CN107607103A - MEMS gyroscope Hybrid Learning control method based on interference observer - Google Patents

MEMS gyroscope Hybrid Learning control method based on interference observer Download PDF

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CN107607103A
CN107607103A CN201711073630.1A CN201711073630A CN107607103A CN 107607103 A CN107607103 A CN 107607103A CN 201711073630 A CN201711073630 A CN 201711073630A CN 107607103 A CN107607103 A CN 107607103A
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msub
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CN107607103B (en
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许斌
张睿
张安龙
刘瑞鑫
邵添羿
赵万良
吴枫
成宇翔
谷丛
林建华
刘洋
慕容欣
刘美霞
应俊
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Northwestern Polytechnical University
Shanghai Aerospace Control Technology Institute
Shenzhen Institute of Northwestern Polytechnical University
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Northwestern Polytechnical University
Shanghai Aerospace Control Technology Institute
Shenzhen Institute of Northwestern Polytechnical University
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Abstract

The invention discloses a kind of MEMS gyroscope Hybrid Learning control method based on interference observer, for solving the technical problem of the modal control method poor practicability of existing MEMS gyroscope.Technical scheme is to design interference observer first, and interference is estimated and compensated, and reduces sliding formwork and buffets；Simultaneously according to fuzzy prediction error and tracking error, the compound adaptive rule rule of design fuzzy logic weights, the weight coefficient of fuzzy logic is corrected, realizes unknown dynamic (dynamical) effective dynamic estimation.The present invention considers prediction error and tracking error, designs the Hybrid Learning more new law of fuzzy logic weights, corrects the weight coefficient of fuzzy logic, realize unknown dynamic (dynamical) effective dynamic estimation.With reference to sliding mode control theory, dynamic (dynamical) feedforward compensation unknown to MEMS gyro is realized, further improves the control accuracy of MEMS gyroscope.Interference observer is designed, interference is compensated in sliding formwork control, is buffeted so as to reduce sliding formwork, practicality is good.

Description

MEMS gyroscope Hybrid Learning control method based on interference observer
Technical field
It is more particularly to a kind of based on interference observer the present invention relates to a kind of modal control method of MEMS gyroscope MEMS gyroscope Hybrid Learning control method.
Background technology
With the development of nonlinear control techniques, Park S et al. draw advanced intelligence learning and Non-Linear Control Theory During entering MEMS gyroscope Model control, to improving system robustness, improve MEMS gyroscope performance and be made that significant contribution. Consider unknown and dynamic change uncertain in MEMS gyro system and interference, how to realize unknown dynamic (dynamical) effectively study and The feedforward compensation of sliding formwork control, it is the key for improving gyro performance.
《Robust adaptive sliding mode control of MEMS gyroscope using T-S fuzzy model》(Shitao Wang and Juntao Fei,《Nonlinear Dynamics》, 2014 volume 77 the 1st- 2 phases) in a text, Fei Juntao et al. using the dynamic (dynamical) indeterminate of T-S fuzzy logic systems study MEMS gyro and interference, then Uncertain and interference is compensated using sliding mode controller.Although this method realizes the MEMS under uncertain unknown situation Gyro control, but uncertain original idea on the one hand is approached due to having run counter to fuzzy logic, it is difficult to realize unknown dynamic (dynamical) effective Dynamic estimation, on the other hand to eliminate uncertain and disturbing the handoff gain, it is necessary to very big, bring serious sliding formwork and buffet.
The content of the invention
In order to overcome the shortcomings of the modal control method poor practicability of existing MEMS gyroscope, the present invention provides one kind and is based on The MEMS gyroscope Hybrid Learning control method of interference observer.This method designs interference observer first, and interference is estimated Meter and compensation, reduce sliding formwork and buffet；Simultaneously according to fuzzy prediction error and tracking error, design fuzzy logic weights it is compound from Rule rule is adapted to, the weight coefficient of fuzzy logic is corrected, realizes unknown dynamic (dynamical) effective dynamic estimation.The present invention considers prediction Error and tracking error, the Hybrid Learning more new law of fuzzy logic weights is designed, correct the weight coefficient of fuzzy logic, realized not Know dynamic (dynamical) effective dynamic estimation.With reference to sliding mode control theory, dynamic (dynamical) feedforward compensation unknown to MEMS gyro is realized, is entered One step improves the control accuracy of MEMS gyroscope.Interference observer is designed, interference is compensated in sliding formwork control, so as to drop Low sliding formwork is buffeted, and practicality is good.
The technical solution adopted for the present invention to solve the technical problems：A kind of MEMS gyroscope based on interference observer is answered Learning control method is closed, is characterized in comprising the following steps：
(a) kinetic model of the MEMS gyroscope of consideration quadrature error is：
Wherein, m is the quality of detection mass；ΩzFor gyro input angular velocity；For electrostatic drive power； x*It is acceleration of the MEMS gyroscope detection mass along drive shaft, speed and displacement respectively；y*It is detection respectively Acceleration of the mass along detection axle, speed and displacement；dxx, dyyIt is damped coefficient；kxx, kyyIt is stiffness coefficient；dxyIt is damping The coefficient of coup, kxyIt is stiffness coupling coefficient.
To improve the Analysis on Mechanism degree of accuracy, nondimensionalization processing is carried out to MEMS gyro kinetic model.Take nondimensionalization Time t*=ωoT, then formula (1) both sides simultaneously divided by reference frequency squareReference length q0With detection mass matter M is measured, the nondimensionalization model for obtaining MEMS gyro is
Wherein,
Redefining relevant system parameters is
Then the nondimensionalization model abbreviation of MEMS gyro is
Make A=2S-D, B=Ω2- K, parameter fluctuation caused by considering environmental factor and non-modeling factors and outside are dry Disturb, then formula (4) is expressed as
The model is by state variable q=[x y]TWith control input u=[ux uy]TComposition.Wherein, x, y are respectively immeasurable Mass is detected after guiding principle along drive shaft and the moving displacement of detection axle；ux, uyRepresent that nondimensionalization is after-applied in drive shaft respectively With the power of detection axle；A, B, C are the parameters of model, and its value is relevant with the structural parameters and dynamics of gyroscope；P is mould The uncertain unknown dynamics brought of shape parameter, andΔ A, Δ B are that environmental factor and non-modeling factors are made Into unknown parameter fluctuation；D (t) is external disturbance.
(b) fuzzy logic system is constructedApproachThe fuzzy logic system is by M bar IF-THEN languages Sentence description, wherein the i-th rule has following form：
Using the average defuzzifier in product inference machine, monodrome fuzzy device and center, the output of fuzzy system is
Wherein, XinIt is the input vector of fuzzy logic system, and For the weights of fuzzy logic Matrix；θ(Xin) it is the fuzzy base vector of M dimensions.I-th of element of fuzzy base vector be
Wherein,It is respectivelyxi, yiTo domain A1i, A2i, A3i, A4iDegree of membership,Membership function be designed as following Gaussian function：
Wherein,σiIt is center and the standard deviation of the Gaussian function respectively.
Define optimal estimation parameter w*For
Wherein, ψ is w set.
Therefore, the indeterminate of kinetic model is expressed as
Wherein, ε is the approximate error of fuzzy system.
And the evaluated error of indeterminate is
Wherein,And
(c) design interference observer is
Wherein,For external disturbance d (t) estimate；L is positive definite matrix；Z is intermediate variable.
Define interference observer evaluated error be
Therefore have
(d) the dynamics reference model for establishing MEMS gyro is
Wherein,qdTo refer to vibration displacement signal,For qdTwo Order derivative；Ax, AyMass is respectively detected along drive shaft and the reference amplitude of detection shaft vibration；ωx, ωyRespectively detect matter Gauge block along drive shaft and detection shaft vibration reference angular frequency.
Building tracking error is
E=q-qd (15)
Define sliding-mode surface
Wherein,β meets Hurwitz conditions.Then
Sliding mode controller design is
Wherein, K0For positive definite matrix.
Sliding mode controller formula (18) is substituted into formula (17), had
Definition And define new signal
Define modeling errorTo predict error.In order that closed-loop system ensure s andConvergence, consider pre- Survey error and sliding formwork function, the Hybrid Learning more new law of fuzzy logic weight matrix are designed as
Wherein, λ,For positive definite matrix.
(e) according to obtained interference observer (12), sliding mode controller formula (18) and Hybrid Learning weight more new law formula (21) the kinetic simulation pattern (5) of MEMS gyro, is returned to, the vibration displacement of mass is detected to gyro and speed is tracked Control.
The beneficial effects of the invention are as follows：This method designs interference observer first, and interference is estimated and compensated, is reduced Sliding formwork is buffeted；Simultaneously according to fuzzy prediction error and tracking error, the compound adaptive rule rule of design fuzzy logic weights, repair The weight coefficient of positive fuzzy logic, realizes unknown dynamic (dynamical) effective dynamic estimation.The present invention considers that prediction error and tracking miss Difference, the Hybrid Learning more new law of fuzzy logic weights is designed, correct the weight coefficient of fuzzy logic, realizing unknown dynamic (dynamical) has Imitate dynamic estimation.With reference to sliding mode control theory, dynamic (dynamical) feedforward compensation unknown to MEMS gyro is realized, further improves MEMS The control accuracy of gyroscope.Interference observer is designed, interference is compensated in sliding formwork control, is buffeted so as to reduce sliding formwork, Practicality is good.
The present invention is elaborated with reference to the accompanying drawings and detailed description.
Brief description of the drawings
Fig. 1 is the flow chart of the MEMS gyroscope Hybrid Learning control method of the invention based on interference observer.
Embodiment
Reference picture 1.MEMS gyroscope Hybrid Learning control method of the invention based on interference observer comprises the following steps that：
(a) kinetic model of the MEMS gyroscope of consideration quadrature error is：
Wherein, m is the quality of detection mass；ΩzFor gyro input angular velocity；For electrostatic drive power； x*It is acceleration of the MEMS gyroscope detection mass along drive shaft, speed and displacement respectively；y*It is detection respectively Acceleration of the mass along detection axle, speed and displacement；dxx, dyyIt is damped coefficient；kxx, kyyIt is stiffness coefficient；dxyIt is damping The coefficient of coup, kxyIt is stiffness coupling coefficient.
To improve the Analysis on Mechanism degree of accuracy, nondimensionalization processing is carried out to MEMS gyro kinetic model.Take nondimensionalization Time t*=ωoT, then formula (1) both sides simultaneously divided by reference frequency squareReference length q0With detection mass matter M is measured, the nondimensionalization model that can obtain MEMS gyro is
Wherein,
Redefining relevant system parameters is
Then the nondimensionalization model of MEMS gyro can abbreviation be
Make A=2S-D, B=Ω2- K, parameter fluctuation caused by considering environmental factor and non-modeling factors and outside are dry Disturb, then formula (4) is represented by
The model is by state variable q=[x y]TWith control input u=[ux uy]TComposition.Wherein, wherein, x, y are respectively Mass is detected after nondimensionalization along drive shaft and the moving displacement of detection axle；ux uyRepresent that nondimensionalization is after-applied respectively driving The power of moving axis and detection axle；A, B, C are the parameters of model, and its value is relevant with the structural parameters and dynamics of gyroscope；P The unknown dynamics for not knowing to bring for model parameter, andΔ A, Δ B be environmental factor and do not model because Unknown parameter fluctuation caused by element；D (t) is external disturbance.
According to the oscillatory type silicon micromechanical gyro of certain model, it is m=0.57 × 10 to choose each parameter of gyro-7Kg, q0= [10-6 10-6]TM, ω0=1kHz, Ωz=5.0rad/s, kxx=80.98N/m, kyy=71.62N/m, kxy=0.05N/m, dxx =0.429 × 10-6Ns/m, dyy=0.0429 × 10-6Ns/m, dxy=0.0429 × 10-6Ns/m, then it can be calculatedChoose external disturbance
(b) the uncertain unknown dynamics brought of fuzzy logic dynamic estimation model parameter is utilized.
Construct fuzzy logic systemApproachThe fuzzy logic system is retouched by M bar IF-THEN sentences State, wherein the i-th rule has following form：
Using the average defuzzifier in product inference machine, monodrome fuzzy device and center, the output of fuzzy system is
Wherein, XinIt is the input vector of fuzzy logic system, and For the weights of fuzzy logic Matrix；θ(Xin) it is M=44The fuzzy base vector of=256 dimensions, its i-th of element are
Wherein,It is respectivelyxi, yiTo domain A1i, A2i, A3i, A4iDegree of membership, WithExemplified by, membership function may be designed as following Gaussian function：
Wherein,σiIt is center and the standard deviation of the Gaussian function respectively.xmi, ymiRespectively [- 20 20], [- 0.24 0.24], [- 10 10], any value between [- 0.12 0.12], σi=1.
Define optimal estimation parameter w*For
Wherein, ψ is w set.
Therefore, the indeterminate of kinetic model is represented by
Wherein, ε is the approximate error of fuzzy system.
And the evaluated error of indeterminate is
Wherein,And
(c) design interference observer is estimated and compensates external disturbance.
Designing interference observer is
Wherein,For external disturbance d (t) estimate；L is positive definite matrix, and value isZ is middle anaplasia Amount.
Define interference observer evaluated error be
Therefore have
(d) sliding formwork control is introduced, realizes unknown dynamic (dynamical) feedforward compensation, and provide the Hybrid Learning of neural network weight Rule.
The dynamics reference model for establishing MEMS gyro is
Wherein,qdTo refer to vibration displacement signal,For qdTwo Order derivative；Ax, AyMass is respectively detected along drive shaft and the reference amplitude of detection shaft vibration, and Ax=10 μm, Ay=0.12 μm；ωx, ωyMass is respectively detected along drive shaft and the reference angular frequency of detection shaft vibration, and ωx=2000rad/s, ωy=2000rad/s.
Building tracking error is
E=q-qd (15)
Define sliding-mode surface
Wherein,β meets Hurwitz conditions, and value isThen
Sliding mode controller may be designed as
Wherein, K0For positive definite matrix, value is
Controller formula (18) is substituted into formula (17), had
Definition And define new signal
Define modeling errorTo predict error.In order that closed-loop system ensure s andConvergence, consider pre- Survey error and sliding formwork function, the Hybrid Learning more new law of fuzzy logic weight matrix may be designed as
Wherein, λ,For positive definite matrix, value is
(e) according to obtained interference observer (12), controller formula (18) and Hybrid Learning weight more new law formula (21), return The kinetic simulation pattern (5) of MEMS gyro is returned to, the vibration displacement of mass is detected to gyro and speed is tracked control.
Unspecified part of the present invention belongs to art personnel's common knowledge.

Claims (1)

1. a kind of MEMS gyroscope Hybrid Learning control method based on interference observer, it is characterised in that comprise the following steps：
(a) kinetic model of the MEMS gyroscope of consideration quadrature error is：
<mrow> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msubsup> <mi>f</mi> <mi>x</mi> <mo>*</mo> </msubsup> </mtd> </mtr> <mtr> <mtd> <msubsup> <mi>f</mi> <mi>y</mi> <mo>*</mo> </msubsup> </mtd> </mtr> </mtable> </mfenced> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mi>m</mi> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mi>m</mi> </mtd> </mtr> </mtable> </mfenced> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msup> <mover> <mi>x</mi> <mo>&amp;CenterDot;&amp;CenterDot;</mo> </mover> <mo>*</mo> </msup> </mtd> </mtr> <mtr> <mtd> <msup> <mover> <mi>y</mi> <mo>&amp;CenterDot;&amp;CenterDot;</mo> </mover> <mo>*</mo> </msup> </mtd> </mtr> </mtable> </mfenced> <mo>+</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msub> <mi>d</mi> <mrow> <mi>x</mi> <mi>x</mi> </mrow> </msub> </mtd> <mtd> <mrow> <msub> <mi>d</mi> <mrow> <mi>x</mi> <mi>y</mi> </mrow> </msub> <mo>-</mo> <mn>2</mn> <msub> <mi>m&amp;Omega;</mi> <mi>z</mi> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>d</mi> <mrow> <mi>x</mi> <mi>y</mi> </mrow> </msub> <mo>+</mo> <mn>2</mn> <msub> <mi>m&amp;Omega;</mi> <mi>z</mi> </msub> </mrow> </mtd> <mtd> <msub> <mi>d</mi> <mrow> <mi>y</mi> <mi>y</mi> </mrow> </msub> </mtd> </mtr> </mtable> </mfenced> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msup> <mover> <mi>x</mi> <mo>&amp;CenterDot;</mo> </mover> <mo>*</mo> </msup> </mtd> </mtr> <mtr> <mtd> <msup> <mover> <mi>y</mi> <mo>&amp;CenterDot;</mo> </mover> <mo>*</mo> </msup> </mtd> </mtr> </mtable> </mfenced> <mo>+</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <msub> <mi>k</mi> <mrow> <mi>x</mi> <mi>x</mi> </mrow> </msub> <mo>-</mo> <msubsup> <mi>m&amp;Omega;</mi> <mi>z</mi> <mn>2</mn> </msubsup> </mrow> </mtd> <mtd> <msub> <mi>k</mi> <mrow> <mi>x</mi> <mi>y</mi> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>k</mi> <mrow> <mi>x</mi> <mi>y</mi> </mrow> </msub> </mtd> <mtd> <mrow> <msub> <mi>k</mi> <mrow> <mi>y</mi> <mi>y</mi> </mrow> </msub> <mo>-</mo> <msubsup> <mi>m&amp;Omega;</mi> <mi>z</mi> <mn>2</mn> </msubsup> </mrow> </mtd> </mtr> </mtable> </mfenced> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msup> <mi>x</mi> <mo>*</mo> </msup> </mtd> </mtr> <mtr> <mtd> <msup> <mi>y</mi> <mo>*</mo> </msup> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow>
Wherein, m is the quality of detection mass；ΩzFor gyro input angular velocity；For electrostatic drive power； x* It is acceleration of the MEMS gyroscope detection mass along drive shaft, speed and displacement respectively；y*It is detection quality respectively Acceleration of the block along detection axle, speed and displacement；dxx, dyyIt is damped coefficient；kxx, kyyIt is stiffness coefficient；dxyIt is damping couple Coefficient, kxyIt is stiffness coupling coefficient；
To improve the Analysis on Mechanism degree of accuracy, nondimensionalization processing is carried out to MEMS gyro kinetic model；Take nondimensionalization time t* =ωoT, then formula (1) both sides simultaneously divided by reference frequency squareReference length q0With detection mass quality m, obtain Nondimensionalization model to MEMS gyro is
<mrow> <mfrac> <msup> <mover> <mi>q</mi> <mo>&amp;CenterDot;&amp;CenterDot;</mo> </mover> <mo>*</mo> </msup> <msub> <mi>q</mi> <mn>0</mn> </msub> </mfrac> <mo>+</mo> <mfrac> <msup> <mi>D</mi> <mo>*</mo> </msup> <mrow> <msub> <mi>m&amp;omega;</mi> <mn>0</mn> </msub> </mrow> </mfrac> <mfrac> <msup> <mover> <mi>q</mi> <mo>&amp;CenterDot;</mo> </mover> <mo>*</mo> </msup> <msub> <mi>q</mi> <mn>0</mn> </msub> </mfrac> <mo>+</mo> <mn>2</mn> <mfrac> <msup> <mi>S</mi> <mo>*</mo> </msup> <msub> <mi>&amp;omega;</mi> <mn>0</mn> </msub> </mfrac> <mfrac> <msup> <mover> <mi>q</mi> <mo>&amp;CenterDot;</mo> </mover> <mo>*</mo> </msup> <msub> <mi>q</mi> <mn>0</mn> </msub> </mfrac> <mo>-</mo> <mfrac> <msup> <mi>&amp;Omega;</mi> <mn>2</mn> </msup> <msubsup> <mi>&amp;omega;</mi> <mn>0</mn> <mn>2</mn> </msubsup> </mfrac> <mfrac> <msup> <mi>q</mi> <mo>*</mo> </msup> <msub> <mi>q</mi> <mn>0</mn> </msub> </mfrac> <mo>+</mo> <mfrac> <msup> <mi>K</mi> <mo>*</mo> </msup> <mrow> <msubsup> <mi>m&amp;omega;</mi> <mn>0</mn> <mn>2</mn> </msubsup> </mrow> </mfrac> <mfrac> <msup> <mi>q</mi> <mo>*</mo> </msup> <msub> <mi>q</mi> <mn>0</mn> </msub> </mfrac> <mo>=</mo> <mfrac> <msup> <mi>f</mi> <mo>*</mo> </msup> <mrow> <msubsup> <mi>m&amp;omega;</mi> <mn>0</mn> <mn>2</mn> </msubsup> <msub> <mi>q</mi> <mn>0</mn> </msub> </mrow> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> </mrow>
Wherein,
Redefining relevant system parameters is
<mrow> <mi>q</mi> <mo>=</mo> <mfrac> <msup> <mi>q</mi> <mo>*</mo> </msup> <msub> <mi>q</mi> <mn>0</mn> </msub> </mfrac> <mo>,</mo> <mi>f</mi> <mo>=</mo> <mfrac> <msup> <mi>f</mi> <mo>*</mo> </msup> <mrow> <msubsup> <mi>m&amp;omega;</mi> <mn>0</mn> <mn>2</mn> </msubsup> <msub> <mi>q</mi> <mn>0</mn> </msub> </mrow> </mfrac> <mo>,</mo> <mi>&amp;Omega;</mi> <mo>=</mo> <mfrac> <msub> <mi>&amp;Omega;</mi> <mi>z</mi> </msub> <msub> <mi>&amp;omega;</mi> <mn>0</mn> </msub> </mfrac> <mo>,</mo> <mi>D</mi> <mo>=</mo> <mfrac> <msup> <mi>D</mi> <mo>*</mo> </msup> <mrow> <msub> <mi>m&amp;omega;</mi> <mn>0</mn> </msub> </mrow> </mfrac> <mo>,</mo> <mi>K</mi> <mo>=</mo> <mfrac> <msup> <mi>K</mi> <mo>*</mo> </msup> <mrow> <msubsup> <mi>m&amp;omega;</mi> <mn>0</mn> <mn>2</mn> </msubsup> </mrow> </mfrac> <mo>,</mo> <mi>S</mi> <mo>=</mo> <mo>-</mo> <mfrac> <msup> <mi>S</mi> <mo>*</mo> </msup> <msub> <mi>&amp;omega;</mi> <mn>0</mn> </msub> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>3</mn> <mo>)</mo> </mrow> </mrow>
Then the nondimensionalization model abbreviation of MEMS gyro is
<mrow> <mover> <mi>q</mi> <mo>&amp;CenterDot;&amp;CenterDot;</mo> </mover> <mo>=</mo> <mrow> <mo>(</mo> <mn>2</mn> <mi>S</mi> <mo>-</mo> <mi>D</mi> <mo>)</mo> </mrow> <mover> <mi>q</mi> <mo>&amp;CenterDot;</mo> </mover> <mo>+</mo> <mrow> <mo>(</mo> <msup> <mi>&amp;Omega;</mi> <mn>2</mn> </msup> <mo>-</mo> <mi>K</mi> <mo>)</mo> </mrow> <mi>q</mi> <mo>+</mo> <mi>f</mi> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>4</mn> <mo>)</mo> </mrow> </mrow>
Make A=2S-D, B=Ω2- K, consider parameter fluctuation and external disturbance caused by environmental factor and non-modeling factors, then formula (4) it is expressed as
<mrow> <mover> <mi>q</mi> <mo>&amp;CenterDot;&amp;CenterDot;</mo> </mover> <mo>=</mo> <mi>A</mi> <mover> <mi>q</mi> <mo>&amp;CenterDot;</mo> </mover> <mo>+</mo> <mi>B</mi> <mi>q</mi> <mo>+</mo> <mi>C</mi> <mi>u</mi> <mo>+</mo> <mi>P</mi> <mo>+</mo> <mi>d</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>5</mn> <mo>)</mo> </mrow> </mrow>
The model is by state variable q=[x y]TWith control input u=[ux uy]TComposition；Wherein, after x, y are respectively nondimensionalization Mass is detected along drive shaft and the moving displacement of detection axle；ux, uyRepresent that nondimensionalization is after-applied in drive shaft and detection respectively The power of axle；A, B, C are the parameters of model, and its value is relevant with the structural parameters and dynamics of gyroscope；P is model parameter The uncertain unknown dynamics brought, andΔ A, Δ B be caused by environmental factor and non-modeling factors not The parameter fluctuation known；D (t) is external disturbance；
(b) fuzzy logic system is constructedApproachThe fuzzy logic system is retouched by M bar IF-THEN sentences State, wherein the i-th rule has following form：
<mrow> <mi>R</mi> <mi>u</mi> <mi>l</mi> <mi>e</mi> <mi> </mi> <mi>i</mi> <mo>:</mo> <mi>I</mi> <mi>F</mi> <mi> </mi> <msub> <mover> <mi>x</mi> <mo>&amp;CenterDot;</mo> </mover> <mi>i</mi> </msub> <mi>i</mi> <mi>s</mi> <mi> </mi> <msub> <mi>A</mi> <mrow> <mn>1</mn> <mi>i</mi> </mrow> </msub> <mi>a</mi> <mi>n</mi> <mi>d</mi> <mi> </mi> <msub> <mover> <mi>y</mi> <mo>&amp;CenterDot;</mo> </mover> <mi>i</mi> </msub> <mi>i</mi> <mi>s</mi> <mi> </mi> <msub> <mi>A</mi> <mrow> <mn>2</mn> <mi>i</mi> </mrow> </msub> <mi>a</mi> <mi>n</mi> <mi>d</mi> <mi> </mi> <msub> <mi>x</mi> <mi>i</mi> </msub> <mi>i</mi> <mi>s</mi> <mi> </mi> <msub> <mi>A</mi> <mrow> <mn>3</mn> <mi>i</mi> </mrow> </msub> <mi>a</mi> <mi>n</mi> <mi>d</mi> <mi> </mi> <msub> <mi>y</mi> <mi>i</mi> </msub> <mi>i</mi> <mi>s</mi> <mi> </mi> <msub> <mi>A</mi> <mrow> <mn>4</mn> <mi>i</mi> </mrow> </msub> </mrow>
<mrow> <mi>T</mi> <mi>H</mi> <mi>E</mi> <mi>N</mi> <mi> </mi> <mover> <mi>P</mi> <mo>^</mo> </mover> <msub> <mrow> <mo>(</mo> <msub> <mi>X</mi> <mrow> <mi>i</mi> <mi>n</mi> </mrow> </msub> <mo>|</mo> <mi>&amp;theta;</mi> <mo>)</mo> </mrow> <mi>i</mi> </msub> <mi>i</mi> <mi>s</mi> <mi> </mi> <msub> <mi>B</mi> <mi>i</mi> </msub> <mo>,</mo> <mi>i</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mn>...</mn> <mo>,</mo> <mi>M</mi> </mrow>
Using the average defuzzifier in product inference machine, monodrome fuzzy device and center, the output of fuzzy system is
<mrow> <mover> <mi>P</mi> <mo>^</mo> </mover> <mrow> <mo>(</mo> <msub> <mi>X</mi> <mrow> <mi>i</mi> <mi>n</mi> </mrow> </msub> <mo>|</mo> <mi>&amp;theta;</mi> <mo>)</mo> </mrow> <mo>=</mo> <msup> <mover> <mi>w</mi> <mo>^</mo> </mover> <mi>T</mi> </msup> <mi>&amp;theta;</mi> <mrow> <mo>(</mo> <msub> <mi>X</mi> <mrow> <mi>i</mi> <mi>n</mi> </mrow> </msub> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>6</mn> <mo>)</mo> </mrow> </mrow>
Wherein, XinIt is the input vector of fuzzy logic system, and For the weights square of fuzzy logic Battle array；θ(Xin) it is the fuzzy base vector of M dimensions；I-th of element of fuzzy base vector be
<mrow> <msub> <mi>&amp;theta;</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>X</mi> <mrow> <mi>i</mi> <mi>n</mi> </mrow> </msub> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mrow> <msub> <mi>&amp;mu;</mi> <msub> <mi>A</mi> <mrow> <mn>1</mn> <mi>i</mi> </mrow> </msub> </msub> <mrow> <mo>(</mo> <msub> <mover> <mi>x</mi> <mo>&amp;CenterDot;</mo> </mover> <mi>i</mi> </msub> <mo>)</mo> </mrow> <msub> <mi>&amp;mu;</mi> <msub> <mi>A</mi> <mrow> <mn>2</mn> <mi>i</mi> </mrow> </msub> </msub> <mrow> <mo>(</mo> <msub> <mover> <mi>y</mi> <mo>&amp;CenterDot;</mo> </mover> <mi>i</mi> </msub> <mo>)</mo> </mrow> <msub> <mi>&amp;mu;</mi> <msub> <mi>A</mi> <mrow> <mn>3</mn> <mi>i</mi> </mrow> </msub> </msub> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <msub> <mi>&amp;mu;</mi> <msub> <mi>A</mi> <mrow> <mn>4</mn> <mi>i</mi> </mrow> </msub> </msub> <mrow> <mo>(</mo> <msub> <mi>y</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> </mrow> <mrow> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>M</mi> </munderover> <msub> <mi>&amp;mu;</mi> <msub> <mi>A</mi> <mrow> <mn>1</mn> <mi>i</mi> </mrow> </msub> </msub> <mrow> <mo>(</mo> <msub> <mover> <mi>x</mi> <mo>&amp;CenterDot;</mo> </mover> <mi>i</mi> </msub> <mo>)</mo> </mrow> <msub> <mi>&amp;mu;</mi> <msub> <mi>A</mi> <mrow> <mn>2</mn> <mi>i</mi> </mrow> </msub> </msub> <mrow> <mo>(</mo> <msub> <mover> <mi>y</mi> <mo>&amp;CenterDot;</mo> </mover> <mi>i</mi> </msub> <mo>)</mo> </mrow> <msub> <mi>&amp;mu;</mi> <msub> <mi>A</mi> <mrow> <mn>3</mn> <mi>i</mi> </mrow> </msub> </msub> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <msub> <mi>&amp;mu;</mi> <msub> <mi>A</mi> <mrow> <mn>4</mn> <mi>i</mi> </mrow> </msub> </msub> <mrow> <mo>(</mo> <msub> <mi>y</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> </mrow> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>7</mn> <mo>)</mo> </mrow> </mrow>
Wherein,It is respectivelyxi, yiTo domain A1i, A2i, A3i, A4iDegree of membership,'s Membership function is designed as following Gaussian function：
<mrow> <msub> <mi>&amp;mu;</mi> <msub> <mi>A</mi> <mrow> <mn>1</mn> <mi>i</mi> </mrow> </msub> </msub> <mo>=</mo> <msup> <mi>e</mi> <mrow> <mo>-</mo> <mfrac> <msup> <mrow> <mo>(</mo> <msub> <mover> <mi>x</mi> <mo>&amp;CenterDot;</mo> </mover> <mi>i</mi> </msub> <mo>-</mo> <msub> <mover> <mi>x</mi> <mo>&amp;CenterDot;</mo> </mover> <mrow> <mi>m</mi> <mi>i</mi> </mrow> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mrow> <mn>2</mn> <msup> <msub> <mi>&amp;sigma;</mi> <mi>i</mi> </msub> <mn>2</mn> </msup> </mrow> </mfrac> </mrow> </msup> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>8</mn> <mo>)</mo> </mrow> </mrow>
Wherein,σiIt is center and the standard deviation of the Gaussian function respectively；
Define optimal estimation parameter w*For
<mrow> <munder> <msup> <mi>w</mi> <mo>*</mo> </msup> <mrow> <mi>w</mi> <mo>&amp;Element;</mo> <mi>&amp;psi;</mi> </mrow> </munder> <mo>=</mo> <munder> <mrow> <mi>arg</mi> <mi>min</mi> </mrow> <mrow> <mover> <mi>q</mi> <mo>&amp;CenterDot;</mo> </mover> <mo>,</mo> <mi>q</mi> <mo>&amp;Element;</mo> <msup> <mi>R</mi> <mrow> <mn>2</mn> <mo>&amp;times;</mo> <mn>2</mn> </mrow> </msup> </mrow> </munder> <mo>&amp;lsqb;</mo> <mi>sup</mi> <mo>|</mo> <mover> <mi>P</mi> <mo>^</mo> </mover> <mrow> <mo>(</mo> <msub> <mi>X</mi> <mrow> <mi>i</mi> <mi>n</mi> </mrow> </msub> <mo>|</mo> <mi>&amp;theta;</mi> <mo>)</mo> </mrow> <mo>-</mo> <mi>P</mi> <mrow> <mo>(</mo> <mover> <mi>q</mi> <mo>&amp;CenterDot;</mo> </mover> <mo>,</mo> <mi>q</mi> <mo>)</mo> </mrow> <mo>|</mo> <mo>&amp;rsqb;</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>9</mn> <mo>)</mo> </mrow> </mrow>
Wherein, ψ is w set；
Therefore, the indeterminate of kinetic model is expressed as
<mrow> <mi>P</mi> <mrow> <mo>(</mo> <mover> <mi>q</mi> <mo>&amp;CenterDot;</mo> </mover> <mo>,</mo> <mi>q</mi> <mo>)</mo> </mrow> <mo>=</mo> <msup> <mi>w</mi> <mrow> <mo>*</mo> <mi>T</mi> </mrow> </msup> <mi>&amp;theta;</mi> <mo>+</mo> <mi>&amp;epsiv;</mi> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>10</mn> <mo>)</mo> </mrow> </mrow>
Wherein, ε is the approximate error of fuzzy system；
And the evaluated error of indeterminate is
<mrow> <mover> <mi>P</mi> <mo>~</mo> </mover> <mo>=</mo> <mi>P</mi> <mrow> <mo>(</mo> <mover> <mi>q</mi> <mo>&amp;CenterDot;</mo> </mover> <mo>,</mo> <mi>q</mi> <mo>)</mo> </mrow> <mo>-</mo> <mi>P</mi> <mrow> <mo>(</mo> <msub> <mi>X</mi> <mrow> <mi>i</mi> <mi>n</mi> </mrow> </msub> <mo>|</mo> <mi>&amp;theta;</mi> <mo>)</mo> </mrow> <mo>=</mo> <msup> <mi>w</mi> <mrow> <mo>*</mo> <mi>T</mi> </mrow> </msup> <mi>&amp;theta;</mi> <mo>+</mo> <mi>&amp;epsiv;</mi> <mo>-</mo> <msup> <mover> <mi>w</mi> <mo>^</mo> </mover> <mi>T</mi> </msup> <mi>&amp;theta;</mi> <mo>=</mo> <msup> <mover> <mi>w</mi> <mo>~</mo> </mover> <mi>T</mi> </msup> <mi>&amp;theta;</mi> <mo>+</mo> <mi>&amp;epsiv;</mi> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>11</mn> <mo>)</mo> </mrow> </mrow>
Wherein,And
(c) design interference observer is
<mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <mover> <mi>d</mi> <mo>^</mo> </mover> <mo>=</mo> <mi>L</mi> <mrow> <mo>(</mo> <mi>z</mi> <mo>-</mo> <mover> <mi>q</mi> <mo>&amp;CenterDot;</mo> </mover> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mover> <mi>z</mi> <mo>&amp;CenterDot;</mo> </mover> <mo>=</mo> <mi>A</mi> <mover> <mi>q</mi> <mo>&amp;CenterDot;</mo> </mover> <mo>+</mo> <mi>B</mi> <mi>q</mi> <mo>+</mo> <mi>C</mi> <mi>u</mi> <mo>+</mo> <msup> <mover> <mi>w</mi> <mo>^</mo> </mover> <mi>T</mi> </msup> <mi>&amp;theta;</mi> <mo>+</mo> <mover> <mi>d</mi> <mo>^</mo> </mover> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>12</mn> <mo>)</mo> </mrow> </mrow>
Wherein,For external disturbance d (t) estimate；L is positive definite matrix；Z is intermediate variable；
Define interference observer evaluated error be
<mrow> <mover> <mi>d</mi> <mo>~</mo> </mover> <mo>=</mo> <mi>d</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>-</mo> <mover> <mi>d</mi> <mo>^</mo> </mover> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>13</mn> <mo>)</mo> </mrow> </mrow>
Therefore have
(d) the dynamics reference model for establishing MEMS gyro is
<mrow> <msub> <mover> <mi>q</mi> <mo>&amp;CenterDot;&amp;CenterDot;</mo> </mover> <mi>d</mi> </msub> <mo>=</mo> <msub> <mi>A</mi> <mi>d</mi> </msub> <msub> <mi>q</mi> <mi>d</mi> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>14</mn> <mo>)</mo> </mrow> </mrow>
Wherein,qdTo refer to vibration displacement signal,For qdSecond order lead Number；Ax, AyMass is respectively detected along drive shaft and the reference amplitude of detection shaft vibration；ωx, ωyRespectively detect mass Along drive shaft and the reference angular frequency of detection shaft vibration；
Building tracking error is
E=q-qd (15)
Define sliding-mode surface
<mrow> <mi>s</mi> <mo>=</mo> <mover> <mi>e</mi> <mo>&amp;CenterDot;</mo> </mover> <mo>+</mo> <mi>&amp;beta;</mi> <mi>e</mi> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>16</mn> <mo>)</mo> </mrow> </mrow>
Wherein,β meets Hurwitz conditions；Then
<mrow> <mover> <mi>s</mi> <mo>&amp;CenterDot;</mo> </mover> <mo>=</mo> <mover> <mi>e</mi> <mo>&amp;CenterDot;&amp;CenterDot;</mo> </mover> <mo>+</mo> <mi>&amp;beta;</mi> <mover> <mi>e</mi> <mo>&amp;CenterDot;</mo> </mover> <mo>=</mo> <mi>A</mi> <mover> <mi>q</mi> <mo>&amp;CenterDot;</mo> </mover> <mo>+</mo> <mi>B</mi> <mi>q</mi> <mo>+</mo> <mi>C</mi> <mi>u</mi> <mo>+</mo> <mi>P</mi> <mo>+</mo> <mi>d</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>-</mo> <msub> <mover> <mi>q</mi> <mo>&amp;CenterDot;&amp;CenterDot;</mo> </mover> <mi>d</mi> </msub> <mo>+</mo> <mi>&amp;beta;</mi> <mover> <mi>e</mi> <mo>&amp;CenterDot;</mo> </mover> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>17</mn> <mo>)</mo> </mrow> </mrow>
Sliding mode controller design is
<mrow> <mi>u</mi> <mo>=</mo> <mo>-</mo> <msup> <mi>C</mi> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <mo>&amp;lsqb;</mo> <mi>A</mi> <mover> <mi>q</mi> <mo>&amp;CenterDot;</mo> </mover> <mo>+</mo> <mi>B</mi> <mi>q</mi> <mo>+</mo> <msup> <mover> <mi>w</mi> <mo>^</mo> </mover> <mi>T</mi> </msup> <mi>&amp;theta;</mi> <mo>+</mo> <mover> <mi>d</mi> <mo>^</mo> </mover> <mo>-</mo> <msub> <mover> <mi>q</mi> <mo>&amp;CenterDot;&amp;CenterDot;</mo> </mover> <mi>d</mi> </msub> <mo>+</mo> <mi>&amp;beta;</mi> <mover> <mi>e</mi> <mo>&amp;CenterDot;</mo> </mover> <mo>+</mo> <msub> <mi>K</mi> <mn>0</mn> </msub> <mi>s</mi> <mo>&amp;rsqb;</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>18</mn> <mo>)</mo> </mrow> </mrow>
Wherein, K0For positive definite matrix；
Sliding mode controller formula (18) is substituted into formula (17), had
<mrow> <mtable> <mtr> <mtd> <mrow> <mover> <mi>s</mi> <mo>&amp;CenterDot;</mo> </mover> <mo>=</mo> <mi>A</mi> <mover> <mi>q</mi> <mo>&amp;CenterDot;</mo> </mover> <mo>+</mo> <mi>B</mi> <mi>q</mi> <mo>-</mo> <mo>&amp;lsqb;</mo> <mi>A</mi> <mover> <mi>q</mi> <mo>&amp;CenterDot;</mo> </mover> <mo>+</mo> <mi>B</mi> <mi>q</mi> <mo>+</mo> <msup> <mover> <mi>w</mi> <mo>^</mo> </mover> <mi>T</mi> </msup> <mi>&amp;theta;</mi> <mo>+</mo> <mover> <mi>d</mi> <mo>^</mo> </mover> <mo>-</mo> <msub> <mover> <mi>q</mi> <mo>&amp;CenterDot;&amp;CenterDot;</mo> </mover> <mi>d</mi> </msub> <mo>+</mo> <mi>&amp;beta;</mi> <mover> <mi>e</mi> <mo>&amp;CenterDot;</mo> </mover> <mo>+</mo> <msub> <mi>K</mi> <mn>0</mn> </msub> <mi>s</mi> <mo>&amp;rsqb;</mo> <mo>+</mo> <mi>P</mi> <mo>+</mo> <mi>d</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>-</mo> <msub> <mover> <mi>q</mi> <mo>&amp;CenterDot;&amp;CenterDot;</mo> </mover> <mi>d</mi> </msub> <mo>+</mo> <mi>&amp;beta;</mi> <mover> <mi>e</mi> <mo>&amp;CenterDot;</mo> </mover> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>=</mo> <msup> <mover> <mi>w</mi> <mo>~</mo> </mover> <mi>T</mi> </msup> <mi>&amp;theta;</mi> <mo>+</mo> <mover> <mi>d</mi> <mo>~</mo> </mover> <mo>+</mo> <mi>&amp;epsiv;</mi> <mo>-</mo> <msub> <mi>K</mi> <mn>0</mn> </msub> <mi>s</mi> </mrow> </mtd> </mtr> </mtable> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>19</mn> <mo>)</mo> </mrow> </mrow>
DefinitionAnd define new signal
<mrow> <mtable> <mtr> <mtd> <mrow> <msub> <mi>C</mi> <mi>q</mi> </msub> <mo>=</mo> <msubsup> <mo>&amp;Integral;</mo> <mrow> <mi>t</mi> <mo>-</mo> <msub> <mi>&amp;tau;</mi> <mi>d</mi> </msub> </mrow> <mi>t</mi> </msubsup> <msub> <mi>C</mi> <msub> <mi>q</mi> <mn>0</mn> </msub> </msub> <mi>d</mi> <mi>&amp;tau;</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>=</mo> <msubsup> <mo>&amp;Integral;</mo> <mrow> <mi>t</mi> <mo>-</mo> <msub> <mi>&amp;tau;</mi> <mi>d</mi> </msub> </mrow> <mi>t</mi> </msubsup> <mrow> <mo>(</mo> <mover> <mi>s</mi> <mo>&amp;CenterDot;</mo> </mover> <mo>+</mo> <msup> <mover> <mi>w</mi> <mo>^</mo> </mover> <mi>T</mi> </msup> <mi>&amp;theta;</mi> <mo>+</mo> <mover> <mi>d</mi> <mo>^</mo> </mover> <mo>+</mo> <msub> <mi>K</mi> <mn>0</mn> </msub> <mi>s</mi> <mo>)</mo> </mrow> <mi>d</mi> <mi>&amp;tau;</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>=</mo> <mi>s</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>-</mo> <mi>s</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>-</mo> <msub> <mi>t</mi> <mi>d</mi> </msub> <mo>)</mo> </mrow> <mo>+</mo> <msubsup> <mo>&amp;Integral;</mo> <mrow> <mi>t</mi> <mo>-</mo> <msub> <mi>&amp;tau;</mi> <mi>d</mi> </msub> </mrow> <mi>t</mi> </msubsup> <mrow> <mo>(</mo> <msup> <mover> <mi>w</mi> <mo>^</mo> </mover> <mi>T</mi> </msup> <mi>&amp;theta;</mi> <mo>+</mo> <mover> <mi>d</mi> <mo>^</mo> </mover> <mo>+</mo> <msub> <mi>K</mi> <mn>0</mn> </msub> <mi>s</mi> <mo>)</mo> </mrow> <mi>d</mi> <mi>&amp;tau;</mi> </mrow> </mtd> </mtr> </mtable> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>20</mn> <mo>)</mo> </mrow> </mrow>
Define modeling errorTo predict error；In order that closed-loop system ensure s andConvergence, consider prediction miss Difference and sliding formwork function, the Hybrid Learning more new law of fuzzy logic weight matrix are designed as
Wherein, λ,For positive definite matrix；
(e) according to obtained interference observer (12), sliding mode controller formula (18) and Hybrid Learning weight more new law formula (21), return The kinetic simulation pattern (5) of MEMS gyro is returned to, the vibration displacement of mass is detected to gyro and speed is tracked control.
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