A method and system for self-compensation of frequency drift in a MEMS device
By calculating the temperature disturbance coefficient and hysteresis coefficient, and combining them with changes in non-temperature parameters, an adaptive dynamic compensation method was adopted to solve the problem of frequency drift of MEMS devices in dynamic environments, and to achieve high-precision and stable frequency compensation.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- SUZHOU XINSHIJI MICROELECTRONICS CO LTD
- Filing Date
- 2026-04-24
- Publication Date
- 2026-07-24
AI Technical Summary
The resonant frequency of MEMS devices is easily affected by changes in ambient temperature, leading to frequency drift. Existing compensation methods based on static models have large compensation errors under rapid temperature changes or thermal shock scenarios, affecting the stability and accuracy of devices in dynamic environments.
By calculating the temperature disturbance coefficient and hysteresis coefficient, and considering the changes in non-temperature parameters, an adaptive dynamic compensation method is adopted, and a PI controller is used for frequency correction to eliminate frequency overshoot and hysteresis, thereby improving frequency stability.
Significantly improves the accuracy and stability of frequency drift compensation for MEMS devices under dynamic thermal conditions, reduces frequency overshoot and loopback, and ensures frequency stability.
Smart Images
Figure CN122457012A_ABST
Abstract
Description
Technical Field
[0001] This application relates to the field of communication network measurement instrument technology, specifically to a method and system for self-compensation of frequency drift in MEMS devices. Background Technology
[0002] With the rapid development of fields such as the Internet of Things, autonomous driving, aerospace, and high-precision navigation, microelectromechanical systems (MEMS) devices, as core sensors for perceiving the physical world, directly determine the reliability and accuracy of the entire system. Among these, the frequency stability of the MEMS resonator is a key parameter for evaluating its performance. However, due to the physical properties of silicon, the resonant frequency of MEMS devices is highly susceptible to changes in ambient temperature, resulting in significant frequency drift. This drift can lead to sensor scaling factor inaccuracies and zero-bias divergence. Therefore, achieving high-precision, high-real-time frequency drift self-compensation has become a key technical challenge in overcoming the bottleneck of MEMS device applications in complex environments.
[0003] The current mainstream approach is a compensation method based on a static "frequency-temperature" model. However, this traditional method has significant limitations and sources of error in practical applications. Temperature compensation inherently suffers from a "thermal hysteresis" effect. Due to the differences in heat capacity and thermal conductivity between MEMS microstructures, substrates, and packaging materials, there is a spatiotemporal difference between the substrate temperature measured by the on-chip temperature sensor and the actual instantaneous temperature of the sensitive microstructure when the ambient temperature changes rapidly. This hysteresis in heat transfer means that the compensation amount based on the current temperature measurement cannot accurately match the true state of the microstructure. Especially when dealing with drastic temperature changes or thermal shock scenarios, the compensation error will be significantly amplified, severely restricting the long-term stability and measurement accuracy of the device in dynamic and highly mobile environments. Summary of the Invention
[0004] To address the technical problem of low measurement accuracy, this application provides a self-compensation method and system for frequency drift in MEMS devices. The specific technical solution adopted is as follows: Firstly, this application proposes a self-compensation method for frequency drift in MEMS devices, which includes the following steps: Monitoring parameters of MEMS devices are collected through various sensors; For each moment, the correlation between temperature and frequency in the monitoring parameters from previous moments is calculated, and the temperature disturbance coefficient is calculated by combining the temperature change rate from previous moments, the time offset of temperature and frequency, and the difference between the predicted frequency obtained through temperature and the actual frequency. All parameters in the monitoring parameters other than temperature and frequency are designated as non-temperature parameters. For each time moment, the delay factor is obtained based on the data of the non-temperature parameters at all previous time moments and the time offset of the temperature. Based on the data of the non-temperature parameters at each time moment, the correlation between each pair of non-temperature parameters is calculated to form a correlation matrix, and the average of the absolute values of all off-diagonal elements of the matrix is used as the coupling factor. The lag coefficient is determined based on the coupling factor at each time moment, the minimum ratio of the temperature disturbance coefficient to the temperature disturbance coefficient at a preset number of time moments before it, the fluctuation of the non-temperature parameters at previous time moments, and the delay factor. The thermal hysteresis compensation factor is calculated using the temperature disturbance coefficient and the hysteresis degree coefficient. The dynamic compensation amount is determined by using the thermal hysteresis compensation factor at each moment, the frequency error, and the frequency errors at all moments before that moment through proportional gain and integral gain. The dynamic compensation amount is then used to correct the static frequency after compensation by the "frequency-temperature" static model to obtain the corrected frequency. The compensation is then completed.
[0005] In the above scheme, this application calculates a temperature disturbance coefficient based on the temporal changes in temperature and frequency. This coefficient, combined with the influence between temperature and frequency, helps improve the identification of frequency drift in feedforward compensation and increases the compensation response speed. Then, it calculates a hysteresis coefficient by combining changes in non-temperature characteristics. This coefficient, by introducing fluctuations in non-temperature parameters, improves the accuracy of identifying and quantifying the effects of frequency drift and temperature hysteresis, thus helping to improve the quality of subsequent frequency compensation. Finally, dynamic compensation for the frequency drift of MEMS devices is achieved through thermal hysteresis compensation factors and PI control. By adjusting the compensation strategy to a combination of static model compensation and adaptive dynamic correction, this method significantly eliminates frequency overshoot, loop hysteresis, and non-monotonic phenomena during rapid temperature changes. This allows MEMS devices to maintain near-steady-state frequency stability under dynamic thermal environments, improving the accuracy and quality of frequency drift compensation for MEMS devices.
[0006] In one embodiment, the monitoring parameters include temperature, frequency, amplitude, voltage, phase, and quality factor.
[0007] In one embodiment, the temperature disturbance coefficient is positively correlated with the temperature change rate, the frequency residual factor, and the lag time factor; and negatively correlated with the correlation factor.
[0008] In one embodiment, the normalized value of the time offset corresponding to the maximum cross-correlation function value between temperature and frequency at all times prior to each time step of the lag time factor.
[0009] In one embodiment, the method for obtaining the frequency residual factor is as follows: The predicted frequency at a given moment is obtained by substituting the temperature at a given moment into the static temperature model. The difference between the predicted frequency and the actual frequency at a given moment is the frequency residual at that moment. For each moment, its moving window is obtained, and the normalized value of the root mean square value of the frequency residuals at that moment and all moments within the moving window is calculated and recorded as the frequency residual factor.
[0010] In one embodiment, the hysteresis coefficient is positively correlated with the minimum ratio of the temperature disturbance coefficient at each moment and the previous preset number of moments, the delay factor, and the abnormal fluctuation factor, and negatively correlated with the coupling factor.
[0011] In one embodiment, the lag factor is the mean of the lag time factors of all data before each time step for the non-temperature parameter and the temperature; the abnormal fluctuation factor is the mean of the normalized values of the standard deviations of the first differences of all data before each time step for the non-temperature parameter.
[0012] In one embodiment, the method for calculating the thermal hysteresis compensation factor using the temperature disturbance coefficient and the hysteresis degree coefficient is as follows: , This represents the temperature disturbance coefficient at time t. This represents the lag coefficient at time t. The activation threshold representing the temperature perturbation coefficient. This represents the thermal hysteresis compensation factor at time t. express Kernel function.
[0013] In one embodiment, the method for determining the dynamic compensation amount by using the thermal hysteresis compensation factor and frequency error at each moment, as well as the frequency errors at all moments prior to that moment, through proportional gain and integral gain, is as follows: , This represents the thermal hysteresis compensation factor at time t. This represents the frequency error at time t. This represents the frequency error at time j. This represents the time interval between two adjacent moments. This represents the initial proportional gain. Indicates the initial integral gain. This represents the dynamic compensation amount at time t. The frequency error is calculated as the difference between the frequency value obtained from the "frequency-temperature" static model and the actual frequency value.
[0014] On the other hand, embodiments of this application also provide a MEMS device frequency drift self-compensation system, including a memory, a processor, and a computer program stored in the memory and running on the processor. When the processor executes the computer program, it implements the steps of any of the above-described MEMS device frequency drift self-compensation methods.
[0015] The beneficial effects of this application are as follows: This application calculates a temperature disturbance coefficient based on the temporal changes in temperature and frequency. This coefficient, combined with the influence between temperature and frequency, helps improve the identification of frequency drift in feedforward compensation and increases the compensation response speed. Then, it calculates a hysteresis coefficient by incorporating changes in non-temperature characteristics. This coefficient, by introducing fluctuations in non-temperature parameters, improves the accuracy of identifying and quantifying the effects of frequency drift and temperature hysteresis, thus contributing to improved frequency compensation quality. Finally, dynamic compensation for frequency drift in MEMS devices is achieved through a thermal hysteresis compensation factor and PI control. This method, by adjusting the compensation strategy to a combination of static model compensation and adaptive dynamic correction, significantly eliminates frequency overshoot, hysteresis, and non-monotonicity during rapid temperature changes. This allows MEMS devices to maintain near-steady-state frequency stability even under dynamic thermal environments, improving the accuracy and quality of frequency drift compensation for MEMS devices. Attached Figure Description
[0016] To more clearly illustrate the technical solutions and advantages in the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.
[0017] Figure 1 This is a flowchart of a frequency drift self-compensation method for MEMS devices provided in one embodiment of this application. Detailed Implementation
[0018] To further illustrate the technical means and effects adopted by this application to achieve the intended inventive purpose, the following, in conjunction with the accompanying drawings and preferred embodiments, details the specific implementation, structure, features, and effects of a MEMS device frequency drift self-compensation method and system proposed in this application. In the following description, different "one embodiment" or "another embodiment" do not necessarily refer to the same embodiment. Furthermore, specific features, structures, or characteristics in one or more embodiments can be combined in any suitable form.
[0019] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application pertains.
[0020] An embodiment of a self-compensation method and system for frequency drift in MEMS devices: The following description, in conjunction with the accompanying drawings, details a specific scheme for a self-compensation method for frequency drift in MEMS devices provided in this application.
[0021] Please see Figure 1 The diagram illustrates a flowchart of a frequency drift self-compensation method for a MEMS device according to an embodiment of this application. The method includes the following steps: Step S001: Collect monitoring parameters of MEMS devices.
[0022] The substrate temperature is acquired in real time by an on-chip temperature sensor integrated within the MEMS resonator chip. The temperature signal is converted by an on-chip ADC and output as temperature data. Simultaneously, the resonant frequency is acquired by a frequency counting module in the oscillation control loop or a digital counting unit within the phase-locked loop (PLL). The original frequency counting sampling rate is 1kHz, and after averaging via a sliding time window, 100Hz effective frequency data is output. The resonant amplitude data is acquired by sampling the amplified resonant signal envelope through the ADC. The AGC control voltage signal is acquired through the control port of the automatic gain control (AGC) circuit. Phase data is obtained through the IQ demodulation module within the PLL. The quality factor Q is indirectly calculated using the frequency or amplitude of the driving signal. The calculation of the quality factor is a well-known technique and will not be elaborated further; the frequency response method is used in this embodiment. The sampling rate for all data types is 100Hz. Then, the acquired data types are normalized using a maximum-minimum normalization method, where the maximum value equals the minimum value, and 0 is output. The acquired temperature, frequency, amplitude, voltage, phase, and quality factor are collectively referred to as monitoring parameters.
[0023] At this point, data for all monitoring parameters has been obtained.
[0024] Step S002: Calculate the temperature disturbance coefficient by the correlation between temperature and frequency, the rate of temperature change, the time offset between temperature and frequency, and the actual frequency difference.
[0025] MEMS devices are used to generate stable clock signals, which is crucial for ensuring the stability and reliability of electronic systems. The frequency of a MEMS device is a key parameter in clock signal generation, and its accuracy directly affects the device's performance. The silicon material used in MEMS devices is highly susceptible to ambient temperature, causing frequency shifts. Current technologies often utilize the correlation between frequency and temperature for temperature compensation to stabilize the operating temperature of MEMS devices. However, existing temperature compensation methods often use static models, neglecting the "thermal hysteresis" problem under varying temperature conditions. This results in errors in the obtained temperature compensation and fails to guarantee the frequency stability of the MEMS device. Therefore, a more accurate temperature compensation method that considers the "thermal hysteresis" problem is needed to further improve the frequency and quality of MEMS devices.
[0026] When the system is in a thermally stable state, the temperature changes slowly and smoothly, and the frequency change keeps pace with the temperature change, exhibiting a stable one-to-one correspondence between the two. The frequency curve and the temperature curve basically coincide on the time axis, with no obvious delay or abnormal deviation. At the same time, the difference between the frequency value predicted based on the static temperature model and the actual frequency is small, and the residual change is stable.
[0027] When the external environment experiences rapid temperature changes or sudden changes in heating power, the thermal equilibrium is disrupted. Essentially, the delay in heat transfer causes the temperature field to split spatially (forming a gradient) and become disjointed temporally (the measured temperature leads the actual temperature of the microstructure). This results in a path dependence between frequency and temperature, forming a dynamic hysteresis loop. First, the temperature curve shows a significantly increased slope, and the rate of temperature change accelerates considerably. At this point, the temperature rises or falls rapidly within a short period, creating thermal disturbances. Second, as the rate of temperature change increases, heat conduction within the structure, limited by thermal capacity and resistance, cannot immediately achieve energy balance, leading to a deviation between the actual and measured temperatures. During this stage, the frequency response to temperature changes begins to exhibit asynchrony, manifesting as frequency changes lagging behind temperature changes, or changes in magnitude inconsistent with the theoretical model. Simultaneously, the frequency prediction residual is significantly amplified, and the correlation between temperature and frequency decreases. The more drastic the temperature change, the more pronounced these asynchrony characteristics become, and the greater the fluctuation in the frequency residual.
[0028] MEMS devices are affected by the operating environment temperature, resulting in a "thermal hysteresis" problem. First, significant fluctuations in the operating environment temperature exacerbate the "thermal hysteresis" problem. In existing technologies, the growth rate can be used to measure the degree of data fluctuation. This solution also measures the fluctuation of the operating environment temperature by calculating the temperature growth rate.
[0029] Secondly, when the operating environment temperature fluctuates significantly, the thermal capacity and thermal resistance of the MEMS device limit the device itself from immediately changing the temperature, resulting in a lag between the measured temperature change and the actual frequency change. In the prior art, the lag between the two types of data can be measured by cross-correlation analysis. This application also obtains the lag between temperature and frequency through cross-correlation analysis. At the same time, by utilizing the deviation between the predicted value and the actual value of the static model, the accuracy of measuring the "thermal lag" problem can be further enhanced.
[0030] Finally, the more severe the "thermal hysteresis" problem, the weaker the correlation between temperature and frequency changes. Existing technologies can measure the correlation through correlation coefficients, and this application also uses the Pearson correlation coefficient to measure the change in the correlation between temperature and frequency.
[0031] Specifically, for each time moment, all temperatures prior to that time moment are recorded as a temperature sequence, and all frequencies are recorded as a frequency sequence. First, the rate of temperature change is obtained, and the average of the absolute values of the differences between the temperatures of all adjacent time moments in the temperature sequence is taken as the rate of temperature change. Then, the normalized value of the time offset corresponding to the maximum cross-correlation function value between the temperature sequence and the frequency sequence is calculated and recorded as the lag time factor. The normalization algorithm adopts the maximum-minimum value normalization algorithm, and its mapping range is 0-1.
[0032] The predicted frequency at a given moment is obtained by substituting the temperature into the static temperature model. The difference between the predicted frequency and the actual frequency at a given moment is the frequency residual at that moment. For each moment, a moving window is obtained, and the normalized value of the root mean square value of the frequency residuals at that moment and all moments within the moving window is calculated and recorded as the frequency residual factor. In this embodiment, the length of the moving window is 1 second.
[0033] For temperature and frequency series, the Pearson correlation coefficient is calculated after trending the series and used as the correlation factor. In this embodiment, the trending algorithm is the STL time series algorithm. As a well-known technique, the STL time series algorithm will not be described in detail here.
[0034] Therefore, the temperature disturbance coefficient at each moment is determined based on the temperature change rate, frequency residual factor, lag time factor, and correlation factor at each moment.
[0035] The temperature disturbance coefficient is positively correlated with the temperature change rate, frequency residual factor, and lag time factor; and negatively correlated with the correlation factor.
[0036] It should be noted that positive correlation means that when one variable increases, the other variable also increases, and the two variables change in the same direction. When one variable changes from large to small or from small to large, the other variable also changes from large to small or from small to large. The specific relationship is determined by the actual application, and this application does not impose any special restrictions.
[0037] It should be noted that negative correlation means that when one variable increases, the other variable decreases accordingly, and the two variables change in opposite directions. When one variable changes from large to small or from small to large, the other variable also changes from small to large or from large to small. The specific relationship is determined by practical application, and this application does not impose any special restrictions.
[0038] Preferably, the expression for the temperature disturbance coefficient is: , This represents the rate of temperature change at time t. This represents the lag time factor at time t. Represents the frequency residual factor at time t. This represents the correlation factor at time t. Let represent the temperature perturbation coefficient at time t, and norm represent the linear normalization function. This represents the parameter tuning factor, which is used to prevent the denominator from being 0. In this embodiment, it is set to 1.
[0039] At this point, the temperature perturbation coefficient at each moment has been obtained.
[0040] Step S003: Calculate the coupling factor by constructing a correlation matrix from the correlation between the remaining parameters and temperature, and calculate the lag coefficient by combining the time offset between the remaining parameters and temperature, the temperature disturbance coefficient, and the temperature fluctuation.
[0041] The temperature disturbance coefficient mentioned above only measures the temperature lag from the perspective of the correlation between temperature and frequency. However, since different temperature lags have different degrees of frequency disturbance, it is impossible to accurately quantify the degree of temperature lag using only temperature fluctuations. Therefore, it is necessary to further combine the changes of other non-temperature characteristics to quantify and predict the degree of temperature lag.
[0042] Under thermally stable conditions, parameters such as quality factor, amplitude, and phase exhibit smooth and predictable trends with temperature changes, their direction of change being consistent with temperature changes, and the coupling relationship between parameters is stable, without significant delays or abnormal fluctuations. This indicates that heat conduction within the structure is complete, and the actual thermal state is basically consistent with the measured temperature value. When thermal hysteresis begins to appear, due to the limitations of the internal heat capacity and thermal resistance of the structure, the actual temperature has not yet changed synchronously. Initially, this manifests as a slight delay in the change of the quality factor relative to the temperature change, a slower amplitude establishment process, continuous fine-tuning of the voltage signal, and a small shift in the phase response. The synchronicity between the parameters and the temperature decreases, but the overall trend remains consistent. As the degree of hysteresis further increases, this asynchrony gradually amplifies: the change of the quality factor lags significantly or even exhibits abnormal amplitude, the amplitude shows brief fluctuations or overshoot, the voltage signal frequently adjusts or experiences abrupt changes, the phase shift increases, and the frequency curve may show brief non-monotonic changes or local pullback phenomena, indicating that the actual stiffness and damping state of the structure has significantly deviated from the theoretical state corresponding to the temperature measurement. The more severe the hysteresis, the more obvious the disruption of the coupling relationship between various non-temperature parameters, the more violent the fluctuation of the control signal, and the more irregular the curve shape.
[0043] Under the influence of thermal hysteresis, the internal temperature of the structure cannot be synchronized with the measured temperature value simultaneously, resulting in a hysteresis between the changes of various non-temperature features and temperature features. Existing technologies can measure the hysteresis between different data through cross-correlation analysis. This application also uses cross-correlation analysis to measure the hysteresis between various non-temperature features and temperature features. Secondly, as thermal hysteresis increases, significant abnormal fluctuations will occur in various non-temperature features, and the fluctuation trends of the data will be inconsistent. Existing technologies can measure the dispersion of data distribution through standard deviation. This application also uses standard deviation to measure the volatility of various non-temperature feature changes. Finally, in a thermally stable state, since all parameters are driven by the same thermodynamic state, their changes are synchronous. However, as thermal hysteresis increases, the speed and manner in which each parameter responds to the real temperature are different, causing their changes to become asynchronous and the coupling degree to decrease. Existing technologies can measure the correlation between different data through correlation coefficients. This application also uses the Pearson correlation coefficient to measure the correlation between various non-temperature parameters, thereby realizing the measurement of the coupling relationship between different non-temperature parameters.
[0044] Since the relationship between temperature and frequency has been analyzed in the previous step, amplitude, voltage, phase, and quality factor are treated as non-temperature parameters. For each time moment, the data of each non-temperature parameter before that time moment are obtained to form the corresponding sequence. For each non-temperature sequence, the lag time factor between it and the temperature sequence is calculated, and the mean of the lag time factors between all non-temperature sequences and the temperature sequence is calculated as the delay factor. The mean of the normalized values of the standard deviations of the first differences of all non-temperature sequences is used as the abnormal fluctuation factor. The normalization algorithm is the maximum-minimum normalization algorithm.
[0045] Calculate the Pearson correlation coefficients between each pair of the four non-temperature series to form a... The correlation coefficient matrix is used, and the average of the absolute values of all off-diagonal elements is calculated as the coupling factor. For each time step, a pre-defined adjacent time window is obtained before it.
[0046] The lag coefficient for each time step is determined based on the delay factor, abnormal fluctuation factor, coupling factor, and the minimum ratio of the temperature disturbance coefficient of each time step to the time step within the preceding time window.
[0047] The lag coefficient is positively correlated with the minimum ratio of the temperature disturbance coefficient at each time point and the time point in the preceding time window, the delay factor, and the abnormal fluctuation factor, and negatively correlated with the coupling factor.
[0048] Preferably, in this embodiment, the expression for the lag coefficient is: , This represents the temperature disturbance coefficient at time t. This represents the maximum temperature disturbance coefficient across all times within the time window up to time t. This represents the delay factor at time t. This represents the abnormal fluctuation factor at time t. This represents the coupling factor at time t. Indicates the parameter tuning factor. This represents the lag coefficient at time t.
[0049] Thus, the lag coefficient at time t is obtained.
[0050] Step S004: Based on the thermal hysteresis compensation factor, a proportional-integral controller is used to determine the dynamic compensation amount, and thereby complete the frequency correction compensation.
[0051] In the operation of MEMS devices, timely temperature compensation is necessary to reduce frequency drift caused by temperature effects. Current technologies often employ static models to determine existing frequency errors and then calculate specific temperature compensation amounts based on these errors. This is achieved through heating or cooling to adjust the temperature and ensure the stability of the MEMS operating environment. However, this hardware-level temperature compensation cannot avoid thermal hysteresis caused by factors such as the MEMS device's structure or materials, leading to unavoidable errors. The calculated temperature disturbance coefficient and hysteresis coefficient, through analysis of the variation characteristics of various parameters during MEMS device operation, provide a quantitative analysis of thermal hysteresis. Therefore, further software-based frequency compensation can be implemented to ensure the accuracy of the final frequency data.
[0052] To achieve accurate compensation, a dynamic and adaptive frequency compensation value must first be determined based on the temperature disturbance coefficient and the hysteresis coefficient, and this value is denoted as the thermal hysteresis compensation factor.
[0053] The expression for the thermal hysteresis compensation factor is: , This represents the temperature disturbance coefficient at time t. This represents the lag coefficient at time t. The activation threshold representing the temperature perturbation coefficient. This represents the thermal hysteresis compensation factor at time t. express The kernel function is used to achieve a smooth transition, ensuring that the system only performs significant dynamic compensation when the external thermal disturbance is large enough, thus reducing unnecessary large-scale compensation adjustments in the thermally stable state. In this embodiment, the activation threshold is the upper limit of three times the standard deviation of the mean temperature disturbance coefficient in the thermally stable state. The first 10 minutes after the system is powered on are used as the initialization window, and the data within this window is taken as the thermally stable state data.
[0054] It is worth noting that since the calculation of the temperature disturbance coefficient requires setting a moving window, when the system powers on or runs for less than the moving window length, it is determined to be in the initial data accumulation phase, and the thermal hysteresis compensation factor is forcibly set. Only static model compensation is performed; subsequent frequency correction processes are not executed.
[0055] Furthermore, using the existing "frequency-temperature" static model, a certain temperature compensation is first performed. Based on this temperature compensation, a proportional-integral (PI) controller is used to enhance stability and eliminate steady-state error, and a thermal hysteresis compensation factor is used for certain corrections.
[0056] The dynamic compensation amount is determined by using the thermal hysteresis compensation factor and frequency error at each moment, as well as the frequency errors at all moments prior to that moment, through proportional gain and integral gain.
[0057] Preferably, the expression for the dynamic compensation amount is: , This represents the thermal hysteresis compensation factor at time t. This represents the frequency error at time t. This represents the frequency error at time j. This represents the time interval between two adjacent moments. This represents the initial proportional gain. Indicates the initial integral gain. This represents the dynamic compensation amount at time t. The frequency error is calculated as the difference between the frequency value obtained from the "frequency-temperature" static model and the actual frequency value. The purpose is to approximate a discrete summation as a continuous integral. In this embodiment, the initial proportional gain and the initial integral gain are set to 0.1 and 0.01, respectively.
[0058] The dynamic compensation amount is used to correct the static frequency after compensation by the "frequency-temperature" static model to obtain the corrected frequency. The expression for this corrected frequency is: , This represents the static frequency at time t after compensation using the "frequency-temperature" static model. This represents the dynamic compensation amount at time t. This indicates the preset maximum dynamic compensation amount. Describes the minimum value function. This represents the corrected frequency at time t. In this embodiment, the maximum dynamic compensation amount is determined by the maximum frequency adjustment range allowed by the MEMS device.
[0059] In MEMS devices, the higher the temperature, the lower the resonant frequency, so when When cooling is required to increase the frequency, but due to thermal hysteresis, the cooling rate inside the device is slower than the predicted value of the static model. This means the frequency obtained from the static model is higher than the actual frequency of the MEMS device. Therefore, the dynamic compensation amount should be subtracted from the static frequency. Conversely, when... At that time, the static frequency is increased by the dynamic compensation amount.
[0060] This completes the frequency drift compensation.
[0061] Based on the same inventive concept as the above method, this embodiment of the invention also provides a MEMS device frequency drift self-compensation system, including a memory, a processor, and a computer program stored in the memory and running on the processor. When the processor executes the computer program, it implements the steps of any one of the above-described MEMS device frequency drift self-compensation methods.
[0062] It should be noted that the above embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of this application, and should all be included within the protection scope of this application.
[0063] The various embodiments in this specification are described in a progressive manner. The same or similar parts between the various embodiments can be referred to each other. Each embodiment focuses on describing the differences from other embodiments.
Claims
1. A method for self-compensation of frequency drift in MEMS devices, characterized in that, The method includes the following steps: Monitoring parameters of MEMS devices are collected through various sensors; For each moment, the correlation between temperature and frequency in the monitoring parameters from previous moments is calculated, and the temperature disturbance coefficient is calculated by combining the temperature change rate from previous moments, the time offset of temperature and frequency, and the difference between the predicted frequency obtained through temperature and the actual frequency. All parameters in the monitoring parameters other than temperature and frequency are designated as non-temperature parameters. For each time moment, the delay factor is obtained based on the data of the non-temperature parameters at all previous time moments and the time offset of the temperature. Based on the data of the non-temperature parameters at each time moment, the correlation between each pair of non-temperature parameters is calculated to form a correlation matrix, and the average of the absolute values of all off-diagonal elements of the matrix is used as the coupling factor. The lag coefficient is determined based on the coupling factor at each time moment, the minimum ratio of the temperature disturbance coefficient to the temperature disturbance coefficient at a preset number of time moments before it, the fluctuation of the non-temperature parameters at previous time moments, and the delay factor. The thermal hysteresis compensation factor is calculated using the temperature disturbance coefficient and the hysteresis degree coefficient; the dynamic compensation amount is determined by using the thermal hysteresis compensation factor at each moment, the frequency error, and the frequency errors at all moments before that moment through proportional gain and integral gain; the dynamic compensation amount is used to correct the static frequency after compensation by the "frequency-temperature" static model to obtain the corrected frequency; the compensation is then completed.
2. The self-compensation method for frequency drift of a MEMS device as described in claim 1, characterized in that, The monitoring parameters include temperature, frequency, amplitude, voltage, phase, and quality factor.
3. The self-compensation method for frequency drift of a MEMS device as described in claim 1, characterized in that, The temperature disturbance coefficient is positively correlated with the temperature change rate, frequency residual factor, and lag time factor; and negatively correlated with the correlation factor.
4. The self-compensation method for frequency drift of a MEMS device as described in claim 3, characterized in that, The normalized value of the time offset corresponding to the maximum cross-correlation function value between temperature and frequency at all times prior to each time step of the lag time factor.
5. The frequency drift self-compensation method for MEMS devices as described in claim 3, characterized in that, The method for obtaining the frequency residual factor is as follows: The predicted frequency at a given moment is obtained by substituting the temperature at a given moment into the static temperature model. The difference between the predicted frequency and the actual frequency at a given moment is the frequency residual at that moment. For each moment, its moving window is obtained, and the normalized value of the root mean square value of the frequency residuals at that moment and all moments within the moving window is calculated and recorded as the frequency residual factor.
6. The self-compensation method for frequency drift of a MEMS device as described in claim 1, characterized in that, The lag coefficient is positively correlated with the minimum ratio of the temperature disturbance coefficient at each time point and its preset number of time points, the delay factor, and the abnormal fluctuation factor, and negatively correlated with the coupling factor.
7. The self-compensation method for frequency drift of a MEMS device as described in claim 6, characterized in that, The lag factor is the mean of the lag time factors of all data before each time step for the non-temperature parameter and the temperature; the abnormal fluctuation factor is the mean of the normalized values of the standard deviations of the first differences of all data before each time step for the non-temperature parameter.
8. The frequency drift self-compensation method for MEMS devices as described in claim 1, characterized in that, The method for calculating the thermal hysteresis compensation factor using the temperature disturbance coefficient and the hysteresis degree coefficient is as follows: , This represents the temperature disturbance coefficient at time t. This represents the lag coefficient at time t. The activation threshold representing the temperature perturbation coefficient. This represents the thermal hysteresis compensation factor at time t. express Kernel function.
9. The frequency drift self-compensation method for MEMS devices as described in claim 1, characterized in that, The method for determining the dynamic compensation amount by using the thermal hysteresis compensation factor and frequency error at each moment, as well as the frequency errors at all moments before that moment, through proportional gain and integral gain, is as follows: , This represents the thermal hysteresis compensation factor at time t. This represents the frequency error at time t. This represents the frequency error at time j. This represents the time interval between two adjacent moments. This represents the initial proportional gain. Indicates the initial integral gain. This represents the dynamic compensation amount at time t. The frequency error is calculated as the difference between the frequency value obtained from the "frequency-temperature" static model and the actual frequency value.
10. A frequency drift self-compensation system for MEMS devices, comprising a memory, a processor, and a computer program stored in the memory and running on the processor, characterized in that, When the processor executes the computer program, it implements the steps of the frequency drift self-compensation method for MEMS devices as described in any one of claims 1-9.