CN108227504A - Microthrust test fractional order adaptive fuzzy nerve inverting TSM control method - Google Patents
Microthrust test fractional order adaptive fuzzy nerve inverting TSM control method Download PDFInfo
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Abstract
The invention discloses a kind of microthrust test fractional order adaptive fuzzy nerve inverting TSM control method, including：Establish the dimensionless kinetics equation mathematical model of microthrust test system and reference locus model；Build the inverting TSM control device based on fractional order.The present invention can realize the target of microthrust test real-time tracking, make error in Finite-time convergence to zero, and enhance the robustness of system, and good performance is still maintained in the case where there is external interference；Fractional order adaptive law is designed according to fractional order terminal sliding mode face, a kind of Adaptive Identification method, every unknown system parameter of online real-time estimation microthrust test, compared with integer rank are designed based on Lyapunov stability criterias, more adjustable items, improve control effect and parameter Estimation effect.
Description
Technical field
The present invention relates to microthrust test control technology field, the fractional order adaptive fuzzy nerve of specifically a kind of microthrust test is anti-
Drill TSM control method.
Background technology
Microthrust test is the sensor for measuring inertial navigation and inertial guidance system angular speed, because it is in any environment all
Can independent navigation, so just having got more and more people's extensive concerning since appearance, in fields such as space flight, navigation, aviation and military affairs
Universal application is obtained.But be affected by temperature in production and manufacturing process there are error and easily, element characteristic is caused with setting
Difference between meter, so as to cause the reduced performance of microthrust test.In addition, microthrust test belongs to multi-input multi-output system and system
Parameter exists uncertain and is easily influenced by external environment so that gyro tracking effect is unsatisfactory.Traditional sliding formwork control
The design of sliding-mode surface is all the rank using the linear combination, wherein differential or integration of the ratio of error, differential or integration in method
Number is all integer, and the tracking effect of microthrust test is poor, and systematic parameter and Attitude rate estimator effect are also poor, easily cause and tremble
It shakes.
In the fractional order adaptive fuzzy nerve inverting TSM control method of the present invention, Based Inverse Design Method is will be multiple
Miscellaneous nonlinear system resolves into the subsystem no more than systematic education, then separately designs Liapunov for each subsystem
Function " is retreated " always to entire subsystem, the design until completing entire control law.In the design process, using fractional order
Terminal sliding mode face is restrained according to inverting TSM control of the liapunov function design with fractional order, and terminal sliding mode ensures
The tracking error of system is in Finite-time convergence to zero.Again by adjusting fractional order exponent number, to improve the tracking performance of system.
Then, with item function is switched, that system is replaced not know is total with distracter in the inverting TSM control rule with fractional order
With, using adaptive fuzzy nerve control method by it is discontinuous switching item serialization, effectively reduce system chatter.
Lyapunov (Liapunov) function V (x, t) can freely choose, but be to fit to Li Ya as needed
The requirement (i.e. Liapunov's stability criterion) of Pu Nuofu functions, i.e. V (x, t) is positive definite, as x ≠ 0, V (x, t) ＞ 0；
As x=0, V (0, t)=0 has continuous partial derivative；The single order of V (x, t) is ledIt is negative semidefinite.
Invention content
The present invention proposes that a kind of fractional order adaptive fuzzy nerve inverting of microthrust test is whole in order to avoid above-mentioned shortcoming
Sliding-mode control is held, online real-time estimation gyro parameter matrix effectively improves control effect and parameter Estimation effect, ensures system
The tracking error of system in Finite-time convergence to zero, and effectively reduce buffet.
The present invention solves its technical problem and is achieved through the following technical solutions：
Microthrust test fractional order adaptive fuzzy nerve inverting TSM control method, includes the following steps：
(1) the dimensionless kinetics equation mathematical model of microthrust test system is established；
(2) the reference locus model of microthrust test system is built；
(3) the adaptive fuzzy nerve inverting TSM control device based on fractional order is built：It is the one of microthrust test first
A subsystem design Li Ya spectrum promise husband's functions, then design fractional order inverting TSM control rule, finally design is based on score
The adaptive fuzzy nerve inverting TSM control rule of rank.
Further, the dimensionless kinetics equation mathematical model for the microthrust test system that the step (1) is established is：
Wherein, q is the position vector after microthrust test mathematical model nondimensionalization,Expression asks single order to lead position vector q
Number,Expression seeks second dervative to position vector q；DbFor damping matrix after nondimensionalization, K is spring constant square after nondimensionalization
Battle array, Ω are angular velocity matries after nondimensionalization, and u is that the control of microthrust test system inputs, and f is systematic uncertainty and external interference
Summation, and have：
Wherein, Δ DbFor inertial matrix DbThe uncertainty of the unknown parameter of+2 Ω, Δ K are the unknown parameter of inertial matrix K
Uncertainty, d (t) is external interference, it is assumed that | fi| ＜ ρi, i=1,2, fiRepresent systematic uncertainty and external interference on axis
Summation, ρiRepresent the upper bound of systematic uncertainty and external interference summation on axis.
Further, the reference locus model of the step (2) structure microthrust test system is：
qr1=A1sin(ω1T), qr2=A2sin(ω2t) (3)
Wherein qr1Refer to the reference locus model of x-axis, qr2Refer to the reference locus model of y-axis；A1It is microthrust test in x-axis side
Upward amplitude, A2It is the amplitude of microthrust test in the y-axis direction；ω1It is the vibration frequency that microthrust test gives in the direction of the x axis,
ω2It is the vibration frequency that microthrust test gives in the y-axis direction；T is time variable.
Further, it is that a subsystem of microthrust test designs the specific of Li Ya spectrum promise husband's functions in the step (3)
Step includes：
Define vector x1,x2Respectively：
Based on back-stepping design technology, the dimensionless kinetics equation mathematical model (1) of microthrust test system is converted to as follows
Form：
Define the tracking error e between microthrust test physical location and reference locus1For：
e1=x1-qr (6)
Wherein, qrFor microthrust test system x, the reference locus of y-axis,
The first derivative of tracking error derivativeFor：
Take virtual controlling amount α1For：
Wherein, c1It is the normal number of non-zero for error coefficient；
Define tracking error function e2For：
e2=x2-α1 (9)
To with tracking error e1Microthrust test subsystem choose Li Ya spectrum promise husband's function V1For：
Wherein：e1 TFor tracking error vector e1Transposition,
To V1It is obtained along the derivation of time t：
Work as e2=0,Meet negative definiteness, it is stable to ensure system.
Further, in the step (3), fractional order inverting TSM control rule u1Design procedure includes：
It is for microthrust test design fractional order terminal sliding mode face s：
Wherein, λ1,λ2,p2,p1For arithmetic number, 1 ＜ p2/p1＜ 2, Dα-1e1It represents to e1α -1 ranks is asked to lead, D represents derivation, α
Refer to the exponent number of fractional order；
The then derivative of microthrust test fractional order terminal sliding mode face sFor：
Wherein, Dαe1It is to Dα-1e1The result of derivation；
It enables
Then
Wherein, R1*R2=I, I are unit matrix,e21,e22It is respectively
Tracking error e2Component in x-axis and y-axis direction；
To with tracking error e2Microthrust test subsystem choose Li Ya spectrums promise husband's function V2For：
Promise husband's function V is composed according to Li Ya2Design fractional order inverting TSM control rule u1For：
Wherein, ρisgn(si) represent sliding formwork switching item, for replacing systematic uncertainty and external interference summation fi, | | s |
| sliding-mode surface vector field homoemorphism value is sought in expression,When gyro system be stable.
Further, in the step (3), the adaptive fuzzy nerve inverting TSM control rule based on fractional order
U' design procedures include：
Defining evaluated error in microthrust test nondimensionalization model is respectively：
Ambiguity in definition neural network weight evaluated errorFor：
Wherein,It is microthrust test parameter matrix D respectivelyb, the estimated value of K, Ω,Respectively parameter matrix
Db, the parameter estimating error of K, Ω；wiIt is the weights of fuzzy neural network, wi *For optimal fuzzy neural network weights；
Adaptive fuzzy nerve inverting TSM control based on fractional order restrains u'：
WhereinIt is the output of fuzzy neural network, is to sliding formwork switching item gain i.e. systematic uncertainty and axis
The upper bound ρ of upper systematic uncertainty and external interference summationiEstimation；
The form of expression of fuzzy neural network output is as follows：
Wherein, φiThe referred to as normalization confidence level of fuzzy neural network；
The adaptive fuzzy nerve inverting TSM control rule u' of fractional order is controlled into input u as microthrust test system,
It brings into the mathematical model of microthrust test system, realizes the tracing control to microthrust test system；
Define third Li Ya spectrum promise husband's functions V3For：
Wherein, M=MT＞ 0, N=NT＞ 0, P=PT＞ 0 is symmetric positive definite matrix, and tr { } representing matrix asks mark to transport
It calculates, η is normal number；
In order to ensure the derivative of third Li Ya spectrum promise husband's functionsThe systematic parameter of online real-time estimation microthrust test,
Design microthrust test parameter matrix Db, the estimated value of K, ΩWith fuzzy neural network weight wiAdaptive law be respectively：
Wherein, si, i=1,2 refer to component of the sliding-mode surface in x-axis and y-axis direction, ri, i=1,2 is in formula (14)
r1,r2,For gyro system damping matrix DbEstimated value adaptive law transposition,Spring constant for gyro system
The transposition of the adaptive law of the estimated value of matrix K,The transposition of the adaptive law of estimated value for gyro angular velocity matries,It is
The adaptive law of fuzzy neural network weights；When choosing above-mentioned parameter adaptive law,Meet Lyapunov stability
Property theorem, ensure microthrust test system Global asymptotic stability.
Beneficial effects of the present invention are：
The present invention by microthrust test system decomposition into simple subsystem, then is the design of each subsystem by inversion technique
Lyapunov functions so that entire control process is clear；On the basis of back stepping control method, design terminal sliding-mode surface, really
System tracking error has been protected in Finite-time convergence to zero；Fractional order is introduced on this basis, i.e., with fractional order devious
The terminal sliding mode face of derivative, then more derivative orders that can be adjusted are several, increase adjusting degree of freedom so that control effect is
Improve；When microthrust test systematic parameter and angular speed regard known variables as, based on Lyapunov Theory of Stability, design parameter
Adaptive law, the angular speed of real-time update microthrust test and the estimated value of other systems parameter；The present invention, which has, improves gyro system
The characteristics of control performance and robustness, can realize the preferable tracking effect of microthrust test, tracking error is made to be received in finite time
It holds back to zero and reduces system chatter and pick out systematic parameter and angular speed, identification system parameter will be seen that system
Physical parameter if some parameter distance specified value is far, illustrates that internal system goes wrong, needs replacing original paper etc..
Description of the drawings
Fig. 1 is the schematic diagram of fractional order adaptive fuzzy nerve inverting TSM control system of the present invention；
Fig. 2 is the microthrust test axis tracking effect that the present invention uses adaptive fuzzy nerve inverting TSM control method
Figure；
Fig. 3 is the tracking error figure that the present invention uses adaptive fuzzy nerve inverting TSM control method；
Fig. 4 is that the present invention is bent using the two axis control input response of adaptive fuzzy nerve inverting TSM control method
Line chart.
Specific embodiment
Below by specific embodiment, the invention will be further described, and following embodiment is descriptive, is not limit
Qualitatively, it is impossible to which protection scope of the present invention is limited with this.
As shown in Figure 1, microthrust test fractional order adaptive fuzzy nerve inverting TSM control method, including following step
Suddenly：
First, the dimensionless kinetics equation mathematical model of microthrust test system is established
General Micromachined Vibrated Gyroscope is made of three parts：The supported and suspended mass block of elastic material, electrostatic drive
Dynamic device, sensing device further, be reduced to one has damped oscillation system by what mass block and spring were formed.To z-axis microthrust test
For, it is believed that mass block can only be moved by limitation in x-y plane, and cannot be moved along z-axis, only be rotated around z-axis.
Newton's law in being according to rotation considers processing and manufacturing error, then carries out nondimensionalization processing to mathematical model
And after equivalent transformation, the mathematical model of obtained microthrust test is as follows：
Wherein：Q be microthrust test mathematical model nondimensionalization after position vector, q1,q2Respectively gyro mathematics
X-axis, the position vector of y-axis after model nondimensionalization；q0To refer to displacement, Q1, Q2Respectively microthrust test
The position of x-axis, y-axis；Expression seeks first derivative to position vector q,Expression seeks second dervative to position vector q；
Control for microthrust test inputs, ux,uyThe control input of x-axis and y-axis is represented respectively；After immeasurable tempering
Damping matrix, wherein,Arrow → expression the latter is calculated by the former is
In relationship, Dxx,DyyThe respectively damped coefficient of microthrust test x-axis, y-axis, DxyFor the Coupling Damping coefficient of x-axis, y-axis, m is gyro
Quality, ω0Resonant frequency for two axis；For spring constant matrix after nondimensionalization, wherein,kxx,kyyThe respectively spring constant of microthrust test x-axis, y-axis, kxyFor x
Axis, the spring constant of y-axis coupling；For angular velocity matries after nondimensionalization, whereinΩzFor nothing
Z-axis angular speed after dimension, Ω *zFor the input angular velocity on z-axis direction, gyro is moved along x-y plane, but simultaneously
It is also rotated around z-axis, so there is z-axis angular speed；ΔDbFor inertial matrix DbThe uncertainty of the unknown parameter of+2 Ω, Δ K
The uncertainty of unknown parameter for inertial matrix K, d (t) are external interferences.
So as to which formula (1) can be rewritten as：
Wherein, f is systematic uncertainty and external interference summation, and is had：
Assuming that | fi| ＜ ρi, i=1,2, fiRepresent the summation of systematic uncertainty and external interference on axis, ρiIt represents on axis
The upper bound of systematic uncertainty and external interference summation.
2nd, the reference locus model of microthrust test system is built；
The preferable dynamic characteristic of microthrust test is a kind of noenergy loss, and x-axis, stabilization of two between centers of y-axis without Dynamic Coupling are just
String vibrates, and reference locus model is described as follows：
qr1=A1sin(ω1T), qr2=A2sin(ω2t) (4)
Wherein qr1、qr2Refer to x-axis, two axis of y-axis reference locus model；A1、A2It is microthrust test respectively in x-axis, y-axis direction
On amplitude；ω1、ω2It is the vibration frequency that microthrust test gives on x-axis, y-axis direction respectively；T is time variable.
(4) formula is converted to differential equation form is：
Wherein, qr=[qr1 qr2]TFor the reference locus of microthrust test system x-axis, y-axis,Represent the reference to x-axis, y-axis
Track qrSecond order is asked to lead, Kr=diag { ω1 2,ω2 2, diag { } represents diagonal matrix, matrix KrRepresent microthrust test in x-axis, y-axis
The diagonal matrix of the vibration frequency given on direction.
3rd, the adaptive fuzzy nerve inverting TSM control device based on fractional order is built；
In order to which application inversion technique is theoretical, the common version of microthrust test mathematical model, that is, formula (2) is converted first,
Define vector x1And x2,
Then formula (2) can be rewritten as：
Adaptive fuzzy nerve inverting TSM control device design procedure based on fractional order is as follows：
For the two subsystems of microthrust test, suitable Lyapunov functions are separately designed, ensure the stabilization of microthrust test system
Property：
3.1)：For a subsystem of microthrust test, Lyapunov functions are designed, ensure the stability of microthrust test system；
Define the tracking error e between microthrust test physical location and reference locus1For：
e1=x1-qr (8)
The then first derivative of tracking error derivativeFor：
Take virtual controlling amount α1For：
Wherein c1It is the normal number of non-zero for error coefficient.
Define tracking error function e2For：
e2=x2-α1 (11)
To with tracking error e1Microthrust test subsystem choose a Lyapunov functions V1For：
Wherein, e1 TFor tracking error vector e1Transposition.
To V1It is obtained along the derivation of time t：
Work as e2=0, then it can obtain
Meet negative Semi-qualitative, meet Liapunov's stability criterion, therefore tracking error e1Meet global progressive steady
It is fixed, asymptotic convergence to zero, it is ensured that system is stable.Therefore, further design fractional order inverting TSM control is restrained
u1, sliding-mode surface is made to go to zero.When system is stablized, sliding-mode surface function s goes to zero.
3.2) for the control law u of microthrust test design fractional order inverting TSM control device1：
To second tracking error e2It is obtained along time derivation：
It is for microthrust test design fractional order terminal sliding mode face s：
Wherein, λ1,λ2,p2,p1For arithmetic number, 1 ＜ p2/p1＜ 2, Dα-1e1Refer to e1α -1 ranks is asked to lead, this is that fractional order is special
Literary style, D represent derivation, and α refers to the exponent number of fractional order, then the derivative of microthrust test fractional order terminal sliding mode face sFor：
Wherein, Dαe1It is to Dα-1e1The result of derivation.
It enables
Then
Wherein, R1*R2=I, I are unit matrix,e21,e22It is respectively
Tracking error e2Component in x-axis, y-axis.
With reference to sliding-mode surface, to tracking error e2Microthrust test subsystem design second Lyapunov functions V2For：
To formula (20) Lyapunov functions V2Both sides derivation can obtain：
By Liapunov's stability criterion it is found that onlyIt is stable for just can guarantee microthrust test system；In order to protect
CardFor microthrust test system, the inverting TSM control rule u based on fractional order is designed1For：
Wherein, ρisgn(si) represent sliding formwork switching item, for replacing systematic uncertainty and external interference summation fi, i=
1,2, two axis components are represented, | | s | | sliding-mode surface vector field homoemorphism value is sought in expression.
Inverting TSM control based on fractional order is restrained into u1Substitute into formula (21)：
Wherein, si, i=1,2 refer to component of the sliding-mode surface in x-axis and y-axis direction, ri, in i=1,2 representation formulas (18)
r1,r2。It can prove that microthrust test system is stable according to Lyapunov stability criterias；
3.3) the control law u' of the adaptive fuzzy nerve inverting TSM control device based on fractional order is designed：
Due to D in microthrust test nondimensionalization modelb, tri- parameters of K, Ω are unknown, and in actual application,
There is uncertain and external interference, therefore backstepping control law u in system1Formula (22) cannot be applied directly.Based on adaptive reason
By knowledge, estimated value is usedInstead of three gyro parameter matrixs in (22), the adaptive of three estimates of parameters is designed
Algorithm, online real-time update estimation；Simultaneously with fuzzy neural network output come the upper of approximation system uncertainty and external interference f
Boundary.Fuzzy neural network is made of input layer, blurring layer, fuzzy reasoning layer and output layer, is approached using fuzzy neural network
The upper bound of parameter uncertainty and external interference, is described as：
Wherein, φiThe referred to as normalization confidence level of fuzzy neural network, wiIt is the weights of fuzzy neural network,It is fuzzy
The output of neural network is to sliding formwork switching item gain i.e. systematic uncertainty and external interference upper bound ρiEstimation.
The optimal output of fuzzy neural network is assumed hereinFor：
Wherein, wi *For optimal fuzzy neural network weights.
Defining evaluated error in microthrust test nondimensionalization model is respectively：
Ambiguity in definition neural network weight evaluated error is：
Wherein,It is microthrust test parameter matrix D respectivelyb, the estimated value of K, Ω,Respectively parameter matrix
Db, the parameter estimating error of K, Ω；wiIt is the weights of fuzzy neural network, wi *For optimal fuzzy neural network weights；
Inverting TSM control rule formula (22) based on fractional order can be converted to the adaptive mode based on fractional order
The neural inverting TSM control rule u' of paste：
The adaptive fuzzy nerve inverting TSM control rule u' of fractional order is controlled into input u as microthrust test system,
It brings into the mathematical model of microthrust test system, realizes the tracing control to microthrust test system.
Defining third liapunov function is：
Wherein, M=MT＞ 0, N=NT＞ 0, P=PT＞ 0 is symmetric positive definite matrix, referred to as adaptive fixed gain square
Battle array, they are adjustable parameters, can artificially be chosen；η is normal number；Tr { } representing matrix asks mark operation.
Third Lyapunov function equations both sides derivation is obtained：
Due to Db=Db T, K=KT, Ω=- ΩT,R1=R1 T, andFor mark
Amount, therefore：
It can similarly obtain：
So
To ensureDesigning adaptive law is：
For gyro system damping matrix DbEstimated value adaptive law transposition,Spring system for gyro system
The transposition of the adaptive law of the estimated value of matrix number K,The transposition of the adaptive law of estimated value for gyro angular velocity matries,It is the adaptive law of fuzzy neural network weights.
So V becomes the differential of time t：
Due toMeet Lyapunov theorem of stability, it is hereby achieved that with tracking error e1Subsystem
System has tracking error e2Subsystem, terminal sliding mode surface function s will be in Finite-time convergence to zero, so as to verify this
The itd is proposed control method of invention can realize the fractional order adaptive fuzzy nerve inverting TSM control to microthrust test, tool
There is robust effect, improve system control performance so that tracking effect more preferably can be in Finite-time convergence to zero, and reduces
It buffets, while on-line identification microthrust test systematic parameter, so as to understand the physical parameter of microthrust test system, if parameter identificationIn some estimated value apart from specified value Db, K, Ω is far, illustrates that internal system goes wrong, needs replacing original paper
Deng.
In order to more intuitively show the superior of the adaptive inverting modified fuzzy sliding mode controlling method of fractional order proposed by the present invention
Property, computer simulation experiment is carried out to control method of the present invention in MATLAB/SIMULINK.
With reference to existing literature, the parameter for choosing microthrust test is：
M=1.8 × 10-7Kg, Dxx=1.8 × 10-6N s/m, Dyy=1.8 × 10-6N s/m,
Dxy=3.6 × 10-7N s/m, kxx=63.955N/m, kyy=95.92N/m, kxy=12.779N/m.
It is assumed that unknown input angular velocity is Ωz *=100rad/s.Microthrust test parameter carries out nondimensionalization processing first, right
In oscillating micro gyroscope, for mass of foundation block along x-axis, y-axis vibration amplitude is chosen for q in sub-micron rank with reference to displacement0=1 μm
It is relatively reasonable.Because the operating frequency of microthrust test, in kHz ranges, selection intrinsic frequency is ω0=1kHz.Obtain microthrust test
Nondimensionalization parameter be：
ωx 2=355.3, ωy 2=532.9, ωxy=70.99, dxx=0.01
dyy=0.01, dxy=0.002, Ωz=0.1
In emulation experiment, if the primary condition of system is：q1(0)=0.5,q2(0)=0.5,q1
(0), q2(0) refer to initial position of the microthrust test in x-axis, y-axis, this moment t=0, two axis of microthrust test it is expected running orbit (reference
Track) be：qr1=sin (4.17t), qr2=1.2sin (5.11t), the estimation initial value of three parameter matrixs are respectively：
In sliding formwork control ratio, sliding-mode surface parameter takes p1=3, p2=5, error coefficient takes c1=1, take M=N=P=diag
(150,150) take fractional order exponent number α=0.9.
When external interference takes white noise signal d=[0.5*randn (1,1)；0.5*randn (1,1)] when, randn (1,1)
It represents to generate random number, simulation result is as shown in Figures 2 to 4.
Fig. 2 is microthrust test X, the aircraft pursuit course of Y-axis, as can be seen from the figure using fractional order adaptive fuzzy nerve inverting
The X of microthrust test, Y-axis track can be good at tracking reference locus after TSM control method.
Fig. 3 is tracking error curve figure, it can be seen from the figure that the tracking error e in X, Y-axis1It can be in finite time
Converge to zero.
Fig. 4 is two axis control input response curve.The sliding formwork switching item in controller is increased with fuzzy-neural network method
The benefit i.e. upper bound of systematic uncertainty and external interference summation is approached, and can sliding formwork be switched item serialization, effectively reduced
It buffets.
The present invention simplifies system by back stepping control so that entire controller design process is clear；It is micro- simultaneously
Each subsystem design liapunov function of gyro, based on adaptation mechanism, designs adaptive law, real-time estimation gyro system
The parameter and angular speed of system；Fractional order terminal sliding mode face is chosen, on the basis of sliding formwork control advantage is retained, and more can be adjusted
The derivative order of section is several, increases adjusting degree of freedom, improves control performance；Terminal sliding mode face ensure that systematic error limited
Zero is converged in time, improves tracking performance；It is in addition, total to systematic uncertainty and external interference using fuzzy neural network
The upper bound of sum is approached, and effectively reduces buffeting.
The above is only the preferred embodiment of the present invention, it is noted that for the ordinary skill people of the art
For member, various improvements and modifications may be made without departing from the principle of the present invention, these improvements and modifications also should
It is considered as protection scope of the present invention.
Claims (6)
1. microthrust test fractional order adaptive fuzzy nerve inverting TSM control method, it is characterised in that：Include the following steps：
(1) the dimensionless kinetics equation mathematical model of microthrust test system is established；
(2) the reference locus model of microthrust test system is built；
(3) the adaptive fuzzy nerve inverting TSM control device based on fractional order is built：It is a son of microthrust test first
System design Li Ya spectrum promise husband's functions, then design fractional order inverting TSM control rule, finally design based on fractional order
Adaptive fuzzy nerve inverting TSM control is restrained.
2. microthrust test fractional order adaptive fuzzy nerve inverting TSM control method as described in claim 1, feature
It is：The dimensionless kinetics equation mathematical model for the microthrust test system that the step (1) is established is：
Wherein, q is the position vector after microthrust test mathematical model nondimensionalization,Expression seeks first derivative to position vector q,
Expression seeks second dervative to position vector q；DbFor damping matrix after nondimensionalization, K is spring constant matrix after nondimensionalization, Ω
For angular velocity matries after nondimensionalization, u is that the control of microthrust test system inputs, and f is systematic uncertainty and external interference summation,
And have：
Wherein, Δ DbFor inertial matrix DbThe uncertainty of the unknown parameter of+2 Ω, Δ K be inertial matrix K unknown parameter not
Certainty, d (t) are external interferences, it is assumed that | fi| ＜ ρi, i=1,2, fiRepresent the total of systematic uncertainty and external interference on axis
With ρiRepresent the upper bound of systematic uncertainty and external interference summation on axis.
3. microthrust test fractional order adaptive fuzzy nerve inverting TSM control method as claimed in claim 2, feature
It is：The reference locus model of step (2) structure microthrust test system is：
qr1=A1sin(ω1T), qr2=A2sin(ω2t) (3)
Wherein qr1Refer to the reference locus model of x-axis, qr2Refer to the reference locus model of y-axis；A1Be microthrust test in the direction of the x axis
Amplitude, A2It is the amplitude of microthrust test in the y-axis direction；ω1It is the vibration frequency that microthrust test gives in the direction of the x axis, ω2It is
The vibration frequency that microthrust test gives in the y-axis direction；T is time variable.
4. microthrust test fractional order adaptive fuzzy nerve inverting TSM control method as claimed in claim 3, feature
It is：In the step (3), the specific steps that a subsystem for microthrust test designs Li Ya spectrum promise husband's functions include：
Define vector x1,x2Respectively：
Based on back-stepping design technology, the dimensionless kinetics equation mathematical model (1) of microthrust test system is converted into following form：
Define the tracking error e between microthrust test physical location and reference locus1For：
e1=x1-qr (6)
Wherein, qrFor microthrust test system x, the reference locus of y-axis,
The first derivative of tracking error derivativeFor：
Take virtual controlling amount α1For：
Wherein, c1It is the normal number of non-zero for error coefficient；
Define tracking error function e2For：
e2=x2-α1 (9)
To with tracking error e1Microthrust test subsystem choose Li Ya spectrum promise husband's function V1For：
Wherein：e1 TFor tracking error vector e1Transposition,
To V1It is obtained along the derivation of time t：
Work as e2=0,Meet negative definiteness, it is stable to ensure system.
5. microthrust test fractional order adaptive fuzzy nerve inverting TSM control method as claimed in claim 4, feature
It is：In the step (3), fractional order inverting TSM control rule u1Design procedure includes：
It is for microthrust test design fractional order terminal sliding mode face s：
Wherein, λ1,λ2,p2,p1For arithmetic number, 1 ＜ p2/p1＜ 2, Dα-1e1It represents to e1α -1 ranks is asked to lead, D represents derivation, and α refers to
The exponent number of fractional order；
The then derivative of microthrust test fractional order terminal sliding mode face sFor：
Wherein, Dαe1It is to Dα-1e1The result of derivation；
It enables
Then
Wherein, R1*R2=I, I are unit matrix,e21,e22It is tracking respectively
Error e2Component in x-axis and y-axis direction；
To with tracking error e2Microthrust test subsystem choose Li Ya spectrums promise husband's function V2For：
Promise husband's function V is composed according to Li Ya2Design fractional order inverting TSM control rule u1For：
Wherein, ρisgn(si) represent sliding formwork switching item, for replacing systematic uncertainty and external interference summation fi, | | s | | table
Show and seek sliding-mode surface vector field homoemorphism value,When gyro system be stable.
6. microthrust test fractional order adaptive fuzzy nerve inverting TSM control method as claimed in claim 5, feature
It is：In the step (3), the adaptive fuzzy nerve inverting TSM control rule u' design procedure packets based on fractional order
It includes：
Defining evaluated error in microthrust test nondimensionalization model is respectively：
Ambiguity in definition neural network weight evaluated errorFor：
Wherein,It is microthrust test parameter matrix D respectivelyb, the estimated value of K, Ω,Respectively parameter matrix Db,
The parameter estimating error of K, Ω；wiIt is the weights of fuzzy neural network, wi* it is optimal fuzzy neural network weights；
Adaptive fuzzy nerve inverting TSM control based on fractional order restrains u'：
WhereinIt is the output of fuzzy neural network, is to being on sliding formwork switching item gain i.e. systematic uncertainty and axis
The uncertain upper bound ρ with external interference summation of systemiEstimation；
The form of expression of fuzzy neural network output is as follows：
Wherein, φiThe referred to as normalization confidence level of fuzzy neural network；
The adaptive fuzzy nerve inverting TSM control rule u' of fractional order is controlled into input u as microthrust test system, is brought into
In the mathematical model of microthrust test system, the tracing control to microthrust test system is realized；
Define third Li Ya spectrum promise husband's functions V3For：
Wherein, M=MT＞ 0, N=NT＞ 0, P=PT＞ 0 is symmetric positive definite matrix, and tr { } representing matrix asks mark operation, η
For normal number；
In order to ensure the derivative of third Li Ya spectrum promise husband's functionsThe systematic parameter of online real-time estimation microthrust test, design
Microthrust test parameter matrix Db, the estimated value of K, ΩWith fuzzy neural network weight wiAdaptive law be respectively：
Wherein, si, i=1,2 refer to component of the sliding-mode surface in x-axis and y-axis direction, ri, i=1,2 is the r in formula (14)1,r2,For gyro system damping matrix DbEstimated value adaptive law transposition,Spring constant matrix K for gyro system
Estimated value adaptive law transposition,The transposition of the adaptive law of estimated value for gyro angular velocity matries,It is fuzzy
The adaptive law of neural network weight；When choosing above-mentioned parameter adaptive law,Meet Liapunov stability to determine
Reason ensures microthrust test system Global asymptotic stability.
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