A modeling method for optimizing electric field coupling noise of a quartz flexible accelerometer

Abstract

The application discloses a modeling method for optimizing electric field coupling noise of a quartz flexible accelerometer, and comprises the following steps: constructing a closed loop system of a quartz flexible accelerometer table head, including a quartz pendulum piece assembly, a variable-pole-distance differential capacitor sensor, a differential capacitor detection circuit, a torque motor control system and a torque motor; the closed loop system comprises an electric field coupling system, including internal distribution capacitance between a torque motor coil and the differential capacitor sensor, the variable-pole-distance differential capacitor sensor, the differential capacitor detection circuit and the torque motor control system, and a model of the internal distribution capacitance is constructed; the internal distribution capacitance is considered, a transfer function of the electric field coupling system is calculated when a torque motor driving signal is regarded as a noise source; and then a transfer function of the accelerometer closed loop system considering the electric field coupling noise is solved. The modeling method considers the electric field coupling noise inside the accelerometer table head, reduces measurement error and improves the performance of an inertial navigation system.

Description

Technical Field

[0001] This invention relates to the field of inertial navigation technology, and in particular to a modeling method for optimizing electric field coupling noise in a quartz flexible accelerometer. Background Technology

[0002] Gyroscopes and accelerometers, as the main inertial sensors in an inertial navigation system, are among the most significant sources of error, accounting for approximately 70% of the system's error and significantly impacting navigation accuracy. Therefore, inertial sensors must possess sufficiently high accuracy to meet the precision requirements of the navigation system. In recent years, gyroscope technology has seen considerable development. Advanced gyroscope technologies, such as fiber optic gyroscopes, have achieved a zero-bias repeatability of 0.005° / h and have been applied in various equipment. However, the zero-bias repeatability of accelerometer technology, primarily based on quartz flexible accelerometers, remains stagnant at around 10. -5 Near g, the key technical indicators of quartz flexible accelerometers, such as accuracy and stability, still have significant room for improvement. The measurement accuracy and stability of quartz flexible accelerometers are gradually becoming one of the important factors restricting the navigation accuracy of inertial navigation systems.

[0003] To improve accelerometer performance, related research has modified the closed-loop system structure, adding a differential proportional element to the forward path to increase the bandwidth of the closed-loop system. The impact of parameter drift caused by temperature changes on accelerometer performance is also significant; mathematical algorithms are used for parameter drift estimation and temperature compensation to improve the long-term stability of the system. To reduce complex temperature drift during the cold start phase, a temperature compensation method based on a high-order Fourier transform combined model is employed to improve compensation accuracy. Research on accelerometer resolution measurement and parameter calibration techniques also greatly contributes to improving accelerometer system performance and ensuring long-term stable use. Therefore, current research mainly focuses on accelerometer closed-loop system optimization, temperature influence analysis, zero-bias stability analysis, and test calibration.

[0004] However, the phenomenon of internal electric field coupling noise in the accelerometer head, caused by the inherent structure and working principle of quartz flexible accelerometers, affecting the performance of the accelerometer system has not yet attracted sufficient attention from researchers. The variation law of internal electric field coupling noise and its influence on accelerometer performance still need to be studied. Therefore, it is necessary to invent an optimized modeling method for electric field coupling noise in the closed-loop system of a quartz flexible accelerometer to analyze the impact of internal electric field coupling noise in the accelerometer head on accelerometer measurement error. This is of great significance for reducing accelerometer measurement error and improving the performance of inertial navigation systems. Summary of the Invention

[0005] (a) Technical problems to be solved

[0006] To address the aforementioned issues, this invention provides a modeling method for optimizing electric field coupling noise in quartz flexible accelerometers, solving the problem of lacking an analysis method for electric field coupling noise inside the accelerometer head, thereby reducing accelerometer measurement errors and improving the performance of inertial navigation systems.

[0007] (II) Technical Solution

[0008] To address the aforementioned technical problems, this invention provides a modeling method for optimizing electric field coupling noise in a quartz flexible accelerometer, comprising the following steps:

[0009] S1. Construct a closed-loop system for the quartz flexible accelerometer head;

[0010] The quartz flexible accelerometer head includes a quartz pendulum assembly, a variable-gap differential capacitance sensor that varies with the offset of the quartz pendulum, and a torque converter. The variable-gap differential capacitance sensor is connected to a differential capacitance detection circuit, which is connected to a torque converter control system. The torque converter control system is connected to both ends of the torque converter coil. The torque converter control system includes a control circuit and a drive circuit, which generates a control signal based on the detection value of the differential capacitance detection circuit, and then amplifies the control signal to generate a drive signal for adjusting the torque converter coil.

[0011] The closed-loop system of the quartz flexible accelerometer head includes the quartz pendulum assembly, the variable pole distance differential capacitance sensor, the differential capacitance detection circuit, the torque control system, and the torque.

[0012] S2. The closed-loop system includes an electric field coupling system, which includes the internal distributed capacitance between the torque coil and the differential capacitance sensor, the variable pole gap differential capacitance sensor, the differential capacitance detection circuit, and the torque control system. A model of the internal distributed capacitance is constructed.

[0013] S3. Considering the internal distributed capacitance, calculate the transfer function N(s) of the electric field coupling system when the torque drive signal Vd is regarded as a noise source;

[0014] S4. Based on the transfer function N(s) of the electric field coupling system, solve for the transfer function Hn(s) of the accelerometer closed-loop system considering electric field coupling noise:

[0015]

[0016] Where mL represents the pendulum property of the quartz pendulum, θ(s), Ks, Ka, M(s), K I and K T These are the quartz pendulum assembly, differential capacitor sensor, differential capacitor detection circuit, control circuit in the torque control system, drive circuit in the torque control system, and transfer function of the torque, respectively.

[0017] (III) Beneficial Effects

[0018] The above-described technical solution of the present invention has the following advantages:

[0019] (1) This invention targets the closed-loop system of a quartz flexible accelerometer head. By studying the electric field coupling mechanism inside the accelerometer head, an electric field coupling model inside the accelerometer head is established. The transfer function model of the electric field coupling system considering the internal distributed capacitance and taking the torque drive signal as a noise source is obtained. Thus, the transfer function model of the accelerometer closed-loop system considering electric field coupling noise is obtained. When establishing the accelerometer closed-loop system model, the influence of electric field coupling noise is considered, which can reduce the accelerometer measurement error and thus improve the performance of the inertial navigation system.

[0020] (2) The present invention can model accelerometers using differential capacitor detection circuits with current detection method and voltage detection method respectively. The coupling coefficient matrix of the transfer function model of the electric field coupling system is determined by the size of the internal distributed capacitance, the grounding state of the outer shell, and the differential capacitor detection method. The transfer function of the closed-loop system calculated from this is also different.

[0021] (3) This invention analyzes the variation law of internal electric field coupling noise, analyzes the transmission characteristics of electric field coupling noise under different shell states and different detection methods, and analyzes the influence of electric field coupling system on accelerometer performance: when the low frequency signal is applied, the electric field coupling noise of the differential capacitor detected by the current method is smaller, and the electric field coupling noise when the accelerometer shell is grounded is smaller than that when the shell is suspended; when the voltage method is used for detection, the output voltage drop caused by electric field coupling noise will reduce the actual resolution by 50%; the magnitude of electric field coupling noise gain is positively correlated with the performance degradation of the accelerometer closed-loop system such as bandwidth. The influence of electric field coupling noise on the closed-loop system can be compensated by increasing the gain of the drive control system, but this will lead to an increase in system power consumption. Attached Figure Description

[0022] The features and advantages of the invention will be more clearly understood by referring to the accompanying drawings, which are schematic and should not be construed as limiting the invention in any way. In the drawings:

[0023] Figure 1 This is a structural diagram of the quartz flexible accelerometer head according to an embodiment of the present invention;

[0024] Figure 2 This is a schematic diagram of the accelerometer rebalancing circuit according to an embodiment of the present invention;

[0025] Figure 3 This is a schematic diagram illustrating the working principle of the differential capacitance sensor according to an embodiment of the present invention;

[0026] Figure 4This is a schematic diagram illustrating the working principle of the electric field coupling circuit in the quartz flexible accelerometer head according to an embodiment of the present invention.

[0027] Figure 5 This is a schematic diagram of the electric field coupling circuit according to an embodiment of the present invention;

[0028] Figure 6 This is a distributed capacitance model inside the accelerometer head according to an embodiment of the present invention;

[0029] Figure 7 This is an accelerometer structural model according to an embodiment of the present invention;

[0030] Figure 8 The above are simulation results of differential capacitance and distributed capacitance in an embodiment of the present invention.

[0031] Figure 9 This is the transmission path of electric field coupling noise in the voltage detection method of this invention embodiment;

[0032] Figure 10 The electric field coupling system characteristics of the voltage detection method in this embodiment of the invention;

[0033] Figure 11 This is the transmission path of electric field coupling noise in the current detection method of this invention embodiment;

[0034] Figure 12 The electric field coupling system characteristics of the current detection method in this embodiment of the invention;

[0035] Figure 13 This invention provides a comparison of the characteristics of electric field coupling systems under different detection methods in embodiments of the invention.

[0036] Figure 14 This is a schematic diagram illustrating the effect of the electric field coupling system on differential capacitance detection according to an embodiment of the present invention;

[0037] Figure 15 This invention provides a comparison of the characteristics of the differential capacitance detection process under different detection methods in various embodiments.

[0038] Figure 16 This is a schematic diagram of an accelerometer closed-loop system including electric field coupling noise according to an embodiment of the present invention;

[0039] Figure 17 A comparison of the characteristics of the accelerometer closed-loop system under different operating conditions in embodiments of the present invention;

[0040] Figure 18 The characteristics of the compensated accelerometer closed-loop system in this embodiment of the invention are shown. Detailed Implementation

[0041] The specific embodiments of the present invention will be described in further detail below with reference to the accompanying drawings and examples. The following examples are for illustrative purposes only and are not intended to limit the scope of the invention.

[0042] This invention discloses a modeling method for optimizing electric field coupling noise in a quartz flexible accelerometer, comprising the following steps:

[0043] S1. Construct a closed-loop system for the quartz flexible accelerometer head;

[0044] The quartz flexible accelerometer head includes a variable-gap differential capacitance sensor and a torque converter that vary with the offset of the quartz pendulum. The structure of the quartz flexible accelerometer head in this embodiment is as follows: Figure 1 As shown, the device includes a quartz pendulum assembly, a torque generator, a magnet assembly, and a housing. The torque generator comprises a torque coil, an upper yoke, a lower yoke, and a support belt. The support belt is fixed to both ends of the upper and lower yokes. The upper and lower yokes and the support belt are laser-welded to form a closed space. The magnet assembly includes an upper magnet assembly and a lower magnet assembly. The upper / lower magnet assembly includes upper / lower magnets bonded together, magnetic pole pieces, and a compensation ring. The compensation ring fixes the upper / lower magnets in the middle of the upper / lower yokes. The magnetic pole pieces are fixed to the upper / lower magnets and... The torque coil is located within the magnetic gap formed by the upper and lower magnet assemblies on the surfaces where the upper and lower yokes do not contact. The quartz pendulum assembly includes a tongue-shaped quartz pendulum with metal films coated on its upper and lower surfaces. One end of the quartz pendulum is fixed to the belt and is equidistant from the upper and lower yokes. The metal films and the surfaces of the upper and lower yokes constitute a variable-gap differential capacitor sensor. The metal films on both sides of the quartz pendulum are the upper and lower moving plates of the differential capacitor, and the yoke surfaces are the fixed plates of the differential capacitor. The torque coil, torque coil frame, and quartz pendulum constitute a mass unit.

[0045] The closed-loop system of the quartz flexible accelerometer head includes the quartz pendulum assembly, a variable-gap differential capacitance sensor, a torque converter, a differential capacitance detection circuit, and a torque converter control system. The upper and lower surfaces of the quartz pendulum and the upper and lower yoke surfaces, i.e., the variable-gap differential capacitance sensor, are connected to the differential capacitance detection circuit. The differential capacitance detection circuit is connected to the torque converter control system. The torque converter control system is connected to both ends of the torque converter coil. The torque converter control system includes a control circuit and a drive circuit, which are used to generate a control signal based on the detection value of the differential capacitance detection circuit, and then amplify the control signal to generate a drive signal for adjusting the torque converter coil.

[0046] The quartz pendulum assembly, differential capacitance sensor, torque drive control system, and torquer in the accelerometer structure constitute a rebalancing loop, i.e., a closed-loop system. The structure of the accelerometer rebalancing loop system is as follows: Figure 2As shown. When acceleration occurs along the sensitive axis, the quartz pendulum assembly deviates from its equilibrium position under the action of the inertial torque Ma. The degree of deviation Δθ is detected by the capacitance change ΔC of the differential capacitance sensor. The differential capacitance detection circuit converts ΔC into a voltage change ΔV, which is then converted into a current ΔI by the torque control system and fed to the torque coil in a constant magnetic field. The interaction between the coil's magnetic field and the magnet's magnetic field generates a feedback torque Mb that balances Ma, causing the mass unit to return to its equilibrium position, thus achieving closed-loop operation.

[0047]

[0048] Where mL represents the pendulum property of the pendulum assembly, and θ(s), Ks, Ka, M(s), KI, and KT are the transfer functions of the quartz pendulum assembly, the differential capacitance sensor, the differential capacitance detection circuit, the control circuit in the torque control system, the drive circuit in the torque control system, and the torque, respectively. The pendulum transfer function θ(s) of the quartz flexural accelerometer is:

[0049]

[0050] Where J is the moment of inertia, C is the damping coefficient, and K is the elastic coefficient, substituting equation (2) into H(s) yields:

[0051]

[0052] From equation (3), we can see that the magnitude of the input acceleration Δa can be measured by detecting the magnitude of the driving current ΔI, and its direction depends on the direction of the driving current.

[0053] The working principle of a differential capacitance sensor is as follows: Figure 3 As shown. When the pendulum is in equilibrium, the initial capacitance C0 formed by the fixed plate and the moving plate can be expressed as:

[0054]

[0055] ε is the dielectric constant, S is the area of ​​the plates facing each other, and d0 is the nominal distance between the stationary and moving plates when the pendulum is in equilibrium. Due to inertia, the pendulum undergoes a slight deflection. When the offset of the differential capacitor plate distance is Δd, the differential changes in the capacitances Cs1 and Cs2 formed between the plates can be expressed as:

[0056]

[0057]

[0058] The change in differential capacitance ΔC can be expressed as:

[0059]

[0060] The differential capacitor detection circuit, based on the law of charge conservation, charges and discharges the differential capacitor through a pair of reverse excitation sources Vs, obtaining a voltage or current signal related to the change in capacitance. Depending on the feedback loop structure of the operational amplifier, differential capacitor detection circuits are mainly divided into three types: current detection, voltage detection, and switched capacitor charge detection. This invention focuses on analyzing the operation when using voltage and current detection circuits.

[0061] When the differential capacitor detection circuit uses the current detection method, the feedback loop only consists of Rf forming the current detection circuit, and the detected output voltage Vout can be expressed as:

[0062]

[0063] The current detection circuit is equivalent to a differentiator and has a high-pass frequency response characteristic. High-frequency noise in the circuit will be amplified along with the measurement signal.

[0064] When the differential capacitor detection circuit uses the voltage detection method, the feedback loop consists of Rf and Cf connected in parallel to form the voltage detection, and Vout can be expressed as:

[0065]

[0066] Voltage detection circuits are not differentiators and have better stability than current detection circuits, but they require a large feedback resistor Rf, otherwise the measurement signal will be attenuated. A large feedback resistor will increase circuit noise and affect circuit performance.

[0067] S2. The closed-loop system includes an electric field coupling system, which includes an internal distributed capacitance between the torque coil and the differential capacitance sensor, a differential capacitance detection circuit, and a torque control system. A model of the internal distributed capacitance is constructed.

[0068] In a quartz flexible accelerometer, the accelerometer housing, yoke, torque coil, and differential capacitor plates are all made of metal. These components are independent of each other and do not come into contact. When the meter is working, there is a potential difference between the different components, which in turn forms a distributed capacitance.

[0069] The distributed capacitance between the torque coil and the differential capacitance sensor, along with the differential capacitance sensor, differential capacitance detection circuit, and torque drive control system, constitutes an electric field coupling loop. This loop becomes a branch loop in the accelerometer rebalancing loop. A schematic diagram of the coupling loop operation is shown below. Figure 4 and Figure 5As shown, the torque drive signal ΔVd is transmitted to the plates of the differential capacitor through the distributed capacitor Cd, acting as a noise signal superimposed on the excitation source Vs and transmitted to the differential capacitor detection circuit. This interferes with the differential capacitor measurement, which in turn causes errors in the drive signal generated by the torque control system, ultimately leading to errors in the acceleration measurement.

[0070] To clarify the impact of distributed capacitance on differential capacitance measurement, this invention establishes a distributed capacitance model inside the accelerometer head. The model of the distributed capacitance formed between various components is as follows: Figure 6 As shown, the differential capacitance sensor has variable-gap capacitors Cs1 and Cs2 between the upper moving plate and the fixed plate, and between the lower moving plate and the fixed plate; distributed capacitances Cd1, Cd2, and Cd3 between the torque coil and the lower moving plate, the fixed plate, and the upper moving plate, respectively; distributed capacitances Ce1, Ce2, Ce3, and Ce4 between the accelerometer housing and the fixed plate, the upper moving plate, the lower moving plate, and the torque coil, respectively; distributed capacitance Cbb between the upper and lower moving plates; and internal resistances Rs1 and Rs2 of the excitation signal source for the capacitance detection circuit. The distributed capacitances of all components are connected together to form a distributed capacitance network.

[0071] S3. Considering the internal distributed capacitance, calculate the transfer function N(s) of the electric field coupling system when the torque drive signal Vd is regarded as a noise source;

[0072] When the torque drive signal Vd is considered as a noise source, the electric field coupling system composed of the internal distributed capacitance between the components of the meter head, the differential capacitance sensor, the differential capacitance detection circuit, and the torque control system is a high-order linear system, and its transfer function can be expressed as:

[0073]

[0074] Where n is the system order, m and k are the coefficients of the numerator and denominator, respectively. The internal structure of the accelerometer head is symmetrical about the quartz pendulum, with the upper and lower structures being of the same size. The torque coil and the pendulum are bonded and fixed with no relative movement. The distributed capacitance between the components does not change or changes very little with the pendulum offset and can be considered a constant value. In this case, the transfer function N(s) is only related to the size of the differential capacitance, i.e., the pendulum offset Δd.

[0075] Define the polynomial coupling coefficient matrices of the transfer function numerator and denominator as follows:

[0076]

[0077]

[0078] Where P is the numerator polynomial coupling coefficient matrix, Q is the denominator polynomial coupling coefficient matrix, and i is the current system order, i = 1, 2, ..., n. The coupling coefficient matrix is ​​determined by the inherent characteristics of the accelerometer system, such as the size of the distributed capacitance, the grounding status of the casing, and the differential capacitance detection method.

[0079] The relationship between the polynomial coefficients of the numerator polynomial coefficient vector M and the denominator polynomial coefficient vector K of the transfer function N(s) and the change in differential capacitance can be expressed as:

[0080] M = P[1 C s1 C s2 C s1 C s2 ] T (13)

[0081] K = Q[1 C] s1 C s2 C s1 C s2 ] T (14)

[0082] Substituting equations (5) and (6) into equations (13) and (14), we get:

[0083]

[0084]

[0085] As can be seen from equations (15) and (16), the polynomial coefficient vector is related to the pendulum offset Δd and its quadratic term.

[0086] The internal electric field coupling of a quartz flexible accelerometer head was simulated and analyzed using the finite element method to verify the influence of the outer casing grounding state and the differential capacitance detection method on the electric field coupling.

[0087] A. Model the structure of the quartz flexible accelerometer head, solve for the internal distributed capacitance, and set parameters according to the accuracy requirements;

[0088] In order to determine the magnitude of the distributed capacitance between the components and its variation with the offset of the pendulum, this invention uses the finite element method to analyze the electric field coupling inside the meter head.

[0089] A1. Modeling the Accelerometer Head Structure: This embodiment establishes a head structure model based on the assembly structure and materials of a certain type of quartz flexible accelerometer. The main structural geometric dimensions are shown in Table 1. The accelerometer structure simulation model is as follows: Figure 7 As shown. This method is also applicable to accelerometer head structures of any other specifications.

[0090] The material types and their relative permittivity of each component in the simulation model of this embodiment are shown in Table 2, which are consistent with the actual situation of a certain type of accelerometer.

[0091] Table 1. Main geometric dimensions of the accelerometer (mm)

[0092]

[0093] Table 2 Material properties of various components of the accelerometer

[0094]

[0095] A2. Voltage excitation settings: Apply voltage excitation to each component according to the actual operating conditions of the meter. The voltage excitation settings are shown in Table 3.

[0096] Table 3 Excitation voltage values ​​(V) for each component

[0097]

[0098] A negative displacement with a step size of 0.50 μm was applied to the quartz pendulum assembly along the sensitive axis, and the changes in differential capacitance and distributed capacitance of the pendulum assembly from the equilibrium position to a displacement of 19.00 μm were analyzed. Due to the limited performance of the computer used for the simulation experiment, the simulation calculation accuracy was set to 1% to balance simulation efficiency and data accuracy.

[0099] A3. Solving the simulation of the internal distributed capacitance of the accelerometer head: When the quartz pendulum deflects, the simulation results of the differential capacitance and distributed capacitance formed between the internal components of the accelerometer are as follows: Figure 8 As shown. By Figure 8 As shown in Figure (a), the differential capacitance Cs1 decreases monotonically with the offset of the pendulum, while Cs2 increases monotonically with the offset, which is consistent with the trend of theoretical analysis. Figure 8 Figure (b) shows the simulation results of the distributed capacitances Cd1 to Cd3. The distributed capacitance between the torque coil and the differential capacitor plate tends to increase or decrease with the offset of the pendulum, but the change is small and can be regarded as a fixed value within ±0.05pF; Figure 8 Figure (c) shows the simulation results of distributed capacitances Ce1 to Ce5. Ce1 does not change significantly with the offset of the pendulum, and the capacitance values ​​of Ce2 to Ce5 are extremely small and can be ignored. Figure 8 Figure (d) shows the simulation results of the distributed capacitance Cbb. The distributed capacitance between the upper and lower moving plates tends to decrease with the offset of the pendulum, but the change is small, only 0.03pF, which can be regarded as a fixed value.

[0100] A4. Setting the internal distributed capacitance model: When analyzing the electric field coupling noise inside the accelerometer head, set the parameters related to the analysis, such as the size of the distributed capacitance and the capacitance of the feedback loop of the detection circuit. Ignore the extremely small distributed capacitances Ce2 to Ce4. The parameter values ​​of other components are shown in Table 4.

[0101] Table 4 Analytical Parameter Value Setting Table

[0102]

[0103] B. When using differential capacitor detection circuits with voltage detection method and current detection method respectively, obtain the coupling coefficient matrix, transfer function and amplitude-frequency characteristic diagram of electric field coupling system under different shell grounding states;

[0104] B1. When the voltage detection method is used in the differential capacitor detection circuit, calculate the transfer function of the electric field coupling system at the zero bias position under the shell floating state and the shell ground state, and analyze the relationship between the amplitude-frequency characteristics of the electric field coupling system and the pendulum offset Δd.

[0105] When using the voltage detection method to detect differential capacitance, the electric field coupling system is a fourth-order linear system, and the noise transmission path is as follows: Figure 9 As shown.

[0106] With the accelerometer housing suspended in the air, the numerator and denominator polynomial coupling coefficient matrices of the transfer function of the electric field coupling system using the voltage detection method are as follows:

[0107]

[0108]

[0109] P Vnc Q Vnc Substituting the capacitance values ​​of the differential capacitors Cs1 and Cs2 at the zero-bias position (Δd = 0 μm) into equations (13) and (14), the transfer function of the electric field coupling system at the zero-bias position with the shell suspended is obtained as follows:

[0110]

[0111] With the casing grounded, the numerator and denominator polynomial coupling coefficient matrices of the transfer function of the electric field coupling system using the voltage detection method are as follows:

[0112]

[0113]

[0114] The transfer function of the electric field coupling system at the zero bias position is:

[0115]

[0116] When using the voltage detection method, the relationship between the amplitude-frequency characteristics of the electric field coupling system and the pendulum offset in the suspended and grounded states are as follows: Figure 10 As shown in Figures (a) and (b), when the system input signal (Vd) frequency is in the range of 10Hz to 20kHz, the gain in both states is stable at around -11.6dB. Above 20kHz, the system gain decreases with increasing frequency, and the rate of decrease increases with the increase of the pendulum offset. This indicates that the magnitude of the electric field coupling noise is negatively correlated with the pendulum offset, and the attenuation is greater in the grounded state than in the ungrounded state. Grounding the casing helps reduce electric field coupling noise.

[0117] B2. When the current detection method is used in the differential capacitor detection circuit, calculate the transfer function of the electric field coupling system at the zero bias position under the shell floating state and the shell ground state, and analyze the relationship between the amplitude-frequency characteristics of the electric field coupling system and the pendulum offset Δd.

[0118] When using the current detection method to detect differential capacitance, the electric field coupling system is a third-order linear system, and the noise transmission path is as follows: Figure 11 As shown.

[0119] With the accelerometer housing suspended in the air, the numerator and denominator polynomial coupling coefficient matrices of the transfer function of the electric field coupling system using the current detection method are as follows:

[0120]

[0121]

[0122] The transfer function of the electric field coupling system at the zero bias position is:

[0123]

[0124] With the casing grounded, the numerator and denominator polynomial coupling coefficient matrices of the transfer function of the electric field coupling system using the current detection method are as follows:

[0125]

[0126]

[0127] The transfer function of the electric field coupling system at the zero bias position is:

[0128]

[0129] When using the current detection method, the relationship between the amplitude-frequency characteristics of the electric field coupling system and the pendulum offset in the suspended and grounded states is as follows: Figure 12As shown in Figures (a) and (b), the system gain increases monotonically with increasing input signal (Vd) frequency in both states. Within the range of 10Hz to 100kHz, the system amplitude-frequency characteristics are consistent in both states; above 100kHz, the rate of increase in system gain decreases with increasing pendulum offset, and the increase is less pronounced in the grounded state than in the ungrounded state. Grounding the casing helps reduce the electric field coupling noise of the accelerometer.

[0130] C. Compare the amplitude-frequency characteristic diagrams and analyze the impact of different detection methods and different shell grounding states on electric field coupling noise when the differential capacitor detection circuit adopts different detection methods.

[0131] Comparing the amplitude-frequency characteristics of the electric field coupling system when the casing is grounded and the pendulum is in the zero-bias position, the voltage method and the current method are used to detect the differential capacitor, respectively. Figure 13 As shown.

[0132] When using the voltage method to detect differential capacitance, the electric field coupling system consistently attenuates the noise as the noise source (Vd) frequency increases. However, when using the current method, the attenuation of the noise by the electric field coupling system gradually decreases as the noise source frequency increases, eventually transitioning from attenuation to amplification around 3.6kHz. When the signal torque drive signal frequency is below 950Hz, the electric field coupling noise is lower with the current method; above 950Hz, the voltage method is more advantageous in controlling electric field coupling noise.

[0133] In summary, when using both voltage and current sensing methods, the electric field coupling noise of the accelerometer is lower when the casing is grounded than when it is suspended. When the torque drive signal frequency is below 950Hz, the electric field coupling noise of the current sensing method is lower; when the torque drive signal frequency is above 950Hz, the voltage method, with its lower coupling noise, should be preferred. Especially when using torque drive signals containing high-order harmonics, such as PWM inputs, the harmonic components are easily amplified by the current sensing method, leading to increased noise and affecting accelerometer performance. Therefore, when using high-frequency signals for torque amplification, the voltage sensing method produces lower electric field coupling noise.

[0134] S4. Based on the transfer function N(s) of the electric field coupling system, solve for the transfer function H of the differential capacitor detection circuit considering electric field coupling noise. Ka The transfer function Hn(s) of the accelerometer closed-loop system:

[0135] The effect of electric field coupling system on differential capacitance detection is as follows: Figure 14As shown, the voltage change ΔV obtained by detecting the change in differential capacitance ΔC is used as the excitation of the electric field coupling system N(s) by the torque drive signal Vd output after the torque controller is controlled by the torque controller. The electric field coupling noise Vnoise is superimposed on ΔV, which increases the output voltage noise of the differential capacitance detection.

[0136] The transfer function HKa(s) of the differential capacitor detection circuit considering electric field coupling noise can be expressed as:

[0137] H Ka (s)=K a (1+K M N(s)) (29)

[0138] In an accelerometer closed-loop system considering electric field coupling noise, an electric field coupling loop exists in addition to the rebalancing loop. The structure of the accelerometer closed-loop system considering electric field coupling noise is as follows: Figure 16 As shown, its system transfer function Hn(s) can be expressed as:

[0139]

[0140] Combine equations (3), (19), (22) and (28) to calculate the transfer function H(s) of the accelerometer closed-loop system when there is no electric field coupling noise, the transfer function HnV(s) of the closed-loop system using the voltage detection method and the transfer function HnI(s) of the closed-loop system using the current detection method when there is electric field coupling noise.

[0141] Verify the impact of the electric field coupling system on the performance of the quartz flexible accelerometer head, including verifying the impact of the electric field coupling system on differential capacitance detection and the accelerometer closed-loop system;

[0142] The closed-loop system parameters of the quartz flexible accelerometer involved in this embodiment are as follows: mL = 6.3 × 10⁻⁶ kg·m, J = 1.1 × 10⁻⁸ kg·m², C = 2.0 × 10⁻⁴ N·m·s / rad, K = 2.2 × 10⁻³ N·m / rad, Ks = 12000 pF / rad, KT = 1 g / mA. When using voltage and current detection methods, the typical value of Ka is 0.128 V / pF. M(s) uses proportional feedback to meet the closed-loop bandwidth requirement, with a gain KM = 2.5. The torque drive circuit uses a VI circuit, KI = 10 mA / V, and the system bandwidth is 200 Hz.

[0143] Verification of the impact of the electric field coupling system on the performance of the quartz flexible accelerometer head: With the accelerometer housing grounded, when the differential capacitance is detected using the voltage method and the current method, H Ka The amplitude-frequency characteristic of (s) is as follows Figure 15As shown. Ignoring electric field coupling noise, the gain of the differential capacitance detection circuit is -17.9 dB (Ka = 0.128 V / pF). When using the voltage method to detect the differential capacitance, the output voltage ΔV of the differential capacitance detection circuit decreases as the rate of change of ΔC increases. The average gain over the system bandwidth is -23.7 dB, and the differential capacitance detection sensitivity is 0.065 V / pF, decreasing to 50% of its original value. Therefore, if the output voltage resolution of the accelerometer differential capacitance detection circuit remains constant at ΔVmin, the output voltage drop caused by electric field coupling noise reduces the actual resolution to 50% of the original resolution. When using the current method to detect the differential capacitance, the output voltage ΔV remains constant at -17.9 dB over the system bandwidth, having no significant impact on the differential capacitance detection sensitivity and resolution.

[0144] Verification of the impact of the electric field coupling system on the accelerometer closed-loop system: With electric field coupling noise present, the transfer function HnV(s) of the closed-loop system using the voltage detection method and the transfer function HnI(s) of the closed-loop system using the current detection method are shown below. The amplitude-frequency characteristics and step response characteristics of each system are as follows: Figure 17 As shown in Figures (a) and (b), the bandwidth of the accelerometer closed-loop system without electric field coupling noise is 203Hz, which is basically consistent with the design parameters. With electric field coupling noise, the bandwidth of the closed-loop system using the voltage detection method is 120Hz, and the gain of the electric field coupling system is -11.6dB, indicating that the system bandwidth is significantly attenuated by electric field coupling. The bandwidth of the closed-loop system using the current detection method is 240Hz, slightly larger than the system design bandwidth, and the gain of the electric field coupling system is -25dB. With electric field coupling noise, the rise time of the closed-loop step response of the system using the voltage detection method is 3ms, which is about 58% higher than the design parameters, indicating that electric field coupling noise reduces the system response sensitivity. The rise time under the current method is 1.7ms, which is slightly faster than the system design parameters.

[0145] The performance degradation of the accelerometer closed-loop system, such as bandwidth, caused by electric field coupling noise when using the voltage detection method is mainly due to the large gain of the electric field coupling system near the signal frequency of 200Hz, which leads to a large electric field coupling noise. Its gain is approximately twice that of the current detection method (see...). Figure 13 To compensate for the influence of the electric field coupling system on the bandwidth of the accelerometer closed-loop system, this can be achieved by increasing the gain of the torque drive control system. Let ΔKM be the compensation amount for the drive control system gain. The amplitude-frequency characteristics and step response characteristics of the compensated closed-loop system are calculated for ΔKM values ​​of 2, 4, and 6, respectively, as shown below. Figure 18As shown in Figures (a) and (b), when ΔKM = 4 (KM = 6.5), the bandwidth of the compensated closed-loop system is close to the design parameters. At this time, the gain of the drive control system is 2.6 times that of the current sensing method. Increasing the gain of the drive control system will lead to an increase in system power consumption. Therefore, in order to ensure the bandwidth of the accelerometer closed-loop system, the system power consumption of the voltage sensing method is greater than that of the current sensing method.

[0146] The above analysis shows that the gain of the electric field coupling system is a crucial factor affecting the performance degradation of the accelerometer closed-loop system, including its bandwidth. A smaller gain in the electric field coupling system has a smaller impact on the performance of the accelerometer closed-loop system; when the gain is less than -25dB, the impact on system performance is extremely weak. To offset the effect of electric field coupling on the closed-loop system, compensation can be achieved by increasing the gain of the drive control system, but this method leads to increased system power consumption. Therefore, when compensating for system performance, both the closed-loop system bandwidth and power consumption should be considered comprehensively.

[0147] The modeling method for optimizing electric field coupling noise in a quartz flexible accelerometer, as described in this invention, has the following advantages:

[0148] (1) This invention targets the closed-loop system of a quartz flexible accelerometer head. By studying the electric field coupling mechanism inside the accelerometer head, an electric field coupling model inside the accelerometer head is established. The transfer function model of the electric field coupling system considering the internal distributed capacitance and taking the torque drive signal as a noise source is obtained. Thus, the transfer function model of the accelerometer closed-loop system considering electric field coupling noise is obtained. When establishing the accelerometer closed-loop system model, the influence of electric field coupling noise is considered, which can reduce the accelerometer measurement error and thus improve the performance of the inertial navigation system.

[0149] (2) The present invention can model accelerometers using differential capacitor detection circuits with current detection method and voltage detection method respectively. The coupling coefficient matrix of the transfer function model of the electric field coupling system is determined by the size of the internal distributed capacitance, the grounding state of the outer shell, and the differential capacitor detection method. The transfer function of the closed-loop system calculated from this is also different.

[0150] (3) This invention analyzes the variation law of internal electric field coupling noise, analyzes the transmission characteristics of electric field coupling noise under different shell states and different detection methods, and analyzes the influence of electric field coupling system on accelerometer performance: when the low frequency signal is applied, the electric field coupling noise of the differential capacitor detected by the current method is smaller, and the electric field coupling noise when the accelerometer shell is grounded is smaller than that when the shell is suspended; when the voltage method is used for detection, the output voltage drop caused by electric field coupling noise will reduce the actual resolution by 50%; the magnitude of electric field coupling noise gain is positively correlated with the performance degradation of the accelerometer closed-loop system such as bandwidth. The influence of electric field coupling noise on the closed-loop system can be compensated by increasing the gain of the drive control system, but this will lead to an increase in system power consumption.

[0151] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit it; although the embodiments of the present invention have been described in conjunction with the accompanying drawings, those skilled in the art can make various modifications and variations without departing from the spirit and scope of the present invention, and such modifications and variations all fall within the scope defined by the appended claims.

Claims

1. A modeling method for optimizing electric field coupling noise in a quartz flexible accelerometer, characterized in that, Includes the following steps: S1. Construct a closed-loop system for the quartz flexible accelerometer head; The quartz flexible accelerometer head includes a quartz pendulum assembly, a variable-gap differential capacitance sensor that varies with the offset of the quartz pendulum, and a torque converter. The variable-gap differential capacitance sensor is connected to a differential capacitance detection circuit, which is connected to a torque converter control system. The torque converter control system is connected to both ends of the torque converter coil. The torque converter control system includes a control circuit and a drive circuit, which generates a control signal based on the detection value of the differential capacitance detection circuit, and then amplifies the control signal to generate a drive signal for adjusting the torque converter coil. The closed-loop system of the quartz flexible accelerometer head includes the quartz pendulum assembly, the variable pole distance differential capacitance sensor, the differential capacitance detection circuit, the torque control system, and the torque. S2. The closed-loop system includes an electric field coupling system, which includes the internal distributed capacitance between the torque coil and the differential capacitance sensor, the variable pole gap differential capacitance sensor, the differential capacitance detection circuit, and the torque control system. A model of the internal distributed capacitance is constructed. S3. Considering the internal distributed capacitance, calculate the transfer function N(s) of the electric field coupling system when the torque drive signal Vd is regarded as a noise source; S4. Based on the transfer function N(s) of the electric field coupling system, solve for the transfer function Hn(s) of the accelerometer closed-loop system considering electric field coupling noise: Where mL represents the pendulum property of the quartz pendulum, θ(s), Ks, Ka, M(s), K I and K T These are the quartz pendulum assembly, differential capacitor sensor, differential capacitor detection circuit, control circuit in the torque control system, drive circuit in the torque control system, and transfer function of the torque, respectively.

2. The modeling method for optimizing electric field coupling noise of a quartz flexible accelerometer according to claim 1, characterized in that, In step S2, the differential capacitor detection circuit includes a differential capacitor detection circuit using a current detection method and a differential capacitor detection circuit using a voltage detection method.

3. The modeling method for optimizing electric field coupling noise of a quartz flexible accelerometer according to claim 2, characterized in that, In step S2, the internal distributed capacitance includes: distributed capacitances Cd1, Cd2, and Cd3 between the torque coil and the lower moving plate, the fixed plate, and the upper moving plate, respectively; distributed capacitances Ce1, Ce2, Ce3, and Ce4 between the accelerometer housing and the fixed plate, the upper moving plate, the lower moving plate, and the torque coil, respectively; and distributed capacitance Cbb between the upper and lower moving plates.

4. The modeling method for optimizing electric field coupling noise of a quartz flexible accelerometer according to claim 2, characterized in that, In step S3, when the torque drive signal Vd is considered as a noise source, the transfer function N(s) of the electric field coupling system is: Where n is the system order, m and k are the coefficients of the numerator and denominator, respectively, and the polynomial coupling coefficient matrices of the transfer function numerator and denominator of the electric field coupling system are defined as follows: Where P is the numerator polynomial coupling coefficient matrix, Q is the denominator polynomial coupling coefficient matrix, i is the current system order, i = 1, 2, ..., n, and the coupling coefficient matrix is ​​determined by the inherent characteristics of the accelerometer system, such as the size of the distributed capacitance, the grounding status of the outer casing, and the differential capacitance detection method. The relationship between the polynomial coefficients of the numerator polynomial coefficient vector M and the denominator polynomial coefficient vector K of the transfer function N(s) of the electric field coupling system and the change of the differential capacitance is as follows: Where ε is the dielectric constant, S is the area of ​​the plates facing each other, d0 is the nominal distance between the fixed plate and the moving plate when the pendulum is in equilibrium, and Δd is the offset of the differential capacitor plate distance.

5. The modeling method for optimizing electric field coupling noise of a quartz flexible accelerometer according to claim 4, characterized in that, Step S4 also includes solving the transfer function H of the differential capacitor detection circuit containing electric field coupling noise. Ka (s): H Ka (s)=K a (1+K M N(s)), Among them, K M For gain.

6. The modeling method for optimizing electric field coupling noise of a quartz flexible accelerometer according to claim 1, characterized in that, In step S1, the quartz flexible accelerometer head includes a quartz pendulum assembly, a torque generator, a magnet assembly, and a housing. The torque generator includes a torque coil, an upper yoke, a lower yoke, and a belt. The magnet assembly includes an upper magnet assembly and a lower magnet assembly. The upper / lower magnet assembly includes upper / lower magnets, magnetic pole pieces, and a compensation ring bonded together. The belt is fixed to both ends of the upper and lower yokes, forming a closed space. The compensation ring fixes the upper / lower magnets in the middle of the upper / lower yokes. The magnetic pole piece is fixed on the surface of the upper / lower magnet that is not in contact with the upper / lower yoke. The torque coil is located in the magnetic gap formed by the upper and lower magnet assemblies. The quartz pendulum assembly includes a tongue-shaped quartz pendulum with metal films plated on its upper and lower surfaces. One end of the quartz pendulum is fixed on the belt and is equidistant from the upper and lower yokes. The metal films and the surfaces of the upper and lower yokes constitute a variable-gap differential capacitor sensor. The metal films on both sides of the quartz pendulum are the upper and lower moving plates of the differential capacitor, and the surface of the yoke is the fixed plate of the differential capacitor.

7. The modeling method for optimizing electric field coupling noise of a quartz flexible accelerometer according to claim 1, characterized in that, The transfer function θ(s) of the quartz pendulum assembly is: Where J is the moment of inertia, C is the damping coefficient, and K is the elastic coefficient.

8. The modeling method for optimizing electric field coupling noise of a quartz flexible accelerometer according to claim 4, characterized in that, The modeling method also includes: simulating and analyzing the internal electric field coupling of the quartz flexible accelerometer head using the finite element method, and verifying the influence of the outer casing grounding state and differential capacitance detection method on the electric field coupling. A. Model the structure of the quartz flexible accelerometer head, solve for the internal distributed capacitance, and set parameters according to the accuracy requirements; B. When using differential capacitor detection circuits with voltage detection method and current detection method respectively, obtain the coupling coefficient matrix, transfer function and amplitude-frequency characteristic diagram of electric field coupling system under different shell grounding states; C. Comparing the amplitude-frequency characteristic diagrams, analyze the impact of different detection methods and different shell grounding states on electric field coupling noise of the differential capacitor detection circuit: When using the voltage detection method and the current detection method, the electric field coupling noise in the accelerometer shell grounding state is less than that in the shell floating state; when the torque drive signal frequency is less than 950Hz, the electric field coupling noise of the current detection method is smaller, and when the torque drive signal frequency is higher than 950Hz, the electric field coupling noise of the voltage detection method is smaller; when using a high-frequency signal for torque application, the electric field coupling noise of the voltage detection method is smaller.

9. The modeling method for optimizing electric field coupling noise of a quartz flexible accelerometer according to claim 6, characterized in that, The modeling method further includes: verifying the impact of the electric field coupling system on the performance of the quartz flexible accelerometer head, including verifying the impact of the electric field coupling system on differential capacitance detection; verifying the impact of the electric field coupling system on the accelerometer closed-loop system: the bandwidth performance degradation of the accelerometer closed-loop system caused by electric field coupling noise when using the voltage detection method.

10. The modeling method for optimizing electric field coupling noise of a quartz flexible accelerometer according to claim 9, characterized in that, The step S4 is followed by S5, obtaining noise compensation measures: compensating for the influence of the electric field coupling system on the bandwidth of the accelerometer closed-loop system by increasing the gain of the torque drive control system.

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