CN110389528B - Data-driven MEMS gyroscope driving control method based on disturbance observation - Google Patents
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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
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:
where m is the mass of the proof mass, ΩzIn order to input the angular velocity for the gyro,and x*Respectively the acceleration, the speed and the displacement of the MEMS gyroscope detection mass block along the driving shaft,and y are acceleration, velocity and displacement along the detection axis respectively,andas an electrostatic driving force, cxxAnd cyyAs damping coefficient, kxxAnd kyyIn order to be a stiffness factor, the stiffness factor,andis a nonlinear coefficient, cxyAnd cyxTo damp the coupling coefficient, kxyAnd kyxIn order to be a stiffness-coupling coefficient,andexternal disturbances on the drive shaft and the detection shaft, respectively; and is Wherein Andis a parameter nominal value, is selected according to a certain model of vibrating silicon micromechanical gyroscope, and is delta kxx、Δkyy、Δcxx、Δcyy、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 simultaneouslyTo obtain
Wherein,and x is the dimensionless acceleration, the dimensionless speed and the dimensionless displacement of the MEMS gyroscope proof mass along the driving shaft respectively,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
The formula (2) can be represented as
Suppose thatIs the unknown parameter matrix to be identified,is a continuous micro regression function vector, and performs linear parameterization on F (z) to obtain
F(z)=W*TΦ(z) (5)
Wherein,is the input vector of the neural network and,is the weight matrix of the neural network, M is the number of nodes of the neural network to be designed,is a basis vector whose q-th element is defined as a gaussian function where q is 1,2, …, M;
wherein σqIs the standard deviation of the gaussian to be designed,is the center of the gaussian function to be designed;
step 2: the reference trajectory given for MEMS gyroscopic dynamics (1) is
Wherein,andrespectively reference vibration displacement signals of the proof mass along the drive axis and the detection axis,andreference amplitudes, ω, of drive and sense shaft vibrations, respectively1And ω2Respectively the reference angular frequencies of the drive shaft and the detection shaft vibrations,andthe phases of the drive shaft and the detection shaft vibration respectively;
the reference trajectory of the dimensionless kinetic equation (4) is
Defining a tracking error as
The controller is designed as
U=Un+Upd-Uad (11)
Upd=K1e1+K2e2 (13)
Wherein the parameter to be designedAndthe Hurwitz condition is met,is W*Is determined by the estimated value of (c),is an estimate of the external disturbance D;
giving an adaptation law of the parameters
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,F(zi) Is F (z) value at the time point of i, and the parameter to be designedSatisfying the Hurwitz condition, B ═ 02×2,I2×2]T;
Giving an update law of the weight of the neural network as
design a disturbance observer as
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 andlet p be*Is the last point in time at which the data was stored,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:
② ifThen 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 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:
where m is the mass of the proof mass, ΩzIn order to input the angular velocity for the gyro,and x*Respectively the acceleration, the speed and the displacement of the MEMS gyroscope detection mass block along the driving shaft,and y*Acceleration, velocity and displacement along the detection axis,andas an electrostatic driving force, cxxAnd cyyAs damping coefficient, kxxAnd kyyIn order to be a stiffness factor, the stiffness factor,andis a nonlinear coefficient, cxyAnd cyxTo damp the coupling coefficient, kxyAnd kyxIn order to be a stiffness-coupling coefficient,andexternal disturbances on the drive shaft and the detection shaft, respectively. And is Wherein Andthe 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, Δkxx、Δkyy、Δcxx、Δcyy、Δkxy、Δkyx、ΔcxyAnd Δ cyxIs an unknown parameter of uncertainty that is,
taking dimensionless timeDimensionless 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
Wherein,and x is the dimensionless acceleration, the dimensionless speed and the dimensionless displacement of the MEMS gyroscope proof mass along the driving shaft respectively,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.
Redefining the kinetic parameters to
The formula (3) can be represented as
Definition of
The formula (4) can be rewritten as
Suppose thatIs the unknown parameter matrix to be identified,is a continuous micro-regression function vector, for F (z)) Performing linear parameterization to obtain
F(z)=W*TΦ(z) (7)
Wherein,is the input vector of the neural network and,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,is a base vector, the q (q is 1,2, …, M) th element of which is defined as the following Gaussian function
Wherein σqIs the standard deviation of the Gaussian function, selected as σq=1,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
Wherein,andreference 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
Defining a tracking error as
The controller is designed as
U=Un+Upd-Uad (13)
Upd=K1e1+K2e2 (15)
giving an adaptation law of the parameter to be identified
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,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
design a disturbance observer as
(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 andlet p be*Is the last point in time at which the data was stored,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:
② ifThen 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 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:
where m is the mass of the proof mass, ΩzIn order to input the angular velocity for the gyro,and x*Respectively the acceleration, the speed and the displacement of the MEMS gyroscope detection mass block along the driving shaft,and y*Acceleration, velocity and displacement along the detection axis,andas an electrostatic driving force, cxxAnd cyyAs damping coefficient, kxxAnd kyyIn order to be a stiffness factor, the stiffness factor,andis a nonlinear coefficient, cxyAnd cyxTo damp the coupling coefficient, kxyAnd kyxIn order to be a stiffness-coupling coefficient,andexternal disturbances on the drive shaft and the detection shaft, respectively; and is Wherein Andis a parameter nominal value, is selected according to a certain model of vibrating silicon micromechanical gyroscope, and is delta kxx、Δkyy、Δcxx、Δcyy、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 simultaneouslyTo obtain
Wherein,and x is the dimensionless acceleration, the dimensionless speed and the dimensionless displacement of the MEMS gyroscope proof mass along the driving shaft respectively,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
The formula (2) can be represented as
Suppose thatIs the unknown parameter matrix to be identified,is a continuous micro regression function vector, and performs linear parameterization on F (z) to obtain
F(z)=W*TΦ(z) (5)
Wherein,is the input vector of the neural network and,is the weight matrix of the neural network, M is the number of nodes of the neural network to be designed,is a basis vector whose q-th element is defined as a gaussian function where q is 1,2, …, M;
wherein σqIs the standard deviation of the gaussian to be designed,is the center of the gaussian function to be designed;
step 2: the reference trajectory given for MEMS gyroscopic dynamics (1) is
Wherein,andrespectively reference vibration displacement signals of the proof mass along the drive axis and the detection axis,andreference amplitudes, ω, of drive and sense shaft vibrations, respectively1And ω2Respectively the reference angular frequencies of the drive shaft and the detection shaft vibrations,andthe phases of the drive shaft and the detection shaft vibration respectively;
the reference trajectory of the dimensionless kinetic equation (4) is
Defining a tracking error as
The controller is designed as
U=Un+Upd-Uad (11)
Upd=K1e1+K2e2 (13)
Wherein the parameter to be designedAndthe Hurwitz condition is met,is W*Is determined by the estimated value of (c),is an estimate of the external disturbance D;
giving an adaptation law of the parameters
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,F(zi) Is F (z) value at the time point of i, and the parameter to be designedSatisfying the Hurwitz condition, B ═ 02×2,I2×2]T;
Giving an update law of the weight of the neural network as
design a disturbance observer as
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 andlet p be*Is the last point in time at which the data was stored,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:
② ifThen 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 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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