Accelerometer and vibration rectification error compensation method thereof

Abstract

The invention belongs to the field of accelerometers, and particularly discloses an accelerometer and a vibration rectification error compensation method thereof, and the design of the accelerometer needs to meet the condition that the quality factor of the accelerometer is smaller than or equal to the ratio of the accelerometer range to the maximum vibration acceleration in an application environment; the square of the resonance angular frequency of the accelerometer is greater than or equal to the ratio of the accelerometer range to the check mass displacement upper limit; the ratio of the resonance angular frequency to the quality factor is smaller than or equal to a preset value related to a preset mechanical thermal noise upper limit; the quality factor is the gain at the resonant angular frequency of the accelerometer, and the gain is the ratio of the accelerometer response corresponding to the acceleration input at different frequency points to the accelerometer response corresponding to the constant acceleration input with the same amplitude. According to the invention, the sensitivity of the mechanical structure of the accelerometer can be improved, output signal saturation is avoided, the sensitivity of the accelerometer is ensured, accurate vibration rectification error compensation can be carried out on the accelerometer, and the overall performance of the accelerometer is improved.

Description

Technical Field

[0001] The present application belongs to the field of accelerometers, and more specifically, relates to an accelerometer and a vibration rectification error compensation method thereof. Background Art

[0002] Vibration Rectification Error (VRE) is the response of the accelerometer to vibration (rectified to DC), which manifests as an abnormal offset of the accelerometer zero bias, that is, the phenomenon that the vibration signal is converted into the DC output of the accelerometer. It changes with the change of environmental vibration and is a DC error caused by the interaction of the accelerometer's second-order nonlinearity and environmental vibration. In inertial applications, VRE must be reduced because it will cause zero bias drift in a high-vibration environment. The acceleration signal is integrated twice to obtain position information. Once the zero bias of the accelerometer signal has a sudden change, due to the integration effect, it will directly lead to a rapid increase in position information, resulting in a large position error.

[0003] At present, there are only two ways to improve the vibration rectification error performance index of accelerometers. One is to start from the structural design of the accelerometer: including: the first way is to design the mechanical resonant frequency of the accelerometer to be large enough so that the vibration signal in the application environment is far away from the resonant frequency, ensuring a wider flat frequency band, not to produce resonance, and reducing the displacement amplitude of the inspection mass, effectively reducing nonlinearity, thereby reducing VRE, but this method sacrifices mechanical sensitivity and reduces the gain of the acceleration-to-displacement conversion link, which puts forward higher displacement resolution requirements for the subsequent displacement detection link; the other way is to achieve it by reducing the resonant peak of the accelerometer mechanical mechanism: by applying over-damping, the resonant peak of the accelerometer mechanical structure is suppressed, so that the vibration signal outside the bandwidth in the application environment does not respond, thereby suppressing VRE, but the amplitude-related nonlinearity in the flat frequency band still exists, and the damping is difficult to control. The larger damping affects the dynamic characteristics of the system such as the response time, resulting in the inability to capture rapidly changing signals in time. Summary of the invention

[0004] In view of the defects of the prior art, the purpose of the present application is to provide an accelerometer and a vibration rectification error compensation method thereof, aiming to solve the problem that the vibration rectification error performance index of the existing accelerometer cannot be taken into account at the same time as the accelerometer performance.

[0005] To achieve the above-mentioned purpose, in a first aspect, the present application provides an accelerometer, including: the design of the accelerometer must meet the following requirements: the quality factor of the accelerometer is less than or equal to the ratio of the accelerometer range to the maximum value of the vibration acceleration in the application environment; the square of the accelerometer resonant angular frequency is greater than or equal to the ratio of the accelerometer range to the upper limit of the accelerometer inspection mass displacement; and the ratio of the resonant angular frequency to the quality factor is less than or equal to a preset value, and the preset value is related to a preset mechanical thermal noise upper limit; Among them, the quality factor is the gain at the resonant angular frequency of the accelerometer, and the gain is the ratio of the accelerometer response corresponding to the acceleration input at different frequency points to the accelerometer response corresponding to the acceleration input with the same constant amplitude; for an open-loop accelerometer, the accelerometer response refers to the displacement of the proof mass in the accelerometer; for a closed-loop accelerometer, the accelerometer response refers to the feedback signal acting on the proof mass in the accelerometer to balance it at zero position.

[0006] Optionally, the quality factor and the resonance angular frequency of the accelerometer are respectively a combination of a maximum value of the quality factor and a minimum value of the resonance angular frequency when the ratio satisfies a preset value.

[0007] Optionally, the quality factor and resonant angular frequency of the accelerometer are respectively a combination of a larger quality factor and a smaller resonant angular frequency, and the combination satisfies that the ratio is less than or equal to a preset value; the larger value is that the absolute value of the difference compared to the maximum value does not exceed a first threshold, and the smaller value is that the absolute value of the difference compared to the minimum value does not exceed a second threshold.

[0008] Optionally, the resonant angular frequency of the accelerometer is regulated by a structural design of the accelerometer, the quality factor of the accelerometer is regulated by a damping design of the accelerometer, and the damping of the accelerometer is designed to be underdamped.

[0009] Optionally, the preset value is: ; Indicates the preset upper limit of mechanical thermal noise, represents the Boltzmann constant, m represents the mass of the accelerometer proof mass, T Indicates the ambient temperature.

[0010] In a second aspect, the present application provides a vibration rectification error compensation method for an accelerometer provided in the first aspect, comprising the following steps: Determining a second-order nonlinear model of the accelerometer; the second-order nonlinear model is used to describe the mapping relationship between the accelerometer output signal and the accelerometer input; Performing a first-order low-pass filtering on the output signal of the accelerometer, and performing vibration rectification error compensation on the output signal after the first-order low-pass filtering based on the second-order nonlinear model to obtain a compensated output signal; Performing secondary low-pass filtering on the compensated output signal, and then outputting the signal after the secondary low-pass filtering as the compensated original acceleration input signal; Among them, the cut-off frequency of the first-stage low-pass filter is greater than the resonance angular frequency, and the cut-off frequency of the second-stage low-pass filter is less than the resonance angular frequency.

[0011] Optionally, the cut-off frequency of the first-stage low-pass filter is greater than the resonant angular frequency and is the frequency when the gain drops to a preset gain; the preset gain is less than the gain of the frequency segment of the second-stage low-pass filter; The cutoff frequency of the secondary low-pass filter is less than the resonant angular frequency, which is determined based on the frequency of the vibration acceleration in the application environment and the gain, and takes a value greater than or equal to the upper limit of the vibration acceleration frequency in the application environment and less than or equal to the preset frequency. In the frequency band less than the preset frequency, the gain changes flatly.

[0012] Optionally, the compensated output signal for:

[0013] in, K 0 is the zero bias of the accelerometer, K 1 is the scale factor of the accelerometer, K 2 is the second-order nonlinear coefficient of the accelerometer, is the output signal of the accelerometer.

[0014] In general, the above technical solutions conceived by this application have the following beneficial effects compared with the prior art: The present application provides an accelerometer and a vibration rectification error compensation method thereof. The accelerometer quality factor is designed by considering the accelerometer range and the maximum value of the vibration acceleration in the application environment to ensure that the accelerometer output does not exceed the range, so that the vibration rectification error compensation method can be effectively applied to the accelerometer; the accelerometer resonant angular frequency is designed by the accelerometer range and the upper limit of the accelerometer inspection mass displacement to avoid the accelerometer displacement exceeding the above displacement upper limit when the full-scale input is applied, thereby damaging the accelerometer. The design quality factor and the accelerometer resonant angular frequency are comprehensively evaluated by presetting the mechanical thermal noise upper limit to ensure that the mechanical thermal noise of the designed accelerometer does not exceed the above preset upper limit; on the basis of the above design, the maximum value or relatively large value of the quality factor is taken, and the minimum value or relatively small value of the resonant angular frequency is taken, so as to improve the mechanical sensitivity of the accelerometer, reduce the requirements for the displacement resolution of the subsequent displacement detection link, and ensure that the accelerometer does not exceed the upper limit of displacement when the full-scale input is applied, so that the vibration rectification error compensation method can be effectively implemented, and the accelerometer vibration rectification error performance index is ensured. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] Figure 1 is a flow chart of an accelerometer design method provided in an embodiment of the present application; Figure 2 is a schematic diagram of an over-damped amplitude-frequency response curve provided in an embodiment of the present application; Figure 3 is a flow chart of a vibration rectification error software compensation method provided in an embodiment of the present application; Figure 4 is a schematic diagram of an amplitude-frequency response curve of an underdamped accelerometer provided in an embodiment of the present application; Figure 5 is a diagram showing the effectiveness criterion of the vibration rectification error software compensation method provided in an embodiment of the present application; Figure 6 It is a numerical simulation comparison diagram of the second-order nonlinearity and vibration rectification error before and after compensation provided by the embodiment of the present application; Figure 7 It is a comparison diagram before and after compensation of the vibration rectification error of the accelerometer under random vibration input provided in the embodiment of the present application. DETAILED DESCRIPTION

[0016] In order to make the purpose, technical solution and advantages of the present application more clearly understood, the present application is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and are not used to limit the present application.

[0017] The embodiments of the present application are described below in conjunction with the drawings in the embodiments of the present application.

[0018] Figure 1is a flow chart of the accelerometer design method provided in the embodiment of the present application; Figure 1 As shown, the following steps are included: Step S101, controlling the quality factor of the accelerometer to be less than or equal to the ratio of the accelerometer range to the maximum value of the vibration acceleration in the application environment; Step S102, controlling the square of the accelerometer resonant angular frequency to be greater than or equal to the ratio of the accelerometer range to the upper limit of the accelerometer test mass displacement; Step S103, controlling the ratio of the resonant angular frequency to the quality factor to be less than or equal to a preset value, where the preset value is related to a preset upper limit of mechanical thermal noise; Among them, the quality factor is the gain at the resonant angular frequency of the accelerometer, and the gain is the ratio of the accelerometer response corresponding to the acceleration input at different frequency points to the accelerometer response corresponding to the acceleration input with the same constant amplitude; for an open-loop accelerometer, the accelerometer response refers to the displacement of the proof mass in the accelerometer; for a closed-loop accelerometer, the accelerometer response refers to the feedback signal acting on the proof mass in the accelerometer to balance it at zero position.

[0019] It should be noted that existing accelerometer designs generally adopt two strategies: The first strategy is to design the mechanical resonant frequency of the accelerometer to be large enough so that the vibration signal in the application environment is far away from the resonant frequency, ensuring a wider flat frequency band to avoid resonance, and reducing the displacement amplitude of the test mass, effectively reducing nonlinearity and thus reducing VRE. However, this method sacrifices mechanical sensitivity and reduces the gain of the acceleration-to-displacement conversion link, which puts higher displacement resolution requirements on the subsequent displacement detection link.

[0020] In the displacement detection stage, the smaller the displacement of the inspection mass, the higher the displacement resolution requirement, which requires a more sensitive detection method. A highly sensitive detection system is more susceptible to noise interference, affecting the accuracy of the measurement; secondly, high resolution requires a more complex circuit design, which increases cost and design complexity.

[0021] The second strategy is to suppress the resonance peak of the accelerometer mechanical structure by applying overdamping, so that the vibration signal outside the bandwidth of the application environment does not respond, thereby suppressing VRE. For details, see Figure 2 As shown; however, the disadvantages of this method are also obvious: first, the nonlinearity related to the amplitude still exists in the flat frequency band; second, the larger damping affects the dynamic characteristics of the system such as the response time, resulting in the inability to capture rapidly changing signals in time; in addition, it can be seen from the figure that since the damping is difficult to control, the larger damping will significantly reduce the passband of the accelerometer, that is, area IV, resulting in a reduction in the available mechanical bandwidth of the accelerometer and a cutoff frequency of the first-stage low-pass filter. fcut_off Too small, limiting the scope of application scenarios. f 3 is the frequency point corresponding to when the gain is reduced to the flat section -3dB on the amplitude-frequency response curve.

[0022] The amplitude-frequency response curve includes: gain information at different frequency points; the gain is the ratio of the accelerometer response corresponding to the acceleration input at the corresponding frequency point to the accelerometer response corresponding to the acceleration input of the same amplitude constant.

[0023] This application designs the quality factor Q value and resonant angular frequency of the accelerometer 1. Design Q by considering the accelerometer range and the maximum value of vibration acceleration in the application environment to ensure that the accelerometer output does not exceed the range, so that the vibration rectification error compensation method can be effectively applied to the accelerometer; 2. Design the upper limit of the displacement of the accelerometer by the accelerometer range and the accelerometer inspection mass , to prevent the accelerometer from exceeding the upper limit of displacement when the full-scale input is applied, thus damaging the accelerometer. 3. Comprehensively evaluate the design Q and , ensuring that the mechanical thermal noise of the designed accelerometer does not exceed the above preset upper limit.

[0024] Further, on this basis, those skilled in the art can know that the larger the Q is, the smaller the mechanical thermal noise of the accelerometer is, so Q can take the maximum value. In addition, The smaller the value, the greater the mechanical sensitivity of the acceleration-displacement conversion link, and the smaller the circuit equivalent acceleration noise. Therefore, the value that meets the requirements should be selected. Minimum value.

[0025] Therefore, the quality factor and the resonance angular frequency of the above accelerometer are respectively taken as a combination of the maximum value of the quality factor and the minimum value of the resonance angular frequency when the ratio is less than or equal to the preset value.

[0026] Furthermore, those skilled in the art may also use Q and The value of is appropriately relaxed to avoid the above conditions being too harsh; therefore, the quality factor and resonant angular frequency of the above accelerometer can respectively take a combination of a larger quality factor and a smaller resonant angular frequency, and the combination satisfies that the ratio is less than or equal to a preset value; the larger value is that the absolute value of the difference compared to the maximum value does not exceed the first threshold, and the smaller value is that the absolute value of the difference compared to the minimum value does not exceed the second threshold.

[0027] Among them, those skilled in the art can set the above-mentioned first threshold and second threshold according to actual needs, and this application does not impose any limitation on this.

[0028] It can be understood that the resonant angular frequency of the above-mentioned accelerometer is regulated by the structural design of the accelerometer, the quality factor of the accelerometer is regulated by the damping design of the accelerometer, and the damping of the accelerometer is designed to be underdamped.

[0029] In some optional scenarios, the resonant angular frequency of the accelerometer can be adjusted by adjusting the stiffness of the spring beam; the smaller the stiffness of the spring beam, the smaller the resonant angular frequency, and the width of the spring beam can be shortened and the length of the spring beam can be increased accordingly; combined with spring beam forms including but not limited to folded beams (the stiffness is reduced by connecting spring beams in parallel to avoid the reliability being reduced due to the spring beam being too thin), and referring to finite element simulation, it is ensured that the displacement of the inspection mass is always within the linear range.

[0030] In some optional scenarios, the accelerometer quality factor adjustment can be achieved by adjusting the accelerometer damping, including but not limited to air damping, magnetic damping and electrostatic damping; taking air damping as an example, it can be adjusted by increasing the distance between the movable pole plate and the fixed pole plate, changing the gas pressure inside the accelerometer, adding damping holes, etc., so as to reduce the accelerometer damping and increase the accelerometer quality factor.

[0031] It should be noted that when the above accelerometer is designed to be underdamped, the regulation of its damping will not cause a significant shift in the resonant angular frequency: ;in, represents the resonant angular frequency without damping, represents the actual resonant angular frequency when there is damping, c represents the damping coefficient, and k represents the system stiffness; it can be seen that the underdamped state near , so in the underdamped state, the change of the above-mentioned resonant angular frequency can be ignored in the process of adjusting the damping.

[0032] In some embodiments, in order to ensure the effectiveness of the vibration rectification compensation method, the output of the accelerometer must not be greater than the range of the accelerometer. For the convenience of analysis, the maximum amplitude of the known external input vibration acceleration at the resonant angular frequency is , a FS represents the range of the accelerometer to be tested, and the gain The maximum value Q is reached at the resonant angular frequency. When designing the accelerometer, the amplified accelerometer output should meet the following requirements:

[0033] The larger the Q value, the smaller the mechanical thermal noise of the accelerometer, so Q can take the maximum value.

[0034] In order to limit the nonlinearity between acceleration and displacement of the mechanical structure itself, the test mass has a maximum displacement limit X. The amplitude-frequency response of the acceleration-to-displacement conversion for:

[0035] in, ω 0. ω They represent the inherent angular frequency of the accelerometer and the angular frequency of the external input acceleration signal, Q Indicates the quality factor. When the angular frequency of the input acceleration signal is much smaller than the natural angular frequency of the accelerometer, that is, When (i.e., gain flat section), the relationship between the displacement of the movable mass block of the accelerometer and the input acceleration can be expressed as:

[0036] Therefore, the displacement of the proof mass corresponding to the full-scale acceleration input with the resonant angular frequency within the flat frequency band should satisfy: ;Right now .

[0037] In addition, for the design of the accelerometer resonant frequency, the preset mechanical thermal noise needs to be considered. NEA mech The design should meet the following requirements:

[0038] in, k b represents the Boltzmann constant, m Represents the mass of the movable mass block of the accelerometer, which can generally be uniquely determined based on the accelerometer size constraints. T Indicates the ambient temperature.

[0039] therefore, ; It can be understood that, combined with the formula: It can be seen that the smaller the resonant angular frequency, the greater the mechanical sensitivity of the acceleration-to-displacement conversion link, and the smaller the circuit equivalent acceleration noise. Therefore, the minimum resonant frequency that meets the requirements can be taken.

[0040] Figure 3 is a flow chart of the vibration rectification error software compensation method provided in the embodiment of the present application; Figure 3 As shown, the following steps are included: Step S201, determining a second-order nonlinear model of the accelerometer; the second-order nonlinear model is used to describe the mapping relationship between the accelerometer output signal and the accelerometer input; Step S202, performing a first-order low-pass filtering on the output signal of the accelerometer, and performing vibration rectification error compensation on the output signal after the first-order low-pass filtering based on the second-order nonlinear model to obtain a compensated output signal; Step S203, performing secondary low-pass filtering on the compensated output signal, and then outputting the signal after the secondary low-pass filtering as the compensated original acceleration input signal; Among them, the cut-off frequency of the first-stage low-pass filter is greater than the resonance angular frequency, and the cut-off frequency of the second-stage low-pass filter is less than the resonance angular frequency.

[0041] For example, the cutoff frequency of the first-stage low-pass filter is greater than the resonance angular frequency and is the frequency when the gain drops to a preset gain; the preset gain is less than the gain of the frequency segment of the second-stage low-pass filter; The cutoff frequency of the secondary low-pass filter is less than the resonant angular frequency, which is determined based on the frequency of the vibration acceleration in the application environment and the gain, and takes a value greater than or equal to the upper limit of the vibration acceleration frequency in the application environment and less than or equal to the preset frequency. In the frequency band less than the preset frequency, the gain changes flatly or the amplitude of the change is small.

[0042] It should be noted that Figure 4 It is the amplitude-frequency response curve of the underdamped accelerometer, which is divided into three areas, including: Area I, the passband of the accelerometer, in which it can be considered that the external input acceleration is almost distortion-free (there will be no obvious gain change with the frequency change, that is, the gain changes flatly or the change amplitude is small), which more truly reflects the change of the input acceleration; Area II, the uneven area of ​​the amplitude-frequency response curve of the accelerometer, the external input acceleration with a frequency falling within this frequency band will be amplified, which is manifested as the accelerometer output increases with the frequency until it is fully deflected; Area III, the signal attenuation band of the accelerometer, in which the external input acceleration signal is greatly attenuated, and it can be considered that the accelerometer does not respond to the input signal within this frequency band and can be ignored.

[0043] Among them, the left boundary of the above region II f 1 and right border f 2 respectively correspond to the frequencies when the amplitude is increased / decreased by 3dB compared to the gain at DC. As a further example, the frequency corresponding to the gain being increased to 3dB can be used as the cutoff frequency of the second-order low-pass filter, and the frequency corresponding to the gain being reduced to -3dB can be used as the cutoff frequency of the first-order low-pass filter. Furthermore, the cutoff frequency of the second-order low-pass filter can be less than the frequency at which the gain is increased to 3dB, so as to take a frequency band with a flatter gain as the measurement frequency of the accelerometer; or the cutoff frequency of the second-order low-pass filter can be determined according to the measurement frequency band of the accelerometer. The upper limit frequency of the above-mentioned measurement frequency band should be less than or equal to the upper limit frequency of the flat section or less than the frequency at which the gain is increased to 3dB.

[0044] According to the accelerometer resonant frequency f 0 and the second-stage low-pass filter cutoff frequency f cut-off-2 The relative relationship can be divided into the following two situations: when f cut-off-2≪ f 0, that is, the mechanical resonance frequency of the accelerometer is designed to be very large, so that the vibration signal in the application environment is far away from the resonance frequency, ensuring a wider flat frequency band, that is, the vibration noise is contained in f cut-off-2 In the flat frequency band on the left, resonance will not occur, and the displacement amplitude of the test mass is reduced, which can effectively reduce the nonlinear response caused by the input acceleration whose frequency is in the flat frequency band, thereby reducing VRE. In this case, you only need to set the cutoff frequency to f cut-off-2 A low-pass filter is sufficient. It can be seen that this method sacrifices mechanical sensitivity and reduces the sensitivity of the acceleration-to-displacement conversion link, which puts forward higher displacement resolution requirements for the subsequent displacement detection link; when f cut-off-2 and f 0, that is, the mechanical resonance frequency of the accelerometer is included in the vibration signal frequency in the application environment. In order to collect the complete vibration signal, the complete vibration signal includes the vibration signals in the frequency bands of region I and region II. Therefore, the cutoff frequency of the first-stage low-pass filter of the accelerometer is f cut-off-1 , should not be less than the right boundary of region II f 2; The output of the low-pass filter enters the compensation link, and the output after compensation is restored to , that is, the vibration signal amplified in the II region, and the vibration rectification error is also compensated to zero; the output back end after compensation is further provided with a second-stage low-pass filter, and the cutoff frequency of the second-stage low-pass filter is f cut-off-2 , should not be greater than the left boundary of region II f 1, its function is to filter out the useless amplified vibration signal outside the bandwidth of area II. f cut-off-2 and f 0, through reasonable accelerometer design, the gain of the acceleration-to-displacement conversion link is guaranteed, the requirements for displacement detection resolution in subsequent links are relaxed, and the vibration rectification error caused by the vibration acceleration signal in areas I and II can be effectively compensated.

[0045] In a more specific embodiment, the vibration rectification error software compensation scheme provided in the embodiment of the present application specifically includes: the accelerometer model including the second-order nonlinear coefficient is actually a quadratic function with acceleration input as a variable and acceleration output as a target quantity, and the symmetry axis of the quadratic function is determined by the second-order nonlinear coefficient and the scale factor. When the area on one side of the symmetry axis covers the accelerometer range, the compensation method is effective; the second-order nonlinear coefficient of the accelerometer is calibrated using a vibration table or a centrifuge, substituted into the accelerometer model equation and a inverse function compensation model based on the quadratic function is constructed; finally, the distorted output of the accelerometer including the vibration rectification error and the second harmonic is substituted into the compensation model, and the output of the compensation model is the compensated output, which is restored to the original input size.

[0046] As an example: Step S1, the external environment changes with time t The changing input acceleration signal a (t)= B + A sin(2π ft ), acting on the accelerometer, the external input acceleration includes a constant acceleration (amplitude is B ), vibration acceleration signal (amplitude is A ), f The angular rate of the acceleration signal input from the outside world; Step S2, the external input acceleration signal enters the accelerometer second-order nonlinear system model, and the accelerometer second-order nonlinear system model is shown in the following formula:

[0047] in, K 0 is the zero bias of the accelerometer, and the unit is g , K 1 is the scale factor of the accelerometer, in units of g / g , K 2 is the second-order nonlinear coefficient of the accelerometer, in units of g / g 2 .

[0048] Step S3: external input acceleration over time t Changing input acceleration signal a (t)= B + C sin(2π ft ), after the accelerometer second-order nonlinear model equation, the expression of the accelerometer system output y(a) changing with time is:

[0049] Due to the existence of the second-order nonlinear coefficient, the accelerometer output signal y(t) contains both the frequency of the external input acceleration signalf , also includes the frequency of 2 f False acceleration signal.

[0050] Step S4 is the criterion for the effectiveness of the vibration rectification error compensation method. Figure 5 part), the compensation method is valid, otherwise, the compensation method cannot be used for vibration rectification error compensation of the current accelerometer.

[0051] Step S5, the second-order nonlinear system model of the accelerometer is actually a quadratic function. The quadratic equation has two solutions. For an accelerometer, one acceleration input must correspond to only one acceleration output. In the two equations, it is hoped that the second-order nonlinear coefficient K The contribution of 2 is zero, so we can use L'Hôpital's rule to find K 2 approaches the limit of zero, a + and a - There are two solutions:

[0052] In the second-order nonlinear system model, K 2 is zero, the relationship between the accelerometer input and output is considered to be linear. K 2 is zero y ( a ) expression, we can see that a + is a reasonable solution of the quadratic function, and its inverse function is a ˆ( y ), the final second-order nonlinear and vibration rectification error compensation model equation is:

[0053] Step S6: Substituting the distorted output shown in FIG. 1 into the second-order nonlinear compensation model, the compensated original acceleration input signal can be obtained.

[0054]

[0055] Figure 5 The effectiveness criterion of the vibration rectification error software compensation method provided in the embodiment of the present application is that the accelerometer model equation is a quadratic function, and its symmetry axis can be expressed as:

[0056] The effectiveness of the compensation algorithm is determined by the vibration acceleration amplitude. A and constant acceleration amplitudeB , initial zero bias K 0 jointly decided. Figure 5 As shown in (a), when the second-order nonlinear coefficient K When 2>0, the quadratic function describing the accelerometer model opens upward and the axis of symmetry is S Located on the negative half axis of the acceleration input axis, in order to make the output of the accelerometer monotonic, it is necessary to ensure that the acceleration input is all located on the symmetry axis. S One side; and because the input acceleration range of the accelerometer includes positive and negative directions, it will definitely not be a decreasing interval on the left side, but an increasing interval on the right side. Its physical meaning is that one acceleration input must correspond to only one acceleration output. Similarly, if Figure 5 As shown in (b), when the second-order nonlinear coefficient K When 2<0, it is necessary to ensure that all acceleration inputs are located on the symmetry axis. S Based on the above analysis, this application introduces the criterion for whether the software compensation algorithm is effective or not, which can be expressed as follows:

[0057] That is, the peak value of vibration acceleration ([ C sin(2π ft )] max) / trough([ C sin(2π ft )] min ), constant acceleration amplitude B and initial zero bias K The sum of 0s cannot exceed the axis of symmetry of the quadratic function S The acceleration represented by this can ensure that the full-scale output of the accelerometer is monotonically increasing with respect to the input, that is, the output corresponds to only one acceleration input. g For an accelerometer with a full-scale range, if its full-scale second-order nonlinear coefficient is K 2 Absolute value greater than 1 / 60 g / g 2 , then the symmetry axis determined by its quadratic model equation S Less than 30 g In this case, the compensation algorithm is ineffective over the full range. For a properly functioning accelerometer, its second-order nonlinear coefficient is K 2 is often larger than the scale factor K 1 is several orders of magnitude smaller, so its symmetry axis S The value of is very large, which is definitely far away from the range of the accelerometer. The output of the accelerometer system will always increase monotonically with the increase of input acceleration. Therefore, the compensation algorithm is effective. K When 2>0, the symmetry axis of the quadratic function SThe acceleration input represented by the right area must cover the range of the accelerometer; otherwise, K When 2<0, the symmetry axis of the quadratic function S The acceleration input represented by the left area must also cover the range of the accelerometer. Therefore, this compensation method is effective.

[0058] Figure 6 The numerical simulation results of the software compensation method based on the improved accelerometer in the embodiment of the present application are shown in Figure 1. Through the accelerometer design scheme provided in the embodiment of the present application, the accelerometer resonant frequency is designed to be 566Hz, the 3dB bandwidth is designed to be 317Hz, and the Q value is designed to be 3.3. Figure 6 (a) is a comparison of the output signal spectrum before and after compensation. Due to the existence of the second-order nonlinear coefficient, the output signal spectrum before compensation contains a false double frequency signal. After compensation, the double frequency signal is removed and the original input signal is restored. Figure 6 (b) is a comparison of the accelerometer before and after bias compensation. After compensation, the DC output of the accelerometer is restored to the original input constant acceleration. B =1000m g The vibration rectification error term caused by the second-order nonlinearity, the bias contribution term of the constant acceleration combined with the second-order nonlinearity, and the initial zero bias of the accelerometer are all eliminated. The vibration rectification error compensation method can not only compensate for the vibration rectification error, but also eliminate the initial zero bias of the accelerometer.

[0059] Figure 7 This is the real-time compensation result of the random vibration rectification error software provided in the embodiment of this application. The vibration rectification error compensation system is constructed using FPGA, and the measured second-order nonlinear coefficient is substituted. The random vibration frequency range is 20Hz-2000Hz, and the effective value is 2 g rms . The second-order nonlinear coefficient used for compensation can be obtained by relevant test equipment; the test equipment includes but is not limited to a vibration table or a centrifuge. The output of the accelerometer before and after compensation is low-pass filtered to obtain a DC signal. It can be observed from the figure that before compensation, during the application of the vibration signal, the zero bias change caused by random vibration is the vibration rectification error; after compensation, during the application of the vibration signal, the zero bias has no obvious change compared with before and after the vibration is applied, and the vibration rectification error compensation effect is significant.

[0060] It should be noted that using the above compensation model to compensate for the vibration rectification error of the accelerometer is usually not very smooth, and the corresponding prerequisites need to be met. First of all, the premise of nonlinear compensation, that is, finding the inverse function, is two parts. The first part is that the accelerometer signal transmission process must meet the following conditions: the conversion from capacitance to output voltage is linear and independent of frequency; the nonlinearity is generated in the displacement to capacitance conversion link, and the nonlinearity of this link is independent of frequency; the acceleration to displacement conversion link is linear, and the ratio of displacement to input acceleration (gain) changes with frequency. But it presents a linear function relationship.

[0061] First, let's analyze the first part, the amplitude-frequency response of the acceleration-to-displacement conversion for:

[0062] in, ω 0. ω They represent the inherent angular frequency of the accelerometer and the angular frequency of the external input acceleration signal, Q Indicates the quality factor. When the angular frequency of the input acceleration signal is much smaller than the natural angular frequency of the accelerometer, that is, When , the relationship between the displacement of the movable mass block of the accelerometer and the input acceleration can be expressed as:

[0063] On the contrary, when ω and ω When the normalized acceleration-to-displacement conversion gain z is close to 0 It can be written as:

[0064] Relative to the The ratio can be 1, 2, 3... until the maximum quality factor Q is reached, which represents the ratio of the displacement amplitude of the accelerometer detection mass block to the input acceleration.

[0065] Assume that the conversion relationship from displacement to capacitance is:

[0066] Assume that the conversion relationship from capacitance to voltage is linear, as shown below:

[0067] The final voltage output can be listed as U for:

[0068] make , then the nonlinear expression is as follows:

[0069] k 1 and k The definitions of 2 are the same as those of the second-order nonlinear model, representing the scale factor and second-order nonlinear coefficient of the accelerometer, respectively. Represents the amplified vibration acceleration signal. Therefore, the compensation method can be used to first solve the inverse function to obtain the amplified acceleration signal. It is worth noting that the purpose of this application is to eliminate the vibration rectification error. Therefore, the amplified vibration signal is usually a useless signal outside the application bandwidth, which will be filtered out after the compensation link.

[0070] The second part is to avoid the saturation problem of nonlinear output signals, including: when designing an accelerometer, ensure that its range can cover the maximum displacement at the possible resonant frequency to avoid signal saturation; during use, ensure a sufficient sampling rate to ensure that a voltage signal sufficient to reflect the input acceleration is collected; adapt to the application environment and ensure sufficient bandwidth so that the wide-band output signal is not attenuated, resulting in an inability to reflect the actual acceleration input; this part can be overcome by designing the above-mentioned accelerometer.

[0071] It should be understood that expressions such as "including" and "may include" that may be used in the present application indicate the existence of the disclosed functions, operations, or constituent elements, and do not limit one or more additional functions, operations, and constituent elements. In the present application, terms such as "including" and / or "having" may be interpreted as indicating specific characteristics, numbers, operations, constituent elements, components, or combinations thereof, but may not be interpreted as excluding the existence or possibility of adding one or more other characteristics, numbers, operations, constituent elements, components, or combinations thereof.

[0072] In addition, in the present application, the expression "and / or" includes any and all combinations of the associated listed words. For example, the expression "A and / or B" may include A, may include B, or may include both A and B.

[0073] In the description of the embodiments of the present application, it should be noted that, unless otherwise clearly specified and limited, the term "connection" should be understood in a broad sense. For example, "connection" can be a detachable connection or a non-detachable connection; it can be a direct connection or an indirect connection through an intermediate medium. Among them, "fixed connection" means that the relative position relationship after connection remains unchanged. "Rotational connection" means that the two are connected to each other and can rotate relative to each other after connection. "Sliding connection" means that the two are connected to each other and can slide relative to each other after connection. The directional terms mentioned in the embodiments of the present application, such as "top", "bottom", "inside", "outside", "left", "right", etc., are only reference directions of the accompanying drawings. Therefore, the directional terms used are for better and clearer explanation and understanding of the embodiments of the present application, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as a limitation on the embodiments of the present application.

[0074] In addition, in the embodiments of the present application, the mathematical concepts mentioned are symmetry, equality, parallelism, verticality, etc. These limitations are all for the current state of the art, rather than being absolutely strict definitions in a mathematical sense, and allow a small amount of deviation, approximation to symmetry, approximation to equality, approximation to parallelism, approximation to verticality, etc. are all possible. For example, A and B are parallel, which means that A and B are parallel or approximately parallel, and the angle between A and B can be between 0 and 10 degrees. A and B are perpendicular, which means that A and B are perpendicular or approximately perpendicular, and the angle between A and B can be between 80 and 100 degrees.

[0075] The above is only a specific implementation of the present application, but the protection scope of the present application is not limited thereto. Any person skilled in the art who is familiar with the present technical field can easily think of changes or substitutions within the technical scope disclosed in the present application, which should be included in the protection scope of the present application. Therefore, the protection scope of the present application should be based on the protection scope of the claims.

Claims

1. An accelerometer, characterized in that: include: The design of the accelerometer must meet the following requirements: the quality factor of the accelerometer is less than or equal to the ratio of the accelerometer range to the maximum value of the vibration acceleration in the application environment; The square of the accelerometer resonant angular frequency is greater than or equal to the ratio of the accelerometer range to the upper limit of the accelerometer test mass displacement; and the ratio of the resonant angular frequency to the quality factor is less than or equal to a preset value, and the preset value is related to the preset mechanical thermal noise upper limit; Among them, the quality factor is the gain at the resonant angular frequency of the accelerometer, and the gain is the ratio of the accelerometer response corresponding to the acceleration input at different frequency points to the accelerometer response corresponding to the acceleration input with the same constant amplitude; for an open-loop accelerometer, the accelerometer response refers to the displacement of the proof mass in the accelerometer; for a closed-loop accelerometer, the accelerometer response refers to the feedback signal acting on the proof mass in the accelerometer to balance it at zero position.

2. The accelerometer according to claim 1, characterized in that The quality factor and the resonance angular frequency of the accelerometer are respectively a combination of a maximum value of the quality factor and a minimum value of the resonance angular frequency when the ratio is less than or equal to a preset value.

3. The accelerometer according to claim 1, characterized in that The quality factor and resonant angular frequency of the accelerometer are respectively a combination of a larger quality factor and a smaller resonant angular frequency, and the combination satisfies that the ratio is less than or equal to a preset value; the larger value is that the absolute value of the difference compared to the maximum value does not exceed the first threshold, and the smaller value is that the absolute value of the difference compared to the minimum value does not exceed the second threshold.

4. The accelerometer according to claim 1 or 2, characterized in that: The resonant angular frequency of the accelerometer is regulated by the structural design of the accelerometer, the quality factor of the accelerometer is regulated by the damping design of the accelerometer, and the damping of the accelerometer is designed to be underdamped.

5. The accelerometer according to claim 1, characterized in that The preset values ​​are: ; Indicates the preset upper limit of mechanical thermal noise, represents the Boltzmann constant, m represents the mass of the accelerometer proof mass, T Indicates the ambient temperature.

6. A vibration rectification error compensation method for an accelerometer according to any one of claims 1 to 5, characterized in that: The following steps are involved: Determining a second-order nonlinear model of the accelerometer; the second-order nonlinear model is used to describe the mapping relationship between the accelerometer output signal and the accelerometer input; Performing a first-order low-pass filtering on the output signal of the accelerometer, and performing vibration rectification error compensation on the output signal after the first-order low-pass filtering based on the second-order nonlinear model to obtain a compensated output signal; Performing secondary low-pass filtering on the compensated output signal, and then outputting the signal after the secondary low-pass filtering as the compensated original acceleration input signal; Among them, the cut-off frequency of the first-level low-pass filter is greater than the resonance angular frequency, and the cut-off frequency of the second-level low-pass filter is less than the resonance angular frequency.

7. The method according to claim 6, characterized in that The cut-off frequency of the first-stage low-pass filter is greater than the resonant angular frequency and is the frequency when the gain drops to a preset gain; the preset gain is less than the gain of the frequency segment of the second-stage low-pass filter; The cutoff frequency of the secondary low-pass filter is less than the resonant angular frequency, which is determined based on the frequency of the vibration acceleration in the application environment and the gain, and takes a value greater than or equal to the upper limit of the vibration acceleration frequency in the application environment and less than or equal to the preset frequency. In the frequency band less than the preset frequency, the gain changes flatly.

8. The method according to claim 6, characterized in that The compensated output signal for: in, K 0 is the zero bias of the accelerometer, K 1 is the scale factor of the accelerometer, K 2 is the second-order nonlinear coefficient of the accelerometer, is the output signal of the accelerometer.

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