A method for evaluating dynamic accuracy of accelerometer

Abstract

This application discloses a method for evaluating the dynamic accuracy of an accelerometer, relating to the field of dynamic accuracy evaluation technology. The method comprises the following steps: Step 1, inputting the relevant dynamic accuracy requirements of the accelerometer system; Step 2, calculating the critical damping coefficient of the accelerometer system under the condition of meeting the effective operating bandwidth; Step 3, adjusting the control parameters of the accelerometer closed-loop system; Step 4, acquiring the step response and half-sine response data of the accelerometer system; Step 5, calculating the dynamic stability index and time-frequency domain correlation index of the accelerometer system under the step response and half-sine response according to formulas; and Step 6, determining whether the accelerometer meets the specified dynamic accuracy requirements based on the relationship curves between the dynamic stability and correlation indexes of the step response and half-sine response of the accelerometer system under a fixed effective operating bandwidth. This application facilitates the evaluation of the dynamic accuracy of accelerometers.

Description

Technical Field

[0001] The present application relates to the technical field of dynamic accuracy assessment, and in particular to a method for assessing the dynamic accuracy of an accelerometer. Background Art

[0002] Accelerometers are widely used in military and civilian fields such as inertial navigation, vibration monitoring, and drilling inclination measurement. However, in the actual measurement process, since most of the measured signals are dynamic signals and with the continuous development of related science and technology, the application occasions of accelerometers have been continuously expanded, the amplitude of the measured signal is getting higher and higher, and the pulse width is getting narrower and narrower, which requires the accelerometer to have good dynamic characteristics.

[0003] One part of the research on the dynamic accuracy evaluation of traditional accelerometers is to evaluate the dynamic performance based on static performance indicators. This "static-versus-dynamic" evaluation method is obviously unscientific; the other part of the research is based on GJB1037A-2004 "Test Method for Single-Axis Pendulum Servo Accelerometer" to obtain the sensitivity function and frequency response function of the accelerometer from both time domain and frequency domain, and calculate the dynamic mathematical model and dynamic characteristic indicators of the accelerometer, including time domain dynamic characteristic indicators (rise time, peak time, overshoot, etc.) and frequency domain dynamic characteristic indicators (bandwidth, resonant frequency, etc.) for evaluation.

[0004] In the process of implementing the above application, the inventors found that there are at least the following problems in this technology: the time domain index is a transient characteristic index, which can only reflect the dynamic performance of the accelerometer to a certain extent, but cannot directly evaluate the dynamic performance of the accelerometer itself; the bandwidth in the traditional frequency domain index only considers the dynamic error influence caused by the amplitude-frequency attenuation due to the increase in frequency, but does not consider the dynamic error influence caused by the amplitude-frequency amplification caused by the resonance of the system; that is, it is impossible to evaluate the dynamic accuracy while ensuring the static accuracy of the accelerometer. Summary of the invention

[0005] In order to facilitate the assessment of the dynamic accuracy of an accelerometer, the present application provides a method for assessing the dynamic accuracy of an accelerometer.

[0006] The present application provides a method for evaluating the dynamic accuracy of an accelerometer using the following technical solution:

[0007] A method for evaluating the dynamic accuracy of an accelerometer comprises the following steps:

[0008] Step 1: Input the requirements for dynamic accuracy of the accelerometer system;

[0009] Step 2: Calculate the critical damping coefficient of the accelerometer system under the condition of effective working bandwidth according to the given index;

[0010] Step 3: Debug the accelerometer closed-loop system control parameters;

[0011] Step 4: Conduct experiments and collect step response and half-sine response data of the accelerometer system;

[0012] Step 5: Calculate the dynamic stability index and time-frequency domain correlation index of the accelerometer system under step response and half-sine response;

[0013] Step 6: Determine whether the accelerometer meets the specified dynamic accuracy index requirements based on the dynamic stability and related index relationship curves of the accelerometer system step response and half-sine response under a fixed effective working bandwidth.

[0014] By adopting the above technical scheme, during the evaluation process, this method can directly determine whether the dynamic accuracy of the accelerometer system meets the requirements through the system response, and can evaluate the accelerometer from the time domain and frequency domain respectively. Compared with the model identification method and the sine sweep frequency determination method of the accelerometer frequency domain characteristics in the traditional accelerometer dynamic accuracy research, the indicator definition in the proposed method is more scientific and reasonable, the experimental steps are simpler, and the demand for equipment is greatly reduced. In addition, the dynamic accuracy can be evaluated while ensuring the static accuracy of the accelerometer.

[0015] Optionally, the dynamic accuracy related indicators in step one include allowable error of amplitude-frequency gain and effective working bandwidth.

[0016] By adopting the above technical solution, the allowable error of amplitude-frequency gain refers to the error allowed by the amplitude-frequency response of the system frequency domain function within the entire frequency band; the maximum error caused by the amplitude-frequency response of the system within a certain frequency band in the frequency domain is not greater than the specified allowable error of amplitude-frequency gain, and this frequency band is the effective working bandwidth; the indicator here is the basic indicator for calculation, and the dynamic accuracy of acceleration is evaluated by recording the allowable error of amplitude-frequency gain and the effective working bandwidth.

[0017] Optionally, in step 2, the critical damping coefficient is calculated by using the allowable amplitude-frequency gain error, the accelerometer dynamic model and the effective working bandwidth definition, and the critical damping coefficient is the coefficient when the resonant peak of the accelerometer amplitude-frequency characteristic curve just meets the allowable amplitude-frequency gain error.

[0018] By adopting the above technical solution, the critical damping coefficient is calculated by defining the allowable error of the amplitude-frequency gain, the accelerometer dynamic model and the effective working bandwidth, which provides a basis for the subsequent calculation of related indicators for evaluating the dynamic accuracy of the accelerometer.

[0019] Optionally, the debugging in step three is to first control the accelerometer closed-loop system to a stable output, and secondly put the accelerometer system in an underdamped state.

[0020] By adopting the above technical solution, the control parameters of the accelerometer closed-loop system are debugged; first, the accelerometer closed-loop system needs to be controlled to a stable output; secondly, according to the curve of the dynamic stability index changing with the damping parameter, in order to ensure the accelerometer response speed and dynamic stability index, the accelerometer system needs to be in an underdamped state, that is, the damping coefficient is in the range of 0 to 1, and needs to be as close to and less than the critical damping as possible.

[0021] Optionally, in step 4, before performing step response and half-sine response experimental tests, parameters are determined in advance, the parameters including step response amplitude, half-sine response period, and half-sine response amplitude.

[0022] By adopting the above technical solution, before conducting step response and half-sine response experimental tests, it is necessary to determine in advance parameters such as the step response amplitude, half-sine response period and amplitude, which directly affect the curve of the dynamic stability index changing with the damping parameter.

[0023] Optionally, a high-precision standard vibration table is used for experimental testing and data acquisition.

[0024] By adopting the above technical solution, the step response and half-sine response data of the accelerometer system can be collected, and a high-precision standard vibration table can be used for experimental testing and data collection. For digital closed-loop accelerometers, digital drive methods can also be implemented through programming to carry out experimental testing and data collection.

[0025] Optionally, step five includes defining correlation indicators related to the time-frequency domain:

[0026]

[0027] In the formula, is the frequency domain correlation index of the accelerometer, σ is the step response overshoot, t p is the step response peak time.

[0028] By adopting the above technical solution, after collecting the step response and half-sine response data of the accelerometer system according to the steps, the dynamic stability index under different response conditions can be calculated according to the formula, and the correlation of the time-frequency domain indexes can be established through the above formula, so as to facilitate the comprehensive analysis of the dynamic accuracy of the accelerometer system from the time-frequency domain.

[0029] Optionally, in step six, under a fixed effective working bandwidth, the time-frequency domain correlation index and the dynamic stability index have a one-to-one correspondence.

[0030] By adopting the above technical solution, the time-frequency domain correlation index and the dynamic stability index have a one-to-one correspondence, which facilitates the subsequent analysis process of the accelerometer dynamic accuracy index.

[0031] Optionally, under the same time-frequency domain correlation index, as the effective working bandwidth increases, the dynamic stability index gradually decreases.

[0032] By adopting the above technical scheme, under the condition of fixed effective working bandwidth, the relationship curves of dynamic stability and correlation index of step response and half-sine response of accelerometer system are satisfied. Under the condition of fixed effective working bandwidth, the time-frequency domain correlation index and dynamic stability index have a one-to-one correspondence. As the effective working bandwidth increases, the dynamic stability index gradually decreases. After calculating the dynamic stability and time-frequency domain correlation index of the accelerometer system under different response conditions, they are compared with the change curve of dynamic stability with time-frequency domain correlation index of the accelerometer system in step response and half-sine response under fixed bandwidth. If the time-frequency domain correlation index of the tested acceleration system and the dynamic stability characteristic point are above the curve, the accelerometer system does not meet the specified dynamic accuracy index; otherwise, the accelerometer system meets the specified dynamic accuracy index.

[0033] In summary, the present application includes at least one of the following beneficial technical effects:

[0034] 1. By adopting the evaluation method in this scheme, the defined time domain index overcomes the defects of transient characteristic index in traditional dynamic accuracy research, and can evaluate the accuracy of accelerometer dynamic measurement process; the defined frequency domain index overcomes the defect of only considering the amplitude-frequency attenuation effect of bandwidth in traditional dynamic accuracy research, and comprehensively considers the overall flatness of amplitude-frequency response;

[0035] 2. This evaluation method defines its performance indicators from the perspectives of time domain and frequency domain respectively, and combines the two through correlation indicators to facilitate comprehensive optimization of time and frequency domain performance indicators;

[0036] 3. The characteristic responses selected by this evaluation method are step response and half-sine response. The step response is considered to be the response of the vibration measurement system under the worst working conditions, and the half-sine response condition is considered to be the response closest to the actual vibration waveform. That is, the evaluation method is more convincing by considering the most extreme and closest to the actual measurement conditions of the accelerometer system respectively.

[0037] 4. This evaluation method uses step and half-sine characteristic responses to directly evaluate the dynamic accuracy of the accelerometer system. It is simpler and more convenient than the traditional method of using a vibration table to perform a sine frequency sweep to obtain the frequency characteristics of the accelerometer system, and has less equipment requirements.

[0038] 5. This evaluation method has been successfully applied to digital quartz flexible accelerometers and is suitable for dynamic accuracy evaluation of different types of accelerometers. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1Flowchart of the accelerometer dynamic accuracy assessment method.

[0040] Figure 2 Schematic diagram of the frequency domain for the defined effective bandwidth.

[0041] Figure 3 The figure is a curve diagram showing the dynamic stability index and dynamic integral error index of the accelerometer system changing with damping under unit step response conditions with a fixed effective bandwidth.

[0042] Figure 4 The figure is a curve diagram showing the dynamic stability index and dynamic integral error index of the accelerometer system under unit half-sine response conditions with the change of damping under the condition of fixed effective bandwidth.

[0043] Figure 5 This is a relationship diagram between the dynamic stability index and related index of the unit step response and half-sine response of the accelerometer system under different effective working bandwidths.

[0044] Figure 6 The time domain diagram is used to collect the unit step response and unit half-sine response of the accelerometer system and calculate the corresponding correlation index and dynamic stability index.

[0045] Figure 7 The following is a curve showing the change of the dynamic stability index of the accelerometer system according to the unit step response and the unit half-sine response under a fixed effective working bandwidth along with the associated index, as well as a comparison chart of the dynamic stability index and the associated index obtained from actual tests. DETAILED DESCRIPTION

[0046] The following is combined with Figure 1-7 This application is described in further detail.

[0047] The present application embodiment discloses a method for evaluating the dynamic accuracy of an accelerometer. Figure 1 ,The accelerometer dynamic accuracy assessment method includes the following steps:

[0048] Step 1: Input the requirements for dynamic accuracy related indicators of the accelerometer system, including: allowable error of amplitude-frequency gain and corresponding effective working bandwidth;

[0049] Step 2, according to the given amplitude-frequency gain allowable error index, the critical damping coefficient of the accelerometer system under the condition of meeting the effective working bandwidth is calculated;

[0050] Step 3, debugging the accelerometer closed-loop system control parameters;

[0051] Step 4, collecting the step response and half-sine response data of the accelerometer system;

[0052] Step 5, calculating the dynamic stability index and time-frequency domain correlation index of the accelerometer system under step response and half-sine response according to the formula;

[0053] Step six, judging whether the accelerometer meets the specified dynamic accuracy index requirements based on the dynamic stability and related index relationship curves of the accelerometer system step response and half-sine response under a fixed effective working bandwidth.

[0054] Reference Figure 2 In step 1, before the accelerometer is evaluated for dynamic accuracy, the dynamic performance index requirements of the accelerometer system need to be input, including: allowable error of amplitude-frequency gain and effective working bandwidth. The corresponding index meanings are as follows: Figure 2 As shown in the figure, the allowable error of amplitude-frequency gain refers to the error allowed by the amplitude-frequency response of the system frequency domain function within the entire frequency band, corresponding to Figure 2 Δ; the maximum error of the amplitude-frequency response of the system in a certain frequency band in the frequency domain is not greater than the specified amplitude-frequency gain allowable error. This frequency band is the effective working bandwidth, corresponding to Figure 2 Medium e1 、w e2 and w e3 .

[0055] In step 2, based on the specified amplitude-frequency gain allowable error, the accelerometer dynamic model, and the definition of the effective working bandwidth, the critical damping coefficient when the resonance peak of the accelerometer amplitude-frequency characteristic curve just meets the amplitude-frequency gain allowable error can be calculated, providing a basis for the subsequent calculation of related indicators used for dynamic accuracy assessment of the accelerometer:

[0056] The accelerometer system adopts the standard second-order system model, and its amplitude-frequency response function is

[0057]

[0058] Where H(w) is the amplitude-frequency response function of the accelerometer system, K is the system gain coefficient, and w n is the natural frequency parameter of the system, ξ is the damping parameter of the system, and w is the input frequency parameter.

[0059] when When H(w) reaches the maximum value, if the amplitude-frequency gain allowable error Δ is satisfied at this time, then

[0060]

[0061] The critical damping coefficient is further calculated as:

[0062]

[0063] Reference Figure 3 and Figure 4In step 3, the control parameters of the accelerometer closed-loop system are debugged. First, the accelerometer closed-loop system needs to be controlled to a stable output. Secondly, based on the critical damping formula, the accelerometer system amplitude-frequency response function and the definition of effective working bandwidth, the effective working bandwidth w can be calculated. e The formula is:

[0064]

[0065] Based on the use of effective working bandwidth to describe the frequency domain dynamic performance of the accelerometer system, the time domain dynamic performance index, namely, dynamic stability ε d :

[0066]

[0067] ε(t)=(x(t)-y(t)) / x(t)

[0068] In the formula, ε d is the defined dynamic stability index, T is the response test time, ε(t) is the relative dynamic error of the system response, x(t) is the system response input signal, and y(t) is the system response output signal.

[0069] At the same time, in order to analyze the impact of the dynamic accuracy of the accelerometer system on the accuracy of application systems such as navigation and attitude control, the dynamic integral error is defined for comprehensive evaluation. The dynamic integral error expression is:

[0070]

[0071] According to the effective working bandwidth formula, the dynamic stability index and dynamic integral error index changes of the accelerometer system under step response and half-sine response conditions are analyzed as follows: Figure 3 , Figure 4 shown.

[0072] Therefore, according to the curves of dynamic stability index and dynamic integral error index changing with damping parameter, in order to ensure the response speed and dynamic stability index of the accelerometer, the accelerometer system needs to be in an underdamped state, that is, the damping coefficient is in the range of 0 to 1, and needs to be as close to and less than the critical damping ξ as possible. c .

[0073] In step 4, the step response and half-sine response data of the accelerometer system are collected. A high-precision standard vibration table can be used for experimental testing and data collection. For digital closed-loop accelerometers, digital drive methods can also be programmed for experimental testing and data collection. In addition, before conducting step response and half-sine response experimental tests, it is necessary to determine in advance the parameters such as the step response amplitude, half-sine response period and amplitude, which directly affect the curve of the dynamic stability index changing with the damping parameter. It should also be noted that when the response input amplitude is small, the dynamic stability index is easily affected by noise; when the response input amplitude is large, the dynamic stability index is easily affected by the nonlinearity of the system, so it is necessary to comprehensively consider the selected response amplitude.

[0074] In step 5, after collecting the step response and half-sine response data of the accelerometer system according to the steps, the dynamic stability index under different response conditions can be calculated according to the formula. In traditional accelerometer dynamic research, time domain indicators and frequency domain indicators are often analyzed separately, and the correlation between time and frequency domain indicators is not established. Therefore, in order to comprehensively analyze the dynamic accuracy of the accelerometer system from the time and frequency domain, a correlation index related to the time and frequency domain is defined:

[0075]

[0076] In the formula, is the frequency domain correlation index of the accelerometer, σ is the step response overshoot, t p is the step response peak time.

[0077] In step six, after the dynamic stability and time-frequency domain correlation indexes under different response conditions are obtained according to the steps, the accelerometer system step response, half-sine response dynamic stability and correlation index relationship curve under fixed effective working bandwidth is used to determine whether the accelerometer meets the specified dynamic accuracy index requirements; Figure 5 The figure shows the relationship curve between the dynamic stability index and the correlation index of the unit step response and half-sine response of the accelerometer system under different effective working bandwidths. The relationship curve meets two characteristics: the first characteristic is that under the condition of fixed effective working bandwidth, the time-frequency domain correlation index and the dynamic stability index have a one-to-one correspondence; the second characteristic is that under the same time-frequency domain correlation index, as the effective working bandwidth increases, the dynamic stability index gradually decreases.

[0078] Based on these two characteristics, after calculating the dynamic stability and time-frequency domain correlation index of the accelerometer system under different response conditions, compare it with the dynamic stability curve of the accelerometer system under step response and half-sine response with the time-frequency domain correlation index under fixed bandwidth. If the time-frequency domain correlation index of the tested accelerometer system and the characteristic point of dynamic stability are above the curve, the accelerometer system does not meet the specified dynamic accuracy index; otherwise, the accelerometer system meets the specified dynamic accuracy index.

[0079] Reference Figure 5 , Figure 6 and Figure 7 In this embodiment, a digital quartz flexible accelerometer system is used as an example, and the system dynamic accuracy evaluation experiment adopts a digital drive experimental test method.

[0080] Step 1: Input the requirements for the dynamic accuracy of the accelerometer system: the amplitude-frequency gain allowable error Δ = 10%, the effective working bandwidth w e =200Hz;

[0081] Step 2: Calculate the critical damping coefficient ξ of the accelerometer system under the condition of effective working bandwidth according to the given amplitude-frequency gain allowable error Δ=10% c =0.5401;

[0082] Step 3: Debug the accelerometer closed-loop system control parameters. The accelerometer system PID controller parameters are: k p =0.076,k i =0.6,k d =0.00003;

[0083] Step 4: Collect the step response and half-sine response data of the accelerometer system. The step input amplitude is 1g, the half-sine input amplitude is 1g, and the period is 0.2s. The test response time domain diagram is as follows: Figure 6 As shown;

[0084] Step 5: Calculate the dynamic stability index and time-frequency domain correlation index of the accelerometer system under step response and half-sine response according to the formula. The index calculation results are as follows: Figure 6 As shown;

[0085] Step 6: Based on the dynamic stability and related index relationship curves of the accelerometer system step response and half-sine response under a fixed effective working bandwidth, determine whether the accelerometer meets the specified dynamic accuracy index requirements. The accelerometer dynamic accuracy assessment diagram is shown in the figure below: Figure 7 As shown;

[0086] Finally, based on Figure 7 The accelerometer dynamic accuracy evaluation diagram shown and Figure 5The characteristics of the relationship between the accelerometer stability index and the related index are shown in the figure. The step response, half-sine response related index and dynamic stability index of the tested accelerometer system are above the related curve. Therefore, the dynamic performance of the accelerometer system does not meet the effective working bandwidth requirement of 200Hz. Figure 1 As shown in the flowchart, when the dynamic accuracy of the accelerometer system does not meet the requirements, return to step 3 to re-adjust the accelerometer system control parameters. The goal is to optimize the dynamic stability index as much as possible while meeting the effective working bandwidth.

[0087] The implementation principle of a method for evaluating the dynamic accuracy of an accelerometer in an embodiment of the present application is as follows: the relationship curve between the dynamic stability index and the correlation index of the unit step response and the half-sine response of the accelerometer system under different effective working bandwidths is obtained through calculations in steps one to six; the relationship curve satisfies two characteristics: the first characteristic is that under a fixed effective working bandwidth, the time-frequency domain correlation index and the dynamic stability index have a one-to-one correspondence; the second characteristic is that under the same time-frequency domain correlation index, as the effective working bandwidth increases, the dynamic stability index gradually decreases; based on these two characteristics, after calculating the dynamic stability and time-frequency domain correlation index of the accelerometer system under different response conditions, it is compared with the dynamic stability curve of the accelerometer system under a fixed bandwidth when it is in step response and half-sine response. If the time-frequency domain correlation index of the tested acceleration system and the characteristic point of the dynamic stability are above the curve, the accelerometer system does not meet the specified dynamic accuracy index; otherwise, the accelerometer system meets the specified dynamic accuracy index.

[0088] The above are all preferred embodiments of the present application, and the protection scope of the present application is not limited thereto. Therefore, any equivalent changes made according to the structure, shape, and principle of the present application should be included in the protection scope of the present application.

Claims

1. A method for evaluating the dynamic accuracy of an accelerometer, characterized in that: The following steps are involved: Step 1: Input the requirements for dynamic accuracy of the accelerometer system; Step 2: Calculate the critical damping coefficient of the accelerometer system under the condition of effective working bandwidth according to the given index; Step 3: Debug the accelerometer closed-loop system control parameters; Step 4: Conduct experiments and collect step response and half-sine response data of the accelerometer system; Step 5: Calculate the dynamic stability index and time-frequency domain correlation index of the accelerometer system under step response and half-sine response; Step 6: Determine whether the accelerometer meets the specified dynamic accuracy index requirements based on the dynamic stability and related index relationship curves of the accelerometer system step response and half-sine response under a fixed effective working bandwidth.

2. The method for evaluating the dynamic accuracy of an accelerometer according to claim 1, characterized in that: The dynamic accuracy related indicators in step one include the allowable error of amplitude-frequency gain and the effective working bandwidth.

3. The method for evaluating the dynamic accuracy of an accelerometer according to claim 1, characterized in that: In step 2, the critical damping coefficient is calculated by the allowable error of the amplitude-frequency gain, the dynamic model of the accelerometer and the definition of the effective working bandwidth, and the critical damping coefficient is the coefficient when the resonance peak of the amplitude-frequency characteristic curve of the accelerometer just meets the allowable error of the amplitude-frequency gain.

4. The method for evaluating the dynamic accuracy of an accelerometer according to claim 1, characterized in that: The debugging in step three is to first control the accelerometer closed-loop system to a stable output, and secondly to put the accelerometer system in an underdamped state.

5. The method for evaluating the dynamic accuracy of an accelerometer according to claim 1, characterized in that: In step 4, before performing step response and half-sine response experimental tests, parameters are determined in advance, including step response amplitude, half-sine response period, and half-sine response amplitude.

6. The method for evaluating the dynamic accuracy of an accelerometer according to claim 5, characterized in that: A high-precision standard vibration table is used for test and data collection.

7. The method for evaluating the dynamic accuracy of an accelerometer according to claim 1, characterized in that: Step five involves defining the correlation metrics in the time-frequency domain: In the formula, is the frequency domain correlation index of the accelerometer, σ is the step response overshoot, t p is the step response peak time.

8. The method for evaluating the dynamic accuracy of an accelerometer according to claim 1, characterized in that: In step six, under the condition of fixed effective working bandwidth, the time-frequency domain correlation index and the dynamic stability index have a one-to-one correspondence.

9. The method for evaluating the dynamic accuracy of an accelerometer according to claim 8, characterized in that: Under the same time-frequency domain correlation index, as the effective working bandwidth increases, the dynamic stability index gradually decreases.

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