CN102508433A - Method for compensating digital control delay of magnetic bearing switch power amplifier - Google Patents

Abstract

The invention discloses a method for compensating digital control delay of a magnetic bearing switch power amplifier, which is a method capable of compensating the digital control delay of a magnetic bearing switch power amplifier. The method comprises the steps of setting asymmetric factors of asymmetric sampling resistor networks according to a linear model predictive control theory on the basis of measuring the digital control delay of a switch power amplifier system and equivalent inductance and resistance of a magnetic bearing winding, and finally setting the asymmetric sampling resistance networks according to the asymmetric factors. The method for compensating the digital control delay of the magnetic bearing switch power amplifier belongs to the technical field of magnetic bearing control and can be applied to the fast response and high-stable control of a high-speed magnetic suspension rotor system.

Description

A kind of method that compensates the digital control time-delay of magnetic bearing switch power amplifier

Technical field

The present invention relates to a kind of method that compensates the digital control time-delay of magnetic bearing switch power amplifier, be applicable to the fast-response and the high stable control of high-speed magnetic levitation rotor-support-foundation system, belong to the magnetic bearings control technical field.

Background technology

Magnetic suspension bearing does not have friction because of having, hangs down vibration, is easy to realize that outstanding advantage such as high precision and long-life has wide application prospect in fields such as Aero-Space, commercial production, modern militaries.

In magnetic bearing control system, the effect of switch power amplifier is to provide corresponding electric current to produce needed electromagnetic force to the electromagnetic bearing coil.The electromagnetic bearing switch power amplifier mainly contains width 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 minimum conducting and the width that turn-offs pulse, and the output waveform quality is good, stable state accuracy is high, reliability is high, in electromagnetic bearing, has obtained widespread use.Electromagnetic bearing PWM close power amplifier mainly comprises controller, PWM generator, full-bridge main circuit and current sensor.

For PWM H full-bridge switch power amplifier, can be divided into single-polarity PWM close power amplifier and bipolarity PWM close power amplifier again according to the difference of drive controlling mode.Compare with bipolarity PWM close power amplifier, the current ripples of single-polarity PWM close power amplifier does not increase along with the increase of DC bus-bar voltage, so the single-polarity PWM close power amplifier is applied even more extensively in the magnetic bearing switch power amplification system.

Traditional single-polarity PWM close power amplifier is by Realization of Analog Circuit, along with the development of digital signal processor (DSP), and the digital control magnetic bearing switch power amplification system that is applied to more and more widely.Compare with conventional analogue control, digital control have many advantages, and such as moving more complicated control algolithm, variation has stronger robustness with parameter to environment, but overprogram, and be convenient to fault diagnosis and fault-tolerant control etc.Yet digital control the introduction inevitably comprises that A/D transfer delay, calculating are delayed time and the digital control time-delay of PWM MDL modulation delay.These time-delays will cause the phase lag of power amplification system inevitably, thereby influence the system dynamics response speed even influence the stability of system.Particularly for the magnetic suspension rotor system with high rotating speed, big inductance and strong gyroscopic effect, too big phase lag has had a strong impact on the stability of system.

The phase lag of electromagnetic bearing switch power amplifier mainly comprises digital control time-delay and controlled device time-delay two parts.Wherein, digital control time-delay is a pure lag system, and its size is by digital control system decision itself, and is irrelevant with controlled device; And the object time-delay is to be caused by inductive load, and its size is also irrelevant with digital control system.In PWM H bridge unipolarity close power amplifier, for onesize inductive load, DC bus-bar voltage is big more, and is just more little in the object time-delay at same frequency place, but the control of system time-delay does not change with the change of DC bus-bar voltage size.Therefore, improve the object time-delay that DC bus-bar voltage can only compensate magnetic bearing, can not compensate its digital control time-delay.At present, the method for the digital control time-delay of compensation magnetic bearing mainly contains various Model Predictive Control, independent control etc.These control methods can realize precise current control in theory, but make it very sensitive to system parameter variations owing to these methods depend on system's precise math model.Especially, these advanced control methods often need more computational resource, cause the calculating time-delay of system to increase, and this has further increased the digital control time-delay of system again.Therefore these methods also fail in commercial production, to be used widely at present.Though TRAJECTORY CONTROL and tracking Control are simple relatively, it needs higher and switching frequency that change usually, and this has not only increased the power consumption of switching tube but also has strengthened the output filter difficulty of design.

In order to overcome the deficiency of above control method, in recent years, the linear prediction control theory has obtained bigger development, and is widely used in the commercial production such as rectifier, inverter.Compare with model predictive control method, linear prediction control is a kind of simple and stronger method of robustness, and its main shortcoming is that steady-state tracking precision is relatively poor bigger with current noise.

Summary of the invention

The objective of the invention is: overcome that linear prediction control method current noise is big, tracking accuracy is not high and the deficiency of needs increase extra computation resource; On the basis that does not increase any hardware circuit and computed in software amount; Through asymmetric sampling resistor network, realize effective compensation to the digital control time-delay of magnetic bearing power amplification system.

Technical solution of the present invention is: on the basis of the digital control time-delay of measuring switch power amplification system and magnetic bearing winding equivalent inductance, resistance; According to the linear prediction control theory; The dissymmetry factor of asymmetric sampling resistor network is set, disposes asymmetric sampling resistor network according to dissymmetry factor at last.May further comprise the steps:

(1) the digital control time-delay T of measuring switch power amplification system _d

T _d＝T _ad+T _cal+T _awa+0.5T _c

Wherein, T _AdExpression power amplification system AD sampling time-delay, T _CalTime-delay, T are calculated in expression _AwaExpression PWM waits for time-delay, T _cThe servo period of expression power amplification system;

(2) measure magnetic bearing winding equivalent resistance R and inductance L respectively with multimeter and electric inductance measuring-testing instrument;

(3) confirm the big or small R of current sampling resistor _mWith the ratio k of current sample with divider resistance _Ab

(4), confirm the degree of asymmetry factor of asymmetric sampling resistor network according to the linear prediction control theory

T wherein _sBe the sampling period of power amplification system;

(5) take into account the power consumption and the signal to noise ratio (S/N ratio) of sampling resistor network, according to the R of dissymmetry factor γ configuration sampling resistor network _a, R _b, R _cAnd R _d, R wherein _a=R _d,

Principle of the present invention is: utilize the linear prediction control principle, in conjunction with this concrete object of electromagnetic bearing switch power amplifier, provided the phase compensating method based on the digital control time-delay of magnetic bearing switch power amplifier of asymmetric sampling resistor network.This phase compensating method has been realized the compensation to the digital control time-delay of close power amplifier through the design of sampling resistor network degree of asymmetry when realizing current detecting.

Specifically, the digital control time-delay of magnetic bearing mainly comprises AD sampling time-delay T again _Ad, calculate time-delay T _Cal, PWM waits for time-delay T _AwaWith PWM MDL modulation delay T _AdjFour parts.Transform time-delay T for AD _Ad, its size uses the delay time of each passage to multiply by the sampling channel number can obtain its transport function G _Ad(s) can be expressed as:

$G_{\mathrm{ad}}\left(s\right)=e^{-s\·T_{\mathrm{ad}}}---\left(1\right)$

Wherein s representes the variable of the mathematical model-transport function of control system in complex field.In like manner, for same calculated amount, the processing speed of DSP is depended in the calculating of DSP time-delay, and its The whole calculations delay time can draw through measuring mode, and then obtains its transport function G _Cal(s) be:

$G_{\mathrm{cal}}\left(s\right)=e^{-s\·T_{\mathrm{cal}}}---\left(2\right)$

For the digital control system of fixed switching frequency, because the dutycycle d that calculates can only could upgrade in the beginning in each PWM cycle, it also brings a time-delay inevitably, promptly waits for time-delay T _Awa, this time-delay can be expressed as:

$T_{\mathrm{awa}}=\mathrm{rem}\left(\frac{T_c-T_{\mathrm{cal}}}{T_p}\right)---\left(3\right)$

T wherein _pThe switch periods of expression power amplification system, symbol " rem " expression removes the back complementation.Wait for time-delay transport function G _Awa(s) expression formula is:

$G_{\mathrm{awa}}\left(s\right)=e^{-s\·T_{\mathrm{awa}}}---\left(4\right)$

Because each servo period T _cOnly upgrade the PWM dutycycle one time, so the PWM modulation is equivalent to sampling-maintenance link, its transport function G _Adj(s) can be expressed as:

$G_{\mathrm{adj}}\left(s\right)=\frac{1-e^{-s\·T_c}}{s}---\left(5\right)$

S=j ω (5) formula of bringing into is got,

$G_{\mathrm{adj}}\left(\mathrm{j\ω}\right)=\frac{1-e^{-\mathrm{j\ω}{T}_c}}{\mathrm{j\ω}}=\frac{2e^{-\mathrm{j\ω}{T}_c/2}(e^{{\mathrm{j\ωT}}_c/2}-e^{-\mathrm{j\ω}{T}_c/2})}{2\mathrm{j\ω}}=T_c\frac{\sin ({\mathrm{\ωT}}_c/2)}{{\mathrm{\ωT}}_c/2}{e}^{-\mathrm{j\ω}{T}_c/2}---\left(6\right)$

So, PWM MDL modulation delay T _AdjFor

T _adj＝0.5T _c (7)

Therefore, whole digital control system time-delay is:

T _d＝T _ad+T _cal+T _awa+T _adj (8)

Fig. 2 representes the H bridge unipolarity magnetic bearing power amplification system theory diagram based on asymmetric sampling resistor network; Its control signal and electric current loop feedback signal are done to export controlled quentity controlled variable through controller after the difference; Carry out the PWM modulation then and generate the PWM ripple; The PWM ripple drives the H full-bridge inverter and comes the track reference electric current to produce corresponding control current, and last asymmetric sampling resistor network (shown in empty frame among Fig. 2) is realized the detection of coil current and the compensation of magnetic bearing system phase place.R among the figure _mIt is sampling resistor; R _a, R _b, R _cAnd R _dConstitute asymmetric resistor voltage divider network, asymmetric resistor voltage divider network and sampling resistor R _mConstitute asymmetric sampling resistor network; K is the operational amplifier gain of current sampling circuit; i _cIt is the electric current loop feedback factor; Q1, Q2, Q3, Q4 constitute four power switch pipes of H full-bridge, carry out conducting and shutoff according to pwm signal.

At first utilize the state space method of average, set up the small-signal model of H bridge unipolarity close power amplifier.According to the principle of H bridge single-polarity PWM close power amplifier, in the cycle, (0≤t＜dT) (dT≤t＜equivalent electrical circuit topological structure T) is respectively like Fig. 3 and shown in Figure 4 with the afterflow state can to get its charged state at a PWM.

According to Kirchhoff's current law (KCL), can proper 0≤t＜during dT,

$\left\{\begin{array}{cc}\begin{array}{c}{i}_m\left(t\right)=i_L\left(t\right)+i_{\mathrm{cd}}\left(t\right)\\ U_d\left(t\right)=R_m{i}_m\left(t\right)+{\mathrm{Ri}}_L\left(t\right)+L\frac{{\mathrm{di}}_L\left(t\right)}{\mathrm{dt}}\\ (R_c+R_d)i_{\mathrm{cd}}\left(t\right)={\mathrm{Ri}}_L\left(t\right)+L\frac{{\mathrm{di}}_L\left(t\right)}{\mathrm{dt}}\\ u_s\left(t\right)={\mathrm{kk}}_{\mathrm{ab}}{U}_d-{\mathrm{kk}}_{\mathrm{cd}}({\mathrm{Ri}}_L\left(t\right)+L\frac{{\mathrm{di}}_L\left(T\right)}{\mathrm{dt}})\end{array}& \end{array}0\&le;t<\mathrm{dT}\right.---\left(9\right)$

Wherein, $k_{\mathrm{Ab}}=\frac{R_b}{R_a+R_b},$ $k_{\mathrm{Cd}}=\frac{R_d}{R_c+R_d}.$

Definition status variable x=i _L, input variable u=U _dWith output variable y=u _sCorrespondingly, t state variable, input variable and output variable constantly is designated as x (t)=i respectively arbitrarily _L(t), u (t)=U _d(t) and y (t)=u _s(t).So the state equation that can obtain system is:

$\left\{\begin{array}{c}\frac{\mathrm{dx}\left(t\right)}{\mathrm{dt}}=-\frac{a}{b}x\left(t\right)+\frac{1}{b}u\left(t\right)\\ y\left(t\right)=(\frac{{\mathrm{kk}}_{\mathrm{cd}}{d}_0}{c}-{\mathrm{kk}}_{\mathrm{cd}}R)x\left(t\right)+({\mathrm{kk}}_{\mathrm{ab}}-\frac{{\mathrm{kk}}_{\mathrm{cd}}}{c})u\left(t\right)\end{array}\right.---\left(10\right)$

Wherein $a=R_m+\frac{{\mathrm{RR}}_m}{R_c+R_d}+R,$ $b=L(1+\frac{R_m}{R_c+R_d}),$ $c=1+\frac{R_m}{R_c+R_d}$ And ${\mathrm{<figure-callout\; id="0"\; label="d"\; filenames="HDA0000105859300000032.png,HDA0000105859300000033.png"\; state="\{\{state\}\}">d</figure-callout>}}_0=R_m+R+\frac{{\mathrm{RR}}_m}{R_c+R_d}.$

Consider and in real system, R is arranged _c+ R _d＞＞R _mAnd R _c+ R _d＞＞RR _m, so a ≈ R _m+ R, b ≈ L, c ≈ 1 and d ₀≈ R _m+ R can get its substitution (10),

$\left\{\begin{array}{c}\frac{\mathrm{dx}\left(t\right)}{\mathrm{dt}}=-\frac{R+R_m}{L}x\left(t\right)+\frac{1}{L}u\left(t\right)\\ y\left(t\right)={\mathrm{kk}}_{\mathrm{cd}}{R}_{m}x\left(t\right)+k(k_{\mathrm{ab}}-k_{\mathrm{cd}})u\left(t\right)\end{array}\right.---\left(11\right)$

In like manner utilize Kirchhoff's current law (KCL), when dT≤t＜T, can get,

$\left\{\begin{array}{cc}\begin{array}{c}{i}_m\left(t\right)=i_L\left(t\right)+i_{\mathrm{cd}}\left(t\right)\\ 0=R_m{i}_m\left(t\right)+{\mathrm{Ri}}_L\left(t\right)+L\frac{{\mathrm{di}}_L\left(t\right)}{\mathrm{dt}}\\ (R_c+R_d)i_{\mathrm{cd}}\left(t\right)=-R_m{i}_m\left(t\right)\\ u_s\left(t\right)=-k{R}_c{i}_{\mathrm{cd}}\left(t\right)\end{array}& \mathrm{dT}\&le;t<T\end{array}\right.---\left(12\right)$

Wherein, i _Cd(t) any t of expression flows through divider resistance R constantly _cAnd R _dElectric current, i _m(t) any t of expression flows through sampling resistor R constantly _mElectric current.The state equation that likewise, can get system is:

$\left\{\begin{array}{c}\frac{\mathrm{dx}\left(t\right)}{\mathrm{dt}}=-\frac{R}{L}x\left(t\right)-\frac{R_m(R_c+R_d)}{L(R_c+R_d+R_m)}x\left(t\right)\\ y\left(t\right)=\frac{k{R}_c{R}_m}{R_c+R_d+R_m}x\left(t\right)\end{array}\right.---\left(13\right)$

Consider R in real system _c+ R _d＞＞R _m, so following formula can further be reduced to:

$\left\{\begin{array}{c}\frac{\mathrm{dx}\left(t\right)}{\mathrm{dt}}=-\frac{R+R_m}{L}x\left(t\right)\\ y\left(t\right)={\mathrm{kk}}_{\mathrm{cd}}{R}_{m}x\left(t\right)\end{array}\right.---\left(14\right)$

According to the state space method of average, (11) * d+ (14) * (1-d) can obtain at an average state space equation of PWM cycle be:

$\left\{\begin{array}{c}\frac{\mathrm{dx}\left(t\right)}{\mathrm{dt}}=-\frac{R+R_m}{L}x\left(t\right)+\frac{d}{L}u\left(t\right)\\ y\left(t\right)={\mathrm{kk}}_{\mathrm{cd}}{R}_{m}x\left(t\right)+\mathrm{dk\&gamma;u}\left(t\right)\end{array}\right.---\left(15\right)$

Wherein, γ=k _Ab-k _Cd

Equation (15) is a continuous nonlinear equation of time; Can get its linear model through the small-signal disturbance; Make

and

wherein "～" represent small-signal; Correspondingly,

and represent the small-signal variable of any t state variable, input variable and output variable constantly respectively.So can obtain the steady-state equation and the small-signal state equation of system is respectively:

$\left\{\begin{array}{c}\frac{\mathrm{dX}}{\mathrm{dt}}=-\frac{R+R_m}{L}X+\frac{D}{L}U\\ Y={\mathrm{kk}}_{\mathrm{cd}}{R}_{m}X+\mathrm{Dk\&gamma;U}\end{array}\right.---\left(16\right)$

$\left\{\begin{array}{c}\frac{d\tilde{x}\left(t\right)}{\mathrm{dt}}=-\frac{R+R_m}{L}\tilde{x}\left(t\right)+\frac{D}{L}\tilde{u}\left(t\right)+\frac{U}{L}\tilde{d}\left(t\right)\\ \tilde{y}\left(t\right)={\mathrm{kk}}_{\mathrm{cd}}{R}_m\tilde{x}\left(t\right)+\mathrm{Dk\&gamma;}\tilde{u}\left(t\right)+\mathrm{k\&gamma;U}\tilde{d}\left(t\right)\end{array},-,-,-,\left(17\right)\right.$

Like this, according to the Laplace conversion, the small-signal transport function that can obtain system is:

$G_i\left(s\right)=\frac{\tilde{x}\left(s\right)}{\tilde{u}\left(s\right)}=\frac{{\tilde{i}}_L\left(s\right)}{{\tilde{u}}_d\left(s\right)}=\frac{D}{R+R_m+\mathrm{Ls}}---\left(18\right)$

$G_y\left(s\right)=\frac{\tilde{y}\left(s\right)}{\tilde{u}\left(s\right)}=\frac{{\tilde{u}}_s\left(s\right)}{{\tilde{u}}_d\left(s\right)}=\mathrm{Dk}\frac{k_{\mathrm{ab}}{R}_m+\mathrm{\&gamma;R}+\mathrm{\&gamma;Ls}}{R+R_m+\mathrm{Ls}}---\left(19\right)$

Therefore, the transport function from

to can be expressed as:

$G_s\left(s\right)=\frac{{\tilde{u}}_s\left(s\right)}{{\tilde{i}}_L\left(s\right)}=k(k_{\mathrm{ab}}{R}_m+\mathrm{\&gamma;R}+\mathrm{\&gamma;Ls})---\left(20\right)$

Simultaneously, in the H bridge single-polarity PWM close power amplifier,

$\frac{u_c}{U_{\mathrm{tri}}}=d---\left(21\right)$

U wherein _TriIt is the amplitude of triangular carrier.

The tube voltage drop of ignoring MOSFET and diode can obtain at a PWM in the cycle, a, the internodal average terminal voltage u of b _AbWith the relation of DC bus-bar voltage be:

u _ab＝dU _d (22)

Therefore, the transport function of whole PWM modulator can be expressed as following form:

$G_m\left(s\right)=\frac{u_{\mathrm{ab}}\left(s\right)}{u_c\left(s\right)}=\frac{U_d}{U_{\mathrm{tri}}}---\left(23\right)$

U wherein _c(s) be controller output u _cTransport function expression formula in frequency.In conjunction with (18) and (23), the transport function G of whole PWM modulator and H bridge power amplifier _p(s) be:

$G_p\left(s\right)=\frac{{\tilde{i}}_L\left(s\right)}{{\tilde{u}}_c\left(s\right)}=\frac{{\tilde{i}}_L\left(s\right)}{D{\tilde{u}}_d\left(s\right)}\frac{u_{\mathrm{ab}}\left(s\right)}{u_c\left(s\right)}=\frac{U_d}{U_{\mathrm{tri}}}\frac{1}{R+R_m+\mathrm{Ls}}---\left(24\right)$

Fig. 5 is electromagnetic bearing switch power amplification system equivalence closed loop controlling structure block diagram of the present invention, wherein G _p(s) transport function of expression whole PWM modulator and H bridge power amplifier, G _d(s) transport function of the digital control time-delay of expression, G _c(s) transport function of the digital control time-delay of expression, G _s(s) transport function of the asymmetric sampling resistor network of expression, i _cBe the electric current loop feedback factor, i _RefBe the electric current set-point of close power amplifier system, i _cBe the output valve of magnetic bearing power amplification system controller, i _LBe winding current.

For traditional electric current detecting method; γ=0; With getting in its substitution

G _s(s)＝kk _abR _m (25)

It is thus clear that traditional electric current detecting method is a proportional component in essence.In like manner, if γ＞0, the current detecting network then has ratio-differential function.That is to say, compare, introduced the current differential item in the feedback channel of power amplification system with γ=0.

Have forecast function owing to differentiate, moreover traditional linear prediction control theory just is being based on the prediction of numerical differentiation computing realization to the state in future.Therefore, based on the linear prediction control theory, the parameter of utilizing the method for undetermined coefficients can adjust asymmetric sampling resistor network.

According to the linear prediction control theory, be compensating digits control time-delay T _d, PREDICTIVE CONTROL expression formula G _Pred(z) be:

$G_{\mathrm{pred}}\left(z\right)=1+\frac{T_d}{T_c}-\frac{T_d}{T_c}{z}^{-1}---\left(26\right)$

Wherein z representes the variable of the mathematical model-transport function of discrete control system, T _cBe servo period.G _Pred(z) the differential expressions i of correspondence _{Pred, k}Can be expressed as:

$i_{\mathrm{pred},k}=(1+\frac{T_d}{T_c})\&CenterDot;i_{L,k}-\frac{T_d}{T_c}\&CenterDot;i_{L,k-1}---\left(27\right)$

I wherein _{L, k}The sample rate current of representing current (k is constantly), i _{L, k-1}The sample rate current of expression previous moment (k-1 constantly).

The differential equation that the method for application backward difference can draw (20) is:

$u_{s,k}=k(k_{\mathrm{ab}}{R}_m+\mathrm{\&gamma;R}+\frac{\mathrm{\&gamma;L}}{T_s})i_{L,k}-\frac{\mathrm{k\&gamma;L}}{T_s}{i}_{L,k-1}---\left(28\right)$

U wherein _{S, k}Expression current time (k constantly) output valve of asymmetric sampling resistor network behind operational amplifier.

In conjunction with (27) and (28), make u _{S, k}=i _{Pred, k}, utilize the method for undetermined coefficients can draw the dissymmetry factor γ of asymmetric sampling resistor network and the gain k of operational amplifier is:

$\left\{\begin{array}{c}\mathrm{\&gamma;}=\frac{T_s{T}_d{k}_{\mathrm{ab}}{R}_m}{{\mathrm{LT}}_c-T_s{T}_{d}R}\\ k=\frac{{\mathrm{LT}}_c-T_s{T}_{d}R}{k_{\mathrm{ab}}{R}_m{\mathrm{LT}}_c}\end{array}\right.---\left(29\right)$

On this basis, according to dissymmetry factor γ and current sample ratio k with divider resistance _AbCan further confirm the R of asymmetric sampling resistor network _a, R _b, R _cAnd R _dUsually choose R _a=R _d, with k _Ab, R _aSubstitution

In obtain R _b, again with R _a, R _b, R _dWith the γ substitution

In can obtain R _c

The present invention is with the advantage that the linear prediction control method of the digital control time-delay of existing compensation magnetic bearing power amplification system is compared: the inventive method replaces the numerical differentiation computing of conventional linear forecast Control Algorithm through the analog differentiation function of utilizing asymmetric sampling resistor network; Calculating time-delay itself that not only avoided traditional forecast Control Algorithm to bring; And overcome that the factor word is differentiated and the problem of introducing excessive noise, improved the tracking accuracy of electric current.

Description of drawings

Fig. 1 is the process flow diagram of the inventive method;

Fig. 2 is the magnetic bearing power amplification system structural drawing based on asymmetric sampling resistor network;

Fig. 3 is the equivalent topologies figure under the asymmetric sampling resistor network charged state of the present invention;

Fig. 4 is the equivalent topologies figure under the asymmetric sampling resistor network afterflow state of the present invention;

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

Fig. 6 is the contrast current-responsive figure of the inventive method and conventional digital control method;

Fig. 7 is the contrast current-responsive figure of the inventive method and conventional linear forecast Control Algorithm;

Embodiment

As shown in Figure 1, in the practical implementation process, practical implementation step of the present invention is following:

(1) measures the total digital control system time-delay T of magnetic bearing switch power amplifier _d:

T _d＝T _ad+T _cal+T _awa+0.5T _c

Wherein, T _AdExpression power amplification system AD sampling time-delay, T _CalTime-delay, T are calculated in expression _AwaExpression PWM waits for time-delay, T _cThe servo period of expression system.T _AdCan be multiply by total sampling channel number by the delay time of each sampling channel just can draw; Calculating time-delay can draw through testing directly; T _AwaCan be according to formula Calculate, wherein T _pThe switch periods of expression power amplification system, symbol " rem " expression removes the back complementation.

(2) in radially load-bearing and dropping under the state of protection on the bearing of magnetic suspension rotor, adopt multimeter and secohmmeter can measure the equivalent resistance R and the inductance L of bearing coil winding respectively.

(3) confirm the big or small R of current sampling resistor _mWith the ratio k of current sample with divider resistance _Ab, wherein

R _mAnd k _AbChoose the scope that will combine the magnetic bearing winding current, the size and the current sample in power amplifier voltage source taken all factors into consideration with the factors such as sample range of AD chip.

(4), confirm the dissymmetry factor of asymmetric sampling resistor network according to the linear prediction control theory

T wherein _sBe the sampling period of power amplification system, γ is defined as

(5) take into account the power consumption and the signal to noise ratio (S/N ratio) of sampling resistor network, according to the R of dissymmetry factor γ configuration sampling resistor network _a, R _b, R _cAnd R _d

For the power consumption that reduces system as much as possible and improve signal to noise ratio (S/N ratio), 1000R should be arranged _m＜R _a＜10000R _mAnd 1000R＜R _a＜10000R simultaneously for simplicity, chooses R usually _a=R _d, according to

With

Further obtain R _bAnd R _c

Validity for checking the inventive method; Close power amplifier system with the radially Ax passage of magnetic suspension control torque gyroscope magnetic bearing is that example is verified; This system adopts 40-MIPS DSP TMS320C32 as control chip, and AD1671 is as sampling A, and DC bus-bar voltage is 28V.Current sample cycle and servo period all are set to 150 μ s, and switch periods is set to 50 μ s.At t=0.001s, the magnetic bearing reference current steps to 1A from 0.

Because be 800ns the switching time of each passage of AD1671, total sampling time of five passages of magnetic suspension control torque gyroscope electric current loop is 4 μ s so.The calculating that can get system through test about 38 μ s that delay time, according to

The wait time-delay that can draw PWM is 12 μ s, adds the MDL modulation delay of 75 μ s, draws the digital control time-delay T of system _d=129 μ s.Adopt the equivalent resistance R=2.0 Ω of multimeter and secohmmeter test bearing coil winding respectively, inductance L=21.3mH.Scope, the current sample of taking all factors into consideration the magnetic bearing winding current are set to R with the sample range of AD chip and the signal to noise ratio (S/N ratio) sampling resistor of sampled signal _m=1.0 Ω, the ratio of divider resistance is set to k _Ab=1/6.The degree of asymmetry factor of calculating sampling resistor network

Choose R _a=R _d=7.500k Ω, certificate

According to

Can get the corresponding linear predictive control algorithm does $i_{\mathrm{Pred},k}=(1+\frac{T_d}{T_c})\&CenterDot;i_{L,k}-\frac{T_d}{T_c}\&CenterDot;i_{L,k-1}=1.86i_{L,k}-0.86i_{L,k-1}.$

The contrast test waveform that the inventive method and traditional digital control method (not having prediction) are compared with the conventional linear forecast Control Algorithm is respectively like Fig. 6 and shown in Figure 7; Wherein thick line representes to adopt the step response waveform of the inventive method, and fine rule is represented traditional digital control method or conventional linear forecast Control Algorithm.

In Fig. 6,7, horizontal ordinate express time, unit are s, and ordinate is represented the electric current of magnetic bearing radial passage, and unit is A.Can get from Fig. 6; Compare with traditional digital control method (not having prediction), the inventive method does not almost have overshoot, and have an appointment 12% the overshoot of traditional digital control method; The rise time of system roughly remains unchanged when adopting the inventive method simultaneously, so system bandwidth remains unchanged basically.As can beappreciated from fig. 7, reach after the stable state that (the electric current jerk value of the inventive method of t＞0.2s) is little and winding current waveform is Paint Gloss than the conventional linear forecast Control Algorithm.Therefore, compare with traditional linear prediction control method, the inventive method has higher current tracking precision and littler current noise.

The content of not doing in the instructions of the present invention to describe in detail belongs to this area professional and technical personnel's known prior art.

Claims (1)

1. method that compensates the digital control time-delay of magnetic bearing switch power amplifier; It is characterized in that: on the basis of the digital control time-delay of measuring switch power amplification system and magnetic bearing winding equivalent inductance, resistance; According to the linear prediction control theory; The dissymmetry factor of asymmetric sampling resistor network is set, disposes asymmetric sampling resistor network according to dissymmetry factor at last, may further comprise the steps:

(1) the digital control time-delay T of measuring switch power amplification system _d

T _d＝T _ad+T _cal+T _awa+0.5T _c

Wherein, T _AdExpression power amplification system AD sampling time-delay, T _CalTime-delay, T are calculated in expression _AwaExpression PWM waits for time-delay, T _cThe servo period of expression system;

(2) measure magnetic bearing winding equivalent resistance R and inductance L respectively with multimeter and electric inductance measuring-testing instrument;

(3) confirm the big or small R of current sampling resistor _mWith the ratio k of current sample with divider resistance _Ab

(4), confirm the degree of asymmetry factor of asymmetric sampling resistor network according to the linear prediction control theory T wherein _sBe the sampling period of power amplification system;

(5) take into account the power consumption and the signal to noise ratio (S/N ratio) of sampling resistor network, according to the R of dissymmetry factor γ configuration sampling resistor network _a, R _b, R _cAnd R _d, R wherein _a=R _d,

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