A method for determining and optimizing the loop parameters of a MEMS gyroscope electromechanically combined Σ-Δ closed loop

Abstract

This invention belongs to the field of inertial sensor control technology, specifically relating to a method for determining and optimizing the parameters of a MEMS gyroscope electromechanical integrated Σ-Δ closed-loop circuit. The method incorporates an electronic compensator into the loop to compensate for the zeros of the z-domain transfer function of the gyroscope's sensitive mode and the poles of the MEMS gyroscope electromechanical integrated Σ-Δ closed-loop detection loop. Based on the equivalent parameters of the electronic Σ-Δ modulator and the MEMS gyroscope electromechanical integrated Σ-Δ closed-loop detection loop, the optimal parameters are obtained by using a multi-objective optimization algorithm to optimize the performance loss caused during the approximate equivalence process.

Description

Technical Field

[0001] This invention belongs to the field of inertial sensor control technology, specifically relating to a method for determining and optimizing the parameters of a MEMS gyroscope electromechanical Σ-Δ closed-loop circuit. Background Technology

[0002] MEMS gyroscopes are inertial sensors that measure the angular rate of a carrier using microelectromechanical systems technology. They have advantages such as low cost, small size, light weight, low power consumption, and ease of mass production, and are currently widely used in aerospace, automotive, consumer electronics, medical, and industrial fields.

[0003] MEMS gyroscope control schemes are divided into open-loop control and closed-loop control. Although the open-loop control method, which does not apply external force to control the sensitive mode, is simple to implement, it cannot meet the requirements of large bandwidth and high sensitivity. It also has problems such as small range and poor robustness. High-performance gyroscopes generally use closed-loop control technology, which suppresses the vibration of the sensitive mode through negative feedback, thereby improving the performance of range, bandwidth and scaling factor nonlinearity.

[0004] MEMS gyroscopes generally employ modulation and demodulation methods to achieve closed-loop control of the sensitive mode. The output of the sensitive mode must undergo drive frequency demodulation, filtering, PI control, and drive frequency modulation before the feedback voltage can be applied to the feedback electrode to complete the closed-loop control of the sensitive mode. Σ-Δ modulator technology is often used in high-precision analog-to-digital conversion. This modulation method achieves a high signal-to-noise ratio through oversampling and noise shaping, and can obtain a quantized digital signal output. If Σ-Δ technology is combined with the closed-loop control of the gyroscope, the quantizer outputs a 1-bit high-frequency pulse density signal. This signal directly acts on the feedback electrode through a feedback DAC (digital-to-analog converter), completing the sensitive mode closed-loop control without the need for modulation and demodulation. It can also directly output a low-quantization-noise digital signal, greatly simplifying the complexity of closed-loop control. This technology is called electromechanical Σ-Δ closed-loop detection technology.

[0005] Designing the parameters of an electromechanical Σ-Δ closed-loop detection circuit presents several challenges: the inability to extract the integral node within the gyroscope reduces degrees of freedom; the gyroscope's mechanical characteristics constrain the parameter design; and the loop's operating signal is a mixture of analog and digital domains. The design of the electromechanical Σ-Δ closed-loop detection circuit parameters directly impacts the performance and stability of the gyroscope's closed-loop control. Therefore, it is necessary to develop a method to determine the optimal loop parameters based on the loop structure and the gyroscope's mechanical characteristics. Summary of the Invention

[0006] Purpose of the invention: To provide a method for determining and optimizing the electromechanical Σ-Δ closed-loop parameters of a MEMS gyroscope.

[0007] Technical solution:

[0008] A method for determining and optimizing the parameters of a MEMS gyroscope electromechanical Σ-Δ closed-loop circuit includes:

[0009] Step 1: Determine the electronic Σ-Δ modulator;

[0010] Step 2: Discretize the gyroscope's sensitive modes;

[0011] Step 3: Linearize the y / v conversion and the v / f conversion. The y / v conversion module linearizes the gain of the shift to voltage near the zero position, denoted as gain K. yv The V / F conversion module linearizes the voltage-to-force gain near the zero position, denoted as gain K. vf ;

[0012] Step 4: Establish a MEMS gyroscope electromechanical Σ-Δ closed-loop detection circuit model. Specifically, determine the transfer function H of the electronic filter based on the selected electronic Σ-Δ modulator architecture. e (z), of order (N-2), in the form of Where z e1 ,z e2 ,…,z e(N-2) It is the zero point of the electronic filter, p e1 ,p e2 ,,…,p e(N-2) These are the poles of the electronic filter, and a, b, c… are the undetermined coefficients in the electronic filter; determine the transfer function H of the electronic compensator. com (z), in the form of Where z c1 For the zero point of the electronic compensator, p c1 For the electronic compensator pole, the electronic compensator pole p c1 With the zero point of the z-domain transfer function of the gyroscope-sensitive mode m equal;

[0013] Step 5: Based on steps 2-4, determine the open-loop transfer function L of the MEMS gyroscope electromechanical Σ-Δ closed-loop detection loop. em (z);

[0014] Step 6: Based on Steps 1 and 5, determine the undetermined coefficients a, b, c… and the zero point z of the electronic compensator. c1 Undetermined coefficients a, b, c… and the zero point z of the electronic compensator c1 This refers to the Σ-Δ closed-loop detection circuit parameters of the MEMS gyroscope electromechanical combination.

[0015] Step 7: Optimize the parameters of the MEMS gyroscope electromechanical Σ-Δ closed-loop detection circuit using a multi-objective optimization algorithm;

[0016] Step 8: Determine a set of MEMS gyroscope electromechanical Σ-Δ closed-loop detection loop parameters based on the multiple Pareto optimal solutions obtained in Step 7 and the root locus method.

[0017] Further, step 1: determine the electronic Σ-Δ modulator, specifically:

[0018] Based on the target signal-to-noise ratio (SNR), the architecture, order N, and oversampling rate (OSR) of the electronic Σ-Δ modulator are determined. The noise transfer function (NTF) of the electronic Σ-Δ modulator is designed using the DS Toolbox design tool. The open-loop transfer function (L(z)) of the electronic Σ-Δ modulator is then calculated based on the NTF(z). The calculation process is as follows: The obtained open-loop transfer function L(z) of the electronic Σ-Δ modulator is in the form of: Where z1, z2, ..., z N These are the zeros of the open-loop transfer function L(z) of the electronic Σ-Δ modulator, p1, p2, ..., p N These are the poles of the open-loop transfer function L(z) of the electronic Σ-Δ modulator.

[0019] Further, step 2 specifically involves:

[0020] The s-domain transfer function is determined based on the quality factor Q and resonant frequency ω of the gyroscope's sensitive mode: Where s pm and s pm * represents a pair of conjugate poles of the s-domain transfer function of the gyroscope-sensitive mode, K sm It is the gain of the s-domain transfer function of the gyroscope-sensitive mode;

[0021] The s-domain transfer function of the gyroscope-sensitive mode is converted into a z-domain transfer function using a discretization method. The z-domain transfer function is of the form: Where z m It is a zero of the z-domain transfer function of the gyroscope-sensitive mode, p m and p m * represents a pair of conjugate poles of the z-domain transfer function of the gyroscope-sensitive mode, K zm It is the gain of the z-domain transfer function of the gyroscope-sensitive mode.

[0022] Furthermore, in step 2, the discretization method for converting the s-domain transfer function of the gyroscope-sensitive mode into the z-domain transfer function is as follows:

[0023] Given that the force feedback pulse begins to act at time t. fb1 The duration of the action is t. fb2 The sampling time is T s The s-domain transfer function of the gyroscope-sensitive mode can be further transformed into Where Ksm1 and K sm2 The gain is the result of the partial expansion of the s-domain transfer function of the gyroscope-sensitive mode. The transformation process from the s-domain transfer function to the z-domain transfer function is expressed as follows:

[0024] The z-domain transfer function can be simplified to the form:

[0025] Further, step 5 specifically includes:

[0026] L em (z)=K em H gyro (z)H e (z)H com (z), where K em =K yv K DAC K vf K q K DAC Let L be the gain of the DAC module, Kq be the gain of the quantizer, and L be the open-loop transfer function. em The zero point of the z-domain transfer function of the gyroscope-sensitive mode in (z) m and electronic compensator pole p c1 To cancel out, to reduce the order.

[0027] Further, step 7 specifically includes: optimizing the parameters of the MEMS gyroscope electromechanical Σ-Δ closed-loop detection circuit using a genetic algorithm, particle swarm optimization algorithm, or gradient descent algorithm.

[0028] Further, step 7 specifically includes:

[0029] Step 7.1: Establish the objective function of the multi-objective optimization algorithm:

[0030] maxf1 = SNR(a,b,c,...)

[0031] minf2 = max[y rm (a,b,c,...)]

[0032] st|NTF| ∞ <1.5

[0033] Where SNR(a,b,c,…) represents the signal-to-noise ratio of the output signal under the current values ​​of the MEMS gyro-electromechanical combined Σ-Δ closed-loop detection loop parameters, y rm (a,b,c,…) represents the residual motion of the sensitive mode under the current values ​​of the MEMS gyro-electromechanical combined Σ-Δ closed-loop detection loop parameters, |NTF| ∞ Denotes the H-∞ norm of NTF, |NTF| ∞<1.5 is a constraint condition to ensure the stability of the MEMS gyroscope electromechanical Σ-Δ closed-loop detection loop;

[0034] Step 7.2: Solve the objective function in sub-step 7.1 using a multi-objective optimization algorithm to obtain multiple sets of Pareto optimal solutions for the MEMS gyroscope electromechanical Σ-Δ closed-loop detection loop parameters.

[0035] Furthermore, in step 7, a -6dBFS sine wave is selected as the input for the optimization simulation to prevent overload, and the initial value of the optimization algorithm is selected from the MEMS gyroscope electromechanical combined Σ-Δ closed-loop detection loop parameters obtained in step 6.

[0036] Beneficial effects:

[0037] This invention employs a single-feedback architecture to simplify loop complexity and can automatically compensate for loop gain mismatch. An electronic compensator is added to the loop to compensate for the zeros of the z-domain transfer function of the gyroscope's sensitive mode and the poles of the MEMS gyroscope electromechanical combined Σ-Δ closed-loop detection loop. Based on the equivalent parameters of the electronic Σ-Δ modulator and the MEMS gyroscope electromechanical combined Σ-Δ closed-loop detection loop, a multi-objective optimization algorithm is used to optimize the performance loss caused in the approximate equivalence process to obtain the optimal parameters. Attached Figure Description

[0038] Figure 1 This is a diagram of a MEMS gyroscope electromechanical integrated Σ-Δ closed-loop detection circuit architecture. In the diagram:

[0039] 01 - The gyroscope-sensitive mode module generates displacement when subjected to external forces, and the displacement signal is transmitted to the next module;

[0040] 02- Displacement to Voltage Conversion Module converts the displacement signal of the gyroscope into a voltage signal. In the linearization approximation, this process is approximated as a constant gain.

[0041] 03-Electronic filter module modulates the voltage signal into a digital signal and outputs it to the electronic compensator module;

[0042] 04-Electronic compensator module, which performs lead and lag compensation on digital signals to improve loop stability;

[0043] 05 - Quantizer module, which quantizes digital signals into 1-bit code streams and outputs pulse density modulated voltage signals;

[0044] The 06-DAC module converts digital voltage signals into analog voltage signals;

[0045] 07-Voltage to Force Conversion Module converts voltage signals into force outputs. In the linearization approximation, this process is approximated as a constant gain.

[0046] 08 - Coriolis force input, the difference between which is calculated and the feedback signal is used to input the gyroscope's sensitive mode;

[0047] 09 - Loop output, which is the output of the quantizer module, outputting a pulse density modulated voltage signal;

[0048] Figure 2 A flowchart illustrating the method for determining and optimizing the Σ-Δ closed-loop parameters of a MEMS gyroscope.

[0049] Figure 3 This is an example of determining the parameters of a MEMS gyroscope electromechanical combined with a Σ-Δ closed-loop detection circuit, as shown in the figure:

[0050] 01 - The gyroscope-sensitive mode module generates displacement when subjected to external forces, and the displacement signal is transmitted to the next module;

[0051] 02- Displacement to Voltage Conversion Module: This module converts the displacement signal from the gyroscope into a voltage signal. In the linearization approximation, this process is approximated as a constant gain K. yv ;

[0052] 03-Electronic filter module, the low-pass electronic filter architecture in the dashed box is shown in the embodiment, which modulates the voltage signal into a digital signal and outputs it to the electronic compensator module;

[0053] 04-Electronic compensator module, which performs lead and lag compensation on digital signals to improve loop stability;

[0054] 05 - Quantizer module, which quantizes digital signals into 1-bit code streams and outputs pulse density modulated voltage signals;

[0055] The 06-DAC module converts digital voltage signals into analog voltage signals, denoted as gain K. DAC ;

[0056] 07 - The voltage-to-force conversion module converts voltage signals into force outputs. In the linearization approximation, this process is approximated as a constant gain K. vf ;

[0057] Figure 4 This is an example of determining the parameters of a MEMS gyroscope electromechanical combined with a Σ-Δ closed-loop detection circuit, as shown in the figure:

[0058] 01 - The gyroscope-sensitive mode module generates displacement when subjected to external forces, and the displacement signal is transmitted to the next module;

[0059] 02- Displacement to Voltage Conversion Module: This module converts the displacement signal from the gyroscope into a voltage signal. In the linearization approximation, this process is approximated as a constant gain K. yv ;

[0060] 03-Electronic filter module, the low-pass electronic filter architecture in the dashed box is shown in the embodiment, which modulates the voltage signal into a digital signal and outputs it to the electronic compensator module;

[0061] 04-Electronic compensator module, which performs lead and lag compensation on digital signals to improve loop stability;

[0062] 05 - Quantizer module, which quantizes digital signals into 1-bit code streams and outputs pulse density modulated voltage signals;

[0063] The 06-DAC module converts digital voltage signals into analog voltage signals, denoted as gain K. DAC ;

[0064] 07 - The voltage-to-force conversion module converts voltage signals into force outputs. In the linearization approximation, this process is approximated as a constant gain K. vf . Detailed Implementation

[0065] like Figure 1-2 This invention provides a method for determining and optimizing the parameters of a Σ-Δ closed-loop detection circuit for MEMS gyroscope electromechanical integration.

[0066] The MEMS gyroscope electromechanical integrated Σ-Δ closed-loop detection loop consists of the following components: gyroscope sensitive mode module, displacement-to-voltage gain module, electronic filter module, electronic compensator module, quantizer module, DAC gain module, and voltage-to-force gain module. Among them:

[0067] When the gyroscope-sensitive mode module is subjected to an external force, it generates displacement, and the displacement signal is transmitted to the next module.

[0068] The displacement to voltage gain module converts the gyroscope's displacement signal into a voltage signal, and in the linearization approximation, this process is approximated as a constant gain;

[0069] The electronic filter module modulates the voltage signal into a digital signal and outputs it to the electronic compensator module;

[0070] The electronic compensator module performs lead-lag compensation on digital signals to improve loop stability;

[0071] The quantizer module quantizes the digital signal into a 1-bit code stream and outputs a pulse density modulated voltage signal;

[0072] The DAC gain module converts digital voltage signals into analog voltage signals;

[0073] The voltage-to-force gain module converts voltage signals into force outputs, and in the linearization approximation, this process is approximated as a constant gain.

[0074] The method for determining and optimizing the parameters of the MEMS gyroscope electromechanical integrated Σ-Δ closed-loop detection circuit, based on the equivalence of the electronic Σ-Δ modulator and the MEMS gyroscope electromechanical integrated Σ-Δ closed-loop detection circuit, is briefly described below:

[0075] Step 1: Determine the electronic Σ-Δ modulator. Based on the target signal-to-noise ratio (SNR), determine the architecture, order N, and oversampling rate (OSR) of the electronic Σ-Δ modulator. Use the electronic Σ-Δ modulator design tool DS Toolbox to design the noise transfer function NTF(z), and calculate the open-loop transfer function L(z) of the electronic Σ-Δ modulator based on the noise transfer function NTF(z). The calculation process is as follows: The obtained open-loop transfer function L(z) of the electronic Σ-Δ modulator is in the form of: Where z1, z2, ..., z N These are the zeros of the open-loop transfer function L(z) of the electronic Σ-Δ modulator, p1, p2, ..., p N These are the poles of the open-loop transfer function L(z) of the electronic Σ-Δ modulator.

[0076] Step 2: Discretize the gyroscope-sensitive mode. Given the quality factor Q and resonant frequency ω of the gyroscope-sensitive mode, the s-domain transfer function is written as... Where s pm and s pm * represents a pair of conjugate poles of the s-domain transfer function of the gyroscope-sensitive mode, K sm This represents the gain of the s-domain transfer function of the gyroscope-sensitive mode. The s-domain transfer function of the gyroscope-sensitive mode is converted to a z-domain transfer function using a discretization method. The z-domain transfer function takes the form... Where z m It is a zero of the z-domain transfer function of the gyroscope-sensitive mode, p m and p m * represents a pair of conjugate poles of the z-domain transfer function of the gyroscope-sensitive mode, K zm It is the gain of the z-domain transfer function of the gyroscope-sensitive mode.

[0077] Sub-step 2.1: The discretization method for converting the s-domain transfer function of the gyroscope-sensitive mode into the z-domain transfer function is described as follows: Given that the start time of the force feedback pulse is t... fb1 The duration of the action is t. fb2 The sampling time is T s The s-domain transfer function of the gyroscope-sensitive mode can be further written as... Where K sm1 and K sm2 This is the gain after partial expansion of the s-domain transfer function of the gyroscope-sensitive mode. The transformation process from the s-domain transfer function to the z-domain transfer function is expressed as follows: The z-domain transfer function can be simplified to the form:

[0078] Step 3: Linearize the y / v conversion and the v / f conversion. The y / v conversion module linearizes the gain of the shift to voltage near the zero position, denoted as gain K. yv The V / F conversion module linearizes the voltage-to-force gain near the zero position, denoted as gain K. vf .

[0079] Step 4: Establish a MEMS gyroscope electromechanical integrated Σ-Δ closed-loop detection circuit model. Determine the transfer function H of the electronic filter based on the selected electronic Σ-Δ modulator architecture. e (z), of order (N-2), in the form of Where z e1 ,z e2 ,…,z e(N-2) It is the zero point of the electronic filter, p e1 ,p e2 ,,…,p e(N-2) These are the poles of the electronic filter, and a, b, c… are the undetermined coefficients in the electronic filter; determine the transfer function H of the electronic compensator. com (z), in the form of Where z c1 For the zero point of the electronic compensator, p c1 For the electronic compensator pole, the electronic compensator pole p c1 With the zero point of the z-domain transfer function of the gyroscope-sensitive mode m equal.

[0080] Step 5: Based on steps 2-4, determine the open-loop transfer function L of the MEMS gyroscope electromechanical Σ-Δ closed-loop detection loop. em (z), the calculation process is L em (z)=K em H gyro (z)H e (z)H com (z), where K em =K yv K DAC K vf K q K DAC Let L be the gain of the DAC module, and Kq be the gain of the quantizer. Open-loop transfer function L... em The zero point of the z-domain transfer function of the gyroscope-sensitive mode in (z) m and electronic compensator pole p c1 To cancel out, to reduce the order.

[0081] Step 6: Let L em(z)=L(z), with equal numerators and equal denominators, determine the undetermined coefficients a, b, c… and the zero point z of the electronic compensator. c1 Undetermined coefficients a, b, c… and the zero point z of the electronic compensator c1 This refers to the Σ-Δ closed-loop detection circuit parameters of the MEMS gyroscope electromechanical combination. The two poles (p) of the gyroscope's sensitive mode z-domain transfer function. m and p m The two poles closest to each other in the open-loop transfer function L(z) of the electronic Σ-Δ modulator are equivalent, and the zero point z of the electronic compensator is... c1 The zero z of the electronic filter is equal to one of the real zeros of the open-loop transfer function L(z) of the electronic Σ-Δ modulator. e1 ,…,z eN-2 and the extreme point p e1 ,…p eN-2 The undetermined coefficients a, b, c… of the electronic filter are determined by the remaining zeros and poles of L(z).

[0082] Step 7: Optimize the MEMS gyroscope electromechanical Σ-Δ closed-loop detection loop parameters using a multi-objective optimization algorithm. Since an approximate equivalent was used when determining the MEMS gyroscope electromechanical Σ-Δ closed-loop detection loop parameters in Step 6, a multi-objective optimization algorithm (such as genetic algorithm, particle swarm optimization algorithm, or gradient descent algorithm) is used to optimize the MEMS gyroscope electromechanical Σ-Δ closed-loop detection loop parameters based on the obtained parameters.

[0083] Sub-step 7.1: Establish the objective function of the multi-objective optimization algorithm. The objective of the multi-objective optimization algorithm is to adjust the parameters of the MEMS gyro-electromechanical integrated Σ-Δ closed-loop detection loop while ensuring the stability of the MEMS gyro-electromechanical integrated Σ-Δ closed-loop detection loop, thereby maximizing the signal-to-noise ratio (SNR) of the output signal and minimizing the residual motion y of the sensitive mode. rm The maximum value of . Therefore, the objective function is expressed as

[0084] maxf1 = SNR(a,b,c,...)

[0085] minf2 = max[y rm (a,b,c,...)]

[0086] st|NTF| ∞ <1.5

[0087] Where SNR(a,b,c,…) represents the signal-to-noise ratio of the output signal under the current values ​​of the MEMS gyro-electromechanical combined Σ-Δ closed-loop detection loop parameters, y rm(a,b,c,…) represents the residual motion of the sensitive mode under the current values ​​of the MEMS gyro-electromechanical combined Σ-Δ closed-loop detection loop parameters, |NTF| ∞ Denotes the H-∞ norm of NTF, |NTF| ∞ The constraint <1.5 ensures the stability of the MEMS gyroscope electromechanical Σ-Δ closed-loop detection circuit.

[0088] When optimizing the simulation, a sine wave of -6dBFS is generally selected as the input to prevent overload. The initial value of the optimization algorithm is selected from the MEMS gyroscope electromechanical combined Σ-Δ closed-loop detection loop parameters obtained in step 6. The optimization parameters are generally selected as gain and local feedback parameters.

[0089] Sub-step 7.2: Solve the objective function in sub-step 7.1 using a multi-objective optimization algorithm, such as genetic algorithm, particle swarm optimization algorithm, gradient descent algorithm, etc., to obtain multiple sets of Pareto optimal solutions for the MEMS gyroscope electromechanical combined Σ-Δ closed-loop detection loop parameters.

[0090] Step 8: Based on the multiple Pareto optimal solutions obtained from the simulation results in Step 7 and the root locus method, determine a set of MEMS gyroscope electromechanical Σ-Δ closed-loop detection loop parameters.

[0091] Sub-step 8.1: For each set of MEMS gyroscope electromechanical Σ-Δ closed-loop detection loop parameters corresponding to the Pareto optimal solution, perform simulation using a sinusoidal input from -6dBFS to 0dBFS to determine the stable input range of the Pareto optimal solution for each set of MEMS gyroscope electromechanical Σ-Δ closed-loop detection loop parameters.

[0092] Sub-step 8.2: Analyze the open-loop transfer function L of the MEMS gyro-electromechanical integrated Σ-Δ closed-loop detection loop corresponding to the Pareto optimal solution of the parameters of each group of MEMS gyro-electromechanical integrated Σ-Δ closed-loop detection loops using the root locus method. em (z), determine the stable range of the gain Kem;

[0093] Sub-step 8.3: Based on the results of sub-steps 8.1-8.2, the designer selects the Pareto optimal solution of the best set of MEMS gyroscope electromechanical Σ-Δ closed-loop detection loop parameters that meets the performance requirements. This is the optimized MEMS gyroscope electromechanical Σ-Δ closed-loop detection loop parameters.

[0094] Example 1:

[0095] like Figure 3 The specific steps of the method for determining and optimizing the Σ-Δ closed-loop parameters of the MEMS gyroscope electromechanical combination of the present invention are as follows:

[0096] Step 1: Electronic Σ-Δ Modulator Design. Based on the target signal-to-noise ratio (SNR), determine the electronic Σ-Δ modulator architecture (CRFF), order N=4, and OSR=128. Use the electronic Σ-Δ modulator design tool DS Toolbox to design the modulator's noise transfer function (NTF(z)). Calculate the open-loop transfer function (L(z)) of the electronic Σ-Δ modulator based on the NTF(z). The calculation process is as follows: The obtained open-loop transfer function L(z) of the electronic Σ-Δ modulator is in the form of: Where z1, z2, z3, z4 are the zeros of the open-loop transfer function L(z) of the electronic Σ-Δ modulator, and p1, p2, p3, p4 are the poles of the open-loop transfer function L(z) of the electronic Σ-Δ modulator.

[0097] Step 2: Discretization of the gyroscope-sensitive mode. Given the quality factor Q and resonant frequency ω of the gyroscope-sensitive mode, the s-domain transfer function is written as... Where s pm and s pm * represents a pair of conjugate poles of the s-domain transfer function of the gyroscope-sensitive mode, K sm This represents the gain of the s-domain transfer function of the gyroscope-sensitive mode. The s-domain transfer function of the gyroscope-sensitive mode is converted to a z-domain transfer function using a discretization method. The z-domain transfer function takes the form... Where z m It is a zero of the z-domain transfer function of the gyroscope-sensitive mode, p m and p m * represents a pair of conjugate poles of the z-domain transfer function of the gyroscope-sensitive mode, K zm It is the gain of the z-domain transfer function of the gyroscope-sensitive mode.

[0098] Sub-step 2.1: The discretization method for converting the s-domain transfer function of the gyroscope-sensitive mode into the z-domain transfer function is described as follows: Given that the start time of the force feedback pulse is t... fb1 The duration of the action is t. fb2 The sampling time is T s The s-domain transfer function of the gyroscope-sensitive mode can be further written as... Where K sm1 and K sm2 This is the gain after partial expansion of the s-domain transfer function of the gyroscope-sensitive mode. The transformation process from the s-domain transfer function to the z-domain transfer function is expressed as follows: The z-domain transfer function can be simplified to the form:

[0099] Step 3: Linearization of y / v and v / f conversions. The y / v conversion module represents the gain linearization of the shift to voltage near the zero position, denoted as gain K. yvThe V / F conversion module represents the linearization of the voltage-to-force gain near the zero position, denoted as gain K. vf .

[0100] Step 4: Establish a MEMS gyroscope electromechanical Σ-Δ closed-loop detection circuit model. Establish the transfer function H of the loop electronic filter section. e (z), of order 2, write the transfer function according to the given architecture.

[0101]

[0102] Where z e1 ,z e2 It is the zero point of the electronic filter, p e1 ,p e2 , where are the poles of the electronic filter, and a, b, c, d are the undetermined coefficients in the electronic filter; write the transfer function H of the electronic compensator. com (z), in the form of Where z c1 For the zero point of the electronic compensator, p c1 For the electronic compensator pole, the electronic compensator pole p c1 With the zero point of the z-domain transfer function of the gyroscope-sensitive mode m equal.

[0103] Step 5: Based on steps 2-4, write the open-loop transfer function L of the MEMS gyroscope electromechanical Σ-Δ closed-loop detection circuit. em (z), the calculation process is L em (z)=K em H gyro (z)H e (z)H com (z), where K em =K yv K DAC K vf K q Open-loop transfer function L em The zero point of the z-domain transfer function of the gyroscope-sensitive mode in (z) m and electronic compensator pole p c1 To cancel out, to reduce the order.

[0104] Step 6: Let L em (z) = L(z), with equal numerators and denominators, determine the undetermined coefficients a, b, c, d and the zero point z of the electronic compensator. c1 Undetermined coefficients a, b, c… and the zero point z of the electronic compensator c1 This refers to the Σ-Δ closed-loop detection circuit parameters of the MEMS gyroscope electromechanical combination. The two poles (p) of the gyroscope's sensitive mode z-domain transfer function. m and p mThe two poles closest to each other in the open-loop transfer function L(z) of the electronic Σ-Δ modulator are equivalent, and the zero point z of the electronic compensator is... c1 The zero z of the electronic filter is equal to one of the real zeros of the open-loop transfer function L(z) of the electronic Σ-Δ modulator. e1 ,z e2 and the extreme point p e1 ,p e2 The undetermined coefficients a, b, c, d of the electronic filter are determined by the remaining zeros and poles of L(z).

[0105] Step 7: Optimize the MEMS gyroscope electromechanical integrated Σ-Δ closed-loop detection loop parameters using a multi-objective optimization algorithm. Since an approximate equivalent was used when determining the MEMS gyroscope electromechanical integrated Σ-Δ closed-loop detection loop parameters in Step 6, a multi-objective genetic algorithm is used to optimize the MEMS gyroscope electromechanical integrated Σ-Δ closed-loop detection loop parameters based on the obtained parameters.

[0106] Sub-step 7.1: Establish the objective function of the multi-objective optimization algorithm. The objective of the multi-objective optimization algorithm is to adjust the parameters of the MEMS gyro-electromechanical integrated Σ-Δ closed-loop detection loop while ensuring the stability of the MEMS gyro-electromechanical integrated Σ-Δ closed-loop detection loop, thereby maximizing the signal-to-noise ratio (SNR) of the output signal and minimizing the residual motion y of the sensitive mode. rm Therefore, the objective function is expressed as:

[0107] maxf1 = SNR(a,b,c,...)

[0108] minf2 = max[y rm (a,b,c,...)]

[0109] st|NTF| ∞ <1.5

[0110] Where SNR(a,b,c,…) represents the signal-to-noise ratio of the output signal under the current values ​​of the MEMS gyro-electromechanical combined Σ-Δ closed-loop detection loop parameters, y rm (a,b,c,…) represents the residual motion of the sensitive mode under the current values ​​of the MEMS gyro-electromechanical combined Σ-Δ closed-loop detection loop parameters, |NTF| ∞ Denotes the H-∞ norm of NTF, |NTF| ∞ The constraint <1.5 ensures the stability of the MEMS gyroscope electromechanical Σ-Δ closed-loop detection circuit.

[0111] When optimizing the simulation, a sine wave of -6dBFS is generally selected as the input to prevent overload. The initial value of the optimization algorithm is selected from the MEMS gyroscope electromechanical combined Σ-Δ closed-loop detection loop parameters obtained in step 6. The optimization parameters are generally selected as gain and local feedback parameters.

[0112] Sub-step 7.2: Solve the objective function from sub-step 7.1 using a multi-objective genetic algorithm, setting the population size to 200 and the maximum number of generations to 200. Obtain multiple sets of Pareto optimal solutions for the MEMS gyroscope electromechanical combined Σ-Δ closed-loop detection loop parameters.

[0113] Step 8: Determine a set of MEMS gyroscope electromechanical Σ-Δ closed-loop detection circuit parameters based on simulation results and root locus method.

[0114] Sub-step 8.1: Use simulation methods to determine the stable input range of the Pareto optimal solution for the electromechanical combined Σ-Δ closed-loop detection loop parameters of each MEMS gyroscope.

[0115] Sub-step 8.2: Analyze the open-loop transfer function L of the MEMS gyro-electromechanical integrated Σ-Δ closed-loop detection loop corresponding to the Pareto optimal solution of the parameters of each group of MEMS gyro-electromechanical integrated Σ-Δ closed-loop detection loops using the root locus method. em (z), determine the gain stability range

[0116] Sub-step 8.3: Based on the results of sub-steps 8.1-8.2, the designer selects the Pareto optimal solution of the best set of MEMS gyroscope electromechanical Σ-Δ closed-loop detection loop parameters that meets the performance requirements. This is the optimized MEMS gyroscope electromechanical Σ-Δ closed-loop detection loop parameters.

[0117] Example 2:

[0118] like Figure 4 The specific steps of the method for determining and optimizing the Σ-Δ closed-loop parameters of the MEMS gyroscope electromechanical combination of the present invention are as follows:

[0119] Step 1: Electronic Σ-Δ Modulator Design. Based on the target signal-to-noise ratio (SNR), determine the electronic Σ-Δ modulator architecture (CRFF), order N=5, and OSR=64. Use the electronic Σ-Δ modulator design tool DS Toolbox to design the modulator's noise transfer function (NTF(z)). Calculate the open-loop transfer function (L(z)) of the electronic Σ-Δ modulator based on the NTF(z). The calculation process is as follows: The obtained open-loop transfer function L(z) of the electronic Σ-Δ modulator is in the form of: Where z1, z2, z3, z4, z5 are the zeros of the open-loop transfer function L(z) of the electronic Σ-Δ modulator, and p1, p2, p3, p4, p5 are the poles of the open-loop transfer function L(z) of the electronic Σ-Δ modulator.

[0120] Step 2: Discretization of the gyroscope-sensitive mode. Given the quality factor Q and resonant frequency ω of the gyroscope-sensitive mode, the s-domain transfer function is written as... Where s pm and s pm * represents a pair of conjugate poles of the s-domain transfer function of the gyroscope-sensitive mode, K sm This represents the gain of the s-domain transfer function of the gyroscope-sensitive mode. The s-domain transfer function of the gyroscope-sensitive mode is converted to a z-domain transfer function using a discretization method. The z-domain transfer function takes the form... Where z m It is a zero of the z-domain transfer function of the gyroscope-sensitive mode, p m and p m * represents a pair of conjugate poles of the z-domain transfer function of the gyroscope-sensitive mode, K zm It is the gain of the z-domain transfer function of the gyroscope-sensitive mode.

[0121] Sub-step 2.1: The discretization method for converting the s-domain transfer function of the gyroscope-sensitive mode into the z-domain transfer function is described as follows: Given that the start time of the force feedback pulse is t... fb1 The duration of the action is t. fb2 The sampling time is T s The s-domain transfer function of the gyroscope-sensitive mode can be further written as... Where K sm1 and K sm2 This is the gain after partial expansion of the s-domain transfer function of the gyroscope-sensitive mode. The transformation process from the s-domain transfer function to the z-domain transfer function is expressed as follows: The z-domain transfer function can be simplified to the form:

[0122] Step 3: Linearization of y / v and v / f conversions. The y / v conversion module represents the linearization of the gain from displacement to voltage near the zero position, denoted as gain K. yv The V / F conversion module represents the linearization of the voltage-to-force gain near the zero position, denoted as gain K. vf .

[0123] Step 4: Establish a MEMS gyroscope electromechanical Σ-Δ closed-loop detection circuit model. Establish the transfer function H of the loop electronic filter section. e (z), of order 3, write the transfer function according to the given architecture.

[0124]

[0125] Where z e1 ,z e2 ,z e3 It is the zero point of the electronic filter, p e1 ,p e2 ,p e3 Here are the poles of the electronic filter, and a, b, c, d, e are the undetermined coefficients in the electronic filter; write the transfer function H of the electronic compensator. com (z), in the form of Where z c1 For the zero point of the electronic compensator, p c1 For the electronic compensator pole, the electronic compensator pole p c1 With the zero point of the z-domain transfer function of the gyroscope-sensitive mode m equal.

[0126] Step 5: Based on steps 2-4, write the open-loop transfer function L of the MEMS gyroscope electromechanical Σ-Δ closed-loop detection circuit. em (z), the calculation process is L em (z)=K em H gyro (z)H e (z)H com (z), where K em =K yv K DAC K vf K q Open-loop transfer function L em The zero point of the z-domain transfer function of the gyroscope-sensitive mode in (z) m and electronic compensator pole p c1 To cancel out, to reduce the order.

[0127] Step 6: Let L em (z) = L(z), with equal numerators and denominators, determine the undetermined coefficients a, b, c, d, e and the zero point z of the electronic compensator. c1 Undetermined coefficients a, b, c, d, e and the zero point z of the electronic compensator c1 This refers to the Σ-Δ closed-loop detection circuit parameters of the MEMS gyroscope electromechanical combination. The two poles (p) of the gyroscope's sensitive mode z-domain transfer function. m and p m The two poles closest to each other in the open-loop transfer function L(z) of the electronic Σ-Δ modulator are equivalent, and the zero point z of the electronic compensator is... c1 The zero z of the electronic filter is equal to one of the real zeros of the open-loop transfer function L(z) of the electronic Σ-Δ modulator. e1 ,z e2 ,z e3 and the extreme point p e1 ,p e2 ,pe3 The undetermined coefficients a, b, c, d, e of the electronic filter are determined by the remaining zeros and poles of L(z).

[0128] Step 7: Optimize the MEMS gyroscope electromechanical integrated Σ-Δ closed-loop detection loop parameters using a multi-objective optimization algorithm. Since an approximate equivalent was used when determining the MEMS gyroscope electromechanical integrated Σ-Δ closed-loop detection loop parameters in Step 6, a multi-objective particle swarm optimization algorithm is used to optimize the MEMS gyroscope electromechanical integrated Σ-Δ closed-loop detection loop parameters based on the obtained parameters.

[0129] Sub-step 7.1: Establish the objective function of the multi-objective optimization algorithm. The objective of the multi-objective optimization algorithm is to adjust the parameters of the MEMS gyro-electromechanical integrated Σ-Δ closed-loop detection loop while ensuring the stability of the MEMS gyro-electromechanical integrated Σ-Δ closed-loop detection loop, thereby maximizing the signal-to-noise ratio (SNR) of the output signal and minimizing the residual motion y of the sensitive mode. rm Therefore, the objective function is expressed as:

[0130] maxf1 = SNR(a,b,c,...)

[0131] minf2 = max[y rm (a,b,c,...)]

[0132] st|NTF| ∞ <1.5

[0133] Where SNR(a,b,c,…) represents the signal-to-noise ratio of the output signal under the current values ​​of the MEMS gyro-electromechanical combined Σ-Δ closed-loop detection loop parameters, y rm (a,b,c,…) represents the residual motion of the sensitive mode under the current values ​​of the MEMS gyro-electromechanical combined Σ-Δ closed-loop detection loop parameters, |NTF| ∞ Denotes the H-∞ norm of NTF, |NTF| ∞ The constraint <1.5 ensures the stability of the MEMS gyroscope electromechanical Σ-Δ closed-loop detection circuit.

[0134] When optimizing the simulation, a sine wave of -6dBFS is generally selected as the input to prevent overload. The initial value of the optimization algorithm is selected from the MEMS gyroscope electromechanical combined Σ-Δ closed-loop detection loop parameters obtained in step 6. The optimization parameters are generally selected as gain and local feedback parameters.

[0135] Sub-step 7.2: Solve the objective function from sub-step 7.1 using a multi-objective particle swarm optimization algorithm, setting the population size to 200 and the maximum number of generations to 200. Obtain multiple sets of Pareto optimal solutions for the MEMS gyroscope electromechanical combined Σ-Δ closed-loop detection loop parameters.

[0136] Step 8: Determine a set of MEMS gyroscope electromechanical Σ-Δ closed-loop detection circuit parameters based on simulation results and root locus method.

[0137] Sub-step 8.1: Use simulation methods to determine the stable input range of the Pareto optimal solution for the electromechanical combined Σ-Δ closed-loop detection loop parameters of each MEMS gyroscope.

[0138] Sub-step 8.2: Analyze the open-loop transfer function L of the MEMS gyro-electromechanical integrated Σ-Δ closed-loop detection loop corresponding to the Pareto optimal solution of the parameters of each group of MEMS gyro-electromechanical integrated Σ-Δ closed-loop detection loops using the root locus method. em (z), determine the gain stability range

[0139] Sub-step 8.3: Based on the results of sub-steps 8.1-8.2, the designer selects the Pareto optimal solution of the best set of MEMS gyroscope electromechanical Σ-Δ closed-loop detection loop parameters that meets the performance requirements. This is the optimized MEMS gyroscope electromechanical Σ-Δ closed-loop detection loop parameters.

[0140] Invention point 1: Combining electrical Σ-Δ modulator design technology, a multi-objective evolutionary algorithm is used to optimize the parameters of the electromechanical Σ-Δ closed-loop detection circuit, reducing the amount of computation while improving the performance of the electromechanical Σ-Δ closed-loop detection circuit.

[0141] Invention point 2: The optimization of the electromechanical Σ-Δ closed-loop detection circuit parameters is regarded as a constrained multi-objective optimization problem, which can find a set of Pareto optimal solutions, thereby expanding the selection of optimal parameters.

[0142] Invention point 3: Because parameter optimization is used, there is no need to worry about approximations in the previous steps, thereby expanding the range of architecture choices.

[0143] Invention point 4: The lead-lag compensation provided by the electronic compensator can accurately cancel out the redundant zeros and poles in the open-loop transfer function.

Claims

1. A method for determining and optimizing the parameters of a MEMS gyroscope electromechanical Σ-Δ closed-loop circuit, characterized in that, include: Step 1: Determine the electronic Σ-Δ modulator; Step 2: Discretize the gyroscope's sensitive modes; Step 3: Linearize the y / v conversion and the v / f conversion. The y / v conversion module linearizes the gain of the shift to voltage near the zero position, expressed as the gain. The V / F conversion module linearizes the voltage-to-force gain near the zero position, expressed as the gain. ; Step 4: Establish a MEMS gyroscope electromechanical Σ-Δ closed-loop detection circuit model. Specifically, determine the transfer function H of the electronic filter based on the selected electronic Σ-Δ modulator architecture. e (z), of order (N-2), in the form of , where z e1 , z e2 , …, z e(N-2) It is the zero point of the electronic filter, p e1 , p e2 ,…, p e(N-2) These are the poles of the electronic filter, and a, b, c… are the undetermined coefficients in the electronic filter; determine the transfer function H of the electronic compensator. com (z), in the form of , where z c1 For the zero point of the electronic compensator, p c1 For the electronic compensator pole, the electronic compensator pole p c1 With the zero point of the z-domain transfer function of the gyroscope-sensitive mode m equal; Step 5: Based on steps 2-4, determine the open-loop transfer function L of the MEMS gyroscope electromechanical Σ-Δ closed-loop detection loop. em (z); Step 6: Based on Steps 1 and 5, determine the undetermined coefficients a, b, c… and the zero point z of the electronic compensator. c1 Undetermined coefficients a, b, c… and the zero point z of the electronic compensator c1 This refers to the Σ-Δ closed-loop detection circuit parameters of the MEMS gyroscope electromechanical combination. Step 7: Optimize the MEMS gyroscope electromechanical Σ-Δ closed-loop detection loop parameters using a multi-objective optimization algorithm. Specifically: Step 7.1: Establish the objective function of the multi-objective optimization algorithm: Where SNR(a,b,c,…) represents the signal-to-noise ratio of the output signal under the current values ​​of the MEMS gyro-electromechanical combined Σ-Δ closed-loop detection loop parameters, y rm (a,b,c,…) represents the residual motion of the sensitive mode under the current values ​​of the MEMS gyro-electromechanical combined Σ-Δ closed-loop detection loop parameters, |NTF| ∞ Denotes the H-∞ norm of NTF, |NTF| ∞ <1.5 is a constraint condition to ensure the stability of the MEMS gyroscope electromechanical Σ-Δ closed-loop detection circuit; Step 7.2: Solve the objective function in sub-step 7.1 using a multi-objective optimization algorithm to obtain multiple sets of Pareto optimal solutions for the MEMS gyroscope electromechanical Σ-Δ closed-loop detection loop parameters; Step 8: Determine a set of MEMS gyroscope electromechanical Σ-Δ closed-loop detection loop parameters based on the multiple Pareto optimal solutions obtained in Step 7 and the root locus method.

2. The method according to claim 1, characterized in that, Step 1: Determine the electronic Σ-Δ modulator, specifically: Based on the target signal-to-noise ratio (SNR), the architecture, order N, and oversampling rate (OSR) of the electronic Σ-Δ modulator are determined. The noise transfer function (NTF) of the electronic Σ-Δ modulator is designed using the DS Toolbox design tool. The open-loop transfer function (L(z)) of the electronic Σ-Δ modulator is then calculated based on the NTF(z). The calculation process is as follows: The open-loop transfer function L(z) of the obtained electronic Σ-Δ modulator takes the form of: Where z1, z2, ..., z N These are the zeros of the open-loop transfer function L(z) of the electronic Σ-Δ modulator, p1, p2, ..., p N These are the poles of the open-loop transfer function L(z) of the electronic Σ-Δ modulator.

3. The method according to claim 2, characterized in that, Step 2, specifically: The s-domain transfer function is determined based on the quality factor Q and resonant frequency ω of the gyroscope's sensitive mode: , where s pm and s pm * represents a pair of conjugate poles of the s-domain transfer function of the gyroscope-sensitive mode, K sm It is the gain of the s-domain transfer function of the gyroscope-sensitive mode; The s-domain transfer function of the gyroscope-sensitive mode is converted into a z-domain transfer function using a discretization method. The z-domain transfer function is of the form: , where z m It is a zero of the z-domain transfer function of the gyroscope-sensitive mode, p m and p m * represents a pair of conjugate poles of the z-domain transfer function of the gyroscope-sensitive mode, K zm It is the gain of the z-domain transfer function of the gyroscope-sensitive mode.

4. The method according to claim 3, characterized in that, In step 2, the discretization method for converting the s-domain transfer function of the gyroscope-sensitive mode into the z-domain transfer function is as follows: Given that the force feedback pulse begins to act at time t. fb1 The duration of the action is t. fb2 The sampling time is T s The s-domain transfer function of the gyroscope-sensitive mode can be further transformed into K sm1 and K sm2 The gain is the result of the partial expansion of the s-domain transfer function of the gyroscope-sensitive mode. The transformation process from the s-domain transfer function to the z-domain transfer function is expressed as follows: The z-domain transfer function can be simplified to the form of .

5. The method according to claim 4, characterized in that, Step 5, specifically: ,in K DAC Let L be the gain of the DAC module, Kq be the gain of the quantizer, and L be the open-loop transfer function. em The zero point of the z-domain transfer function of the gyroscope-sensitive mode in (z) m and electronic compensator pole p c1 To cancel out, to reduce the order.

6. The method according to claim 5, characterized in that, Step 7 specifically includes: optimizing the parameters of the MEMS gyroscope electromechanical Σ-Δ closed-loop detection circuit using a genetic algorithm, particle swarm optimization algorithm, or gradient descent algorithm.

7. The method according to claim 6, characterized in that, In step 7, a -6dBFS sine wave is selected as the input for the optimization simulation to prevent overload, and the initial value of the optimization algorithm is selected from the MEMS gyroscope electromechanical combined Σ-Δ closed-loop detection loop parameters obtained in step 6.

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