CN107727088A - A kind of full active magnet bearing systems axes of inertia discrimination method based on nonlinear autoregressive - Google Patents

A kind of full active magnet bearing systems axes of inertia discrimination method based on nonlinear autoregressive Download PDF

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CN107727088A
CN107727088A CN201710955197.8A CN201710955197A CN107727088A CN 107727088 A CN107727088 A CN 107727088A CN 201710955197 A CN201710955197 A CN 201710955197A CN 107727088 A CN107727088 A CN 107727088A
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inertia
rotor
formula
displacement
displacement transducer
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张会娟
陈红梅
袁航
刘楠嶓
王伟生
钱进
姚艳艳
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Henan University of Technology
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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
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
    • G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
    • G05B13/04—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators
    • G05B13/042—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators in which a parameter or coefficient is automatically adjusted to optimise the performance

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Abstract

The invention discloses a kind of full active magnet bearing systems axes of inertia discrimination method based on nonlinear autoregressive, this method comprises the following steps：Initially set up the full active magnetic bearings dynamical model of rotor comprising rotor unbalance and displacement transducer harmonic noise；Next proposes a kind of nonlinear autoregressive rule and estimation rule, and the stability of system and the convergence of estimation parameter are demonstrated, ensure to estimate displacement transducer harmonic noise order harmonic component Fourier coefficient while magnetic suspension rotor axes of inertia Displacement Estimation value converges on zero；Then utilize variable speed strategy, increase displacement transducer harmonic noise with frequency component and rotor unbalance can identification, solve two Fourier coefficient values with frequency component, finally realize full active magnet bearing systems axes of inertia identification.The present invention only need a raising speed or reduction of speed just can the identification of the canbe used on line magnetic bearing axes of inertia, magnetic suspension rotor is rotated around the axes of inertia.

Description

A kind of full active magnet bearing systems axes of inertia identification based on nonlinear autoregressive Method
Technical field
The invention belongs to magnetic bearing system Vibration Active Control field, and in particular to one kind is based on nonlinear autoregressive Full active magnet bearing systems axes of inertia discrimination method, for recognize include rotor unbalance and sensor harmonic noise The full active magnet bearing systems axes of inertia of (Sensor Runout), make magnetic suspension rotor be rotated around the axes of inertia, so as to realize magnetic axis The harmonic vibration for holding system suppresses.
Background technology
Relative to traditional mechanical bearing, magnetic bearing can be realized between high speed rotor and stator by changing itself bearing It is contactless, there is high accuracy, high rotating speed, low-power consumption, the long-life, itself is with small vibration.In addition, most prominent excellent of magnetic bearing Point can exactly change itself damping, stiffness coefficient realizes Vibration Active Control, therefore be widely used in high-speed electric expreess locomotive, compression The high-precision occasions such as machine, molecular pump, magnetic suspension inertia actuator.Whether controllable according to bearing, magnetic bearing can be divided into actively Magnetic bearing and passive magnetic bearing.Control except motor one of magnetic suspension rotor is rotatably mounted to be outside one's consideration, remaining five freedom Degree has been required to magnetic bearing suspension bearing.Five frees degree of magnetic suspension rotor can not be realized due to relying solely on passive magnetic bearing Stable suspersion with active magnetic bearings, it is necessary to be combined.According to the number of magnetic suspension rotor controllable degrees of freedom, single freedom can be divided into Five kinds of degree, two-freedom, Three Degree Of Freedom, four-degree-of-freedom and five degree of freedom.Five degree of freedom magnetic bearing is generally referred to as full active magnetic Bearing.Full active magnet bearing systems have the advantages that control accuracy is high, stiffness and damping adjustability is high, strong antijamming capability, can be real Existing high-precision Vibration Active Control, it is widely used in the vibration such as magnetically levitated flywheel, magnetic suspension control torque gyroscope requirement height Inertia actuator in.
The essence of magnetic suspension inertia actuator Vibration Active Control is exactly magnetic suspension rotor is rotated around the axes of inertia, not right It is outer to transmit vibration.Therefore, the identification of the magnetic suspension rotor axes of inertia is the basis of magnetic bearing Vibration Active Control.Existing discrimination method Two classes can be divided into：One kind is direct identification method, and the same frequency that sensor exports when directly magnetic suspension rotor low speed is run is into being allocated as It is big for displacement transducer harmonic noise (Sensor Runout) same to frequency component, this kind of method Identification Errors；Another kind of is adaptive Identification algorithm is answered, but existing algorithm mainly realizes that rotor rotates around geometrical axis, can externally pass out sizable vibration, is only applicable In being directed at magnetic bearing system in high precision, magnetic suspension inertia actuator is not suitable for.
The content of the invention
The technical problem to be solved in the present invention is：Overcome the deficiencies in the prior art, there is provided one kind is based on nonlinear adaptive The full active magnet bearing systems axes of inertia discrimination method of control, magnetcisuspension is made by nonlinear adaptive algorithm and ART network rule Floating rotor rotates around the nominal axes of inertia, and picks out displacement transducer harmonic noise (Sensor Runout) order harmonic Component, then by changing the strategy of magnetic suspension rotor rotating speed, increase displacement transducer harmonic noise (Sensor Runout) is together Frequency component and rotor unbalance two with frequency amount can identification, finally realize full active magnetic bearings axes of inertia identification.In addition, this Nonlinear autoregressive rule in invention is solved using initial current during conventional linear algorithm is excessive and parameter convergence rate The problems such as slow.
The present invention solves the technical scheme that above-mentioned technical problem uses：It is a kind of based on the complete of nonlinear autoregressive Active magnet bearing systems axes of inertia discrimination method, it is characterised in that：Comprise the following steps：
(1) δ containing rotor unbalance is establishedmWith displacement transducer harmonic noise hsrFull active magnet bearing systems rotor dynamic Learn model；
In formula, m is the quality of magnetic suspension rotor；χIFor the magnetic suspension rotor center of inertia displacement arrow under magnetic bearing coordinate system Amount；KiAnd KhRespectively current stiffness coefficient and displacement rigidity coefficient matrix；Remember magnetic suspension rotor inertia four passages of Axial and radial Current stiffness coefficient is identical with displacement rigidity coefficient, then Ki=kiI4×4, Kh=khI4×4, I4×4For quadravalence unit matrix；GcAnd Gw The respectively transmission function of magnetic bearing controller and power amplifier；It is magnetic suspension rotor geometric center displacement by magnetic bearing Transformational relation matrix of the coordinate system to sensor coordinate system；kadFor the multiplication factor of a/d converter；
(2) nonlinear autoregressive rule and estimation rule design
A kind of nonlinear autoregressive algorithm is designed on the basis of step (1), the algorithm includes two parts：(1) it is non- Linear adaption control law, with the axes of inertia Displacement Estimation value of magnetic suspension rotorTo control variable, ensureConverge to zero； (2) ART network is restrained, and estimates the Fourier of rotor unbalance and displacement transducer harmonic noise (Sensor Runout) respectively Coefficient matrix ΦδAnd Φs.The stability of closed-loop system is proved using Lyapunov stability principles and estimates the convergence of parameter；
(3) variable speed realizes that the magnetic bearing system axes of inertia recognize
Magnetic suspension rotor, using the nonlinear adaptive algorithm of step (2), obtains difference under the conditions of two different rotating speeds Displacement transducer harmonic noise with frequency component and rotor unbalance value Fourier coefficient estimate.
Based on above-mentioned, step (1) concretely comprises the following steps：
Magnetic suspension rotor kinetic model when establishing the magnetic suspension rotor axes of inertia near equilbrium position：
M is the quality of magnetic suspension rotor in formula (2)；χIAnd χgMagnetic suspension rotor inertia respectively under magnetic bearing coordinate system The center displacement vector geometric center displacement vector；ImFor coil current vector；KiAnd KhRespectively current stiffness coefficient and displacement Stiffness coefficient matrix；Remember that the current stiffness coefficient of magnetic suspension rotor inertia four passages of Axial and radial is identical with displacement rigidity coefficient, Then Ki=kiI4×4, Kh=khI4×4, I4×4For quadravalence unit matrix；
Magnetic suspension rotor center of inertia displacement χ under magnetic bearing coordinate systemIWith geometric center displacement χgBetween relation be：
χg=χI+δm (3)
In formula (3)For the rotor unbalance vector under magnetic bearing coordinate system；For generalized coordinates system to magnetic The transition matrix of bearing coordinate system；δIFor the rotor unbalance value under generalized coordinates system；
By δmSine and cosine and form are deployed, and are write as matrix form：
Wherein
Φδ=[ua va ub vb] (6)
In formula (5) (6)And ΦδRespectively rotor unbalance value δmTrigonometric function matrix and Fourier coefficient Vector, Ω are turning frequently for magnetic suspension rotor；
Include multiple-harmonic noise hsrDisplacement transducer output signal χsFor：
In formula (7)Conversion for the displacement of magnetic suspension rotor geometric center by magnetic bearing coordinate system to sensor coordinate system Relational matrix；hsrFor the displacement transducer harmonic noise under sensor coordinate system：
S in formula (8)aiAnd sbiThe respectively amplitude of the ith harmonic component of a, b both ends displacement transducer harmonic noise； ξasiAnd ξbsiThe respectively initial phase of the ith harmonic component of displacement transducer harmonic noise；N is total harmonic number；
By hsrBeing write as matrix form has：
Φs=[Φs1 … Φsn] (11)
P in formula (10) (11)sAnd ΦsThe respectively trigonometric function matrix and Fourier coefficient of displacement transducer harmonic noise Vector；PsiAnd ΦsiRespectively the trigonometric function matrix of the ith harmonic component of displacement transducer harmonic noise and Fourier system Number vector；
Coil current ImExpression formula on displacement transducer output signal is：
K in formula (12)adFor the multiplication factor of a/d converter, GcAnd GwRespectively magnetic bearing controller and power amplifier Transmission function.
Based on above-mentioned, nonlinear autoregressive algorithm is designed as in step (2)：
ρ is normal number in formula (13), and its value size decides the size and convergence of algorithm speed of initial current；KamFor The equieffective ratio coefficient of power amplification system；ForFirst derivative；E be withWithRelated weight function：
A and b is normal number in formula (14), and its value determines the receipts of control electric current initial size and Fourier coefficient estimate Hold back speed；
According to e definition, the positive definite matrix Ξ in nonlinear autoregressive rule is expressed as：
In formula (15)WithRespectivelyFour channel components of radial direction；
Rotor unbalance δmWith displacement transducer harmonic noise hsrFourier coefficient ART network rule separately design for：
In formula (16) (17) WithRespectively trigonometric function matrix PdAnd PδSecond dervative；WithRespectively displacement transducer harmonic noise (Sensor Runout) each harmonic component and the Fourier coefficient evaluated error of rotor unbalance value；WithRespectively displacement transducer is humorous The first derivative of each harmonic component of ripple noise (Sensor Runout) and the Fourier coefficient evaluated error of rotor unbalance value；WithRespectively adaptive positive definite gain matrix.
Based on above-mentioned, the concrete methods of realizing of step (3) is, when the center of inertia Displacement Estimation value level off to zero when, displacement Sensor harmonic noise meets with the Fourier coefficient estimate of frequency component and rotor unbalance value：
OrderAndFormula (18) is rewritten as：
In formula (19)For Φss1Evaluated error, be defined as
By Prδ=m Ω2Pδ, Pδ=Pd1, formula (19) expands into：
DefinitionDefined by the evaluated error of Fourier coefficient, (20) formula is rewritten as：
If magnetic suspension rotor rotating speed is respectively Ω1And Ω2, it is correspondingRespectively：
Magnetic suspension rotor rotating speed distinguishes Ω1And Ω2When, obtain different same frequency Fourier coefficient stable state estimates WithThen obtain four equation groups：
In formula
Φ is solved according to (23) formulaδAnd Φss, then the same frequency component Fourier coefficient Φ of displacement transducer harmonic noises1 For：
Solve (24) equation and can obtain displacement transducer harmonic noise with the Fourier of frequency component and rotor unbalance system Number actual value.
The present invention principle be：Rotor unbalance and displacement transducer harmonic noise (Sensor Runout) are magnetic bearings Two primary oscillation sources of system, because both presence cause magnetic suspension rotor to be rotated around non-inertial axle so that the axes of inertia are not It can directly can survey.Directly measurable in magnetic bearing control system is coil current and displacement transducer signal.Wherein displacement sensing Not only include rotor unbalance value relevant information, in addition to displacement transducer harmonic noise (Sensor in device output signal Runout relevant information), and both include and turn frequently related same frequency component to rotor.For permanent magnet bias mixing magnetic axis Hold system, can only by changing the method for rotor speed, increase by two with frequency component can identification, so as to realize that magnetic suspension turns The identification of the sub- axes of inertia.
The present invention has prominent substantive distinguishing features and marked improvement compared with the prior art, specifically：
1) it present invention can be suitably applied to the axes of inertia identification of four-degree-of-freedom and five degree of freedom magnetic bearing system；
2) instant invention 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；
3) instant invention overcomes initial control electric current caused by conventional linear adaptive algorithm is excessive and parameter identification convergence The shortcomings of speed is slow, being restrained using nonlinear autoregressive improves algorithm performance.
Brief description of the drawings
Fig. 1 is a kind of full active magnet bearing systems axes of inertia discrimination method based on nonlinear autoregressive of the present invention Implementation process figure.
Fig. 2 is the structural representation of full Active Magnetic Bearings Control System.
Fig. 3 is the full active magnet bearing systems schematic diagram containing rotor unbalance and displacement transducer harmonic noise.
Fig. 4 is the magnetic bearing system axes of inertia identification principle figure based on nonlinear autoregressive.
Fig. 5 is that displacement transducer harmonic noise recognizes flow chart with frequency component and rotor unbalance.
Embodiment
The present invention will be further described for implementation steps below in conjunction with the accompanying drawings and specifically.
A kind of as shown in figure 1, full active magnet bearing systems axes of inertia identification based on nonlinear autoregressive of the present invention Method, its implementation process are：Initially set up comprising rotor unbalance and displacement transducer harmonic noise (Sensor Runout) Full active magnet bearing systems dynamical model of rotor；Its secondary design nonlinear autoregressive is restrained and estimation rule, and proof system Stability and estimation parameter convergence；Then by changing the strategy of rotor speed, the same frequency component of magnetic bearing system is increased Can identification, realize displacement transducer harmonic noise (Sensor Runout) with the identification of frequency component and rotor unbalance, most The identification of the magnetic bearing system axes of inertia is realized eventually.
Specific implementation step of the present invention is as follows：
(1) the full active magnetic bearings containing rotor unbalance and displacement transducer harmonic noise (Sensor Runout) are established System rotor kinetic model
The axial displacement of the magnetic suspension rotor axes of inertia directly can detect to obtain by shaft position sensor, therefore the axes of inertia The main displacement considered radially in four channel directions of identification, its structural representation is as shown in Fig. 2, magnetic suspension rotor work Gyroscopic effect can be neglected at low speeds, four passages mutually decouple.When magnetic suspension rotor is operated near equilbrium position Kinetic model can be reduced to：
M is the quality of magnetic suspension rotor in formula (1)；kiax、kiay、kibxAnd kibyRespectively tetra- passages of ax, ay, bx and by Current stiffness coefficient；khax、khay、khbxAnd khbyThe respectively displacement rigidity coefficient of tetra- passages of ax, ay, bx and by；icax、 icay、icbxAnd icbyThe coil current of respectively four passages；(xIa,yIa)、(xIb,yIb) it is respectively a, b under magnetic bearing coordinate system The center of inertia displacement at both ends；(xga,yga)、(xgb,ygb) be respectively a, b both ends under magnetic bearing coordinate system geometric center displacement.
Formula (1) is rewritten as matrix form：
χ in formula (2)I=[xIa yIa xIb yIb]TAnd χg=[xga yga xgb ygb]TRespectively under magnetic bearing coordinate system Magnetic suspension rotor center of inertia displacement vector and geometric center displacement vector；Im=[icax icay icbx icby]TFor coil current Vector；Ki=diag ([kiax kiay kibx kiby]) and Kh=diag ([khax khay khbx khby]) it is respectively current stiffness system Number and displacement rigidity coefficient matrix.It has been generally acknowledged that the current stiffness coefficient and displacement rigidity coefficient of four passages are identicals, i.e., kiax=kiay=kibx=kiby=ki, khax=khay=khbx=khby=kh。
Due to the presence of rotor unbalance, the magnetic suspension rotor center of inertia displacement χ under magnetic bearing coordinate systemIIn geometry Heart displacement χgIn the presence of certain deviation, relation between the two is：
χg=χI+δm (3)
δ in formulamFor the rotor unbalance vector under magnetic bearing coordinate system.According to generalized coordinates system and magnetic bearing coordinate system it Between relation, δm=[δmax δmay δmbx δmby]TIt is represented by：
In formulaTransition matrix for generalized coordinates system to magnetic bearing coordinate system；δIFor the rotor under generalized coordinates system not Aequum, both are expressed as：
L in formula (5) (6)mRepresent radial direction magnetic bearing center to the distance of generalized coordinates system origin；λ and θ is respectively magnetic suspension Rotor static unbalance and the amplitude of unbalance dynamic；It is respectively the initial phase of magnetic suspension rotor static unbalance and unbalance dynamic with ψ Position；Ω is turning frequently for magnetic suspension rotor.
Formula (5) and formula (6) are substituted into formula (4) to obtain：
Sine and cosine in formula (7) and form are deployed, and write as matrix form：
Order
Φδ=[ua va ub vb] (10)
In formula (9) (10)And ΦδRespectively rotor unbalance value δmTrigonometric function matrix and Fourier system Number vector.It can be seen that by formula (9)I4×4For quadravalence unit matrix.
Then δmIt can be reduced to：
If the estimate of rotor unbalance value Fourier coefficient matrix isIts evaluated error may be defined as：
Therefore, the rotor unbalance estimate under magnetic bearing coordinate system is：
Due to displacement transducer harmonic noise (Sensor Runout), displacement transducer output not only turns comprising magnetic suspension Sub- geometric center displacement relevant information, also include multiple-harmonic noise hsr, therefore the output signal χ of displacement transducersFor：
In formula (16)Conversion for the displacement of magnetic suspension rotor geometric center by magnetic bearing coordinate system to sensor coordinate system Relational matrix, and be expressed as：
L in formulasRepresent displacement transducer detection faces geometric center to the distance of generalized coordinates system origin；ksRepresent that displacement passes Sensor multiplication factor.
H in formula (16)srFor the displacement transducer harmonic noise (Sensor Runout) under sensor coordinate system, and represent For：
S in formula (18)aiAnd sbiRespectively a, b both ends displacement transducer displacement transducer harmonic noise (Sensor Runout the amplitude of ith harmonic component)；ξasiAnd ξbsiRespectively displacement transducer harmonic noise (Sensor Runout) Ith harmonic component initial phase；N is total harmonic number.
By hsrBeing write as matrix form has：
Φs=[Φs1 … Φsn] (22)
Φsi=[pai qai pbi qbi] (23)
pai=sai sinξasi, qai=sai cosξasi, pbi=sbi sinξbsi, qbi=sbi cosξbsi (24)
P in formula (19)~(24)sAnd ΦsThe respectively trigonometric function of displacement transducer harmonic noise (Sensor Runout) Matrix and Fourier coefficient vector；PsiAnd ΦsiThe ith of respectively displacement transducer harmonic noise (Sensor Runout) is humorous Trigonometric function matrix and the Fourier coefficient vector of wave component；pai、qai、pbiAnd qbiFor ΦsiVector element.
If the Fourier coefficient Matrix Estimation value of displacement transducer harmonic noise (Sensor Runout) isIt is estimated Error may be defined as：
Therefore, displacement transducer harmonic noise (Sensor Runout), geometric center displacement and center of inertia Displacement Estimation Value is respectively：
In formula (26)~(28)Transition matrix for sensor coordinate system to magnetic bearing coordinate system；WithThe respectively evaluated error of rotor unbalance and displacement transducer harmonic noise (Sensor Runout), and be respectively defined as：
Coil current ImExpression formula on displacement transducer output signal is：
K in formula (31)adFor the multiplication factor of a/d converter；GcAnd GwRespectively magnetic bearing controller and power amplifier Transmission function.Because the identification of the magnetic bearing system axes of inertia realizes that magnetic bearing power amplification system can be equivalent to ratio at low speeds Link, then Gw=KamI4×4=diag ([kamax kamay kambx kamby]), kamax、kamay、kambxAnd kambyRespectively four logical The equieffective ratio coefficient of road power amplification system.
The kinetic model of magnetic suspension rotor is the expression formula on the displacement of the magnetic suspension rotor center of inertia, magnetic bearings control Device is by reference of displacement transducer output signal to carry out that control signal is calculated, and displacement rigidity power is with magnetic bearing coordinate system The displacement of lower rotor part geometric center is reference.Therefore formula (3), formula (16), formula (31) are substituted into formula (2), it is uneven can must includes rotor Weigh and the magnetic suspension rotor kinetic model of displacement transducer harmonic noise (Sensor Runout) is：
The then full active magnetic bearings control comprising rotor unbalance and displacement transducer harmonic noise (Sensor Runout) Systematic schematic diagram is as shown in Figure 3.
The identification of the magnetic bearing system axes of inertia is exactly to obtain magnetic suspension rotor center of inertia displacement χI, by formula (3) and formula (16) understand, the identification key of the axes of inertia is identification rotor unbalance δmWith displacement transducer harmonic noise (Sensor Runout)hsr。
(2) nonlinear autoregressive rule and estimation rule design
In order to realize the identification of the magnetic bearing system axes of inertia, the present invention proposes a kind of non-thread on the basis of step (1) Property adaptive control algorithm, the algorithm mainly include two parts：1) nonlinear autoregressive is restrained, with the inertia of magnetic suspension rotor The center displacement estimateTo control variable, not only to suppress rotor unbalance and displacement transducer harmonic noise (Sensor Runout multiple-harmonic current caused by), also same-frequency displacement rigidity power caused by rotor unbalance is compensated, finally made Converge to zero；2) ART network is restrained, and estimates rotor unbalance and displacement transducer harmonic noise (Sensor Runout) respectively Fourier coefficient matrix ΦδAnd Φs.Rotor unbalance and displacement transducer harmonic wave based on nonlinear autoregressive algorithm Noise (Sensor Runout) identification principle figure is as shown in Figure 4.Nonlinear autoregressive rule is designed as in figure：
ρ is normal number in formula (33), and its value size decides the size and convergence of algorithm speed of initial current.E is WithWithRelated weight function.
In order to overcome initial current caused by conventional linear weight function excessive, the shortcomings of convergence rate is slow, the present invention carries A kind of nonlinear weight value function is gone out：
A and b is normal number in formula (34), and its value determines the receipts of control electric current initial size and Fourier coefficient estimate Hold back speed.Therefore, the positive definite diagonal matrix Ξ in formula (33) is represented by：
In addition, in formula (33)Purpose of design is to compensate for displacement rigidity power caused by rotor unbalance.
The Fourier coefficient ART network of rotor unbalance and displacement transducer harmonic noise (Sensor Runout) is restrained Separately design for：
Γs=diag (τs1 τs1 τs1 τs1 … τsn τsn τsn τsn) (38)
Γδ=diag (τδ τδ τδ τδ) (39)
In formula (36)~(39)WithRespectively adaptive positive definite gain matrix, its diagonal entry decide the stability of system.
In order to prove the magnetic bearing system stability based on nonlinear autoregressive, following Lyapunov functions are chosen：
In formula (40)Δδii= τδmΩ2, i=1,2,3,4；
In order to ensure V ＞ 0, ΔsAnd ΔδThe selection of diagonal entry should meet：
0 ＜ (Δssii+Δδii) ＜ 1, i=1,2,3,4 (41)
Due toV is asked Lead：
From formula (42)For bear semidefinite, according to Barbalet theorems, magnetic bearing system be it is asymptotically stable, therefore, As t → ∞,WithZero is all converged on, if willBe to be considered as the nominal principal axis of inertia at zero, then whenConverge on zero When, magnetic suspension rotor rotates around the nominal principal axis of inertia；
As t → ∞, e → 0,AndWithAll converge on zero.Therefore, rotor is uneven The Fourier coefficient estimate of weighing apparatus and displacement transducer harmonic noise (Sensor Runout)WithIt will converge on a certain normal Value；
As t → ∞, can be obtained by formula (28), formula (32) and formula (33)：
During due to t → ∞,WithZero is all converged on, then formula (43) can be reduced to：
According to the orthogonal property of trigonometric function, by PrsIt is split as same frequency part Ps1With higher hamonic wave part Psi, then formula (44) It is rewritable to be：
OrderNormal number φ then be present2≥φ1＞ 0, the time is normal Number T0, make YsiMeet：
Therefore YsiEncouraged for continuation.As t → ∞,I.e. Show the Fourier coefficient estimation of displacement transducer harmonic noise (Sensor Runout) higher harmonic components Value will converge on actual value.
In formula (45)Continuation excitation condition is unsatisfactory for, thereforeWith Zero can not be converged to, i.e., the Fourier coefficient estimate with frequency composition not converged arrives actual value.In order to realize the magnetic bearing axes of inertia Identification, it is necessary to further identification two with frequency component Fourier coefficients.
(3) variable speed realizes that the magnetic bearing system axes of inertia recognize
Order
BecauseThen formula (45) can be exchanged into：
In formulaFor Φss1Evaluated error, be defined as
Because Prδ=m Ω2Pδ, Pδ=Pd1, formula (49) is deployable to be：
DefinitionDefined and formula (50) can be rewritten as by the evaluated error of Fourier coefficient：
From formula (51), eight unknown numbers, four equations are unsolvable, if it is desired to which solving equation needs to changeFor 5-freedom permanent magnetism off-set hybrid magnetic bearing, the identification of the magnetic bearing system axes of inertia can be realized by changing rotor speed, distinguished Knowledge process is as shown in Figure 5.
Assuming that magnetic suspension rotor rotating speed is respectively Ω1And Ω2, it is correspondingRespectively：
Rotor is set to be separately operable in Ω1And Ω2Under, it can obtain different same frequency Fourier coefficient stable state estimates WithIt then can obtain four equation groups：
In formula
Φ is solved according to formula (53)ss, then in same frequency component Fu of displacement transducer harmonic noise (Sensor Runout) Leaf system number Φs1For：
By solve above-mentioned equation can obtain displacement transducer harmonic noise (Sensor Runout) with frequency component and turn The unbalanced Fourier coefficient actual value of son.The identification of the magnetic bearing system axes of inertia can be finally realized with reference to step (2).
The content not being described in detail in description of the invention belongs to prior art known to this professional domain technical staff.
Finally it should be noted that:The above embodiments are merely illustrative of the technical scheme of the present invention and are not intended to be limiting thereof；To the greatest extent The present invention is described in detail with reference to preferred embodiments for pipe, those of ordinary skills in the art should understand that：Still The embodiment of the present invention can be modified or equivalent substitution is carried out to some technical characteristics；Without departing from this hair The spirit of bright technical scheme, it all should cover among the claimed technical scheme scope of the present invention.

Claims (4)

  1. A kind of 1. full active magnet bearing systems axes of inertia discrimination method based on nonlinear autoregressive, it is characterised in that：Bag Include following steps：
    (1) δ containing rotor unbalance is establishedmWith displacement transducer harmonic noise hsrFull active magnet bearing systems rotor dynamics mould Type；
    M is the quality of magnetic suspension rotor in formula (1)；χIFor the magnetic suspension rotor center of inertia displacement vector under magnetic bearing coordinate system； KiAnd KhRespectively current stiffness coefficient and displacement rigidity coefficient matrix；Remember the electricity of magnetic suspension rotor inertia four passages of Axial and radial It is identical with displacement rigidity coefficient to flow stiffness coefficient, then Ki=kiI4×4, Kh=khI4×4, I4×4For quadravalence unit matrix；GcAnd GwPoint Not Wei magnetic bearing controller and power amplifier transmission function；It is the displacement of magnetic suspension rotor geometric center by magnetic axis landing Transformational relation matrix of the mark system to sensor coordinate system；kadFor the multiplication factor of a/d converter；
    (2) nonlinear autoregressive rule and estimation rule design
    A kind of nonlinear autoregressive algorithm is designed on the basis of step (1), the algorithm includes two parts：1) it is non-linear from Suitable solution is restrained, with the axes of inertia Displacement Estimation value of magnetic suspension rotorTo control variable, ensureZero is converged to, makes magnetcisuspension Floating rotor rotates around the nominal principal axis of inertia；2) ART network is restrained, and estimates that rotor unbalance and displacement transducer harmonic wave are made an uproar respectively The Fourier coefficient matrix Φ of sound (Sensor Runout)δAnd Φs；Closed-loop system is proved using Lyapunov stability principles The convergence of stability and parameter；
    (3) variable speed realizes that the magnetic bearing system axes of inertia recognize
    The identification of full active permanent magnet biased hybrid magnetic bearing system inertia axle is realized by variable speed strategy, magnetic suspension rotor is two The nonlinear adaptive algorithm that step (2) proposes is realized under the conditions of individual different rotating speeds, different displacement transducer harmonic waves is obtained and makes an uproar Sound with the Fourier coefficient estimate of frequency component and rotor unbalance value, improve same frequency component can identification, realize that displacement passes Sensor harmonic noise finally realizes full active magnet bearing systems axes of inertia identification with the identification of frequency component and rotor unbalance value.
  2. 2. the full active magnet bearing systems axes of inertia identification side according to claim 1 based on nonlinear autoregressive Method, it is characterised in that step (1) concretely comprises the following steps：
    Magnetic suspension rotor kinetic model when establishing the magnetic suspension rotor axes of inertia near equilbrium position:
    M is the quality of magnetic suspension rotor in formula (2)；χIAnd χgThe magnetic suspension rotor center of inertia respectively under magnetic bearing coordinate system Displacement vector and geometric center displacement vector；ImFor coil current vector；KiAnd KhRespectively current stiffness coefficient and displacement rigidity Coefficient matrix；Remember that the current stiffness coefficient of magnetic suspension rotor inertia four passages of Axial and radial is identical with displacement rigidity coefficient, then Ki =kiI4×4, Kh=khI4×4, I4×4For quadravalence unit matrix；
    Magnetic suspension rotor center of inertia displacement χ under magnetic bearing coordinate systemIWith geometric center displacement χgBetween relation be：
    χg=χI+δm (3)
    In formula (3)For the rotor unbalance vector under magnetic bearing coordinate system；For generalized coordinates system to magnetic bearing The transition matrix of coordinate system；δIFor the rotor unbalance value under generalized coordinates system；
    By δmSine and cosine and form are deployed, and are write as matrix form：
    Wherein
    Φδ=[ua va ub vb] (6)
    In formula (5) (6)And ΦδRespectively rotor unbalance value δmTrigonometric function matrix and Fourier coefficient to Amount, Ω are turning frequently for magnetic suspension rotor；
    Include multiple-harmonic noise hsrDisplacement transducer output signal χsFor：
    In formula (7)Transformational relation square for the displacement of magnetic suspension rotor geometric center by magnetic bearing coordinate system to sensor coordinate system Battle array；hsrFor the displacement transducer harmonic noise under sensor coordinate system：
    S in formula (8)aiAnd sbiThe respectively amplitude of the ith harmonic component of a, b both ends displacement transducer harmonic noise；ξasiWith ξbsiThe respectively initial phase of the ith harmonic component of displacement transducer harmonic noise；N is total harmonic number；
    By hsrBeing write as matrix form has：
    Φs=[Φs1 … Φsn] (11)
    P in formula (9) (10) (11)sAnd ΦsRespectively the trigonometric function matrix of displacement transducer harmonic noise and Fourier coefficient to Amount；PsiAnd ΦsiThe respectively trigonometric function matrix and Fourier coefficient of the ith harmonic component of displacement transducer harmonic noise Vector；
    Coil current ImExpression formula on displacement transducer output signal is：
    K in formula (12)adFor the multiplication factor of a/d converter, GcAnd GwThe respectively transmission of magnetic bearing controller and power amplifier Function.
  3. 3. the full active magnet bearing systems axes of inertia identification side according to claim 1 based on nonlinear autoregressive Method, it is characterised in that：Nonlinear autoregressive algorithm is designed as in step (2)：
    ρ is normal number in formula (13), and its value size decides the size and convergence of algorithm speed of initial current；KamFor power amplifier The equieffective ratio coefficient of system；ForFirst derivative；E be withWithRelated weight function：
    A and b is normal number in formula (14), and its value determines the convergence speed of control electric current initial size and Fourier coefficient estimate Degree；
    According to e definition, the positive definite matrix Ξ in nonlinear autoregressive rule is expressed as：
    In formula (15)WithRespectivelyFour channel components of radial direction；
    Rotor unbalance δmWith displacement transducer harmonic noise hsrFourier coefficient ART network rule separately design for：
    In formula (16) (17) With Respectively trigonometric function matrix PdAnd PδSecond dervative；WithRespectively displacement transducer harmonic noise (Sensor Runout) each harmonic component and the Fourier coefficient evaluated error of rotor unbalance value；WithRespectively displacement transducer is humorous The first derivative of each harmonic component of ripple noise (Sensor Runout) and the Fourier coefficient evaluated error of rotor unbalance value；WithRespectively adaptive positive definite gain matrix.
  4. 4. the full active magnet bearing systems axes of inertia identification side according to claim 1 based on nonlinear autoregressive Method, it is characterised in that step (3) is same using variable speed strategy increase displacement transducer harmonic noise on the basis of step (2) Frequency component and rotor unbalance value Fourier coefficient can identification, finally realize that the full active magnet bearing systems principal axis of inertia is distinguished Know；
    Based on step (2) propose nonlinear adaptive algorithm, when the center of inertia Displacement Estimation value level off to zero when, displacement sensing Device harmonic noise meets with the Fourier coefficient estimate of frequency component and rotor unbalance value：
    OrderAndFormula (18) is rewritten as：
    In formula (19)For Φss1Evaluated error, be defined as
    Due to Prδ=m Ω2Pδ, Pδ=Pd1, (19) formula expands into：
    DefinitionDefined by the evaluated error of Fourier coefficient, formula (20) is rewritten as：
    If magnetic suspension rotor rotating speed is respectively Ω1And Ω2, corresponding θ is respectively：
    Magnetic suspension rotor rotating speed distinguishes Ω1And Ω2When, obtain different same frequency Fourier coefficient stable state estimates WithThen obtain four equation groups：
    In formula (23)
    Φ is solved according to (23) formulaδAnd Φss, then the same frequency component Fourier coefficient Φ of displacement transducer harmonic noises1For：
    It is true with the Fourier coefficient of frequency component and rotor unbalance that solution (24) equation can obtain displacement transducer harmonic noise Real value.
CN201710955197.8A 2017-10-13 2017-10-13 A kind of full active magnet bearing systems axes of inertia discrimination method based on nonlinear autoregressive Pending CN107727088A (en)

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CN108828951A (en) * 2018-07-20 2018-11-16 南京航空航天大学 Magnetic suspension bearing multi-model robust switching undisturbed control method
CN109062274A (en) * 2018-09-03 2018-12-21 河南工业大学 A kind of magnetic bearing oscillatory torque suppressing method based on complex variable finite-dimensional repetitive control
CN109086533A (en) * 2018-08-10 2018-12-25 国家电网有限公司 A kind of three-phase transformer D.C. magnetic biasing frequency-domain calculations method
CN110333667A (en) * 2019-08-14 2019-10-15 大连海事大学 A kind of Simulation of ship motion and control method based on non-linear new breath identification model
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CN108828951A (en) * 2018-07-20 2018-11-16 南京航空航天大学 Magnetic suspension bearing multi-model robust switching undisturbed control method
CN109086533A (en) * 2018-08-10 2018-12-25 国家电网有限公司 A kind of three-phase transformer D.C. magnetic biasing frequency-domain calculations method
CN109086533B (en) * 2018-08-10 2023-04-18 国家电网有限公司 Three-phase transformer direct-current magnetic bias frequency domain calculation method
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CN111220061A (en) * 2019-04-26 2020-06-02 上海电机学院 Fault diagnosis method for magnetic bearing displacement sensor
CN110333667A (en) * 2019-08-14 2019-10-15 大连海事大学 A kind of Simulation of ship motion and control method based on non-linear new breath identification model
CN110848256A (en) * 2019-12-16 2020-02-28 常州工学院 Method for compensating interference force borne by rotor in magnetic suspension bearing system in real time
CN112729338A (en) * 2020-12-23 2021-04-30 北京航空航天大学 Magnetic suspension turntable with fifteen degrees of freedom applied to semi-physical simulation platform

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