The proportionality factor that relates the change in the accelerometer's output to the product of the accelerations acting perpendicular to and parallel to the input reference axis is called the accelerometer's cross-coupling coefficient, and it varies with the direction of the cross-acceleration.

[0190] (4) Temperature drift

[0191] The elastic modulus and dielectric constant of the materials within the new multi-beam, single-island, complementary, high-precision flexible digital accelerometer are highly sensitive to temperature. This results in varying temperature drift, causing changes in capacitance and, consequently, in the accelerometer's signal output. Because multiple variables within the multi-beam, single-island, complementary, high-precision flexible digital accelerometer system are affected by temperature, introducing new errors and accounting for each variable in the system increases the computational complexity of the solution. Temperature compensation primarily focuses on the bias error metric, establishing a mathematical model that operates over the full temperature range.

[0192] According to the differential capacitance detection principle of the new multi-beam single-island complementary high-precision flexible digital accelerometer, when the accelerometer is in the zero state, the capacitance of the two comb teeth is equal:

[0193]

[0194] When acceleration acts, the distance between the capacitors changes and the difference between them changes:

[0195]

[0196] When x<<d0, due to Combining the above formulas, we can get:

[0197]

[0198] Where k is the elastic coefficient of the support beam, m is the mass of the mass block, is the natural frequency of the system without damping, x is the relative displacement of the mass block, and a is the accelerometer to be measured.

[0199] The error compensation of the multi-beam single-island complementary high-precision flexible digital accelerometer is to establish a compensation model based on the difference between the input v and the output V. The output data of the accelerometer is compensated using the established error compensation model, and the compensated output result is v′.

[0200] Error analysis reveals that high-precision flexible digital accelerometers contain numerous error terms, and variations in operating environments can introduce different types of error parameters. This embodiment strives to simplify the calibration process while ensuring accuracy. By considering only the primary error terms and ignoring higher-order noise, this reduces computational effort and time.

[0201] The error model of the new multi-beam single-island complementary high-precision flexible digital accelerometer can be expressed as:

[0202] a=CR a ·SFa2 ·[SF a1 ·(AN a0 )-N aT ]+ε a

[0203] Where a represents the acceleration output after error compensation; A represents the original angular velocity output of the accelerometer; SF a1 is the rough calibration scale factor; N a0 For coarse calibration zero position output; N aT It is temperature zero output; SF a2 Indicates the proportional coefficient of the corresponding output acceleration; CR a represents the three-axis acceleration cross-coupling matrix; ε a is the random error of the accelerometer.

[0204] Expand the error model as follows:

[0205]

[0206] Where a=[a x a y a z ] T is the compensated digital output of the three-axis accelerometer; A=[A x A y A z ] T is the raw data output of the three-axis accelerometer; N a0 =[N ax0 N ay0 N az0 ] T is the zero position error of the three-axis accelerometer; is the temperature-related zero output of the accelerometer, T is the temperature output of the accelerometer, S ij is the least squares fitting coefficient; R = [R x R y R z ] T k is the distance between the triaxial accelerometer and the center of the device; ax1 , k ay1 , k az1 are the rough calibration scale coefficients of the three-axis accelerometer; K ax2 , K ay2 , K az2 are the proportional coefficients of the three-axis accelerometer corresponding to the output acceleration; is the cross-coupling coefficient matrix of the three-axis accelerometer; ε a =[ε ax ε ay ε az ] Tis the random error of the triaxial accelerometer.

[0207] In response to the future development of accelerometers requiring high precision, high reliability, and no calibration, this embodiment breaks through key technologies such as the configuration of a multi-beam single-island sapphire pendulum, the design of a fully digital high-resolution acceleration signal analysis circuit, and high-precision error compensation, providing a multi-beam single-island complementary high-precision flexible digital accelerometer that achieves a resolution of 0.1μg.

[0208] The serial numbers of the above embodiments of the present application are for description only and do not represent the advantages or disadvantages of the embodiments.

[0209] The above is only a preferred embodiment of the present application. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principles of the present application. These improvements and modifications should also be regarded as the scope of protection of the present application.

Claims

1. A sapphire pendulum of an accelerometer, characterized in that: include: a disc connected to a fixed ring on the outer ring of said disc by a plurality of flexible flat beams; a plurality of flexible flat beams, each of the flexible flat beams being flexible in a direction along an acceleration input axis of the accelerometer, and each of the flexible flat beams being made of a flexible material in a direction close to the acceleration input axis and being made of a rigid material in a direction away from the acceleration input axis; The fixed ring has raised structures distributed at equal intervals for installing gaskets to support the sapphire pendulum.

2. The sapphire pendulum according to claim 1, characterized in that: Semicircular conductive layers are formed on the upper and lower surfaces of the disk, serving as electrode plates of the differential capacitance sensor of the accelerometer. The conductive layers are formed by vacuum depositing a metal film.

3. The sapphire pendulum according to claim 2, characterized in that: A conducting wire for transmitting differential capacitance sensor signals and torquer coil driving current is formed on each of the flexible flat beams.

4. The sapphire pendulum according to claim 1, characterized in that: The structural dimensions of the sapphire pendulum are determined by formulating selection criteria by selecting the size constraint relationship of the sapphire pendulum and using the orthogonal test method and deep learning optimization method, wherein the determined structural dimensions make the first-order natural frequency of the sapphire pendulum less than the preset first frequency threshold, and the second-order torsional frequency of the sapphire pendulum greater than the preset second frequency threshold.

5. The sapphire pendulum piece according to claim 1, characterized in that: The structural dimensions of the sapphire pendulum are determined by the cantilever beam model of the sapphire pendulum, wherein the determined structural dimensions make the first-order natural frequency of the sapphire pendulum less than a preset first frequency threshold, and the second-order torsional frequency of the sapphire pendulum greater than a preset second frequency threshold.

6. The sapphire pendulum piece according to claim 5, characterized in that: The cantilever beam model is obtained by: Determining the relationship between the rotation angle of any cross section on each of the flexible flat beams and the deflection at the cross section; Based on the determined relationship, the width of the flexible flat beam, and the thickness of the flexible flat beam, a deflection equation and a stiffness equation of the flexible flat beam are determined.

7. The sapphire pendulum according to claim 6, characterized in that: After the deflection equation of the cantilever beam model is determined, the maximum deflection is also determined based on the maximum angular displacement of the flexible flat beam.

8. An accelerometer, characterized in that: include: A mechanical watch head, comprising a sapphire pendulum according to any one of claims 1 to 7; A servo loop is used to obtain a measurement value representing acceleration information based on the vibration of the sapphire pendulum.

9. The accelerometer according to claim 8, wherein: The servo loop comprises: The pendulum deflection angle detection module includes a differential capacitance detection circuit, which includes: Two completely symmetrical current detection circuits are configured to detect the capacitance signal output by the accelerometer head using a differential unbalanced bridge detection method; a differential amplifier circuit configured to load the capacitance signal onto a sinusoidal carrier signal having a frequency greater than a preset frequency threshold; Wherein, the pendulum piece deflection angle detection module is further configured to modulate the sinusoidal carrier signal; The signal processing module is configured to demodulate the modulated sinusoidal carrier signal, filter out components greater than a preset frequency threshold and noise greater than a preset noise threshold in the modulated sinusoidal carrier signal, and obtain a measurement value representing acceleration information.

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