CN110389528B - Data-driven MEMS gyroscope driving control method based on disturbance observation - Google Patents

Data-driven MEMS gyroscope driving control method based on disturbance observation Download PDF

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CN110389528B
CN110389528B CN201910648370.9A CN201910648370A CN110389528B CN 110389528 B CN110389528 B CN 110389528B CN 201910648370 A CN201910648370 A CN 201910648370A CN 110389528 B CN110389528 B CN 110389528B
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许斌
张睿
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Northwestern Polytechnical University
Shenzhen Institute of Northwestern Polytechnical University
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Abstract

The invention relates to a data-driven MEMS gyroscope drive control method based on disturbance observation, and belongs to the field of intelligent instruments. The method converts a gyroscope kinetic model into a dimensionless kinetic linear parameterized model; selecting proper historical data by a given data screening method, and designing a parameter adaptive law by combining current data and the historical data to realize parameter identification; estimating system uncertainty caused by working environment changes such as temperature, air pressure, magnetic field and the like by adopting a neural network; designing a disturbance observer to estimate dynamic disturbance brought by an external vibration environment; and designing a controller to improve the driving control precision of the gyroscope through closed-loop feedback. The disturbance observation-based data-driven MEMS gyroscope driving control method can realize high-precision driving control of the gyroscope under the condition of system uncertainty and external interference, and further improve the performance of the MEMS gyroscope.

Description

Data-driven MEMS gyroscope driving control method based on disturbance observation
Technical Field
The invention relates to a drive control method of an MEMS gyroscope, in particular to a data drive MEMS gyroscope drive control method based on disturbance observation, and belongs to the field of intelligent instruments.
Background
In practical engineering application, dynamic parameters are changed due to changes of working environments such as temperature, air pressure and magnetic field of the MEMS gyroscope, external interference is brought to dynamics due to a vibration environment, and the two phenomena cause that a controller which lacks self-regulation capacity is difficult to adapt to a dynamically changing environment. Two commonly used solutions are: (1) the hardware design is improved, and the influence of shielding the external environment by the isolation component is increased; (2) the design scheme of the controller is improved, and the self-adaptive capacity of the controller is enhanced.
The concept of the applied Global Sliding Mode Control for MEMS Gyroscope Using RBF Neural Network (Yundi Chu and Juntao Fei, physical schemes in Engineering, 2015) is consistent with that of the second method, a Global Sliding Mode Control method for an MEMS Gyroscope based on an RBF Neural Network is provided, the Neural Network is adopted to adjust Sliding Mode switching gain, and a dynamic model parameter identification result is provided. However, the sliding mode buffeting problem is mainly concerned in the method, the system dynamic uncertainty and the external disturbance are difficult to be effectively estimated, and the control precision is further limited.
Disclosure of Invention
Technical problem to be solved
In order to solve the problem of limited driving control precision in the prior art, the invention provides a data-driven MEMS gyroscope driving control method based on disturbance observation. The method provides a data screening method to select proper historical data, and designs a parameter adaptive law by combining current data and the historical data to realize parameter identification; estimating system uncertainty caused by working environment changes such as temperature, air pressure, magnetic field and the like by adopting a self-adaptive neural network; designing a disturbance observer to estimate dynamic disturbance brought by an external vibration environment; and designing a controller to improve the driving control precision of the gyroscope through closed-loop feedback.
Technical scheme
A data-driven MEMS gyroscope driving control method based on disturbance observation is characterized by comprising the following steps:
step 1: the MEMS gyroscopic dynamics model considering the existence of quadrature error, system uncertainty and external interference is as follows:
Figure BDA0002134332730000021
where m is the mass of the proof mass, ΩzIn order to input the angular velocity for the gyro,
Figure BDA0002134332730000022
and x*Respectively the acceleration, the speed and the displacement of the MEMS gyroscope detection mass block along the driving shaft,
Figure BDA0002134332730000023
and y are acceleration, velocity and displacement along the detection axis respectively,
Figure BDA0002134332730000024
and
Figure BDA0002134332730000025
as an electrostatic driving force, cxxAnd cyyAs damping coefficient, kxxAnd kyyIn order to be a stiffness factor, the stiffness factor,
Figure BDA0002134332730000026
and
Figure BDA0002134332730000027
is a nonlinear coefficient, cxyAnd cyxTo damp the coupling coefficient, kxyAnd kyxIn order to be a stiffness-coupling coefficient,
Figure BDA0002134332730000028
and
Figure BDA0002134332730000029
external disturbances on the drive shaft and the detection shaft, respectively; and is
Figure BDA00021343327300000210
Figure BDA00021343327300000211
Figure BDA00021343327300000212
Wherein
Figure BDA00021343327300000213
Figure BDA00021343327300000214
And
Figure BDA00021343327300000215
is a parameter nominal value, is selected according to a certain model of vibrating silicon micromechanical gyroscope, and is delta kxx、Δkyy、Δcxx、Δcyy、
Figure BDA00021343327300000216
Δkxy、Δkyx、ΔcxyAnd Δ cyxIs an unknown uncertain parameter;
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 BDA00021343327300000217
To obtain
Figure BDA00021343327300000218
Wherein,
Figure BDA00021343327300000219
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 BDA00021343327300000220
and y is dimensionless acceleration, dimensionless speed and dimensionless displacement along the detection axis, respectively, dx(t) and dy(t) dimensionless external disturbances on the drive shaft and the detection shaft, respectively;
redefining
Figure BDA0002134332730000031
Figure BDA0002134332730000032
Figure BDA0002134332730000033
Figure BDA0002134332730000034
Figure BDA0002134332730000035
Figure BDA0002134332730000036
Figure BDA0002134332730000037
Figure BDA0002134332730000038
Figure BDA0002134332730000039
Figure BDA00021343327300000310
The formula (2) can be represented as
Figure BDA00021343327300000311
Definition of theta1＝[x,y]T，
Figure BDA00021343327300000312
Then formula (3) can be written as
Figure BDA00021343327300000313
Wherein U is [ U ]1,u2]T，F(z)＝[f1,f2]T，ΔF(z)＝[Δf1,Δf2]T，
Figure BDA00021343327300000314
Figure BDA00021343327300000315
Suppose that
Figure BDA00021343327300000316
Is the unknown parameter matrix to be identified,
Figure BDA00021343327300000317
is a continuous micro regression function vector, and performs linear parameterization on F (z) to obtain
F(z)＝W*TΦ(z) (5)
Wherein,
Figure BDA0002134332730000041
Φ(z)＝z；
constructing neural networks
Figure BDA0002134332730000042
Approaches Δ F (z) to obtain
Figure BDA0002134332730000043
Wherein,
Figure BDA0002134332730000044
is the input vector of the neural network and,
Figure BDA0002134332730000045
is the weight matrix of the neural network, M is the number of nodes of the neural network to be designed,
Figure BDA0002134332730000046
is a basis vector whose q-th element is defined as a gaussian function where q is 1,2, …, M;
Figure BDA0002134332730000047
wherein σqIs the standard deviation of the gaussian to be designed,
Figure BDA0002134332730000048
is the center of the gaussian function to be designed;
step 2: the reference trajectory given for MEMS gyroscopic dynamics (1) is
Figure BDA0002134332730000049
Wherein,
Figure BDA00021343327300000410
and
Figure BDA00021343327300000411
respectively reference vibration displacement signals of the proof mass along the drive axis and the detection axis,
Figure BDA00021343327300000412
and
Figure BDA00021343327300000413
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 BDA00021343327300000414
and
Figure BDA00021343327300000415
the phases of the drive shaft and the detection shaft vibration respectively;
the reference trajectory of the dimensionless kinetic equation (4) is
Figure BDA00021343327300000416
Wherein,
Figure BDA00021343327300000417
Figure BDA00021343327300000418
and the parameters to be designed
Figure BDA00021343327300000419
Defining a tracking error as
Figure BDA0002134332730000051
The controller is designed as
U＝Un+Upd-Uad (11)
Figure BDA0002134332730000052
Upd＝K1e1+K2e2 (13)
Figure BDA0002134332730000053
Wherein the parameter to be designed
Figure BDA0002134332730000054
And
Figure BDA0002134332730000055
the Hurwitz condition is met,
Figure BDA0002134332730000056
is W*Is determined by the estimated value of (c),
Figure BDA0002134332730000057
is an estimate of the external disturbance D;
giving an adaptation law of the parameters
Figure BDA0002134332730000058
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 pHCalculation of stored data of a point in time, phi (z)i) Is the value of phi (z) at the time point i, wherein i is 1,2, …, pH，
Figure BDA0002134332730000059
F(zi) Is F (z) value at the time point of i, and the parameter to be designed
Figure BDA00021343327300000510
Satisfying the Hurwitz condition, B ═ 02×2,I2×2]T；
Giving an update law of the weight of the neural network as
Figure BDA00021343327300000511
Wherein,
Figure BDA00021343327300000512
a matrix is to be designed;
design a disturbance observer as
Figure BDA00021343327300000513
Wherein,
Figure BDA00021343327300000514
for the positive definite matrix to be designed,
Figure BDA00021343327300000515
is an intermediate variable;
and step 3: defining a matrix ZtStorage data phi (z), the number of rows of the matrix is 6, the number of columns p varies with the amount of storage data and
Figure BDA0002134332730000061
let p be*Is the last point in time at which the data was stored,
Figure BDA0002134332730000062
is p*Phi (z) of the time point, epsilon is a normal number; the data screening process selected by the parameter adaptive law (15) is as follows:
if
Figure BDA0002134332730000063
Or rank ([ Z ]t,Φ(z)])>rank([Zt]) Executing the step II, otherwise, abandoning the data phi (z);
② if
Figure BDA0002134332730000066
Then p will beHStoring phi (Z) of time into ZtMatrix, i.e. pH＝pH+1，Zt(:,pH) If not, executing step c;
calculating current ZtThe minimum singular value of the matrix is denoted Sold(ii) a Then, storing phi (Z) into Z at time itMatrix, where i ═ 1,2, …, pHTo obtain a set of matrices
Figure BDA0002134332730000064
Figure BDA0002134332730000065
Calculating difference ZtAnd selecting the maximum value S of all the minimum singular values; continuing to execute the step IV;
if S>SoldA 1 is to pHStoring phi (Z) of time into ZtMatrix, i.e. Zt(:,pH) Otherwise, p is discardedHΦ (z) of time; returning to the step I to continue to screen data;
and 4, step 4: and (3) driving the dimensionless dynamics formula (4) by using a controller formula (11) designed based on the data screening method in the step (3), the parameter adaptive law formula (15), the neural network weight updating law formula (16) and the disturbance observer formula (17), and returning to the MEMS gyro dynamics model formula (1) through dimension conversion to realize gyro driving control.
Advantageous effects
Compared with the prior art, the data-driven MEMS gyroscope driving control method based on disturbance observation provided by the invention has the beneficial effects that:
(1) aiming at uncertain dynamics and external interference of the MEMS gyroscope, a self-adaptive neural network and a disturbance observer are respectively designed for estimation, and the driving control precision of the gyroscope is improved through feedback compensation.
(2) Aiming at the problem that the dynamic parameters are unknown in actual engineering, a data screening method is designed to select proper historical data, and a parameter adaptive law is constructed by using the current data and the historical data together to realize parameter identification.
Drawings
FIG. 1 is a flow chart of an embodiment of the present invention
FIG. 2 is a flow chart of data screening according to the present invention
Detailed Description
The invention will now be further described with reference to the following examples and drawings:
the invention discloses a data-driven MEMS gyroscope driving control method based on disturbance observation, which comprises the following specific design steps in combination with figure 1:
(a) the MEMS gyroscopic dynamics model considering the existence of quadrature error, system uncertainty and external interference is as follows:
Figure BDA0002134332730000071
where m is the mass of the proof mass, ΩzIn order to input the angular velocity for the gyro,
Figure BDA0002134332730000072
and x*Respectively the acceleration, the speed and the displacement of the MEMS gyroscope detection mass block along the driving shaft,
Figure BDA0002134332730000073
and y*Acceleration, velocity and displacement along the detection axis,
Figure BDA0002134332730000074
and
Figure BDA0002134332730000075
as an electrostatic driving force, cxxAnd cyyAs damping coefficient, kxxAnd kyyIn order to be a stiffness factor, the stiffness factor,
Figure BDA0002134332730000076
and
Figure BDA0002134332730000077
is a nonlinear coefficient, cxyAnd cyxTo damp the coupling coefficient, kxyAnd kyxIn order to be a stiffness-coupling coefficient,
Figure BDA0002134332730000078
and
Figure BDA0002134332730000079
external disturbances on the drive shaft and the detection shaft, respectively. And is
Figure BDA00021343327300000710
Figure BDA00021343327300000711
Figure BDA00021343327300000712
Wherein
Figure BDA00021343327300000713
Figure BDA00021343327300000714
And
Figure BDA00021343327300000715
the parameters are nominal values, and according to a certain type of vibrating silicon micromechanical gyroscope, each parameter of the gyroscope is selected to be m-5.7 multiplied by 10-9kg，q0＝10-5m，ω0＝1kHz，Ωz＝5.0rad/s，
Figure BDA00021343327300000716
Figure BDA00021343327300000717
Δkxx、Δkyy、Δcxx、Δcyy、
Figure BDA00021343327300000718
Δkxy、Δkyx、ΔcxyAnd Δ cyxIs an unknown parameter of uncertainty that is,
Figure BDA00021343327300000719
taking dimensionless time
Figure BDA0002134332730000081
Dimensionless displacement x ═ x*/q0，y＝y*/q0Wherein ω is0As reference frequency, q0Carrying out dimensionless processing on the MEMS gyro dynamic model to obtain a reference length
Figure BDA0002134332730000082
Wherein,
Figure BDA0002134332730000083
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 BDA0002134332730000084
and y is dimensionless acceleration, dimensionless speed and dimensionless displacement along the detection axis, respectively, dx(t)＝5.7×10-8sin (2t) and dy(t)＝5.7×10-8sin (1.2t) is the dimensionless external disturbance on the drive and detection axes, respectively.
On both sides of formula (2) simultaneously by
Figure BDA0002134332730000085
Simplify it into
Figure BDA0002134332730000086
Redefining the kinetic parameters to
Figure BDA0002134332730000087
The formula (3) can be represented as
Figure BDA0002134332730000088
Wherein,
Figure BDA0002134332730000089
Figure BDA00021343327300000810
and is
Figure BDA00021343327300000811
Figure BDA0002134332730000091
Definition of
Figure BDA0002134332730000092
Figure BDA0002134332730000093
Figure BDA0002134332730000094
Figure BDA0002134332730000095
The formula (4) can be rewritten as
Figure BDA0002134332730000096
Definition of theta1＝[x,y]T，
Figure BDA0002134332730000097
Figure BDA0002134332730000098
Then formula (5) can be written as
Figure BDA0002134332730000099
Wherein U is [ U ]1,u2]T，F(z)＝[f1,f2]T，ΔF(z)＝[Δf1,Δf2]T，
Figure BDA00021343327300000910
Figure BDA00021343327300000911
Suppose that
Figure BDA00021343327300000912
Is the unknown parameter matrix to be identified,
Figure BDA00021343327300000913
is a continuous micro-regression function vector, for F (z)) Performing linear parameterization to obtain
F(z)＝W*TΦ(z) (7)
Wherein,
Figure BDA00021343327300000914
Φ(z)＝z。
constructing neural networks
Figure BDA0002134332730000101
Approaches Δ F (z) to obtain
Figure BDA0002134332730000102
Wherein,
Figure BDA0002134332730000103
is the input vector of the neural network and,
Figure BDA0002134332730000104
is a weight matrix of the neural network, M is the number of nodes of the neural network, M is selected to be 5 multiplied by 3 multiplied by 225,
Figure BDA0002134332730000105
is a base vector, the q (q is 1,2, …, M) th element of which is defined as the following Gaussian function
Figure BDA0002134332730000106
Wherein σqIs the standard deviation of the Gaussian function, selected as σq＝1，
Figure BDA0002134332730000107
Is the center of the Gaussian function and has a value of-29.202, 29.202]×[-25.55,25.55]×[-6.2,6.2]×[-5,5]Can be selected arbitrarily.
(b) The reference trajectory given for MEMS gyroscopic dynamics (1) is
Figure BDA0002134332730000108
Wherein,
Figure BDA0002134332730000109
and
Figure BDA00021343327300001010
reference vibration displacement signals of the proof mass along the drive axis and the proof axis, respectively.
The reference trajectory of the dimensionless kinetic equation (6) is
Figure BDA00021343327300001011
Wherein x isd＝6.2sin(4.71t+π/3)，yd＝5sin(5.11t-π/6)，
Figure BDA00021343327300001012
Figure BDA00021343327300001013
Defining a tracking error as
Figure BDA00021343327300001014
The controller is designed as
U＝Un+Upd-Uad (13)
Figure BDA00021343327300001015
Upd＝K1e1+K2e2 (15)
Figure BDA00021343327300001016
Wherein,
Figure BDA0002134332730000111
is W*Is determined by the estimated value of (c),
Figure BDA0002134332730000112
is an estimate of the value of D,
Figure BDA0002134332730000113
giving an adaptation law of the parameter to be identified
Figure BDA0002134332730000114
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 pHCalculation of stored data of a point in time, phi (z)i) Is phi (z) at i (i ═ 1,2, …, pH) The value of the time point is selected,
Figure BDA0002134332730000115
F(zi) Is F (z) in i (i ═ 1,2, …, pH) The value of the time point, and FW＝diag([10,12,8,3,71,31])，B＝[02×2,I2×2]T，P＝diag([10,12,71,31])。
Giving an update law of the weight of the neural network as
Figure BDA0002134332730000116
Wherein,
Figure BDA0002134332730000117
design a disturbance observer as
Figure BDA0002134332730000118
Wherein,
Figure BDA0002134332730000119
is the intermediate variable(s) of the variable,
Figure BDA00021343327300001110
(c) defining a matrix ZtStorage data phi (z), the number of rows of the matrix is 6, the number of columns p varies with the amount of storage data and
Figure BDA00021343327300001111
let p be*Is the last point in time at which the data was stored,
Figure BDA00021343327300001112
is p*Phi (z), epsilon at the time point is 0.08. Referring to fig. 2, the data filtering process selected by the parameter adaptive law (17) is as follows:
if
Figure BDA00021343327300001113
Or rank ([ Z ]t,Φ(z)])>rank([Zt]) Step two is executed, otherwise, the data phi (z) is abandoned.
② if
Figure BDA00021343327300001114
Then p will beHStoring phi (Z) of time into ZtMatrix, i.e. pH＝pH+1，Zt(:,pH) If not, executing step c.
Calculating current ZtThe minimum singular value of the matrix is denoted Sold. Then, the measured values are respectively measured at i (i is 1,2, …, p)H) Store phi (Z) into Z at timetMatrix to obtain a set of matrices
Figure BDA0002134332730000121
Figure BDA0002134332730000122
Calculating difference ZtAnd selecting the maximum value S of all the minimum singular values. And continuing to execute the step (iv).
If S>SoldA 1 is to pHStoring phi (Z) of time into ZtMatrix, i.e. Zt(:,pH) Otherwise, p is discardedHPhi (z) of time. And returning to the step (i) to continue screening data.
(d) And (c) driving the dimensionless dynamics formula (6) by a controller formula (13) designed based on a partial data screening method (c), a parameter self-adaptive formula (17), a neural network weight updating formula (18) and a disturbance observer formula (19), and returning to the MEMS gyro dynamics model formula (1) through dimension conversion to realize gyro driving control.

Claims (1)

1. A data-driven MEMS gyroscope driving control method based on disturbance observation is characterized by comprising the following steps:
step 1: the MEMS gyroscopic dynamics model considering the existence of quadrature error, system uncertainty and external interference is as follows:
Figure FDA0002134332720000011
where m is the mass of the proof mass, ΩzIn order to input the angular velocity for the gyro,
Figure FDA0002134332720000012
and x*Respectively the acceleration, the speed and the displacement of the MEMS gyroscope detection mass block along the driving shaft,
Figure FDA0002134332720000013
and y*Acceleration, velocity and displacement along the detection axis,
Figure FDA0002134332720000014
and
Figure FDA0002134332720000015
as an electrostatic driving force, cxxAnd cyyAs damping coefficient, kxxAnd kyyIn order to be a stiffness factor, the stiffness factor,
Figure FDA0002134332720000016
and
Figure FDA0002134332720000017
is a nonlinear coefficient, cxyAnd cyxTo damp the coupling coefficient, kxyAnd kyxIn order to be a stiffness-coupling coefficient,
Figure FDA0002134332720000018
and
Figure FDA0002134332720000019
external disturbances on the drive shaft and the detection shaft, respectively; and is
Figure FDA00021343327200000110
Figure FDA00021343327200000111
Figure FDA00021343327200000112
Wherein
Figure FDA00021343327200000113
Figure FDA00021343327200000114
And
Figure FDA00021343327200000115
is a parameter nominal value, is selected according to a certain model of vibrating silicon micromechanical gyroscope, and is delta kxx、Δkyy、Δcxx、Δcyy、
Figure FDA00021343327200000116
Δkxy、Δkyx、ΔcxyAnd Δ cyxIs an unknown uncertain parameter;
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 FDA00021343327200000117
To obtain
Figure FDA00021343327200000118
Wherein,
Figure FDA00021343327200000119
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 FDA00021343327200000120
and y is dimensionless acceleration, dimensionless speed and dimensionless displacement along the detection axis, respectively, dx(t) and dy(t) dimensionless external disturbances on the drive shaft and the detection shaft, respectively;
redefining
Figure FDA0002134332720000021
Figure FDA0002134332720000022
Figure FDA0002134332720000023
Figure FDA0002134332720000024
Figure FDA0002134332720000025
Figure FDA0002134332720000026
Figure FDA0002134332720000027
Figure FDA0002134332720000028
Figure FDA0002134332720000029
Figure FDA00021343327200000210
The formula (2) can be represented as
Figure FDA00021343327200000211
Definition of theta1＝[x,y]T，
Figure FDA00021343327200000212
Then formula (3) can be writtenIs composed of
Figure FDA00021343327200000213
Wherein U is [ U ]1,u2]T，F(z)＝[f1,f2]T，ΔF(z)＝[Δf1,Δf2]T，
Figure FDA00021343327200000214
Figure FDA00021343327200000215
Suppose that
Figure FDA00021343327200000216
Is the unknown parameter matrix to be identified,
Figure FDA00021343327200000217
is a continuous micro regression function vector, and performs linear parameterization on F (z) to obtain
F(z)＝W*TΦ(z) (5)
Wherein,
Figure FDA0002134332720000031
Φ(z)＝z；
constructing neural networks
Figure FDA0002134332720000032
Approaches Δ F (z) to obtain
Figure FDA0002134332720000033
Wherein,
Figure FDA0002134332720000034
is the input vector of the neural network and,
Figure FDA0002134332720000035
is the weight matrix of the neural network, M is the number of nodes of the neural network to be designed,
Figure FDA0002134332720000036
is a basis vector whose q-th element is defined as a gaussian function where q is 1,2, …, M;
Figure FDA0002134332720000037
wherein σqIs the standard deviation of the gaussian to be designed,
Figure FDA0002134332720000038
is the center of the gaussian function to be designed;
step 2: the reference trajectory given for MEMS gyroscopic dynamics (1) is
Figure FDA0002134332720000039
Wherein,
Figure FDA00021343327200000310
and
Figure FDA00021343327200000311
respectively reference vibration displacement signals of the proof mass along the drive axis and the detection axis,
Figure FDA00021343327200000312
and
Figure FDA00021343327200000313
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 FDA00021343327200000314
and
Figure FDA00021343327200000315
the phases of the drive shaft and the detection shaft vibration respectively;
the reference trajectory of the dimensionless kinetic equation (4) is
Figure FDA00021343327200000316
Wherein,
Figure FDA00021343327200000317
Figure FDA00021343327200000318
and the parameters to be designed
Figure FDA00021343327200000319
Defining a tracking error as
Figure FDA00021343327200000320
The controller is designed as
U＝Un+Upd-Uad (11)
Figure FDA0002134332720000041
Upd＝K1e1+K2e2 (13)
Figure FDA0002134332720000042
Wherein the parameter to be designed
Figure FDA0002134332720000043
And
Figure FDA0002134332720000044
the Hurwitz condition is met,
Figure FDA0002134332720000045
is W*Is determined by the estimated value of (c),
Figure FDA0002134332720000046
is an estimate of the external disturbance D;
giving an adaptation law of the parameters
Figure FDA0002134332720000047
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 pHCalculation of stored data of a point in time, phi (z)i) Is the value of phi (z) at the time point i, wherein i is 1,2, …, pH，
Figure FDA0002134332720000048
F(zi) Is F (z) value at the time point of i, and the parameter to be designed
Figure FDA0002134332720000049
Satisfying the Hurwitz condition, B ═ 02×2,I2×2]T；
Giving an update law of the weight of the neural network as
Figure FDA00021343327200000410
Wherein,
Figure FDA00021343327200000411
a matrix is to be designed;
design a disturbance observer as
Figure FDA00021343327200000412
Wherein,
Figure FDA00021343327200000413
for the positive definite matrix to be designed,
Figure FDA00021343327200000414
is an intermediate variable;
and step 3: defining a matrix ZtStorage data phi (z), the number of rows of the matrix is 6, the number of columns p varies with the amount of storage data and
Figure FDA00021343327200000415
let p be*Is the last point in time at which the data was stored,
Figure FDA00021343327200000416
is p*Phi (z) of the time point, epsilon is a normal number; the data screening process selected by the parameter adaptive law (15) is as follows:
if
Figure FDA0002134332720000051
Or rank ([ Z ]t,Φ(z)])>rank([Zt]) Executing the step II, otherwise, abandoning the data phi (z);
② if
Figure FDA0002134332720000052
Then p will beHStoring phi (Z) of time into ZtThe matrix is a matrix of a plurality of matrices,instant pH＝pH+1，Zt(:,pH) If not, executing step c;
calculating current ZtThe minimum singular value of the matrix is denoted Sold(ii) a Then, storing phi (Z) into Z at time itMatrix, where i ═ 1,2, …, pHTo obtain a set of matrices
Figure FDA0002134332720000053
Figure FDA0002134332720000054
Calculating difference ZtAnd selecting the maximum value S of all the minimum singular values; continuing to execute the step IV;
if S>SoldA 1 is to pHStoring phi (Z) of time into ZtMatrix, i.e. Zt(:,pH) Otherwise, p is discardedHΦ (z) of time; returning to the step I to continue to screen data;
and 4, step 4: and (3) driving the dimensionless dynamics formula (4) by using a controller formula (11) designed based on the data screening method in the step (3), the parameter adaptive law formula (15), the neural network weight updating law formula (16) and the disturbance observer formula (17), and returning to the MEMS gyro dynamics model formula (1) through dimension conversion to realize gyro driving control.
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