CN112146637A - Full-angle mode circuit gain error self-compensation system of micro-electromechanical gyroscope - Google Patents
Full-angle mode circuit gain error self-compensation system of micro-electromechanical gyroscope Download PDFInfo
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
- G01C19/00—Gyroscopes; Turn-sensitive devices using vibrating masses; Turn-sensitive devices without moving masses; Measuring angular rate using gyroscopic effects
- G01C19/56—Turn-sensitive devices using vibrating masses, e.g. vibratory angular rate sensors based on Coriolis forces
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
- G01C19/00—Gyroscopes; Turn-sensitive devices using vibrating masses; Turn-sensitive devices without moving masses; Measuring angular rate using gyroscopic effects
- G01C19/56—Turn-sensitive devices using vibrating masses, e.g. vibratory angular rate sensors based on Coriolis forces
- G01C19/5776—Signal processing not specific to any of the devices covered by groups G01C19/5607 - G01C19/5719
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- H—ELECTRICITY
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- H03M—CODING; DECODING; CODE CONVERSION IN GENERAL
- H03M1/00—Analogue/digital conversion; Digital/analogue conversion
- H03M1/06—Continuously compensating for, or preventing, undesired influence of physical parameters
Abstract
The invention discloses a full-angle mode circuit gain error self-compensation system of a micro-electromechanical gyroscope, which comprises a gyroscope preamplification circuit, an ADC (analog to digital converter) module, a gain compensation module, a demodulation module, a parameter calculation module, a PI (proportional-integral) controller module, a coordinate conversion module, a compensation coefficient calculation module, a modulation module and a DAC (digital to analog converter) module, wherein the gyroscope preamplification circuit is connected with the ADC module; the preamplification circuit module is connected with a detection electrode of the micro-electromechanical multi-ring gyroscope; the ADC module is connected with the pre-amplification circuit; the gain compensation module is connected with the ADC module; the demodulation module is connected with the gain compensation module; the PI controller module is connected with the parameter calculation module; the compensation coefficient calculation module is connected with the PI controller module; the coordinate conversion module is connected with the PI controller module; the modulation module is connected with the coordinate conversion module; the DAC module is connected with the modulation module; the digital control oscillator module is connected with the PI controller; the invention can realize the real-time circuit gain error self-compensation in the full-angle mode of the micro-electromechanical gyroscope.
Description
Technical Field
The invention belongs to the field of micro-electro-mechanical systems, and particularly relates to a full-angle mode circuit gain error self-compensation system of a micro-electro-mechanical gyroscope.
Background
A Micro Electro Mechanical System (MEMS) gyroscope is used as a novel gyroscope, monocrystalline silicon is used as a main body processing material, and the MEMS gyroscope is processed by adopting a mature MEMS technology and has the advantages of small energy dissipation, high mechanical sensitivity, concentrated quality, small mechanical noise and the like compared with a traditional mechanical structure gyroscope. Micro-electromechanical (MEMS) gyroscopes occupy an important position in the gyroscopic field, because of their advantages mentioned above.
In practical application, a micro-electromechanical system (MEMS) gyroscope can work in a full-angle mode, and although the structure of a full-angle measurement and control circuit system is complex, the rotation angle of the gyroscope can be directly output. However, in most application cases, the Q values (quality factors) of the two modes of the micro-electromechanical gyroscope are different, so the actual gains of the x and y axes are also different, and meanwhile, because two circuits in the full-angle mode have gain errors, the two gain errors are integrated into a circuit gain error. The angle resolution of the full angle mode can introduce the error, so that the residual error of the angle output becomes large, and the angle detection precision and accuracy are reduced.
Disclosure of Invention
The invention aims to provide a full-angle mode circuit gain error self-compensation system of a micro-electromechanical gyroscope, so as to realize automatic compensation of circuit gain errors in a full-angle circuit of the micro-electromechanical gyroscope.
The technical solution for realizing the purpose of the invention is as follows:
a full-angle mode circuit gain error self-compensation system of a micro electro mechanical gyroscope comprises a pre-amplification circuit module, an ADC (analog to digital converter) module, a gain compensation module, a demodulation module, a parameter calculation module, a PI (proportional-integral) controller module, a compensation coefficient calculation module, a coordinate conversion module, a modulation module, a DAC (digital to analog converter) module and a digital control oscillator module;
the preamplification circuit module is connected with a driving electrode and a detection electrode of the micro-electromechanical multi-ring gyroscope and is used for amplifying a detection signal output by a differential detection electrode of the micro-electromechanical multi-ring gyroscope;
the ADC module is used for converting the analog signal output by the pre-amplification circuit into a digital signal;
the gain compensation module multiplies the digital signals output by the ADC module by a first gain compensation coefficient and a second gain compensation coefficient respectively to realize circuit gain error compensation;
the demodulation module is used for demodulating out signals with orthogonal and in-phase phases in the digital signals and outputting four paths of signals;
the parameter calculator module is used for carrying out logical operation on the demodulated signals to obtain the total energy change, the orthogonal error energy change, the phase error of the vibration signals and the rotation angle of the gyroscope of the micro-electro-mechanical multi-ring gyroscope;
the PI controller module enables the obtained change signal to be stable and outputs a stable energy control signal, an orthogonal energy control signal and a phase error control signal;
the coordinate conversion module is used for distributing the total energy control signal and the orthogonal energy control signal output by the PI controller module to four paths of outputs according to the rotation angle of the gyroscope;
the modulation module is used for modulating the four paths of output signals of the coordinate conversion module to carrier signals generated by the digital control oscillator module, and adding the four paths of output signals to obtain two paths of output;
the DAC module is used for converting the two paths of digital signals output by the modulation module into analog signals; analog signals are input to a driving electrode of the micro-electro-mechanical multi-ring gyroscope through a voltage buffer circuit of the preamplifier circuit;
the compensation coefficient calculation module is used for recording Eout signals of the gyroscope rotating by 0 degree and 90 degrees, calculating a first gain compensation coefficient and a second gain compensation coefficient, and sending the coefficients into the gain compensation module;
the digital control oscillator module is controlled by the phase error control signal to generate two paths of orthogonal reference sinusoidal signals for modulation and demodulation, and the frequency and the phase of the reference sinusoidal signals track the frequency and the phase of the vibration signals of the micro-electromechanical multi-ring gyroscope harmonic oscillator.
Compared with the prior art, the invention has the following remarkable advantages:
(1) according to the invention, the currently required gain error compensation coefficient is calculated by recording the Eout signals of the gyroscope rotating by 0 degree and 90 degrees, so that automatic gain compensation is realized, and the angle detection precision and the control precision of the whole full-angle mode circuit are improved.
(2) The invention can directly output the detection angle, and has the advantages of higher angle detection precision and higher response speed because of the reduction of one-stage time integration compared with other speed detection circuits of the micro-electromechanical multi-ring gyroscope.
(3) Compared with the common full-angle gain compensation circuit, the gain coefficient of the full-angle gain compensation circuit is calculated in real time, the gain error compensation of the circuit can be well realized under the condition that environmental factors such as temperature, pressure and the like change, and the full-angle gain compensation circuit has wide environmental adaptability and reliability.
Drawings
FIG. 1 shows a method for self-compensating gain error of a full angle mode circuit of a micro electro mechanical gyroscope according to the present invention.
Detailed Description
The invention is further described with reference to the following figures and embodiments.
The micro-electromechanical gyroscope applicable to the system has two electrode axes, namely an x axis and a y axis, wherein the x axis comprises 1 driving electrode DB and 2 differential detection electrodes (SB & lt- & gt & lt- & gt); the y-axis contains 1 drive electrode DA, 2 differential detection electrodes (SA-, SA +). Because the micro-electro-mechanical multi-ring gyroscope has structural asymmetry and asymmetry of damping and rigidity caused by processing process errors, the rotation angle theta of the micro-electro-mechanical multi-ring gyroscope is a result of the comprehensive action of factors such as an error of unmatched attenuation time constants caused by an actual rotation angle and time delay, frequency difference delta omega of two electrode axes, a phase mismatch error existing in an actual loop and the like.
The invention relates to a full-angle measurement and control circuit method of a micro-electromechanical multi-ring gyroscope, which comprises a preamplification circuit module 1, an ADC module 2, a gain compensation module 3, a demodulation module 4, a parameter calculation module 5, a PI controller module 6, a compensation coefficient calculation module 7, a coordinate conversion module 8, a digital control oscillator module 9, a modulation module 10 and a DAC module 11;
the preamplification circuit module 1 is connected with a driving electrode and a detection electrode of the micro-electromechanical gyroscope and is used for amplifying detection signals output by differential detection electrodes (SA-, SA +) and (SB-, SB +) of the micro-electromechanical multi-ring gyroscope; the preamplification circuit 1 is a charge detection circuit and can detect electrode charge change caused by vibration of an internal harmonic oscillator in the micro-electromechanical multi-ring gyroscope.
The ADC module 2 is connected with the pre-amplification circuit 1, and the ADC module 2 is used for converting the analog signals output by the pre-amplification circuit into digital signals. The ADC module 2 employs an ADC chip AD7903 commercially available from AD corporation. The digital signal converted by the ADC module 2 comprises amplitude and phase signals of a vibration signal of a harmonic oscillator inside the micro-electromechanical multi-ring gyroscope.
When the micro-electromechanical gyroscope works, the motion equation is as follows:
x is the vibration displacement of the 0 degree electrode axis of the micro-electromechanical multi-ring gyroscope, theta is the rotation angle of the gyroscope, omega1Is the resonant frequency of the electrode axis at 0 DEG, y is the vibrational displacement of the electrode axis at 45 DEG, omega2Is the resonant frequency of the 45 deg. electrode axis. a is the amplitude of the antinode of the harmonic oscillator standing wave of the micro-electromechanical multi-ring gyroscope, and q is the amplitude of the node. In the case of mode matching, ω1＝ω2And ω is the resonance frequency of the electrode shaft after mode matching, i.e. the frequency difference Δ ω between the two electrode shafts is 0. t is the rotation time of the gyroscope,
is the phase of the vibration signal.
In an actual circuit, due to the difference of x and y axis Q values of the micro-electromechanical gyroscope and gain errors in an amplifying circuit, circuit gain errors are caused. The actual ADC block outputs signals:
x'＝x*gainx
y′＝y*gainy
gainxgain of the circuit for the x-axisyIn the y-axisAnd (4) circuit gain. x 'is the vibration displacement of the x axis of the micro-electromechanical multi-ring gyroscope after considering the actual gain, and y' is the vibration displacement of the y axis of the micro-electromechanical multi-ring gyroscope after considering the actual gain.
The gain compensation module 3 is connected with the ADC module 2, and is used for compensating circuit gain errors. The gain compensation module 3 multiplies the first path of signal in the ADC module 2 by a gain compensation coefficient k1Multiplying the second path signal in the ADC module 2 by a gain compensation coefficient k2The circuit gain error is compensated by changing the coefficients. The signal after the circuit gain error compensation is as follows.
x″＝x′*k1
y″＝y′*k2
And x 'is the vibration displacement of the x axis of the micro-electromechanical multi-ring gyroscope after gain compensation, and y' is the vibration displacement of the y axis of the micro-electromechanical multi-ring gyroscope after gain compensation.
The demodulation module 4 is connected to the gain compensation module 3, and the demodulation module 4 is configured to demodulate out signals with orthogonal and in-phase phases existing in the digital signal. The demodulation module 4 outputs four paths of signals cx, sx, cy, sy. Signals cx and sx respectively represent an in-phase part and an orthogonal part of the harmonic oscillator x-axis vibration signal; the signals cy, sy represent the in-phase and quadrature parts of the harmonic oscillator y-axis vibration signal, respectively.
cx＝LPF(x″*cos(ωt+φ))
sx＝LPF(x″*sin(ωt+φ))
cy＝LPF(y″*cos(ωt+φ))
sy＝LPF(y″*sin(ωt+φ))
cos (ω t + φ) is the in-phase reference signal for demodulation, sin (ω t + φ) is the quadrature reference signal, LPF represents low pass filtering; phi is the phase of the reference signal.
And the parameter calculator module 5 is connected with the demodulation module 4 and is used for carrying out logical operation on the demodulated signals to obtain the total energy change E, the orthogonal error energy change Q, the phase error L of the vibration signal and the rotation angle theta of the gyroscope of the micro-electro-mechanical multi-ring gyroscope. The algorithm of the parameter calculation module 5 is as follows:
E＝cx2+cy2+sx2+sy2
Q＝2*(cx*sy-cy*sx)
L＝2*(cx*sx+cy*sy)
the PI controller module 6 is connected to the parameter calculation module 5, and has a proportional and integral control link, so that the obtained change signals (total energy change E, quadrature error energy change Q, and phase error L) are kept stable, and stable energy control signal Eout, quadrature energy control signal Qout, and phase error control signal Lout are output.
The compensation coefficient calculation module 7 is connected with the PI controller module, and the compensation coefficient calculation module 7 is used for recording the Eout signal size when the rotation angle theta is 0 DEG and 90 DEG, namely Eout0And Eout90. At initial state, gain compensation coefficient k1，k21, Eout when the rotation angle is 0 DEG0The output signal contains an x-axis gainx(ii) a Eout when the rotation angle is 90 DEG90The output signal contains a y-axis gainy. By comparing Eout0And Eout90Obtaining the gain error ratio of x and y axes, writing the gain compensation coefficient k2。
Setting gain compensation coefficient k when general compensation circuit is working1Is 1 constant, gain compensation coefficient k2Obtained by calculation. Gain compensation coefficient k for every 360 degrees of rotation of the gyroscope2All will be recalculated once, k after calculation2And k1And sending the signal into a gain compensation module.
The coordinate conversion module 8 is connected to the PI controller module 6, and is configured to distribute the total energy control signal Eout and the orthogonal energy control signal Qout output by the PI controller module 6 to four paths of outputs Fcx, Fsx, Fcy, and Fsy according to the gyro rotation angle θ. The algorithm of the coordinate transformation module 8 is as follows:
Fcx＝Eout*cosθ
Fcy＝-Qout*sinθ
Fcy＝Eout*sinθ
Fsy＝Qout*sinθ
the modulation module 10 is connected to the coordinate conversion module 8, and is configured to modulate the four output signals Fcx, Fsx, Fcy, Fsy of the coordinate conversion module 8 onto a carrier signal generated by the numerically controlled oscillator module 9, perform logical operation after modulation, and obtain two output signals Fx and Fy after operation. The algorithm of the modulation module is as follows:
Fx＝Fcx*cos(ωt+φ)+Fsx*sin(ωt+φ)
Fy＝Fcy*cos(ωt+φ)+Fsy*sin(ωt+φ)
the DAC module 11 is connected to the modulation module 10, and is configured to convert the two paths of digital signals Fx and Fy output by the modulation module 10 into analog signals.
The micro-electromechanical gyroscope is connected with the DAC module 11, and analog signals converted by the DAC module 11 are directly input to driving electrodes (DA, DB) of the micro-electromechanical gyroscope.
The digital control oscillator module 9 is connected with the PI controller module 6, a phase error control signal Lout of the PI controller module 6 is input into the digital control oscillator module 9, the digital control oscillator module 9 is controlled by the phase error control signal Lout to generate two paths of phase orthogonal reference sinusoidal signals for modulation and demodulation, and the frequency and the phase of the reference sinusoidal signals track the frequency and the phase of vibration signals of the MEMS multi-ring gyroscope harmonic oscillator. The reference signal generated by the numerically controlled oscillator module 9 is formulated as follows:
singalin_pasefor in-phase reference signals, singleout_pahseIs a quadrature reference signal.
In this embodiment, the preamplifier circuit 1 of the measurement and control circuit system adopts analog devices including an amplifier chip AD8642, a voltage stabilization chip ADR01, and an ADR 02; the ADC and DAC modules adopt high-precision ADC and DAC chips of an AD company, and the ADC and DAC chips comprise AD7903 and AD 7173; the gain compensation module, the modulation module, the demodulation module and the digital control oscillator module are all designed in a commercialized FPGA chip; the coordinate conversion module, the parameter calculation module, the compensation coefficient calculation module and the PI controller module are all designed in an ARM-Cortex-A9 processor designed by ARM company. The communication between the FPGA chip and the ARM-Cortex-A9 processor in the measurement and control circuit system adopts the AXI protocol.
In the embodiment, signals output by the x axis and the y axis of two electrode axes of the micro-electromechanical multi-ring gyroscope are amplified by the preamplification circuit 1 and converted into digital signals by the ADC module 2; the output signal comprises harmonic oscillator amplitude signal frequency and phase signal of the micro-electro-mechanical multi-ring gyroscope, and the signal is multiplied by a corresponding compensation coefficient through the gain compensation module 3 to carry out gain compensation; the compensated signal is demodulated out by the demodulation module 4 from the same direction and orthogonal components in the signal; the parameter calculator module 5 performs logical operation on the demodulated signals cx, sx, cy and sy through logical operation, so as to obtain the total energy change E, the orthogonal error energy change Q, the phase error L and the rotation angle theta of the micro-electromechanical multi-ring gyroscope. The total energy change E, the quadrature error energy change Q and the phase error L signal of the vibration signal pass through a PI controller module 6 to obtain an energy control signal Eout and a quadrature energy control signal Qout, and are distributed to corresponding four paths of output signals Fcx, Fsx, Fcy and Fsy after passing through a coordinate conversion module 8; two paths of digital feedback signals Fx and Fy are generated after passing through the modulation module 10, and are converted into analog signals through the DAC module 11, and the signals are directly input into a driving electrode of the micro-electro-mechanical multi-ring gyroscope. Meanwhile, the compensation coefficient calculation module 7 records the magnitude of the energy control signal Eout when the rotation angle theta of the gyroscope is 0 degree and 90 degrees each time, and obtains the gain compensation coefficient k in real time through division2While at the same time setting the gain compensation coefficient k1Is 1. The compensation coefficient calculation module 7 sends the gain compensation coefficient to the gain compensation module 3 to realize the self-compensation of the circuit gain error. Meanwhile, the phase error L signal of the vibration signal generates a phase after passing through the PI controller module 6The error control signal Lout, the phase error control signal Lout are input into the digitally controlled oscillator module 9 to generate corresponding in-phase and quadrature reference signals. In the full-angle measurement and control circuit system, a phase error L signal of a vibration signal obtained by logical operation of the parameter calculation module 5 can reflect the phase difference between a gyro resonance signal and a reference signal, two paths of phase in-phase and orthogonal reference signals are generated through the PI controller 6 and the digital control oscillator module 9, and the reference signals are used for the demodulation module 4 and the modulation module 10, so that a special-shaped phase-locked loop structure is formed. In this embodiment, the mems gyroscope is in an ideal mode matching state, i.e. the natural frequencies of the x-axis and the y-axis are the same (ω)x＝ωy＝ω)。
Claims (9)
1. A full-angle mode circuit gain error self-compensation system of a micro electro mechanical gyroscope is characterized by comprising a pre-amplification circuit module, an ADC (analog to digital converter) module, a gain compensation module, a demodulation module, a parameter calculation module, a PI (proportional-integral) controller module, a compensation coefficient calculation module, a coordinate conversion module, a modulation module, a DAC (digital to analog converter) module and a digital control oscillator module;
the preamplification circuit module is connected with a driving electrode and a detection electrode of the micro-electromechanical multi-ring gyroscope and is used for amplifying a detection signal output by a differential detection electrode of the micro-electromechanical multi-ring gyroscope;
the ADC module is used for converting the analog signal output by the pre-amplification circuit into a digital signal;
the gain compensation module multiplies the digital signals output by the ADC module by a first gain compensation coefficient and a second gain compensation coefficient respectively to realize circuit gain error compensation;
the demodulation module is used for demodulating out signals with orthogonal and in-phase phases in the digital signals and outputting four paths of signals;
the parameter calculator module is used for carrying out logical operation on the demodulated signals to obtain the total energy change, the orthogonal error energy change, the phase error of the vibration signals and the rotation angle of the gyroscope of the micro-electro-mechanical multi-ring gyroscope;
the PI controller module enables the obtained change signal to be stable and outputs a stable energy control signal, an orthogonal energy control signal and a phase error control signal;
the coordinate conversion module is used for distributing the total energy control signal and the orthogonal energy control signal output by the PI controller module to four paths of outputs according to the rotation angle of the gyroscope;
the modulation module is used for modulating the four paths of output signals of the coordinate conversion module to carrier signals generated by the digital control oscillator module, and adding the four paths of output signals to obtain two paths of output;
the DAC module is used for converting the two paths of digital signals output by the modulation module into analog signals; analog signals are input to a driving electrode of the micro-electro-mechanical multi-ring gyroscope through a voltage buffer circuit of the preamplifier circuit;
the compensation coefficient calculation module is used for recording Eout signals of the gyroscope rotating by 0 degree and 90 degrees, calculating a first gain compensation coefficient and a second gain compensation coefficient, and sending the coefficients into the gain compensation module;
the digital control oscillator module is controlled by the phase error control signal to generate two paths of orthogonal reference sinusoidal signals for modulation and demodulation, and the frequency and the phase of the reference sinusoidal signals track the frequency and the phase of the vibration signals of the micro-electromechanical multi-ring gyroscope harmonic oscillator.
2. The system of claim 1, wherein the gain compensation module compensates the signals as follows:
x"＝x'*k1
y"＝y'*k2
wherein x 'is the vibration displacement of the x axis of the micro-electromechanical multi-ring gyroscope after gain compensation, y' is the vibration displacement of the y axis of the micro-electromechanical multi-ring gyroscope after gain compensation, x 'is the vibration displacement of the x axis of the micro-electromechanical multi-ring gyroscope after actual gain is considered, y' is the vibration displacement of the y axis of the micro-electromechanical multi-ring gyroscope after actual gain is considered, k1A first gain compensation coefficient, k, multiplied by the first signal in the ADC module2First multiplication for second path signal in ADC moduleThe compensation coefficient is increased.
3. The system of claim 1, wherein the demodulation module outputs cx, sx, cy, sy as:
cx＝LPF(x"*cos(ωt+φ))
sx＝LPF(x"*sin(ωt+φ))
cy＝LPF(y"*cos(ωt+φ))
sy＝LPF(y"*sin(ωt+φ))
signals cx and sx respectively represent an in-phase part and a quadrature part of a harmonic oscillator 0-degree electrode axis vibration signal; the signals cy and sy respectively represent the in-phase part and the quadrature part of the harmonic oscillator 45-degree electrode axis vibration signal; cos (ω t + φ) is the in-phase reference signal for demodulation, sin (ω t + φ) is the quadrature reference signal, LPF represents low pass filtering; phi is the phase of the reference signal; omega is the resonant frequency of the tuned electrode shaft, and t is the gyro rotation time.
4. The system of claim 1, wherein the parameter calculator module calculates the following procedure:
E＝cx2+cy2+sx2+sy2
Q＝2*(cx*sy-cy*sx)
L＝2*(cx*sx+cy*sy)
wherein x is the vibration displacement of the 0-degree electrode axis of the micro-electromechanical multi-ring gyroscope, y is the vibration displacement of the 45-degree electrode axis, E is the total energy change of the micro-electromechanical multi-ring gyroscope, Q is the orthogonal error energy change, L is the phase error of the vibration signal, and theta is the rotation angle of the gyroscope.
5. The system of claim 1, wherein the compensation factor meter is configured to compensate for the gain error of the mems gyroscope in full-angle modeThe process of calculating the gain compensation coefficient by the calculation module is as follows: setting a first gain compensation coefficient k1To be 1, the second gain compensation coefficient k is obtained by comparing the signal magnitude of the energy control signal when the rotation angle theta is 0 DEG and 90 DEG2：
Wherein Eout0And Eout90The magnitudes of the energy control signals are respectively at the rotation angles theta of 0 DEG and 90 deg.
6. The system of claim 1, wherein the coordinate transformation module has the following algorithm:
Fcx＝Eout*cosθ
Fcy＝-Qout*sinθ
Fcy＝Eout*sinθ
Fsy＝Qout*sinθ
wherein, Fcx, Fsx, Fcy, Fsy are four output signals of the coordinate conversion module; eout and Qout are respectively an energy control signal and an orthogonal energy control signal output by the PI controller module, and θ is a rotation angle of the gyroscope.
7. The system of claim 1, wherein the modulation module has the following algorithm:
Fx＝Fcx*cos(ωt+φ)+Fsx*sin(ωt+φ)
Fy＝Fcy*cos(ωt+φ)+Fsy*sin(ωt+φ)
wherein Fx and Fy are two paths of outputs obtained after modulation operation; fcx, Fsx, Fcy and Fsy are four paths of output signals of the coordinate conversion module; phi is the phase of the reference signal; omega is the resonant frequency of the tuned electrode shaft, and t is the gyro rotation time.
8. The system of claim 1, wherein the reference signals generated by the numerically controlled oscillator module are as follows:
singalin_pasefor in-phase reference signals, singleout_pahseIs a quadrature reference signal, phi is the phase of the reference signal; omega is the resonant frequency of the tuned electrode shaft, and t is the gyro rotation time.
9. The system for self-compensating the gain error of the full-angle mode circuit of the micro-electromechanical gyroscope according to claim 1, wherein when the micro-electromechanical gyroscope is operated, the motion equation is as follows:
wherein x is the vibration displacement of the 0-degree electrode axis of the micro-electromechanical multi-ring gyroscope, theta is the rotation angle of the gyroscope, and omega1Is the resonant frequency of the electrode axis at 0 DEG, y is the vibrational displacement of the electrode axis at 45 DEG, omega2Is the resonance frequency of the electrode shaft of 45 degrees, a is the amplitude of the antinode of the harmonic wave standing wave of the micro-electromechanical multi-ring gyroscope, q is the amplitude of the wave node, omega is the resonance frequency of the tuned electrode shaft, t is the rotation time of the gyroscope,
is the phase of the vibration signal.
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