A method for establishing an electromagnetically driven MEMS galvanometer model

Abstract

The invention discloses a method for establishing an electromagnetically driven MEMS galvanometer model. The method firstly continuously excites all modes of the galvanometer system by inputting a sinusoidal signal whose amplitude and frequency decay over time to the galvanometer, and samples the input and output signals of the galvanometer. The model structure is obtained by analyzing the mechanism of electromagnetically driven MEMS galvanometer, and then discretization is performed to obtain a galvanometer model parameter matrix to be identified. Considering that the traditional recursive least squares method may have data saturation in the parameter identification process, in order to ensure that the low-frequency signal has a certain correction effect on the parameter identification, a variable forgetting factor is added to the traditional recursive least squares algorithm, and finally the accuracy of the galvanometer model parameter identification is improved, thereby improving the model accuracy. At the same time, the identification algorithm can also be used for online identification of galvanometer model parameters.

Description

Technical Field

[0001] The invention relates to the technical field of MEMS galvanometer model establishment, and in particular to a method for building an electromagnetically driven MEMS galvanometer model. Background Art

[0002] With the continuous development of MEMS technology, MEMS LiDAR meets the current development trend of miniaturization and solidification of LiDAR, and has become a hot topic of research in recent years. According to different driving methods, MEMS galvanometers can be divided into four different types: electrostatic drive, piezoelectric drive, electrothermal drive, and electromagnetic drive. Comparing the characteristics of galvanometers under different driving methods, electromagnetically driven MEMS galvanometers have the advantages of large reflective mirror surface, low driving voltage, large deflection angle, good linearity, and fast response speed, which are more suitable for application in LiDAR. In order to improve the scanning accuracy of electromagnetically driven MEMS galvanometers, model-based closed-loop control is the main method at present. At the same time, considering that LiDAR will be affected by the external environment during use, the dynamic performance of MEMS galvanometers may change. Therefore, a suitable online modeling method is needed to establish an accurate galvanometer model.

[0003] Regarding the model of electromagnetically driven MEMS galvanometer, Cao et al. established a model structure of a nonlinear dynamic model with pre-hysteresis for the slow axis of an electromagnetically driven two-dimensional MEMS galvanometer. However, it is a complex process to establish an accurate model to describe underdamping and hysteresis behavior. Iskiman et al. proposed a dynamic model of a MEMS micro-mirror driven by a soft magnetic film based on the mechanism of galvanometer drive and the dynamic deflection theory of magnetic film drivers. Qin et al. obtained a mathematical model of a hard magnetic micro-mirror driven by hard magnetic materials by analyzing the coil part, the hard magnetic film magnetic actuator part and the torsional mechanical part. The model structure established by the two is a second-order linear system, and the modeling method adopted is the mechanism modeling method, that is, by analyzing the physical and mechanical structure of the galvanometer and combining the specific design parameters of the MEMS galvanometer mirror and the coil, the mathematical model of the hard magnetic micro-mirror is obtained. Galvanometer model, but this method is not suitable for MEMS galvanometers whose internal structural parameters cannot be obtained; in addition to the mechanism modeling method, there is also input-output modeling, that is, modeling is performed based on the input and output signals of the galvanometer. Li et al. analyzed the input and output signals of the galvanometer system from the frequency domain perspective, and established a galvanometer model based on the Bode diagram. Although this method does not require the internal structural parameters of the galvanometer, it cannot be used for online identification; Zhang et al. proposed a recursive damped least squares-differential evolution algorithm for system identification from the time domain perspective. Although this method can improve the identification accuracy of the galvanometer system parameters, the algorithm process is relatively complex; Wu et al. also used the recursive least squares method to identify the parameters of the galvanometer model from the time domain perspective. Although it can be used for online identification, the traditional recursive least squares method will experience "data saturation" as the data grows. Summary of the invention

[0004] In view of the problems in the prior art that the process of establishing an electromagnetically driven MEMS galvanometer model is complicated, the internal structure parameters cannot be obtained, and the modeling method is not conducive to online identification, the present invention provides a method for establishing an electromagnetically driven MEMS galvanometer model. The method can realize online identification of the electromagnetically driven MEMS galvanometer model parameters, and the identification algorithm can effectively improve the parameter identification accuracy compared with the traditional recursive least squares algorithm.

[0005] To achieve the above object, the present invention provides a method for establishing an electromagnetically driven MEMS galvanometer model, comprising the following steps:

[0006] Step 1, inputting a sinusoidal signal whose amplitude and frequency both decay over time to the electromagnetically driven MEMS galvanometer, and sampling the input signal and output signal of the electromagnetically driven MEMS galvanometer respectively;

[0007] Step 2, obtaining a galvanometer system equilibrium state torque equation by analyzing the mechanism of the electromagnetically driven MEMS galvanometer, and analyzing the galvanometer system equilibrium state torque equation to obtain a discretized galvanometer model structure;

[0008] Step 3, designing a recursive least squares algorithm with a variable forgetting factor for the discretized galvanometer model structure;

[0009] Step 4, inputting the sampling point data of the input signal and the output signal into the recursive least squares algorithm with a variable forgetting factor to perform galvanometer model parameter identification;

[0010] Step 5: Substitute the galvanometer model parameters obtained after the parameter identification into the discretized galvanometer model structure to obtain an electromagnetically driven MEMS galvanometer model.

[0011] In another embodiment, in step 1, the sinusoidal signal is specifically:

[0012]

[0013] In the formula, A represents the amplitude, e represents the base of the natural logarithm function, a represents the attenuation factor of the amplitude, k represents the number of sampling times, b represents the attenuation factor of the frequency, f represents the frequency, and t represents the time.

[0014] In another embodiment, in step 1, the input signal is the sinusoidal signal, and the output signal is a voltage signal output by a piezoresistive sensor in the MEMS galvanometer.

[0015] In another embodiment, in step 1, a sinusoidal signal whose amplitude and frequency both decay over time is input to the electromagnetically driven MEMS galvanometer, and the input signal and output signal of the electromagnetically driven MEMS galvanometer are sampled respectively, including:

[0016] The sampling point data determined after the ADC sampling module samples the input signal and the output signal of the electromagnetically driven MEMS galvanometer respectively is obtained.

[0017] In another embodiment, in step 2, the equilibrium state torque equation of the galvanometer system is:

[0018]

[0019] In the formula, Indicates the deflection angle of the galvanometer when it is working. It represents the angular velocity of the galvanometer when it is working. It represents the angular acceleration of the galvanometer when it is working. It indicates the driving torque generated when the MEMS galvanometer applies a driving signal. represents the effective moment of inertia of the galvanometer, represents the friction damping coefficient, It represents the spring constant of the galvanometer torsion arm beam.

[0020] In another embodiment, in step 3, before designing the recursive least squares algorithm with a variable forgetting factor for the discretized galvanometer model structure, the method further includes:

[0021] The galvanometer model structure is discretized to obtain the corresponding differential equation, which is:

[0022]

[0023] In the formula, is the kth input signal of the galvanometer, is the k-th output signal of the galvanometer, is the k-1th output signal of the galvanometer, is the k-2th output signal of the galvanometer, is the k-1th input signal of the galvanometer, is the k-2th input signal of the galvanometer; are the galvanometer model parameters to be identified.

[0024] In another embodiment, in step 3, the recursive formula of the recursive least squares algorithm with a variable forgetting factor is:

[0025]

[0026] In the formula, represents the kth identification result of the parameter matrix to be identified, is the variable forgetting factor, represents the covariance matrix of the k-th error, represents the correction gain matrix, I represents the unit matrix, The observation matrix representing the input and output data of the galvanometer system, express The transpose of The expression is:

[0027]

[0028] In another embodiment, the functional expression of the variable forgetting factor is:

[0029]

[0030]

[0031] In the formula, is an adjustable parameter, It represents the difference between the actual output value of the system at the current k moment and the output value of the last theoretically estimated model.

[0032] In another embodiment, in step 4, the sampling point data of the input signal and the output signal are input into the recursive least squares algorithm with a variable forgetting factor for parameter identification, including:

[0033] Substitute the observation matrix of the input and output of the system into the recursive least squares algorithm with a variable forgetting factor to obtain the parameter matrix The value of

[0034] Said The expression is:

[0035]

[0036] In another embodiment, in step 5, the galvanometer model parameters obtained after the parameter identification are substituted into the discretized galvanometer model structure to obtain the electromagnetically driven MEMS galvanometer model, including:

[0037] The parameter matrix Substitute the value of into the differential equation to obtain the model of the MEMS galvanometer.

[0038] Compared with the prior art, the method for establishing an electromagnetically driven MEMS galvanometer model provided by the present invention has the following beneficial technical effects:

[0039] 1. Aiming at the problems of complicated process of establishing electromagnetic driven MEMS galvanometer model, inability to obtain internal structure parameters and modeling method not being conducive to online identification, a model establishment method based on galvanometer input and output data is provided. This method improves the traditional recursive least squares algorithm in the parameter identification process, that is, introduces a dynamically changing forgetting factor, effectively avoids the data saturation problem in the parameter identification of the traditional recursive least squares algorithm, and improves the parameter identification accuracy;

[0040] 2. The present invention first uses a sinusoidal signal whose frequency and amplitude decay over time as the input signal of the galvanometer system to continuously excite all modes of the galvanometer system, and obtains the parameter matrix to be identified by sampling the input and output data of the galvanometer and combining the model obtained by analyzing the galvanometer mechanism. In the process of establishing the dynamic change function of the forgetting factor, the influence of the forgetting factor on the correction gain matrix K is taken into account, and the change law of the forgetting factor is combined with the difference between the actual output signal at the current moment and the output signal estimated by the model, so as to finally improve the parameter identification accuracy, realize the accurate identification of the electromagnetically driven MEMS galvanometer model parameters, and thus realize the accurate construction of the electromagnetically driven MEMS galvanometer model. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the structures shown in these drawings without paying creative work.

[0042] Figure 1 A flow chart of a method for establishing an electromagnetically driven MEMS galvanometer model in an embodiment of the present invention;

[0043] Figure 2 It is a schematic diagram of a sinusoidal signal in which both the amplitude and the frequency decay over time according to an example in an embodiment of the present invention;

[0044] Figure 3 Schematic diagram of a galvanometer input signal according to an example of an embodiment of the present invention;

[0045] Figure 4 Schematic diagram of the galvanometer output signal used as an example in an embodiment of the present invention. DETAILED DESCRIPTION

[0046] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0047] In view of the problems that the process of establishing an electromagnetically driven MEMS galvanometer model is complicated, the internal structure parameters cannot be obtained, and the identification algorithm is not conducive to online identification, this embodiment provides a simple model establishment method suitable for online identification, specifically a method for establishing an electromagnetically driven MEMS galvanometer model. The method first uses a sinusoidal signal whose frequency and amplitude decay over time as the input signal of the galvanometer system to continuously excite all modes of the galvanometer system, and samples the input and output data of the galvanometer, and obtains the parameter matrix to be identified based on the analysis of the galvanometer mechanism. Considering that the recursive least squares method will have data saturation during the parameter identification process, it should be ensured that the low-frequency signal has a certain correction effect on the parameter identification, that is, a variable forgetting factor is added to the recursive least squares algorithm, and finally the accuracy of parameter identification is improved. At the same time, it can also be used for online parameter identification.

[0048] refer to Figure 1 In the specific implementation process, the method for establishing the electromagnetically driven MEMS galvanometer model specifically includes the following steps 1 to 5.

[0049] In step 1, in order to make the input signal meet the requirements of the model parameter identification input signal, that is, to excite all modes of the galvanometer system during the entire observation period, a sinusoidal signal whose amplitude and frequency decay over time is selected as the input signal of the galvanometer system. The signal is specifically:

[0050] )

[0051] In the formula, A represents the amplitude, e represents the base of the natural logarithm function, a represents the attenuation factor of the amplitude, k represents the number of sampling times, b represents the attenuation factor of the frequency, f represents the frequency, and t represents the time.

[0052] The voltage signal output by the piezoresistive sensor of the MEMS galvanometer is used as the output signal. The input and output signals of the galvanometer are sampled respectively through the ADC sampling module to obtain the input and output data of the system.

[0053] In step 2, in order to obtain a suitable galvanometer model structure, the mechanism of the electromagnetically driven MEMS galvanometer is first analyzed. When a driving signal is applied to the galvanometer, the galvanometer will be subjected to the Lorentz force, gravity, and the elastic force of the torsion beam, forming a balanced state.

[0054] When the galvanometer is working, the torque generated by the torsion arm beam is proportional to the torsion angle of the galvanometer, and its expression is:

[0055] =

[0056] In the formula, represents the moment generated by the torsion beam, represents the spring constant of the galvanometer torsion arm beam, Indicates the deflection angle of the galvanometer when it is working;

[0057] When the galvanometer is working, the friction torque it receives is proportional to the angular velocity ω, and its expression is:

[0058]

[0059] In the formula, represents the friction torque, represents the friction damping coefficient, Indicates the angular velocity of the galvanometer when it is working;

[0060] When the galvanometer is working, the mirror torque expression is:

[0061]

[0062] In the formula, represents the mirror moment, represents the effective moment of inertia of the galvanometer, Indicates the angular acceleration of the galvanometer when it is working;

[0063] The torque equation of the entire system in equilibrium is expressed as:

[0064]

[0065] In the formula, It indicates the driving torque generated when the MEMS galvanometer is driven by a driving signal. For an electromagnetic galvanometer, the greater the current flowing through the driving coil, the greater the Ampere force generated, and the greater the driving torque on the galvanometer.

[0066] By analyzing the torque equation of the galvanometer system, we know that the galvanometer system model is a second-order linear system. The parameters in the torque equation are , , The internal structural parameters of the galvanometer, such as the mirror area, thickness, material density, Young's modulus, the length, width, thickness, Young's modulus of the torsion beam, and the thickness of the magnetic film of the galvanometer system, are jointly determined. Since these parameters cannot be obtained in the finished MEMS galvanometer purchased directly, the model parameters are identified through input and output signals. In order to be able to use the sampled input and output signals for identification, the galvanometer model is discretized, and the corresponding differential equation is obtained as follows:

[0067]

[0068] In the formula, is the kth input signal of the galvanometer, is the k-th output signal of the galvanometer, is the k-1th output signal of the galvanometer, is the k-2th output signal of the galvanometer, is the k-1th input signal of the galvanometer, is the k-2th input signal of the galvanometer; are the galvanometer model parameters to be identified.

[0069] In step 3, in order to meet the demand for online identification of electromagnetically driven MEMS galvanometers and to avoid data saturation in the traditional recursive least squares algorithm during parameter identification, a recursive least squares algorithm with a variable forgetting factor is designed. The recursive formula of the algorithm is:

[0070]

[0071] In the formula, represents the kth identification result of the parameter matrix to be identified, is the variable forgetting factor, represents the covariance matrix of the k-th error, represents the correction gain matrix, I represents the unit matrix, The observation matrix representing the input and output data of the galvanometer system, express The transpose of The expression is:

[0072]

[0073] Expressed as the dynamic forgetting factor introduced, The smaller the value, the lower the impact of old data on parameter estimation and the greater the impact of new data.

[0074] Variable forgetting factor The function expression is:

[0075]

[0076]

[0077] In the formula, is an adjustable parameter, It represents the difference between the actual output value of the system at the current k moment and the theoretical model. The value of affects the size of the forgetting factor. When the forgetting factor is large, becomes smaller, the dynamic changes in the algorithm identification process are enhanced; when When the forgetting factor is small, Becomes larger, making the algorithm more stable; when hour, , at this time the algorithm becomes the traditional recursive least squares algorithm.

[0078] In step 4, the sampling point data of the input signal and the output signal, that is, the observation matrix of the input and output quantities of the system , bring in the recursive least squares algorithm with variable forgetting factor to perform parameter identification and obtain the parameter matrix The value of

[0079] Said The expression is:

[0080]

[0081] In step 5, the galvanometer model parameters obtained after the parameter identification are substituted into the discretized galvanometer model structure to obtain the MEMS galvanometer model, including:

[0082] The parameter matrix Substitute the value of into the differential equation to obtain the discrete model of the electromagnetically driven MEMS galvanometer.

Claims

1. A method for establishing an electromagnetically driven MEMS galvanometer model, characterized in that: The steps include: Step 1, inputting a sinusoidal signal whose amplitude and frequency both decay over time to the electromagnetically driven MEMS galvanometer, and sampling the input signal and output signal of the electromagnetically driven MEMS galvanometer respectively; Step 2, obtaining a galvanometer system equilibrium state torque equation by analyzing the mechanism of the electromagnetically driven MEMS galvanometer, and analyzing the galvanometer system equilibrium state torque equation to obtain a discretized galvanometer model structure; Step 3, designing a recursive least squares algorithm with a variable forgetting factor for the discretized galvanometer model structure; Step 4, inputting the sampling point data of the input signal and the output signal into the recursive least squares algorithm with a variable forgetting factor for parameter identification; Step 5, substituting the galvanometer model parameters obtained after the parameter identification into the discretized galvanometer model structure to obtain an electromagnetically driven MEMS galvanometer model; In step 3, the recursive formula of the recursive least squares algorithm with a variable forgetting factor is: In the formula, represents the kth identification result of the parameter matrix to be identified, is the variable forgetting factor, represents the covariance matrix of the k-th error, represents the correction gain matrix, I represents the unit matrix, The observation matrix representing the input and output data of the galvanometer system, express The transpose of The expression is: ； The functional expression of the variable forgetting factor is: In the formula, is an adjustable parameter, It represents the difference between the actual output value of the system at the current k moment and the output value of the last theoretically estimated model.

2. The method for establishing an electromagnetically driven MEMS galvanometer model according to claim 1, characterized in that: In step 1, the sinusoidal signal is specifically: In the formula, A represents the amplitude, e represents the base of the natural logarithm function, a represents the attenuation factor of the amplitude, k represents the number of sampling times, b represents the attenuation factor of the frequency, f represents the frequency, and t represents the time.

3. The method for establishing an electromagnetically driven MEMS galvanometer model according to claim 1, characterized in that: In step 1, the input signal is the sinusoidal signal, and the output signal is a voltage signal output by the piezoresistive sensor in the MEMS galvanometer.

4. The method for establishing an electromagnetically driven MEMS galvanometer model according to claim 1, characterized in that: In the step 1, a sinusoidal signal whose amplitude and frequency both decay over time is input to the electromagnetically driven MEMS galvanometer, and the input signal and output signal of the electromagnetically driven MEMS galvanometer are sampled respectively, including: The sampling point data determined after the ADC sampling module samples the input signal and the output signal of the electromagnetically driven MEMS galvanometer respectively is obtained.

5. The method for establishing an electromagnetically driven MEMS galvanometer model according to claim 1, characterized in that: In step 2, the equilibrium state torque equation of the galvanometer system is: In the formula, Indicates the deflection angle of the galvanometer when it is working. It represents the angular velocity of the galvanometer when it is working. It represents the angular acceleration of the galvanometer when it is working. It indicates the driving torque generated when the MEMS galvanometer applies a driving signal. represents the effective moment of inertia of the galvanometer, represents the friction damping coefficient, It represents the spring constant of the galvanometer torsion arm beam.

6. The method for establishing an electromagnetically driven MEMS galvanometer model according to claim 5, characterized in that: In the step 3, before designing a recursive least squares algorithm with a variable forgetting factor for the discretized galvanometer model structure, the method further includes: The galvanometer model structure is discretized to obtain the corresponding differential equation, which is: In the formula, is the kth input signal of the galvanometer, is the k-th output signal of the galvanometer, is the k-1th output signal of the galvanometer, is the k-2th output signal of the galvanometer, is the k-1th input signal of the galvanometer, is the k-2th input signal of the galvanometer; are the galvanometer model parameters to be identified.

7. The method for establishing an electromagnetically driven MEMS galvanometer model according to claim 6, characterized in that: In step 4, the sampling point data of the input signal and the output signal are input into the recursive least squares algorithm with a variable forgetting factor for parameter identification, including: Substitute the observation matrix of the input and output data of the system into the recursive least squares algorithm recursive formula with a variable forgetting factor to obtain the parameter matrix The value of Said The expression is: 。 8. The method for establishing an electromagnetically driven MEMS galvanometer model according to claim 7, characterized in that: In step 5, the galvanometer model parameters obtained after the parameter identification are substituted into the discretized galvanometer model structure to obtain an electromagnetically driven MEMS galvanometer model, including: The parameter matrix Substitute the value of into the differential equation to obtain the model of the electromagnetically driven MEMS galvanometer.

Images