CN102281029B - Method for constructing bearing-free synchronous reluctance motor suspension system - Google Patents

Abstract

The invention discloses a method for constructing a bearing-free synchronous reluctance motor suspension system. During construction of the system, the method comprises the following steps of: constructing an expanded displacement observer; then transmitting three-phase detection current, which is subjected to coordination transformation, of a motor suspension winding and a torque winding into the input end of the expanded displacement observer; synchronously outputting a rotor displacement observed value and a suspension force reference value by the expanded displacement observer as input signals of an expanded suspension force/current modulator; transmitting deviations between two output current component rated values and two-phase detection current subjected to the coordination transformation into two input ends of an inner die controller respectively, and outputting two voltage rated signals as input voltage of a space vector pulse width modulation (SVPWM) inverter; supplying power to the motor suspension winding by the SVPWM inverter so as to generate an expected suspension force, and thus realizing rotor displacement observation for a controlled motor and decoupling control for the inner die of current of the suspension winding. The constructed suspension system has the advantages of high response speed, simple structure, high performance and the like.

Description

A kind of method for constructing bearing-free synchronous reluctance motor suspension system

Technical field

The present invention relates to the AC Motor Control technical field, particularly a kind of method for constructing bearing-free synchronous reluctance motor suspension system based on rotor displacement observation and electric current Internal Model Decoupling control method is applicable to the bearingless synchronous reluctance motor Current Decoupling control of without gap sensors under the high-speed condition.

Background technology

Bearingless synchronous reluctance motor is the additional winding (suspending windings) of a cover that superposes again on common synchronous magnetic resistance motor stator winding (torque winding), in order to produce the axial magnetic power of a constant suspension of supporting rotor, the electric current of control motor double winding just can make motor produce simultaneously electromagnetic torque and suspending power.Special structures shape bearingless synchronous reluctance motor has outstanding high-quality: low noise, low-power consumption, high rotating speed, exempt to lubricate, high-cleanness etc.Compare with the bearing-free motor of other types, bearingless synchronous reluctance motor has firm reliable, the advantage such as control is simple, torque pulsation is low.The Electric Drive field of bearingless synchronous reluctance motor in the advanced automatically controlled equipments such as high-speed precise machine tool main shaft drives, flywheel energy storage electricity generation system, household electrical appliance, industrial robot has using value.

In the bearingless synchronous reluctance motor suspension system mechanical type eddy current displacement sensor is mostly adopted in the accurate detection of rotor radial displacement at present, the defective that adopts displacement transducer to bring has: displacement transducer increases the manufacturing cost of electric system, cause simultaneously the volume of motor to increase, reduce the reliability of motor.Disclose one in the prior art about the without gap sensors control method national inventing patent application (application number: 201010017952.6) of bearingless synchronous reluctance motor, but the algorithm of method described in this application is complicated, soft and hardware to control system is had relatively high expectations, and the extra high-frequency signal that injects can increase torque pulsation.

On the other hand, the suspending windings stator current of bearingless synchronous reluctance motor has the complicated coupling relation under the high-speed condition, cause traditional suspension system transient state adjusting function not good, realize the high-performance high-speed cruising of motor, the essential phase mutual interference of removing between the suspending windings stator current there is no at present relevant patent and document and relates to this problem.

For further improving the control performance of bearingless synchronous reluctance motor suspension system, realize the without gap sensors rotor displacement observation of motor, remove simultaneously suspending windings stator current coupled relation, essential some new control methods that adopt.

Summary of the invention

The object of the present invention is to provide a kind of method for constructing bearing-free synchronous reluctance motor suspension system that can improve the suspension operation performance, the system that makes up based on the inventive method can need not to adopt mechanical displacement sensor, realize simultaneously suspending windings stator current decouple control, and have the advantage such as simple in structure, function admirable.

For achieving the above object, the technical scheme that the present invention takes is: a kind of method for constructing bearing-free synchronous reluctance motor suspension system may further comprise the steps:

1) makes up the displacement observation device of expanding, detect respectively motor suspending windings and torque winding three-phase electric current, after coordinate transform, obtain the biphase current under the synchronously rotating reference frame, as the input signal of the displacement observation device of expanding; The displacement observation device output signal of expansion is rotor radial displacement observation value under the static coordinate and the reference value of suspending power;

2) suspending power of foundation expansion/current modulator model, the suspending power reference value of the displacement observation device output of expansion is as the input signal of the suspending power/current modulator of expansion;

3) structure internal mode controller is with step 2) in two current components and the steps 1 of suspending power/current modulator output of expansion) in synchronously rotating reference frame under biphase current between deviation, send into respectively two inputs of internal mode controller; The two-phase reference voltage of internal mode controller output suspending windings;

4) structure SVPWM inverter, with step 3) in the stator voltage set-point signal of internal mode controller output as the input reference signal of SVPWM voltage source inverter, the three-phase voltage of SVPWM inverter output actual needs is powered to suspending windings, produce the required radial suspension force of rotor, realize the stable suspersion operation of rotor.

As a kind of improvement, step 1 of the present invention) the displacement observation device of expansion comprises PI adaptive rate, PID adjuster, suspending power observer and Park inverse transformation in; The corresponding rotor displacement observation procedure of displacement observation device of expansion may further comprise the steps:

11) make up the suspending power observer: the radial suspension force component F on bearingless synchronous reluctance motor rotor two vertical direction under synchronous rotary d, the q coordinate system _x, F _yFor:

$\left\{\begin{array}{c}{F}_x=K_d{i}_d{i}_x+K_q{i}_q{i}_y\\ F_y=K_q{i}_q{i}_x-K_d{i}_d{i}_y\end{array}\right.---\left(1\right)$

Formula (1) consists of the Mathematical Modeling of suspending power observer, K in the formula _d, K _qBe respectively motor d, q axle suspension buoyancy/current constant, i _d, i _qBe respectively torque winding equivalence biphase current, i _x, i _yBe respectively suspending windings equivalence biphase current;

The specific implementation of suspending power observer is: detect respectively motor suspending windings and torque winding three-phase electric current, after Clark conversion and Park conversion, obtain the biphase current under the synchronously rotating reference frame, based on the size of formula (1) observation suspending power.

1.2) through coordinate transform, produce the suspending power measured value F under the static coordinate _α, F _β: with the radial suspension force component F under the above-mentioned rotational coordinates _x, F _yConvert component F under the static coordinate to through the Park inverse transformation _α, F _βFor:

$\left[\begin{array}{c}{F}_{\mathrm{\α}}\\ F_{\mathrm{\β}}\end{array}\right]=\left[\begin{array}{cc}\cos \mathrm{\θ}& -\sin \mathrm{\θ}\\ \sin \mathrm{\θ}& \cos \mathrm{\θ}\end{array}\right]\left[\begin{array}{c}{F}_x\\ F_y\end{array}\right]---\left(2\right)$

1.3) structure PI adaptive rate: the fundamental relation formula is between rotor radial displacement α, the β of the PI adaptive rate of regulating based on PI and the suspending power:

$\left\{\begin{array}{c}\mathrm{\α}=K_p(F_{\mathrm{\α}}^{*}-F_{\mathrm{\α}})+K_i\∫(F_{\mathrm{\α}}^{*}-F_{\mathrm{\α}})\mathrm{dt}\\ \mathrm{\β}=K_p(F_{\mathrm{\β}}^{*}-F_{\mathrm{\β}})+K_i\∫(F_{\mathrm{\β}}^{*}-F_{\mathrm{\β}})\mathrm{dt}\end{array}\right.---\left(3\right)$

Suspending power F in the formula _α, F _βBe step 2.2) in the suspending power measured value that obtains,

For deviation between rotor displacement set-point and the measured value obtains the suspending power reference value behind the PID adjuster.According to formula (5), can get the measured value of radial displacement on rotor two direction of principal axis, thereby omit mechanical displacement sensor.K _p, K _iScale operation and integral operation coefficient can require to carry out parameter tuning according to different control objects and control respectively.

As a kind of improvement, step 2 of the present invention) in, the suspending power of expansion/current modulator model construction method may further comprise the steps:

2.1) under the static α of two-phase, β coordinate system, the suspending windings current i _{α 2}, i _{β 2}With radial suspension force F _α, F _βThe pass be:

$\left[\begin{array}{c}{i}_{\mathrm{\&alpha;}2}\\ i_{\mathrm{\&beta;}2}\end{array}\right]=\frac{1}{K_d^2{i}_{\mathrm{<figure-callout\; id="2"\; label="d"\; filenames="HDA0000087735010000011.png"\; state="\{\{state\}\}">d</figure-callout>}}^2+K_q^2{i}_{\mathrm{<figure-callout\; id="2"\; label="q"\; filenames="HDA0000087735010000011.png"\; state="\{\{state\}\}">q</figure-callout>}}^2}\left[\begin{array}{cc}\mathrm{<figure-callout\; id="2"\; label="cos"\; filenames="HDA0000087735010000011.png"\; state="\{\{state\}\}">cos</figure-callout>}2\mathrm{\&theta;}& -\sin 2\mathrm{\&theta;}\\ \sin 2\mathrm{\&theta;}& \mathrm{<figure-callout\; id="2"\; label="cos"\; filenames="HDA0000087735010000011.png"\; state="\{\{state\}\}">cos</figure-callout>}2\mathrm{\&theta;}\end{array}\right]\left[\begin{array}{cc}{K}_d{i}_d& K_q{i}_q\\ K_q{i}_q& -K_d{i}_d\end{array}\right]\left[\begin{array}{c}{F}_{\mathrm{\&alpha;}}\\ F_{\mathrm{\&beta;}}\end{array}\right]---\left(4\right)$

K in the formula _d, K _qBe respectively motor d, q axle suspension buoyancy/current constant, in the inventive example, through estimation K _d=75N/A, K _q=32N/A; i _d, i _qBe respectively torque winding equivalence biphase current; The reference value that is input as radial suspension force when suspending power/current modulator

Can obtain the current reference value of suspending windings

2.2) with the suspending windings current i under the two-phase static coordinate _{α 2}, i _{β 2}, be converted to the current i under two-phase synchronous rotary d, the q coordinate _x, i _yFor:

$\left[\begin{array}{c}{i}_x\\ i_y\end{array}\right]=\left[\begin{array}{cc}\cos \mathrm{\&theta;}& \sin \mathrm{\&theta;}\\ -\sin \mathrm{\&theta;}& \cos \mathrm{\&theta;}\end{array}\right]\left[\begin{array}{c}{i}_{\mathrm{\&alpha;}2}\\ i_{\mathrm{\&beta;}2}\end{array}\right]---\left(5\right)$

The suspending power of the common formation expansion of formula (4) and formula (5)/current modulator model.

Preferably, the corresponding suspending windings stator current Internal Model Decoupling method of internal mode controller may further comprise the steps step 3 of the present invention):

3.1) make up the internal mode controller of controlled motor suspending windings voltage equation

3.2) the structure low pass filter

3.3) making up equivalent feedback controller F (s), it is output as the component of voltage set-point under the static coordinate

Before feedback controller F (s) serial connection and controlled motor suspending windings, realize the decoupling zero control of motor suspending windings stator current;

Step 3.1) internal mode controller of controlled motor suspending windings voltage equation in

Construction method may further comprise the steps:

3.1.1) under high speed and Super High Speed Condition, the bearingless synchronous reluctance motor suspending windings based on the voltage equation of synchronous rotating frame (d, q coordinate system) is:

$\left\{\begin{array}{c}{u}_x=R_s{i}_x+L_x\frac{{\mathrm{di}}_x}{\mathrm{dt}}-\mathrm{\&omega;}{L}_y{i}_y\\ u_y=R_s{i}_y+L_y\frac{{\mathrm{di}}_y}{\mathrm{dt}}+\mathrm{\&omega;}{L}_x{i}_x\end{array}\right.---\left(6\right)$

U in the formula _x, u _yBe stator voltage d, q axle component, L _x, L _yBe d, q axle inductance, R _sBe the every phase resistance of stator; ω is motor angular velocity; By formula (6) as seen, there is the cross-couplings relation between suspending windings stator current two components, and corresponding generation cross-couplings electromotive force, further affect the output of stator current component, thereby affect the stability of radial suspension force, need it is carried out decoupling zero.

3.1.2) formula (6) being carried out Laplace transform, can get:

$\left\{\begin{array}{c}{u}_x\left(s\right)=(R_s+s{L}_x)i_x\left(s\right)-\mathrm{\&omega;}{L}_y{i}_y\left(s\right)\\ u_y\left(s\right)=(R_s+s{L}_y)i_y\left(s\right)+\mathrm{\&omega;}{L}_x{i}_x\left(s\right)\end{array}\right.---\left(7\right)$

Formula (7) conversion can be got:

$\left\{\begin{array}{c}{i}_x=u_x\left(\frac{1}{R_s+s{L}_x}\right)+\mathrm{\&omega;}{L}_y{i}_y\left(\frac{1}{R_s+s{L}_x}\right)\\ i_y=u_y\left(\frac{1}{R_s+s{L}_y}\right)-\mathrm{\&omega;}{L}_x{i}_x\left(\frac{1}{R_s+s{L}_y}\right)\end{array}\right.---\left(8\right)$

3.1.3) supposition

Be the internal mold of controlled device, parallel with controlled device G (s), U (s) and I (s) be corresponding bearingless synchronous reluctance motor suspending windings stator voltage and electric current respectively, order $U\left(s\right)=\left[\begin{array}{c}{U}_d\left(s\right)\\ U_q\left(s\right)\end{array}\right],$ $Y\left(s\right)=I\left(s\right)=\left[\begin{array}{c}{I}_d\left(s\right)\\ I_q\left(s\right)\end{array}\right],$ Then have following formula to set up:

Y(s)＝G(s)U( (9)

In the formula $G\left(s\right)={\left[\begin{array}{cc}{R}_s+s{L}_x& -\mathrm{\&omega;}{L}_y\\ \mathrm{\&omega;}{L}_x& R_s+s{L}_y\end{array}\right]}^{-1};$

According to internal model control theory and motor characteristic, the internal mode controller of bearingless synchronous reluctance motor optimization can be expressed as:

$\hat{C}\left(s\right)={\hat{G}}^{-1}\left(s\right)\hat{L}(---\left(10\right)$

In the formula ${\hat{G}}^{-1}\left(s\right)=\left[\begin{array}{cc}{\hat{R}}_s+s{\hat{L}}_x& -\mathrm{\&omega;}{\hat{L}}_y\\ \mathrm{\&omega;}{\hat{L}}_x& {\hat{R}}_s+s{\hat{L}}_y\end{array}\right],$ Wherein

With

Be respectively the estimated value of suspending windings stator inductance and resistance; Be low pass filter, be used for guaranteeing Systems balanth.

Preferably, low pass filter of the present invention is a mode filter, namely

Elect as:

$L\left(s\right)=\frac{1}{{(1+T_{f}s)}^2}---\left(11\right)$

T in the formula _fBe the suspension system time constant.

Preferably, step 3.3 of the present invention) construction method of described equivalent feedback controller F (s) may further comprise the steps:

3.3.1) according to formula (10), (11), can get internal mode controller

Expression formula be:

$\hat{C}\left(s\right)={\hat{G}}^{-1}\left(s\right)\hat{L}\left(s\right)=\left[\begin{array}{cc}{\hat{R}}_s+s{\hat{L}}_x& -\mathrm{\&omega;}{\hat{L}}_y\\ \mathrm{\&omega;}{\hat{L}}_x& {\hat{R}}_s+s{\hat{L}}_y\end{array}\right]\frac{1}{{(1+T_{f}s)}^2}---\left(12\right)$

3.3.2) be the feedback controller model with the internal mode controller equivalence, then the feedback controller of equivalence is:

$F\left(s\right)={[1-\frac{1}{{(1+T_{f}s)}^2}]}^{-1}{\hat{G}}^{-1}\left(s\right)\frac{1}{{(1+T_{f}s)}^2}=\left[\begin{array}{cc}\frac{{\hat{R}}_s+s{\hat{L}}_x}{T_f^2{\mathrm{<figure-callout\; id="2"\; label="s"\; filenames="HDA0000087735010000011.png"\; state="\{\{state\}\}">s</figure-callout>}}^2+2T_{f}s}& -\frac{\mathrm{\&omega;}{\hat{L}}_y}{T_f^2{\mathrm{<figure-callout\; id="2"\; label="s"\; filenames="HDA0000087735010000011.png"\; state="\{\{state\}\}">s</figure-callout>}}^2+2T_{f}s}\\ \frac{\mathrm{\&omega;}{\hat{L}}_x}{T_f^2{\mathrm{<figure-callout\; id="2"\; label="s"\; filenames="HDA0000087735010000011.png"\; state="\{\{state\}\}">s</figure-callout>}}^2+2T_{f}s}& \frac{{\hat{R}}_s+s{\hat{L}}_y}{T_f^2{\mathrm{<figure-callout\; id="2"\; label="s"\; filenames="HDA0000087735010000011.png"\; state="\{\{state\}\}">s</figure-callout>}}^2+2T_{f}s}\end{array}\right]---\left(13\right)$

By formula (13) as seen, internal mode controller has increased back-diagonal integration item, thereby forms Decoupling network, and it is serially connected with before this controlled device of motor suspending windings couple current, then can eliminate the cross-couplings between the suspending windings electric current;

3.3.3) formula (13) is serially connected in the suspending windings current channel, and form the current closed-loop negative feedback control, can be connected in series the Internal Model Decoupling controller after suspension winding voltage component set-point be:

$\left\{\begin{array}{c}{u}_x^{*}=\frac{{\hat{R}}_s+s{\hat{L}}_x}{T_f^2{\mathrm{<figure-callout\; id="2"\; label="s"\; filenames="HDA0000087735010000011.png"\; state="\{\{state\}\}">s</figure-callout>}}^2+2T_{f}s}(i_x^{*}-i_x)-\frac{\mathrm{\&omega;}{\hat{L}}_y}{T_f^2{\mathrm{<figure-callout\; id="2"\; label="s"\; filenames="HDA0000087735010000011.png"\; state="\{\{state\}\}">s</figure-callout>}}^2+2T_{f}s}(i_y^{*}-i_y)\\ u_y^{*}=\frac{\mathrm{\&omega;}{\hat{L}}_x}{T_f^2{\mathrm{<figure-callout\; id="2"\; label="s"\; filenames="HDA0000087735010000011.png"\; state="\{\{state\}\}">s</figure-callout>}}^2+2T_{f}s}(i_x^{*}-i_x)+\frac{{\hat{R}}_s+s{\hat{L}}_y}{T_f^2{\mathrm{<figure-callout\; id="2"\; label="s"\; filenames="HDA0000087735010000011.png"\; state="\{\{state\}\}">s</figure-callout>}}^2+2T_{f}s}(i_y^{*}-i_y)\end{array}\right.---\left(14\right)$

With the voltage given in the following formula

Bring into respectively in the formula (8), then can eliminate the cross-couplings relation between the control object variable;

3.3.4) with the voltage given under the above-mentioned rotational coordinates

Convert the component u under the static coordinate to _x, u _y, with the input signal as the SVPWM inverter:

$\left[\begin{array}{c}{u}_{\mathrm{\&alpha;}2}^{*}\\ u_{\mathrm{\&beta;}2}^{*}\end{array}\right]=\left[\begin{array}{cc}\cos \mathrm{\&theta;}& -\sin \mathrm{\&theta;}\\ \sin \mathrm{\&theta;}& \cos \mathrm{\&theta;}\end{array}\right]\left[\begin{array}{c}{u}_x^{*}\\ u_y^{*}\end{array}\right]---\left(15\right).$

It is pointed out that above-mentionedly only for the foundation on the structure supplying method of Internal Model Decoupling controller, in implementation of the present invention, comprise and to utilize the conversion etc. that proves and derive of existing corresponding theory, so can skip.

Being achieved as follows of described motor suspending windings electric current Internal Model Decoupling control method:

1) with the biphase current set-point of motor suspending windings under the synchronously rotating reference frame, and from the deviation between the detection of motor suspending windings and the biphase current detected value through obtaining after the coordinate transform, send into respectively two inputs of Internal Model Decoupling controller, carry out computing according to formula (14), can get two voltage givens of Internal Model Decoupling controller

2) with two output variables

Two input variable u of controlled device in the difference substituted (8) _x, u _y, can realize the Internal Model Decoupling control of bearingless synchronous reluctance motor suspending windings electric current.

Principle of the present invention adopts bearingless synchronous reluctance motor suspending windings terminal voltage, electric current as auxiliary variable on the one hand, thereby the size of estimation suspending power, make up position rotor displacement observer based on the PI adaptive method, omitted traditional mechanical displacement sensor, the principle of the invention is that the internal model control in the industrial process control is incorporated in the control of motor suspending windings stator current decouple on the other hand, realizes the electric current dynamic Decoupling Control of Load Torque of controlled motor.

Beneficial effect of the present invention is:

1. constructed the displacement observation device, response is quick, and algorithm is simple, has removed the mechanical displacement transducer, has widened application and the suitable environment of bearingless synchronous reluctance motor.

2. provide suspension system stator current decouple method, the advantage such as the method has simplicity of design, and robust performance is good, and the dynamic decoupling effect is good.

3. the suspension system building method based on above-mentioned displacement observation device and the control of electric current Internal Model Decoupling is provided, use the suspension system of the method structure to be easy to realize, with low cost, simple in structure, can realize the high-performance suspension operation of controlled motor under the high-speed condition, be widely used in take bearingless synchronous reluctance motor in the power transmission system of power core, having broad application prospects.

Description of drawings

Fig. 1 is the structure principle chart of the displacement observation device 5 of expansion; Wherein, comprise suspending power observer 1, Park inverse transformation 2, PID adjuster 3, PI adaptive rate 4;

Fig. 2 is the structure principle chart that 6 pairs of motor suspending windings of serial connection internal mode controller 7 are carried out decoupling zero;

Fig. 3 is bearingless synchronous reluctance motor suspension system schematic diagram of structure of the present invention.

Embodiment

For content of the present invention is become apparent more, be described further below in conjunction with the drawings and specific embodiments.

Construct a kind of suspension system based on the observation of bearingless synchronous reluctance motor rotor displacement and the control of suspending windings electric current Internal Model Decoupling, a kind of preferred implementation structural principle of the present invention such as Fig. 3:

Make up the displacement observation device 5 of expansion, in conjunction with Fig. 1, the displacement observation device of this expansion is made of jointly 1, PI adaptive rate 4 of a suspending power observation, a PID adjuster 3 and a Park inverse transformation 2.

Suspending windings and the torque winding three-phase electric current of motor obtained in detection, through obtaining the biphase current under the synchronously rotating reference frame after the coordinate transform, is respectively torque winding equivalence biphase current i _d, i _q, and suspending windings equivalence biphase current i _x, i _yIt is sent into the displacement observation device of expansion.Coordinate transform herein comprises Clark conversion 8 and Park conversion 9.

The output signal of the displacement observation device 5 of expansion is displacement observation value and suspending power reference value

The displacement observation device of this expansion is placed before the suspending power/current modulator 7 of expansion the suspending power reference value

Input as suspending power/current modulator of expanding.The biphase current component set-point that suspending power/current modulator is exported with above-mentioned expansion

Detect current i with the two-phase that detects from the motor suspending windings and after coordinate transform, obtain _x, i _yBetween deviation, send into respectively two inputs of internal mode controller 6, two stator voltage set-points of these internal mode controller 6 outputs

After Park inverse transformation 10, input reference voltage as SVPWM inverter 11, powered to motor suspending windings 12 by this SVPWM inverter 11, produce desired radial suspension force, thereby realize rotor displacement observation and the suspending windings electric current Internal Model Decoupling control system 13 of bearingless synchronous reluctance motor.

Specific embodiments of the present invention is divided into following steps:

1, by the derivation of equation, theory analysis, the displacement observation device of the expansion of structure bearingless synchronous reluctance motor.The construction method of the displacement observation device of described expansion comprises following several step:

11) make up the suspending power observer.Radial suspension force component F on bearingless synchronous reluctance motor rotor two vertical direction under synchronous rotary d, the q coordinate system _x, F _yFor:

$\left\{\begin{array}{c}{F}_x=K_d{i}_d{i}_x+K_q{i}_q{i}_y\\ F_y=K_q{i}_q{i}_x-K_d{i}_d{i}_y\end{array}\right.---\left(1\right)$

Above-mentioned formula has consisted of the Mathematical Modeling of suspending power observer.K in the formula _d, K _qBe respectively motor d, q axle suspension buoyancy/current constant, in the inventive example, through estimation K _d=75N/A, K _q=32N/A.i _d, i _qBe respectively torque winding equivalence biphase current, i _x, i _yBe respectively suspending windings equivalence biphase current.

The specific implementation of above-mentioned suspending power observer is: detect respectively motor suspending windings and torque winding three-phase electric current, after Clark conversion and Park conversion, obtain the suspending windings biphase current under the synchronously rotating reference frame, based on the size of following formula observation suspending power.

1.2) with the suspending power component F under the above-mentioned rotational coordinates _x, F _yConvert the component F under the static coordinate to _α, F _βFor:

$\left[\begin{array}{c}{F}_{\mathrm{\&alpha;}}\\ F_{\mathrm{\&beta;}}\end{array}\right]=\left[\begin{array}{cc}\cos \mathrm{\&theta;}& -\sin \mathrm{\&theta;}\\ \sin \mathrm{\&theta;}& \cos \mathrm{\&theta;}\end{array}\right]\left[\begin{array}{c}{F}_x\\ F_y\end{array}\right]---\left(2\right)$

1.3) structure PI adaptive rate.Displacement and the suspending power fundamental relation formula of regulating adaptive method observation strategy based on PI are:

$\left\{\begin{array}{c}\mathrm{\&alpha;}=K_p(F_{\mathrm{\&alpha;}}^{*}-F_{\mathrm{\&alpha;}})+K_i\&Integral;(F_{\mathrm{\&alpha;}}^{*}-F_{\mathrm{\&alpha;}})\mathrm{dt}\\ \mathrm{\&beta;}=K_p(F_{\mathrm{\&beta;}}^{*}-F_{\mathrm{\&beta;}})+K_i\&Integral;(F_{\mathrm{\&beta;}}^{*}-F_{\mathrm{\&beta;}})\mathrm{dt}\end{array}\right.---\left(3\right)$

Suspending power F in the following formula _α, F _βBe step 1.2) in the suspending power measured value that obtains,

For the deviation of rotor displacement set-point and estimated value obtains the suspending power reference value behind the PID adjuster.According to following formula, can get the measured value of radial displacement on rotor two direction of principal axis, thereby omit mechanical displacement sensor.K _p, K _iScale operation and integral operation coefficient can require to carry out parameter tuning according to different control objects and control respectively.

2, the suspending power of foundation expansion/current modulator model:

2.1) under the static α of two-phase, β coordinate system, the suspending windings current i _{α 2}, i _{β 2}With radial suspension force F _α, F _βThe pass be:

$\left[\begin{array}{c}{i}_{\mathrm{\&alpha;}2}\\ i_{\mathrm{\&beta;}2}\end{array}\right]=\frac{1}{K_d^2{i}_{\mathrm{<figure-callout\; id="2"\; label="d"\; filenames="HDA0000087735010000011.png"\; state="\{\{state\}\}">d</figure-callout>}}^2+K_q^2{i}_{\mathrm{<figure-callout\; id="2"\; label="q"\; filenames="HDA0000087735010000011.png"\; state="\{\{state\}\}">q</figure-callout>}}^2}\left[\begin{array}{cc}\mathrm{<figure-callout\; id="2"\; label="cos"\; filenames="HDA0000087735010000011.png"\; state="\{\{state\}\}">cos</figure-callout>}2\mathrm{\&theta;}& -\mathrm{<figure-callout\; id="2"\; label="sin"\; filenames="HDA0000087735010000011.png"\; state="\{\{state\}\}">sin</figure-callout>}2\mathrm{\&theta;}\\ \mathrm{<figure-callout\; id="2"\; label="sin"\; filenames="HDA0000087735010000011.png"\; state="\{\{state\}\}">sin</figure-callout>}2\mathrm{\&theta;}& \mathrm{<figure-callout\; id="2"\; label="cos"\; filenames="HDA0000087735010000011.png"\; state="\{\{state\}\}">cos</figure-callout>}2\mathrm{\&theta;}\end{array}\right]\left[\begin{array}{cc}{K}_d{i}_d& K_q{i}_q\\ K_q{i}_q& -K_d{i}_d\end{array}\right]\left[\begin{array}{c}{F}_{\mathrm{\&alpha;}}\\ F_{\mathrm{\&beta;}}\end{array}\right]---\left(4\right)$

Be input as the reference value of radial suspension force when suspending power/current modulator

Can obtain the current reference value of suspending windings

2.2) with the suspending windings current i under the two-phase static coordinate _{α 2}, i _{β 2}, be converted to the current i under two-phase synchronous rotary d, the q coordinate _x, i _yFor:

$\left[\begin{array}{c}{i}_x\\ i_y\end{array}\right]=\left[\begin{array}{cc}\cos \mathrm{\&theta;}& \sin \mathrm{\&theta;}\\ -\sin \mathrm{\&theta;}& \cos \mathrm{\&theta;}\end{array}\right]\left[\begin{array}{c}{i}_{\mathrm{\&alpha;}2}\\ i_{\mathrm{\&beta;}2}\end{array}\right]---\left(5\right)$

The suspending power of above-mentioned formula (4) and the expansion of formula (5) formation/current modulator model, the suspending power/current modulator of this expansion is output as and revolves synchronously two current components under the coordinate.

3, by the derivation of equation, theory analysis, the internal mode controller of structure bearingless synchronous reluctance motor.The construction method of described internal mode controller comprises following several step:

3.1) set up the coupling model of motor suspending windings electric current.Under high speed and Super High Speed Condition, the bearingless synchronous reluctance motor suspending windings based on the voltage equation of synchronous rotating frame (d-q coordinate system) is:

$\left\{\begin{array}{c}{u}_x=R_s{i}_x+L_x\frac{{\mathrm{di}}_x}{\mathrm{dt}}-\mathrm{\&omega;}{L}_y{i}_y\\ u_y=R_s{i}_y+L_y\frac{{\mathrm{di}}_y}{\mathrm{dt}}+\mathrm{\&omega;}{L}_x{i}_x\end{array}\right.---\left(6\right)$

U in the formula _x, u _yBe stator voltage d, q axle component, L _x, L _yBe d, q axle inductance, R _sBe the every phase resistance of stator.

By following formula as seen, there is the cross-couplings relation between suspending windings stator current two components, and corresponding generation cross-couplings electromotive force, further affect the output of stator current component, thereby affect the stability of radial suspension force, need it is carried out decoupling zero.

3.2) make up the contrary internal mold of voltage equation

Formula (6) is carried out Laplace transform, can get:

$\left\{\begin{array}{c}{u}_x\left(s\right)=(R_s+s{L}_x)i_x\left(s\right)-\mathrm{\&omega;}{L}_y{i}_y\left(s\right)\\ u_y\left(s\right)=(R_s+s{L}_y)i_y\left(s\right)+\mathrm{\&omega;}{L}_x{i}_x\left(s\right)\end{array}\right.---\left(7\right)$

The following formula conversion can be got:

$\left\{\begin{array}{c}{i}_x=u_x\left(\frac{1}{R_s+s{L}_x}\right)+\mathrm{\&omega;}{L}_y{i}_y\left(\frac{1}{R_s+s{L}_x}\right)\\ i_y=u_y\left(\frac{1}{R_s+s{L}_y}\right)-\mathrm{\&omega;}{L}_x{i}_x\left(\frac{1}{R_s+s{L}_y}\right)\end{array}\right.---\left(8\right)$

Suppose Be the internal mold of controlled device, parallel with controlled device G (s), U (s) and I (s) be corresponding bearingless synchronous reluctance motor suspending windings stator voltage and electric current respectively, order $U\left(s\right)=\left[\begin{array}{c}{U}_d\left(s\right)\\ U_q\left(s\right)\end{array}\right],$ $Y\left(s\right)=I\left(s\right)=\left[\begin{array}{c}{I}_d\left(s\right)\\ I_q\left(s\right)\end{array}\right],$ Then have following formula to set up:

Y(s)＝G(s)U(s) (9)

In the formula $G\left(s\right)={\left[\begin{array}{cc}{R}_s+s{L}_x& -\mathrm{\&omega;}{L}_y\\ \mathrm{\&omega;}{L}_x& R_s+s{L}_y\end{array}\right]}^{-1}.$

According to internal model control theory and motor characteristic, the internal mode controller of bearingless synchronous reluctance motor optimization can be expressed as:

$\hat{C}\left(s\right)={\hat{G}}^{-1}\left(s\right)\hat{L}\left(s\right)---\left(10\right)$

In the formula ${\hat{G}}^{-1}\left(s\right)=\left[\begin{array}{cc}{\hat{R}}_s+s{\hat{L}}_x& -\mathrm{\&omega;}{\hat{L}}_y\\ \mathrm{\&omega;}{\hat{L}}_x& {\hat{R}}_s+s{\hat{L}}_y\end{array}\right],$ Wherein

With

Be respectively the estimated value of suspending windings stator inductance and resistance;

Be low pass filter, it act as the realizability of guaranteeing Systems balanth, robustness and internal mode controller.

3.4) the structure low pass filter.Low pass filter is elected a mode filter as, namely

For:

$L\left(s\right)=\frac{1}{{(1+T_{f}s)}^2}---\left(11\right)$

T in the formula _fBe the suspension system time constant.

3.5) the structure internal mode controller.According to formula (10), (11), can get internal mode controller Expression formula be:

$\hat{C}\left(s\right)={\hat{G}}^{-1}\left(s\right)\hat{L}\left(s\right)=\left[\begin{array}{cc}{\hat{R}}_s+s{\hat{L}}_x& -\mathrm{\&omega;}{\hat{L}}_y\\ \mathrm{\&omega;}{\hat{L}}_x& {\hat{R}}_s+s{\hat{L}}_y\end{array}\right]\frac{1}{{(1+T_{f}s)}^2}---\left(12\right)$

Be the feedback controller model with above-mentioned internal mode controller equivalence, then the feedback controller Mathematical Modeling of equivalence is:

$F\left(s\right)={[1-\frac{1}{{(1+T_{f}s)}^2}]}^{-1}{\hat{G}}^{-1}\left(s\right)\frac{1}{{(1+T_{f}s)}^2}=\left[\begin{array}{cc}\frac{{\hat{R}}_s+s{\hat{L}}_x}{T_f^2{\mathrm{<figure-callout\; id="2"\; label="s"\; filenames="HDA0000087735010000011.png"\; state="\{\{state\}\}">s</figure-callout>}}^2+2T_{f}s}& -\frac{\mathrm{\&omega;}{\hat{L}}_y}{T_f^2{\mathrm{<figure-callout\; id="2"\; label="s"\; filenames="HDA0000087735010000011.png"\; state="\{\{state\}\}">s</figure-callout>}}^2+2T_{f}s}\\ \frac{\mathrm{\&omega;}{\hat{L}}_x}{T_f^2{\mathrm{<figure-callout\; id="2"\; label="s"\; filenames="HDA0000087735010000011.png"\; state="\{\{state\}\}">s</figure-callout>}}^2+2T_{f}s}& \frac{{\hat{R}}_s+s{\hat{L}}_y}{T_f^2{\mathrm{<figure-callout\; id="2"\; label="s"\; filenames="HDA0000087735010000011.png"\; state="\{\{state\}\}">s</figure-callout>}}^2+2T_{f}s}\end{array}\right]---\left(13\right)$

By formula (13) as seen, internal mode controller has increased back-diagonal integration item, thereby forms Decoupling network, it is serially connected with before this controlled device of motor suspending windings couple current, as shown in Figure 2; Then can eliminate the cross-couplings between the suspending windings electric current;

Formula (13) is serially connected in the suspending windings current channel, and forms the current closed-loop negative feedback control, can be connected in series the Internal Model Decoupling controller after suspension winding voltage component set-point be:

$\left\{\begin{array}{c}{u}_x^{*}=\frac{{\hat{R}}_s+s{\hat{L}}_x}{T_f^2{\mathrm{<figure-callout\; id="2"\; label="s"\; filenames="HDA0000087735010000011.png"\; state="\{\{state\}\}">s</figure-callout>}}^2+2T_{f}s}(i_x^{*}-i_x)-\frac{\mathrm{\&omega;}{\hat{L}}_y}{T_f^2{\mathrm{<figure-callout\; id="2"\; label="s"\; filenames="HDA0000087735010000011.png"\; state="\{\{state\}\}">s</figure-callout>}}^2+2T_{f}s}(i_y^{*}-i_y)\\ u_y^{*}=\frac{\mathrm{\&omega;}{\hat{L}}_x}{T_f^2{\mathrm{<figure-callout\; id="2"\; label="s"\; filenames="HDA0000087735010000011.png"\; state="\{\{state\}\}">s</figure-callout>}}^2+2T_{f}s}(i_x^{*}-i_x)+\frac{{\hat{R}}_s+s{\hat{L}}_y}{T_f^2{\mathrm{<figure-callout\; id="2"\; label="s"\; filenames="HDA0000087735010000011.png"\; state="\{\{state\}\}">s</figure-callout>}}^2+2T_{f}s}(i_y^{*}-i_y)\end{array}\right.---\left(14\right)$

With the voltage given in the following formula

Bring into respectively in the formula (8), then can eliminate the cross-couplings relation between the control object variable;

With the voltage given under the above-mentioned rotational coordinates

Convert the component u under the static coordinate to _x, u _y, with the input signal as the SVPWM inverter:

$\left[\begin{array}{c}{u}_{\mathrm{\&alpha;}2}^{*}\\ u_{\mathrm{\&beta;}2}^{*}\end{array}\right]=\left[\begin{array}{cc}\cos \mathrm{\&theta;}& -\sin \mathrm{\&theta;}\\ \sin \mathrm{\&theta;}& \cos \mathrm{\&theta;}\end{array}\right]\left[\begin{array}{c}{u}_x^{*}\\ u_y^{*}\end{array}\right]---\left(15\right).$

3.8) structure SVPWM inverter.With the voltage signal of the above-mentioned internal mode controller output input reference signal as the SVPWM voltage source inverter, the three-phase voltage of this inverter output actual needs is powered to suspending windings, produce the required radial suspension force of rotor, thereby realize rotor displacement observation and the control of suspending windings stator current Internal Model Decoupling under the machinery-free transducer condition.

The case of implementation described in the present invention only is better case study on implementation of the present invention, is not to limit practical range of the present invention.Be that all equivalences of doing according to the content of the present patent application claim change and modification, all should be as technology category of the present invention.

Claims (3)

1. a method for constructing bearing-free synchronous reluctance motor suspension system is characterized in that, may further comprise the steps:

1) makes up the displacement observation device of expanding, detect respectively motor suspending windings and torque winding three-phase electric current, after coordinate transform, obtain the biphase current under the synchronously rotating reference frame, as the input signal of the displacement observation device of expanding; The displacement observation device output signal of expansion is rotor radial displacement observation value under the static coordinate and the reference value of suspending power;

2) suspending power of foundation expansion/current modulator model, the suspending power reference value of the displacement observation device output of expansion is as the input signal of the suspending power/current modulator of expansion;

3) structure internal mode controller is with step 2) in two current components and the steps 1 of suspending power/current modulator output of expansion) in synchronously rotating reference frame under biphase current between deviation, send into respectively two inputs of internal mode controller; The two-phase reference voltage of internal mode controller output suspending windings;

4) structure SVPWM inverter, with step 3) in the stator voltage set-point signal of internal mode controller output as the input reference signal of SVPWM voltage source inverter, the three-phase voltage of SVPWM inverter output actual needs is powered to suspending windings, produce the required radial suspension force of rotor, realize the stable suspersion operation of rotor;

Step 3) the corresponding suspending windings stator current Internal Model Decoupling method of internal mode controller may further comprise the steps in:

3.1) make up the internal mode controller of controlled motor suspending windings voltage equation

3.2) the structure low pass filter

3.3) making up equivalent feedback controller F (s), it is output as the component of voltage set-point under the static coordinate

Feedback controller F (s) is serially connected with before the controlled motor suspending windings, realizes the decoupling zero control of motor suspending windings stator current;

Step 3.1) internal mode controller of controlled motor suspending windings voltage equation in

Construction method may further comprise the steps:

3.1.1) under high speed and Super High Speed Condition, the bearingless synchronous reluctance motor suspending windings based on the voltage equation of synchronous rotating frame (d, q coordinate system) is:

$\left\{\begin{array}{c}{u}_x=R_s{i}_x+L_x\frac{{\mathrm{di}}_x}{\mathrm{dt}}-\mathrm{\&omega;}{L}_y{i}_y\\ u_y=R_s{i}_y+L_y\frac{{\mathrm{di}}_y}{\mathrm{dt}}+\mathrm{\&omega;}{L}_x{i}_x\end{array}\right.---\left(6\right)$

U in the formula _x, u _yBe stator voltage d, q axle component, L _x, L _yBe d, q axle inductance, R _sBe the every phase resistance of stator; ω is motor angular velocity; i _x, i _yBe respectively the suspending windings equivalence biphase current under synchronous rotary d, the q coordinate;

3.1.2) formula (6) being carried out Laplace transform, can get:

$\left\{\begin{array}{c}{u}_x\left(s\right)=(R_s+s{L}_x)i_x\left(s\right)-\mathrm{\&omega;}{L}_y{i}_y\left(s\right)\\ u_y\left(s\right)=(R_s+s{L}_y)i_y\left(s\right)+\mathrm{\&omega;}{L}_x{i}_x\left(s\right)\end{array}\right.---\left(7\right)$

Formula (7) conversion can be got:

$\left\{\begin{array}{c}{i}_x=u_x\left(\frac{1}{R_s+s{L}_x}\right)+\mathrm{\&omega;}{L}_y{i}_y\left(\frac{1}{R_s+s{L}_x}\right)\\ i_y=u_{\text{y}}\left(\frac{1}{R_s+s{L}_y}\right)-\mathrm{\&omega;}{L}_x{i}_x\left(\frac{1}{R_s+s{L}_y}\right)\end{array}\right.---\left(8\right)$

3.1.3) supposition

Be the internal mold of controlled device, parallel with controlled device G (s), U (s) and I (s) be corresponding bearingless synchronous reluctance motor suspending windings stator voltage and electric current respectively, order $U\left(s\right)=\left[\begin{array}{c}{U}_d\left(s\right)\\ U_q\left(s\right)\end{array}\right],$ $Y\left(s\right)=I\left(s\right)=\left[\begin{array}{c}{I}_d\left(s\right)\\ I_q\left(s\right)\end{array}\right],$ Then have following formula to set up:

Y(s)＝G(s)U(s) (9)

In the formula $G\left(s\right)={\left[\begin{array}{cc}{R}_s+s{L}_x& -\mathrm{\&omega;}{L}_y\\ \mathrm{\&omega;}{L}_x& R_s+s{L}_y\end{array}\right]}^{-1};$

According to internal model control theory and motor characteristic, the internal mode controller of bearingless synchronous reluctance motor optimization can be expressed as:

$\hat{C}\left(s\right)={\hat{G}}^{-1}\left(s\right)\hat{L}\left(s\right)---\left(10\right)$

In the formula ${\hat{G}}^{-1}\left(s\right)=\left[\begin{array}{cc}{\hat{R}}_s+s{\hat{L}}_x& -\mathrm{\&omega;}{\hat{L}}_y\\ \mathrm{\&omega;}{\hat{L}}_x& {\hat{R}}_s+s{\hat{L}}_y\end{array}\right],$ Wherein

With

Be respectively the estimated value of suspending windings stator inductance and resistance;

Be low pass filter, be used for guaranteeing Systems balanth;

Step 3.2) low pass filter described in is a mode filter, namely

Elect as:

$L\left(s\right)=\frac{1}{{(1+T_{f}s)}^2}---\left(11\right)$

T in the formula _fBe the suspension system time constant;

Step 3.3) construction method of equivalent feedback controller F (s) may further comprise the steps described in:

3.3.1) according to formula (10), (11), can get internal mode controller

Expression formula be:

$\hat{C}\left(s\right)={\hat{G}}^{-1}\left(s\right)\hat{L}\left(s\right)=\left[\begin{array}{cc}{\hat{R}}_s+s{\hat{L}}_x& -\mathrm{\&omega;}{\hat{L}}_y\\ \mathrm{\&omega;}{\hat{L}}_x& {\hat{R}}_s+s{\hat{L}}_y\end{array}\right]\frac{1}{{(1+T_{f}s)}^2}---\left(12\right)$

3.3.2) be the feedback controller model with the internal mode controller equivalence, then the feedback controller of equivalence is:

$F\left(s\right)={[1-\frac{1}{{(1+T_{f}s)}^2}]}^{-1}{\hat{G}}^{-1}\left(s\right)\frac{1}{{(1+T_{f}s)}^2}=\left[\begin{array}{cc}\frac{{\hat{R}}_s+s{\hat{L}}_x}{T_f^2{s}^2+2T_{f}s}& -\frac{\mathrm{\&omega;}{\hat{L}}_y}{T_f^2{s}^2+2T_{f}s}\\ \frac{\mathrm{\&omega;}{\hat{L}}_x}{T_f^2{s}^2+2T_{f}s}& \frac{{\hat{R}}_s+s{\hat{L}}_y}{T_f^2{s}^2+2T_{f}s}\end{array}\right]---\left(13\right)$

By formula (13) as seen, internal mode controller has increased back-diagonal integration item, thereby forms Decoupling network, and it is serially connected with before this controlled device of motor suspending windings couple current, then can eliminate the cross-couplings between the suspending windings electric current;

3.3.3) formula (13) is serially connected in the suspending windings current channel, and form the current closed-loop negative feedback control, can be connected in series the Internal Model Decoupling controller after suspension winding voltage component set-point be:

$\left\{\begin{array}{c}{u}_x^{*}=\frac{{\hat{R}}_s+s{\hat{L}}_x}{T_f^2{s}^2+2T_{f}s}(i_x^{*}-i_x)-\frac{\mathrm{\&omega;}{\hat{L}}_y}{T_f^2{s}^2+2T_{f}s}(i_y^{*}-i_y)\\ u_y^{*}=\frac{\mathrm{\&omega;}{\hat{L}}_x}{T_f^2{s}^2+2T_{f}s}(i_x^{*}-i_x)+\frac{{\hat{R}}_s+s{\hat{L}}_y}{T_f^2{s}^2+2T_{f}s}(i_y^{*}-i_y)\end{array}\right.---\left(14\right)$

With the voltage given in the following formula

Bring into respectively in the formula (8), then can eliminate the cross-couplings relation between the control object variable;

3.3.4) with the voltage given under the above-mentioned rotational coordinates

Convert the component u under the static coordinate to _x, u _y, with the input signal as the SVPWM inverter:

$\left[\begin{array}{c}{u}_{\mathrm{\&alpha;}2}^{*}\\ u_{\mathrm{\&beta;}2}^{*}\end{array}\right]=\left[\begin{array}{cc}\cos \mathrm{\&theta;}& -\sin \mathrm{\&theta;}\\ \sin \mathrm{\&theta;}& \cos \mathrm{\&theta;}\end{array}\right]\left[\begin{array}{c}{u}_x^{*}\\ u_y^{*}\end{array}\right]---\left(15\right).$

2. method for constructing bearing-free synchronous reluctance motor suspension system according to claim 1 is characterized in that step 1) in the expansion the displacement observation device comprise PI adaptive rate, PID adjuster, suspending power observer and Park inverse transformation; Rotor displacement observation construction method may further comprise the steps:

1.1) structure suspending power observer: the radial suspension force component F on bearingless synchronous reluctance motor rotor two vertical direction under synchronous rotary d, the q coordinate system _x, F _yFor:

$\left\{\begin{array}{c}{F}_x=K_d{i}_d{i}_x+K_q{i}_q{i}_y\\ F_y=K_q{i}_q{i}_x-K_d{i}_d{i}_y\end{array}\right.---\left(1\right)$

Formula (1) consists of the Mathematical Modeling of suspending power observer, K in the formula _d, K _qBe respectively motor d, q axle suspension buoyancy/current constant, i _d, i _qBe respectively torque winding equivalence biphase current, i _x, i _yBe respectively suspending windings equivalence biphase current;

1.2) with the radial suspension force component F under the above-mentioned rotational coordinates _x, F _yConvert component F under the static coordinate to through the Park inverse transformation _α, F _βFor:

$\left[\begin{array}{c}{F}_{\mathrm{\&alpha;}}\\ F_{\mathrm{\&beta;}}\end{array}\right]=\left[\begin{array}{cc}\cos \mathrm{\&theta;}& -\sin \mathrm{\&theta;}\\ \sin \mathrm{\&theta;}& \cos \mathrm{\&theta;}\end{array}\right]\left[\begin{array}{c}{F}_x\\ F_y\end{array}\right]---\left(2\right)$

1.3) structure PI adaptive rate: the fundamental relation formula is between rotor radial displacement α, the β of the PI adaptive rate of regulating based on PI and the suspending power:

$\left\{\begin{array}{c}\mathrm{\&alpha;}=K_p(F_{\mathrm{\&alpha;}}^{*}-F_{\mathrm{\&alpha;}})+K_i\&Integral;(F_{\mathrm{\&alpha;}}^{*}-F_{\mathrm{\&alpha;}})\mathrm{dt}\\ \mathrm{\&beta;}=K_p(F_{\mathrm{\&beta;}}^{*}-F_{\mathrm{\&beta;}})+K_i\&Integral;(F_{\mathrm{\&beta;}}^{*}-F_{\mathrm{\&beta;}})\mathrm{dt}\end{array}\right.---\left(3\right)$

K in the formula _p, K _iDifference scale operation and integral operation coefficient, suspending power F _α, F _βBe step 1.2) in the suspending power measured value that obtains,

For the deviation of rotor displacement set-point and estimated value obtains the suspending power reference value behind the PID adjuster; According to formula (3), can get the measured value of radial displacement on rotor two direction of principal axis.

3. method for constructing bearing-free synchronous reluctance motor suspension system according to claim 1 is characterized in that step 2) in the suspending power/current modulator model construction method of expansion may further comprise the steps:

2.1) under the static α of two-phase, β coordinate system, the suspending windings current i _{α 2}, i _{β 2}With radial suspension force F _α, F _βThe pass be:

$\left[\begin{array}{c}{i}_{\mathrm{\&alpha;}2}\\ i_{\mathrm{\&beta;}2}\end{array}\right]=\frac{1}{K_d^2{i}_d^2+K_q^2{i}_q^2}\left[\begin{array}{cc}\cos 2\mathrm{\&theta;}& -\sin 2\mathrm{\&theta;}\\ \sin 2\mathrm{\&theta;}& \cos 2\mathrm{\&theta;}\end{array}\right]\left[\begin{array}{cc}{K}_d{i}_d& K_q{i}_q\\ K_q{i}_q& -K_d{i}_d\end{array}\right]\left[\begin{array}{c}{F}_{\mathrm{\&alpha;}}\\ F_{\mathrm{\&beta;}}\end{array}\right]---\left(4\right)$

K in the formula (1) _d, K _qBe respectively motor d, q axle suspension buoyancy/current constant, i _d, i _qBe respectively torque winding equivalence biphase current; The reference value that is input as radial suspension force when suspending power/current modulator

Can obtain the current reference value of suspending windings

2.2) with the suspending windings current i under the two-phase static coordinate _{α 2}, i _{β 2}, be converted to the current i under two-phase synchronous rotary d, the q coordinate _x, i _yFor:

$\left[\begin{array}{c}{i}_x\\ i_y\end{array}\right]=\left[\begin{array}{cc}\cos \mathrm{\&theta;}& \sin \mathrm{\&theta;}\\ -\sin \mathrm{\&theta;}& \cos \mathrm{\&theta;}\end{array}\right]\left[\begin{array}{c}{i}_{\mathrm{\&alpha;}2}\\ i_{\mathrm{\&beta;}2}\end{array}\right]---\left(5\right)$

The suspending power of the common formation expansion of above-mentioned formula (4) and formula (5)/current modulator model.

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