Mode matching rapid tuning and open loop holding method and system based on double-sideband modulation

Abstract

The invention provides a mode matching rapid tuning and open-loop holding method and system based on double-sideband modulation, and the method comprises the following steps: generating a double-sideband modulation signal at a tuning stage, and applying the double-sideband modulation signal to a detection mode; collecting a detection modal output signal, and obtaining an upper sideband and lower sideband response amplitude difference by using phase-sensitive demodulation; the amplitude difference serves as input of a PI controller, the voltage of a frequency tuning electrode is adjusted in real time, and the optimal resonance voltage needed by mode matching is obtained; and after the judgment condition is met, closing the double-sideband modulation signal, and only keeping the resonance voltage acting on the tuning electrode, so that the detection mode output is not interfered by double sidebands any more. According to the method, frequency splitting can be quickly eliminated, noise and coupling caused by long-term excitation of double sidebands are avoided, and the measurement precision of the gyroscope is improved.

Description

Technical Field

[0001] This invention relates to the field of microelectromechanical systems (MEMS) inertial sensor technology, and in particular to a method and system for fast tuning and open-loop holding of mode matching based on double-sideband modulation. Background Technology

[0002] A resonant gyroscope is an inertial sensor based on the Coriolis effect. When an external angular velocity input is present, the vibration of the driving mode acts on the detection mode through the Coriolis force, thereby generating a signal proportional to the angular velocity in the detection mode. Ideally, the natural frequencies of the driving mode and the detection mode should be consistent to ensure effective energy coupling, thus obtaining a highly sensitive angular velocity output.

[0003] However, due to factors such as manufacturing errors and structural asymmetry, there is often an inherent frequency difference between the driving mode and the detection mode in actual devices, a phenomenon known as frequency splitting. Frequency splitting leads to a weakening of the angular velocity signal response in the detection mode, and may even cause it to become mixed with damping signals and orthogonal error signals caused by structural errors, thus severely affecting the measurement accuracy and zero-bias stability of the gyroscope.

[0004] Currently, most commonly used mode matching methods are based on closed-loop control. For example, a double-sideband modulated signal is injected into the detection mode, and the tuning voltage is adjusted in real time by a closed-loop controller to make the response amplitudes of the upper and lower sidebands tend to be consistent, thereby achieving mode matching. This type of method can dynamically track frequency drift during operation, ensuring that the gyroscope is always in a matched state. However, the double-sideband signal will continuously act on the detection mode during closed-loop operation, generating additional coupling effects, which will affect the purity of the angular velocity signal and the detection accuracy; and in some application scenarios, it may limit the dynamic measurement range of the gyroscope. Summary of the Invention

[0005] The purpose of this invention is to provide a mode matching method and system for a resonant gyroscope, in order to solve the problem that the existing closed-loop double-sideband mode matching method introduces additional signal coupling and affects the accuracy of angular velocity detection during continuous operation, so as to achieve fast and accurate mode matching and maintain high-precision angular velocity measurement performance after matching.

[0006] The technical solution for achieving the objective of this invention is as follows:

[0007] A mode-matching fast tuning and open-loop hold system based on double-sideband modulation includes:

[0008] The first signal amplification module is used to amplify the output signal of the detection electrode of the gyroscope detection mode;

[0009] The first analog-to-digital converter module is used to convert the output analog signal of the first signal amplification module into a digital signal and input it to the amplitude demodulation module.

[0010] The second signal amplification module is used to amplify the output signal of the detection electrode of the gyroscope driving mode;

[0011] The second analog-to-digital converter module is used to convert the output analog signal of the second signal amplification module into a digital signal and input it to the phase-locked loop module.

[0012] The phase-locked loop module is used to track the center frequency and generate cosine reference signals for the frequencies corresponding to the upper and lower sideband signals.

[0013] The first adder is used to add the cosine components corresponding to the upper and lower sideband signals output by the phase-locked loop module to generate a double-sideband modulated signal.

[0014] The second adder is used to superimpose the double-sideband modulated signal with the signal output from the first analog-to-digital converter module to obtain a composite signal. The driving electrode that acts on the sensing mode;

[0015] The first digital-to-analog converter module is used to convert the double-sideband signal generated by the second adder into an analog signal;

[0016] Amplitude demodulation module: used to demodulate the amplitude difference of the double-sideband response;

[0017] The tuning voltage PI control module uses the difference in amplitude of the double-sideband response as input to tune the voltage. The output voltage is controlled by a PI controller to adjust the tuning voltage.

[0018] Interval Comparison Module: Connected to the amplitude demodulation module, it takes the double-sideband response amplitude as the input signal, sets the interval reference as the comparison interval, compares the values, and outputs a judgment signal.

[0019] The controller receives the judgment signal from the interval comparison module and controls the working state of the first adder. If the judgment signal is "1", the first adder is controlled not to work, that is, no double-sideband signal is generated, and the tuning voltage at that time is recorded. If the judgment signal is "0", the first adder is controlled to work.

[0020] The data selector is used to select the tuning voltage recorded by the tuning voltage PI control module and the controller. The selection is based on the judgment signal output by the interval comparison module: when the judgment signal is "1", the tuning voltage recorded by the controller is selected; when the judgment signal is "0", the output signal of the tuning voltage PI control module is selected.

[0021] The second digital-to-analog converter module is used to convert the output signal of the data selector into an analog signal and output it to the gyroscope tuning electrode.

[0022] A fast mode-matching tuning and open-loop hold method based on double-sideband modulation includes:

[0023] Step 1: Detect the double-sideband modulation signal generated by the gyroscope driving mode, and use the double-sideband modulation signal as input and the composite signal acting on the driving electrode of the sensing mode as output to form a negative feedback system, and obtain the transfer function of the negative feedback system.

[0024] Step 2: Based on the negative feedback system transfer function, the double-sideband modulation signal is input to the detection mode driving electrode to obtain the double-sideband response signal. ;

[0025] Step 3: Demodulate the double-sideband response signal using it as a reference signal to obtain the amplitude difference of the double-sideband response. ;

[0026] Step 4: Using the difference in amplitude of the two-sideband response as input, tune the voltage. The output voltage is controlled by a PI controller to adjust the tuning voltage.

[0027] Step 5: Adjust the natural frequency of the detection mode using the tuning voltage. This enables the gyroscope to achieve modal matching.

[0028] Compared with the prior art, the significant advantages of the present invention are:

[0029] In the tuning phase, this invention generates a double-sideband modulation signal and applies it to the detection mode; it acquires the output signal of the detection mode and uses phase-sensitive demodulation to obtain the amplitude difference between the upper and lower sideband responses; it uses this amplitude difference as input to a PI controller to adjust the voltage of the frequency tuning electrode in real time to obtain the optimal resonant voltage required for mode matching; after the judgment condition is met, the double-sideband modulation signal is turned off, and only the resonant voltage is applied to the tuning electrode, so that the output of the detection mode is no longer affected by double-sideband interference. This method can quickly eliminate frequency splitting while avoiding noise and coupling introduced by long-term double-sideband excitation, thus improving the measurement accuracy of the gyroscope. Attached Figure Description

[0030] The accompanying drawings, which form part of this application, are used to provide a further understanding of this application. The illustrative embodiments and descriptions of this application are used to explain this application and do not constitute an undue limitation of this application. In the drawings:

[0031] Figure 1 This is a schematic flowchart of a mode matching fast tuning and open-loop hold method based on double-sideband modulation according to Embodiment 1 of the present invention;

[0032] Figure 2 This is a structural diagram of a four-mass gyroscope according to Embodiment 1 of the present invention;

[0033] Figure 3 This is a signal processing diagram of a mode matching fast tuning and open-loop hold system based on double-sideband modulation according to Embodiment 1 of the present invention;

[0034] Figure 4 This is a circuit system block diagram of Embodiment 1 of the present invention; Detailed Implementation

[0035] As described above, this embodiment achieves fast mode matching and open-loop hold of a resonant four-mass gyroscope through double-sideband modulation. Each step is explained below in conjunction with signal relationships and an ideal model.

[0036] A mode-matching fast tuning and open-loop hold system based on double-sideband modulation includes:

[0037] First signal amplification module: connected to the detection electrode of the detection mode, used to amplify the output signal of the detection electrode of the gyroscope detection mode;

[0038] First analog-to-digital conversion module: connected to the first signal amplification module, used to convert the output analog signal of the first signal amplification module into a digital signal and input it into the FPGA chip;

[0039] Second signal amplification module: connected to the detection electrode of the driving mode, used to amplify the output signal of the detection electrode of the gyroscope driving mode;

[0040] Second analog-to-digital conversion module: connected to the second signal amplification module, used to convert the output analog signal of the second signal amplification module into a digital signal and input it into the phase-locked loop module in the FPGA chip;

[0041] Phase-locked loop module: connected to the second analog-to-digital converter module, used to track the center frequency and generate cosine reference signals for the frequencies corresponding to the upper and lower sideband signals;

[0042] The first adder is used to add the cosine components corresponding to the upper and lower sideband signals output by the phase-locked loop module to generate a double-sideband modulated signal. ;

[0043] Second adder: Connected to the first adder and the first analog-to-digital converter module, used to convert the double-sideband modulated signal... The signal output by the first analog-to-digital converter module Superposition yields a composite signal. ;

[0044] Amplitude demodulation module: Connected to the first analog-to-digital converter module, it includes two multipliers, two low-pass filter circuits, and a third adder. The first multiplier is used to convert the upper sideband cosine reference signal with the double sideband response signal. Multiplication; the second multiplier is used to multiply the lower sideband cosine reference signal with the double sideband response signal. Multiplication. The first low-pass filter circuit filters the output signal of the first multiplier to obtain a DC signal, representing the amplitude of the upper sideband response. The second low-pass filter circuit filters the output signal of the second multiplier to obtain a DC signal, representing the amplitude of the lower sideband response. The third adder adds the output signals of the first and second low-pass filter circuits to obtain the difference in amplitude of the double sideband responses. ;

[0045] Tuning voltage PI control module: Connected to the amplitude demodulation module, it controls the magnitude of the tuning voltage to achieve a double-sideband response amplitude difference. Input, tuning voltage For output, the reference value is set to 0. Since this is done within an FPGA circuit and uses digital signals, the control principle is as follows: ,in For the first The tuning voltage at each sampling time For the first The difference in amplitude of the double-sideband response at each sampling time. This is the proportional coefficient for the tuning voltage PI control module. The integral coefficient of the tuning voltage PI control module. The time interval between two sampling points. For the front Each sampling time The sum of For summation index.

[0046] Interval Comparison Module: Connected to the amplitude demodulation module, it compares the amplitude differences of the two-sideband response. As the input signal, the set interval reference is the comparison interval, which is compared by the interval comparator and a judgment signal is output. If the double-sideband response amplitude difference is... If the signal remains stable within the comparison range for a period of time, the output judgment signal is "1"; otherwise, it is "0".

[0047] Controller: Connected to the interval comparison module, it receives the judgment signal from the interval comparison module and controls the working state of the first adder. If the judgment signal is "1", the first adder is controlled to not work, that is, no double-sideband signal is generated, and the current tuning voltage is recorded; if the judgment signal is "0", the first adder is controlled to work.

[0048] Data selector: Connected to the controller and the tuning voltage PI control module, it is used to select the tuning voltage recorded by the tuning voltage PI control module and the controller. The selection is based on the judgment signal output by the interval comparison module: when the judgment signal is "1", the tuning voltage recorded by the controller is selected; when the judgment signal is "0", the output signal of the tuning voltage PI control module is selected.

[0049] First digital-to-analog converter module: connected to the second adder, used to convert the double-sideband signal generated by the first adder into an analog signal;

[0050] The second analog-to-digital converter module is connected to the data selector and is used to convert the output signal of the data selector into an analog signal and output it to the gyroscope tuning electrode.

[0051] It should be noted that the phase-locked loop module, the first adder, the second adder, the amplitude demodulation module, the tuning voltage PI control module, the interval comparison module, the controller, the data selector, the first digital-to-analog converter module, and the second digital-to-analog converter module are all located within the FPGA processor.

[0052] Example 1

[0053] like Figure 1 As shown, this invention provides a method for fast mode matching tuning and open-loop hold based on double-sideband modulation, comprising the following steps:

[0054] Step 1: Obtain the transfer function of the negative feedback system

[0055] Once the gyroscope drive mode is working properly, based on the center frequency The double-sideband signal is generated by the phase-locked loop and adder 1, and the lower sideband signal frequency is... and the upper sideband signal frequency Regarding the center frequency Symmetrical distribution, where For the purpose of setting , for , The frequency interval is set to 50Hz. A larger interval results in poor mode matching; in this example, it is set to 50Hz. The two sideband signals are added together to obtain a double-sideband signal. .

[0056]

[0057] Where t is time, representing the double-sideband signal. and the output signal of the first analog-to-digital converter module Adding them together yields a composite signal. . By utilizing the FPGA to directly act on the driving electrodes of the sensing mode, a system is formed. For input, This is a negative feedback system for the output. The transfer function is based on the detection mode. According to the principles of automatic control, the transfer function of a two-sided negative feedback system The derivation is as follows:

[0058]

[0059]

[0060] in Represents the complex frequency variable in the Laplace transform. It is the mass block mass for detecting modalities. It is the natural frequency of the detection mode. The quality factor of the detection mode, It is the electromechanical conversion coefficient of the first signal amplification module. It is the feedback coefficient on the negative feedback path, usually 1. When the loop gain When it is much greater than 1, It can be approximated as:

[0061]

[0062] The transfer function demonstrates an inverse relationship between the transfer function of the double-sideband signal negative feedback system and the detection mode. This provides a basis for selecting the frequency interval. It provided very favorable conditions. It solved the problem caused by... The limitation of bandwidth due to practical constraints expands the dynamic measurement range of the gyroscope.

[0063] Step 2: Obtain the response signal of the double-sideband signal.

[0064] Based on the negative feedback system transfer function described in step 1 double-sideband signal The input is given to the detection mode driving electrode, and after passing through the negative feedback system combining the detection mode and the negative feedback path, the output response signal is obtained. The specific calculation process is as follows:

[0065] The above First transform it into complex form

[0066]

[0067] Amplitude-frequency response is

[0068]

[0069] Phase frequency characteristics are

[0070]

[0071]

[0072] in The imaginary unit, The angular frequency variable of the sinusoidal input signal is given to the system. for The plural form, For negative feedback systems amplitude-frequency characteristics, For negative feedback systems The phase frequency characteristics. Because the input signal consists of two frequency components, upper and lower. and The output response also includes corresponding upper and lower sideband components, denoted as . and Therefore, the response signal It can be represented in the following form:

[0073]

[0074]

[0075]

[0076]

[0077]

[0078] and They are and The response amplitude, and and They are and The response phase.

[0079] Step 3: Obtain the amplitude difference of the double-sideband response signal

[0080] In order to extract and The response amplitude is determined by demodulating a double-sideband signal as a reference signal, passing it through a first low-pass filter and a second low-pass filter, and then through an adder to obtain the demodulated signal. This is expressed as follows. Furthermore, the cutoff frequencies of the two low-pass filters should be set to be less than the frequency interval. This is to avoid interference with the demodulation of the in-phase channel and the normal traffic channel.

[0081]

[0082] According to step 2 Choose an appropriate frequency interval Can make The value is 0°, while The value is 180°. Therefore It can be further simplified to

[0083]

[0084] That is, the amplitude difference, and They are directly proportional; therefore, the demodulated signal It can be used to represent the difference in response amplitude and as a real-time measurement signal to determine frequency splitting.

[0085] Step 4: Obtain the tuning voltage for adjusting the detection mode based on the amplitude difference.

[0086] When the gyroscope achieves modal matching, i.e., at the center frequency... With the inherent frequency of the detection module When they are equal, and about symmetry, The theoretical value should be around 0. The demodulated signal... As the input signal, the PI control module inputs the tuning voltage, which generates the first... Tuning voltage at each sampling time Since the FPGA only processes digital signals, the input tuning voltage PI control module... The expression is as follows

[0087]

[0088] in For the first The sequence number of each sampling time. This is the proportional coefficient for the tuning voltage PI control module. The integral coefficient of the tuning voltage PI control module. The time interval between two sampling points. For the first The tuning voltage at each sampling time For the first The difference in amplitude of the double-sideband response at each sampling time. This is the proportional coefficient for the tuning voltage PI control module. The integral coefficient of the tuning voltage PI control module. The time interval between two sampling points. For the front Each sampling time The sum of For summation index.

[0089] Then it is converted into an analog signal by a digital-to-analog converter module. The input is fed into the tuning electrode of the detection mode.

[0090] Step 5: Adjust the natural frequency of the detection mode using the tuning voltage. This enables the gyroscope to achieve modal matching.

[0091] Based on the tuning voltage obtained in step 4 It acts on the tuning electrode of the detection mode in real time through the electrostatic negative stiffness effect, thereby dynamically adjusting the natural frequency of the detection mode. ,make Gradually approaching the natural frequency of the driving mode The relationship between the natural frequency and the tuning voltage is as follows:

[0092]

[0093] in The natural frequency of the current detection mode. The adjusted natural frequency, where b is the electro-mechanical coupling coefficient. The theoretical formula for calculating b is: ,in Substituting, we can get m is the effective mass of the detected mode, C is the capacitance of the tuning electrode of the detected mode, and x is the displacement of the parallel plate. Let A be the vacuum dielectric constant, and A be the effective area of ​​the detection mode tuning electrode. This refers to the gap between the parallel plate capacitors.

[0094] Obtained using step 4 After being input to the tuning electrode, the natural frequency of the detection mode becomes ,when hour, and about symmetry, The theoretical value should be around 0. Therefore, when Convergence is determined when the value stabilizes at the interval reference for a period of time. The interval reference is derived from: manually adjusting to the modal matching state in the open-loop state, collecting amplitude difference data for a period of time, and using it as the interval reference for comparison.

[0095] Will As an input signal interval comparison module, a judgment signal is obtained. If convergence occurs at this time, the judgment signal is "1", and the controller records the tuning voltage at that time. , recorded as The adder is then deactivated, meaning the double-sideband input is turned off and the system switches to open-loop hold mode. Afterwards, the second digital-to-analog converter module only maintains the acquired tuning voltage. This ensures that the double-sideband signal remains unchanged, thereby avoiding the introduction of additional coupling during subsequent operation and ensuring the purity and measurement accuracy of the angular velocity signal.

Claims

1. A mode-matching fast tuning and open-loop hold system based on double-sideband modulation, characterized in that, include: The first signal amplification module is used to amplify the output signal of the detection electrode of the gyroscope detection mode; The first analog-to-digital converter module is used to convert the output analog signal of the first signal amplification module into a digital signal and input it to the amplitude demodulation module. The second signal amplification module is used to amplify the output signal of the detection electrode of the gyroscope driving mode; The second analog-to-digital converter module is used to convert the output analog signal of the second signal amplification module into a digital signal and input it to the phase-locked loop module. The phase-locked loop module is used to track the center frequency and generate cosine reference signals for the frequencies corresponding to the upper and lower sideband signals. The first adder is used to add the cosine components corresponding to the upper and lower sideband signals output by the phase-locked loop module to generate a double-sideband modulated signal. The second adder is used to superimpose the double-sideband modulated signal with the signal output from the first analog-to-digital converter module to obtain a composite signal. The driving electrode that acts on the sensing mode; The first digital-to-analog converter module is used to convert the double-sideband signal generated by the second adder into an analog signal; Amplitude demodulation module: used to demodulate the amplitude difference of the double-sideband response; The tuning voltage PI control module uses the difference in amplitude of the double-sideband response as input to tune the voltage. The output voltage is controlled by a PI controller to adjust the tuning voltage. Interval Comparison Module: Connected to the amplitude demodulation module, it takes the double-sideband response amplitude as the input signal, sets the interval reference as the comparison interval, compares the values, and outputs a judgment signal. The controller receives the judgment signal from the interval comparison module and controls the working state of the first adder. If the judgment signal is "1", the first adder is controlled not to work, that is, no double-sideband signal is generated, and the current tuning voltage is recorded. If the judgment signal is "0", the first adder is controlled to work. The data selector is used to select the tuning voltage recorded by the tuning voltage PI control module and the controller. The selection is based on the judgment signal output by the interval comparison module: when the judgment signal is "1", the tuning voltage recorded by the controller is selected; when the judgment signal is "0", the output signal of the tuning voltage PI control module is selected. The second digital-to-analog converter module is used to convert the output signal of the data selector into an analog signal and output it to the gyroscope tuning electrode.

2. The mode-matching fast tuning and open-loop hold system based on double-sideband modulation according to claim 1, characterized in that, The amplitude demodulation module includes: The first multiplier is used to multiply the upper sideband cosine reference signal with the double sideband response signal; The second multiplier is used to multiply the lower sideband cosine reference signal with the double sideband response signal; The first low-pass filter circuit is used to filter the output signal of the first multiplier to obtain a DC signal, which represents the amplitude of the upper sideband response. The second low-pass filter circuit is used to filter the output signal of the second multiplier to obtain a DC signal, i.e., the amplitude of the lower sideband response; The third adder is used to add the output signals of the first low-pass filter circuit and the second low-pass filter circuit to obtain the difference in amplitude of the double-sideband response.

3. The mode-matching fast tuning and open-loop hold system based on double-sideband modulation according to claim 1 or 2, characterized in that, The difference in amplitude of the double-sideband response is: ； In the formula ; in and These are the response amplitudes of the upper sideband component and the lower sideband component, respectively. It is the mass block mass for detecting modalities. It is the natural frequency of the detection mode. The quality factor of the detection mode, It is the electromechanical conversion coefficient of the first signal amplification module. It is the feedback coefficient. and These are the upper and lower sideband signal frequencies, respectively.

4. The mode-matching fast tuning and open-loop hold system based on double-sideband modulation according to claim 1, characterized in that, The tuning voltage output by the tuning voltage PI control module is: ； in For the first The tuning voltage at each sampling time For the first The difference in amplitude of the double-sideband response at each sampling time. This is the proportional coefficient for the tuning voltage PI control module. The integral coefficient of the tuning voltage PI control module. The time interval between two sampling points. For the front Each sampling time The sum of For summation index.

5. The mode-matching fast tuning and open-loop hold system based on double-sideband modulation according to claim 4, characterized in that, The obtained tuning voltage The natural frequency of the detection mode is dynamically adjusted by applying the electrostatic negative stiffness effect to the tuning electrode of the detection mode in real time. The adjusted natural frequency Gradually approaching the natural frequency of the driving mode The relationship between the natural frequency and the tuning voltage is as follows: ； in The natural frequency of the current detection mode. The adjusted natural frequency, where b is the electro-mechanical coupling coefficient.

6. A method for fast mode matching and open-loop hold based on double-sideband modulation, characterized in that, include: Step 1: Detect the double-sideband modulation signal generated by the gyroscope driving mode, and use the double-sideband modulation signal as input and the composite signal acting on the driving electrode of the sensing mode as output to form a negative feedback system, and obtain the transfer function of the negative feedback system. Step 2: Based on the negative feedback system transfer function, the double-sideband modulation signal is input to the detection mode driving electrode to obtain the double-sideband response signal. ; Step 3: Demodulate the double-sideband response signal using it as a reference signal to obtain the amplitude difference of the double-sideband response. ; Step 4: Using the difference in amplitude of the two-sideband response as input, tune the voltage. The output voltage is controlled by a PI controller to adjust the tuning voltage. Step 5: Adjust the natural frequency of the detection mode using the tuning voltage. This enables the gyroscope to achieve modal matching.

7. The method for fast mode matching and open-loop hold based on double-sideband modulation according to claim 6, characterized in that, Double-side band response signal for: ； ； ； ； ； in and These are the response amplitudes of the upper and lower sideband components, respectively. and These are the corresponding phases of the upper and lower sideband components, respectively. It is the mass block mass for detecting modalities. It is the natural frequency of the detection mode. The quality factor of the detection mode, It is the electromechanical conversion coefficient of the first signal amplification module. It is the feedback coefficient. and These are the upper and lower sideband signal frequencies, respectively, and t is time.

8. The method for fast mode matching and open-loop hold based on double-sideband modulation according to claim 6, characterized in that, The difference in amplitude between the two sides of the band response is: ； In the formula ; in and These are the response amplitudes of the upper sideband component and the lower sideband component, respectively. It is the mass block mass for detecting modalities. It is the natural frequency of the detection mode. The quality factor of the detection mode, It is the electromechanical conversion coefficient of the first signal amplification module. It is the feedback coefficient. and These are the upper and lower sideband signal frequencies, respectively.

9. The method for fast mode matching and open-loop holding based on double-sideband modulation according to claim 6, characterized in that, The tuning voltage is: ； in For the first The tuning voltage at each sampling time For the first The difference in amplitude of the double-sideband response at each sampling time. This is the proportional coefficient for the tuning voltage PI control module. The integral coefficient of the tuning voltage PI control module. The time interval between two sampling points. For the front Each sampling time The sum of For summation index.

10. The method for fast mode matching and open-loop holding based on double-sideband modulation according to claim 6, characterized in that, The obtained tuning voltage The natural frequency of the detection mode is dynamically adjusted by applying the electrostatic negative stiffness effect to the tuning electrode of the detection mode in real time. The adjusted natural frequency Gradually approaching the natural frequency of the driving mode The relationship between the natural frequency and the tuning voltage is as follows: ； in The natural frequency of the current detection mode. The adjusted natural frequency, where b is the electro-mechanical coupling coefficient.

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