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CN110456639B - MEMS gyroscope self-adaptive driving control method based on historical data parameter identification - Google Patents

MEMS gyroscope self-adaptive driving control method based on historical data parameter identification Download PDF

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CN110456639B
CN110456639B CN201910648280.XA CN201910648280A CN110456639B CN 110456639 B CN110456639 B CN 110456639B CN 201910648280 A CN201910648280 A CN 201910648280A CN 110456639 B CN110456639 B CN 110456639B
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许斌
张睿
魏琦
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Abstract

本发明涉及一种基于历史数据参数辨识的MEMS陀螺仪自适应驱动控制方法，属于智能化仪器仪表领域。该方法将陀螺仪动力学模型转化为无量纲的动力学线性参数化模型；充分挖掘历史数据信息，定义预测误差，基于预测误差和跟踪误差共同构建参数自适应律，实现参数精确辨识；设计控制器实现陀螺驱动控制。本发明设计的基于历史数据参数辨识的MEMS陀螺仪自适应驱动控制方法可解决参数辨识难以获取真值的问题，获取精确的动力学模型，同时实现陀螺仪驱动控制，进一步改善MEMS陀螺仪性能。

Figure 201910648280

The invention relates to a MEMS gyroscope adaptive drive control method based on historical data parameter identification, and belongs to the field of intelligent instruments. This method transforms the gyroscope dynamic model into a dimensionless dynamic linear parameterization model; fully mines the historical data information, defines the prediction error, and jointly constructs a parameter adaptive law based on the prediction error and tracking error to achieve accurate parameter identification; design control The device realizes the gyro drive control. The MEMS gyroscope adaptive drive control method based on historical data parameter identification designed by the invention can solve the problem that the parameter identification is difficult to obtain the true value, obtain an accurate dynamic model, realize the gyroscope drive control at the same time, and further improve the performance of the MEMS gyroscope.

Figure 201910648280

Description

基于历史数据参数辨识的MEMS陀螺仪自适应驱动控制方法Adaptive drive control method of MEMS gyroscope based on historical data parameter identification

技术领域technical field

本发明涉及一种MEMS陀螺仪的驱动控制方法，特别是涉及一种基于历史数据参数辨识的MEMS陀螺仪自适应驱动控制方法，属于智能化仪器仪表领域。The invention relates to a driving control method of a MEMS gyroscope, in particular to an adaptive driving control method of a MEMS gyroscope based on historical data parameter identification, belonging to the field of intelligent instruments.

背景技术Background technique

精确的动力学模型是进行MEMS陀螺仪硬件设计、控制系统设计和系统仿真的重要条件，而动力学模型参数辨识是其中的关键技术。《Adaptive nonsingular terminalsliding mode control of MEMS gyroscope based on backstepping design》(JuntaoFei，Weifeng Yan and Yuzheng Yang，《International Journal of Adaptive ControlSignal Processing》，2015)一文中提出了一种基于反步法的MEMS陀螺仪非奇异终端滑模控制方法，同时给出了动力学模型参数辨识结果。然而这种方法所辨识的参数仅能保证稳态收敛，并不能确保最终收敛至参数的真值。Accurate dynamic model is an important condition for MEMS gyroscope hardware design, control system design and system simulation, and the identification of dynamic model parameters is the key technology. "Adaptive nonsingular terminalsliding mode control of MEMS gyroscope based on backstepping design" (JuntaoFei, Weifeng Yan and Yuzheng Yang, "International Journal of Adaptive ControlSignal Processing", 2015) proposes a nonsingular MEMS gyroscope based on backstepping method The terminal sliding mode control method is used, and the parameter identification results of the dynamic model are also given. However, the parameters identified by this method can only guarantee steady-state convergence, and cannot guarantee the final convergence to the true value of the parameters.

发明内容SUMMARY OF THE INVENTION

要解决的技术问题technical problem to be solved

为克服现有技术仅能保证动力学参数收敛，并不一定能收敛到参数真值及角速率难以直接获取的问题，本发明提出一种基于历史数据参数辨识的MEMS陀螺仪自适应驱动控制方法。该方法一方面充分挖掘历史数据信息，定义预测误差，基于预测误差和跟踪误差共同构建参数自适应律，实现参数精确辨识；另一方面基于MEMS陀螺动力学及参数辨识结果，设计控制器实现陀螺驱动控制。In order to overcome the problem that the prior art can only guarantee the convergence of dynamic parameters, but not necessarily to the true value of the parameters and the angular rate, which is difficult to obtain directly, the present invention proposes a MEMS gyroscope adaptive drive control method based on historical data parameter identification. . On the one hand, the method fully mines the historical data information, defines the prediction error, and jointly constructs a parameter adaptive law based on the prediction error and tracking error to achieve accurate parameter identification; drive control.

技术方案Technical solutions

一种基于历史数据参数辨识的MEMS陀螺仪自适应驱动控制方法，其特征在于步骤如下：A MEMS gyroscope adaptive drive control method based on historical data parameter identification is characterized in that the steps are as follows:

步骤1：考虑存在正交误差的MEMS陀螺动力学模型为：Step 1: Consider the MEMS gyroscope dynamics model with quadrature error as:

Figure BDA0002134298580000021
Figure BDA0002134298580000021

其中，m为检测质量块的质量；Ωz为陀螺输入角速度，

Figure BDA0002134298580000022
和x*分别为MEMS陀螺仪检测质量块沿驱动轴的加速度、速度和位移，
Figure BDA0002134298580000023
和y*分别为沿检测轴的加速度、速度和位移，
Figure BDA0002134298580000024
和
Figure BDA0002134298580000025
为静电驱动力，cxx和cyy为阻尼系数，kxx和kyy为刚度系数，
Figure BDA0002134298580000026
和
Figure BDA0002134298580000027
为非线性系数，cxy和cyx为阻尼耦合系数，kxy和kyx为刚度耦合系数；上述参数根据振动式硅微机械陀螺参数选取；Among them, m is the quality of the detection mass; Ω z is the input angular velocity of the gyro,
Figure BDA0002134298580000022
and x * are the acceleration, velocity and displacement of the MEMS gyroscope detection mass along the drive axis, respectively,
Figure BDA0002134298580000023
and y * are the acceleration, velocity and displacement along the detection axis, respectively,
Figure BDA0002134298580000024
and
Figure BDA0002134298580000025
is the electrostatic driving force, c xx and c yy are damping coefficients, k xx and k yy are stiffness coefficients,
Figure BDA0002134298580000026
and
Figure BDA0002134298580000027
is the nonlinear coefficient, c xy and c yx are the damping coupling coefficients, k xy and k yx are the stiffness coupling coefficients; the above parameters are selected according to the parameters of the vibrating silicon micromachined gyroscope;

取无量纲化时间t＝ωot*，无量纲化位移x＝x*/q0，y＝y*/q0，其中ω0为参考频率，q0为参考长度，对MEMS陀螺动力学模型进行无量纲化处理，并在等式两边同时除以

Figure BDA0002134298580000028
得到Take the dimensionless time t=ω o t * , the dimensionless displacement x=x * /q 0 , y=y * /q 0 , where ω 0 is the reference frequency, q 0 is the reference length, for the MEMS gyro dynamics The model is dimensionless and divided by both sides of the equation
Figure BDA0002134298580000028
get

Figure BDA0002134298580000029
Figure BDA0002134298580000029

其中，

Figure BDA00021342985800000210
和x分别为MEMS陀螺仪检测质量块沿驱动轴的无量纲加速度、无量纲速度和无量纲位移，
Figure BDA00021342985800000211
和y分别为沿检测轴的无量纲加速度、无量纲速度和无量纲位移；in,
Figure BDA00021342985800000210
and x are the dimensionless acceleration, dimensionless velocity and dimensionless displacement of the MEMS gyroscope detection mass along the drive axis, respectively,
Figure BDA00021342985800000211
and y are the dimensionless acceleration, dimensionless velocity and dimensionless displacement along the detection axis, respectively;

重新定义redefine

Figure BDA00021342985800000212
Figure BDA00021342985800000212

Figure BDA00021342985800000213
Figure BDA00021342985800000213

Figure BDA00021342985800000214
Figure BDA00021342985800000214

Figure BDA00021342985800000215
Figure BDA00021342985800000215

则式(2)可以改写为The formula (2) can be rewritten as

Figure BDA0002134298580000031
Figure BDA0002134298580000031

定义θ1＝[x,y]T，

Figure BDA0002134298580000032
则式(3)可写为Define θ 1 =[x,y] T ,
Figure BDA0002134298580000032
The formula (3) can be written as

Figure BDA0002134298580000033
Figure BDA0002134298580000033

其中，U＝[u1,u2]T，F(Φ)＝[f1,f2]T，

Figure BDA0002134298580000034
Wherein, U=[u 1 , u 2 ] T , F(Φ)=[f 1 , f 2 ] T ,
Figure BDA0002134298580000034

定义definition

Figure BDA0002134298580000035
Figure BDA0002134298580000035

对F(Φ)进行线性参数化，得到Linear parameterization of F(Φ), we get

F(Φ)＝WΦ (5)F(Φ)=WΦ (5)

步骤2：给出MEMS陀螺动力学式(1)的参考轨迹为Step 2: The reference trajectory of the MEMS gyrodynamic equation (1) is given as

Figure BDA0002134298580000036
Figure BDA0002134298580000036

其中，

Figure BDA0002134298580000037
和
Figure BDA0002134298580000038
分别为检测质量块沿驱动轴和检测轴的参考振动位移信号，
Figure BDA0002134298580000039
和
Figure BDA00021342985800000310
分别为驱动轴和检测轴振动的参考振幅，ω1和ω2分别为驱动轴和检测轴振动的参考角频率，
Figure BDA00021342985800000311
和
Figure BDA00021342985800000312
分别为驱动轴和检测轴振动的相位；in,
Figure BDA0002134298580000037
and
Figure BDA0002134298580000038
are the reference vibration displacement signals of the proof mass along the drive axis and the detection axis, respectively,
Figure BDA0002134298580000039
and
Figure BDA00021342985800000310
are the reference amplitudes of the vibration of the drive shaft and the detection shaft, respectively, ω 1 and ω 2 are the reference angular frequencies of the vibration of the drive shaft and the detection shaft, respectively,
Figure BDA00021342985800000311
and
Figure BDA00021342985800000312
are the vibration phases of the drive shaft and the detection shaft, respectively;

则无量纲动力学式(4)的参考轨迹为Then the reference trajectory of the dimensionless dynamic equation (4) is

Figure BDA00021342985800000313
Figure BDA00021342985800000313

其中，

Figure BDA00021342985800000314
Figure BDA00021342985800000315
且待设计参数
Figure BDA00021342985800000316
in,
Figure BDA00021342985800000314
Figure BDA00021342985800000315
And the parameters to be designed
Figure BDA00021342985800000316

定义跟踪误差为The tracking error is defined as

Figure BDA00021342985800000317
Figure BDA00021342985800000317

则控制器设计为Then the controller is designed as

U＝Un+Upd-Uad (9)U=U n +U pd -U ad (9)

Figure BDA0002134298580000041
Figure BDA0002134298580000041

Upd＝K1e1+K2e2 (11)U pd =K 1 e 1 +K 2 e 2 (11)

Figure BDA0002134298580000042
Figure BDA0002134298580000042

其中，

Figure BDA0002134298580000043
是W的估计值，待设计参数
Figure BDA0002134298580000044
和
Figure BDA0002134298580000045
满足Hurwitz条件；in,
Figure BDA0002134298580000043
is the estimated value of W, the parameters to be designed
Figure BDA0002134298580000044
and
Figure BDA0002134298580000045
Satisfy the Hurwitz condition;

步骤3：定义预测误差Step 3: Define Forecast Error

Figure BDA0002134298580000046
Figure BDA0002134298580000046

其中，

Figure BDA0002134298580000047
τd为待设计正常数；in,
Figure BDA0002134298580000047
τ d is the constant to be designed;

给出参数的自适应律为The adaptive law for the given parameters is

Figure BDA0002134298580000048
Figure BDA0002134298580000048

其中，等式右边第一项采用当前时刻数据计算，第二项采用τ∈[t-τd,t]区间内历史数据计算，且待设计参数

Figure BDA0002134298580000049
和
Figure BDA00021342985800000410
满足Hurwitz条件；Among them, the first term on the right side of the equation is calculated using the current moment data, the second term is calculated using the historical data in the interval τ∈[t-τ d ,t], and the parameters to be designed
Figure BDA0002134298580000049
and
Figure BDA00021342985800000410
Satisfy the Hurwitz condition;

步骤4：基于参数自适应律式(14)设计控制器式(9)驱动无量纲动力学式(4)，并通过量纲转换返回MEMS陀螺动力学模型式(1)，实现陀螺驱动控制及动力学参数辨识。Step 4: Design the controller formula (9) based on the parameter adaptive law formula (14) to drive the dimensionless dynamics formula (4), and return to the MEMS gyro dynamics model formula (1) through dimension conversion to realize the gyro drive control and Dynamic parameter identification.

有益效果beneficial effect

本发明提出的一种基于历史数据参数辨识的MEMS陀螺仪自适应驱动控制方法，与现有技术相比的有益效果为：A MEMS gyroscope adaptive drive control method based on historical data parameter identification proposed by the present invention has the following beneficial effects compared with the prior art:

(1)针对参数辨识难以辨识出真值的问题，充分挖掘历史数据信息，定义预测误差，基于预测误差和跟踪误差共同构建参数自适应律，实现参数精确辨识。(1) For the problem that it is difficult to identify the true value of parameter identification, the historical data information is fully mined, the prediction error is defined, and the parameter adaptive law is jointly constructed based on the prediction error and the tracking error to achieve accurate parameter identification.

(2)针对动力学参数难以在线辨识的问题，将动力学改写为线性参数化形式，结合参数更新律设计控制器，同时实现陀螺驱动控制和动力学参数辨识。(2) Aiming at the problem that the dynamic parameters are difficult to be identified online, the dynamics are rewritten into a linear parameterized form, and the controller is designed in combination with the parameter update law, and the gyro drive control and dynamic parameter identification are realized at the same time.

附图说明Description of drawings

图1本发明具体实施流程图1 is a flow chart of the specific implementation of the present invention

具体实施方式Detailed ways

现结合实施例、附图对本发明作进一步描述：The present invention will now be further described in conjunction with the embodiments and accompanying drawings:

本发明公开了一种基于历史数据参数辨识的MEMS陀螺仪自适应驱动控制方法，结合图1，具体设计步骤如下：The invention discloses a MEMS gyroscope adaptive drive control method based on historical data parameter identification. With reference to Fig. 1, the specific design steps are as follows:

(a)考虑存在正交误差的MEMS陀螺动力学模型为：(a) The dynamic model of MEMS gyro considering the existence of quadrature error is:

Figure BDA0002134298580000051
Figure BDA0002134298580000051

其中，m为检测质量块的质量，Ωz为陀螺输入角速度，

Figure BDA0002134298580000052
和x*分别为MEMS陀螺仪检测质量块沿驱动轴的加速度、速度和位移，
Figure BDA0002134298580000053
和y*分别为沿检测轴的加速度、速度和位移，
Figure BDA0002134298580000054
和
Figure BDA0002134298580000055
为静电驱动力，cxx和cyy为阻尼系数，kxx和kyy为刚度系数，
Figure BDA0002134298580000056
和
Figure BDA0002134298580000057
为非线性系数，cxy和cyx为阻尼耦合系数，kxy和kyx为刚度耦合系数。根据某型号的振动式硅微机械陀螺，选取陀螺各参数为m＝5.7×10-9kg，q0＝10-5m，ω0＝1kHz，Ωz＝5.0rad/s，kxx＝80.98N/m，kyy＝71.62N/m，kxy＝0.05N/m，kyx＝0.05N/m，
Figure BDA0002134298580000058
cxx＝4.29×10-7Ns/m，cyy＝4.29×10-8Ns/m，cxy＝4.29×10-8Ns/m，cyx＝4.29×10-8Ns/m。Among them, m is the quality of the detection mass, Ω z is the input angular velocity of the gyro,
Figure BDA0002134298580000052
and x* are the acceleration, velocity and displacement of the MEMS gyroscope detection mass along the drive axis, respectively,
Figure BDA0002134298580000053
and y* are the acceleration, velocity and displacement along the detection axis, respectively,
Figure BDA0002134298580000054
and
Figure BDA0002134298580000055
is the electrostatic driving force, c xx and c yy are damping coefficients, k xx and k yy are stiffness coefficients,
Figure BDA0002134298580000056
and
Figure BDA0002134298580000057
are nonlinear coefficients, c xy and c yx are damping coupling coefficients, and k xy and k yx are stiffness coupling coefficients. According to a certain type of vibrating silicon micromachined gyroscope, the parameters of the gyroscope are selected as m=5.7×10 -9 kg, q 0 =10 -5 m, ω 0 =1kHz, Ω z =5.0rad/s, k xx =80.98 N/m, k yy =71.62N/m, k xy =0.05N/m, k yx =0.05N/m,
Figure BDA0002134298580000058
c xx =4.29×10 −7 Ns/m, c yy =4.29×10 −8 Ns/m, c xy =4.29×10 −8 Ns/m, c yx =4.29×10 −8 Ns/m.

取无量纲化时间t＝ωot*，无量纲化位移x＝x*/q0，y＝y*/q0，其中ω0为参考频率，q0为参考长度，对MEMS陀螺动力学模型进行无量纲化处理，得到Take the dimensionless time t=ω o t * , the dimensionless displacement x=x * /q 0 , y=y * /q 0 , where ω 0 is the reference frequency, q 0 is the reference length, for the MEMS gyro dynamics The model is dimensionless, and we get

Figure BDA0002134298580000059
Figure BDA0002134298580000059

其中，

Figure BDA00021342985800000510
和x分别为MEMS陀螺仪检测质量块沿驱动轴的无量纲加速度、无量纲速度和无量纲位移，
Figure BDA00021342985800000511
和y分别为沿检测轴的无量纲加速度、无量纲速度和无量纲位移。in,
Figure BDA00021342985800000510
and x are the dimensionless acceleration, dimensionless velocity and dimensionless displacement of the MEMS gyroscope detection mass along the drive axis, respectively,
Figure BDA00021342985800000511
and y are the dimensionless acceleration, dimensionless velocity and dimensionless displacement along the detection axis, respectively.

在式(2)两边同时除以

Figure BDA00021342985800000512
将之简化为Divide both sides of equation (2) by
Figure BDA00021342985800000512
simplify it to

Figure BDA0002134298580000061
Figure BDA0002134298580000061

重新定义动力学参数为Redefine the kinetic parameters as

Figure BDA0002134298580000062
Figure BDA0002134298580000062

Figure BDA0002134298580000063
Figure BDA0002134298580000063

式(3)可以表示为Equation (3) can be expressed as

Figure BDA0002134298580000064
Figure BDA0002134298580000064

定义definition

Figure BDA0002134298580000065
Figure BDA0002134298580000065

Figure BDA0002134298580000066
Figure BDA0002134298580000066

则式(4)可以改写为Equation (4) can be rewritten as

Figure BDA0002134298580000067
Figure BDA0002134298580000067

定义θ1＝[x,y]T，

Figure BDA0002134298580000068
则式(5)可写为Define θ 1 =[x,y] T ,
Figure BDA0002134298580000068
The formula (5) can be written as

Figure BDA0002134298580000069
Figure BDA0002134298580000069

其中，U＝[u1,u2]T，F(Φ)＝[f1,f2]T，

Figure BDA00021342985800000610
Wherein, U=[u 1 , u 2 ] T , F(Φ)=[f 1 , f 2 ] T ,
Figure BDA00021342985800000610

定义definition

Figure BDA00021342985800000611
Figure BDA00021342985800000611

对F(Φ)进行线性参数化，得到Linear parameterization of F(Φ), we get

F(Φ)＝WΦ (7)F(Φ)=WΦ (7)

(b)给出MEMS陀螺动力学式(1)的参考轨迹为(b) The reference trajectory of the MEMS gyrodynamic equation (1) is given as

Figure BDA0002134298580000071
Figure BDA0002134298580000071

其中，

Figure BDA0002134298580000072
和
Figure BDA0002134298580000073
分别为检测质量块沿驱动轴和检测轴的参考振动位移信号。in,
Figure BDA0002134298580000072
and
Figure BDA0002134298580000073
are the reference vibration displacement signals of the proof mass along the drive axis and the detection axis, respectively.

则无量纲动力学式(6)的参考轨迹为Then the reference trajectory of the dimensionless dynamic equation (6) is

Figure BDA0002134298580000074
Figure BDA0002134298580000074

其中，xd＝6.2sin(4.71t+π/3)，yd＝5sin(5.11t-π/6)，

Figure BDA0002134298580000075
Figure BDA0002134298580000076
where x d =6.2sin(4.71t+π/3), y d =5sin(5.11t-π/6),
Figure BDA0002134298580000075
Figure BDA0002134298580000076

定义跟踪误差为The tracking error is defined as

Figure BDA0002134298580000077
Figure BDA0002134298580000077

则控制器设计为Then the controller is designed as

U＝Un+Upd-Uad (11)U=U n +U pd -U ad (11)

Figure BDA0002134298580000078
Figure BDA0002134298580000078

Upd＝K1e1+K2e2 (13)U pd =K 1 e 1 +K 2 e 2 (13)

Figure BDA0002134298580000079
Figure BDA0002134298580000079

其中，

Figure BDA00021342985800000710
是W的估计值，
Figure BDA00021342985800000711
in,
Figure BDA00021342985800000710
is the estimated value of W,
Figure BDA00021342985800000711

(c)定义预测误差(c) Define prediction error

Figure BDA00021342985800000712
Figure BDA00021342985800000712

其中，

Figure BDA00021342985800000713
in,
Figure BDA00021342985800000713

给出参数的自适应律为The adaptive law for the given parameters is

Figure BDA00021342985800000714
Figure BDA00021342985800000714

其中，等式右边第一项采用当前时刻数据计算，第二项采用τ∈[t-τd,t]区间内历史数据计算，且

Figure BDA0002134298580000081
Among them, the first term on the right side of the equation is calculated using the data at the current moment, and the second term is calculated using the historical data in the interval τ∈[t-τ d ,t], and
Figure BDA0002134298580000081

(d)基于参数自适应律式(16)设计控制器式(11)驱动无量纲动力学式(6)，并通过量纲转换返回MEMS陀螺动力学模型式(1)，实现陀螺驱动控制及动力学参数辨识。(d) Design the controller formula (11) based on the parameter adaptive law formula (16) to drive the dimensionless dynamics formula (6), and return to the MEMS gyro dynamics model formula (1) through dimension conversion, so as to realize the gyro drive control and Dynamic parameter identification.

Claims (1)

1. A MEMS gyroscope self-adaptive driving control method based on historical data parameter identification is characterized by comprising the following steps:
step 1: the MEMS gyroscopic dynamics model considering the presence of quadrature errors is:
Figure FDA0003476815710000011
wherein m is the mass of the proof mass; omegazIn order to input the angular velocity for the gyro,
Figure FDA0003476815710000012
and x*Respectively the acceleration, the speed and the displacement of the MEMS gyroscope detection mass block along the driving shaft,
Figure FDA0003476815710000013
and y*Acceleration, velocity and displacement along the detection axis,
Figure FDA0003476815710000014
and
Figure FDA0003476815710000015
as an electrostatic driving force, cxxAnd cyyAs damping coefficient, kxxAnd kyyIn order to be a stiffness factor, the stiffness factor,
Figure FDA0003476815710000016
and
Figure FDA0003476815710000017
is a nonlinear coefficient, cxyAnd cyxTo damp the coupling coefficient, kxyAnd kyxIs the stiffness coupling coefficient;
taking the dimensionless time t as omegaot*Non-dimensionalized displacement x ═ x*/q0，y＝y*/q0Wherein ω is0As reference frequency, q0For reference length, the MEMS gyroscopic dynamics model is dimensionless and divided by the equation on both sides simultaneously
Figure FDA0003476815710000018
To obtain
Figure FDA0003476815710000019
Wherein,
Figure FDA00034768157100000110
and x is the dimensionless acceleration, the dimensionless speed and the dimensionless displacement of the MEMS gyroscope proof mass along the driving shaft respectively,
Figure FDA00034768157100000111
and y is the dimensionless acceleration, the dimensionless speed and the dimensionless displacement along the detection axis, respectively;
redefining
Figure FDA00034768157100000112
Figure FDA00034768157100000113
Figure FDA00034768157100000114
Figure FDA0003476815710000021
The formula (2) can be rewritten as
Figure FDA0003476815710000022
Definition of theta1＝[x,y]T，
Figure FDA0003476815710000023
Then formula (3) can be written as
Figure FDA0003476815710000024
Wherein U is [ U ]1,u2]T，F(Φ)＝[f1,f2]T，
Figure FDA0003476815710000025
Definition of
Figure FDA0003476815710000026
Carrying out linear parameterization on F (phi) to obtain
F(Φ)＝WΦ (5)
Step 2: the reference trajectory given for MEMS gyroscopic dynamics (1) is
Figure FDA0003476815710000027
Wherein,
Figure FDA0003476815710000028
and
Figure FDA0003476815710000029
respectively reference vibration displacement signals of the proof mass along the drive axis and the detection axis,
Figure FDA00034768157100000210
and
Figure FDA00034768157100000211
reference amplitudes, ω, of drive and sense shaft vibrations, respectively1And ω2Respectively the reference angular frequencies of the drive shaft and the detection shaft vibrations,
Figure FDA00034768157100000212
and
Figure FDA00034768157100000213
the phases of the drive shaft and the detection shaft vibration respectively;
the reference trajectory of the dimensionless kinetic equation (4) is
Figure FDA00034768157100000214
Wherein,
Figure FDA00034768157100000215
Figure FDA00034768157100000216
and the parameters to be designed
Figure FDA00034768157100000217
Defining a tracking error as
Figure FDA00034768157100000218
The controller is designed as
U＝Un+Upd-Uad (9)
Figure FDA0003476815710000031
Upd＝K1e1+K2e2 (11)
Figure FDA0003476815710000032
Wherein,
Figure FDA0003476815710000033
is an estimate of W, the parameter to be designed
Figure FDA0003476815710000034
And
Figure FDA0003476815710000035
meets the Hurwitz condition;
and step 3: defining prediction error
Figure FDA0003476815710000036
Wherein,
Figure FDA0003476815710000037
τdis a normal number to be designed;
giving an adaptation law of the parameters
Figure FDA0003476815710000038
Wherein, the first term on the right side of the equation is calculated by using the data at the current moment, and the second term is calculated by using tau epsilon [ t-tau ]d,t]Historical data calculation in interval and parameter to be designed
Figure FDA0003476815710000039
And
Figure FDA00034768157100000310
meets the Hurwitz condition;
and 4, step 4: and designing a controller formula (9) to drive a dimensionless dynamic formula (4) based on a parameter adaptive law formula (14), and returning to the MEMS gyro dynamic model formula (1) through dimension conversion to realize gyro drive control and dynamic parameter identification.
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