CN106289208A - A kind of magnetic bearing system axes of inertia discrimination method based on nonlinear adaptive algorithm - Google Patents

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 propose a kind of nonlinear autoregressive rule and estimate rule, it is ensured that while magnetic suspension rotor center of inertia Displacement Estimation value goes to zero, the Fourier coefficient of Sensor Runout higher harmonic components can be estimated again；Then by changing the strategy of rotor speed, the observability degree of system is increased, it is achieved Sensor Runout, with frequency component and the identification of rotor unbalance value, i.e. realizes the identification of the axes of inertia；Finally revise in adaptive algorithm with frequency component Fourier coefficient, exactly suppression multiple-harmonic current and compensation displacement rigidity power, it is achieved 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 identification Comprise rotor unbalance and the magnetic bearing system axes of inertia of sensor harmonic noise (Sensor Runout), it is achieved magnetic suspension is used to Property actuator multiple-harmonic vibration suppression, make magnetic suspension inertia actuator meet following " super quiet super steady " satellite platform to pole The requirement of micro-vibration, belongs to magnetic bearing system Vibration Active Control field.

Background technology

Along with the development of the ultrahigh resolution satellites such as high-resolution earth observation, survey of deep space, Space laser communications, super quiet Two important indicators weighing satellite platform performance are become with agility.Super static stability can be to ensure that high-resolution payload becomes picture element The key factor of amount, quick performance is to solve high-resolution imaging and cover this technology shortcut to contradiction on a large scale.More Carry out the highest resolution index more and more higher to the pointing accuracy of satellite platform and the requirement of attitude stability, to spaceborne movable part Vibration caused by part is more and more sensitive.Satellite Vibration is broadly divided into two big classes, and a class is the low-frequency high-amplitude vibration of a few to tens of Hz Dynamic, this kind of vibration can be suppressed by satellite gravity anomaly；The vibration of another kind of frequency low-amplitude is main by flywheel, control moment The inertia actuator such as gyro cause, and this kind of vibration cannot be suppressed by gesture stability algorithm, are to affect satellite to put down The technical bottleneck of platform level of vibration.

Suppression to inertia actuator vibration mainly has isolation mounting and magnetic suspension Vibration Active Control two kinds.Mechanical type Inertia actuator generally use vibration isolation technique to suppress dither, but frequency low-amplitude vibration is simply converted by isolation mounting Become low-frequency high-amplitude vibration, from source, do not eliminate vibration.One important advantage of magnetic suspension inertia actuator is to have actively The ability of vibration suppression, its essence is to realize rotor by the control power of regulation magnetic bearing to rotate around the principal axis of inertia, fundamentally Eliminate the dither of high speed rotor.Owing to processing the machineries such as alignment error, material is uneven, electronic devices and components are non-linear and electricity Gas non-ideal characteristic, magnetic suspension inertia actuator also exists the vibration source such as rotor unbalance, Sensor Runout, thus passes Pass out multiple-harmonic vibration.At present, magnetic bearing system Vibration Active Control focuses primarily upon the research of rotor unbalance vibration control, The magnetic bearing system Vibration Active Control comprising rotor unbalance and Sensor Runout is studied less.Due to displacement sensing The same frequency composition of device output comprises Sensor Runout with frequency component and rotor unbalance, when carrying out displacement rigidity and compensating only Need to compensate the impact of rotor unbalance, it is therefore desirable to carry out Sensor Runout with frequency component and the identification of rotor unbalance, The i.e. identification of the axes of inertia.Existing discrimination method can be divided into two classes: a class is direct identification method, directly by magnetic suspension rotor low speed During operation, the same frequency composition of sensor output is as the same frequency component of Sensor Runout, and this kind of method Identification Errors is big；Another Class is Adaptive Identification algorithm, but existing algorithm mainly realizes rotor and rotates around geometrical axis, can externally pass out sizable shaking Dynamic, it is only applicable to high accuracy aligned magnetic bearing arrangement, is not suitable for magnetic suspension inertia actuator.

Summary of the invention

The technology of the present invention solves problem: overcome the deficiencies in the prior art, and invention is a kind of calculates 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, improves used Property axle identification precision, it is achieved magnetic suspension rotor rotates around the axes of inertia, suppression magnetic bearing system multiple-harmonic vibration.Additionally, the present invention In nonlinear autoregressive rule solve that initial current when utilizing conventional linear algorithm is excessive and parameter convergence rate is slow etc. Problem.

The technical solution of the present invention is: 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, analyzes vibration and produces Mechanism and existence form；Secondly invention a kind of nonlinear autoregressive rule and estimation rule, in ensureing magnetic suspension rotor inertia While the estimated value of heart displacement converges on zero, it is achieved rotor unbalance and Sensor Runout each harmonic component Fourier system The estimation of number；Then by changing the strategy of rotating speed, the observability degree with frequency component is increased, it is achieved Sensor Runout is with frequency Component and the identification of rotor unbalance value, estimate the axes of inertia；Finally realize the multiple-harmonic of magnetic suspension inertia actuator actively Vibration suppression.The present invention specifically comprises the following steps that

(1) set up containing rotor unbalance and the magnetic bearing system kinetic model of Sensor Runout

Two-freedom magnetic bearing system, x-axis and y-axis two passage are mutually decoupled.Assume the displacement rigidity of x-axis and y-axis Coefficient is identical with current stiffness coefficient, when magnetic suspension rotor moves near equilbrium position, and its linearizing kinetics equation For:

In formula, m is the quality of magnetic suspension rotor；k_iAnd k_hThe current stiffness coefficient and the displacement that are respectively magnetic bearing system are firm Degree coefficient；I_c=[i_cx, i_cy]^T, i_cxAnd i_cyIt is respectively x-axis and y-axis magnetic bearing coil controls electric current；χ_I=[x_I, y_I]^T, x_IAnd y_I It is respectively center of inertia displacement in x-axis and y-axis direction,For χ_ISecond dervative；χ_g=[x_g, y_g]^T, x_gAnd y_gIt is respectively Geometric center displacement in x-axis and y-axis direction.

Impact due to rotor unbalance so that rotor inertia center is misaligned with geometric center, then magnetic suspension rotor is several What relation between center and center of inertia displacement is:

χ_I=χ_g-δ

In formula,For rotor unbalance value；λ andIt is respectively the amplitude of rotor unbalance value And phase place；ω is rotor speed.Change δ into matrix form to have:

$\mathrm{\δ}=P_{\mathrm{\δ}}{\mathrm{\Φ}}_{\mathrm{\δ}}^T$

$P_{\mathrm{\δ}}=\left[\begin{array}{cc}-sin\left(\mathrm{\ω}t\right)& cos\left(\mathrm{\ω}t\right)\\ \cos \left(\mathrm{\ω}t\right)& sin\left(\mathrm{\ω}t\right)\end{array}\right]$

Wherein, P_δAnd Φ_δIt is respectively trigonometric function matrix and the Fourier coefficient of rotor unbalance value.

Additionally, affected by displacement transducer multiple-harmonic noise Sensor Runout, the geometric center position of sensor output Move χ_sWith actual geometric center displacement χ_gThere is deviation, relation between the two is:

χ_s=χ_g+d

In formula,For Sensor Runout vector；σ_iAnd ξ_iIt is respectively Sensor The amplitude of Runout i & lt harmonic component and phase place；K is overtone order.D is rewritten as matrix form:

$d=P_d{\mathrm{\Φ}}_d^T$

$P_{di}=\left[\begin{array}{cc}-sin\left(i\mathrm{\ω}t\right)& cos\left(i\mathrm{\ω}t\right)\\ \cos \left(i\mathrm{\ω}t\right)& sin\left(i\mathrm{\ω}t\right)\end{array}\right],i=1,...,k$

Φ_d=[Φ_d1 … Φ_dk]

Φ_di=[p_i q_i], p_i=σ_isinξ_i, q_i=σ_icosξ_i

Wherein, P_dAnd Φ_dIt is respectively trigonometric function matrix and the Fourier coefficient of Sensor Runout；P_diAnd Φ_diRespectively Trigonometric function matrix and Fourier coefficient for Sensor Runout i & lt harmonic component.

Magnetic bearing coil controls electric current I_cFor:

I_c=-k_adk_sG_w(s)G_c(s)χ_s

In formula, k_adFor AD downsampling factor；k_sFor displacement transducer amplification；G_c(s) and G_w(s) be respectively controller and The transmission function of power amplifier.

The magnetic bearing system kinetic model then comprising rotor unbalance and Sensor Runout is:

$m{\stackrel{\·\·}{\mathrm{\χ}}}_I=-k_i{k}_{ad}{k}_s{G}_w\left(s\right)G_c\left(s\right)({\mathrm{\χ}}_I+\mathrm{\δ}+d)+k_h({\mathrm{\χ}}_I+\mathrm{\δ})$

(2) nonlinear autoregressive algorithm design

On the basis of the model described in step (1), designing nonlinear autoregressive algorithm, this algorithm mainly includes two Point: adaptive control laws and estimation rule.ART network rule is by the estimated value of magnetic suspension rotor center of inertia displacementAs control Variable processed, it is ensured thatConverge on zero.ART network rule can estimate rotor unbalance value and Sensor Runout adaptively The Fourier coefficient Φ of each harmonic component_δ、Φ_d, it is ensured that each Fourier coefficient estimated value restrains.Nonlinear autoregressive is calculated Method is designed as:

$u_{ic}=-(k_h{\widehat{\mathrm{\χ}}}_I+m\mathrm{\Ξ}{\stackrel{\·}{\widehat{\mathrm{\χ}}}}_I+\mathrm{\ρ}e+k_h{P}_{\mathrm{\δ}}{\widehat{\mathrm{\Φ}}}_{\mathrm{\δ}}^T)/\left(K_{am}{k}_i\right)$

In formula, Ξ is positive definite matrix；ρ is normal number；Estimated value for rotor unbalance value Fourier coefficient； Purpose of design is to compensate for the displacement rigidity power that rotor unbalance value causes；K_amEquieffective ratio coefficient for power amplification system；E is WithWithRelevant weight function；ForFirst derivative.

The ART network rule of each harmonic component of Sensor Runout and rotor unbalance value Fourier coefficient is respectively as follows:

${\stackrel{\·}{\widetilde{\mathrm{\Φ}}}}_d=e^T{P}_{rd}{\mathrm{\Γ}}_d,{\stackrel{\·}{\widetilde{\mathrm{\Φ}}}}_{\mathrm{\δ}}=e^T{P}_{r\mathrm{\δ}}{\mathrm{\Γ}}_{\mathrm{\δ}}$

In formula, WithIt is respectively triangle Jacobian matrix P_dAnd P_δSecond dervative；WithIt is respectively each harmonic component of Sensor Runout and rotor unbalance value Fourier coefficient estimation difference；WithIt is respectively each harmonic component of Sensor Runout and the Fourier of rotor unbalance value The first derivative of coefficient estimation error；WithFor positive definite adaptive gain matrix, determine Fourier coefficient The convergence rate of estimated value and the stability of system.

(3) magnetic bearing system axes of inertia identification

The nonlinear adaptive algorithm that step (2) proposes can estimate Sensor Runout higher harmonic components exactly Fourier coefficient, and ensure Sensor Runout with frequency component and rotor unbalance value Fourier coefficient estimated value receive Hold back.In order to further identification Sensor Runout is with frequency component and rotor unbalance value, need by step (3) variable speed side Formula realizes, and i.e. realizes axes of inertia identification.Axes of inertia identification mainly includes three steps: a) working rotor is in rotational speed omega₁Under, obtain Sensor Runout is with the Fourier coefficient estimated value of frequency component and rotor unbalance valueWithB) change turns Rotor speed, makes magnetic suspension rotor be operated in rotational speed omega₂Under, obtain the estimated value under current rotating speed WithC) root Have according to the same frequency component Fourier coefficient obtained under two speed conditions:

$\begin{array}{c}\left\{\begin{array}{c}(p_1-{\hat{p}}_{11})+{\mathrm{\η}}_1(u-{\hat{u}}_1)=0\\ (p_1-{\hat{p}}_{12})+{\mathrm{\η}}_2(u-{\hat{u}}_2)=0\end{array}\right.\\ \left\{\begin{array}{c}(q_1-{\hat{q}}_{11})+{\mathrm{\η}}_1(v-{\hat{v}}_1)=0\\ (q_1-{\hat{q}}_{12})+{\mathrm{\η}}_2(v-{\hat{v}}_2)=0\end{array}\right.\end{array}\⇒\begin{array}{c}\left[\begin{array}{c}{p}_1\\ u\end{array}\right]=A^{-1}{B}_1\\ \left[\begin{array}{c}{q}_1\\ u\end{array}\right]=A^{-1}{B}_2\end{array}$

In formula,With

Finally solve actual value p₁、q₁, u and v, then the magnetic bearing system axes of inertia obtain identification.

(4) magnetic bearing system multiple-harmonic Active vibration suppression

Sensor Runout in being restrained by step (2) nonlinear autoregressive is with in frequency component and rotor unbalance Fu The estimated value of leaf system number replaces with the actual value that step (3) calculates, then the displacement rigidity power caused by rotor unbalance obtains Accurately compensating for, the multiple-harmonic current that rotor unbalance value and Sensor Runout cause is effectively suppressed, the most accurately The multiple-harmonic inhibiting magnetic suspension inertia actuator vibrates.

The principle of the present invention is: rotor unbalance and Sensor Runout are two primary oscillation source of magnetic bearing system, Both produce the approach vibrated and form is different.Rotor unbalance produces position not only by magnetic bearing system itself Move rigidity power, produce current stiffness power also by controller and current stiffness coefficient；And Sensor Runout only to produce electric current firm Degree power.Therefore the suppression of the suppression multiple-harmonic current to be realized of magnetic bearing system multiple-harmonic vibration, i.e. at displacement transducer Two kinds of effect of noise of reference-junction compensation, and the displacement rigidity power that rotor unbalance to be compensated causes.But displacement sensing The same frequency component of device output both comprises rotor unbalance component, comprises again the same frequency component of Sensor Runout.Therefore entering The premise that line displacement rigidity power accurately compensates, rotor unbalance to be carried out and Sensor Runout are with the identification of frequency amount, i.e. inertia The identification of axle.Thus, it is achieved the high accuracy multiple-harmonic vibration suppression of magnetic suspension inertia actuator.

Present invention advantage compared with prior art is: a kind of magnetic bearing system based on nonlinear adaptive algorithm is used to Property axle discrimination method, (1) overcomes tradition directly identification algorithm and causes the shortcoming that Identification Errors is 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) overcome that conventional linear adaptive algorithm causes initially controls electricity Flow through the shortcomings such as big and parameter identification convergence rate is slow, utilize nonlinear autoregressive to restrain and improve algorithm performance；(3) avoid In tradition magnetic bearing system multiple-harmonic vibration control algorithm, Sensor Runout draws with frequency component and rotor unbalance value aliasing The displacement rigidity force compensating error risen, utilizes the Fourier coefficient after identification to be modified, thus it is high-precision to realize magnetic bearing system Degree multiple-harmonic vibration suppression.

Accompanying drawing explanation

Fig. 1 is the flowchart of the present invention；

Fig. 2 is system principle diagram based on nonlinear autoregressive algorithm；

Fig. 3 is axes of inertia identification flow charts.

Detailed description of the invention

Below in conjunction with the accompanying drawings and concrete enforcement step the present invention will be further described.

As it is 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, it realizes process and is: initially set up the magnetic bearing system kinetic model comprising rotor unbalance and Sensor Runout, Analysis of magnetic bearing arrangement multiple-harmonic vibration producing cause and existence form；Secondly design nonlinear autoregressive algorithm, it is achieved 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 component of Runout；Then Sensor Runout is realized with frequency by the strategy of change rotor speed Component and the identification of rotor unbalance, i.e. realize the identification of the axes of inertia；Finally by Sensor in nonlinear adaptive algorithm The each harmonic component of Runout and rotor unbalance Fourier coefficient are modified, and make magnetic suspension rotor rotate around the real axes of inertia, Thus 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 through AD sampling, it is achieved close Ring controls.Estimation rule in nonlinear adaptive algorithm estimates rotor unbalance value and each harmonic component of Sensor Runout WithAt controller input χ_sBoth are eliminated, to realize the suppression of multiple-harmonic current；Nonlinear adaptive algorithm utilizes to be estimated The rotor unbalance value counted outObtainCarry out the compensation of displacement rigidity power, finally give control signal u_ic.Magnetic bearing Power amplification system drives magnetic bearing coil according to control signal, produces and controls electric current I_c, produce corresponding magnetic axis load F and act on magnetic Suspension rotor, thus change the position χ of rotor_g.Fig. 3 is axes of inertia identification flow charts, for Fig. 1 step (3) be embodied as stream Journey, respectively in rotational speed omega₁And ω₂Under estimated value when obtaining stable state WithPass through Solving equation obtains real Fourier coefficient p₁, q₁, u and v, finally by uneven for adaptive algorithm rotor and Sensor Runout replaces with actual value with the estimated value of frequency component, thus realizes magnetic suspension rotor and rotate around the real axes of inertia.The present invention It is embodied as step as follows:

(1) set up containing rotor unbalance and the magnetic bearing system kinetic model of Sensor Runout

Two-freedom magnetic bearing system, x-axis and y-axis two passage are mutually decoupled.Assume the displacement rigidity of x-axis and y-axis Coefficient is identical with current stiffness coefficient, when magnetic suspension rotor moves near equilbrium position, and its linearizing kinetics equation For:

$\{\begin{array}{c}m{\stackrel{\·\·}{x}}_I=k_i{i}_{cx}+k_h{x}_g\\ m{\stackrel{\·\·}{y}}_I=k_i{i}_{cy}+k_h{y}_g\end{array}---\left(1\right)$

In formula, m is the quality of magnetic suspension rotor；k_iAnd k_hThe current stiffness coefficient and the displacement that are respectively magnetic bearing system are firm Degree coefficient；i_cxAnd i_cyIt is respectively x-axis and y-axis magnetic bearing coil controls electric current；x_IAnd y_IIt is respectively the axes of inertia in x-axis and y-axis side Displacement upwards；x_gAnd y_gIt is respectively geometrical axis displacement in x-axis and y-axis direction.

Being write formula (1) as matrix form is:

$m{\stackrel{\·\·}{\mathrm{\χ}}}_I=k_i{I}_c+k_h{\mathrm{\χ}}_g---\left(2\right)$

In formula, χ_I=[x_I, y_I]^T, χ_g=[x_g, y_g]^T, I_c=[i_cx, i_cy]^T。

Impact due to rotor unbalance so that rotor inertia center is misaligned with geometric center, then rotor inertia center Displacement χ_IWith geometric center displacement χ_gBetween relation be:

χ_I=χ_g-δ (3)

In formula, δ is rotor unbalance, is expressed as:

Wherein, λ andIt is respectively amplitude and the phase place of rotor unbalance value；ω is rotor speed.Write formula (4) as matrix Form is:

$\mathrm{\δ}=P_{\mathrm{\δ}}{\mathrm{\Φ}}_{\mathrm{\δ}}^T---\left(5\right)$

$P_{\mathrm{\δ}}=\left[\begin{array}{cc}-\sin \left(\mathrm{\ω}t\right)& cos\left(\mathrm{\ω}t\right)\\ \cos \left(\mathrm{\ω}t\right)& sin\left(\mathrm{\ω}t\right)\end{array}\right]---\left(6\right)$

Wherein, P_δAnd Φ_δIt is respectively trigonometric function matrix and the Fourier coefficient of rotor unbalance value.

OrderThe then Fourier coefficient vector Φ of rotor unbalance value_δIt is represented by:

Φ_δ=[u v] (8)

Additionally, affected by displacement transducer multiple-harmonic noise Sensor Runout, the geometric center position of sensor output Move χ_sWith actual geometric center displacement χ_gThere is deviation, relation between the two is:

χ_s=χ_g+d (9)

In formula,For Sensor Runout vector；σ_iAnd ξ_iIt is respectively Sensor The amplitude of Runout i & lt harmonic component and phase place；K is overtone order.D is rewritten as matrix form:

$d=P_d{\mathrm{\Φ}}_d^T---\left(10\right)$

$P_{di}=\left[\begin{array}{cc}-sin\left(i\mathrm{\ω}t\right)& cos\left(i\mathrm{\ω}t\right)\\ \cos \left(i\mathrm{\ω}t\right)& sin\left(i\mathrm{\ω}t\right)\end{array}\right],i=1,...,k---\left(12\right)$

Φ_d=[Φ_d1 … Φ_dk] (13)

Φ_di=[p_i q_i], p_i=σ_isinξ_i, q_i=σ_icosξ_i (14)

Wherein, P_dAnd Φ_dIt is respectively trigonometric function matrix and the Fourier coefficient of Sensor Runout；P_diAnd Φ_diRespectively Trigonometric function matrix and Fourier coefficient for Sensor Runout i & lt harmonic component.

Magnetic bearing coil controls electric current I_cFor:

I_c=-k_adk_sG_w(s)G_c(s)χ_s (15)

In formula, k_adFor AD downsampling factor；k_sFor displacement transducer amplification；G_c(s) and G_w(s) be respectively controller and The transmission function of power amplifier.

The kinetic model of the magnetic bearing system then comprising rotor unbalance and Sensor Runout is:

$m{\stackrel{\·\·}{\mathrm{\χ}}}_I=-k_i{k}_{ad}{k}_s{G}_w\left(s\right)G_c\left(s\right)({\mathrm{\χ}}_I+\mathrm{\δ}+d)+k_h({\mathrm{\χ}}_I+\mathrm{\δ})---\left(16\right)$

Then the relation between vibration force F and two kinds of vibration source δ and d is:

F=Q^-1[(k_hI_2×2-k_ik_adk_sG_w(s)G_c(s))δ-k_ik_adk_sG_w(s)G_c(s)d] (17)

Q=I_2×2-k_hP(s)+k_ik_adk_sG_w(s)G_c(s)P(s) (18)

In formula, I_2×2For second order unit matrix；P (s) is that magnetic bearing system transmits function.

(2) nonlinear autoregressive algorithm design

Assume that the estimated value of rotor unbalance value and Sensor Runout is respectivelyWithThe then position at rotor inertia center Move estimated valueIt is represented by:

${\widehat{\mathrm{\χ}}}_I={\widehat{\mathrm{\χ}}}_g-\widehat{\mathrm{\δ}}={\mathrm{\χ}}_s-\hat{d}-\widehat{\mathrm{\δ}}={\mathrm{\χ}}_I+\tilde{d}+\widetilde{\mathrm{\δ}}---\left(19\right)$

In formula,The Displacement Estimation value of geometric center；WithIt is respectively rotor unbalance value and Sensor Runout Estimation difference, is defined as:

$\widetilde{\mathrm{\δ}}\stackrel{\mathrm{\Δ}}{=}\mathrm{\δ}-\widehat{\mathrm{\δ}}=P_{\mathrm{\δ}}{\widetilde{\mathrm{\Φ}}}_{\mathrm{\δ}}^T---\left(20\right)$

$\tilde{d}\stackrel{\mathrm{\Δ}}{=}d-\hat{d}=P_d{\widetilde{\mathrm{\Φ}}}_d^T---\left(21\right)$

In formula,WithIt is respectively estimating of rotor unbalance value and Sensor Runout each harmonic component Fourier coefficient Meter error.

In order to ensure that rotor inertia the center displacement estimated value converges on zero, and rotor unbalance can be estimated adaptively With Sensor Runout Fourier coefficient, nonlinear autoregressive algorithm is designed as:

$u_{ic}=-(k_h{\widehat{\mathrm{\χ}}}_I+m\mathrm{\Ξ}{\stackrel{\·}{\widehat{\mathrm{\χ}}}}_I+\mathrm{\ρ}e+k_h{P}_{\mathrm{\δ}}{\widehat{\mathrm{\Φ}}}_{\mathrm{\δ}}^T)/\left(K_{am}{k}_i\right)---\left(22\right)$

In formula, ρ is normal number；In order to compensate the displacement rigidity power that rotor unbalance value causes；ForOne Order derivative；E be withWithRelevant weight function.For the initial control electric current mistake overcoming conventional linear weight function to cause Greatly, estimating the shortcomings such as parameter convergence rate is slow, the present invention proposes a kind of nonlinear weight value function:

$e={\stackrel{\·}{\widehat{\mathrm{\χ}}}}_I+aarctan\left(b{\widehat{\mathrm{\χ}}}_I\right)---\left(23\right)$

In formula, a and b is normal number.Then in formula (22), positive definite matrix Ξ is represented by:

$\mathrm{\Ξ}=\left[\begin{array}{cc}\frac{ab}{1+b^2{\hat{x}}_I^2}& 0\\ 0& \frac{ab}{1+b^2{\hat{y}}_I^2}\end{array}\right]---\left(24\right)$

The each harmonic component of Sensor Runout and rotor unbalance value Fourier coefficient ART network rule are respectively as follows:

${\stackrel{\·}{\widetilde{\mathrm{\Φ}}}}_d=e^T{P}_{rd}{\mathrm{\Γ}}_d,{\stackrel{\·}{\widetilde{\mathrm{\Φ}}}}_{\mathrm{\δ}}=e^T{P}_{r\mathrm{\δ}}{\mathrm{\Γ}}_{\mathrm{\δ}}---\left(25\right)$

Γ_d=diag (τ_d1 τ_d1 τ_d2 τ_d2 … τ_dk τ_dk) (26)

Γ_δ=diag (τ_δ τ_δ) (27)

In formula, WithIt is respectively triangle Jacobian matrix P_dAnd P_δSecond dervative；WithIt is respectively each harmonic component of Sensor Runout and rotor unbalance value The first derivative of Fourier coefficient estimation difference；WithFor positive definite adaptive gain matrix, determine in Fu The convergence rate of leaf system number estimated value and the stability of system.In order to ensure the stability of system, choosing of matrix element should Meet 0≤(Δ_dii+Δ_δii)≤1,Δ_δii=τ_δmω²。

(3) magnetic bearing system axes of inertia identification

Due to system asymptotically stability, as t → ∞,WithAll will converge on zero, then the inertia of magnetic suspension rotor The center displacement estimated value converges on zero.Understand according to formula (23) and (25), as t → ∞, Then rotor unbalance value estimated valueWith Sensor Runout Fourier coefficient estimated valueTo converge on Definite value.Have according to formula (1), (19) and (22):

$m\stackrel{\·\·}{\tilde{d}}+m\stackrel{\·\·}{\widetilde{\mathrm{\δ}}}=k_h\tilde{d}---\left(28\right)$

Due toWithAll trend towards zero, then formula (28) is reduced to:

$P_{rd}{\widetilde{\mathrm{\Φ}}}_d^T+P_{r\mathrm{\δ}}{\widetilde{\mathrm{\Φ}}}_{\mathrm{\δ}}^T=0---\left(29\right)$

According to trigonometric function orthogonal property, can obtain:

$(k_h+{\mathrm{m\ω}}^2)P_{d1}{\widetilde{\mathrm{\Φ}}}_{d1}^T+P_{r\mathrm{\δ}}{\widetilde{\mathrm{\Φ}}}_{\mathrm{\δ}}^T=0---\left(30\right)$

$(k_h+m{\left(i\mathrm{\ω}\right)}^2)P_{di}{\widetilde{\mathrm{\Φ}}}_{di}^T=0,i=2,...,k---\left(31\right)$

From formula (30) and (31): the higher harmonic components Fourier coefficient of Sensor Runout converges on actual value, And the Fourier coefficient of the same frequency component of Sensor Runout and rotor unbalance does not converge to actual value.It is thus desirable to it is logical Cross a kind of means and increase the observability degree of system, both are carried out identification, thus realizes magnetic bearing system axes of inertia identification.

DefinitionThen can be obtained by formula (32):

$\left\{\begin{array}{c}{\tilde{p}}_1+\mathrm{\η}\tilde{u}=0\\ {\tilde{q}}_1+\mathrm{\η}\tilde{v}=0\end{array}\right.\⇒\left\{\begin{array}{c}(p_1-{\hat{p}}_1)+\mathrm{\η}(u-\hat{u})=0\\ (q_1-{\hat{q}}_1)+\mathrm{\η}(v-\hat{v})=0\end{array}\right.---\left(32\right)$

Four unknown numbers of two equations, above formula equation is unsolvable.Defined from η, change rotor speed to increase Add equation number, it is achieved the identification of the magnetic bearing system axes of inertia.

As it is shown on figure 3, the identification of the magnetic bearing system axes of inertia needs three steps: a) working rotor is in rotational speed omega₁Under, To Sensor Runout with frequency component and the estimated value of rotor unbalance value Fourier coefficientWithChange Become rotor speed so that it is be operated in rotational speed omega₂Under, obtain the estimated value under current rotating speedWithBy two Estimated value under individual speed conditions substitutes into formula (32), has:

$\begin{array}{c}\left\{\begin{array}{c}(p_1-{\hat{p}}_{11})+{\mathrm{\η}}_1(u-{\hat{u}}_1)=0\\ (p_1-{\hat{p}}_{12})+{\mathrm{\η}}_2(u-{\hat{u}}_2)=0\end{array}\right.\\ \left\{\begin{array}{c}(q_1-{\hat{q}}_{11})+{\mathrm{\η}}_1(v-{\hat{v}}_1)=0\\ (q_1-{\hat{q}}_{12})+{\mathrm{\η}}_2(v-{\hat{v}}_2)=0\end{array}\right.\end{array}\⇒\begin{array}{c}\left[\begin{array}{c}{p}_1\\ u\end{array}\right]=A^{-1}{B}_1\\ \left[\begin{array}{c}{q}_1\\ u\end{array}\right]=A^{-1}{B}_2\end{array}---\left(33\right)$

In formula, With

Finally solve actual value p₁、q₁, u and v, then the magnetic bearing system axes of inertia obtain identification.

(4) magnetic bearing system multiple-harmonic vibration suppression

By the Sensor Runout of step (2) Chinese style (22) with frequency component and the estimation of rotor unbalance Fourier coefficient Value replaces with the actual value that step (3) calculates, then the displacement rigidity power caused by rotor unbalance is accurately compensated for, and turns The multiple-harmonic current that sub-amount of unbalance and Sensor Runout cause is effectively suppressed, and the most accurately inhibits magnetic suspension The multiple-harmonic vibration of inertia actuator.

By time above it can be seen that utilize nonlinear adaptive algorithm to carry out axes of inertia identification, it is only necessary at low-speed conditions Under carry out a raising speed or reduction of speed, it is achieved simple, identification precision is higher than direct identification method.Additionally, due to Sensor The each harmonic component of Runout does not changes, the Fourier coefficient that therefore can will pick out under low-speed conditions with rotor speed change 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 field technical staff.

Claims (3)

1. a magnetic bearing system axes of inertia discrimination method based on nonlinear adaptive algorithm, it is characterised in that: include following Step:

(1) set up containing rotor unbalance and the magnetic bearing system kinetic model of Sensor Runout

Two-freedom magnetic bearing system, x-axis and y-axis two passage are mutually decoupled；Assume the displacement rigidity coefficient of x-axis and y-axis Identical with current stiffness coefficient, when magnetic suspension rotor moves near equilbrium position, its linearizing kinetics equation is:

$m{\stackrel{\·\·}{\mathrm{\χ}}}_I=k_i{I}_c+k_h{\mathrm{\χ}}_g$

In formula, m is the quality of magnetic suspension rotor；k_iAnd k_hIt is respectively current stiffness coefficient and the displacement rigidity system of magnetic bearing system Number；I_c=[i_cx, i_cy]^T, i_cxAnd i_cyIt is respectively x-axis and y-axis coil controls electric current；χ_I=[x_I, y_I]^T, x_IAnd y_IIt is respectively inertia Center displacement in x-axis and y-axis direction；For χ_ISecond dervative；χ_g=[x_g, y_g]^T, x_gAnd y_gIt is respectively geometric center to exist Displacement in x-axis and y-axis direction；

Impact due to rotor unbalance so that rotor inertia center is misaligned with geometric center, then in magnetic suspension rotor geometry Relation between the heart and center of inertia displacement is:

χ_I=χ_g-δ

In formula,For rotor unbalance value；λ andIt is respectively amplitude and the phase of rotor unbalance value Position；ω is rotor speed；Change δ into matrix form to have:

$\mathrm{\δ}=P_{\mathrm{\δ}}{\mathrm{\Φ}}_{\mathrm{\δ}}^T$

$P_{\mathrm{\δ}}=\left[\begin{array}{cc}-sin\left(\mathrm{\ω}t\right)& cos\left(\mathrm{\ω}t\right)\\ \cos \left(\mathrm{\ω}t\right)& sin\left(\mathrm{\ω}t\right)\end{array}\right]$

Wherein, P_δAnd Φ_δIt is respectively trigonometric function matrix and the Fourier coefficient of rotor unbalance value；

Additionally, affected by displacement transducer multiple-harmonic noise Sensor Runout, the geometric center displacement χ of sensor output_s With actual geometric center displacement χ_gThere is deviation, relation between the two is:

χ_s=χ_g+d

In formula,For Sensor Runout vector；σ_iAnd ξ_iIt is respectively Sensor The amplitude of Runout i & lt harmonic component and phase place；K is overtone order；D is rewritten as matrix form:

$d=P_d{\mathrm{\Φ}}_d^T$

$P_{di}=\left[\begin{array}{cc}-sin\left(i\mathrm{\ω}t\right)& cos\left(i\mathrm{\ω}t\right)\\ \cos \left(i\mathrm{\ω}t\right)& sin\left(i\mathrm{\ω}t\right)\end{array}\right],i=1,\mathrm{...},k$

Φ_d=[Φ_d1 … Φ_dk]

Φ_di=[p_i q_i], p_i=σ_isinξ_i, q_i=σ_icosξ_i

Wherein, P_dAnd Φ_dIt is respectively trigonometric function matrix and the Fourier coefficient of Sensor Runout；P_diAnd Φ_diIt is respectively The trigonometric function matrix of Sensor Runout i & lt harmonic component and Fourier coefficient；

Magnetic bearing coil controls electric current I_cFor:

I_c=-k_adk_sG_w(s)G_c(s)χ_s

In formula, k_adFor AD downsampling factor；k_sFor displacement transducer amplification；G_c(s) and G_wS () is respectively controller and power The transmission function of amplifier；

The magnetic bearing system kinetic model then comprising rotor unbalance and Sensor Runout is:

$m{\stackrel{\·\·}{\mathrm{\χ}}}_I=-k_i{k}_{ad}{k}_s{G}_w\left(s\right)G_c\left(s\right)({\mathrm{\χ}}_I+\mathrm{\δ}+d)+k_h({\mathrm{\χ}}_I+\mathrm{\δ});$

(2) nonlinear autoregressive algorithm design

On the basis of the model described in step (1), designing nonlinear autoregressive algorithm, this algorithm mainly includes two parts: Adaptive control laws and estimation rule；ART network rule is by the estimated value of magnetic suspension rotor center of inertia displacementAs controlling to become Amount, it is ensured thatConverge on zero；ART network rule can estimate that rotor unbalance value and Sensor Runout are each humorous adaptively The Fourier coefficient Φ of wave component_δ、Φ_d, it is ensured that each Fourier coefficient estimated value restrains；

(3) magnetic bearing system axes of inertia identification

Realized the identification of the magnetic bearing axes of inertia by variable speed strategy, magnetic suspension rotor realizes under the conditions of different rotor speed The nonlinear adaptive algorithm that step (2) proposes, obtains different Sensor Runout with frequency component and rotor unbalance value Fourier coefficient estimated value, improves the observability degree with frequency component, it is achieved Sensor Runout is with frequency component and rotor unbalance The identification of amount, i.e. magnetic bearing system axes of inertia identification；

(4) magnetic bearing system multiple-harmonic vibration suppression

Vibrate to completely inhibit the multiple-harmonic of magnetic bearing system, in step (2) nonlinear autoregressive need to being restrained Sensor Runout with the estimated value of frequency component and rotor unbalance Fourier coefficient replace with that step (3) calculates true Value, then the displacement rigidity power caused by rotor unbalance is accurately compensated for, by rotor unbalance value and Sensor Runout The multiple-harmonic current caused is effectively suppressed.

A kind of magnetic bearing system axes of inertia discrimination method based on nonlinear adaptive algorithm the most 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 self adaptation Estimate rule；Nonlinear autoregressive algorithm is designed as:

$u_{ic}=-(k_h{\widehat{\mathrm{\χ}}}_I+m\mathrm{\Ξ}{\stackrel{\·}{\widehat{\mathrm{\χ}}}}_I+\mathrm{\ρ}e+k_h{p}_{\mathrm{\δ}}{\widehat{\mathrm{\Φ}}}_{\mathrm{\δ}}^T)/\left(K_{am}{k}_i\right)$

In formula, ρ is normal number；Estimated value for rotor unbalance value Fourier coefficient；P_δTriangle for rotor unbalance value Function battle array；Purpose of design is to compensate for the displacement rigidity power that rotor unbalance value causes；K_amFor power amplification system etc. Effect proportionality coefficient；ForFirst derivative；E be withWithRelevant weight function:

$e={\stackrel{\·}{\widehat{\mathrm{\χ}}}}_I+a\arctan \left(b{\widehat{\mathrm{\χ}}}_I\right)$

In formula, a and b is respectively normal number, and its value determines to control electric current initial size and the convergence of Fourier coefficient estimated value Speed；According to the definition of e, the positive definite matrix Ξ in control law is represented by:

$\mathrm{\Ξ}=\left[\begin{array}{cc}\frac{ab}{1+b^2{\hat{x}}_I^2}& 0\\ 0& \frac{ab}{1+b^2{\hat{y}}_I^2}\end{array}\right]$

In formula,WithIt is respectively center of inertia displacement estimated value in x-axis and y-axis direction,

The ART network rule of each harmonic component of Sensor Runout and rotor unbalance value Fourier coefficient is respectively as follows:

${\stackrel{\·}{\widetilde{\mathrm{\Φ}}}}_d=e^T{P}_{rd}{\mathrm{\Γ}}_d,{\stackrel{\·}{\widetilde{\mathrm{\Φ}}}}_{\mathrm{\δ}}=e^T{P}_{r\mathrm{\δ}}{\mathrm{\Γ}}_{\mathrm{\δ}}$

Γ_d=diag (τ_d1 τ_d1 τ_d2 τ_d2 … τ_dk τ_dk)

Γ_δ=diag (τ_δ τ_δ)

In formula, WithIt is respectively trigonometric function Matrix P_dAnd P_δSecond dervative；WithIt is respectively in Fu of each harmonic component of Sensor Runout and rotor unbalance value Leaf system number estimation difference；WithIt is respectively each harmonic component of Sensor Runout and the Fourier coefficient of rotor unbalance value The first derivative of estimation difference；WithFor positive definite adaptive gain matrix, determine that Fourier coefficient is estimated The convergence rate of value and the stability of system；In order to ensure the stability of system, Γ_dAnd Γ_δChoosing of each diagonal entry should Meet 0≤(Δ_dii+Δ_δii)≤1, i=1,2；Δ_δii=τ_δmω²。

A kind of magnetic bearing system axes of inertia discrimination method based on nonlinear adaptive algorithm the most according to claim 1, It is characterized in that: described step (3) uses variable speed strategy realize magnetic bearing system principal axis of inertia identification method particularly includes:

The nonlinear adaptive algorithm proposed based on step (2), when center of inertia Displacement Estimation value level off to zero time, Sensor Runout meets with the Fourier coefficient estimated value of frequency component and rotor unbalance value:

$(k_h+{\mathrm{m\ω}}^2)P_{d1}{\widetilde{\mathrm{\Φ}}}_{d1}^T+P_{r\mathrm{\δ}}{\widetilde{\mathrm{\Φ}}}_{\mathrm{\δ}}^T=0$

Due to P_rδ=m ω²P_d1, above formula is rewritable is:

$\left\{\begin{array}{c}{\tilde{p}}_1+\mathrm{\η}\tilde{u}=0\\ {\tilde{q}}_1+\mathrm{\η}\tilde{v}=0\end{array}\right.\⇒\left\{\begin{array}{c}(p_1-{\hat{p}}_1)+\mathrm{\η}(u-\hat{u})=0\\ (q_1-{\hat{q}}_1)+\mathrm{\η}(v-\hat{v})=0\end{array}\right.$

In formulaFour unknown numbers of two equations, equation is unsolvable；Defined from η, change and turn Rotor speed is to increase equation number, it is achieved the identification of the magnetic bearing system axes of inertia；

Axes of inertia identification mainly includes three steps: a) working rotor is in rotational speed omega₁Under, obtain the same frequency component of Sensor Runout Fourier coefficient estimated value with rotor unbalance valueWithB) change rotor speed, make magnetic suspension rotor work Make in rotational speed omega₂Under, obtain the estimated value under current rotating speedWithC) by the same frequency component under two rotating speeds Fourier coefficient estimated value substitutes into above formula, has:

$\begin{array}{c}\left\{\begin{array}{c}(p_1-{\hat{p}}_{11})+{\mathrm{\η}}_1(u-{\hat{u}}_1)=0\\ (p_1-{\hat{p}}_{12})+{\mathrm{\η}}_2(u-{\hat{u}}_2)=0\end{array}\right.\\ \left\{\begin{array}{c}(q_1-{\hat{q}}_{11})+{\mathrm{\η}}_1(v-{\hat{v}}_1)=0\\ (q_1-{\hat{q}}_{12})+{\mathrm{\η}}_2(v-{\hat{v}}_2)=0\end{array}\right.\end{array}\⇒\begin{array}{c}\left[\begin{array}{c}{p}_1\\ u\end{array}\right]=A^{-1}{B}_1\\ \left[\begin{array}{c}{q}_1\\ v\end{array}\right]=A^{-1}{B}_2\end{array}$

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 obtain identification.