CN106886152A - A kind of magnetic suspension rotor odd harmonic electric current suppressing method based on second order odd repetitive controller - Google Patents

Abstract

The invention discloses a kind of magnetic suspension rotor odd harmonic electric current suppressing method based on second order odd repetitive controller, the magnetic suspension rotor kinetic model of and sensor harmonic wave uneven containing rotor quality is initially set up, next employs the magnetic suspension rotor odd harmonic electric current suppressing method based on second order odd repetitive controller (hereinafter referred to as SOORC).SOORC can improve the harmonic inhibition capability under harmonic frequency change or condition of uncertainty with the second order internal membranous structure suppressed for odd harmonic frequencies, that is, improve system to the control robustness under harmonic frequency change or condition of uncertainty.The present invention is also improved using delayed phase lead compensation to the steady-state behaviour and dynamic property of system, can realize that the odd harmonic current component produced to magnetic bearing coil in magnetic suspension rotor suppresses, it is adaptable to there is the suppression of uneven and sensor harmonic wave the magnetic suspension rotor system odd harmonic current component of rotor quality.

Description

A kind of magnetic suspension rotor odd harmonic electric current suppression based on second order odd repetitive controller Method processed

Technical field

The present invention relates to the technical field of magnetic suspension rotor current harmonics elimination, and in particular to one kind is based on second order odd weight The magnetic suspension rotor odd harmonic electric current suppressing method of multiple controller, is applied in rotor system of magnetically suspended control moment gyroscope The application that current harmonics elimination is magnetic suspension control torque gyroscope on " super quiet " satellite platform provides technical support.

Background technology

It is logical that rotor stability in magnetic suspension control torque gyroscope (Control Moment Gyroscope, CMG) suspends Cross what is realized using magnetic bearing electromagnetic force, contactless friction between the rotor and stator of magnetic bearing.Therefore magnetic bearing and tradition machinery Bearing is compared to be had many advantages, such as：Firstly, since contactless friction between the rotor and stator of magnetic bearing, therefore CMG flywheels turn Rotor speed can be realized increasing substantially compared with mechanical bearing, while increased system working life；Secondly, it is easy to accomplish magnetic The active control of suspending flywheel rotor unbalance vibration force, reduces the oscillation intensity in system work；Additionally, in view of CMG frameworks Equivalent moment of inertia it is related to rotor bearing rigidity, therefore using firm based on bearing can be turned down by the way of magnetic bearing supporting rotor Degree, so as to increase the equivalent moment of inertia of CMG frameworks.Therefore, magnetic bearing can improve under conditions of the output of equal torque and be System framework angle speed precision and CMG torque output accuracies, the final pointing accuracy and stability for improving spacecraft.Magnetic bearing is in boat It is widely used in its device high precision and long service life attitude control actuator.Therefore, the high accuracy based on magnetic bearing is long-lived Life CMG is the ideal chose of Spacecraft Attitude Control executing agency.

Although magnetic suspension control torque gyroscope has many advantages, such as, the dither in system can be passed by magnetic bearing Pass spacecraft influences Spacecraft Attitude Control precision indirectly, so as to cause the pointing accuracy of satellite platform and stability reduction. The dither of magnetic suspension control torque gyroscope CMG is main uneven by rotor quality and sensor harmonic wave causes.Wherein rotor Mass unbalance is the main cause for producing vibration, secondly because the deviation from circular from of sensor detection faces, electromagnetic property are uneven etc. Reason, occurs the current component i.e. sensor harmonic wave with frequency and frequency multiplication, this sensor harmonic wave meeting in displacement transducer signal Cause harmonic vibration.

Harmonic vibration suppresses that zero current, zero shift and zero three classes of vibration can be divided into.Wherein zero current vibration suppression has The small and low in energy consumption advantage of amount of calculation.Current flow suppression technology is realized suppressing mainly for the interference of single-frequency, for humorous The research work that ripple electric current suppresses is then relatively fewer, and main stream approach concentrates on Repetitive controller RC algorithms and many trappers or many in parallel LMS algorithm filters.But many trapper algorithms in parallel can not realize that all vibrations suppress and computationally intensive, while needs are examined simultaneously Consider the convergence rate problem between different wave filters, design is got up relatively complicated；Repetitive controller RC algorithms are without in parallel more Suppress while individual wave filter just can be realized vibrating different frequency composition.Repetitive controller RC algorithms are realized according to internal model principle A kind of method of system zero static error, and the existing repetitive control for being applied to magnetic suspension rotor system is all based on harmonic wave The internal membranous structure design completed under the conditions of power frequency is exactly determined, harmonic current frequency change or uncertain is not considered The problem of time-harmonic wave electric current inhibition decay.

The content of the invention

The object of the invention is：Overcome prior art not enough, invent a kind of magnetcisuspension based on second order odd repetitive controller Floating rotor odd harmonic electric current suppressing method.The introducing that the invention passes through second order repetitive control, improves magnetic suspension rotor Odd harmonic electric current of the system under the change of harmonic current frequency or condition of uncertainty suppresses precision.

The technical solution adopted by the present invention is：A kind of magnetic suspension rotor odd harmonic based on second order odd repetitive controller Electric current suppressing method, comprises the following steps：

Step (1) sets up the magnetic suspension rotor kinetic model of and sensor harmonic wave uneven containing rotor quality；

, by active magnetic bearings control, remaining three degree of freedom is by installed in rotor and calmly for magnetic suspension rotor radial direction two-freedom Permanent-magnetic clamp on son realizes that passive stabilization suspends.Q is magnetic bearing stator geometric center, and O is rotor geometric center, and C is rotor matter The heart.Inertial coodinate system QXY is set up centered on Q, rotating coordinate system O ε η are set up centered on O, (x, y) is in inertial coodinate system The coordinate value of lower rotor part geometric center O.

For X passage harmonic current, model as follows：

Understand that magnetic suspension rotor is as follows in the kinetics equation of X-direction by Newton's second law：

Wherein, m is rotor quality, f_xBe magnetic bearing in the bearing of X-direction, e is between rotor geometric center and barycenter Deviation, Ω is rotor speed, and φ is the initial phase of rotor unbalance quality.

The bearing of main passive magnetic bearing is made up of the electromagnetic force of active magnetic bearings and the permanent magnetic of passive magnetic bearing, and X leads to Road axis load f_xCan be written as：

f_x=f_ex+f_px

Wherein, f_exIt is the electromagnetic force of X passage active magnetic bearings, f_pxIt is the permanent magnetic of X passage passive magnetic bearing.Wherein, forever Magnetic force is linear with displacement, is expressed as：

f_px=K_prx

Wherein, K_prIt is passive magnetic bearing displacement rigidity；

When rotor suspension is near magnetic center, active magnetic bearings electromagnetic force can approximately linear turn to：

f_ex≈K_erx+K_ii_x

Wherein, K_er、K_iRespectively active magnetic bearings displacement rigidity, current stiffness, i_xIt is power amplifier output current；

For the rotor-support-foundation system containing mass unbalance, have：

X (t)=x (t)+Θ_x(t)

Wherein, X (t) is rotor centroid displacement, and x (t) is rotor geometric center displacement, Θ_xT () causes for mass unbalance Shift perturbation, be designated as：

Θ_x(t)=lcos (Ω t+ θ)

Wherein, l is the amplitude of mass unbalance, and θ is phase, and Ω is rotor speed；

In view of actual rotor system, because of the influence of the factor such as uneven of machining accuracy and material, generally sensing Device harmonic wave is inevitable, therefore the actually measured displacement x of sensor_sT () is represented by：

x_s(t)=x (t)+x_d(t)

Wherein, x_dT () is sensor harmonic wave, rewritable to be：

Wherein, c_aIt is the amplitude of sensor harmonic constant, θ_aIt is the phase of sensor harmonic constant, w is sensor harmonic wave Highest number of times；

By i_x、X(t)、Θ_x(t)、x_dT () carries out Laplace transform and obtains i successively_x(s)、X(s)、Θ_x(s)、x_dS (), writes Going out rotor dynamics equation has：

ms²X (s)=(K_er+K_pr)(X(s)-Θ_x(s))+K_ii_x(s)

Wherein,

i_x(s)=- K_sK_iG_c(s)G_w(s)(X(s)-Θ_x(s)+x_d(s))

Wherein, K_sIt is displacement transducer gain link, G_cS () is controller link, G_wS () is power amplifier link；

As can be seen from the above equation, due to mass unbalance and the presence of sensor harmonic wave, cause to exist in coil current with Rotating speed with frequency current component-K_sK_iG_c(s)G_w(s)(X(s)-Θ_x(s)) and frequency multiplication current component-K_sK_iG_c(s)G_w(s)x_d (s)。

In active magnetic bearings controllable radial direction translational degree of freedom X passage and Y passages, two passages decoupling, so Y passages are electric Flow model is similar to X passage, makes a concrete analysis of as follows：

Rotor dynamics equation has：

ms²Y (s)=(K_er+K_pr)(Y(s)-Θ_y(s))+K_ii_y(s)

In formula, Y (s) is the pull-type conversion of rotor centroid displacement y (t), Θ_yS () disturbs for the displacement that mass unbalance causes Dynamic Θ_yThe pull-type conversion of (t), i_yS () is Y passage power amplifier output currents i_yThe pull-type conversion of (t).

In above formula,

i_y(s)=- K_sK_iG_c(s)G_w(s)(Y(s)-Θ_y(s)+y_d(s))

In formula, y_dS () is sensor harmonic wave y_dThe pull-type conversion of (t).

As can be seen from the above equation, due to mass unbalance and the presence of sensor harmonic wave, cause to exist in coil current with Rotating speed with frequency current component-K_sK_iG_c(s)G_w(s)(Y(s)-Θ_y(s)) and frequency multiplication current component-K_sK_iG_c(s)G_w(s)y_d (s)。

Step (2) designs a kind of magnetic suspension rotor odd harmonic electric current suppression side based on second order odd repetitive controller Method；

With harmonic current as control targe, algorithmic controller is embedded in former closed-loop system in the form of " insertion ".By harmonic wave electricity Stream i_xIt is input into the plug-in type repetitive controller module as error signal, the output equivalent of the module feeds back to former control system Power amplifier input.The design of the module mainly includes following two aspects：

1. SOORC structure algorithms are used, for the harmonic current that magnetic suspension rotor system is actually produced under any rotating speed Carry out spectrum analysis to understand, harmonic current dominant frequency component is odd harmonic electric current.According to the general side of SOORC structure designs Formula, SOORC internal model link of the design based on 2k+1 (k=0.1.2.3...) secondary dominant frequency.Occupied an leading position in harmonic current Harmonic component obtained by spectrum analysis；SOORC internal model structures refer to major harmonic component complete design.

2. phase lead-lag compensation link is made up of phase lead-lag correction link and low-pass first order filter, root Determine according to system function phase-frequency characteristic and stability of a system condition.The compensation tache can improve the stability of a system, widen controller The value upper limit of gain, at the same make system stability design redundancy increase and also dynamic property and steady-state behaviour have necessarily Improve.

Further, described step (2) current harmonics elimination algorithm is：

1. the structure design of SOORC controllers

Repetitive controller (RC) is to realize that error signal is tracked based on internal model principle, can be by introducing infinite multiple closed loops Limit is eliminatedMultiplied frequency harmonic component.SOORC structures can be designed as secondary humorous comprising 2k+1 (k=0.1.2.3...) The internal model of wave frequency rate, that is, introduce the internal model link corresponding with odd harmonic power frequency component, realizes odd harmonic frequencies It is accurately positioned and is introduced with limit.So as at the Frequency point for introducing, system frequency response can obtain infinite gain.

SOORC structure transmission functions G_SOORCZ () can be expressed as：

Wherein,k_rcIt is G_SOORCZ the controller gain corresponding to (), Q (z) is low pass Wave filter；N₂Represent the discrete time delay sampling number of SOORC；

Using SOORC structures, the harmonic current actually produced under any rotating speed for magnetic suspension rotor system enters line frequency Analysis of spectrum understands that harmonic current dominant frequency component is odd harmonic electric current.According to the general fashion that SOORC is designed, base is designed In the SOORC internal model links that 2k+1 (k=0.1.2.3...) subfrequency is dominant frequency.

It can be seen from SOORC internal model principles, the frequency response of odd harmonic terms can almost be suppressed to zero.SOORC with Traditional RC is compared, and when harmonic current frequency changes or do not know, the robustness of control system is improved.Meanwhile, control Device gain k processed_rcAppropriate adjustment, dynamic performance can be improved；

2., phase compensation function K_fThe design of (z)

To realize system stabilization, a kind of system amplitude-frequency being composed in series based on multiple differentiation elements and delay component is devised Characteristic correction method, i.e.,：Penalty function K_fZ () is designed as：

K_f(z)=G₁(z)G₂ ^m(z)G₃(z) q (z) (m=0,1,2 ...)

Wherein, G₁Z () is low-frequency compensation link, its general expression-form is：(Z () is discretization mark)

Coefficient b specifically chooses according to system, realizes effective correction of system low-frequency range, meanwhile, the characteristic of medium-high frequency section becomes Change very little.

G₂ ^mZ () is Mid Frequency lead compensation link, General Expression form is：

Coefficient a, parameter T_a, m according to system phase compensate demand specifically choose so that system Mid Frequency is effectively corrected.

G₃Z () is middle low-frequency range correction or lag, General Expression form is：

Coefficient c, parameter T_bAccording to G₂ ^m(z) anticipatory control effect design so that system is by G₂ ^mIn after (z) anticipatory control Frequency range meets system stable condition.

Q (z) is that cut-off frequency is ω_cA low pass filter, General Expression form is：

Wherein, ω_cIt is system cut-off frequency.

Use with upper type, the redundancy of system stability design can be improved and improve the dynamic property of system and stability Energy.

Its general principles：Traditional RC can realize effective suppression of harmonic current, but tradition RC realizes harmonic current The precondition for effectively suppressing is the accurate determination based on harmonic current frequency, when harmonic current frequency changes or does not know, The current harmonics elimination effect of traditional RC occurs very big decay.Order RC is during current harmonics elimination to the change of frequency Or it is uncertain with certain control robustness, the change of harmonic current frequency can be improved or time-harmonic wave electric current suppression essence is not known Degree and convergence rate.

Present invention advantage compared with prior art is：

(1), in order to effectively suppress the harmonic current in magnetic suspension rotor system, the present invention proposes a kind of strange based on second order The magnetic suspension rotor odd harmonic electric current suppressing method of repetitive controller.The internal model link of SOORC can be directed to harmonic frequency (including 2k+1 (k=0.1.2.3...) subfrequency) is realized being accurately positioned and is introduced with limit, so as to realize system harmonicses electricity Stream effectively suppresses.SOORC structures can be by adjusting the parameter w of internal model link₁And w₂To improve the robustness of system.Compared to For traditional RC, SOORC can accelerate to the convergence rate that harmonic current is controlled, and the dynamic property of system is also accordingly improved. Delayed phase-lead compensation link is added, on the one hand can ensure system stabilization, on the other hand widened system controller gain k_rcThe value upper limit, improved dynamic performance.Suitable for there is mass unbalance and the magnetic suspension of sensor harmonic wave Rotor current harmonics elimination.

(2), be combined with each other for SOORC structures and delayed phase-differentiation element by the present invention, improves the dynamic of system Performance and steady-state behaviour, while optimizing the harmonic suppression effect of system.

Brief description of the drawings

Fig. 1 is flow chart of the invention；

Passive magnetic suspension rotor system structural representation based on Fig. 2；

Fig. 3 is rotor static unbalance schematic diagram；

Fig. 4 is sensor harmonic wave schematic diagram；

Fig. 5 is X passage magnetic bearing control system block diagram；

Fig. 6 is Y passage magnetic bearing control system block diagrams；

Fig. 7 is to improve plug-in type repetitive controller overall system diagram for X passage；

Fig. 8 is to improve plug-in type repetitive controller overall system diagram for X passage；

Fig. 9 is plug-in type repetitive controller concrete structure block diagram.

Specific embodiment

Below in conjunction with the accompanying drawings and specific embodiment further illustrates the present invention.

As shown in figure 1, a kind of magnetic suspension rotor odd harmonic electric current suppressing method based on second order odd repetitive controller Implementation process be：Initially set up the magnetic suspension rotor kinetic model of and sensor harmonic wave uneven containing rotor quality；So A kind of magnetic suspension rotor odd harmonic electric current suppressing method based on second order odd repetitive controller is designed afterwards；

Step (1) sets up the magnetic suspension rotor kinetic model containing mass unbalance and sensor harmonic wave

Magnetic suspension rotor system structural representation is as shown in Fig. 2 main by permanent magnet (1), active magnetic bearings (2) and rotor (3) constitute, its radial direction two-freedom by active magnetic bearings control, remaining three degree of freedom by rotor and stator forever Magnet ring realizes that passive stabilization suspends.Fig. 3 is rotor static unbalance schematic diagram, and Q represents the geometric center of magnetic bearing stator, and O is represented The geometric center of rotor, C represents the barycenter of rotor.Inertial coodinate system QXY is set up centered on Q, rotation is set up centered on O and is sat Mark system O ε η, (x, y) represents coordinate values of the rotor geometric center O under inertial coodinate system.For radial direction translational degree of freedom X passage, Modeling is as follows：

According to Newton's second law, magnetic suspension rotor is as follows in the kinetics equation of X-direction：

Wherein, m represents rotor quality, f_xBearing of the magnetic bearing in X-direction is represented, e represents rotor geometric center and matter Deviation between the heart, Ω represents rotor speed, and φ represents the initial phase of rotor unbalance quality.

The structure of main passive magnetic bearing is made up of active magnetic bearings and passive magnetic bearing.The bearing of main passive magnetic bearing by The electromagnetic force of active magnetic bearings and the permanent magnetic composition of passive magnetic bearing, therefore X passage axis load f_xCan be written as：

f_x=f_ex+f_px

Wherein, f_exIt is the electromagnetic force of X passage active magnetic bearings, f_pxIt is the permanent magnetic of X passage passive magnetic bearing.Permanent magnetic It is linear with displacement, it is expressed as：

f_px=K_prx

Wherein, K_prIt is passive magnetic bearing displacement rigidity；

When rotor suspension is near magnetic center, active magnetic bearings electromagnetic force can approximately linear turn to：

f_ex≈K_erx+K_ii_x

Wherein, K_er、K_iRespectively active magnetic bearings displacement rigidity, current stiffness, i_xIt is power amplifier output current；

In actual rotor system, due to the magnetic bearing rigging error in Fig. 2, rotor measurement surface roundness error and electromagnetism The influence of the factor such as uneven, can produce sensor harmonic wave as shown in Figure 4, and in figure, 4 represent sensor, and 5 represent stator, 6 tables Show rotor.The actually measured displacement x of sensor_sT () is represented by：

x_s(t)=x (t)+x_d(t)

Wherein, x_dT () is sensor harmonic wave, rewritable to be：

Wherein, c_aIt is the amplitude of sensor harmonic constant, θ_aIt is the phase of sensor harmonic constant, w is sensor harmonic wave Highest number of times；

Magnetic bearing X-direction translation control system as shown in figure 5, wherein, K_sIt is displacement transducer gain link, G_cS () is control Device link processed, G_wS () is power amplifier link, P (s) is the transmission function of rotor-support-foundation system；By i_x、X(t)、Θ_x(t)、x_dT () enters successively Row Laplace transform obtains i_x(s)、X(s)、Θ_x(s)、x_dS (), writing out rotor dynamics equation has：

ms²X (s)=(K_er+K_pr)(X(s)-Θ_x(s))+K_ii_x(s) wherein,

i_x(s)=- K_sK_iG_c(s)G_w(s)(X(s)-Θ_x(s)+x_d(s))

In formula, X (t) is rotor centroid displacement, and x (t) is rotor geometric center displacement, Θ_xT () causes for mass unbalance Shift perturbation.

As can be seen from the above equation, due to mass unbalance and the presence of sensor harmonic wave, cause to exist in coil current with Rotating speed is with frequency current component-K_sK_iG_c(s)G_w(s)(X(s)-Θ_x(s)) and frequency multiplication current component-K_sK_iG_c(s)G_w(s)x_d (s)。

In active magnetic bearings controllable radial direction translational degree of freedom X passage and Y passages, two passages decoupling, so Y passages are electric Flow model is similar to X passage, makes a concrete analysis of as follows：

Magnetic bearing Y-direction translation control system as shown in fig. 6, wherein, K_sIt is displacement transducer gain link, G_cS () is control Device link processed, G_wS () is power amplifier link, P (s) is the transmission function of rotor-support-foundation system.

Rotor dynamics equation has：

ms²Y (s)=(K_er+K_pr)(Y(s)-Θ_y(s))+K_ii_y(s)

In formula, Y (s) is the pull-type conversion of rotor centroid displacement y (t), Θ_yS () disturbs for the displacement that mass unbalance causes Dynamic Θ_yThe pull-type conversion of (t), i_yS () is Y passage power amplifier output currents i_yThe pull-type conversion of (t).

In above formula,

i_y(s)=- K_sK_iG_c(s)G_w(s)(Y(s)-Θ_y(s)+y_d(s))

In formula, y_dS () is sensor harmonic wave y_dThe pull-type conversion of (t).

As can be seen from the above equation, due to mass unbalance and the presence of sensor harmonic wave, cause to exist in coil current with Rotating speed is with frequency current component-K_sK_iG_c(s)G_w(s)(Y(s)-Θ_y(s)) and frequency multiplication current component-K_sK_iG_c(s)G_w(s)y_d (s)。

Harmonic vibration caused by harmonic current can pass to spacecraft by magnetic bearing, so as to influence spacecraft appearance indirectly State control accuracy.Therefore, effective suppression of harmonic current is very important；

A kind of magnetic suspension rotor odd harmonic electric current suppressing method based on second order odd repetitive controller of step (2)

For there are problems that in step (1) coil current harmonic current this, the present invention is based on second order odd using a kind of The magnetic suspension rotor odd harmonic electric current suppressing method of repetitive controller suppresses to harmonic current.

For X passage harmonic current, SOORC is inserted on the basis of former X passage closed-loop system, as shown in Figure 7.By X passage Offset deviation that rotor unbalance quality causes and sensor harmonic wave are used as interference signal R_x(s) and D_x(s), by controller G_c(s) and power amplifier G_wS () forms harmonic current I afterwards_x(s)。I_xS () feeds back to input through two-way, all the way by rotor-support-foundation system G_p S (), another road is then by the SOORC of " insertion ".The concrete structure block diagram of SOORC is as shown in figure 9, wherein I (z) is X logical in Fig. 7 Harmonic current I in road_xCurrent sequence after (s) discretization, i.e. tracking error, k_rcIt is the gain of SOORC controllers, N is discrete The cycle of current sequence I (z), and have N=f_s/f₀, f₀It is the fundamental frequency in X passage harmonic current component, f_sFor systematic sampling frequently Rate；N₂Represent the discrete time delay sampling number of SOORC.K_fZ () represents in low-frequency range and the phase compensation function of Mid Frequency, is setting In meter,The phase compensation function of high band is represented, Q (z) is low pass filter.

Because X, Y passage are mutually decoupled, therefore above-mentioned X passage can be copied to obtain harmonic current for Y passages current harmonics elimination Suppressor mode.It is as follows that Y channel currents suppress specific implementation step：SOORC, such as Fig. 8 are inserted on the basis of former Y passages closed-loop system Shown, the offset deviation and sensor harmonic wave caused by Y passage rotor unbalance quality are used as interference signal R_y(s) and D_y (s), by controller G_c(s) and power amplifier G_wS () forms harmonic current I afterwards_y(s), I_yS () feeds back to input through two-way, all the way By rotor-support-foundation system G_pS (), another road is then by the SOORC of " insertion ".The concrete structure block diagram of SOORC controllers is such as in Fig. 8 Shown in Fig. 9, now I (z) is Y passage harmonic currents I_yCurrent sequence after (s) discretization, i.e. tracking error, k_rcIt is SOORC The gain of controller, N is the cycle of stray currents sequence I (z), and has N=f_s/f₀, f₀For in Y passage harmonic current components Fundamental frequency, f_sIt is system sampling frequency；N2 represents the discrete time delay sampling number of SOORC.K_f(z),And Q (z) effect, Define consistent with X passage.

As shown in Figure 9, the transmission function G of SOORC structures_SOORCZ () can be expressed as：

Wherein,k_rcIt is G_SOORCZ the controller gain corresponding to (), Q (z) is low pass Wave filter.

SOORC controller design processes are as follows：

The magnetic suspension rotor system of present invention application, under speed conditions high, it can be seen from spectrum analysis, rotor is effectively humorous Wave disturbance is mainly manifested in frequency, frequency tripling, fifth harmonic, seven frequencys multiplication and nine frequencys multiplication.Therefore knowable to result of spectrum analysis, the rotor Odd harmonic frequencies component in system occupies the leading position of harmonic current component.For the magnetic suspension rotor system, design Second order odd harmonic frequencies suppress structure (SOORC) as shown in figure 9, the transmission function G of its internal model structure_SOORCZ () can represent For：

Wherein, w₁-w₂=1

Stability analysis and delayed phase-lead compensation ring layout：

A), stability analysis：

For closed-loop system as shown in Figure 7,8, if meeting following condition simultaneously, closed-loop system is asymptotically stability：

Condition 1：

If 0<w₂<1, then

If -1<w₂<0, then

Condition 2：

Condition 1 and condition 2 are set up and must meet below equation relation：

Wherein,It is system function after phase compensation,WithAfter representing phase compensation respectively System functionAmplitude and phase angle；It is low-frequency compensation function in system,WithRepresent respectivelyAmplitude and phase angle；Original system function is represented,With System function is represented respectivelyAmplitude and phase angle；It is low pass filter；For system high-frequency is mended Repay link；T_sIt is the control system sampling time；N₂It is discrete system time delay sampling number.

For system shown in Figure 9, k_rcSpan given by condition 1, N₂Span given by condition 2.For For one real system,And T_sω(ω≈ω_c) it is that, it is known that therefore, systematic parameter can be with It is determined that.

B), delayed phase-lead compensation ring layout：

Phase compensation link K_fZ the general type of () is：

K_f(z)=G₁(z)G₂ ^m(z)G₃(z) q (z) (m=0,1,2 ...)

Wherein, G₁Z () is low-frequency compensation, its general expression-form is (Z () is discretization mark)：

Coefficient b specifically chooses according to system, realizes that system low-frequency range characteristic is effectively corrected, and medium-high frequency section characteristic variations are very It is small.

G₂ ^mZ () is Mid Frequency lead compensation, General Expression form is：

Mid Frequency phase compensation link G₂ ^mZ () is made up of m phase differentiation element.By each phase differentiation element institute energy The maximum advance angle of offer is no more than 65 °, therefore G₂Z maximum advance angle that () can be provided is no more than m × 65 °.In order to ensure System has certain phase redundancy and signal to noise ratio after correction, typically causes that the advance angle that each differentiation element is provided is arrived at 40 ° Between 50 °.The angle of stable state needs and the advance angle of each differentiation element offer are reached according to system to determine m values.Such as Phase corresponding to system bode figure phase minimum points isThe advance angle that selection differentiation element is provided is 45 °, then：

G₃Z () is middle low-frequency range correction or lag, General Expression form is：

System is by G₂ ^mAfter the leading phase compensation of (z), it is possible to so that system phase generation is larger in middle low-frequency range The change of amplitude, so as to influence systematic entirety energy.To weaken due to G₂ ^mZ the influence of () to low-frequency range in system is, it is necessary to add Correction or lag link G₃(z)。

Coefficient c, parameter T_bAccording to G₂ ^m(z) anticipatory control effect design so that system is by G₂ ^mIn after (z) anticipatory control Frequency range phase meets system stable condition.

Q (z) is that cut-off frequency is ω_cLow pass filter, General Expression form is：

Wherein, ω_cIt is system cut-off frequency, high frequency compensation link can be weakenedTo the phase effect of system high-frequency section.

In sum, by introducing phase compensation function and gain coefficient, it is ensured that the stabilization of system after algorithm addition Property.

The content not being described in detail in description of the invention belongs to prior art known to professional and technical personnel in the field.

Claims (2)

1. a kind of magnetic suspension rotor odd harmonic electric current suppressing method based on second order odd repetitive controller, it is characterised in that： Comprise the following steps：

Step (1)：Set up the magnetic suspension rotor kinetic model containing mass unbalance and sensor harmonic wave；

Radially two translational degree of freedom, respectively by active magnetic bearings control, radially two twist the free degree and axial translation to magnetic suspension rotor The free degree realizes passive stabilization suspension control by the permanent-magnetic clamp on rotor and stator, i.e. passive magnetic bearing respectively, wherein, Q is magnetic bearing stator geometric center, and O is rotor geometric center, and C is rotor centroid, and inertial coodinate system QXY is set up centered on Q, Rotating coordinate system O ε η are set up centered on O, (x, y) represents the coordinate value in inertial coodinate system lower rotor part geometric center O；

For X passage harmonic current, model as follows：

Magnetic suspension rotor kinetics equation in the X direction can be obtained by Newton's second law as follows：

$m\stackrel{\&CenterDot;\&CenterDot;}{x}=f_x+{\mathrm{me\&Omega;}}^{2}cos(\mathrm{\&Omega;}t+\mathrm{\&phi;})$

Wherein, m is rotor quality, f_xBe magnetic bearing in the bearing of X-direction, e is inclined between rotor geometric center and barycenter Difference, Ω is rotor speed, and φ is the initial phase of rotor unbalance quality；

The structure of main passive magnetic bearing is made up of active magnetic bearings and passive magnetic bearing, and the bearing of main passive magnetic bearing is by actively The electromagnetic force of magnetic bearing and the permanent magnetic composition of passive magnetic bearing, therefore X passage axis load f_xCan be written as：

f_x=f_ex+f_px

Wherein, f_exIt is the electromagnetic force of X passage active magnetic bearings, f_pxIt is the permanent magnetic of X passage passive magnetic bearing, wherein, passive magnetic The permanent magnetic of bearing is linear with displacement, is expressed as：

f_px=K_prx

Wherein, K_prIt is passive magnetic bearing displacement rigidity；X is shift values of the inertial coodinate system lower rotor part geometric center O in X passage；

When rotor suspension is near magnetic center, active magnetic bearings electromagnetic force can approximately linear turn to：

f_ex≈K_erx+K_ii_x

Wherein, K_er、K_iRespectively active magnetic bearings displacement rigidity, current stiffness, i_xIt is power amplifier output current；

Then have for the rotor-support-foundation system containing mass unbalance：

X (t)=x (t)+Θ_x(t)

Wherein, X (t) is rotor centroid displacement, and x (t) is rotor geometric center displacement, Θ_xT position that () causes for mass unbalance Disturbance is moved, is designated as：

Θ_x(t)=lcos (Ω t+ θ)

Wherein, l is the amplitude of mass unbalance, and θ is phase, and Ω is rotor speed；

In in view of actual rotor system, because of the influence of the factor such as uneven of machining accuracy and material, usual sensor Harmonic wave is inevitable, therefore the actually measured displacement x of sensor_sT () is represented by：

x_s(t)=x (t)+x_d(t)

Wherein, x_dT () is sensor harmonic wave, rewritable to be：

$x_d\left(t\right)=\underset{a=1}{\overset{w}{\mathrm{\&Sigma;}}}{c}_{a}sin(a\mathrm{\&Omega;}t+{\mathrm{\&theta;}}_a)$

Wherein, c_aIt is the amplitude of sensor harmonic constant, θ_aIt is the phase of sensor harmonic constant, w is the highest of sensor harmonic wave Number of times；

By i_x、X(t)、Θ_x(t)、x_dT () carries out Laplace transform and obtains i successively_x(s)、X(s)、Θ_x(s)、x_dS (), writes out and turns Subdynamics equation has：

ms²X (s)=(K_er+K_pr)(X(s)-Θ_x(s))+K_ii_x(s)

Wherein,

i_x(s)=- K_sK_iG_c(s)G_w(s)(X(s)-Θ_x(s)+x_d(s))

Wherein, K_sIt is displacement transducer gain link, G_cS () is controller link, G_wS () is power amplifier link；

From above formula, the presence of and sensor harmonic wave uneven because of rotor quality causes to exist in coil current same with rotating speed Current component-the K of frequency_sK_iG_c(s)G_w(s)(X(s)-Θ_x(s)) and frequency multiplication current component-K_sK_iG_c(s)G_w(s)x_d(s), and Frequency multiplication electric current can be again converted under magnetic bearing nonlinear interaction with frequency electric current；

In active magnetic bearings controllable radial direction translational degree of freedom X passage and Y passages, two passages decoupling, so Y channel current moulds Type is similar to X passage, makes a concrete analysis of as follows：

Rotor dynamics equation has：

ms²Y (s)=(K_er+K_pr)(Y(s)-Θ_y(s))+K_ii_y(s)

In formula, Y (s) is the pull-type conversion of rotor centroid displacement y (t), Θ_yS shift perturbation Θ that () causes for mass unbalance_y The pull-type conversion of (t), i_yS () is Y passage power amplifier output currents i_yThe pull-type conversion of (t)；

In above formula,

i_y(s)=- K_sK_iG_c(s)G_w(s)(Y(s)-Θ_y(s)+y_d(s))

In formula, y_dS () is sensor harmonic wave y_dThe pull-type conversion of (t)；

From above formula, because of mass unbalance and the presence of sensor harmonic wave, cause to exist with rotating speed with frequency in coil current Current component-K_sK_iG_c(s)G_w(s)(Y(s)-Θ_y(s)) and frequency multiplication current component-K_sK_iG_c(s)G_w(s)y_d(s)；

Step (2)：A kind of magnetic suspension rotor odd harmonic electric current suppressing method based on second order odd repetitive controller of design

Second order odd repetitive controller (SOORC), control targe is suppressed to odd harmonic electric current, and SOORC controllers are with " slotting Enter " the form former closed-loop system of insertion, harmonic current i_xIt is input into the plug-in type repetitive controller module as error signal, should The output of module feeds back to the power amplifier input of former control system, and the design of the module mainly includes three below step：

1. SOORC structure algorithms, frequency spectrum is carried out by the produced harmonic current under any rotating speed of magnetic suspension rotor system Analysis understands that harmonic current frequency content is mainly odd harmonic in magnetic suspension rotor system, and general according to SOORC structures sets Meter mode, design is the corresponding Order RC internal model link of odd harmonic frequency multiplication with dominant frequency, in harmonic current predominantly The odd harmonic component of position is obtained by spectrum analysis；

2. SOORC structural weights factor design, for the RC controllers after improvement, stability analysis is carried out according to stability criteria W in structure is obtained afterwards₁And w₂The relation and term of reference of two weight coefficients, by appropriate regulation weight coefficient may be such that this two Level system control process when harmonic current frequency changes or do not know has certain robustness；

3. phase lead-lag compensation link is made up of phase lead-lag correction link and low-pass first order filter, according to being System function phase-frequency characteristic and stability of a system condition determine that the compensation tache can improve the stability of a system, widen controller gain The value upper limit, while making that the redundancy of system stability design increases and dynamic property and steady-state behaviour have and necessarily change It is kind.

2. a kind of magnetic suspension rotor system odd harmonic based on second order odd repetitive controller according to claim 1 is electric Stream suppressing method, it is characterised in that：Described step (2) electric current restrainable algorithms are：

1. the structure design of SOORC

Repetitive controller (RC) is to realize that error signal is tracked based on internal model principle, can be by introducing infinite multiple closed-loop poles To eliminateMultiplied frequency harmonic component, although traditional reinforced concrete structure can realize the suppression of all multiplied frequency harmonic components, adopts During with traditional RC, control system is poor to the robustness that frequency changes.SOORC structures are introduced and suppress the interior of multiplied frequency harmonic component Modular ring section, can be accurately positioned for the harmonics frequency component realization for needing to suppress and be introduced with limit, so that, in pull-in frequency point Place, system frequency response is infinite gain；

SOORC structure transmission functions G_SOORCZ () can be expressed as：

$G_{SOORC}\left(z\right)=-k_{rc}\&CenterDot;\frac{W\left(z\right)}{1+W\left(z\right)Q\left(z\right)z^{-N_2}}=-k_{rc}\&CenterDot;\frac{\&lsqb;w_1{z}^{-\frac{N}{2}}+w_2{z}^{-N}\&rsqb;}{1+\&lsqb;w_1{z}^{-\frac{N}{2}}+w_2{z}^{-N}\&rsqb;Q\left(z\right)}{z}^{N_2}$

Wherein,k_rcIt is G_SOORCZ the controller gain corresponding to (), Q (z) is LPF Device；N₂Represent the discrete time delay sampling number of SOORC；

It can be seen from spectrum analysis according to the harmonic current that the magnetic suspension rotor system under any rotating speed is produced, the main frequency of harmonic current Rate composition is odd harmonic, and according to the general fashion that SOORC is designed, design is based on 2k+1 (k=0.1.2.3...) secondary dominant pilot The SOORC internal model links of rate；

It can be seen from SOORC internal model principles, the frequency response of odd harmonic terms can almost be suppressed to zero.SOORC and tradition RC is compared, and when harmonic current frequency changes or do not know, the robustness of control system is improved.Meanwhile, controller Gain k_rcAppropriate adjustment, dynamic performance can be improved；

2. phase compensation function K_fThe design of (z)

To ensure the stability of system, a kind of system amplitude-frequency spy being in series based on multiple differentiation elements and delay component is devised Property bearing calibration, i.e.,：Penalty function K_fZ () is designed as：

K_f(z)=G₁(z)G₂ ^m(z)G₃(z) q (z) (m=0,1,2 ...)

Wherein, G₁Z () is low-frequency compensation, its general expression-form is：

$G_1\left(z\right)=Z\left(\frac{bs+1}{s}\right)$

Z () is discretization mark, and coefficient b specifically chooses according to system, realizes effective correction of system low-frequency range, simultaneity factor The characteristic variations very little of medium-high frequency section；

G₂ ^mZ () is the m Mid Frequency phase compensation function of leading phase compensation link of series connection, General Expression form is：

${G_2}^m\left(z\right)=Z\left({\left(\frac{{\mathrm{aT}}_{a}s+1}{T_{a}s+1}\right)}^m\right),(m=0,1,2...)$

Coefficient a, parameter T_a, m according to system phase compensate demand specifically choose, realize effective correction of system Mid Frequency characteristic；

G₃Z () is middle low-frequency range correction or lag, General Expression form is：

$G_3\left(z\right)=Z\left(\frac{1+{\mathrm{cT}}_{b}s}{1+T_{b}s}\right)$

Coefficient c, parameter T_bAccording to G₂ ^m(z) anticipatory control effect design so that system is by G₂ ^mMid Frequency after (z) anticipatory control Meet system stable condition；

Q (z) is that cut-off frequency is ω_cA low pass filter, General Expression form is：

$q\left(z\right)=Z\left(\frac{{\mathrm{\&omega;}}_c}{s+{\mathrm{\&omega;}}_c}\right)$

Wherein, ω_cIt is system cut-off frequency；

By the way of above link is in series, the redundancy of system stability design can be improved, while improving system dynamic Energy and steady-state behaviour.