Method for determining and optimizing loop parameters of MEMS (Micro Electro Mechanical System) gyroscope in electromechanical combination with sigma-delta closed loop

Abstract

The invention belongs to the technical field of inertial sensor control, and particularly relates to a method for determining and optimizing parameters of an MEMS gyroscope electromechanical combination sigma-delta closed loop. According to the method, an electronic compensator is added in a loop to compensate a zero point of a gyro sensitive mode z-domain transfer function and a pole of an MEMS gyro electromechanical combination sigma-delta closed loop detection loop, and parameters are determined based on the equivalent of the electronic sigma-delta modulator and the MEMS gyro electromechanical combination sigma-delta closed loop detection loop. And performance loss caused in the approximate equivalent process is optimized by using a multi-objective optimization algorithm to obtain optimal parameters.

Description

Technical Field

[0001] The present invention belongs to the technical field of inertial sensor control, and in particular relates to a method for determining and optimizing loop parameters of a MEMS gyroscope electromechanically combined Σ-Δ closed loop. Background Art

[0002] MEMS gyroscope is an inertial sensor for measuring the angular velocity of a carrier, which is manufactured using micro-electromechanical system technology. It has the advantages of low cost, small size, light weight, low power consumption, and easy mass production. It is currently widely used in aerospace, automotive, consumer electronics, medical, industrial and other fields.

[0003] The control schemes of MEMS gyroscopes are divided into open-loop control and closed-loop control. Although the open-loop control method that does not apply external force to control sensitive modes is simple to implement, it cannot take into account the requirements of large bandwidth and high sensitivity. There are also problems such as small range and poor robustness. High-performance gyroscopes generally use closed-loop control technology to suppress the vibration of sensitive modes through negative feedback, thereby improving performance such as range, bandwidth, and scale factor nonlinearity.

[0004] MEMS gyroscopes generally use modulation and demodulation methods to achieve closed-loop control of sensitive modes. The output of sensitive modes 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 obtains a higher signal-to-noise ratio through oversampling and noise shaping, and can obtain 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, which directly acts on the feedback electrode through the feedback DAC (digital-to-analog converter). The closed-loop control of the sensitive mode can be completed without going through the modulation and demodulation link, and a low quantization noise digital signal can be directly output, which greatly simplifies the complexity of the closed-loop control. This technology is called electromechanical combined Σ-Δ closed-loop detection technology.

[0005] There are many design difficulties in the design of the electromechanical Σ-Δ closed-loop detection loop parameters: the integral node inside the gyroscope cannot be brought out, resulting in a reduction in degrees of freedom; the mechanical characteristics of the gyroscope will constrain the parameter design; the loop working signal is a mixture of analog and digital domains. The design of the electromechanical Σ-Δ closed-loop detection loop parameters directly affects the performance and stability of the gyroscope closed-loop control, so it is necessary to develop a method that can determine the optimal loop parameters based on the loop structure and the mechanical characteristics of the gyroscope. Summary of the invention

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

[0007] Technical solution:

[0008] A method for determining and optimizing loop parameters of a MEMS gyroscope electromechanically combined Σ-Δ closed loop, comprising:

[0009] Step 1: Determine the electronic sigma-delta modulator;

[0010] Step 2: Discretize the gyro 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 displacement to voltage near the zero position, which is expressed as the gain K yv , the v / f conversion module linearizes the voltage-to-force gain near the zero position, expressed as gain K vf ;

[0012] Step 4: Establish the MEMS gyro electromechanical combined Σ-Δ closed-loop detection loop model, specifically: Determine the transfer function H of the electronic filter according to the selected electronic Σ-Δ modulator architecture e (z), the order is (N-2), the form is where z e1 ,z e2 ,…,z e(N-2) is the zero point of the electronic filter, p e1 ,p e2 ,,…,p e(N-2) is the pole of the electronic filter, a, b, c… are the unknown coefficients in the electronic filter; determine the transfer function H of the electronic compensator com (z), in the form where z c1 is the zero point of the electronic compensator, p c1 is the electronic compensator pole, the electronic compensator pole p c1 The zero point z of the z-domain transfer function of the gyro sensitive mode m equal;

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

[0014] Step 6: According to step 1 and step 5, determine the unknown coefficients a, b, c... and the zero point z of the electronic compensator c1 , the unknown coefficients a, b, c... and the zero point z of the electronic compensator c1 That is, the MEMS gyro electromechanical combined Σ-Δ closed-loop detection loop parameters;

[0015] Step 7: Use a multi-objective optimization algorithm to optimize the parameters of the MEMS gyro electromechanical combined Σ-Δ closed-loop detection loop;

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

[0017] Further, step 1: determining the electronic sigma-delta modulator, specifically:

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

[0019] Furthermore, step 2 is specifically as follows:

[0020] According to the quality factor Q and resonant frequency ω of the gyro sensitive mode, the s-domain transfer function is determined: where s pm and pm * is a pair of conjugate poles of the gyro sensitive mode s-domain transfer function, K sm is the gain of the gyro sensitive mode s-domain transfer function;

[0021] The discretization method is used to convert the s-domain transfer function of the gyro sensitive mode into the z-domain transfer function. The z-domain transfer function is as follows: where z m is the zero point of the z-domain transfer function of the gyro sensitive mode, p m and p m * is a pair of conjugate poles of the z-domain transfer function of the gyro sensitive mode, K zm is the gain of the z-domain transfer function of the gyro sensitive mode.

[0022] Furthermore, in step 2, a discretization method for converting the gyro sensitive mode s-domain transfer function into a z-domain transfer function is specifically:

[0023] It is known that the starting time of the force feedback pulse is t fb1 The end time of the action is t fb2 , the sampling time is T s , the gyro sensitive mode s-domain transfer function can be further converted to Where Ksm1 and K sm2 is the gain of the gyro sensitive mode s-domain transfer function after partial expansion. The conversion process from the s-domain transfer function to the z-domain transfer function is expressed as:

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

[0025] Furthermore, step 5 is specifically as follows:

[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 is the gain of the DAC module, Kq is the gain of the quantizer, and the open-loop transfer function L em (z) The zero point z of the z-domain transfer function of the gyro sensitive mode m and the electronic compensator pole p c1 Offset, reduce the order.

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

[0028] Furthermore, step 7 is specifically as follows:

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

[0034] Step 7.2: Use a multi-objective optimization algorithm to solve the objective function in sub-step 7.1 and obtain the Pareto optimal solution of multiple sets of MEMS gyro electromechanical combined Σ-Δ closed-loop detection loop parameters.

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

[0036] Beneficial effects:

[0037] The present invention adopts a single feedback architecture to simplify the complexity of the loop, and can automatically compensate for the gain mismatch of the loop. An electronic compensator is added to the loop to compensate for the zero point of the z-domain transfer function of the gyro sensitive mode and the pole of the MEMS gyro electromechanical combined Σ-Δ closed-loop detection loop. Parameters are determined based on the equivalence of an electronic Σ-Δ modulator and a MEMS gyro electromechanical combined Σ-Δ closed-loop detection loop, and a multi-objective optimization algorithm is used to optimize the performance loss caused in the approximate equivalence process to obtain optimal parameters. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] Figure 1 This is a diagram of the MEMS gyro electromechanical combined Σ-Δ closed-loop detection loop architecture. In the figure:

[0039] 01-Gyro sensitive mode module, which is displaced by external force, and the displacement signal is transmitted to the next module;

[0040] 02-Displacement to voltage conversion module, which converts the displacement signal of the gyroscope into a voltage signal. In the linearization approximation, this process is approximately a constant gain;

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

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

[0043] 05-Quantizer module, quantizes the digital signal into a 1-bit code stream and outputs a pulse density modulated voltage signal;

[0044] 06-DAC module, converts digital voltage signal into analog voltage signal;

[0045] 07- Voltage to force conversion module, converts the voltage signal into force output, and the process is approximated as constant gain in the linearization approximation;

[0046] 08-Coriolis force input, after subtracting the feedback signal, input the gyro sensitive mode;

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

[0048] Figure 2 A flow chart of the method for determining and optimizing the loop parameters of the MEMS gyroscope electromechanical combined Σ-Δ closed loop;

[0049] Figure 3 This is an embodiment of determining the parameters of a MEMS gyroscope electromechanically combined with a Σ-Δ closed-loop detection loop, in which:

[0050] 01-Gyro sensitive mode module, which is displaced by external force, and the displacement signal is transmitted to the next module;

[0051] 02-Displacement to voltage conversion module, which converts the displacement signal of the gyro into a voltage signal. In the linearization approximation, this process is approximated as a constant gain K yv ;

[0052] 03-Electronic filter module, the dotted box is a low-pass electronic filter architecture of 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-lag compensation on digital signals to improve loop stability;

[0054] 05-Quantizer module, quantizes the digital signal into a 1-bit code stream and outputs a pulse density modulated voltage signal;

[0055] 06-DAC module, converts digital voltage signal into analog voltage signal, expressed as gain K DAC ;

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

[0057] Figure 4 This is an embodiment of determining the parameters of a MEMS gyroscope electromechanically combined with a Σ-Δ closed-loop detection loop, in which:

[0058] 01-Gyro sensitive mode module, which is displaced by external force, and the displacement signal is transmitted to the next module;

[0059] 02-Displacement to voltage conversion module, which converts the displacement signal of the gyro into a voltage signal. In the linearization approximation, this process is approximated as a constant gain K yv ;

[0060] 03-Electronic filter module, the dotted box is a low-pass electronic filter architecture of 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-lag compensation on digital signals to improve loop stability;

[0062] 05-Quantizer module, quantizes the digital signal into a 1-bit code stream and outputs a pulse density modulated voltage signal;

[0063] 06-DAC module, converts digital voltage signal into analog voltage signal, expressed as gain K DAC ;

[0064] 07- Voltage to force conversion module, converts the voltage signal into force. In the linearization approximation, this process is approximated as a constant gain K vf . DETAILED DESCRIPTION

[0065] like Figure 1-2 The present invention provides a method for determining and optimizing loop parameters of a MEMS gyroscope electromechanically combined Σ-Δ closed-loop detection circuit.

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

[0067] The gyro sensitive modal module is displaced by external force, and the displacement signal is transmitted to the next module;

[0068] The displacement-to-voltage gain module converts the gyro's displacement signal into a voltage signal, which is approximated as a constant gain in the linearization approximation.

[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 the digital signal 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 the digital voltage signal into an analog voltage signal;

[0073] The voltage-to-force gain module converts the voltage signal into force output, and the process is approximated as a constant gain in the linearization approximation;

[0074] The parameter determination and optimization method of the MEMS gyro electromechanical combined Σ-Δ closed-loop detection loop is based on the equivalence of the electronic Σ-Δ modulator and the MEMS gyro electromechanical combined Σ-Δ closed-loop detection loop, which is briefly described as follows:

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

[0076] Step 2: Discretize the gyro sensitive mode. Knowing the quality factor Q and resonant frequency ω of the gyro sensitive mode, the s-domain transfer function is written as where s pm and pm * is a pair of conjugate poles of the gyro sensitive mode s-domain transfer function, K sm is the gain of the gyro sensitive mode s-domain transfer function. The gyro sensitive mode s-domain transfer function is converted into a z-domain transfer function using the discretization method. The z-domain transfer function is as follows: where z m is the zero point of the z-domain transfer function of the gyro sensitive mode, p m and p m * is a pair of conjugate poles of the z-domain transfer function of the gyro sensitive mode, K zm is the gain of the z-domain transfer function of the gyro sensitive mode.

[0077] Sub-step 2.1: The discretization method of converting the gyro sensitive mode s-domain transfer function into the z-domain transfer function is as follows: The starting time of the force feedback pulse is known to be t fb1 The end time of the action is t fb2 , the sampling time is T s The gyro sensitive mode s-domain transfer function can be further written as Where K sm1 and K sm2 is the gain of the gyro sensitive mode s-domain transfer function after partial expansion. The conversion process from s-domain transfer function to z-domain transfer function is expressed as 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 displacement to voltage around the zero position, expressed as gain K yv , the v / f conversion module linearizes the voltage-to-force gain near the zero position, expressed as gain K vf .

[0079] Step 4: Establish the MEMS gyro electromechanical combined Σ-Δ closed-loop detection loop model. Determine the transfer function H of the electronic filter according to the selected electronic Σ-Δ modulator architecture. e (z), the order is (N-2), the form is where z e1 ,z e2 ,…,z e(N-2) is the zero point of the electronic filter, p e1 ,p e2 ,,…,p e(N-2) is the pole of the electronic filter, a, b, c… are the unknown coefficients in the electronic filter; determine the transfer function H of the electronic compensator com (z), in the form where z c1 is the zero point of the electronic compensator, p c1 is the electronic compensator pole, the electronic compensator pole p c1 The zero point z of the z-domain transfer function of the gyro sensitive mode m equal.

[0080] Step 5: Based on steps 2-4, determine the open-loop transfer function L of the MEMS gyro electromechanical combined 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 is the gain of the DAC module, and Kq is the gain of the quantizer. The open-loop transfer function L em (z) The zero point z of the z-domain transfer function of the gyro sensitive mode m and the electronic compensator pole p c1 Offset, reduce the order.

[0081] Step 6: Let L em(z)=L(z), the numerator and denominator are equal, determine the unknown coefficients a, b, c... and the zero point z of the electronic compensator c1 , the unknown coefficients a, b, c... and the zero point z of the electronic compensator c1 These are the parameters of the MEMS gyro electromechanical combined Σ-Δ closed-loop detection loop. The two poles of the gyro sensitive mode z-domain transfer function (p m and p m *) is equivalent to the two closest poles in the open-loop transfer function L(z) of the electronic Σ-Δ modulator. The zero point z of the electronic compensator c1 Equal to a real zero of the open-loop transfer function L(z) of the electronic Σ-Δ modulator, the zero z of the electronic filter e1 ,…,z eN-2 and the extreme point p e1 ,…p eN-2 The remaining zeros and poles of L(z) are used to determine the unknown coefficients a, b, c, etc. of the electronic filter.

[0082] Step 7: Use a multi-objective optimization algorithm to optimize the MEMS gyro electromechanical combined Σ-Δ closed-loop detection loop parameters. Since approximate equivalence was used when determining the MEMS gyro electromechanical combined Σ-Δ closed-loop detection loop parameters in step 6, a multi-objective optimization algorithm (such as a genetic algorithm, a particle swarm optimization algorithm, and a gradient descent algorithm) is used nearby to optimize the MEMS gyro electromechanical combined Σ-Δ closed-loop detection loop parameters based on the above-mentioned 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 combined Σ-Δ closed-loop detection loop, maximize the output signal-to-noise ratio (SNR) of the MEMS gyro electromechanical combined Σ-Δ closed-loop detection loop, and minimize the residual motion y of the sensitive mode while ensuring the stability of the MEMS gyro electromechanical combined Σ-Δ closed-loop detection loop. 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 output signal signal-to-noise ratio under the current MEMS gyro electromechanical combined with Σ-Δ closed-loop detection loop parameter values, y rm(a, b, c, …) represents the residual motion of the sensitive mode under the current MEMS gyro electromechanical combined with Σ-Δ closed-loop detection loop parameter values, |NTF| ∞ represents the H-∞ norm of NTF, |NTF| ∞ <1.5 is a constraint condition to ensure the stability of the MEMS gyro electromechanical combined Σ-Δ closed-loop detection loop.

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

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

[0090] Step 8: Determine a set of MEMS gyro electromechanical combined Σ-Δ closed-loop detection loop parameters based on multiple sets of Pareto optimal solutions obtained from the simulation results in step 7 and the root locus method.

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

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

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

[0094] Embodiment 1:

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

[0096] Step 1: Design of electronic Σ-Δ modulator. According to the target signal-to-noise ratio (SNR), the architecture CRFF, order N = 4, and OSR = 128 of the electronic Σ-Δ modulator are determined. The noise transfer function NTF(z) of the modulator is designed using the electronic Σ-Δ modulator design tool DS Toolbox. The open-loop transfer function L(z) of the electronic Σ-Δ modulator is calculated based on the electronic Σ-Δ modulator noise transfer function NTF(z). The calculation process is as follows: The resulting open-loop transfer function L(z) of the electronic Σ-Δ modulator is in the form 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: Discretize the gyro sensitive mode. Knowing the quality factor Q and resonant frequency ω of the gyro sensitive mode, the s-domain transfer function is written as where s pm and pm * is a pair of conjugate poles of the gyro sensitive mode s-domain transfer function, K sm is the gain of the gyro sensitive mode s-domain transfer function. The gyro sensitive mode s-domain transfer function is converted into a z-domain transfer function using the discretization method. The z-domain transfer function is as follows: where z m is the zero point of the z-domain transfer function of the gyro sensitive mode, p m and p m * is a pair of conjugate poles of the z-domain transfer function of the gyro sensitive mode, K zm is the gain of the z-domain transfer function of the gyro sensitive mode.

[0098] Sub-step 2.1: The discretization method of converting the gyro sensitive mode s-domain transfer function into the z-domain transfer function is as follows: The starting time of the force feedback pulse is known to be t fb1 The end time of the action is t fb2 , the sampling time is T s The gyro sensitive mode s-domain transfer function can be further written as Where K sm1 and K sm2 is the gain of the gyro sensitive mode s-domain transfer function after partial expansion. The conversion process from s-domain transfer function to z-domain transfer function is expressed as The z-domain transfer function can be simplified to the form

[0099] Step 3: y / v conversion and v / f conversion linearization. The y / v conversion module represents the linearization of the gain from displacement to voltage near the zero position, expressed as gain K yv, the v / f conversion module represents the linearization of the voltage-to-force gain near the zero position, expressed as gain K vf .

[0100] Step 4: Establish the MEMS gyro electromechanical combined Σ-Δ closed-loop detection loop model. Establish the transfer function H of the loop electronic filter part e (z), the order is 2, and the transfer function is written according to the given architecture

[0101]

[0102] where z e1 ,z e2 is the zero point of the electronic filter, p e1 ,p e2 , is the pole of the electronic filter, a, b, c, d are the unknown coefficients in the electronic filter; write the transfer function H of the electronic compensator com (z), in the form where z c1 is the zero point of the electronic compensator, p c1 is the electronic compensator pole, the electronic compensator pole p c1 The zero point z of the z-domain transfer function of the gyro sensitive mode m equal.

[0103] Step 5: Based on steps 2-4, write the open-loop transfer function L of the MEMS gyro electromechanical combined with the 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 . Open loop transfer function L em (z) The zero point z of the z-domain transfer function of the gyro sensitive mode m and the electronic compensator pole p c1 Offset, reduce the order.

[0104] Step 6: Let L em (z)=L(z), the numerator and denominator are equal, determine the unknown coefficients a, b, c, d and the zero point z of the electronic compensator c1 , the unknown coefficients a, b, c... and the zero point z of the electronic compensator c1 These are the parameters of the MEMS gyro electromechanical combined Σ-Δ closed-loop detection loop. The two poles of the gyro sensitive mode z-domain transfer function (p m and p m*) is equivalent to the two closest poles in the open-loop transfer function L(z) of the electronic Σ-Δ modulator. The zero point z of the electronic compensator c1 Equal to a real zero of the open-loop transfer function L(z) of the electronic Σ-Δ modulator, the zero z of the electronic filter e1 ,z e2 and the extreme point p e1 ,p e2 The remaining zeros and poles of L(z) are used to determine the unknown coefficients a, b, c, and d of the electronic filter.

[0105] Step 7: Use a multi-objective optimization algorithm to optimize the MEMS gyro electromechanical combined Σ-Δ closed-loop detection loop parameters. Since approximate equivalence was used when determining the MEMS gyro electromechanical combined Σ-Δ closed-loop detection loop parameters in step 6, a multi-objective genetic algorithm is used nearby to optimize the MEMS gyro electromechanical combined Σ-Δ closed-loop detection loop parameters based on the above-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 combined Σ-Δ closed-loop detection loop, maximize the output signal-to-noise ratio (SNR) of the MEMS gyro electromechanical combined Σ-Δ closed-loop detection loop, and minimize the residual motion y of the sensitive mode while ensuring the stability of the MEMS gyro electromechanical combined Σ-Δ closed-loop detection loop. 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 output signal signal-to-noise ratio under the current MEMS gyro electromechanical combined with Σ-Δ closed-loop detection loop parameter values, y rm (a, b, c, …) represents the residual motion of the sensitive mode under the current MEMS gyro electromechanical combined with Σ-Δ closed-loop detection loop parameter values, |NTF| ∞ represents the H-∞ norm of NTF, |NTF| ∞ <1.5 is a constraint condition to ensure the stability of the MEMS gyro electromechanical combined Σ-Δ closed-loop detection loop.

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

[0112] Sub-step 7.2: Use a multi-objective genetic algorithm to solve the objective function in sub-step 7.1, set the population size to 200, and set the maximum number of generations to 200. Obtain the Pareto optimal solution of multiple sets of MEMS gyro electromechanical combined Σ-Δ closed-loop detection loop parameters.

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

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

[0115] Sub-step 8.2: Use the root locus method to analyze the open-loop transfer function L of the MEMS gyro electromechanical combined Σ-Δ closed-loop detection loop corresponding to the Pareto optimal solution of each set of MEMS gyro electromechanical combined Σ-Δ closed-loop detection loop parameters 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 best set of MEMS gyro electromechanical combined Σ-Δ closed-loop detection loop parameters Pareto optimal solution that meets the performance, which is the optimized MEMS gyro electromechanical combined Σ-Δ closed-loop detection loop parameters.

[0117] Embodiment 2:

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

[0119] Step 1: Design of electronic Σ-Δ modulator. According to the target signal-to-noise ratio (SNR), the architecture CRFF, order N = 5, and OSR = 64 of the electronic Σ-Δ modulator are determined. The noise transfer function NTF(z) of the modulator is designed using the electronic Σ-Δ modulator design tool DS Toolbox. The open-loop transfer function L(z) of the electronic Σ-Δ modulator is calculated based on the electronic Σ-Δ modulator noise transfer function NTF(z). The calculation process is as follows: The resulting open-loop transfer function L(z) of the electronic Σ-Δ modulator is in the form 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: Discretize the gyro sensitive mode. Knowing the quality factor Q and resonant frequency ω of the gyro sensitive mode, the s-domain transfer function is written as where s pm and pm * is a pair of conjugate poles of the gyro sensitive mode s-domain transfer function, K sm is the gain of the gyro sensitive mode s-domain transfer function. The gyro sensitive mode s-domain transfer function is converted into a z-domain transfer function using the discretization method. The z-domain transfer function is as follows: where z m is the zero point of the z-domain transfer function of the gyro sensitive mode, p m and p m * is a pair of conjugate poles of the z-domain transfer function of the gyro sensitive mode, K zm is the gain of the z-domain transfer function of the gyro sensitive mode.

[0121] Sub-step 2.1: The discretization method of converting the gyro sensitive mode s-domain transfer function into the z-domain transfer function is as follows: The starting time of the force feedback pulse is known to be t fb1 The end time of the action is t fb2 , the sampling time is T s The gyro sensitive mode s-domain transfer function can be further written as Where K sm1 and K sm2 is the gain of the gyro sensitive mode s-domain transfer function after partial expansion. The conversion process from s-domain transfer function to z-domain transfer function is expressed as The z-domain transfer function can be simplified to the form

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

[0123] Step 4: Establish the MEMS gyro electromechanical combined Σ-Δ closed-loop detection loop model. Establish the transfer function H of the loop electronic filter part e (z), the order is 3, and the transfer function is written according to the given architecture

[0124]

[0125] where z e1 ,z e2 ,z e3 is the zero point of the electronic filter, p e1 ,p e2 ,p e3 is the pole of the electronic filter, a, b, c, d, e are the unknown coefficients in the electronic filter; write the transfer function H of the electronic compensator com (z), in the form where z c1 is the zero point of the electronic compensator, p c1 is the electronic compensator pole, the electronic compensator pole p c1 The zero point z of the z-domain transfer function of the gyro sensitive mode m equal.

[0126] Step 5: Based on steps 2-4, write the open-loop transfer function L of the MEMS gyro electromechanical combined with the 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 . Open loop transfer function L em (z) The zero point z of the z-domain transfer function of the gyro sensitive mode m and the electronic compensator pole p c1 Offset, reduce the order.

[0127] Step 6: Let L em (z)=L(z), the numerator and denominator are equal, determine the unknown coefficients a, b, c, d, e and the zero point z of the electronic compensator c1 , the coefficients a, b, c, d, e and the zero point z of the electronic compensator are to be determined c1 These are the parameters of the MEMS gyro electromechanical combined Σ-Δ closed-loop detection loop. The two poles of the gyro sensitive mode z-domain transfer function (p m and p m *) is equivalent to the two closest poles in the open-loop transfer function L(z) of the electronic Σ-Δ modulator. The zero point z of the electronic compensator c1 Equal to a real zero of the open-loop transfer function L(z) of the electronic Σ-Δ modulator, the zero z of the electronic filter e1 ,z e2 ,z e3 and the extreme point p e1 ,p e2 ,pe3 The remaining zeros and poles of L(z) are used to determine the unknown coefficients a, b, c, d, and e of the electronic filter.

[0128] Step 7: Use a multi-objective optimization algorithm to optimize the MEMS gyro electromechanical combined Σ-Δ closed-loop detection loop parameters. Since approximate equivalence was used when determining the MEMS gyro electromechanical combined Σ-Δ closed-loop detection loop parameters in step 6, a multi-objective particle swarm optimization algorithm is used nearby to optimize the MEMS gyro electromechanical combined Σ-Δ closed-loop detection loop parameters based on the above-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 combined Σ-Δ closed-loop detection loop, maximize the output signal-to-noise ratio (SNR) of the MEMS gyro electromechanical combined Σ-Δ closed-loop detection loop, and minimize the residual motion y of the sensitive mode while ensuring the stability of the MEMS gyro electromechanical combined Σ-Δ closed-loop detection loop. 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 output signal signal-to-noise ratio under the current MEMS gyro electromechanical combined with Σ-Δ closed-loop detection loop parameter values, y rm (a, b, c, …) represents the residual motion of the sensitive mode under the current MEMS gyro electromechanical combined with Σ-Δ closed-loop detection loop parameter values, |NTF| ∞ represents the H-∞ norm of NTF, |NTF| ∞ <1.5 is a constraint condition to ensure the stability of the MEMS gyro electromechanical combined Σ-Δ closed-loop detection loop.

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

[0135] Sub-step 7.2: Use the multi-objective particle swarm optimization algorithm to solve the objective function in sub-step 7.1, set the population size to 200, and set the maximum number of generations to 200. Obtain the Pareto optimal solution of multiple sets of MEMS gyro electromechanical combined Σ-Δ closed-loop detection loop parameters.

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

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

[0138] Sub-step 8.2: Use the root locus method to analyze the open-loop transfer function L of the MEMS gyro electromechanical combined Σ-Δ closed-loop detection loop corresponding to the Pareto optimal solution of each set of MEMS gyro electromechanical combined Σ-Δ closed-loop detection loop parameters 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 best set of MEMS gyro electromechanical combined Σ-Δ closed-loop detection loop parameters Pareto optimal solution that meets the performance, which is the optimized MEMS gyro electromechanical combined Σ-Δ closed-loop detection loop parameters.

[0140] Innovation point 1 of the invention: Combining the 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 loop, thereby reducing the amount of calculation and improving the performance of the electromechanical Σ-Δ closed-loop detection loop.

[0141] Invention innovation 2: The optimization of the electromechanical Σ-Δ closed-loop detection loop parameters is considered 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 innovation 3: Since 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 innovation 4: The lead-lag compensation provided by the electronic compensator can accurately offset the redundant zeros and poles in the open-loop transfer function.

Claims

1. A method for determining and optimizing the loop parameters of a MEMS gyroscope electromechanically combined Σ-Δ closed loop, characterized in that: include: Step 1: Determine the electronic sigma-delta modulator; Step 2: Discretize the gyro sensitive modes; Step 3: Linearize the y / v conversion and the v / f conversion. The y / v conversion module linearizes the gain of the displacement to voltage near the zero position, which is expressed as the gain K yv , the v / f conversion module linearizes the voltage-to-force gain near the zero position, expressed as gain K vf ; Step 4: Establish the MEMS gyro electromechanical combined Σ-Δ closed-loop detection loop model, specifically: Determine the transfer function H of the electronic filter according to the selected electronic Σ-Δ modulator architecture e (z), the order is (N-2), the form is where z e1 ,z e2 ,…,z e(N-2) is the zero point of the electronic filter, p e1 ,p e2 ,,…,p e(N-2) is the pole of the electronic filter, a, b, c… are the unknown coefficients in the electronic filter; determine the transfer function H of the electronic compensator com (z), in the form where z c1 is the zero point of the electronic compensator, p c1 is the electronic compensator pole, the electronic compensator pole p c1 The zero point z of the z-domain transfer function of the gyro sensitive mode m equal; Step 5: Based on steps 2-4, determine the open-loop transfer function L of the MEMS gyro electromechanical combined Σ-Δ closed-loop detection loop em (z); Step 6: According to step 1 and step 5, determine the unknown coefficients a, b, c... and the zero point z of the electronic compensator c1 , the unknown coefficients a, b, c... and the zero point z of the electronic compensator c1 That is, the MEMS gyro electromechanical combined Σ-Δ closed-loop detection loop parameters; Step 7: Use a multi-objective optimization algorithm to optimize the parameters of the MEMS gyro electromechanical combined Σ-Δ closed-loop detection loop; Step 8: Determine a set of MEMS gyro electromechanical combined Σ-Δ closed-loop detection loop parameters based on the multiple sets of 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 sigma-delta modulator, specifically: The architecture, order N, and oversampling rate OSR of the electronic Σ-Δ modulator are determined according to the target signal-to-noise ratio SNR. The electronic Σ-Δ modulator noise transfer function NTF(z) is designed using the electronic Σ-Δ modulator design tool DS Toolbox. The electronic Σ-Δ modulator open-loop transfer function L(z) is calculated based on the electronic Σ-Δ modulator noise transfer function NTF(z). The calculation process is as follows: The resulting open-loop transfer function L(z) of the electronic Σ-Δ modulator is in the form where z1,z2,…,z N are the zeros of the open-loop transfer function L(z) of the electronic Σ-Δ modulator, p1, p2, …, p N is the pole 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: According to the quality factor Q and resonant frequency ω of the gyro sensitive mode, the s-domain transfer function is determined: where s pm and pm * is a pair of conjugate poles of the gyro sensitive mode s-domain transfer function, K sm is the gain of the gyro sensitive mode s-domain transfer function; The discretization method is used to convert the s-domain transfer function of the gyro sensitive mode into the z-domain transfer function. The z-domain transfer function is as follows: where z m is the zero point of the z-domain transfer function of the gyro sensitive mode, p m and p m * is a pair of conjugate poles of the z-domain transfer function of the gyro sensitive mode, K zm is the gain of the z-domain transfer function of the gyro sensitive mode.

4. The method according to claim 3, characterized in that: In step 2, the discretization method of converting the gyro sensitive mode s-domain transfer function into the z-domain transfer function is as follows: It is known that the starting time of the force feedback pulse is t fb1 The end time of the action is t fb2 , the sampling time is T s , the gyro sensitive mode s-domain transfer function can be further converted to Where K sm1 and K sm2 is the gain of the gyro sensitive mode s-domain transfer function after partial expansion. The conversion process from the s-domain transfer function to the z-domain transfer function is expressed as: z domain 5. The method according to claim 4, characterized in that Step 5, specifically: 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 is the gain of the DAC module, Kq is the gain of the quantizer, and the open-loop transfer function L em (z) The zero point z of the z-domain transfer function of the gyro sensitive mode m and the electronic compensator pole p c1 Offset, reduce the order.

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

7. The method according to claim 6, characterized in that Step 7, specifically: Step 7.1: Establish the objective function of the multi-objective optimization algorithm: maxf1=SNR(a,b,c,...) minf2=max[y rm (a,b,c,...)] s.t.|NTF| ∞ <1.5 Among them, SNR (a, b, c, ...) represents the output signal signal-to-noise ratio under the current MEMS gyro electromechanical combined with Σ-Δ closed-loop detection loop parameter values, y rm (a, b, c, …) represents the residual motion of the sensitive mode under the current MEMS gyro electromechanical combined with Σ-Δ closed-loop detection loop parameter values, |NTF| ∞ represents the H-∞ norm of NTF, |NTF| ∞ <1.5 is a constraint condition to ensure the stability of the MEMS gyro electromechanical combined Σ-Δ closed-loop detection loop; Step 7.2: Use a multi-objective optimization algorithm to solve the objective function in sub-step 7.1 and obtain the Pareto optimal solution of multiple sets of MEMS gyro electromechanical combined Σ-Δ closed-loop detection loop parameters.

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

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