Non-degraded state micro-electro-mechanical gyroscope force balance detection loop based on proportional integral resonance controller and bandwidth expansion method thereof
Through the microelectromechanical gyro force balance detection circuit based on proportional integral resonant controller, the problem of taking into account high mechanical sensitivity and large detection bandwidth in the existing technology is solved, and higher detection bandwidth and accuracy are achieved, and the application field of microelectromechanical gyro is expanded. .
Patent Information
- Application Number
- CN202411314104.X
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-09-20
- Publication Date
- 2025-01-03
AI Technical Summary
The existing microelectromechanical gyro force balance detection mode is difficult to expand the detection bandwidth while ensuring high mechanical sensitivity, limiting its application areas.
Using the non-degraded state microelectromechanical gyro force balance detection loop based on the proportional integral resonance controller, the resonance term gain coefficient and resonance bandwidth are adjusted by calculating the open-loop transfer function of the equivalent unit negative feedback loop, and the resonance frequency width is suppressed. Rate detection amplitude and frequency curve resonant peaks to achieve bandwidth expansion.
The force balance detection accuracy is improved, the detection bandwidth is expanded, and the in-band flatness is maintained, simplifying the bandwidth design difficulty.
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Figure CN119249031A_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to a micro-electro-mechanical system gyro force balance detection circuit, and in particular to a non-degenerate state micro-electro-mechanical system gyro force balance detection circuit based on a proportional-integral resonant controller and a bandwidth expansion method thereof. Background Art
[0002] According to the requirements of the application field for its dynamic performance and static performance indicators, gyroscopes are divided into three categories: rate level, tactical level and inertial level. The rate level requires the gyroscope detection bandwidth to reach 70Hz, and the tactical level and inertial level require the gyroscope detection bandwidth to be higher than 100Hz. In addition, the MEMS gyroscope also needs to ensure high mechanical sensitivity to meet the requirements of static performance indicators. The MEMS gyroscope that measures angular motion based on the Coriolis effect has three detection modes: rate mode, rate integration mode and frequency modulation mode. Among them, the rate mode has the highest static performance and the lowest control complexity, and is currently the preferred detection mode of the MEMS gyroscope. The MEMS gyroscope working in the rate mode has two working modes: driving and detection. The driving mode tracks the resonant frequency of the driving mode in real time and maintains a constant amplitude in the driving direction. When the gyroscope sensitive axis rotates, the Coriolis force will act on the detection mode. The rate mode can be divided into an open-loop detection mode and a force balance detection mode. The open-loop detection mode characterizes the rate by detecting the vibration of the mode. Its modal frequency difference is positively correlated and negatively correlated with the detection bandwidth and mechanical sensitivity respectively. It is impossible to ensure a large detection bandwidth while ensuring high mechanical sensitivity. The force balance detection mode uses a controller combined with specific force balance comb teeth to suppress the vibration of the detection mode caused by the rotation of the carrier, thereby characterizing the rate information through the output of the controller. The force balance detection mode always maintains the detection mass block in a balanced position, and has the advantages of anti-interference and a large range. However, the existing conventional force balance detection mode also makes it difficult to achieve both high mechanical sensitivity and a large detection bandwidth. How to expand the detection bandwidth of the MEMS gyroscope while ensuring high mechanical sensitivity is a key technology to further expand the application field of MEMS gyroscopes. Summary of the invention
[0003] Purpose of the invention: To solve the above problems, the present invention proposes a non-degenerate state MEMS gyroscope force balance detection circuit based on proportional-integral resonant controller and a bandwidth expansion method thereof, which can ensure that the MEMS gyroscope has a higher detection bandwidth while having a higher mechanical sensitivity.
[0004] Technical solution: The technical solution adopted by the present invention is a non-degenerate state micro-electromechanical gyroscope force balance detection circuit based on a proportional-integral resonant controller, comprising:
[0005] Input angular velocity signal Ω zThe generated Coriolis signal is subtracted from the force balance signal and then input to the gyro detection mode. The output signal of the gyro detection mode is passed through the first gain module to obtain an electrical signal D1. The electrical signal D1 is in phase with the sinusoidal signal sin(ω x t) is multiplied and filtered by a low-pass filter before being input into the proportional-integral resonant controller. The output signal of the proportional-integral resonant controller is multiplied by the sinusoidal signal sin(ω x t), and then converted into a force balance signal by the second gain module and fed back to the gyro detection modal input end to realize gyro force balance detection; ω in the sinusoidal signal x is the driving mode resonant frequency of the MEMS gyroscope; the resonant term resonant frequency of the proportional integral resonant controller is the difference between the driving mode resonant frequency and the detection mode resonant frequency.
[0006] The transfer function of the proportional-integral resonant controller is:
[0007]
[0008] Among them, F pir (s) is the transfer function of the proportional-integral resonant controller, K p is the proportional term coefficient, K i is the integral term coefficient, K r is the resonance gain coefficient, ω c is the resonance bandwidth of the resonance term, Δω is the difference between the resonance frequency of the driving mode and the resonance frequency of the detection mode, and s is a complex variable.
[0009] The input signal of the proportional-integral resonant controller is:
[0010]
[0011] In the formula, F i (s) is the input signal of the proportional-integral resonant controller, K1 and K2 are the first gain coefficient of the first gain module and the second gain coefficient of the second gain module, respectively. y is the MEMS gyro detection modal transfer function, and j is an imaginary unit.
[0012] The output signal V of the proportional-integral resonant controller close (t) reflects the input angular velocity signal Ω z The size of (t).
[0013] The bandwidth expansion method of the non-degenerate state micro-electromechanical system gyroscope force balance detection circuit based on proportional-integral resonant controller of the present invention comprises the following steps:
[0014] (1) According to the equivalent unit negative feedback loop of the MEMS gyro force balance detection loop in the non-degenerate state, the open-loop transfer function of the equivalent unit negative feedback loop is calculated as follows:
[0015] H(s)=G e (s)F pir (s)
[0016] In the formula, G e (s) represents the linearized transfer function in the forward path of the force balance detection loop, which contains sin(ω x t) modulation link, gyro detection modal transfer function and sin(ω x t) Modulation and adjustment link, F pir (s) is the transfer function of the proportional-integral resonant controller;
[0017] Among them G e The transfer function of (s) is as follows:
[0018]
[0019] Where K1 and K2 are the first gain coefficient of the first gain module and the second gain coefficient of the second gain module respectively, m c The angular velocity signal Ω is involved z (t) is the equivalent mass of the vibration caused, s is a complex variable, ω x is the driving modal resonant frequency of the MEMS gyroscope, ω y To detect the modal resonant frequency, Q y To detect the modal quality factor,;
[0020] The transfer function of the proportional-integral resonant controller is:
[0021]
[0022] Where K p is the proportional term coefficient, K i is the integral term coefficient, K r is the resonance gain coefficient, ω c is the resonance bandwidth of the resonance term, Δω is the difference between the resonance frequency of the driving mode and the resonance frequency of the detection mode;
[0023] (2) Calculate the amplitude and phase characteristics of the open-loop transfer function of the equivalent unit negative feedback loop to reflect the bandwidth characteristics of the non-degenerate MEMS gyro force balance detection loop;
[0024] (3) According to the amplitude and phase characteristics of the open-loop transfer function of the equivalent unit negative feedback loop, adjust the characteristic parameter resonant term gain coefficient K r and the resonant bandwidth ω c , suppressing the resonant peak of the rate detection amplitude-frequency curve caused by the modal frequency difference.
[0025] The step (3) includes the following process: firstly, the driving mode resonance frequency ω of the MEMS gyroscope is obtained by frequency sweeping. x , detect the modal resonance frequency ω y and detect modal quality factor Q y ; Then the driving mode resonant frequency ω x , detect the modal resonance frequency ω y and detect modal quality factor Q y Substitute the amplitude and phase characteristics of the open-loop transfer function into the equivalent unit negative feedback loop; finally, by adjusting the characteristic parameter resonant term gain coefficient K r and the resonant bandwidth ω c , so that the amplitude margin, phase margin and open-loop cut-off frequency of the open-loop function of the non-degenerate MEMS gyroscope force balance detection loop meet the design requirements.
[0026] Adjust the proportional term coefficient K p , improve system gain and improve system response speed.
[0027] Adjust the integral coefficient K i , eliminating steady-state errors.
[0028] Adjust the resonance gain factor K r and the resonant bandwidth ω c , suppressing the resonant peak of the rate detection amplitude-frequency curve caused by the modal frequency difference.
[0029] The amplitude margin of the open-loop function of the non-degenerate state MEMS gyro force balance detection loop is between 5dB and 10dB, and the phase margin is between 45° and 60°. According to the requirements of the above amplitude margin and phase margin, the coefficient of the proportional-integral resonant controller is adjusted to achieve bandwidth expansion.
[0030] Beneficial effects: Compared with the prior art, the present invention has the following advantages: The present invention adopts a proportional-integral resonant controller, which can reduce the error of the force balance detection loop and improve the force balance detection accuracy. Compared with the conventional proportional-integral controller, the resonance frequency of the resonance term unique to the proportional-integral resonant controller designed in this scheme is the difference between the driving modal resonance frequency and the detection modal resonance frequency, which effectively suppresses the resonance peak of the rate detection amplitude-frequency curve caused by the modal frequency difference, and maintains good in-band flatness while expanding the rate detection bandwidth. The present invention also derives a unit negative feedback loop that characterizes the amplitude-frequency characteristics of the force balance detection loop, and uses the amplitude-phase characteristics of the open-loop transfer function of the unit negative feedback loop to reflect the bandwidth characteristics of the detection loop, proposing a new bandwidth expansion idea and simplifying the design difficulty of bandwidth expansion. BRIEF DESCRIPTION OF THE DRAWINGS
[0031] Figure 1It is a system block diagram of a non-degenerate state micro-electromechanical gyro force balance detection circuit based on a proportional-integral resonant controller of the present invention;
[0032] Figure 2 (a) is a block diagram of a MEMS gyro force balance detection loop involved in the present invention without equivalent transformation; (b) is a block diagram of a MEMS gyro force balance detection loop involved in the present invention after equivalent transformation of the multiplication term; (c) is a block diagram of an equivalent unit negative feedback loop of a MEMS gyro force balance detection involved in the present invention after equivalent transformation of the feedback path gain;
[0033] Figure 3 The open-loop amplitude-phase curves of the micro-electromechanical gyro force balance detection circuit before and after the bandwidth expansion of the present invention;
[0034] Figure 4 The amplitude-frequency curve of the micro-electromechanical gyro force balance detection circuit before and after the bandwidth expansion of the present invention. DETAILED DESCRIPTION
[0035] The technical solution of the present invention is further described below in conjunction with the accompanying drawings and embodiments.
[0036] The non-degenerate state micro-electromechanical gyroscope force balance detection circuit based on proportional-integral resonant controller of the present invention is as follows: Figure 1 As shown, including: input angular velocity Ω z The Coriolis signal generated by (t) is subtracted from the force balance signal and input to the gyro detection mode. The output signal of the gyro detection mode is converted into an electrical signal D1 through the first gain module. The electrical signal D1 is in phase with the sinusoidal signal sin(ω x t) is multiplied and filtered by a low-pass filter before being input into the proportional-integral resonant controller. The output signal of the proportional-integral resonant controller is multiplied by the sinusoidal signal sin(ω x t), it is converted into a force balance signal by the second gain module and fed back to the gyro detection modal input end to realize gyro force balance detection.
[0037] The working process of the non-degenerate state MEMS gyro force balance detection circuit based on proportional integral resonant controller is described as follows: Input angular velocity Ω z The generated Coriolis signal (t) is input to the gyro detection mode, causing the detection mode to generate mechanical vibration, which is converted into an electrical signal D1 through a gain K1. This signal is a sinusoidal signal sin(ω) in phase with the Coriolis signal. x t) is multiplied and then input to the low-pass filter. The output signal of the low-pass filter is input to the proportional-integral resonant controller. The output signal of the proportional-integral resonant controller is multiplied by the sinusoidal signal sin(ω xt), after being converted into a force balance signal through gain, it acts on the gyro detection mode feedback end to offset the mechanical vibration of the detection mode caused by the Coriolis signal and realize the gyro force balance detection. The output V close (t) reflects the magnitude of the input angular velocity.
[0038] Figure 2 (a) to Figure 2 (c) shows the equivalent transformation process of the MEMS gyro force balance detection circuit in the non-degenerate state. c is the input angular velocity Ω z (t) The generated Coriolis signal, F f is the gyro force balance signal, G y (s) is the gyro detection modal transfer function, K1 is the gain of the forward path of the gyro force balance detection loop, F lpf (s) is the transfer function corresponding to the low-pass filter, F pir (s) is the transfer function of the proportional-integral resonant controller, and K2 is the gain of the feedback path of the gyro force balance detection loop.
[0039] Figure 2 (a) is the block diagram of the MEMS gyroscope force balance detection circuit without equivalent transformation.
[0040] Figure 2 (b) is the block diagram of the MEMS gyro force balance detection circuit after equivalent transformation of the multiplication term. Figure 2 (a) is equivalently transformed to obtain the input angular velocity Ω z (t) The generated Coriolis signal F c Balance signal F with gyroscopic force f In the link sin(ω x t) is equivalently transformed to the subtractor.
[0041] Figure 2 (c) is the equivalent unit negative feedback loop block diagram of the MEMS gyro force balance detection after equivalent transformation of the feedback path gain. Figure 2 (b) is obtained by equivalent transformation, specifically, the gain K2 of the feedback path is equivalently transformed to the forward path. Figure 2 (c) is a block diagram of the equivalent unit negative feedback loop representing the MEMS gyro force balance detection. Figure 2 The unit negative feedback loop in (c) can characterize the amplitude and phase characteristics of the MEMS gyro force balance detection.
[0042] make Figure 2 The input signal of multiplier 1 in (c) is E c (t), then the output signal of the multiplier, i.e. the input signal Y of the MEMS gyro detection modal transfer function i(t) is:
[0043] Y i (t) = E c (t)sin(ω x t)(1) Performing Euler transformation on equation (2) yields:
[0044]
[0045] By performing a pull-type transformation on equation (3), we can obtain:
[0046]
[0047] Let the output signal of the MEMS gyro detection modal transfer function be Y o (t), then the output signal C of multiplier 2 o (t) is:
[0048] C o (t)=Y o (t)K1K2sin(ω x t)(4) Performing Euler transformation on equation (5) yields:
[0049]
[0050] By performing a pull-type transformation on equation (6), we can obtain:
[0051]
[0052] Depend on Figure 2 The forward path of the unit negative feedback loop in (c) can be obtained as follows: o (s)=Y i (s)G y (s). According to the above-mentioned MEMS gyro detection modal transfer function G y The input and output relationship of (s) can be obtained by combining equations (4) and (7):
[0053]
[0054] Since the low-pass filter can effectively filter out the double frequency signal, and the cut-off frequency of the low-pass filter is much higher than the force balance rate detection bandwidth, the output signal of the low-pass filter, that is, the input signal F of the proportional-integral resonant controller i (s) can be simplified as:
[0055]
[0056] In addition, the transfer function of the MEMS gyro detection mode is as follows:
[0057]
[0058] where ω y To detect the modal resonant frequency, Q y To detect the modal quality factor, m c is the equivalent mass that participates in the vibration caused by the input angular velocity.
[0059] Substituting formula (10) into formula (9) yields:
[0060]
[0061] therefore, Figure 2 The open-loop transfer function H(s) of the unit negative feedback loop in (c) is:
[0062] H(s)=G e (s)F pir (s)(11) where F pir (s) is the transfer function of the proportional-integral resonant controller:
[0063]
[0064] K p is the proportional term coefficient, K i is the integral term coefficient, K r is the resonance gain coefficient, ω c is the resonance bandwidth of the resonance term, and Δω is the difference between the resonance frequency of the driving mode and the resonance frequency of the detection mode.
[0065] Proportional term coefficient K p Used to increase system gain and speed up system response; integral term coefficient K i Mainly used to eliminate steady-state errors; resonant gain coefficient K r and the resonant bandwidth ω c The average and detection modal quality factor Q y is proportional to, and the resonance term resonant bandwidth ω c Proportional to the control bandwidth of the resonance term; through the resonance term gain coefficient K r and the resonant bandwidth ω c The resonant frequency of the resonance term is designed to be the difference Δω between the driving mode resonant frequency and the detection mode resonant frequency, which is used to suppress the resonant peak of the rate detection amplitude-frequency curve caused by the modal frequency difference of the MEMS gyroscope.
[0066] For the unit negative feedback loop, under the premise of reasonable amplitude margin and phase margin, the cutoff frequency of the open-loop transfer function is positively correlated with the bandwidth of the unit negative feedback loop. In order to ensure the robustness and good dynamic performance of the unit negative feedback loop, it is necessary to configure the parameters of the proportional-integral resonant controller so that the amplitude margin is between 5dB and 10dB, the phase margin is between 45° and 60°, and the cutoff frequency of the open-loop transfer function is relatively high, so as to expand the bandwidth of the force balance detection loop.
[0067] Figure 3 Open-loop amplitude-phase curves of the MEMS gyroscope force balance detection circuit before and after bandwidth expansion. Figure 3 The middle dotted line is the open-loop amplitude-phase curve of the force balance detection loop using a proportional-integral controller, with an amplitude margin of 22.2 dB, a phase margin of 85.8°, and an open-loop cutoff frequency of 3 Hz. Excessive amplitude margin and phase margin will lead to slow system response and a higher resonance peak in the amplitude-frequency curve. Excessively small open-loop cutoff frequency indicates that the bandwidth of the force balance detection loop is small. Figure 3 The solid line in the middle is the open-loop amplitude-phase curve of the force balance detection loop using a proportional-integral resonant controller. The amplitude margin is 5.6 dB, the phase margin is 58.7°, and the open-loop cutoff frequency is 21 Hz. The reasonable amplitude margin and phase margin as well as the larger cutoff frequency indicate that the force balance detection loop has a larger bandwidth.
[0068] Figure 4 Amplitude-frequency curve of the MEMS gyro force balance detection circuit before and after bandwidth expansion. Figure 4 The middle dashed line is the amplitude-frequency curve of the force balance detection loop using a proportional-integral controller, and the force balance detection bandwidth is 3.4 Hz; Figure 4 The solid line in the middle is the amplitude-frequency curve of the force balance detection loop using the proportional-integral resonant controller. The force balance detection bandwidth is 106Hz, the highest point amplitude in the band is +1.2dB, and the lowest point amplitude in the band is -0.015dB, which has good in-band flatness.
Claims
1. A non-degenerate state micro-electromechanical gyroscope force balance detection circuit based on proportional-integral resonant controller, characterized in that: Input angular velocity signal Ω z The generated Coriolis signal is subtracted from the force balance signal and then input to the gyro detection mode. The output signal of the gyro detection mode is passed through the first gain module to obtain an electrical signal D1. The electrical signal D1 is in phase with the sinusoidal signal sin(ω x t) is multiplied and filtered by a low-pass filter before being input into the proportional-integral resonant controller. The output signal of the proportional-integral resonant controller is multiplied by the sinusoidal signal sin(ω x t), and then converted into a force balance signal by the second gain module and fed back to the gyro detection modal input end to realize gyro force balance detection; ω in the sinusoidal signal x is the driving mode resonant frequency of the MEMS gyroscope; the resonant term resonant frequency of the proportional integral resonant controller is the difference between the driving mode resonant frequency and the detection mode resonant frequency.
2. The non-degenerate state MEMS gyro force balance detection circuit based on proportional-integral resonant controller according to claim 1, characterized in that: The transfer function of the proportional-integral resonant controller is: where F pir (s) is the transfer function of the proportional-integral resonant controller, K p is the proportional term coefficient, K i is the integral term coefficient, K r is the resonance gain coefficient, ω c is the resonance bandwidth of the resonance term, Δω is the difference between the resonance frequency of the driving mode and the resonance frequency of the detection mode, and s is a complex variable.
3. The non-degenerate state MEMS gyro force balance detection circuit based on proportional-integral resonant controller according to claim 1, characterized in that: The input signal of the proportional-integral resonant controller is: In the formula, F i (s) is the input signal of the proportional-integral resonant controller, K1 and K2 are the first gain coefficient of the first gain module and the second gain coefficient of the second gain module, respectively. y is the MEMS gyro detection modal transfer function, and j is an imaginary unit.
4. The non-degenerate state MEMS gyro force balance detection circuit based on proportional-integral resonant controller according to claim 1, characterized in that: The output signal V of the proportional-integral resonant controller close (t) reflects the input angular velocity signal Ω z The size of (t).
5. A bandwidth expansion method for the non-degenerate state micro-electromechanical gyroscope force balance detection circuit based on proportional integral resonant controller according to claim 1, characterized in that: The following steps are involved: (1) According to the equivalent unit negative feedback loop of the MEMS gyro force balance detection loop in the non-degenerate state, the open-loop transfer function of the equivalent unit negative feedback loop is calculated as follows: H(s)=G e (s)F pir (s) In the formula, G e (s) represents the linearized transfer function in the forward path of the force balance detection loop, which contains sin(ω x t) modulation link, gyro detection modal transfer function and sin(ω x t) Modulation and adjustment link, F pir (s) is the transfer function of the proportional-integral resonant controller; Among them G e The expression of (s) is as follows: Where K1 and K2 are the first gain coefficient of the first gain module and the second gain coefficient of the second gain module respectively, m c The angular velocity signal Ω is involved z (t) is the equivalent mass of the vibration caused, s is a complex variable, ω x is the driving modal resonant frequency of the MEMS gyroscope, ω y To detect the modal resonant frequency, Q y To detect the modal quality factor,; The transfer function of the proportional-integral resonant controller is: Where K p is the proportional term coefficient, K i is the integral term coefficient, K r is the resonance gain coefficient, ω c is the resonance bandwidth of the resonance term, Δω is the difference between the resonance frequency of the driving mode and the resonance frequency of the detection mode; (2) Calculate the amplitude and phase characteristics of the open-loop transfer function of the equivalent unit negative feedback loop to reflect the bandwidth characteristics of the non-degenerate MEMS gyro force balance detection loop; (3) According to the amplitude and phase characteristics of the open-loop transfer function of the equivalent unit negative feedback loop, adjust the characteristic parameter resonant term gain coefficient K r and the resonant bandwidth ω c , suppressing the resonant peak of the rate detection amplitude-frequency curve caused by the modal frequency difference.
6. The bandwidth expansion method according to claim 5, characterized in that: The step (3) includes the following process: firstly, the driving mode resonance frequency ω of the MEMS gyroscope is obtained by frequency sweeping. x , detect the modal resonance frequency ω y and detect modal quality factor Q y ; Then the driving mode resonant frequency ω x , detect the modal resonance frequency ω y and detect modal quality factor Q y The amplitude and phase characteristics of the open-loop transfer function brought into the equivalent unit negative feedback loop; Finally, by adjusting the characteristic parameter resonant term gain coefficient K r and the resonant bandwidth ω c , so that the amplitude margin, phase margin and open-loop cut-off frequency of the open-loop function of the non-degenerate MEMS gyroscope force balance detection loop meet the design requirements.
7. The bandwidth expansion method according to claim 5, characterized in that: Adjust the proportional term coefficient K p , improve system gain and improve system response speed.
8. The bandwidth expansion method according to claim 5, characterized in that: Adjust the integral coefficient K i , eliminating steady-state errors.
9. The bandwidth expansion method according to claim 5, characterized in that: Adjust the resonance gain factor K r and the resonant bandwidth ω c , suppressing the resonant peak of the rate detection amplitude-frequency curve caused by the modal frequency difference.
10. The bandwidth expansion method according to claim 5, characterized in that: The amplitude margin of the open-loop function of the non-degenerate state MEMS gyro force balance detection loop is between 5dB and 10dB, and the phase margin is between 45° and 60°. According to the requirements of the above amplitude margin and phase margin, the coefficient of the proportional-integral resonant controller is adjusted to achieve bandwidth expansion.