CN102424117B - Method for compensating phase lag of magnetic bearing of magnetic suspension control moment gyro - Google Patents

Abstract

The invention relates to a method for compensating phase lag of a magnetic bearing of a magnetic suspension control moment gyro, in particular to a method for compensating phase lag of a switching power amplifier of the magnetic bearing of the magnetic suspension control moment gyro. The method provided by the invention comprises the following steps of: calculating a rated nutation frequency according to rated revolution speed of a magnetic suspension control moment gyro rotor and system parameters, testing phase frequency characteristic of a power amplifier system and determining a phase angle required to be compensated at the rated nutation frequency, thus obtaining an asymmetry factor of a double-parallel asymmetric sampling resistance network on the basis of measuring equivalent inductance and resistance of a winding of the magnetic bearing, and finally configuring the double-parallel asymmetric sampling resistance network according to the asymmetry factor. The method provided by the invention belongs to the technical field of control on spacecraft inertia actuating mechanism and can be applied to high-stability control on the magnetic suspension control moment gyro at high rotating speed.

Description

A kind of method that compensates the hysteresis of magnetic suspension control torque gyroscope magnetic bearing phase place

Technical field

The present invention relates to a kind of method that magnetic suspension control torque gyroscope magnetic bearing phase place lags behind that compensates, be applicable to the high stable control under the high rotating speed of magnetic suspension control torque gyroscope, belong to spacecraft inertia actuating mechanism controls technical field.

Background technology

Magnetic suspension control torque gyroscope (MSCMG) does not have friction because having, hangs down vibration, is easy to realize that outstanding advantage such as high precision and long life becomes the important development direction of spacecraft attitudes control inertia actuating units such as space station, space maneuver platform and quick maneuvering satellite.

In the MSCMG magnetic bearings control system, the effect of switch power amplifier is to provide corresponding electric current to produce needed electromagnetic force to the electromagnet bearing coil.The electromagnetic bearing switch power amplifier mainly contains pulse duration modulation (PWM) type, sampling maintenance, the chain rate that stagnates than four kinds of forms such as type and minimum pulse width types.Wherein, the advantage of PWM close power amplifier is that switching frequency is fixed, and can limit the width of minimum turn-on and turn-off pulse, and the output wave shape quality is good, stable state accuracy is high, reliability is high, has obtained widespread use in electromagnet bearing.Electromagnet bearing PWM close power amplifier mainly comprises controller, PWM generator, full-bridge power circuit and current sensor.

Electromagnet bearing PWM close power amplifier is actual to be a current tracking control circuit, and it is control variable with the electric current, and its target is the actual current of output can be tried one's best follow the tracks of input control signal undistortedly.But the phase place hysteresis outwardness of electromagnetic bearing switch power amplifier, it mainly comprises digital control time-delay and controlled object time-delay.

The MSCMG rotor-support-foundation system has strong gyro effect, and gyro effect is mainly reflected in nutating stability and precession stability for the influence of system stability, and wherein nutating stability is the principal element that influences system stability.The basic reason of nutating unstability is that the magnetic bearing control system phase place lags behind.The magnetic bearing control system phase place lags behind and comprises that mainly the phase place that magnetic bearing power amplification system phase place lags behind and various LPF link causes lags behind, and the hysteresis of the phase place of magnetic bearing power amplification system is the main aspect that whole magnetic bearing control system phase place lags behind.Therefore compensate the hysteresis of magnetic bearing power amplification system phase place and become emphasis and the difficult point that improves magnetic suspension rotor system stability.

At present, the method for compensation electromagnetic bearing power amplification system phase place hysteresis mainly comprises methods such as various Prediction Control (as the Smith Prediction Control), anticipatory control control and the control of boosting.The biggest advantage of Prediction Control is that big latency issue is converted into the design problem that does not have big time-delay, yet Prediction Control needs known object math modeling accurately, and is difficult in the reality obtain.So the robustness of Prediction Control is relatively poor, when model is inaccurate, can cause poor system performance, even unstable.Phase angle anticipatory control method need seal in the anticipatory control link in passage, must increase hardware circuit or the software calculated amount of system.Control method can increase the bandwidth of magnetic bearing power amplification system to a certain extent though boost, and it has increased power consumption and hardware circuit inevitably, and can't fundamentally compensate the controlled object time-delay.In addition, improve the proportionality coefficient of magnetic bearing power amplification system controller and the phase place hysteresis that the current feedback coefficient also can reduce system to a certain extent, but because of its restriction that is subjected to power amplifier magnification factor and power amplifier voltage and switching frequency etc., make its effect of phase compensation at high frequency treatment not remarkable.Therefore, the method that existing compensation electromagnetic bearing power amplifier phase place lags behind or reduced the reliability of system because of the hardware circuit that has increased system, because the software complexity that has increased the magnetic bearing power amplification system has brought more calculating time-delay, and calculate the phase place hysteresis that the increase of delaying time has aggravated the magnetic bearing power amplification system conversely.

Summary of the invention

The objective of the invention is: overcoming existing compensation electromagnetic bearing close power amplifier phase place hysteretic method need increase the deficiency of calculating time-delay or increasing a large amount of hardware circuits and method complexity, on the basis that only increases a small amount of hardware circuit, by two parallel asymmetric sampling resistor networks, realize effective compensation that MSCMG magnetic bearing power amplification system phase place is lagged behind.

Technical solution of the present invention is: rated speed of rotation and system parameter according to the magnetic suspension control torque gyroscope rotor are calculated specified nutation frequency, the phase angle of testing the open loop phase-frequency characteristic of magnetic bearing power amplification system and determining to compensate at specified nutation frequency place, and draw the dissymmetry factor of two parallel asymmetric sampling resistor networks on the basis of test magnetic bearing winding equivalent inductance and resistance, at last according to the two parallel asymmetric sampling resistor networks of dissymmetry factor configuration.Specifically may further comprise the steps:

(1) according to the rated speed of rotation Ω of magnetic suspension control torque gyroscope rotor _nSpecified nutation frequency ω with system parameter calculating magnetic suspension rotor _n:

${\mathrm{\ω}}_n=\frac{1}{2}[\left(\frac{J_a}{J_r}{\mathrm{\Ω}}_n\right)+\sqrt{{\left(\frac{J_a}{J_r}{\mathrm{\Ω}}_n\right)}^2+\frac{{8l}_m(l_s{k}_i{\mathrm{\λ}}_k-l_m{k}_x)}{J_r}}]$

Wherein, J _a, J _rBe respectively polar moment of inertia and the equator rotor inertia of rotor; l _m, l _sIt is respectively the magnetic suspension rotor center reaches the radial transducer center to the radial direction magnetic bearing center distance; k _i, k _xBe respectively current stiffness and the displacement rigidity of magnetic bearing; λ _kIt is the amplitude of control electric current amplitude versus frequency characte i (j ω);

(2) phase-frequency characteristic of test magnetic bearing power amplification system obtains the magnetic bearing power amplification system at the phase place hysteresis θ at specified nutation frequency place _n

(3) determine the phase theta that the magnetic bearing power amplification system need compensate at specified nutation frequency place _c=θ _n-θ ₀, θ wherein ₀Be the limit value of magnetic bearing power amplification system in the hysteresis of specified nutation frequency place phase place;

(4) adopt multi-meter and secohmmeter can measure the equivalent resistance R of bearing coil winding respectively _sAnd inductance L _s

(5) determine the big or small R of current sampling resistor _m, current sample is with the ratio k of divider resistance _AbAnd the op amp of current sampling circuit gain k;

(6) dissymmetry factor of definite two parallel asymmetric sampling resistor networks $\mathrm{\δ}=\frac{k_{\mathrm{ab}}{R}_m\tan {\mathrm{\θ}}_c}{L_s{\mathrm{\ω}}_n-(R_m+R_s){\tan \mathrm{\θ}}_c};$

(7) take into account power consumption and the signal to noise ratio of sampling resistor network, according to the divider resistance R of the two parallel asymmetric sampling resistor networks of dissymmetry factor δ configuration _a, R _b, R _cAnd R _d, R wherein _a=R _d,

$R_c=\frac{R_d[R_b-\mathrm{\δ}(R_a+R_b)]}{\mathrm{\δ}(R_a+R_b)+R_a}.$

Principle of the present invention is: utilize the current detecting principle, in conjunction with this concrete object of electromagnetic bearing switch power amplifier, proposed the phase compensating method based on two parallel asymmetric sampling resistor networks.This phase compensating method has been realized the compensation to the close power amplifier phase place by the design of sampling resistor network degree of asymmetry when realizing current detecting.

Below the principle of two parallel asymmetric sampling resistor networks of the present invention is illustrated.

According to the critical speed stability criterion of MSCMG, can get the specified nutation frequency ω of rotor _nWith rated speed of rotation Ω _nReach and satisfy following relation between the system parameter:

${\mathrm{\ω}}_n=\frac{1}{2}[\left(\frac{J_a}{J_r}{\mathrm{\Ω}}_n\right)+\sqrt{{\left(\frac{J_a}{J_r}{\mathrm{\Ω}}_n\right)}^2+\frac{{8l}_m(l_s{k}_i{\mathrm{\λ}}_k-l_m{k}_x)}{J_r}}]$

J wherein _a, J _rBe respectively polar moment of inertia and the equator rotor inertia of rotor; l _m, l _sBe respectively the magnetic suspension rotor center to the radial direction magnetic bearing center and to the radial transducer center apart from k _i, k _xBe respectively current stiffness and the displacement rigidity of magnetic bearing; λ _kBe control electric current amplitude versus frequency characte i (j ω _n) amplitude.

Existing MSCMG magnetic bearing control system adopts two closed loop controlling structures of position ring and electric current loop usually, and wherein position ring is outer shroud, adopts Decentralized PID to add intersection control scheme usually.The phase place that PID control can compensate is less, mainly realize that by intersecting to control the phase place of system is leading, and the phase place that intersection control can compensate is usually in 90 °.Therefore, for the maintenance system has certain stability margin at specified nutation frequency place, the phase place of magnetic bearing power amplification system lags behind and should limit within the specific limits, and the inventive method is used for compensating that part of phase place hysteresis that the magnetic bearing power amplification system surpasses limit value just.The limit value that lags behind in specified nutation frequency place phase place is designated as θ ₀So can get the phase angle that MSCMG magnetic bearing power amplification system need compensate at specified nutation frequency place is θ _c=θ _n-θ ₀

Fig. 2 is the bipolarity PWM close power amplifier schematic diagram based on two parallel asymmetric sampling resistor networks, its control signal and electric current loop feedback signal are done to export controlling quantity through controller after the difference, carry out the PWM modulation then and generate the PWM ripple, the PWM ripple drives bipolarity H full-bridge inverter and comes the track reference electric current to produce corresponding control electric current, and last current detection circuit is realized the detection to coil current.R among the figure _M1And R _M2Be sampling resistor, R _A1, R _B1, R _C1, R _D1And R _M1Constitute asymmetric sampling resistor network I; R _A2, R _B2, R _C2, R _D2And R _M2Constitute asymmetric sampling resistor network II, and the satisfied R that concerns _A1=R _A2=R _a, R _B1=R _B2=R _b, R _C1=R _C2=R _c, R _D1=R _D2=R _dAnd R _M1=R _M2=R _m, i.e. symmetry fully between two sampling resistor networks.Asymmetric sampling resistor network I constitutes two parallel asymmetric sampling resistor networks with II; K is the op amp gain of current sampling circuit; i _CoIt is the electric current loop feedback factor; k _AmpIt is the proportionality coefficient of magnetic bearing power amplification system controller (employing proportional regulator); k _aIt is the ratio magnification factor of PWM modulator; R _sAnd L _sBe respectively resistance and the inductance of the equivalence of magnetic bearing winding; S ₁, S ₂, S ₃, S ₄Constitute four power switch pipes, wherein S of H full-bridge ₁And S ₃The last brachium pontis of forming the H full-bridge, S ₂And S ₄Form the following brachium pontis of H full-bridge, upper and lower bridge arm is according to pwm signal turn-on and turn-off successively; S is digital select switch, works as S ₂And S ₃The sampled value of gating sampling resistor network I is worked as S during conducting ₁And S ₄The sampled value of gating sampling resistor network II during conducting.

S when power switch pipe ₂, S ₃Conducting, S ₁, S ₄During shutoff the principle of equivalence of two parallel asymmetric sampling resistor networks as shown in Figure 3, U wherein ₁And U ₂Represent winding terminal input section point voltage and the terminal voltage signal behind current detection circuit respectively, U _N1And U _N2Expression sampling resistor R _M1The node voltage at two ends, U ₃And U ₄Represent R respectively _A1And R _B1And R _C1And R _D1Between terminal voltage.Can get according to the nodal method of analysis:

$\left\{\begin{array}{c}{U}_{n1}=U_1\\ -U_{n1}\·\frac{1}{R_m}+U_{n2}(\frac{1}{R_m}+\frac{1}{R_c+R_d}+\frac{1}{\frac{R_m(R_c+R_d)}{R_m+R_c+R_d}+{\mathrm{sL}}_s})=0\end{array}\right.---\left(1\right)$

Therefore,

$U_{n2}=\frac{U_{n1}}{R_m}\·\frac{1}{\frac{1}{R_m}+\frac{1}{R_d+R_c}+\frac{1}{R_s+\frac{R_m(R_c+R_d)}{R_m+R_c+R_d}}+s{L}_s}---\left(2\right)$

In the formula, s represents the variable of the math modeling-transfer function of control system in complex domain.Because R _c+ R _d＞＞R _m, therefore,

$U_{n2}=\frac{U_{n1}}{R_m}\·\frac{1}{\frac{1}{R_m}+\frac{1}{R_d+R_c}+\frac{1}{R_s+R_m+s{L}_s}}.$

Can get according to the nodal method of analysis,

$U_3=\frac{R_b}{R_a+R_b}{U}_{n1},$ $U_4=\frac{R_c}{R_c+R_d}{U}_{n2}---\left(3\right)$

U in the formula ₃And U ₄Represent R respectively _A1And R _B1Between and R _C1And R _D1Between node voltage.Can be got by (3),

$U_2=k(U_3-U_4)=\frac{{\mathrm{kR}}_b}{R_a+R_b}{U}_{n1}-\frac{{\mathrm{kR}}_c}{R_c+R_d}\·\frac{U_1}{R_m}\·\frac{1}{\frac{1}{R_m}+\frac{1}{R_c+R_d}+\frac{1}{R_s+R_m+{\mathrm{sL}}_s}}---\left(4\right)$

Therefore with U ₁Be input, U ₂Ssystem transfer function G for output ₁(s) can be expressed as:

$G_1\left(s\right)=\frac{U_2}{U_1}=\frac{k{R}_b}{R_a+R_b}-\frac{k{R}_c}{R_c+R_d}\·\frac{1}{1+\frac{R_m}{R_c+R_d}+\frac{R_m}{R_s+R_m+{\mathrm{sL}}_s}}$

$=\frac{k{R}_b}{R_a+R_b}-\frac{{\mathrm{kR}}_c(R_s+R_m+{\mathrm{sL}}_s)}{(R_d+R_c)(R_m+R_s+R_m)+R_m(R_s+R_m)+{\mathrm{sL}}_s(R_c+R_d+R_m)}---\left(5\right)$

Consider (R _c+ R _d) (R _m+ R _Sm) R _m(R _s+ R _m) and R _c+ R _dR _m, definition

Following formula can further be reduced to:

$G_1\left(s\right)=\frac{U_2}{U_1}=\frac{k{R}_b}{R_a+R_b}-\frac{k{R}_c}{R_c+R_d}\·\frac{R_s+R_m+s{L}_s}{R_m+R_s+R_m+s{L}_s}$

$={\mathrm{kk}}_{\mathrm{ab}}-{\mathrm{kk}}_{\mathrm{cd}}\frac{R_s+R_m+s{L}_s}{R_m+R_s+R_m+s{L}_s}$

$=k\frac{\mathrm{\δ}(R_m+R_s)+k_{\mathrm{ab}}{R}_m+L_s\mathrm{\δs}}{R_m+R_s+R_m+{\mathrm{sL}}_s}---\left(6\right)$

Wherein δ is defined as the dissymmetry factor of two parallel asymmetric sampling resistor networks, δ=k _Ab-k _Cd

S when power switch pipe ₁, S ₄Conducting, S ₂, S ₃The principle of equivalence of two parallel asymmetric sampling resistor networks as shown in Figure 4 during shutoff.As can be seen from the figure, it has the complete symmetrical structure with Fig. 3, therefore can get S ₁, S ₄Conducting, S ₂, S _3`The phase-frequency characteristic of magnetic bearing power amplification system and S during shutoff ₂, S ₃Conducting, S ₁, S ₄Phase-frequency characteristic during shutoff is just the same.Therefore, which kind of conducting state no matter the bipolarity close power amplifier for having two parallel asymmetric sampling resistor networks be in, with U ₁Be input, U ₂For the ssystem transfer function of exporting can be expressed as G _p(s)=G ₁(s).

Fig. 5 is the equivalent structure figure with bipolarity close power amplifier of two parallel asymmetric sampling resistor networks, wherein G _p(s) expression is with U ₁Be input, U ₂Be the ssystem transfer function of output,

The transfer function of representing digital control time-delay, i _CoIt is the electric current loop feedback factor; k _AmpIt is the proportionality coefficient of magnetic bearing power amplification system controller (employing proportional regulator); k _aIt is the ratio magnification factor of PWM modulator.Then the open loop transfer function G (s) of whole magnetic bearing power amplification system is:

$G\left(s\right)=k_a{k}_{\mathrm{amp}}{i}_{\mathrm{co}}{e}^{-T_{d}s}{G}_p\left(s\right)---\left(7\right)$

So,

$G\left(s\right)=k_{\mathrm{amp}}{k}_a{\mathrm{ki}}_{\mathrm{co}}{e}^{-T_{d}s}\frac{\mathrm{\δ}(R_m+R_s)+k_{\mathrm{ab}}{R}_m+L_s\mathrm{\δs}}{R_m+R_s+R_m+s{L}_s}---\left(8\right)$

Symmetric sampling resistance network for traditional has δ=k _Ab-k _Cd=0, its open loop transfer function G ₀(s) can be expressed as:

$G_0\left(s\right)=k_{\mathrm{amp}}{k}_a{\mathrm{ki}}_{\mathrm{co}}{e}^{-T_{d}s}\frac{k_{\mathrm{ab}}{R}_m}{R_m+R_s+R_m+{\mathrm{sL}}_s}---\left(10\right)$

Its phase-frequency characteristic then

For:

When δ ≠ 0, the phase-frequency characteristic of G (s)

Can be expressed as:

Therefore, when δ＞0, two parallel asymmetric sampling resistor networks are at specified nutation frequency ω _nThe place can provide phase lead compensation, its offset angle θ _cCan be expressed as:

Can obtain dissymmetry factor according to (13):

$\mathrm{\δ}=\frac{k_{\mathrm{ab}}{R}_m\mathrm{ta}{\mathrm{n\θ}}_c}{L_s{\mathrm{\ω}}_n-(R_m+R_s)\tan {\mathrm{\θ}}_c}---\left(14\right)$

Can get according to formula (14), obtain dissymmetry factor δ, need to determine sampling resistor R _m, asymmetric divider resistance ratio k _Ab, magnetic bearing winding equivalent inductance L _sAnd resistance R _sAnd the specified nutation frequency ω of magnetic suspension control torque gyroscope _nWherein, L _sBig I get by actual test; R _m, k _AbSelection to take all factors into consideration with the sample range of AD chip in conjunction with the scope of magnetic bearing winding current, size and the current sample in power amplifier voltage source.

On this basis, take into account power consumption and the signal to noise ratio of asymmetric sampling resistor network, according to the divider resistance R of the two parallel asymmetric sampling resistor networks of dissymmetry factor δ configuration _a, R _b, R _cAnd R _dFor the power consumption that reduces system as far as possible and improve signal to noise ratio, R should be arranged _aR _m, and choose R for simplicity usually _a=R _d, according to $R_b=\frac{k_{\mathrm{ab}}}{1-k_{\mathrm{ab}}}{R}_a$ With $R_c=\frac{R_d[R_b-\mathrm{\δ}(R_a+R_b)]}{\mathrm{\δ}(R_a+R_b)+R_a}$ Obtain R _bAnd R _c

The advantage that the present invention compares with the method that existing compensation magnetic bearing power amplification system phase place lags behind is: the inventive method had not both increased any hardware circuit, need not to adopt the control algorithm of various complexity yet, therefore was convenient to engineering and used.

Description of drawings

Fig. 1 is the diagram of circuit of phase compensating method of the current mode switch power amplifier of a kind of magnetic suspension control torque gyroscope magnetic bearing of the present invention;

Fig. 2 is the magnetic bearing power amplification system functional block diagram based on two parallel asymmetric sampling resistor networks;

Fig. 3 works as S for the inventive method ₂, S ₃Conducting, S ₁, S ₄Topology diagram during shutoff;

Fig. 4 works as S for the inventive method ₁, S ₄Conducting, S ₂, S ₃Topology diagram during shutoff;

Fig. 5 is electromagnet bearing power amplification system equivalence closed loop controlling structure block diagram of the present invention;

Fig. 6 is the open loop frequency performance diagram of the electromagnet bearing power amplification system before and after employing the present invention.

The specific embodiment

As shown in Figure 1, in specific implementation process, concrete implementation step of the present invention is as follows:

1, according to the rated speed of rotation Ω of magnetic suspension control torque gyroscope rotor _nCalculate specified nutation frequency ω with system parameter _n:

${\mathrm{\ω}}_n=\frac{1}{2}[\left(\frac{J_a}{J_r}{\mathrm{\Ω}}_n\right)+\sqrt{{\left(\frac{J_a}{J_r}{\mathrm{\Ω}}_n\right)}^2+\frac{{8l}_m(l_s{k}_i{\mathrm{\λ}}_k-l_m{k}_x)}{J_r}}]$

Wherein, J _a, J _rBe respectively polar moment of inertia and the equator rotor inertia of rotor; l _m, l _sIt is respectively the magnetic suspension rotor center reaches radial transducer to the radial direction magnetic bearing center distance; k _i, k _xBe respectively current stiffness and the displacement rigidity of magnetic bearing; λ _kBe control electric current amplitude versus frequency characte i (j ω _n) amplitude.

2, the phase-frequency characteristic of test magnetic bearing power amplification system obtains the magnetic bearing power amplification system at the phase place hysteresis θ at specified nutation frequency place _n

Adopt digital signal analyser (as Agilent35670A etc.) to carry out frequency-response analysis to the magnetic bearing power amplification system, can obtain system at specified nutation frequency ω by the phase-frequency characteristic curve _nThe phase place hysteresis θ at place _n

3, determine the phase theta that magnetic bearing power amplifier electric current loop need compensate at specified nutation frequency place _c

The magnetic bearing control system phase place lags behind and comprises that mainly the phase place that magnetic bearing power amplification system phase place lags behind and various LPF link causes lags behind.Existing MSCMG magnetic bearing control system adopts two closed loop controlling structures of position ring and electric current loop usually, and wherein position ring is outer shroud, adopts Decentralized PID to add usually to intersect control scheme, Decentralized PID to add to intersect and controls the phase place that can compensate usually in 90 °.Electric current loop is interior ring, i.e. the close power amplifier link.For the system that makes keeps stable, control system should have certain phase margin θ at specified nutation frequency place _a(common θ _a＞30 °).Because the phase place that control system can provide is limited in advance, so the phase place of magnetic bearing power amplification system lags behind and will limit within the specific limits.The limit value that lags behind in specified nutation frequency place phase place is designated as θ ₀, the inventive method is used for compensating that part of phase place hysteresis that the magnetic bearing power amplification system surpasses limit value just.So can get the phase angle that MSCMG magnetic bearing power amplification system need compensate at specified nutation frequency place is θ _c=θ _n-θ ₀

4, in radially load-bearing and dropping under the state of protection on the bearing of magnetic suspension rotor, adopt multi-meter and secohmmeter can measure the equivalent resistance R of bearing coil winding respectively _sAnd inductance L _s

5, determine the big or small R of current sampling resistor _m, current sample is with the ratio k of divider resistance _AbAnd the op amp of current sampling circuit gain k.

R _m, k _AbWant power consumption, signal to noise ratio, winding current magnitude range and the sampling of comprehensively sampling resistance network to take all factors into consideration with the sample range of AD chip with choosing of k.Too big R _mTo the power consumption of sampling network be increased, and too small R _mMake that again the signal to noise ratio of current sample network is less, usually R _mThe size of size bearing winding equivalent resistance is on the same order of magnitude and slightly less than normal.The winding current magnitude range multiply by k _AbK should and have certain allowance (being generally about 20%) within sampling is with the sample range of AD chip, and for reaching higher signal to noise ratio, k _AbUsually be chosen between 18 to 14.Equivalent resistance such as the bearing winding is R _s=2.4 Ω, the winding current magnitude range is-3.1A-3.1A that sampling is-5V-5V that then sampling resistor is chosen as R with the sample range of AD chip _m=1 Ω, current sample is k with the ratio selectable of divider resistance _Ab=16, press the sampling allowance of AD chip 20% and calculate, can get the op amp gain of current sampling circuit $k=\frac{5\×(1-0.2)}{3.1k_{\mathrm{ab}}}=7.7.$

6, determine the dissymmetry factor δ of asymmetric sampling resistor network.

With R _m, k _Ab, L _s, ω _nSubstitution

In can get δ, L wherein _sSize for radial direction magnetic bearing winding equivalent inductance.

7, take into account power consumption and the signal to noise ratio of asymmetric sampling resistor network, according to the divider resistance R of the two parallel asymmetric sampling resistor networks of dissymmetry factor δ configuration _a, R _b, R _cAnd R _d

For the power consumption that reduces system as far as possible and improve signal to noise ratio, 1000R should be arranged _m＜R _a＜10000R _mAnd 1000R＜R _a＜10000R, and choose R for simplicity usually _a=R _d, according to

With $R_c=\frac{R_d[R_b-\mathrm{\δ}(R_a+R_b)]}{\mathrm{\δ}(R_a+R_b)+R_a}$ Obtain R _bAnd R _c

For the validity of checking the inventive method, with magnetic suspension rotor rated speed of rotation Ω _nThe magnetic suspension control torque gyroscope of=20000r/min is that example is verified.System parameter is as follows: l _m=62.5mm, l _s=67.2mm, J _a=0.1019kgm ², J _r=0.062kgm ², k _i=269N/A, k _x=-1.9N/ μ m, R _m=1 Ω, R _s=2.4 Ω, L _s=24mH, λ _k=1505, k=7.7, k _a=3.2, i _Co=10, k _Ab=1/6; The electromagnet bearing power amplification system adopts P control, and its parameter is k _Amp=2.5, system delay T _d=150 μ s.ω _n＝600Hz，θ _n＝95°，θ ₀＝50°，θ _c＝θ _n-θ ₀＝95°-50°＝45°。 $\mathrm{\δ}=\frac{k_{\mathrm{ab}}{R}_m\mathrm{ta}{\mathrm{n\θ}}_c}{L_s{\mathrm{\ω}}_n-(R_m+R_s)\tan {\mathrm{\θ}}_c}=0.0019,$ R _a＝R _d＝7.5kΩ，R _b＝1.5kΩ，R _c＝1.473kΩ。

The frequency characteristic of the magnetic bearing power amplification system before and after employing the inventive method compensates is respectively shown in fine rule and thick line among Fig. 6.Wherein abscissa is represented frequency, and unit is Hz, and ordinate is represented phase place, and unit is Degrees.Can get from Fig. 6, thick line is-53 ° at the ordinate of specified nutation frequency 600Hz place correspondence, and fine rule is-95 ° at the ordinate of frequency 600Hz place correspondence, so the system phase compensation value is 42 °, has reached the effect of phase compensation.

The content that is not described in detail in the specification sheets of the present invention belongs to this area professional and technical personnel's known prior art.

Claims (1)

1. one kind compensates the method that magnetic suspension control torque gyroscope magnetic bearing phase place lags behind, it is characterized in that: rated speed of rotation and system parameter according to the magnetic suspension control torque gyroscope rotor are calculated specified nutation frequency, the phase angle of testing the open loop phase-frequency characteristic of magnetic bearing power amplification system and determining to compensate at specified nutation frequency place, and draw the dissymmetry factor of two parallel asymmetric sampling resistor networks on the basis of test magnetic bearing winding equivalent inductance and resistance, according to the two parallel asymmetric sampling resistor networks of dissymmetry factor configuration, specifically may further comprise the steps at last:

(1) according to the rated speed of rotation Ω of magnetic suspension control torque gyroscope rotor _nSpecified nutation frequency ω with system parameter calculating magnetic suspension rotor _n:

${\mathrm{\ω}}_n=\frac{1}{2}[\left(\frac{J_a}{J_r}{\mathrm{\Ω}}_n\right)+\sqrt{{\left(\frac{J_a}{J_r}{\mathrm{\Ω}}_n\right)}^2+\frac{{8l}_m(l_s{k}_i{\mathrm{\λ}}_k-l_m{k}_x)}{J_r}}]$

Wherein, J _a, J _rBe respectively polar moment of inertia and the equator rotor inertia of rotor; l _m, l _sIt is respectively the magnetic suspension rotor center reaches the radial transducer center to the radial direction magnetic bearing center distance; k _i, k _xBe respectively current stiffness and the displacement rigidity of magnetic bearing; λ _kIt is the amplitude of control electric current amplitude versus frequency characte i (j ω);

(2) phase-frequency characteristic of test magnetic bearing power amplification system obtains the magnetic bearing power amplification system at the phase place hysteresis θ at specified nutation frequency place _n

(3) determine the phase theta that the magnetic bearing power amplification system need compensate at specified nutation frequency place _c=θ _n-θ ₀, θ wherein ₀Be the limit value of magnetic bearing power amplification system in the hysteresis of specified nutation frequency place phase place;

(4) adopt multi-meter and secohmmeter can measure the equivalent resistance R of bearing coil winding respectively _sAnd inductance L _s

(5) determine the big or small R of current sampling resistor with the sample range of AD chip according to the power consumption of sampling resistor network, signal to noise ratio, winding current magnitude range and sampling _m, current sample is with the ratio k of divider resistance _AbAnd the op amp of current sampling circuit gain k;

(6) dissymmetry factor of definite two parallel asymmetric sampling resistor networks $\mathrm{\δ}=\frac{k_{\mathrm{ab}}{R}_m\tan {\mathrm{\θ}}_c}{L_s{\mathrm{\ω}}_n-(R_m+R_s){\tan \mathrm{\θ}}_c};$

(7) take into account power consumption and the signal to noise ratio of sampling resistor network, according to the divider resistance R of the two parallel asymmetric sampling resistor networks of dissymmetry factor δ configuration _a, R _b, R _cAnd R _d, R wherein _a=R _d, $R_c=\frac{R_d[R_b-\mathrm{\δ}(R_a+R_b)]}{\mathrm{\δ}(R_a+R_b)+R_a}.$

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