CN1710800A - A Magnetic Bearing Control System for Accurately Compensating the Stiffness of Magnetic Suspension Control Moment Gyro Support - Google Patents

Abstract

The disclosed control system includes flywheel body, power amplifier for magnetic bearing, controller for magnetic bearing and adaptive compensator. Through collecting signals including angular rate of frame, speed of rotor, and displacement of rotor, the adaptive compensator carries out adaptive compensation calculation. Sum of calculated compensation quantity and the output of controller for magnetic bearing is connected to the power amplifier for magnetic bearing in order to eliminate disturbing moment on rotor of magnetic suspension caused by moving frame. The invention lowers displacement of rotor caused by rotation of frame, raises response speed and precision of angular rate of frame, and improves response speed and precision of moment output of magnetic suspension control moment.

Description

A kind of magnetic bearing control system of accurately compensating magnetic suspension control torque gyroscope support rigidity

Affiliated technical field

The present invention relates to a kind of magnetic suspension control system, the magnetic bearing rigidity in the time of can being used for the rotation of accurately compensating magnetic suspension control torque gyroscope (Control Moment Gyroscope-CMG) framework.

Background technology

Control-moment gyro (CMG) is that Large Spacecraft such as space station are carried out attitude and controlled necessary crucial actuator.CMG is made up of high-speed rotor system and framework servo system, and frame system is forced the high speed rotor precession, and the output gyroscopic couple is used to adjust spacecraft attitude.The high speed rotor supporting is the critical component of CMG, and mechanical ball bearing supporting and magnetic bearing supporting dual mode are arranged usually, and corresponding C MG is called mechanical CMG and magnetic suspension CMG.Existing CMG all adopts mechanical support, and the friction and wear in the mechanical support will influence the reliability and the useful life of CMG system, cause higher power consumption simultaneously.The rotating speed of mechanical support rotor is lower, and the volume and weight of mechanical CMG is all bigger under the certain condition of angular momentum.Adopting another drawback of mechanical support is that bearing rigidity is variable hardly, causes the vibration of rotor bigger.This is because the CMG output torque is to come from flywheel bearing rigidity after all.Frame corners speed is high more, and gyroscopic couple is big more, and the bearing and the bearing rigidity that need are also big more, thereby the bearing rigidity that the bearing rigidity that needs during the framework maximum speed needs when more static than framework is much bigger.The rigidity of mechanical support is non-adjustable, maximum demand rigidity that so its rigidity is inevitable when always surpassing corresponding the highest framework rotating speed, rotor when this rigidity is zero for the framework rotating speed obviously is excessive, thereby the rotor oscillation of mechanical CMG and noise are all very big, also influence frame corners speed precision and CMG output torque precision simultaneously.

The introducing magnetic bearing supports as high speed rotor can eliminate the supporting friction and wear, and reduces unbalance vibration but still existing problems.For magnetic suspension CMG; in the control of magnetic bearing requires to be suspended near the protection center, gap rotor stability among a small circle; but magnetic bearing is a kind of elastic bearing; framework rotates and will produce disturbance and rotor displacement is strengthened magnetic suspension rotor; even make rotor run into the protection bearing, have a strong impact on the stability of magnetic suspension rotor system.In order to reduce the rotor response and to improve the stability of a system, must improve the elastic supporting rigidity of magnetic bearing.Prior art adopts the fixing closed loop compensation method of parameter usually, promptly directly improves the closed loop rigidity of magnetic bearing.The control system of this kind compensation comprises the flywheel body, the magnetic bearing power amplifier, magnetic bearing controller, wherein the flywheel body is again by the magnetic bearing electromagnet, rotor, displacement transducer and rotor-drive are formed, the displacement of the continuous detection rotor relative equilibrium of displacement transducer position, as long as displacement signal non-zero, magnetic bearing controller is according to the size of displacement signal, calculate control signal according to set control algolithm, control signal puts on the magnetic bearing power amplifier, make it to produce the magnetic bearing electric current that is directly proportional with control signal, this electric current will produce electromagnetic force after feeding the magnetic bearing magnet spool, act on rotor and make it to get back to the equilbrium position.Yet this real system adopts PID control usually on the one hand, and it is very big that differential coefficient is not wherein allowed by the restriction of noise level, will reduce system damping if rigidity is too high, causes system's instability; On the other hand, there is certain excursion in frame corners speed, cause disturbance even the high rigidity of preset parameter still in stability range, also is difficult to adapt to the frame corners speed of variation, thereby the precision of compensation is relatively poor.

Summary of the invention

Technology of the present invention is dealt with problems: provide a kind of under the prerequisite that does not influence magnetic suspension system stability, overcome influencing each other of magnetic suspension system and frame system, the phenomenon that the magnetic suspension rotor displacement strengthens when overcoming the framework rotation, eliminate framework simultaneously and rotate the magnetic suspension rotor motion cause reaction frame system, improve the angular speed precision of frame system, also improve the magnetic bearing control system of the accurately compensating magnetic suspension CMG support stiffness of the precision of magnetic suspension CMG moment output and response speed.

Technical solution of the present invention: a kind of magnetic bearing control system of accurately compensating magnetic suspension control torque gyroscope support rigidity, comprise the flywheel body, the magnetic bearing power amplifier, magnetic bearing controller, wherein the flywheel body is again by the magnetic bearing electromagnet, rotor, displacement transducer and rotor-drive are formed, it is characterized in that: also comprise adaptive compensator, adaptive compensator is gathered the frame corners rate signal, rotor speed signal and rotor displacement signal, after carrying out the adaptive equalization computing, with be connected to the magnetic bearing power amplifier after the output of the magnetic bearing controller summation, make that magnetic bearing electric current and bearing are corresponding to be compensated, the disturbing moment that when being used to offset frame movement magnetic suspension rotor is applied.

Described adaptive compensator is made up of pseudo-object filter, LMS algorithm and compensation tache, and pseudo-object filter is gathered the rotor speed signal, and to calculate each element value in the pseudo-object filter, these element values all are parameter with rotor speed; Pseudo-object filter is gathered the frame corners rate signal simultaneously and is carried out filtering, and the rotor displacement signal of filtered angle rate signal and sign compensating error is through the computing of LMS algorithm, and operation result is delivered to compensation tache, to regulate the penalty coefficient of compensation tache; Compensation tache be input as the frame corners rate signal, the size of this characterization disturbance through exporting compensating signal after the compensation tache computing, with the output summation of magnetic bearing controller, is delivered to the magnetic bearing power amplifier again.

Basic principle of the present invention is: the influence to the magnetic suspension rotor motion during frame movement is equivalent to rotor has been applied a disturbing moment, and the perturbed force that this disturbing moment is converted each passage of radial direction magnetic bearing is F _G1=F _rk _G1[1-1-1 1] ^Tω _g, wherein ${\mathrm{<figure-callout\; id="1"\; label="k\; g"\; filenames="A20051001213300122.png"\; state="\{\{state\}\}">k</figure-callout>}}_g=\frac{\sqrt{2}}{2}\mathrm{\&pi;}{J}_Z{/l}_m,$ Four components are represented radially four passage AX, AY, BX, BY, ω successively _gAnd F _rBe respectively frame corners speed and rotor speed, J _zBe rotor pole moment of inertia, l _mBe the distance of rotor center to the magnetic bearing center.Under the effect of perturbed force, bigger displacement will appear in suspension rotor, even collision magnetic bearing stator, thereby must the influence of frame movement be compensated.The basic principle of compensation is exactly, according to ω _gSize, suitably increase the input signal of magnetic bearing power amplifier, the corresponding increase of magnetic bearing electric current and bearing, the bearing compensation rate F of increase _G2Must offset F just _G1, i.e. F _G1+ F _G2=0, thus the influence of offsetting perturbed force.The definition disturbance quantity is a magnetic bearing rigidity with the ratio of rotor displacement, rotor displacement is not directly proportional with disturbance quantity when then not doing compensation, rigidity is fixed, and after doing compensation, even disturbance strengthens, rotor displacement also can maintain on the less value, that is to say that rigidity increases with the increasing of disturbance, and this has just realized the compensation to magnetic bearing rigidity.But, the bearing compensation rate is F in theory _G2=k _ik _wu _i, k wherein _i=diag[k _Iaxk _Ibxk _Iayk _Iby] be the current stiffness of magnetic bearing, k _w=diag[k _Waxk _Wbxk _Wayk _Wby] DC current gain of magnetic bearing power amplifier, u _i=[u _Iaxu _Ibxu _Iayu _Iby] ^TCompensation rate for magnetic bearing power amplifier input signal.By F _G1+ F _G2=0 can release, $u_i=-F_r{k}_{g1}{k}_w^{-1}{k}_i^{-1}{\left[\begin{array}{cccc}1& -1& -1& 1\end{array}\right]}^T{\mathrm{\&omega;}}_g.$ But in real system, always there is error in modeling, especially because magnetic bearing-rotor-support-foundation system non-linear, and k _iValue can not be very accurate, and error size also may change with the variation of operating state or drift about, and these errors will have a strong impact on the effect of compensation.In order to improve compensation precision, the present invention introduces adaptive compensator, promptly adopts adaptive algorithm to carry out adaptive equalization in line computation ui value.

The principle of adaptive equalization is: can know that according to above-mentioned compensation principle the theoretical value of compensation tache is $W=-F_r{k}_{g1}{k}_w^{-1}{k}_i^{-1}{\left[\begin{array}{cccc}1& -1& -1& 1\end{array}\right]}^T$ That is ω _gTo u _iWeights.But k _iActual value the unknown, thereby can only adopt adaptive algorithm that weights W is carried out on-line optimization.Adopt the LMS algorithm to be optimized, the target of optimization is the variance minimum of rotor displacement signal.The LMS algorithmic formula is W _i(n+1)=W _i(n)+2 μ p _i(n) q _i(n), i=1 wherein, 2,3,4 representatives are four passages radially, p _iAnd q _iBe respectively filter back angle rate signal and rotor displacement signal.The result of calculation of algorithm is used for upgrading the weights of compensation tache.The characteristics of LMS algorithm are that error behind the weight convergence (being the rotor displacement signal here) (is the compensation tache input here with the weighting input, be the frame corners rate signal) will be incoherent, thereby frame movement will not influence rotor motion, this has just realized the compensation to the framework disturbing influence, has avoided the influence of model error to compensation precision simultaneously.One of input of LMS algorithm is the angle rate signal that adopts after pseudo-object filter is filtered, rather than directly adopts the reason of frame corners rate signal to be, can guarantee weight convergence like this, guarantees the stability of adaptive algorithm.

The present invention's advantage compared with prior art is: (1) adopts open loop approach, according to the height of frame corners speed and rotor speed, compensate the magnetic axis load in proportion, not only simply effectively be easy to realize, and do not influence closed loop characteristic, overcome the shortcoming that the closed loop compensation mode influences the stability of a system; (2) compensation back magnetic bearing rigidity increases and decreases with the lifting of framework rotating speed, the danger that rotor displacement increases when both having avoided frame movement, and the intensity that can not aggravate the rotor unbalance vibration; (3) the compensation tache online adaptive is adjusted penalty coefficient at any time according to compensation effect, eliminated the compensating error that the drift of model error or image parameter causes, significantly improve the precision of bearing compensation, thereby also further improved moment output accuracy and the response speed of magnetic suspension CMG, overcome the relatively poor shortcoming of preset parameter compensation way precision.

Description of drawings

Fig. 1 is a theory diagram of the present invention;

Fig. 2 is a flywheel body schematic diagram of the present invention;

Fig. 3 is an adaptive compensator theory diagram of the present invention;

Fig. 4 is an adaptive algorithm flow chart of the present invention.

Embodiment

As shown in Figure 1, the present invention mainly comprises flywheel body 2, magnetic bearing power amplifier 3, magnetic bearing controller 5, wherein flywheel body 2 is again by magnetic bearing electromagnet 6, rotor 7, displacement transducer 8 and rotor-drive are formed, CMG is also needed subsidiary framework drive system, as driving the device that framework makes it to reach given angular speed, export the needed frame corners rate signal of magnetic suspension control system simultaneously; Flywheel body 2 is also needed subsidiary rotor electric machine drive system,, export the needed rotor speed signal of magnetic suspension control system simultaneously as driving the device that rotor 7 makes it to reach rated speed.The rotor displacement signal is linked controller 5, export control signal through after the computing, frame corners rate signal, rotor speed signal and rotor displacement signal are linked adaptive compensator 4 simultaneously, its middle frame tach signal and flywheel tach signal should adopt the linear optical coupling circuit to isolate, and the rotor displacement signal can directly connect.Act on magnetic bearing power amplifier 3 after the output summation of the output of adaptive compensator 4 and magnetic bearing controller 5, the electric current of output flows into magnetic bearing electromagnet 6 coils of flywheel body 2 inside.The said frame angle rate signal also can be used the given signal of angular speed of frame system instead.

As shown in Figure 2, flywheel body 2 is made up of flywheel rotor 7, magnetic bearing electromagnet 6 and displacement transducer 8.Flywheel body 2 is divided into A, B two ends, and the A end has a pair of radially quadrature to place magnetic bearing electromagnet 6 and displacement transducer 8, and the latter is in the former outside; The B end configuration of flywheel body 2 and the complete symmetry of A end.

As shown in Figure 3, adaptive compensator 4 is made up of pseudo-object filter 10, LMS algorithm 11 and compensation tache 9, and pseudo-object filter 10 is gathered the rotor speed signal, to calculate pseudo-object filter 10F (z, F _r) in each element value; Pseudo-object filter 10 is gathered the frame corners rate signal simultaneously and is carried out filtering, and the rotor displacement signal of filtered angle rate signal and sign compensating error is through 11 computings of LMS algorithm, and the LMS algorithmic formula is W _i(n+1)=W _{I (}N)+2 μ p _i(n) q _i(n), i=1 wherein, 2,3,4 representatives are four passages radially, p _iAnd q _iBe respectively filter back angle rate signal and rotor displacement signal.Operation result is delivered to compensation tache 9, to regulate the penalty coefficient W=[W of compensation tache 9 ₁W ₂W ₃W ₄] ^T, all upgrade in each sampling period; Compensation tache 9 be input as the frame corners rate signal, the size of this characterization disturbance, through exporting compensating signal after compensation tache 9 computings, its value is u _i=-W ω _g, magnetic bearing power amplifier 3 is delivered in the output summation of this compensation rate and magnetic bearing controller 5 again.

The LMS algorithm is adopted in the renewal of penalty coefficient W battle array, and as shown in Figure 4, idiographic flow is:

1. initialization: need initialized variable to be divided into two classes, the first kind is Chang Bianliang, comprises convergence factor μ, magnetic bearing power amplifier 3 nominal multiplication factor k _w, magnetic bearing current stiffness k _i, pseudo-object filter 10F (z, F _r) each rank coefficient f of element _i(l), m is a top step number.F (z, F wherein _r) each element be respectively object model G (z, F _r) row element and, even object model is:

$G(z,F_r)=\left[\begin{array}{cccc}{G}_{11}(z,F_r)& G_{12}(z,F_r)& G_{13}(z,F_r)& G_{14}(z,F_r)\\ G_{21}(z,F_r)& G_{22}(z,F_r)& G_{23}(z,F_r)& G_{24}(z,F_r)\\ G_{31}(z,F_r)& G_{32}(z,F_r)& G_{33}(z,F^r)& G_{34}(z,F_r)\\ G_{41}(z,F_r)& G_{42}(z,F_r)& G_{43}(z,F_r)& G_{44}(z,F_r)\end{array}\right]$

Then pseudo-object filter 10 is:

$F(z,F_r)=\left[\begin{array}{c}{F}_1\\ F_2\\ F_3\\ F_4\end{array}\right]=\left[\begin{array}{c}{G}_{11}(z,F_r)+G_{12}(z,F_r)+G_{13}(z,F_r)+G_{14}(z,F_r)\\ G_{21}(z,F_r)+G_{22}(z,F_r)+G_{23}(z,F_r)+G_{24}(z,F_r)\\ G_{31}(z,F_r)+G_{32}(z,F_r)+G_{33}(z,F_r)+G_{34}(z,F_r)\\ G_{41}(z,F_r)+G_{42}(z,F_r)+G_{43}(z,F_r)+G_{44}(z,F_r)\end{array}\right]$

And object model $G(z,F_r)=G_1(z,F_r)k_w^{-1}{k}_j^{-1},$ G wherein ₁(z, F _r) being output as input in the magnetic suspension system model with adaptive compensator 4, the rotor displacement signal is the pulsed transfer function of output, k _wBe magnetic bearing power amplifier 3 models, k _iBe magnetic bearing electromagnet 6 nominal current stiffnesses (according to the magnetic bearing current stiffness that the calculation of design parameters of the magnetic bearing that has designed is come out, there is certain difference in it with the magnetic bearing current stiffness of reality).The initial value of the variable that second class was upgraded for each sampling period comprises the initial value of penalty coefficient and the frame corners rate value of a preceding m sampling instant, and the former is $W\left(0\right)=-F_r{k}_{g1}{k}_w^{-1}{k}_i^{-1}{\left[\begin{array}{cccc}1& -1& -1& 1\end{array}\right]}^T,$ Calculate according to nominal model, and the latter can directly get null value.

2. sampling instant is judged: sampling instant arrives and then enters the loop body of algorithm, otherwise waits for.The sampling period of program can be got 1ms.

3. algorithm loop body: comprise data acquisition, calculate, steps such as output and renewal.

The content of data acquisition comprises current frame corners speed ω _g(n), current rotor speed F _r(n), current rotor displacement q _i(n); The content of calculating comprises the current output p of pseudo-object filter 10 _i(n), current penalty coefficient W _i(n+1), the current output u of compensation tache 9 _i(n+1), algorithm is:

$P_i\left(n\right)=\underset{l=0}{\overset{m}{\mathrm{\&Sigma;}}}{\mathrm{\&omega;}}_g(n-1)f_i\left(l\right)$

W _i(n+1)＝W _i(n)+2μp _i(n)q _i(n) i＝1，2，3，4

u _i(n+1)＝W _i(n+1)ω _g(n) i＝1，2，3，4

The content of output is current compensating signal u _i(n+1);

The content that numerical value upgrades comprises the output of penalty coefficient and pseudo-object filter 10, that is:

W _i(n)＝W _i(n+1) (i＝1，2，3，4)

ω _g(n-l)＝ω _g(n-l+I) (l＝1，2，...，m)

2. numerical value turn back to step after upgrading again, the circulation of a beginning new round.

Among the present invention, magnetic bearing controller 5 can be an analog or digital, and centralized control or decentralized control can be to adopt PID control, PID to add to intersect to control or other various suitable control methods; Magnetic bearing power amplifier 3 can be analog amplifier or digital power amplifier, can be Linear Power Amplifier or close power amplifier, close power amplifier can be again stagnate ring (Hysteresis) type, sampling maintenance (Sample/Hold) type, pulse-width modulation (PWM) type, minimum pulse width (MPW) type and three level types, and the collocation form of power amplifier power output pipe can be half-bridge or full-bridge; Magnetic bearing electromagnet 6 can be to adopt electromagnetism biasing or permanent magnet bias mode; Displacement transducer 8 can be current vortex type transducer or inductive type transducer.

In a word, the deficiency of magnetic bearing rigidity was avoided magnetic suspension rotor crash protection bearing when the present invention can effectively compensate the rotation of CMG framework.By introducing the frame corners rate signal, the electric current that compensation is directly proportional with this signal to the magnetic bearing electromagnet is realized the corresponding compensation to magnetic bearing rigidity, does not influence closed-loop system stability simultaneously.Regulate the compensating error of avoiding model error and drift to cause by penalty coefficient being carried out self adaptation.Magnetic suspension system rotor motion and frame system angular speed influences each other when adopting this method to eliminate frame movement, significantly reduce framework and rotated the rotor displacement that causes, significantly improve the angular speed response speed and the precision of framework, significantly improved moment output response speed and the precision of magnetic suspension CMG.

Claims (6)

1. A magnetic bearing control system that accurately compensates the rigidity of the gyro support for magnetic suspension control moment, including a flywheel body (2), a magnetic bearing power amplifier (3), and a magnetic bearing controller (5), wherein the flywheel body (2) is controlled by a magnetic bearing An electromagnet (6), a rotor (7), a displacement sensor (8) and a rotor drive system are composed, and it is characterized in that: an adaptive compensator (4) is also included, and the adaptive compensator (4) collects the frame angular rate signal, the rotor The rotational speed signal and the rotor displacement signal, after the adaptive compensation calculation, are summed with the output of the magnetic bearing controller (5) and then connected to the magnetic bearing power amplifier (3), so that the magnetic bearing current and bearing force are compensated accordingly for offsetting The disturbance torque applied to the maglev rotor when the frame moves. 2. The magnetic bearing control system for accurately compensating the rigidity of the gyro support for magnetic suspension control moment according to claim 1, characterized in that: the self-adaptive compensator (4) is composed of pseudo object filter (10), LMS algorithm (11 ) and compensation link (9), the pseudo-object filter (10) collects the rotor speed signal to calculate the value of each element in the pseudo-object filter (10), and these element values take the rotor speed as a parameter; the pseudo-object The filter (10) collects and filters the angular rate signal of the frame at the same time. The filtered angular rate signal and the rotor displacement signal representing the compensation error are calculated by the LMS algorithm (11), and the calculation result is sent to the compensation link (9) to adjust the compensation The compensation coefficient of the link (9); the input of the compensation link (9) is the frame angular rate signal, which represents the size of the disturbance, and the compensation signal is output after the calculation of the compensation link (9), and the output of the magnetic bearing controller (5) The summation is then sent to the magnetic bearing power amplifier (3). 3. The magnetic bearing control system for accurately compensating the stiffness of the gyro support for magnetic suspension control moment according to claim 1, characterized in that: the flywheel body (2) must be driven by the frame system (1) to obtain a frame along the frame axis Angular rate signal; the rotor (7) must reach the rated rotor speed signal under the drive of the rotor drive system. 4. According to claim 2, the magnetic bearing control system for accurately compensating the rigidity of the magnetic levitation control moment gyro support is characterized in that: the compensation link (9) is composed of four channels, and each channel is a proportional link, i.e. W (z)=[W ₁ W ₂ W ₃ W ₄ ] ^T , where the compensation coefficient W _i (i=1, 2, 3, 4) is four real numbers that are updated every sampling period. 5. The magnetic bearing control system for accurately compensating the stiffness of the magnetic levitation control moment gyro support according to claim 2, characterized in that: each element of the pseudo object filter (10) F(z, F _r ) is an object model The sum of row elements of G(z, F _r ), that is, if the object model is: $\mathrm{<span\; class="notranslate">\; G</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; z</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\left[\begin{array}{cccc}{\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; 11</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; z</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; )</span>& {\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; 12</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; z</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; )</span>& {\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; 13</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; z</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; )</span>& {\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; 14</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; z</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; )</span>\\ {\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; twenty\; one</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; z</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; )</span>& {\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; twenty\; two</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; z</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; )</span>& {\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; twenty\; three</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; z</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; )</span>& {\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; twenty\; four</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; z</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; )</span>\\ {\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; 31</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; z</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; )</span>& {\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; 32</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; z</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; )</span>& {\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; 33</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; z</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; )</span>& {\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; 34</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; z</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; )</span>\\ {\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; 41</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; z</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; )</span>& {\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; 42</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; z</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; )</span>& {\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; 43</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; z</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; )</span>& {\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; 44</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; z</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; )</span>\end{array}\right]$ Then the pseudo object filter (10) is: $<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; z</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\left[\begin{array}{c}{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\\ {\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}\\ {\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}\\ {\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}\end{array}\right]<span\; class="notranslate">\; =</span>\left[\begin{array}{c}{\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; 11</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; z</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; 12</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; z</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; 13</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; z</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; 14</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; z</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; )</span>\\ {\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; twenty\; one</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; z</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; twenty\; two</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; z</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; twenty\; three</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; z</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; twenty\; four</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; z</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; )</span>\\ {\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; 31</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; z</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; 32</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; z</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; 33</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; z</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; 34</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; z</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; )</span>\\ {\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; 41</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; z</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; 42</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; z</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; 43</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; z</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; 44</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; z</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; )</span>\end{array}\right]$ The object model $G(z,f_r)=G_1(z,f_r)k_w^{-1}{k}_i^{-1},$ Among them, G ₁ (z, F _r ) is the pulse transfer function of the magnetic levitation system model with the output of the adaptive compensator (4) as the input and the rotor displacement signal as the output, k _w is the model of the magnetic bearing power amplifier (3), and k _i is the current stiffness of the magnetic bearing electromagnet (6), and the rotor speed Fr is a parameter of the model. 6. The magnetic bearing control system for accurately compensating the stiffness of the magnetic levitation control moment gyro support according to claim 2, characterized in that: the formula of the LMS algorithm (11) is W _i (n+1)=W _i (n) +2μp _i (n)q _i (n), where μ is a pre-determined convergence factor, q _i is the rotor displacement signal, p _i is the output of the frame angular rate signal after passing through the pseudo object filter (10), i= 1, 2, 3, 4 represent the number of channels, and n is the number of samples.

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