CN114137253B - Rigidity modulation MEMS accelerometer and closed-loop control method thereof - Google Patents
Rigidity modulation MEMS accelerometer and closed-loop control method thereof Download PDFInfo
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- CN114137253B CN114137253B CN202111405327.3A CN202111405327A CN114137253B CN 114137253 B CN114137253 B CN 114137253B CN 202111405327 A CN202111405327 A CN 202111405327A CN 114137253 B CN114137253 B CN 114137253B
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01P—MEASURING LINEAR OR ANGULAR SPEED, ACCELERATION, DECELERATION, OR SHOCK; INDICATING PRESENCE, ABSENCE, OR DIRECTION, OF MOVEMENT
- G01P15/00—Measuring acceleration; Measuring deceleration; Measuring shock, i.e. sudden change of acceleration
- G01P15/02—Measuring acceleration; Measuring deceleration; Measuring shock, i.e. sudden change of acceleration by making use of inertia forces using solid seismic masses
- G01P15/08—Measuring acceleration; Measuring deceleration; Measuring shock, i.e. sudden change of acceleration by making use of inertia forces using solid seismic masses with conversion into electric or magnetic values
- G01P15/125—Measuring acceleration; Measuring deceleration; Measuring shock, i.e. sudden change of acceleration by making use of inertia forces using solid seismic masses with conversion into electric or magnetic values by capacitive pick-up
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01P—MEASURING LINEAR OR ANGULAR SPEED, ACCELERATION, DECELERATION, OR SHOCK; INDICATING PRESENCE, ABSENCE, OR DIRECTION, OF MOVEMENT
- G01P15/00—Measuring acceleration; Measuring deceleration; Measuring shock, i.e. sudden change of acceleration
- G01P15/02—Measuring acceleration; Measuring deceleration; Measuring shock, i.e. sudden change of acceleration by making use of inertia forces using solid seismic masses
- G01P15/08—Measuring acceleration; Measuring deceleration; Measuring shock, i.e. sudden change of acceleration by making use of inertia forces using solid seismic masses with conversion into electric or magnetic values
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- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05F—SYSTEMS FOR REGULATING ELECTRIC OR MAGNETIC VARIABLES
- G05F1/00—Automatic systems in which deviations of an electric quantity from one or more predetermined values are detected at the output of the system and fed back to a device within the system to restore the detected quantity to its predetermined value or values, i.e. retroactive systems
- G05F1/10—Regulating voltage or current
- G05F1/46—Regulating voltage or current wherein the variable actually regulated by the final control device is dc
- G05F1/56—Regulating voltage or current wherein the variable actually regulated by the final control device is dc using semiconductor devices in series with the load as final control devices
- G05F1/561—Voltage to current converters
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01P—MEASURING LINEAR OR ANGULAR SPEED, ACCELERATION, DECELERATION, OR SHOCK; INDICATING PRESENCE, ABSENCE, OR DIRECTION, OF MOVEMENT
- G01P15/00—Measuring acceleration; Measuring deceleration; Measuring shock, i.e. sudden change of acceleration
- G01P15/02—Measuring acceleration; Measuring deceleration; Measuring shock, i.e. sudden change of acceleration by making use of inertia forces using solid seismic masses
- G01P15/08—Measuring acceleration; Measuring deceleration; Measuring shock, i.e. sudden change of acceleration by making use of inertia forces using solid seismic masses with conversion into electric or magnetic values
- G01P2015/0862—Measuring acceleration; Measuring deceleration; Measuring shock, i.e. sudden change of acceleration by making use of inertia forces using solid seismic masses with conversion into electric or magnetic values being provided with particular means being integrated into a MEMS accelerometer structure for providing particular additional functionalities to those of a spring mass system
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Abstract
The invention discloses a rigidity modulation MEMS accelerometer and a closed-loop control method thereof, belonging to the technical field of acceleration measurement. The MEMS accelerometer comprises a mass block-spring structure, an adjusting capacitor, an amplitude detection capacitor and a force balance capacitor; the adjusting capacitor is a bilateral parallel plate type variable gap capacitor, and the amplitude detection capacitor and the force balance capacitor are variable area capacitors. The accelerometer includes electrostatic stiffness modulation, amplitude detection, force balancing, and temperature drift calibration and compensation functions. By applying direct-current bias voltage and alternating modulation voltage to the bilateral flat plate capacitor (the adjusting capacitor), the equivalent stiffness is adjusted, the voltage signal representing acceleration and the voltage signal representing the capacitor are modulated, a simple method is provided for acceleration detection, force balance control and temperature drift calibration, and the accuracy and the stability of the accelerometer are improved.
Description
Technical Field
The invention belongs to the technical field of acceleration measurement, and particularly relates to a rigidity modulation MEMS accelerometer and a closed-loop control method thereof.
Background
The electrostatic stiffness trimming technology reduces the equivalent stiffness of devices such as MEMS accelerometers by applying direct current bias voltage on a parallel plate capacitor, thereby realizing stiffness modulation accelerometers, even quasi-zero stiffness accelerometers. To improve low stiffness accelerometer range and linearity, a reference position based closed loop control technique is applied to the closed loop accelerometer. Generally, the displacement of the accelerometer under the action of acceleration is directly extracted from a variable-area or variable-gap displacement detection capacitor, and compared with an initial manually calibrated reference position, and PID (proportion integration differentiation) operation is performed based on a deviation value to obtain a feedback control voltage, so that force balance control is realized. According to the closed-loop control method, when the temperature changes, the gains of feed-forward loops such as a capacitance reading circuit and the like are changed along with the temperature change, so that the actual reference position shifts, and the output drift of the closed-loop accelerometer is caused. The resulting temperature drift typically needs to be calibrated and compensated for by means of external sensors or by using complex resonant frequency self-calibration detection methods, adding to the complexity of the accelerometer system.
Disclosure of Invention
Aiming at the defects and shortcomings of the existing closed-loop MEMS accelerometer, the invention provides a rigidity modulation MEMS accelerometer and a closed-loop control method thereof, which utilize a bilateral flat plate type capacitor (a regulating capacitor) to simultaneously apply direct current bias voltage and alternating modulation voltage, on one hand, the equivalent rigidity of the accelerometer is reduced, and on the other hand, the displacement of the accelerometer is modulated to generate an alternating driving force and amplitude related to the displacement; the amplitude signal is calculated based on demodulation and other processing, the reference position does not need to be manually set, PID operation is directly carried out on the amplitude signal to obtain feedback control voltage, a force balance closed loop is established, and a moving electrode of a bilateral plate capacitor connected with the mass block is always positioned at a geometric center position; meanwhile, capacitance change of the bilateral flat plate type capacitor is obtained through demodulation signal processing in parallel, so that feed-forward loop gain change caused by temperature change is detected, and temperature drift calibration and compensation functions are completed.
The technical scheme adopted by the invention is as follows:
a stiffness modulation MEMS accelerometer comprises a mass block-spring structure, an amplitude detection capacitor, an adjusting capacitor, a force balance capacitor and an anchor area;
the mass block-spring structure and the adjusting capacitor form an acceleration sensitive electromechanical system, the spring structure and the adjusting capacitor respectively have positive stiffness and negative stiffness, and the mass block is displaced under the action of acceleration;
the adjusting capacitor consists of a variable-gap type bilateral plate capacitor and comprises a movable plate electrode and a fixed plate electrode which are distributed at equal intervals, the movable plate electrode is connected with the mass block, and the fixed plate electrode is connected with the anchor area; the adjusting capacitor generates electrostatic negative stiffness under the action of direct-current bias voltage, and generates alternating driving force under the action of alternating modulation voltage, and the magnitude of the driving force is related to the displacement of the movable electrode;
the amplitude detection capacitor consists of a group of differential variable-area displacement detection capacitors, and carrier modulation of capacitance change signals is realized by applying carrier voltages with the same amplitude and opposite signs on the differential electrodes;
the force balance capacitor is composed of a group of area-variable force balance capacitors, and the mass block works on the geometric center position by applying force on the differential electrode to balance feedback control voltage.
According to the control method of the stiffness modulation MEMS accelerometer, the equivalent stiffness of the accelerometer is subjected to stiffness modification by applying direct-current bias voltage to a regulating capacitor; meanwhile, alternating-current modulation voltage is applied to the adjusting capacitor to generate alternating driving force, and the magnitude of the driving force is related to displacement of the accelerometer due to external acceleration; the accelerometer generates forced vibration under the action of alternating driving force; and directly carrying out proportional-integral-differential operation on the demodulated vibration amplitude to obtain feedback control voltage output by a closed loop, and applying the feedback control voltage to the force balance electrode to enable the mass block to always work at the geometric center position.
Further, the specific steps of adjusting the capacitance to generate the stiffness adjustment and the displacement modulation are as follows:
1.1) applying a DC bias voltage V to the regulating capacitor dc And an alternating modulation voltage V t (frequency is ω t )；
1.2) the mass block-spring structure generates vibration under the combined action of external acceleration, direct current bias voltage and alternating modulation voltage;
1.3) applying a pair of differential carrier signals with the same amplitude and opposite signs on an amplitude detection capacitor, converting a vibration amplitude signal into a capacitance change signal, and obtaining an alternating voltage signal representing the amplitude through a CV (constant voltage) conversion circuit;
1.4) carrying out twice demodulation signal processing on the alternating voltage signal for representing the amplitude, namely carrier demodulation and 2 omega demodulation t Frequency demodulation, low-pass filtering to obtain voltage signal V representing amplitude 1 (ii) a Wherein, ω is t For alternating modulating voltage V t The frequency of (d);
1.5) directly on the voltage signal V characterizing the amplitude 1 Performing proportional-integral-derivative (PID) operation to obtainFeedback control voltage V 2 And the electrostatic force for counteracting the inertia force is generated to make the moving electrode of the regulating capacitor always in the geometric center position.
Further, while the step of applying the feedback control voltage to the force balance electrode, the method further comprises the steps of calibrating a temperature effect of the feed-forward loop gain and compensating on the feedback control voltage, specifically:
carrying out demodulation signal processing and low-pass filtering processing on the alternating voltage signal representing the amplitude in parallel, wherein the demodulation frequency is omega t Obtaining a voltage signal V representing the capacitance on the regulating capacitor 3 And obtaining feedback control voltage drift amount delta V of closed loop output by a temperature drift calibration method 2 And V 3 Relational expression therebetween Δ V 2 ＝f(V 3 ) Finally, the drift amount DeltaV caused by temperature change is compensated on the feedback control voltage of the closed loop output 2 To obtain feedback control voltage V of compensated closed loop output a ＝V 2 -f(V 3 ) And is applied to the force balance capacitance electrode; wherein V 2 To compensate for the feedback control voltage of the front closed loop output.
Generally, compared with the prior art, the technical scheme of the invention has the following beneficial effects:
(1) the invention applies a novel rigidity modulation mode, and applies direct current bias voltage and alternating modulation voltage on a bilateral flat capacitor (an adjusting capacitor), thereby realizing the adjustment of equivalent rigidity, realizing the modulation of a voltage signal representing displacement and a voltage signal representing the capacitor, and providing a simple method for displacement detection, force balance closed loop and temperature drift calibration.
(2) The invention provides a novel acceleration detection method and a closed-loop control method thereof, displacement change caused by acceleration is further modulated into amplitude change, amplitude is extracted by demodulation signal processing, feedback control voltage is directly obtained through PID operation, and a force balance closed loop is established, so that a movable electrode of a bilateral plate capacitor connected with a mass block is always positioned at a geometric center position. Compared with the conventional closed-loop control method, the method does not need to carry out initial manual calibration or automatic calibration of the reference position and compare the displacement signal with the reference position, is favorable for accelerometer engineering, effectively avoids the calibration error of the reference position and ensures the precision of closed-loop control.
(3) The invention provides a simple temperature calibration and compensation method based on capacitance detection, which can perform feedforward loop gain change detection on capacitance change of a regulating capacitor in parallel without influencing closed-loop control, and establish a temperature drift calibration and compensation loop without depending on an external temperature sensor according to the relation between a voltage signal representing the capacitance on the regulating capacitor and closed-loop output feedback control voltage.
Drawings
FIG. 1 is a schematic structural diagram of a stiffness-modulated MEMS accelerometer provided by an embodiment of the invention;
FIG. 2 is a schematic diagram of control signals of a stiffness-modulated MEMS accelerometer provided by an embodiment of the invention;
in the attached drawing, 1 is a mass block, 2 is a variable area type force balance capacitor, 3 is an elastic beam, 4 is a variable area type amplitude detection capacitor, 5 is a variable gap type bilateral plate capacitor, 6 is an anchor area, V is a For force-balanced closed-loop control of voltage, V b For balancing the circuit bias voltage, V c Is a carrier voltage, V dc Is a DC bias voltage, V t For alternating modulating voltage, V 1 To characterize the amplitude of the voltage signal, V 2 To feed back the control voltage.
Detailed Description
In order to more clearly express the objects, technical solutions and advantages of the present invention, the following derivation is further explained with reference to the drawings and formulas. It is to be understood that the principles herein are to be interpreted as illustrative, and not in a limiting sense.
The invention comprises a speed sensitive unit formed by a mass block-spring structure, an amplitude detection capacitor, an adjusting capacitor, a force balance capacitor and other meter head structures. Fig. 1 is a schematic structural diagram of a stiffness-modulated MEMS accelerometer provided in an embodiment of the present invention, which includes a mass block 1, a variable area force balance capacitor 2, an elastic beam 3, a variable area amplitude detection capacitor 4, a variable gap type bilateral plate capacitor 5, and an anchor region 6.
With reference to fig. 1 and 2, the acceleration sensing unit includes a mass 1 and a flexible beam 3 structure, and the mass 1 is connected to an anchor region 6 in the horizontal sensing axis direction through the flexible beam 3 structure.
The adjusting capacitor is composed of a variable gap type bilateral plate capacitor 5 and comprises a movable plate electrode and a fixed plate electrode, wherein the movable plate electrode is connected with the mass block 1, the fixed plate electrode is connected with the anchor area 6, the movable plate electrode and the fixed plate electrode are symmetrically distributed in a central axis mode, and namely the movable plate electrode is consistent with the gap of the fixed plate electrode along the positive and negative directions of the sensitive axis. The gap-variable type double-side plate capacitor 5 is under the DC bias voltage V dc Generating electrostatic negative rigidity under the action of the static electricity; the gap-variable type double-sided plate capacitor 5 is at the alternating modulation voltage V t (frequency is ω t ) Vibration is generated under the action of the vibration generator.
The amplitude detection capacitor is composed of a group of differential area-variable displacement detection capacitors 4, and carrier voltages +/-V with the same amplitude and opposite signs are applied to differential electrodes c And a capacitance variation signal is extracted through the mass block electrode, and is processed by CV readout circuit and demodulation (carrier demodulation and 2 omega) t Demodulation) and low-pass filtering (LPF) to obtain a voltage signal V representing the amplitude 1 。
The force balance capacitor is composed of a group of area-variable force balance capacitors 2, and a pair of force balance voltages V applied to the differential electrode are obtained by a force balance control signal through a push-pull circuit b ±V a . The mass is operated in a geometrically centered position by applying a force balancing voltage across the differential electrodes.
In the invention, the voltage V modulated by alternating current is adjusted on the capacitor t The resulting vibration amplitude is:
y 2 ＝Ycos(2ω t t-θ)
where Y and theta are the amplitude and phase of forced vibration, epsilon is the dielectric constant, A is the overlapping area of the fixed plate capacitor and the moving plate capacitor, and V t And omega t For alternating modulation voltage and frequency, alpha is the DC bias voltage coefficient, d 0 Initial gap for moving plate capacitor and fixed plate capacitor, mass and damping for accelerometer, k mechanical stiffness for accelerometer, ω n For the resonant frequency of the accelerometer, F 0 And N is alternating electrostatic force, N is the logarithm of the bilateral flat plate capacitance, zeta is the damping ratio, and x is the displacement of the mass block of the accelerometer.
Based on the above characteristics of the MEMS accelerometer of the present invention, in one specific implementation of the present invention, an acceleration signal is obtained based on a stiffness modulation and amplitude detection method, a PID operation is directly performed on the amplitude to obtain a feedback control voltage, and the feedback control voltage is applied to a force balance capacitor to achieve the force balance of the accelerometer.
The closed-loop control method specifically comprises the following steps:
1.1) applying a DC bias voltage V to the regulating capacitor dc And an alternating modulation voltage V t (frequency is ω t )；
1.2) acceleration sensitive unit composed of mass block 1 and elastic beam 3 structure is accelerated at outsideDC/DC bias voltage V dc And an alternating modulation voltage V t The vibration is generated under the combined action;
1.3) by applying a pair of differential carrier signals with the same amplitude and opposite signs on an amplitude detection capacitor c The amplitude signal can be converted into a capacitance change signal, and an alternating voltage signal representing the amplitude is read out through a CV (constant voltage) conversion circuit;
1.4) two demodulation signal processing (carrier demodulation and 2 ω) of the amplitude-characterizing alternating voltage signal t Demodulation) and low-pass filtering to obtain voltage signal V representing amplitude 1 ；
1.5) directly comparing the voltage signal V representing the amplitude 1 Proportional-integral-derivative (PID) operation is carried out to obtain force balance feedback control voltage V 2 And is applied on the force balance electrode to generate an electrostatic force for offsetting the inertia force, so that the mass is always positioned at the geometric center position.
Based on the above characteristics of the MEMS accelerometer of the present invention, in one embodiment of the present invention, the temperature drift of the accelerometer is calibrated and compensated for, thereby maintaining the output of the accelerometer constant during temperature changes.
The accelerometer temperature drift calibration and compensation method proposed by the present invention is described in detail below with reference to the schematic diagram shown in fig. 2.
The temperature drift calibration and compensation method comprises the following steps:
2.1) firstly, placing the accelerometer system in an incubator to prepare for power supply and signal transmission;
2.2) establishing an amplitude detection and force balance closed loop according to the steps 1.1) -1.5);
2.3) demodulating the amplitude signal output from the CV conversion circuit (demodulation frequency of ω t ) Low-pass filtering to obtain voltage signal V representing the capacitance on the regulating capacitor 3 ；
2.4) changing the temperature of the incubator from-45 to 85 ℃ by taking 5 ℃ as a step length, maintaining each temperature test point for more than 20 minutes, and recording V on each temperature test point 3 Variable and closed loop output V 2 Change data;
2.5) according to the data, establishing a voltage signal V representing the capacitance on the regulating capacitor 3 And a closed loop output feedback control voltage V 2 The relation f (V) between 3 ) Obtaining a closed-loop output V after temperature compensation a ＝V 2 -f(V 3 ) I.e. compensated force balance closed loop control voltage V a 。
In conclusion, the invention has the functions of electrostatic rigidity modulation, amplitude detection, force balance and temperature drift calibration and compensation. The electrostatic rigidity modulation is to adjust the equivalent rigidity of the accelerometer and generate forced vibration by adjusting a mode of simultaneously applying bias direct current voltage and alternating modulation voltage on a capacitor; amplitude detection is achieved by applying a differential carrier signal (carrier frequency ω) through an amplitude detection capacitor c ) The amplitude signal is modulated again and finally subjected to secondary demodulation (carrier demodulation and 2 ω demodulation) t Demodulation) and low-pass filtering operation to solve the amplitude signal V 1 (ii) a The force balance being obtained by directly applying an amplitude signal V 1 Obtaining a feedback control voltage V through the operation of a PID controller 2 Applying the feedback control voltage to the force balance capacitor to generate a return electrostatic force for offsetting the inertia force, so that the mass block always works at the geometric center position; the calibration of temperature drift is carried out by processing the output of CV conversion circuit with demodulated signal (frequency of demodulation is omega) t ) And low-pass filtering operation to obtain capacitance signal V on the regulating capacitor 3 Thereby representing the gain change condition of the feedforward loop and obtaining the closed loop output drift and V through a calibration experiment 3 Relational expression f (V) between 3 ) Finally, the drift amount (V) caused by temperature change is compensated on the closed loop output 2 -f(V 3 ))。
The invention creatively modulates the displacement change generated by the acceleration into the amplitude change in the acceleration detection, can directly obtain the position deviated from the geometric center without calculating the relative displacement change, avoids the defect that the relative displacement is easily influenced by the temperature, and can realize more accurate measurement; in addition, the invention directly obtains the feedback control voltage by PID operation, establishes a force balance closed loop and provides a simpler method.
It should be understood by those skilled in the art that the foregoing is only a preferred embodiment of the present invention, and is not intended to limit the invention, and that any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the scope of the present invention.
Claims (3)
1. A control method of a stiffness modulation MEMS accelerometer comprises a mass block-spring structure, an amplitude detection capacitor, an adjusting capacitor, a force balance capacitor and an anchor area;
the mass block-spring structure and the adjusting capacitor form an acceleration sensitive electromechanical system, the spring structure and the adjusting capacitor respectively have positive stiffness and negative stiffness, and the mass block is displaced under the action of acceleration;
the adjusting capacitor consists of a variable-gap type bilateral plate capacitor and comprises a movable plate electrode and a fixed plate electrode which are distributed at equal intervals, the movable plate electrode is connected with the mass block, and the fixed plate electrode is connected with the anchor area; the adjusting capacitor generates electrostatic negative stiffness under the action of direct-current bias voltage, and generates alternating driving force under the action of alternating modulation voltage, and the magnitude of the driving force is related to the displacement of the movable electrode;
the amplitude detection capacitor consists of a group of differential variable-area displacement detection capacitors, and carrier modulation of capacitance change signals is realized by applying carrier voltages with the same amplitude and opposite signs on the differential electrodes;
the force balance capacitor is composed of a group of area-variable force balance capacitors, and the mass block works on the geometric center position by applying force on the differential electrode to balance feedback control voltage;
the method is characterized in that the equivalent rigidity of the accelerometer is subjected to rigidity modification by applying direct-current bias voltage to the adjusting capacitor; meanwhile, alternating-current modulation voltage is applied to the adjusting capacitor to generate alternating driving force, and the magnitude of the driving force is related to displacement of the accelerometer due to external acceleration; the accelerometer generates forced vibration under the action of alternating driving force; directly carrying out proportional-integral-differential operation on the demodulated vibration amplitude to obtain feedback control voltage output by a closed loop, and applying the feedback control voltage to a force balance electrode to enable a mass block to always work at a geometric center position;
the specific steps of adjusting the capacitance to generate rigidity adjustment and displacement modulation are as follows:
1.1) applying a DC bias voltage V to the regulating capacitor dc And an alternating modulation voltage V t ；
1.2) the mass block-spring structure generates vibration under the combined action of external acceleration, direct current bias voltage and alternating modulation voltage;
1.3) applying a pair of differential carrier signals with the same amplitude and opposite signs on an amplitude detection capacitor, converting a vibration amplitude signal into a capacitance change signal, and obtaining an alternating voltage signal representing the amplitude through a CV (constant voltage) conversion circuit;
1.4) carrying out twice demodulation signal processing on the alternating voltage signal representing the amplitude, namely carrier demodulation and 2 omega demodulation t Frequency demodulation, low-pass filtering to obtain voltage signal V representing amplitude 1 (ii) a Wherein, ω is t For alternating modulating voltage V t The frequency of (c);
1.5) directly on the voltage signal V characterizing the amplitude 1 Performing proportional-integral-differential operation to obtain feedback control voltage V 2 And the static force which counteracts the inertia force is generated to ensure that the movable electrode of the adjusting capacitor is always positioned at the geometric center position.
2. The method of claim 1, further comprising the steps of calibrating the temperature effect of the feed forward loop gain and compensating on the feedback control voltage, while the step of applying the feedback control voltage to the force balance electrode, in particular:
carrying out demodulation signal processing and low-pass filtering processing on the alternating voltage signal representing the amplitude in parallel, wherein the demodulation frequency is omega t Obtaining a voltage signal V representing the capacitance on the regulating capacitor 3 And obtaining feedback control voltage drift amount delta V of closed loop output by a temperature drift calibration method 2 And V 3 Relational expression therebetween Δ V 2 ＝f(V 3 ) Finally, the drift amount DeltaV caused by temperature change is compensated on the feedback control voltage of the closed loop output 2 To obtain feedback control voltage V of compensated closed loop output a ＝V 2 -f(V 3 ) And is applied to the force balance capacitance electrode; wherein V 2 To compensate for the feedback control voltage of the front closed loop output.
3. The method of claim 1, wherein the amplitude of the vibration induced on the tuning capacitor by the alternating modulation voltage is:
y 2 ＝Y cos(2ω t t-θ)
where Y and theta are the amplitude and phase of forced vibration, epsilon is the dielectric constant, A is the overlapping area of the fixed plate capacitor and the moving plate capacitor, and V t And ω t For alternating modulation voltage and frequency, alpha is the DC bias voltage coefficient, d 0 Initial gap for moving plate capacitor and fixed plate capacitor, mass and damping for accelerometer, k mechanical stiffness for accelerometer, ω n For the resonant frequency of the accelerometer, F 0 The alternating electrostatic force is N is the bilateral plate capacitance logarithm, zeta is the damping ratio, and x is the displacement of the mass block under the action of the external acceleration.
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