MEMS inter-oscillator frequency stabilization device based on axial force control

Abstract

The application provides a MEMS inter-synchronous oscillator frequency stabilizing device based on axial force control and belongs to the technical field of micro-electro-mechanical systems. The device comprises a linear oscillation loop, a nonlinear oscillation loop, an inter-synchronous injection unit and a frequency regulating unit. First and second comb tooth electrodes are arranged on a linear resonator in the linear oscillation loop. The inter-synchronous injection unit makes the two oscillation loops inter-synchronous and output the same oscillation frequency. A PID controller in the frequency regulating unit outputs an axial voltage control value according to the difference between the current oscillation frequency of the linear resonator and the set frequency. An axial voltage controller applies axial electrostatic force between the comb tooth electrodes according to the control value, changes the equivalent bending stiffness of the linear resonator, adjusts the frequency of the linear oscillation loop, synchronously adjusts the frequency of the nonlinear oscillation loop by using the inter-synchronous injection unit, and realizes the stability of the output frequency. The application has high regulating precision, fast response and low power consumption, and can effectively inhibit frequency drift.

Description

Technical Field

[0001] This invention belongs to the field of microelectromechanical systems (MEMS) technology, specifically relating to a frequency stabilization device for MEMS mutual synchronization oscillators based on axial force control. Background Technology

[0002] Currently, high-stability reference frequencies primarily rely on quartz crystal oscillators, favored for their cost-effectiveness and stable performance. However, quartz devices are incompatible with modern semiconductor processes, hindering integration with densely packaged microsystems. Their size also poses challenges to IC layout, particularly in terms of signal path length and temperature gradients. MEMS oscillators, based on microelectromechanical systems (MEMS) technology, are widely recognized as potential alternatives to quartz crystal oscillators due to their small size, high precision, low cost, and ease of integration. They are already widely used in emerging fields such as precision measurement, biomedicine, and wearable devices. Frequency stability is a key indicator of MEMS oscillator performance, directly affecting system reliability and accuracy; therefore, high frequency stability is crucial for MEMS oscillators.

[0003] The high temperature sensitivity of silicon-based materials causes drastic frequency drift in MEMS oscillators under varying temperatures. Furthermore, noise, radiation, and material aging within the oscillation system can also reduce oscillator frequency stability. To suppress frequency drift in MEMS oscillators, active and passive compensation methods are commonly used for temperature compensation. The most common active compensation method employs a isothermal control scheme, which suffers from problems such as uneven temperature field and large temperature gradients, and introduces significant additional thermal noise. The most common passive compensation method involves improving device structure design and composite material selection to reduce the oscillator's temperature frequency coefficient; however, the improvement in frequency stability is limited and confined to short-term frequency stability, while also increasing manufacturing costs and complexity.

[0004] In recent years, MEMS oscillators, combining sensing and high-stability oscillation, have provided new capabilities for microsystem integration. As oscillators move towards miniaturization, the inherent size effect inevitably brings nonlinear problems and triggers a series of nonlinear effects. Synchronization, as a special phenomenon among nonlinear effects, enables self-excited oscillators to enter a frequency-locked state under weak external disturbances or coupling signals, amplifying weak signal inputs while suppressing noise, and is considered a key principle for next-generation sensors. Recent research shows that by driving MEMS oscillators into the nonlinear synchronization range, their phase noise can be significantly suppressed and the frequency control range greatly improved. However, the frequency stability of uncontrolled nonlinear oscillators is poor, and their frequency is easily disturbed by external factors such as temperature, magnetic fields, and power supply voltage. Linear oscillators, on the other hand, not only avoid the conversion of amplitude-frequency noise, but also, due to their superposition and homogeneity, are simpler to calculate and control. Furthermore, existing mutual synchronization or array synchronization schemes are mostly based on two or more oscillators with similar structures, materials, resonant frequencies, and packaging conditions, achieving noise averaging or frequency locking through coupling between approximately identical oscillating units. These approaches are highly sensitive to device consistency, frequency mismatch, coupling strength, and packaging stress. If the inherent frequencies, nonlinear coefficients, quality factors, or environmental responses of the two oscillators are inconsistent, the synchronization range and frequency stabilization effect will be significantly limited. Therefore, current technology still lacks a solution to improve the frequency stability of MEMS oscillators without relying on a fully symmetrical dual-oscillator structure, significantly increasing thermal power consumption and manufacturing complexity, while simultaneously considering the low-amplitude phase coupling characteristics of linear oscillators and the wide synchronization control capability of nonlinear oscillators. Utilizing the low amplitude-frequency noise conversion characteristics of linear oscillators to provide a stable oscillation reference, while simultaneously leveraging the synchronization locking and frequency control capabilities of nonlinear oscillators to expand the lockable range, offers a highly competitive improvement effect for MEMS oscillators, providing a new approach for further enhancing the performance of micromechanical oscillators. Summary of the Invention

[0005] To address the aforementioned problems, this invention provides a MEMS mutual synchronization oscillator frequency stabilization device based on axial force control. Without increasing system complexity and response time, it compensates for the drift of oscillation frequency caused by external factors, and can achieve synchronous control of linear and nonlinear oscillators, while improving the long-term frequency stability of both linear and nonlinear MEMS oscillators.

[0006] The present invention adopts the following technical solution:

[0007] In a first aspect, the present invention discloses a frequency stabilization device for a MEMS mutual synchronization oscillator based on axial force control, comprising:

[0008] A linear oscillating circuit includes a linear resonator, wherein a first comb-tooth plate and a second comb-tooth plate are disposed on the linear resonator;

[0009] Nonlinear oscillating circuit, including a nonlinear resonator;

[0010] The mutual synchronization injection unit is used to inject the signal of the nonlinear oscillation circuit into the linear oscillation circuit, and the signal of the linear oscillation circuit into the nonlinear oscillation circuit, so that the oscillation frequencies of the two resonators are mutually synchronized.

[0011] The frequency control unit includes a PID controller and an axial voltage controller;

[0012] The PID controller is used to output an axial voltage control quantity based on the difference between the current oscillation frequency of the linear resonator and the set frequency.

[0013] The axial voltage controller is connected to the first comb plate and the second comb plate. According to the axial voltage control amount, an axial electrostatic force is applied between the first comb plate and the second comb plate to change the equivalent bending stiffness of the linear resonator, thereby adjusting the oscillation frequency of the linear oscillation circuit. The oscillation frequency of the nonlinear oscillation circuit is also adjusted synchronously by the mutual synchronization injection unit.

[0014] Preferably, the linear resonator is a rhombic beam structure formed by connecting four straight beams, and the first comb plate and the second comb plate are arranged symmetrically about the axis of the linear resonator and located on the same side of the rhombic beam.

[0015] Preferably, the length of each straight beam is 100~500μm and the width is 5~10μm.

[0016] Preferably, the nonlinear resonator is a tuning fork beam structure with fixed supports at both ends.

[0017] Preferably, the length of each tuning fork beam is 100~500μm and the width is 5~10μm.

[0018] Preferably, the mutual synchronization injection unit includes:

[0019] The first amplitude controller has its input terminal connected to a nonlinear oscillating circuit and its output terminal connected to a linear oscillating circuit.

[0020] The second amplitude controller has its input connected to a linear oscillating circuit and its output connected to a nonlinear oscillating circuit.

[0021] Preferably, the linear oscillation circuit further includes:

[0022] The second transimpedance amplifier has its input terminal connected to a linear resonator;

[0023] A second phase detector, a second loop PI controller, and a second numerically controlled oscillator are connected in series. The input terminal of the second phase detector is connected to the output terminal of the second transimpedance amplifier, and the feedback signal of the second numerically controlled oscillator is connected to the second phase detector.

[0024] The second adder has its first input terminal connected to the output terminal of the second numerically controlled oscillator, its second input terminal connected to the output of the first amplitude controller of the mutual synchronization injection unit, and its output terminal connected to the linear resonator to form a closed-loop oscillation.

[0025] Preferably, the nonlinear oscillation circuit further includes:

[0026] The first transimpedance amplifier has its input terminal connected to a nonlinear resonator;

[0027] A first phase detector, a first loop PI controller, and a first numerically controlled oscillator are connected in series. The input terminal of the first phase detector is connected to the output terminal of the first transimpedance amplifier, and the feedback signal of the first numerically controlled oscillator is connected to the first phase detector.

[0028] The first adder has its first input terminal connected to the output terminal of the first numerically controlled oscillator, its second input terminal connected to the output of the second amplitude controller of the mutual synchronization injection unit, and its output terminal connected to the nonlinear resonator to form a closed-loop oscillation.

[0029] The aforementioned frequency stabilization device for MEMS mutually synchronized oscillators based on axial force control operates as follows: The signal from the nonlinear oscillation loop is injected into the linear oscillation loop via a first amplitude controller, and the signal from the linear oscillation loop is injected into the nonlinear oscillation loop via a second amplitude controller, forming a bidirectional mutual injection. When the oscillation frequency of the nonlinear oscillation loop is adjusted to be close to that of the linear oscillation loop, they synchronize, forming a mutually synchronized oscillator. After synchronization, the oscillation frequencies of the two loops are consistent. Within a certain frequency control range, adjusting either loop can control the oscillation frequency of the entire mutually synchronized oscillator. The PID controller acquires the current oscillation frequency in real time and compares it with the set frequency, outputting an axial voltage control quantity. This control quantity, through the axial voltage controller, changes the electrostatic force on the axial comb plate of the linear resonator in real time, dynamically adjusting the equivalent stiffness and oscillation frequency of the linear resonator. Furthermore, by leveraging the mutual synchronization relationship, the oscillation frequency of the nonlinear oscillator is synchronously controlled, thereby achieving precise control of the oscillation frequency of the mutually synchronized oscillator and effectively improving the long-term frequency stability of both linear and nonlinear MEMS oscillators.

[0030] Secondly, the present invention discloses a frequency stabilization method for MEMS mutual synchronization oscillators based on axial force control, applied to the aforementioned frequency stabilization device for MEMS mutual synchronization oscillators based on axial force control. The method includes the following steps:

[0031] S1. Set the target oscillation frequency;

[0032] S2. Obtain the current oscillation frequency from a linear or nonlinear oscillation circuit;

[0033] S3. Calculate the error between the current oscillation frequency and the target oscillation frequency;

[0034] S4. Based on the error, the axial voltage control quantity is generated by the PID controller;

[0035] S5. According to the axial voltage control quantity, apply axial electrostatic force between the first comb plate and the second comb plate of the linear resonator to change the equivalent bending stiffness of the linear resonator, thereby changing the oscillation frequency of the linear oscillation circuit. And adjust the oscillation frequency of the nonlinear oscillation circuit synchronously through the mutual synchronization injection unit so that the output frequency of the device approaches the target oscillation frequency.

[0036] S6. Repeat steps S2 to S5 to achieve real-time frequency stabilization.

[0037] Preferably, before step S1, the method further includes: pre-adjusting the oscillation frequencies of the nonlinear oscillation circuit and the linear oscillation circuit so that the frequency difference between the two is less than a preset threshold, thereby pre-establishing mutual synchronization.

[0038] The beneficial effects of this invention are:

[0039] This invention proposes a frequency stabilization device for MEMS mutual-synchronous oscillators based on axial force control. It utilizes a mutual coupling synchronization mechanism between nonlinear and linear oscillating circuits, adjusting the equivalent stiffness of the linear oscillator to control the oscillation frequency of the entire mutual-synchronous oscillator. A PID controller calculates the output axial voltage control quantity based on the error between the current and set oscillation frequencies, thereby changing the axial force on the linear oscillator in real time, thus regulating the oscillation frequency of the mutual-synchronous oscillator and improving its frequency stability. This invention offers advantages such as excellent real-time performance and high control precision without increasing the complexity of the microsystem, significantly improving the long-term frequency stability of MEMS oscillators. Furthermore, it effectively suppresses oscillator frequency drift in environments where external factors affecting frequency, such as temperature and voltage, change. Attached Figure Description

[0040] Figure 1 This is a schematic diagram of a MEMS mutual synchronization oscillator frequency stabilization device based on axial force control.

[0041] Figure 2 The graph shows the relationship between the axial voltage control quantity obtained from the experiment and the frequency of the linear oscillator.

[0042] Figure 3 This is a flowchart illustrating a method for stabilizing the frequency of a MEMS mutual synchronous oscillator based on axial force control.

[0043] Figure 4 This is a comparison chart showing the frequency stability characterized by Allan variance before and after applying this invention.

[0044] Wherein: 1-1 First transimpedance amplifier; 1-2 First phase detector; 1-3 First loop PI controller; 1-4 First numerically controlled oscillator; 1-5 First adder; 2-1 Second transimpedance amplifier; 2-2 Second phase detector; 2-3 Second loop PI controller; 2-4 Second numerically controlled oscillator; 2-5 Second adder; 3-1 First amplitude controller; 4-1 Second amplitude controller; 5-1 PID controller; 5-2 Axial voltage controller. Detailed Implementation

[0045] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0046] In the description of this invention, it should be understood that the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of indicated technical features. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of this invention, unless otherwise stated, "a plurality of" means two or more.

[0047] In the description of this invention, it should be noted that, unless otherwise explicitly specified and limited, the terms "installation," "connection," and "linking" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal connection of two components. Those skilled in the art can understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0048] The accompanying drawings illustrate various structural schematic diagrams according to embodiments disclosed in this invention. These drawings are not to scale, and some details have been enlarged for clarity, and some details may have been omitted. The shapes of the various regions and layers shown in the drawings, as well as their relative sizes and positional relationships, are merely exemplary and may deviate from reality due to manufacturing tolerances or technical limitations. Furthermore, those skilled in the art can design regions / layers with different shapes, sizes, and relative positions as needed.

[0049] Please see Figure 1 The present invention provides a frequency stabilization device for a MEMS mutual synchronization oscillator based on axial force control, comprising a linear oscillation circuit and a nonlinear oscillation circuit.

[0050] The signal from the nonlinear oscillation loop is injected into the linear oscillation loop via the first amplitude controller 3-1, while the signal from the linear oscillation loop is injected into the nonlinear oscillation loop via the second amplitude controller 4-1, thus establishing a mutually synchronized oscillator. The oscillation frequencies of the linear and nonlinear oscillation loops remain equal throughout the synchronization process. The PID controller 5-1 outputs an axial voltage control quantity based on the error between the current and set oscillation frequencies, changing the oscillation frequency of the linear oscillation loop and synchronously altering the frequency of the signal injected into the nonlinear oscillation loop, thereby stabilizing the oscillation frequency of the mutually synchronized oscillator.

[0051] A nonlinear oscillation circuit enables the nonlinear resonator to achieve self-excited oscillation. It includes a first transimpedance amplifier 1-1, a first phase detector 1-2, a first loop PI controller 1-3, a first numerically controlled oscillator 1-4, and a first adder 1-5. The input of the first transimpedance amplifier 1-1 is connected to the nonlinear resonator. The output of the first transimpedance amplifier 1-1 is input to the nonlinear resonator after passing through the first phase detector 1-2, the first loop PI controller 1-3, the first numerically controlled oscillator 1-4, and the first adder 1-5, thus achieving closed-loop oscillation. The output signal of the first numerically controlled oscillator 1-4 is then fed back to the input of the first phase detector 1-2.

[0052] The linear oscillation circuit enables the linear resonator to achieve self-excited oscillation. It includes a second transimpedance amplifier 2-1, a second phase detector 2-2, a second-loop PI controller 2-3, a second numerically controlled oscillator 2-4, and a second adder 2-5. The input of the second transimpedance amplifier 2-1 is connected to the linear resonator. The output of the second transimpedance amplifier 2-1 is input to the linear resonator after passing through the second phase detector 2-2, the second-loop PI controller 2-3, the second numerically controlled oscillator 2-4, and the second adder 2-5, thus achieving closed-loop oscillation. The output signal of the second numerically controlled oscillator 2-4 is then fed back to the input of the second phase detector 2-2.

[0053] The signal from the nonlinear oscillation circuit output by the first transimpedance amplifier 1-1 is input to the second adder 2-5 in the linear oscillation circuit after passing through the first amplitude controller 3-1. This signal is added to the signal from the linear oscillation circuit output by the second numerically controlled oscillator 2-4, and both signals are input to the linear resonator, thus injecting the signal from the nonlinear oscillation circuit into the linear oscillation circuit. Simultaneously, the signal from the linear oscillation circuit output by the second transimpedance amplifier 2-1 is input to the first adder 1-5 in the nonlinear oscillation circuit after passing through the second amplitude controller 4-1. This signal is added to the signal from the nonlinear oscillation circuit output by the first numerically controlled oscillator 1-4, and both signals are input to the nonlinear resonator, again injecting the signal from the linear oscillation circuit into the nonlinear oscillation circuit, thus establishing mutual synchronization.

[0054] The linear resonator is provided with a first comb-tooth plate and a second comb-tooth plate, which are symmetrically arranged about the axis of the linear resonator and located on the same side of the rhombic beam, such as the lower side of the linear resonator. The axial voltage controller is connected to the first and second comb-tooth plates. Detection electrodes and drive electrodes are symmetrically arranged on the left and right sides of the linear resonator. The PID controller 5-1 is connected to the axial voltage controller 5-2 and receives the signal of the linear oscillation circuit output by the second transimpedance amplifier 2-1. The PID controller 5-1 outputs a voltage control quantity to the axial voltage controller 5-2 according to the error between the current oscillation frequency and the set oscillation frequency. This applies an axial electrostatic force between the first and second comb-tooth plates according to the axial voltage control quantity. The direction of the axial electrostatic force is parallel to the axis of the linear resonator, changing the equivalent bending stiffness of the linear resonator, thereby adjusting the oscillation frequency of the linear oscillation circuit and simultaneously adjusting the oscillation frequency of the nonlinear oscillation circuit.

[0055] In one specific embodiment of the present invention, the nonlinear resonator employs a tuning fork beam fixed at both ends, with a length of 100–500 μm and a width of 5–10 μm for each tuning fork beam. The linear resonator employs a rhomboid beam composed of four straight beams connected together, with a length of 100–500 μm and a width of 5–10 μm for each straight beam.

[0056] In this embodiment, after mutual synchronization is established, the nonlinear oscillation circuit and the linear oscillation circuit have the same oscillation frequency. Changing the oscillation frequency of any oscillation circuit can control and adjust the oscillation frequency of the entire mutual synchronization oscillator. By controlling the axial force applied to the end of the linear oscillator through axial voltage control, the equivalent stiffness and frequency of the linear oscillator are changed, thereby regulating the oscillation frequency of the mutual synchronization oscillator. Figure 2 The graph shows the effect of the axial voltage change on the frequency of the linear oscillator obtained from the experiment. It can be seen that the axial voltage control can change the linear frequency.

[0057] Please see Figure 3The working process of the device of the present invention is as follows: establishing mutual synchronization between the linear oscillator and the nonlinear oscillator, and after system initialization, setting the oscillation frequency of the mutual synchronization oscillator. To obtain the current real-time oscillation frequency of the mutual synchronization oscillator Next, the error between the current oscillation frequency and the set oscillation frequency is calculated. The PID controller outputs an axial voltage control quantity based on this error value, updates the axial force acting on the end of the linear oscillator in real time, adjusts the oscillation frequency of the linear oscillator, and synchronously controls the oscillation frequency of the nonlinear oscillator, thereby realizing the control of the oscillation frequency of the synchronous oscillator.

[0058] The system initialization process is as follows: the oscillation frequencies of the nonlinear oscillation circuit and the linear oscillation circuit are pre-adjusted so that the frequency difference between the two is less than a preset threshold, thereby establishing mutual synchronization in advance.

[0059] Please see Figure 4 When an oscillator is placed in an environment with varying temperature, its oscillation frequency drifts with temperature changes. Compared to the frequency stability of a high-frequency oscillator without the device of this invention, the frequency stability, characterized by Allan variance, is improved by three orders of magnitude over a long-time integration period of 1000 seconds using the device of this invention. Therefore, this invention can effectively suppress temperature drift and significantly improve frequency stability, providing a solution to the problem of frequency shift in MEMS oscillators operating in environments with varying temperature conditions.

[0060] In summary, this invention provides a frequency stabilization device for MEMS mutual synchronization oscillators based on axial force control. It establishes a mutual synchronization oscillator by adjusting the oscillation frequencies of the nonlinear and linear oscillation loops to be close. The axial force acting on the end of the linear oscillator controls the oscillation frequency of the entire mutual synchronization oscillator. By dynamically updating the equivalent stiffness and frequency of the linear oscillator in real time, the oscillation frequency of the mutual synchronization oscillator is controlled, thereby improving frequency stability. This invention achieves flexible control of the oscillation frequency of MEMS oscillators, significantly improving the long-term frequency stability of MEMS oscillators and solving the practical application problems caused by poor oscillator frequency stability.

[0061] The embodiments described above are merely preferred embodiments of the present invention and are not intended to limit the invention. Those skilled in the art can make various changes and modifications without departing from the spirit and scope of the invention. Therefore, all technical solutions obtained through equivalent substitution or transformation fall within the protection scope of the present invention.

Claims

1. A frequency stabilization device for a MEMS mutual synchronization oscillator based on axial force control, characterized in that, include: A linear oscillating circuit includes a linear resonator, wherein a first comb-tooth plate and a second comb-tooth plate are disposed on the linear resonator; Nonlinear oscillating circuit, including a nonlinear resonator; The mutual synchronization injection unit is used to inject the signal of the nonlinear oscillation circuit into the linear oscillation circuit, and the signal of the linear oscillation circuit into the nonlinear oscillation circuit, so that the oscillation frequencies of the two resonators are mutually synchronized. The frequency control unit includes a PID controller and an axial voltage controller; The PID controller is used to output an axial voltage control quantity based on the difference between the current oscillation frequency of the linear resonator and the set frequency. The axial voltage controller is connected to the first comb plate and the second comb plate. According to the axial voltage control amount, an axial electrostatic force is applied between the first comb plate and the second comb plate to change the equivalent bending stiffness of the linear resonator, thereby adjusting the oscillation frequency of the linear oscillation circuit. The oscillation frequency of the nonlinear oscillation circuit is also adjusted synchronously by the mutual synchronization injection unit.

2. The MEMS mutual synchronization oscillator frequency stabilization device based on axial force control according to claim 1, characterized in that, The linear resonator is a rhombic beam structure formed by connecting four straight beams. The first comb plate and the second comb plate are arranged symmetrically about the axis of the linear resonator and are located on the same side of the rhombic beam.

3. The MEMS mutual synchronization oscillator frequency stabilization device based on axial force control according to claim 2, characterized in that, Each straight beam has a length of 100~500μm and a width of 5~10μm.

4. The MEMS mutual synchronization oscillator frequency stabilization device based on axial force control according to claim 1, characterized in that, The nonlinear resonator is a tuning fork beam structure with fixed supports at both ends.

5. The MEMS mutual synchronization oscillator frequency stabilization device based on axial force control according to claim 4, characterized in that, Each tuning fork beam is 100~500μm long and 5~10μm wide.

6. The MEMS mutual synchronization oscillator frequency stabilization device based on axial force control according to claim 1, characterized in that, The mutual synchronization injection unit includes: The first amplitude controller has its input terminal connected to a nonlinear oscillating circuit and its output terminal connected to a linear oscillating circuit. The second amplitude controller has its input connected to a linear oscillating circuit and its output connected to a nonlinear oscillating circuit.

7. The MEMS mutual synchronization oscillator frequency stabilization device based on axial force control according to claim 6, characterized in that, The linear oscillation circuit also includes: The second transimpedance amplifier has its input terminal connected to a linear resonator; A second phase detector, a second loop PI controller, and a second numerically controlled oscillator are connected in series. The input terminal of the second phase detector is connected to the output terminal of the second transimpedance amplifier, and the feedback signal of the second numerically controlled oscillator is connected to the second phase detector. The second adder has its first input terminal connected to the output terminal of the second numerically controlled oscillator, its second input terminal connected to the output of the first amplitude controller of the mutual synchronization injection unit, and its output terminal connected to the linear resonator to form a closed-loop oscillation.

8. The MEMS mutual synchronization oscillator frequency stabilization device based on axial force control according to claim 6, characterized in that, The nonlinear oscillation circuit also includes: The first transimpedance amplifier has its input terminal connected to a nonlinear resonator; A first phase detector, a first loop PI controller, and a first numerically controlled oscillator are connected in series. The input terminal of the first phase detector is connected to the output terminal of the first transimpedance amplifier, and the feedback signal of the first numerically controlled oscillator is connected to the first phase detector. The first adder has its first input terminal connected to the output terminal of the first numerically controlled oscillator, its second input terminal connected to the output of the second amplitude controller of the mutual synchronization injection unit, and its output terminal connected to the nonlinear resonator to form a closed-loop oscillation.

9. A method for stabilizing the frequency of a MEMS inter-synchronous oscillator based on axial force control, applied to the frequency stabilization device for a MEMS inter-synchronous oscillator based on axial force control as described in any one of claims 1 to 8, characterized in that, The method includes the following steps: S1. Set the target oscillation frequency; S2. Obtain the current oscillation frequency from a linear or nonlinear oscillation circuit; S3. Calculate the error between the current oscillation frequency and the target oscillation frequency; S4. Based on the error, the axial voltage control quantity is generated by the PID controller; S5. According to the axial voltage control quantity, apply axial electrostatic force between the first comb plate and the second comb plate of the linear resonator to change the equivalent bending stiffness of the linear resonator, thereby changing the oscillation frequency of the linear oscillation circuit. And adjust the oscillation frequency of the nonlinear oscillation circuit synchronously through the mutual synchronization injection unit so that the output frequency of the device approaches the target oscillation frequency. S6. Repeat S2 to S5 to achieve real-time frequency stabilization.

10. The method for frequency stabilization of MEMS mutual synchronous oscillators based on axial force control according to claim 9, characterized in that, Before S1, the following steps are also included: pre-adjusting the oscillation frequencies of the nonlinear oscillation circuit and the linear oscillation circuit so that the frequency difference between the two is less than a preset threshold, thereby establishing mutual synchronization in advance.

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