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CN106289208B - A kind of magnetic bearing system axes of inertia discrimination method based on nonlinear adaptive algorithm - Google Patents

A kind of magnetic bearing system axes of inertia discrimination method based on nonlinear adaptive algorithm Download PDF

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Publication number
CN106289208B
CN106289208B CN201610854370.0A CN201610854370A CN106289208B CN 106289208 B CN106289208 B CN 106289208B CN 201610854370 A CN201610854370 A CN 201610854370A CN 106289208 B CN106289208 B CN 106289208B
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mrow
mover
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CN106289208A (en
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房建成
张会娟
刘刚
刘虎
张染
陈曦
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Beihang University
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
    • G01C19/00—Gyroscopes; Turn-sensitive devices using vibrating masses; Turn-sensitive devices without moving masses; Measuring angular rate using gyroscopic effects
    • G01C19/02—Rotary gyroscopes
    • G01C19/04—Details
    • G01C19/16—Suspensions; Bearings
    • G01C19/24—Suspensions; Bearings using magnetic or electrostatic fields
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
    • G01C25/00—Manufacturing, calibrating, cleaning, or repairing instruments or devices referred to in the other groups of this subclass
    • G01C25/005—Manufacturing, calibrating, cleaning, or repairing instruments or devices referred to in the other groups of this subclass initial alignment, calibration or starting-up of inertial devices

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  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Radar, Positioning & Navigation (AREA)
  • Remote Sensing (AREA)
  • Manufacturing & Machinery (AREA)
  • Magnetic Bearings And Hydrostatic Bearings (AREA)

Abstract

The present invention relates to a kind of magnetic bearing system axes of inertia discrimination method based on nonlinear adaptive algorithm.Initially set up the magnetic bearing system dynamical model of rotor comprising rotor unbalance and Sensor Runout；Secondly a kind of nonlinear autoregressive rule and estimation rule are proposed, while ensureing that magnetic suspension rotor center of inertia Displacement Estimation value goes to zero, and can estimates the Fourier coefficient of Sensor Runout higher harmonic components；Then by changing the strategy of rotor speed, increase the observability degree of system, realize identifications of the Sensor Runout with frequency component and rotor unbalance value, that is, realize the identification of the axes of inertia；Finally correct in adaptive algorithm with frequency component Fourier coefficient, suppress multiple-harmonic current and compensation displacement rigidity power exactly, realize the multiple-harmonic vibration suppression of magnetic suspension inertia actuator.

Description

A kind of magnetic bearing system axes of inertia discrimination method based on nonlinear adaptive algorithm
Technical field
The present invention relates to a kind of magnetic bearing system axes of inertia discrimination method based on nonlinear adaptive algorithm, for recognizing The magnetic bearing system axes of inertia comprising rotor unbalance and sensor harmonic noise (Sensor Runout), realize that magnetic suspension is used to Property executing agency multiple-harmonic vibration suppression, make magnetic suspension inertia actuator meet following " super quiet super steady " satellite platform to pole The requirement of micro-vibration, belong to magnetic bearing system Vibration Active Control field.
Background technology
It is super quiet with the development of the ultrahigh resolution satellite such as high-resolution earth observation, survey of deep space, Space laser communications With quick two important indicators for turning into measurement satellite platform performance.Super static stability can ensure high-resolution payload imaging matter The key factor of amount, quick performance are that solve high-resolution imaging and cover this technology shortcut to contradiction on a large scale.More Carry out higher resolution ratio index to the pointing accuracy of satellite platform and the requirement more and more higher of attitude stability, to spaceborne movable part Vibration caused by part is more and more sensitive.Satellite Vibration is broadly divided into two major classes, and one kind is a few to tens of Hz low-frequency high-amplitude vibration Dynamic, this kind of vibration can be suppressed by satellite gravity anomaly；Another kind of frequency low-amplitude vibration is mainly by flywheel, control moment The inertia actuators such as gyro cause, and this kind of vibration can not be suppressed by gesture stability algorithm, are to influence satellite to put down The technical bottleneck of platform level of vibration.
Mainly there are two kinds of isolation mounting and magnetic suspension Vibration Active Control to the suppression of inertia actuator vibration.Mechanically Inertia actuator generally use vibration isolation technique suppresses dither, but frequency low-amplitude simply vibrates and converted by isolation mounting Vibrated into low-frequency high-amplitude, vibration is eliminated not from source.One important advantage of magnetic suspension inertia actuator is that have actively The ability of vibration suppression, its essence are to realize that rotor rotates around the principal axis of inertia by adjusting the controling power of magnetic bearing, fundamentally Eliminate the dither of high speed rotor.Due to processing alignment error, machinery and the electricity such as material is uneven, electronic component is non-linear Gas non-ideal characteristic, magnetic suspension inertia actuator is there is vibration sources such as rotor unbalance, Sensor Runout, so as to pass Pass out multiple-harmonic vibration.At present, magnetic bearing system Vibration Active Control focuses primarily upon the research of rotor unbalance vibration control, It is less to the magnetic bearing system Vibration Active Control research comprising rotor unbalance and Sensor Runout.Due to displacement sensing The same frequency composition of device output includes Sensor Runout with frequency component and rotor unbalance, when carrying out displacement rigidity compensation Need the influence of compensation rotor unbalance, it is therefore desirable to identifications of the Sensor Runout with frequency component and rotor unbalance is carried out, That is the identification of the axes of inertia.Existing discrimination method can be divided into two classes：One kind is direct identification method, directly by magnetic suspension rotor low speed Same frequency component of the same frequency composition that sensor exports during operation as Sensor Runout, this kind of method Identification Errors are big；It is another Class is Adaptive Identification algorithm, but existing algorithm mainly realizes that rotor rotates around geometrical axis, can externally pass out sizable shake It is dynamic, high accuracy alignment magnetic bearing system is only applicable to, is not suitable for magnetic suspension inertia actuator.
The content of the invention
The technology of the present invention solves problem：Overcome the deficiencies in the prior art, invention is a kind of to be calculated based on nonlinear adaptive The magnetic bearing system axes of inertia identification algorithm of method, by nonlinear adaptive algorithm and the strategy of change rotor speed, improve used Property axle identification precision, realize that magnetic suspension rotor rotates around the axes of inertia, suppress the vibration of magnetic bearing system multiple-harmonic.It is in addition, of the invention In nonlinear autoregressive rule solve using initial current during conventional linear algorithm is excessive and parameter convergence rate is slow etc. Problem.
The present invention technical solution be：A kind of magnetic bearing system axes of inertia identification based on nonlinear adaptive algorithm Algorithm, initially sets up the magnetic bearing system kinetic model comprising rotor unbalance and Sensor Runout, and analysis vibration produces Mechanism and existence form；Secondly a kind of nonlinear autoregressive rule of invention and estimation rule, in magnetic suspension rotor inertia is ensured While the estimate of heart displacement converges on zero, rotor unbalance and each harmonic component Fourier systems of Sensor Runout are realized Several estimations；Then by changing the strategy of rotating speed, increase the observability degree of same frequency component, realize Sensor Runout with frequency The identification of component and rotor unbalance value, estimates the axes of inertia；Finally realize the multiple-harmonic of magnetic suspension inertia actuator actively Vibration suppression.The present invention's comprises the following steps that：
(1) the magnetic bearing system kinetic model containing rotor unbalance and Sensor Runout is established
For two-freedom magnetic bearing system, x-axis and the passage of y-axis two mutually decouple.Assuming that the displacement rigidity of x-axis and y-axis Coefficient is identical with current stiffness coefficient, when magnetic suspension rotor moves near equilbrium position, its kinetics equation linearized For：
In formula, m is the quality of magnetic suspension rotor；kiAnd khRespectively the current stiffness coefficient of magnetic bearing system and displacement are firm Spend coefficient；Ic=[icx, icy]T, icxAnd icyRespectively x-axis and y-axis magnetic bearing coil control electric current；χI=[xI, yI]T, xIAnd yI Respectively displacement of the center of inertia in x-axis and y-axis direction,For χISecond dervative；χg=[xg, yg]T, xgAnd ygRespectively Displacement of the geometric center in x-axis and y-axis direction.
Due to the influence of rotor unbalance so that rotor inertia center is misaligned with geometric center, then magnetic suspension rotor is several How the relation between center and center of inertia displacement is：
χI=χg-δ
In formula,For rotor unbalance value；λ andThe respectively amplitude of rotor unbalance value And phase；ω is rotor speed.δ is changed into matrix form has：
Wherein, PδAnd ΦδThe respectively trigonometric function matrix and Fourier coefficient of rotor unbalance value.
In addition, influenceed by displacement transducer multiple-harmonic noise Sensor Runout, the geometric center position of sensor output Move χsWith actual geometric center displacement χgDeviation be present, relation between the two is：
χs=χg+d
In formula,For Sensor Runout vectors；σiAnd ξiRespectively Sensor The amplitude and phase of Runout ith harmonic components；K is overtone order.D is rewritten as matrix form：
Φd=[Φd1 … Φdk]
Φdi=[pi qi], pi=σi sinξi, qi=σicosξi
Wherein, PdAnd ΦdRespectively Sensor Runout trigonometric function matrix and Fourier coefficient；PdiAnd ΦdiRespectively For the trigonometric function matrix and Fourier coefficient of Sensor Runout ith harmonic components.
Magnetic bearing coil control electric current IcFor：
Ic=-kadksGw(s)Gc(s)χs
In formula, kadFor AD downsampling factors；ksFor displacement transducer multiplication factor；GcAnd G (s)w(s) be respectively controller and The transmission function of power amplifier.
Then include rotor unbalance and Sensor Runout magnetic bearing system kinetic model is：
(2) nonlinear autoregressive algorithm designs
On the basis of the model described in step (1), nonlinear autoregressive algorithm is designed, the algorithm mainly includes two Point：Adaptive control laws and estimation are restrained.Adaptive control laws are by the estimate of magnetic suspension rotor center of inertia displacementAs control Variable processed, ensureConverge on zero.ART network rule can adaptively estimate rotor unbalance value and Sensor Runout The Fourier coefficient Φ of each harmonic componentδ、Φd, ensure each Fourier coefficient estimate convergence.Nonlinear autoregressive is restrained It is designed as：
In formula, Ξ is positive definite matrix；ρ is normal number；For the estimate of rotor unbalance value Fourier coefficient； Purpose of design is to compensate for displacement rigidity power caused by rotor unbalance value；KamFor the equieffective ratio coefficient of power amplification system；E is WithWithRelevant weight function；ForFirst derivative.
The ART network of each harmonic components of Sensor Runout and rotor unbalance value Fourier coefficient is restrained：
In formula, WithRespectively trigonometric function Matrix PdAnd PδSecond dervative；WithRespectively in Fu of each harmonic components of Sensor Runout and rotor unbalance value Leaf system number evaluated error；WithThe respectively Fourier coefficient of each harmonic components of Sensor Runout and rotor unbalance value The first derivative of evaluated error；WithFor positive definite adaptive gain matrix, Fourier coefficient estimation is determined The convergence rate of value and the stability of system.
(3) the magnetic bearing system axes of inertia recognize
The nonlinear adaptive algorithm that step (2) proposes can estimate Sensor Runout higher harmonic components exactly Fourier coefficient, and ensure Sensor Runout with the Fourier coefficient estimate of frequency component and rotor unbalance value receive Hold back.In order to further recognize Sensor Runout with frequency component and rotor unbalance value, it is necessary to by step (3) variable speed side Formula is realized, that is, realizes that the axes of inertia recognize.Axes of inertia identification mainly includes three steps：A) working rotor is in rotational speed omega1Under, obtain Fourier coefficient estimates of the Sensor Runout with frequency component and rotor unbalance valueWithB) change and turn Rotor speed, magnetic suspension rotor is set to be operated in rotational speed omega2Under, obtain the estimate under current rotating speed WithC) root Have according to the same frequency component Fourier coefficient obtained under two speed conditions：
In formula, With
Finally solve actual value p1、q1, u and v, then the magnetic bearing system axes of inertia recognized.
(4) magnetic bearing system multiple-harmonic Active vibration suppression
Sensor Runout during step (2) nonlinear autoregressive is restrained are the same as in frequency component and rotor unbalance Fu The estimate of leaf system number replaces with the actual value that step (3) calculates, then displacement rigidity power obtains as caused by rotor unbalance Accurately compensate for, multiple-harmonic current caused by rotor unbalance value and Sensor Runout is effectively suppressed, finally accurately The multiple-harmonic of magnetic suspension inertia actuator is inhibited to vibrate.
The present invention principle be：Rotor unbalance and Sensor Runout are two primary oscillation sources of magnetic bearing system, It is different that both, which produce the approach vibrated and form,.Rotor unbalance not only produces position in itself by magnetic bearing system Rigidity power is moved, current stiffness power is also produced by controller and current stiffness coefficient；And only to produce electric current firm by Sensor Runout Spend power.Therefore the suppression of magnetic bearing system multiple-harmonic vibration will not only realize the suppression of multiple-harmonic current, i.e., in displacement transducer Two kinds of noises of reference-junction compensation influence, and to compensate displacement rigidity power caused by rotor unbalance.But displacement sensing Rotor unbalance component, and the same frequency component comprising Sensor Runout are both included in the same frequency component of device output.Therefore entering The premise that row displacement rigidity power accurately compensates, to carry out the identification of rotor unbalance and Sensor Runout with frequency amount, i.e. inertia The identification of axle.So as to realize magnetic suspension inertia actuator high accuracy multiple-harmonic vibration suppression.
The present invention compared with prior art the advantages of be：A kind of magnetic bearing system based on nonlinear adaptive algorithm is used to Property axle discrimination method, (1) overcomes traditional the shortcomings that directly identification algorithm causes Identification Errors big, it is only necessary to a raising speed or Reduction of speed can realize the identification of the magnetic bearing system axes of inertia；(2) initial control electricity caused by conventional linear adaptive algorithm is overcome The shortcomings of big and parameter identification convergence rate is slow is flowed through, being restrained using nonlinear autoregressive improves algorithm performance；(3) avoid In traditional magnetic bearing system multiple-harmonic vibration control algorithm, Sensor Runout draw with frequency component and rotor unbalance value aliasing The displacement rigidity force compensating error risen, is modified using the Fourier coefficient after identification, so as to realize that magnetic bearing system is high-precision Spend multiple-harmonic vibration suppression.
Brief description of the drawings
Fig. 1 is the implementation process figure of the present invention；
Fig. 2 is the system principle diagram based on nonlinear autoregressive algorithm；
Fig. 3 is that the axes of inertia recognize flow chart.
Embodiment
The present invention will be further described for implementation steps below in conjunction with the accompanying drawings and specifically.
As shown in figure 1, the present invention relates to a kind of magnetic bearing system axes of inertia identification side based on nonlinear adaptive algorithm Method, its implementation process are：The magnetic bearing system kinetic model comprising rotor unbalance and Sensor Runout is initially set up, Analyze magnetic bearing system multiple-harmonic vibration producing cause and existence form；Its secondary design nonlinear autoregressive algorithm, realize The center of inertia Displacement Estimation value of magnetic suspension rotor converges on zero, and ART network rotor unbalance value and Sensor The Fourier coefficient of each harmonic components of Runout；Then realize Sensor Runout with frequency by changing the strategy of rotor speed The identification of component and rotor unbalance, that is, realize the identification of the axes of inertia；Finally by Sensor in nonlinear adaptive algorithm Each harmonic components of Runout and rotor unbalance Fourier coefficient are modified, and magnetic suspension rotor is rotated around the real axes of inertia, So as to realize magnetic bearing system multiple-harmonic vibration suppression.Fig. 2 is the theory diagram of nonlinear autoregressive algorithm.Displacement sensing Device detects the displacement of rotor, and introduces Sensor Runout multiple-harmonic noise d, enters controller by AD samplings, realization is closed Ring controls.Estimation rule in nonlinear adaptive algorithm estimates rotor unbalance value and each harmonic components of Sensor Runout WithIn controller input χsBoth are eliminated, to realize the suppression of multiple-harmonic current；Nonlinear adaptive algorithm, which utilizes, to be estimated The rotor unbalance value counted outObtainThe compensation of displacement rigidity power is carried out, finally gives control signal uic.Magnetic bearing Power amplification system drives magnetic bearing coil according to control signal, produces control electric current Ic, produce corresponding magnetic axis load F and act on magnetic Suspension rotor, so as to change the position χ of rotorg.Fig. 3 is that the axes of inertia recognize flow chart, is the specific implementation stream of Fig. 1 steps (3) Journey, respectively in rotational speed omega1And ω2Under estimate when obtaining stable state WithPass through Solve equation and obtain real Fourier coefficient p1, q1, u and v, finally by rotor unbalance in adaptive algorithm and Sensor Runout replaces with actual value with the estimate of frequency component, so as to realize that magnetic suspension rotor rotates around the real axes of inertia.The present invention Specific implementation step is as follows：
(1) the magnetic bearing system kinetic model containing rotor unbalance and Sensor Runout is established
For two-freedom magnetic bearing system, x-axis and the passage of y-axis two mutually decouple.Assuming that the displacement rigidity of x-axis and y-axis Coefficient is identical with current stiffness coefficient, when magnetic suspension rotor moves near equilbrium position, its kinetics equation linearized For：
In formula, m is the quality of magnetic suspension rotor；kiAnd khRespectively the current stiffness coefficient of magnetic bearing system and displacement are firm Spend coefficient；icxAnd icyRespectively x-axis and y-axis magnetic bearing coil control electric current；xIAnd yIRespectively the axes of inertia are in x-axis and y-axis side Upward displacement；xgAnd ygRespectively displacement of the geometrical axis in x-axis and y-axis direction.
Being write formula (1) as matrix form is：
In formula, χI=[xI, yI]T, χg=[xg, yg]T, Ic=[icx, icy]T。
Due to the influence of rotor unbalance so that rotor inertia center and geometric center are misaligned, then rotor inertia center Displacement χIWith geometric center displacement χgBetween relation be：
χI=χg-δ (3)
In formula, δ is rotor unbalance, is expressed as：
Wherein, λ andThe respectively amplitude and phase of rotor unbalance value；ω is rotor speed.Write formula (4) as matrix Form is：
Wherein, PδAnd ΦδThe respectively trigonometric function matrix and Fourier coefficient of rotor unbalance value.
Order The then Fourier coefficient vector Φ of rotor unbalance valueδIt is represented by：
Φδ=[u v] (8)
In addition, influenceed by displacement transducer multiple-harmonic noise Sensor Runout, the geometric center position of sensor output Move χsWith actual geometric center displacement χgDeviation be present, relation between the two is：
χs=χg+d (9)
In formula,For Sensor Runout vectors；σiAnd ξiRespectively Sensor The amplitude and phase of Runout ith harmonic components；K is overtone order.D is rewritten as matrix form：
Φd=[Φd1 … Φdk] (13)
Φdi=[pi qi], pi=σisinξi, qi=σicosξi (14)
Wherein, PdAnd ΦdRespectively Sensor Runout trigonometric function matrix and Fourier coefficient；PdiAnd ΦdiRespectively For the trigonometric function matrix and Fourier coefficient of Sensor Runout ith harmonic components.
Magnetic bearing coil control electric current IcFor：
Ic=-kadksGw(s)Gc(s)χs (15)
In formula, kadFor AD downsampling factors；ksFor displacement transducer multiplication factor；GcAnd G (s)w(s) be respectively controller and The transmission function of power amplifier.
Then the kinetic model of the magnetic bearing system comprising rotor unbalance and Sensor Runout is：
Then the relation between vibration force F and two kinds of vibration sources δ and d is：
F=Q-1[(khI2×2-kikadksGw(s)Gc(s))δ-kikadksGw(s)Gc(s)d] (17)
Q=I2×2-khP(s)+kikadksGw(s)Gc(s)P(s) (18)
In formula, I2×2For second order unit matrix；P (s) is magnetic bearing system transmission function.
(2) nonlinear autoregressive algorithm designs
Assuming that rotor unbalance value and Sensor Runout estimate are respectivelyWithThe then position at rotor inertia center Move estimateIt is represented by：
In formula,The Displacement Estimation value of geometric center；WithRespectively rotor unbalance value and Sensor Runout Evaluated error, it is defined as：
In formula,WithRespectively rotor unbalance value and each harmonic component Fourier coefficients of Sensor Runout is estimated Count error.
In order to ensure that rotor inertia the center displacement estimate converges on zero, and it can adaptively estimate rotor unbalance With Sensor Runout Fourier coefficients, nonlinear autoregressive rule is designed as：
In formula, ρ is normal number；In order to compensate displacement rigidity power caused by rotor unbalance value；ForOne Order derivative；E be withWithRelevant weight function.In order to overcome initial control electric current mistake caused by conventional linear weight function Greatly, the shortcomings of parameter convergence rate is slow is estimated, the present invention proposes a kind of nonlinear weight value function：
In formula, a and b are normal number.Then positive definite matrix Ξ is represented by formula (22)：
Each harmonic components of Sensor Runout and rotor unbalance value Fourier coefficient ART network rule are respectively：
Γd=diag (τd1 τd1 τd2 τd2 … τdk τdk) (26)
Γδ=diag (τδ τδ) (27)
In formula, WithRespectively trigonometric function Matrix PdAnd PδSecond dervative；WithRespectively in Fu of each harmonic components of Sensor Runout and rotor unbalance value The first derivative of leaf system number evaluated error；WithFor positive definite adaptive gain matrix, Fourier system is determined The convergence rate of number estimate and the stability of system.In order to ensure the stability of system, matrix element τdj(j=1 ..., k) And τδSelection should meet 0≤(△dii+△δii)≤1, i=1,2；△δii=τδmω2。
(3) the magnetic bearing system axes of inertia recognize
Due to system asymptotically stability, as t → ∞,WithZero will be all converged on, then the inertia of magnetic suspension rotor The center displacement estimate converges on zero.Understood according to formula (23) and (25), as t → ∞, Then rotor unbalance value estimateWith Sensor Runout Fourier coefficient estimatesIt will converge on Definite value.Had according to formula (1), (19) and (22)：
Due toWithAll it is intended to zero, then formula (28) is reduced to：
According to trigonometric function orthogonal property, can obtain：
From formula (30) and (31)：Sensor Runout higher harmonic components Fourier coefficient converges on actual value, And the Fourier coefficient of Sensor Runout same frequency component and rotor unbalance does not converge to actual value.Therefore need logical A kind of observability degree of means increase system is crossed, both are recognized, so as to realize that the magnetic bearing system axes of inertia recognize.
DefinitionIt can then be obtained by formula (32)：
Two equations, four unknown numbers, above formula equation is unsolvable.Defined from η, change rotor speed to increase Add equation number, realize the identification of the magnetic bearing system axes of inertia.
As shown in figure 3, the identification of the magnetic bearing system axes of inertia needs three steps：A) working rotor is in rotational speed omega1Under, obtain Estimate to Sensor Runout with frequency component and rotor unbalance value Fourier coefficientWithB) change Rotor speed, it is set to be operated in rotational speed omega2Under, obtain the estimate under current rotating speedWithC) two are turned Estimate under the conditions of speed substitutes into formula (32), has：
In formula, With
Finally solve actual value p1、q1, u and v, then the magnetic bearing system axes of inertia recognized.
(4) magnetic bearing system multiple-harmonic vibration suppression
Estimation by the Sensor Runout of step (2) Chinese style (22) with frequency component and rotor unbalance Fourier coefficient Value replaces with the actual value that step (3) calculates, then displacement rigidity power is accurately compensated for as caused by rotor unbalance, turns Multiple-harmonic current caused by sub- amount of unbalance and Sensor Runout is effectively suppressed, and finally accurately inhibits magnetic suspension The multiple-harmonic vibration of inertia actuator.
When carrying out axes of inertia identification using nonlinear adaptive algorithm it can be seen from more than, it is only necessary in low-speed conditions Raising speed of lower progress or reduction of speed, realize that simply identification precision is higher than direct identification method.Further, since Sensor Each harmonic components of Runout do not change and changed with rotor speed, therefore the Fourier coefficient that will can be picked out under low-speed conditions Value is directly used in the magnetic suspension inertia actuator Vibration Active Control under high speed.
The content not being described in detail in description of the invention belongs to prior art known to this professional domain technical staff.

Claims (3)

  1. A kind of 1. magnetic bearing system axes of inertia discrimination method based on nonlinear adaptive algorithm, it is characterised in that：Including following Step：
    (1) the magnetic bearing system kinetic model containing rotor unbalance and Sensor Runout is established
    For two-freedom magnetic bearing system, x-axis and the passage of y-axis two mutually decouple；Assuming that the displacement rigidity coefficient of x-axis and y-axis Identical with current stiffness coefficient, when magnetic suspension rotor moves near equilbrium position, its kinetics equation linearized is：
    <mrow> <mi>m</mi> <msub> <mover> <mi>&amp;chi;</mi> <mo>&amp;CenterDot;&amp;CenterDot;</mo> </mover> <mi>I</mi> </msub> <mo>=</mo> <msub> <mi>k</mi> <mi>i</mi> </msub> <msub> <mi>I</mi> <mi>c</mi> </msub> <mo>+</mo> <msub> <mi>k</mi> <mi>h</mi> </msub> <msub> <mi>&amp;chi;</mi> <mi>g</mi> </msub> </mrow>
    In formula, m is the quality of magnetic suspension rotor；kiAnd khRespectively the current stiffness coefficient of magnetic bearing system and displacement rigidity system Number；Ic=[icx, icy]T, icxAnd icyRespectively x-axis and y-axis circle control electric current；χI=[xI, yI]T, xIAnd yIRespectively inertia Displacement of the center in x-axis and y-axis direction；For χISecond dervative；χg=[xg, yg]T, xgAnd ygRespectively geometric center exists Displacement in x-axis and y-axis direction；
    Due to the influence of rotor unbalance so that rotor inertia center and geometric center are misaligned, then in magnetic suspension rotor geometry Relation between the heart and center of inertia displacement is：
    χI=χg-δ
    In formula,For rotor unbalance value；λ andThe respectively amplitude and phase of rotor unbalance value Position；ω is rotor speed；δ is changed into matrix form has：
    <mrow> <mi>&amp;delta;</mi> <mo>=</mo> <msub> <mi>P</mi> <mi>&amp;delta;</mi> </msub> <msubsup> <mi>&amp;Phi;</mi> <mi>&amp;delta;</mi> <mi>T</mi> </msubsup> </mrow>
    <mrow> <msub> <mi>P</mi> <mi>&amp;delta;</mi> </msub> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <mo>-</mo> <mi>s</mi> <mi>i</mi> <mi>n</mi> <mrow> <mo>(</mo> <mi>&amp;omega;</mi> <mi>t</mi> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mrow> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mrow> <mo>(</mo> <mi>&amp;omega;</mi> <mi>t</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>cos</mi> <mrow> <mo>(</mo> <mi>&amp;omega;</mi> <mi>t</mi> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mrow> <mi>s</mi> <mi>i</mi> <mi>n</mi> <mrow> <mo>(</mo> <mi>&amp;omega;</mi> <mi>t</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced> </mrow>
    Wherein, PδAnd ΦδThe respectively trigonometric function matrix and Fourier coefficient of rotor unbalance value；
    In addition, influenceed by displacement transducer multiple-harmonic noise Sensor Runout, the geometric center displacement χ of sensor outputs With actual geometric center displacement χgDeviation be present, relation between the two is：
    χs=χg+d
    In formula,For Sensor Runout vectors；σiAnd ξiRespectively Sensor The amplitude and phase of Runout ith harmonic components；K is overtone order；D is rewritten as matrix form：
    <mrow> <mi>d</mi> <mo>=</mo> <msub> <mi>P</mi> <mi>d</mi> </msub> <msubsup> <mi>&amp;Phi;</mi> <mi>d</mi> <mi>T</mi> </msubsup> </mrow>
    <mrow> <msub> <mi>P</mi> <mrow> <mi>d</mi> <mi>i</mi> </mrow> </msub> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <mo>-</mo> <mi>s</mi> <mi>i</mi> <mi>n</mi> <mrow> <mo>(</mo> <mi>i</mi> <mi>&amp;omega;</mi> <mi>t</mi> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mrow> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mrow> <mo>(</mo> <mi>i</mi> <mi>&amp;omega;</mi> <mi>t</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>cos</mi> <mrow> <mo>(</mo> <mi>i</mi> <mi>&amp;omega;</mi> <mi>t</mi> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mrow> <mi>s</mi> <mi>i</mi> <mi>n</mi> <mrow> <mo>(</mo> <mi>i</mi> <mi>&amp;omega;</mi> <mi>t</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> <mi>i</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mo>...</mo> <mo>,</mo> <mi>k</mi> </mrow>
    Φd=[Φd1 … Φdk]
    Φdi=[pi qi], pi=σisinξi, qi=σicosξi
    Wherein, PdAnd ΦdRespectively Sensor Runout trigonometric function matrix and Fourier coefficient；PdiAnd ΦdiRespectively The trigonometric function matrix and Fourier coefficient of Sensor Runout ith harmonic components；
    Magnetic bearing coil control electric current IcFor：
    Ic=-kadksGw(s)Gc(s)χs
    In formula, kadFor AD downsampling factors；ksFor displacement transducer multiplication factor；GcAnd G (s)w(s) it is respectively controller and power The transmission function of amplifier；
    Then include rotor unbalance and Sensor Runout magnetic bearing system kinetic model is：
    <mrow> <mi>m</mi> <msub> <mover> <mi>&amp;chi;</mi> <mo>&amp;CenterDot;&amp;CenterDot;</mo> </mover> <mi>I</mi> </msub> <mo>=</mo> <mo>-</mo> <msub> <mi>k</mi> <mi>i</mi> </msub> <msub> <mi>k</mi> <mrow> <mi>a</mi> <mi>d</mi> </mrow> </msub> <msub> <mi>k</mi> <mi>s</mi> </msub> <msub> <mi>G</mi> <mi>w</mi> </msub> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> <msub> <mi>G</mi> <mi>c</mi> </msub> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <msub> <mi>&amp;chi;</mi> <mi>I</mi> </msub> <mo>+</mo> <mi>&amp;delta;</mi> <mo>+</mo> <mi>d</mi> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>k</mi> <mi>h</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>&amp;chi;</mi> <mi>I</mi> </msub> <mo>+</mo> <mi>&amp;delta;</mi> <mo>)</mo> </mrow> <mo>;</mo> </mrow>
    (2) nonlinear autoregressive algorithm designs
    On the basis of the model described in step (1), nonlinear autoregressive algorithm is designed, the algorithm mainly includes two parts： Adaptive control laws and estimation are restrained；Adaptive control laws are by the estimate of magnetic suspension rotor center of inertia displacementBecome as control Amount, ensureConverge on zero；ART network rule can adaptively estimate that rotor unbalance value and Sensor Runout are each humorous The Fourier coefficient Φ of wave componentδ、Φd, ensure each Fourier coefficient estimate convergence；
    (3) the magnetic bearing system axes of inertia recognize
    The identification of the magnetic bearing axes of inertia is realized by variable speed strategy, magnetic suspension rotor is realized under the conditions of different rotor speed The nonlinear adaptive algorithm that step (2) proposes, different Sensor Runout are obtained with frequency component and rotor unbalance value Fourier coefficient estimate, the observability degree of same frequency component is improved, realize Sensor Runout with frequency component and rotor unbalance The identification of amount, i.e. the magnetic bearing system axes of inertia recognize；
    (4) magnetic bearing system multiple-harmonic vibration suppression
    In order to completely inhibit the vibration of the multiple-harmonic of magnetic bearing system, step (2) nonlinear adaptive need to be estimated in rule Sensor Runout with the estimate of frequency component and rotor unbalance Fourier coefficient replace with step (3) calculate it is true Value, then displacement rigidity power is accurately compensated for as caused by rotor unbalance, by rotor unbalance value and Sensor Runout Caused multiple-harmonic current is effectively suppressed.
  2. 2. a kind of magnetic bearing system axes of inertia discrimination method based on nonlinear adaptive algorithm according to claim 1, It is characterized in that：The nonlinear adaptive algorithm that step (2) proposes includes two parts：Nonlinear autoregressive is restrained and adaptive Estimation rule；Nonlinear autoregressive rule is designed as：
    <mrow> <msub> <mi>u</mi> <mrow> <mi>i</mi> <mi>c</mi> </mrow> </msub> <mo>=</mo> <mo>-</mo> <mrow> <mo>(</mo> <msub> <mi>k</mi> <mi>h</mi> </msub> <msub> <mover> <mi>&amp;chi;</mi> <mo>^</mo> </mover> <mi>I</mi> </msub> <mo>+</mo> <mi>m</mi> <mi>&amp;Xi;</mi> <msub> <mover> <mover> <mi>&amp;chi;</mi> <mo>^</mo> </mover> <mo>&amp;CenterDot;</mo> </mover> <mi>I</mi> </msub> <mo>+</mo> <mi>&amp;rho;</mi> <mi>e</mi> <mo>+</mo> <msub> <mi>k</mi> <mi>h</mi> </msub> <msub> <mi>P</mi> <mi>&amp;delta;</mi> </msub> <msubsup> <mover> <mi>&amp;Phi;</mi> <mo>^</mo> </mover> <mi>&amp;delta;</mi> <mi>T</mi> </msubsup> <mo>)</mo> </mrow> <mo>/</mo> <mrow> <mo>(</mo> <msub> <mi>K</mi> <mrow> <mi>a</mi> <mi>m</mi> </mrow> </msub> <msub> <mi>k</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> </mrow>
    In formula, ρ is normal number；For the estimate of rotor unbalance value Fourier coefficient；PδFor the triangle of rotor unbalance value Function battle array；Purpose of design is to compensate for displacement rigidity power caused by rotor unbalance value；KamFor power amplification system etc. Imitate proportionality coefficient；ForFirst derivative；E be withWithRelevant weight function：
    <mrow> <mi>e</mi> <mo>=</mo> <msub> <mover> <mover> <mi>&amp;chi;</mi> <mo>^</mo> </mover> <mo>&amp;CenterDot;</mo> </mover> <mi>I</mi> </msub> <mo>+</mo> <mi>a</mi> <mi> </mi> <mi>arctan</mi> <mrow> <mo>(</mo> <mi>b</mi> <msub> <mover> <mi>&amp;chi;</mi> <mo>^</mo> </mover> <mi>I</mi> </msub> <mo>)</mo> </mrow> </mrow>
    In formula, a and b are respectively normal number, and its value determines the convergence of control electric current initial size and Fourier coefficient estimate Speed；According to e definition, the positive definite matrix Ξ in control law is represented by：
    <mrow> <mi>&amp;Xi;</mi> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mfrac> <mrow> <mi>a</mi> <mi>b</mi> </mrow> <mrow> <mn>1</mn> <mo>+</mo> <msup> <mi>b</mi> <mn>2</mn> </msup> <msubsup> <mover> <mi>x</mi> <mo>^</mo> </mover> <mi>I</mi> <mn>2</mn> </msubsup> </mrow> </mfrac> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mfrac> <mrow> <mi>a</mi> <mi>b</mi> </mrow> <mrow> <mn>1</mn> <mo>+</mo> <msup> <mi>b</mi> <mn>2</mn> </msup> <msubsup> <mover> <mi>y</mi> <mo>^</mo> </mover> <mi>I</mi> <mn>2</mn> </msubsup> </mrow> </mfrac> </mtd> </mtr> </mtable> </mfenced> </mrow>
    In formula,WithRespectively estimate of the center of inertia displacement in x-axis and y-axis direction,
    The ART network of each harmonic components of Sensor Runout and rotor unbalance value Fourier coefficient is restrained：
    <mrow> <msub> <mover> <mover> <mi>&amp;Phi;</mi> <mo>~</mo> </mover> <mo>&amp;CenterDot;</mo> </mover> <mi>d</mi> </msub> <mo>=</mo> <msup> <mi>e</mi> <mi>T</mi> </msup> <msub> <mi>P</mi> <mrow> <mi>r</mi> <mi>d</mi> </mrow> </msub> <msub> <mi>&amp;Gamma;</mi> <mi>d</mi> </msub> <mo>,</mo> <msub> <mover> <mover> <mi>&amp;Phi;</mi> <mo>~</mo> </mover> <mo>&amp;CenterDot;</mo> </mover> <mi>&amp;delta;</mi> </msub> <mo>=</mo> <msup> <mi>e</mi> <mi>T</mi> </msup> <msub> <mi>P</mi> <mrow> <mi>r</mi> <mi>&amp;delta;</mi> </mrow> </msub> <msub> <mi>&amp;Gamma;</mi> <mi>&amp;delta;</mi> </msub> </mrow>
    Γd=diag (τd1 τd1 τd2 τd2 … τdk τdk)
    Γδ=diag (τδ τδ)
    In formula, WithRespectively trigonometric function Matrix PdAnd PδSecond dervative；WithRespectively in Fu of each harmonic components of Sensor Runout and rotor unbalance value Leaf system number evaluated error；WithThe respectively Fourier coefficient of each harmonic components of Sensor Runout and rotor unbalance value The first derivative of evaluated error；WithFor positive definite adaptive gain matrix, Fourier coefficient estimation is determined The convergence rate of value and the stability of system；In order to ensure the stability of system, ΓdAnd ΓδEach diagonal entry τdj(j= 1 ..., k) and τδSelection should meet 0≤(Δdii+Δδii)≤1, i=1,2；Δδii= τδmω2。
  3. 3. a kind of magnetic bearing system axes of inertia discrimination method based on nonlinear adaptive algorithm according to claim 1, It is characterized in that：Use in the step (3) specific method that variable speed strategy realizes that the magnetic bearing system principal axis of inertia recognizes for：
    Based on step (2) propose nonlinear adaptive algorithm, when the center of inertia Displacement Estimation value level off to zero when, Sensor Runout meets with the Fourier coefficient estimate of frequency component and rotor unbalance value：
    <mrow> <mo>(</mo> <msub> <mi>k</mi> <mi>h</mi> </msub> <mo>+</mo> <msup> <mi>m&amp;omega;</mi> <mn>2</mn> </msup> <mo>)</mo> <msub> <mi>P</mi> <mrow> <mi>d</mi> <mn>1</mn> </mrow> </msub> <msubsup> <mover> <mi>&amp;Phi;</mi> <mo>~</mo> </mover> <mrow> <mi>d</mi> <mn>1</mn> </mrow> <mi>T</mi> </msubsup> <mo>+</mo> <msub> <mi>P</mi> <mrow> <mi>r</mi> <mi>&amp;delta;</mi> </mrow> </msub> <msubsup> <mover> <mi>&amp;Phi;</mi> <mo>~</mo> </mover> <mi>&amp;delta;</mi> <mi>T</mi> </msubsup> <mo>=</mo> <mn>0</mn> </mrow>
    Due to Prδ=m ω2Pd1, above formula is rewritable to be：
    <mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <msub> <mover> <mi>p</mi> <mo>~</mo> </mover> <mn>1</mn> </msub> <mo>+</mo> <mi>&amp;eta;</mi> <mover> <mi>u</mi> <mo>~</mo> </mover> <mo>=</mo> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <msub> <mover> <mi>q</mi> <mo>~</mo> </mover> <mn>1</mn> </msub> <mo>+</mo> <mi>&amp;eta;</mi> <mover> <mi>v</mi> <mo>~</mo> </mover> <mo>=</mo> <mn>0</mn> </mtd> </mtr> </mtable> </mfenced> <mo>&amp;DoubleRightArrow;</mo> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mo>(</mo> <msub> <mi>p</mi> <mn>1</mn> </msub> <mo>-</mo> <msub> <mover> <mi>p</mi> <mo>^</mo> </mover> <mn>1</mn> </msub> <mo>)</mo> <mo>+</mo> <mi>&amp;eta;</mi> <mo>(</mo> <mi>u</mi> <mo>-</mo> <mover> <mi>u</mi> <mo>^</mo> </mover> <mo>)</mo> <mo>=</mo> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mo>(</mo> <msub> <mi>q</mi> <mn>1</mn> </msub> <mo>-</mo> <msub> <mover> <mi>q</mi> <mo>^</mo> </mover> <mn>1</mn> </msub> <mo>)</mo> <mo>+</mo> <mi>&amp;eta;</mi> <mo>(</mo> <mi>v</mi> <mo>-</mo> <mover> <mi>v</mi> <mo>^</mo> </mover> <mo>)</mo> <mo>=</mo> <mn>0</mn> </mtd> </mtr> </mtable> </mfenced> </mrow>
    In formulaTwo equations, four unknown numbers, equation is unsolvable；Defined from η, change and turn Rotor speed realizes the identification of the magnetic bearing system axes of inertia to increase equation number；
    Axes of inertia identification mainly includes three steps：A) working rotor is in rotational speed omega1Under, obtain the same frequency components of Sensor Runout With the Fourier coefficient estimate of rotor unbalance valueWithB) change rotor speed, make magnetic suspension rotor work Make in rotational speed omega2Under, obtain the estimate under current rotating speedWithC) by the same frequency component under two rotating speeds Fourier coefficient estimate substitutes into above formula, has：
    <mrow> <mtable> <mtr> <mtd> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <mo>(</mo> <msub> <mi>p</mi> <mn>1</mn> </msub> <mo>-</mo> <msub> <mover> <mi>p</mi> <mo>^</mo> </mover> <mn>11</mn> </msub> <mo>)</mo> <mo>+</mo> <msub> <mi>&amp;eta;</mi> <mn>1</mn> </msub> <mo>(</mo> <mi>u</mi> <mo>-</mo> <msub> <mover> <mi>u</mi> <mo>^</mo> </mover> <mn>1</mn> </msub> <mo>)</mo> <mo>=</mo> <mn>0</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>(</mo> <msub> <mi>p</mi> <mn>1</mn> </msub> <mo>-</mo> <msub> <mover> <mi>p</mi> <mo>^</mo> </mover> <mn>12</mn> </msub> <mo>)</mo> <mo>+</mo> <msub> <mi>&amp;eta;</mi> <mn>2</mn> </msub> <mo>(</mo> <mi>u</mi> <mo>-</mo> <msub> <mover> <mi>u</mi> <mo>^</mo> </mover> <mn>2</mn> </msub> <mo>)</mo> <mo>=</mo> <mn>0</mn> </mrow> </mtd> </mtr> </mtable> </mfenced> </mtd> </mtr> <mtr> <mtd> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <mo>(</mo> <msub> <mi>q</mi> <mn>1</mn> </msub> <mo>-</mo> <msub> <mover> <mi>q</mi> <mo>^</mo> </mover> <mn>11</mn> </msub> <mo>)</mo> <mo>+</mo> <msub> <mi>&amp;eta;</mi> <mn>1</mn> </msub> <mo>(</mo> <mi>v</mi> <mo>-</mo> <msub> <mover> <mi>v</mi> <mo>^</mo> </mover> <mn>1</mn> </msub> <mo>)</mo> <mo>=</mo> <mn>0</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>(</mo> <msub> <mi>q</mi> <mn>1</mn> </msub> <mo>-</mo> <msub> <mover> <mi>q</mi> <mo>^</mo> </mover> <mn>12</mn> </msub> <mo>)</mo> <mo>+</mo> <msub> <mi>&amp;eta;</mi> <mn>2</mn> </msub> <mo>(</mo> <mi>v</mi> <mo>-</mo> <msub> <mover> <mi>v</mi> <mo>^</mo> </mover> <mn>2</mn> </msub> <mo>)</mo> <mo>=</mo> <mn>0</mn> </mrow> </mtd> </mtr> </mtable> </mfenced> </mtd> </mtr> </mtable> <mo>&amp;DoubleRightArrow;</mo> <mtable> <mtr> <mtd> <mrow> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msub> <mi>p</mi> <mn>1</mn> </msub> </mtd> </mtr> <mtr> <mtd> <mi>u</mi> </mtd> </mtr> </mtable> </mfenced> <mo>=</mo> <msup> <mi>A</mi> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <msub> <mi>B</mi> <mn>1</mn> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msub> <mi>q</mi> <mn>1</mn> </msub> </mtd> </mtr> <mtr> <mtd> <mi>v</mi> </mtd> </mtr> </mtable> </mfenced> <mo>=</mo> <msup> <mi>A</mi> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <msub> <mi>B</mi> <mn>2</mn> </msub> </mrow> </mtd> </mtr> </mtable> </mrow>
    In formulaWith
    Solving equation can obtain really with frequency component Fourier coefficient p1、q1, u and v, then the magnetic bearing system axes of inertia recognized.
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