CN103346726A - PMSM stator flux linkage observation method based on extension flux linkage observer - Google Patents

Abstract

The invention discloses a PMSM stator flux linkage observation method which is characterized in that an extension flux linkage observer is established according to a motor stator voltage phasor u alpha beta, a stator current phasor i alpha beta and a rotor electric angular speed omega in a two-phase static coordinate system (alpha beta coordinate system for short), on the basis of the theory of a state observer and according to a mathematical model of the PMSM in the alpha beta coordinate system, the motor stator voltage phasor u alpha beta, the stator current phasor i alpha beta and the rotor electric angular speed omega are obtained through collection and calculation, and then the relation between the stator flux linkage and the extension flux linkage is utilized for observing a rotor flux linkage psis. According to the PMSM stator flux linkage observation method, the problem of direct-current bias and integral saturation caused by the pure integral stator flux linkage observation method can be solved, the problems of the amplitude value and phase deviation or waveform distortion caused by an improved integrator are solved, and the advantage that parameters of the pure integral stator flux linkage observer are good in robustness is reserved. Due to the fact that only a minimum-order observer is required, engineering practice is benefited. The stator flux linkage observation method can be applied to a surface-mounted-type SPMSM and an inserted-type SPMSM and have the advantage of being good in universality.

Description

Permanent-magnetic synchronous motor stator flux observation method based on the expansion flux observer

Technical field

The present invention relates to a kind of flux observation method, specifically a kind of permanent-magnetic synchronous motor stator flux observation method.

Background technology

Permagnetic synchronous motor (being called for short PMSM) has efficient height, big, little, the advantages such as dynamic response fast, speed-regulating range width of the big pulsation of torque output of power density, has obtained extensive use at wind generator system and electric drive system for electric vehicles field at present.

Common PMSM governing system constitutes two closed-loop control forms by speed outer shroud and current inner loop usually, and interior circular current set-point is given by the speed closed loop adjuster, therefore generally need not electromagnetic torque observation accurately.And in wind power generation and vehicle electric system, PMSM driving governor self generally need not speed closed loop control, usually requires its torque instruction that master control system is issued to follow the tracks of control, and the real-world operation speed of motor is then determined by master control system.Therefore on the basis of electromagnetic torque feedback, carry out the torque closed-loop control and can obtain required current-order, and then guarantee that the PMSM driving control system accurately follows the tracks of the command torque that master control system issues.Yet, the torque sensor that real system usually can the mounting torque instrument and so on, therefore high-precision electromagnetic torque estimates it is the key that realizes accurate torque closed-loop control.According to the Mathematical Modeling of PMSM, its electromagnetic torque can obtain based on the multiplication cross of stator magnetic linkage and stator current, so the accuracy of stator flux observer has directly determined the observation of electromagnetic torque and followed the tracks of control precision.

Conventional PMSM stator flux observer method can be divided into two classes.One class is according to actual measurement stator voltage, electric current, directly calculates the value of stator magnetic linkage under the dq coordinate system based on the Mathematical Modeling of PMSM under two-phase synchronous rotating frame (being called for short the dq coordinate system).This method is calculated simple, but will use permanent magnet magnetic linkage and friendship, d-axis inductance, and these parameters are subject to temperature rise and magnetically saturated influence, cause the stator magnetic linkage error of calculation.Another kind of method is directly to obtain magnetic linkage based on the integral operation of stator voltage model, although this method has parameter robustness preferably, has its intrinsic integral operation problem.At pure integration problem, some scholars have carried out improving research, and the method for proposition has: one, adopt low pass filter to replace pure integrator, it is saturated to overcome direct current biasing and integration that pure integration produces, but can bring phase place and amplitude deviation; Two, adopt the improvement integrator of saturated feedback, it is saturated to suppress integration, but may cause wave distortion; Three, the improvement integrator that adopts amplitude to limit can overcome the wave distortion that method two causes, but constant amplitude limit benchmark setting means is difficult to satisfy the needs of PMSM actual motion; Four, according to the orthogonality principle of back electromotive force and stator magnetic linkage, make up the adaptive compensation method of magnetic linkage amplitude, obtained to adapt to the compensation effect than wide speed regulating range, but its flux observation precision is still limited.

Compare with conventional stator flux observer method, not only can avoid the problem of pure integration based on the observation procedure of state observer, and can realize the closed loop observation of magnetic linkage.Have method to make up the full scalariform attitude observer of stator magnetic linkage under the dq coordinate system, but this method had both needed rotor flux linkage orientation angle accurately, and used the more parameter of electric machine again simultaneously, its parameter of electric machine dependence is stronger.

Summary of the invention

The present invention is the weak point that exists for the state observer method that overcomes under conventional stator flux observer technology and the dq coordinate system, and stator flux observer method a kind of closed loop, that Project Realization is easier, the parameter robustness is good is provided.The present invention is under the α β coordinate system in the two-phase rest frame, makes up a kind of expansion flux observer, and utilizes stator magnetic linkage and the relation of expansion magnetic linkage to calculate stator magnetic linkage.The expansion flux observer that adopts has only 2 rank, and only needs stator resistance and hand over two parameters of electric machine of axle inductance, and the accuracy of observation of stator magnetic linkage is not subjected to hand over an axle inductive impact, and the parameter robustness is good.

What to achieve these goals, the present invention proposed is a kind of based on the permanent-magnetic synchronous motor stator flux observation method of expanding flux observer.The two-phase rest frame that this method at first obtains according to the collection union (being called for short α β coordinate system) is motor stator voltage phasor u down _{α β}, stator current phasor i _{α β}With rotor electric angle speed omega, based on the state observer theory, set up a kind of expansion flux observer according to the Mathematical Modeling of permagnetic synchronous motor under α β coordinate system, utilize stator magnetic linkage and the relation of expansion magnetic linkage to observe stator magnetic linkage ψ then _s

Technical scheme of the present invention realizes according to following step.

Step 1, the stator voltage phasor u of collection permagnetic synchronous motor under α β coordinate system _{α β}, stator current phasor i _{α β}With rotor electric angle speed omega;

Described stator voltage phasor u _{α β}Acquisition mode comprise following two kinds:

(1) the permanent-magnetic synchronous motor stator line voltage u that samples and recorded in real time _AbAnd u _BcAnd obtain u through the coordinate transform of formula (6) _{α β},

$u_{\mathrm{\α\β}}=\left[\begin{array}{cc}\frac{2}{3}& \frac{1}{3}\\ 0& \frac{\sqrt{3}}{3}\end{array}\right]\left[\begin{array}{c}{u}_{\mathrm{ab}}\\ u_{\mathrm{bc}}\end{array}\right]---\left(6\right)$

(2) the inverter modulation signal that directly adopts the electric machine controller arithmetic element to calculate

Replace u _{α β},

Described stator current phasor i _{α β}Gatherer process as follows:

(1) the permagnetic synchronous motor threephase stator current i of sampling and being recorded in real time _A, i _B, i _C,

(2) utilize the coordinate transform of formula (7) to obtain permagnetic synchronous motor stator current phasor i under α β coordinate system _{α β}:

$i_{\mathrm{\α\β}}=\frac{2}{3}\left[\begin{array}{ccc}1& -\frac{1}{2}& -\frac{1}{2}\\ 0& \frac{\sqrt{3}}{2}& -\frac{\sqrt{3}}{2}\end{array}\right]\left[\begin{array}{c}{i}_A\\ i_B\\ i_C\end{array}\right]---\left(7\right)$

The gatherer process of described rotor electric angle speed omega is as follows:

(1) at neighbouring sample moment t ₁, t ₂Sampling is installed in the umber of pulse N that the photoelectric type rotary encoder on the motor shaft sends ₁, N ₂, described neighbouring sample difference constantly is sampling period T,

(2) according to the impulse sampling value N of rotor electric angle speed omega and photoelectric type rotary encoder ₁, N ₂And the relation between the sampling period T can calculate rotor electric angle speed omega, and its expression formula is:

$\mathrm{\ω}=\frac{N_2-N_1}{M\×T}\×N\×2\mathrm{\π}$

In the following formula, the umber of pulse that M rotates a circle and produces for the photoelectric type rotary encoder, N is the permagnetic synchronous motor number of pole-pairs.

Step 2, under α β coordinate system, set up the state-space expression of permagnetic synchronous motor:

${\stackrel{.}{\mathrm{\ψ}}}_{\mathrm{\α\β}}={\mathrm{\ωJ\ψ}}_{\mathrm{\α\β}}$

In the formula (1), ψ _{α β}Be the expansion magnetic linkage, Be ψ _{α β}Differential, y for output phasor, R _sBe stator resistance, L _qFor handing over the axle inductance, p is differential operator, $J=\left[\begin{array}{cc}0& -1\\ 1& 0\end{array}\right];$

According to formula (1) set up shape suc as formula the expansion flux observer of (2) to ψ _{α β}Observe:

${\stackrel{\·}{\widehat{\mathrm{\ψ}}}}_{\mathrm{\α\β}}=\mathrm{\ωJ}{\widehat{\mathrm{\ψ}}}_{\mathrm{\α\β}}+H(u_{\mathrm{\α\β}}-R_s{i}_{\mathrm{\α\β}}-L_q{\mathrm{pi}}_{\mathrm{\α\β}}-\mathrm{\ωJ}{\widehat{\mathrm{\ψ}}}_{\mathrm{\α\β}})---\left(2\right)$

$\hat{y}=\mathrm{\ωJ}{\widehat{\mathrm{\ψ}}}_{\mathrm{\α\β}}$

In the formula (2),

Be ψ _{α β}Measured value,

For

Differential,

Be the measured value of output phasor y, feedback gain matrix $H=\left[\begin{array}{cc}1& \frac{\mathrm{\ρ}}{\mathrm{\ω}}\\ -\frac{\mathrm{\ρ}}{\mathrm{\ω}}& 1\end{array}\right]$ ρ is arithmetic number;

Step 3, to second formula in the formula (1) put in order and integration get:

∫(u _αβ-R _si _αβ)＝L _qi _αβ+ψ _αβ （3）

Formula (3) the equation left side is the pure integration observation expression formula of stator magnetic linkage, gets stator magnetic linkage thus and with the pass of expanding magnetic linkage is:

ψ _s＝L _qi _αβ+ψ _αβ (4)

Get according to formula (4), when adopting the expansion flux observer to realize the expansion flux observation, the stator flux observer value

Expression formula be:

${\widehat{\mathrm{\ψ}}}_s={\hat{L}}_q{i}_{\mathrm{\α\β}}+{\widehat{\mathrm{\ψ}}}_{\mathrm{\α\β}}---\left(5\right)$

In the formula (5),

Friendship axle inductance value for the reality use.

The technical scheme that the present invention is based on the permanent-magnetic synchronous motor stator flux observation method of expansion flux observer is made up of above-mentioned three steps.

In above-mentioned steps, the state-space expression of the described permagnetic synchronous motor of step 2 (1) obtains as follows:

At first, be that voltage equation under the dq coordinate system is write following form with permagnetic synchronous motor at the two-phase synchronous rotating frame:

$\left[\begin{array}{c}{u}_d\\ u_q\end{array}\right]=\left[\begin{array}{cc}{R}_s+{\mathrm{pL}}_d& {-\mathrm{\ωL}}_q\\ {\mathrm{\ωL}}_d& R_s+{\mathrm{pL}}_q\end{array}\right]\left[\begin{array}{c}{i}_d\\ i_q\end{array}\right]+\mathrm{\ω}\left[\begin{array}{c}0\\ {\mathrm{\ψ}}_f\end{array}\right]---\left(8\right)$

In the formula (8), d represents direct axis component, and q represents quadrature axis component, u _dAnd u _qBe stator voltage, i _dAnd i _qBe stator current, L _dBe d-axis inductance, ψ _fBe the rotor permanent magnet magnetic linkage;

Permagnetic synchronous motor voltage equation shown in the formula (8) is expressed as following form again:

$\left[\begin{array}{c}{u}_d\\ u_q\end{array}\right]=\left[\begin{array}{cc}{R}_s+{\mathrm{pL}}_q& {-\mathrm{\ωL}}_q\\ {\mathrm{\ωL}}_q& R_s+{\mathrm{pL}}_q\end{array}\right]\left[\begin{array}{c}{i}_d\\ i_q\end{array}\right]+\mathrm{\ω}\left[\begin{array}{c}0\\ {\mathrm{\ψ}}_f+(L_d-L_q)i_d\end{array}\right]+\left[\begin{array}{c}(L_d-L_q){\mathrm{pi}}_d\\ 0\end{array}\right]---\left(9\right)$

Secondly, the 3rd on equation the right is 0 in the selected formula (9), and with formula (9) transform under the α β coordinate system following form:

u _αβ＝R _si _αβ+L _qpi _αβ+pψ _αβ （10）

pψ _αβ＝ωJψ _αβ （11）

In the formula (10), ${\mathrm{\ψ}}_{\mathrm{\α\β}}=\left[\begin{array}{c}{\mathrm{\ψ}}_f+(L_d-L_q)i_d\end{array}\right]\left[\begin{array}{c}\cos \mathrm{\θ}\\ \sin \mathrm{\θ}\end{array}\right],$ θ is the rotor flux position angle;

Under α β coordinate system, set up the state-space expression (1) of permagnetic synchronous motor according to formula (10) and formula (11):

${\stackrel{.}{\mathrm{\ψ}}}_{\mathrm{\α\β}}={\mathrm{\ωJ\ψ}}_{\mathrm{\α\β}}$

Compared with the prior art, beneficial effect of the present invention is embodied in:

1 and conventional stator flux observer method compare, direct current biasing and integration saturation problem that the present invention not only can avoid pure integration method to cause can also avoid improving the limited problem of phase place and amplitude deviation, wave distortion and application scenario that the integrator method is brought.

2 compare with full scalariform attitude observer under the dq coordinate system, and the state observer exponent number that the present invention makes up is little, is easy to Project Realization; The stator flux observer that obtains is the same with the stator voltage integration method to have higher parameter robustness.

3, the present invention not only can be applied to surface-mount type permagnetic synchronous motor (SPMSM), and can be applied to plug-in permanent magnet synchronous machine (IPMSM), pervasive should getting well.

Description of drawings

Fig. 1 is stator flux observer structure chart of the present invention.

Embodiment

The invention will be further elaborated below in conjunction with drawings and Examples.

Referring to Fig. 1, signals collecting part, u _{α β}And i _{α β}Be by sampling stator line voltage u _Ab, stator line voltage u _Bc, stator A phase current i _A, stator B phase current i _B, stator C phase current i _C, and be tied to the conversion of two-phase rest frame through the three phase static coordinate and obtain, the actual electrical angular velocity omega is to utilize the photoelectric type rotary encoder to obtain.Present embodiment carries out according to the following procedure:

The motor stator line voltage u that step 1, sampling are recorded in real time _AbAnd u _Bc, the threephase stator current i _A, i _B, i _CWith rotor electric angle speed omega, and to u _Ab, u _Bc, i _A, i _B, i _CCarry out the voltage and current u on the coordinate transform acquisition α β coordinate system _{α β}, i _{α β}

1), at first utilize the line potential pulse between line potential pulse between Hall voltage sensor sample stator A, the B two-phase and stator B, the C two-phase, input has the voltage sample passage of low-pass filter circuit then, obtains sine voltage signal u _Ab, u _BcVoltage sample value u to obtaining in digital signal processing chip _Ab, u _BcCarry out coordinate transform as the formula (1), obtain the stator voltage signal u on the α β coordinate system _{α β}

$u_{\mathrm{\α\β}}=\left[\begin{array}{cc}\frac{2}{3}& \frac{1}{3}\\ 0& \frac{\sqrt{3}}{3}\end{array}\right]\left[\begin{array}{c}{u}_{\mathrm{ab}}\\ u_{\mathrm{bc}}\end{array}\right]---\left(1\right)$

2), utilize Hall current sensor to gather stator A phase current i _A, stator B phase current i _B, stator C phase current i _C, then with its input current sampling channel; Current sampling data i to obtaining in digital signal processing chip _A, i _B, i _CCarry out coordinate transform as the formula (2), obtain the stator current signal i on the α β coordinate system _{α β}

$i_{\mathrm{\α\β}}=\frac{2}{3}\left[\begin{array}{ccc}1& -\frac{1}{2}& -\frac{1}{2}\\ 0& \frac{\sqrt{3}}{2}& -\frac{\sqrt{3}}{2}\end{array}\right]\left[\begin{array}{c}{i}_A\\ i_B\\ i_C\end{array}\right]---\left(2\right)$

3), utilize the photoelectric type rotary encoder that is installed on the motor shaft to obtain neighbouring sample t constantly ₁, t ₂Impulse sampling value N ₁, N ₂, according to rotor electric angle speed omega and adjacent pulse sampled value N ₁, N ₂And the relation of sampling period T can calculate ω, and its expression formula as the formula (3).

$\mathrm{\ω}=\frac{N_2-N_1}{M\×T}\×N\×2\mathrm{\π}---\left(3\right)$

In the formula (3), the umber of pulse that M rotates a circle and produces for the photoelectric type rotary encoder, N is the permagnetic synchronous motor number of pole-pairs.

Below referring to Fig. 1.

The foundation of expansion flux observer is carried out according to the following procedure:

Step 2, the voltage equation of permagnetic synchronous motor on the dq coordinate system write following form:

$\left[\begin{array}{c}{u}_d\\ u_q\end{array}\right]=\left[\begin{array}{cc}{R}_s+{\mathrm{pL}}_d& {-\mathrm{\ωL}}_q\\ {\mathrm{\ωL}}_d& R_s+{\mathrm{pL}}_q\end{array}\right]\left[\begin{array}{c}{i}_d\\ i_q\end{array}\right]+\mathrm{\ω}\left[\begin{array}{c}0\\ {\mathrm{\ψ}}_f\end{array}\right]---\left(4\right)$

In the following formula, d represents direct axis component, and q represents quadrature axis component, u _dAnd u _qBe stator voltage, i _dAnd i _qBe stator current, R _sBe stator resistance, L _dBe d-axis inductance, L _qFor handing over axle inductance, ψ _fBe the rotor permanent magnet magnetic linkage, ω is rotor electric angle speed, and p is differential operator.

Permagnetic synchronous motor voltage equation shown in the formula (4) is expressed as following form again:

$\left[\begin{array}{c}{u}_d\\ u_q\end{array}\right]=\left[\begin{array}{cc}{R}_s+{\mathrm{pL}}_q& {-\mathrm{\ωL}}_q\\ {\mathrm{\ωL}}_q& R_s+{\mathrm{pL}}_q\end{array}\right]\left[\begin{array}{c}{i}_d\\ i_q\end{array}\right]+\mathrm{\ω}\left[\begin{array}{c}0\\ {\mathrm{\ψ}}_f+(L_d-L_q)i_d\end{array}\right]+\left[\begin{array}{c}(L_d-L_q){\mathrm{pi}}_d\\ 0\end{array}\right]---\left(5\right)$

Step 3, because electric current loop makes current response rapid, can select that the 3rd on equation the right is 0 in the formula (5), and with formula (5) transform on the α β coordinate system following form:

u _αβ＝R _si _αβ+L _qpi _αβ+pψ _αβ （6）

In the formula (6), ${\mathrm{\ψ}}_{\mathrm{\α\β}}={\left[\begin{array}{cc}{\mathrm{\ψ}}_{\mathrm{\α}}& {\mathrm{\ψ}}_{\mathrm{\β}}\end{array}\right]}^T=\left[\begin{array}{c}{\mathrm{\ψ}}_f+(L_d-L_q)i_d\end{array}\right]\left[\begin{array}{c}\cos \mathrm{\θ}\\ \sin \mathrm{\θ}\end{array}\right],$ u _{α β}Be stator voltage phasor, i _{α β}Be stator current phasor, ψ _{α β}Be the expansion magnetic linkage, θ is the rotor flux position angle.

Because the quick tracing property of electric current can be thought and expand magnetic linkage ψ _{α β}The amplitude differential be 0, get ψ _{α β}Differential expressions:

pψ _αβ＝p[ψ _f+(L _d-L _q)i _d]+ωJψ _αβ （7）

＝ωJψ _αβ

In the formula (7), $J=\left[\begin{array}{cc}0& -1\\ 1& 0\end{array}\right].$

Step 4, set up with expansion magnetic linkage ψ according to formula (6) and formula (7) _{α β}For the state-space expression of state variable is:

${\stackrel{.}{\mathrm{\ψ}}}_{\mathrm{\α\β}}={\mathrm{\ωJ\ψ}}_{\mathrm{\α\β}}$

In the formula (8),

Expression ψ _{α β}Differential, y represents to export phasor.

Because the electrical time constant of motor is little more than mechanical time constant, can think constant two adjacent sampling instant motor electric angle speed omega, can regard system shown in the formula (8) as stational system, so set up expansion magnetic linkage state observer be:

${\stackrel{\·}{\widehat{\mathrm{\ψ}}}}_{\mathrm{\α\β}}=\mathrm{\ωJ}{\widehat{\mathrm{\ψ}}}_{\mathrm{\α\β}}+H(u_{\mathrm{\α\β}}-R_s{i}_{\mathrm{\α\β}}-L_q{\mathrm{pi}}_{\mathrm{\α\β}}-\mathrm{\ωJ}{\widehat{\mathrm{\ψ}}}_{\mathrm{\α\β}})---\left(9\right)$

$\hat{y}=\mathrm{\ωJ}{\widehat{\mathrm{\ψ}}}_{\mathrm{\α\β}}$

In the formula (9), Be ψ _{α β}Measured value,

For

Differential, Be the measured value of y, feedback gain matrix $H=\left[\begin{array}{cc}{h}_1& {-h}_2\\ h_2& h_1\end{array}\right],$ h ₁, h ₂Be undetermined coefficient.

The flux observation error equation must be expanded in comparison expression (8) and (9):

${\stackrel{\·}{\widetilde{\mathrm{\ψ}}}}_{\mathrm{\α\β}}=\mathrm{\ω}(I-H)J{\widetilde{\mathrm{\ψ}}}_{\mathrm{\α\β}}=\mathrm{\ω}\left[\begin{array}{cc}{h}_2& h_1-1\\ {1-h}_1& h_2\end{array}\right]{\widetilde{\mathrm{\ψ}}}_{\mathrm{\α\β}}---\left(10\right)$

In the formula (10),

Be expansion flux observation error.

With the differential equation coefficient matrix shown in the formula (10) $H=\left[\begin{array}{cc}{h}_2& h_1-1\\ {1-h}_1& h_2\end{array}\right]$ POLE PLACEMENT USING be same negative real number-ρ, described ρ is arithmetic number, i.e. the parameter h of coefficient matrix ₁, h ₂Satisfy characteristic equation (ρ-ω h ₂) ²+ ω ²(1-h ₁) ²=0, calculate h ₁=1,

Namely getting feedback gain matrix is:

$H=\left[\begin{array}{cc}1& \frac{\mathrm{\ρ}}{\mathrm{\ω}}\\ -\frac{\mathrm{\ρ}}{\mathrm{\ω}}& 1\end{array}\right]$

If directly according to the form design point observer structure of formula (9), need stator current is differentiated, be easy to introduce noise, introduce intermediate variable for this reason, as follows:

${\widehat{\mathrm{\ψ}}}_{1\mathrm{\α\β}}={\widehat{\mathrm{\ψ}}}_{\mathrm{\α\β}}+{\mathrm{HL}}_q{i}_{\mathrm{\α\β}}---\left(11\right)$

With formula (11) substitution formula (9), the state observation equation can be expressed as again:

$P{\widehat{\mathrm{\ψ}}}_{1\mathrm{\α\β}}=\mathrm{\ω}(I-H)J{\widehat{\mathrm{\ψ}}}_{\mathrm{\α\β}}+H(u_{\mathrm{\α\β}}-R_s{i}_{\mathrm{\α\β}})---\left(12\right)$

Step 5, stator magnetic linkage are observed process.

Referring to Fig. 1, stator flux observer carries out according to the following procedure:

In motor operation course, the parameter of electric machine can change along with operating condition, and the actual parameter of electric machine that uses is in the expansion flux observer According to formula (6) and (9), when the expansion flux observer is realized flux observation, the permanent establishment of formula (13) is arranged:

$u_{\mathrm{\α\β}}=R_s{i}_{\mathrm{\α\β}}+{\hat{L}}_q{\mathrm{pi}}_{\mathrm{\α\β}}+p{\widehat{\mathrm{\ψ}}}_{\mathrm{\α\β}}---\left(13\right)$

Putting in order also to formula (13), integration gets:

$\∫(u_{\mathrm{\α\β}}-R_s{i}_{\mathrm{\α\β}})={\hat{L}}_q{i}_{\mathrm{\α\β}}+{\widehat{\mathrm{\ψ}}}_{\mathrm{\α\β}}---\left(14\right)$

Formula (14) the equation left side is the pure integral expression of stator magnetic linkage voltage model, can get the stator flux observer value thus

Expression formula be:

${\widehat{\mathrm{\ψ}}}_s={\hat{L}}_q{i}_{\mathrm{\α\β}}+{\widehat{\mathrm{\ψ}}}_{\mathrm{\α\β}}---\left(15\right)$

Because formula (14) is permanent the establishment also, the stator flux observer method that makes the present invention propose is not subjected to hand over the axle inductance

The accuracy influence, another parameter of electric machine R of use _sCan obtain in real time by in stator winding, imbedding temperature sensor.

Claims (5)

1. the permanent-magnetic synchronous motor stator flux observation method based on the expansion flux observer is characterized in that comprising the steps:

Step 1, the stator voltage phasor u of collection permagnetic synchronous motor under α β coordinate system _{α β}, stator current phasor i _{α β}With rotor electric angle speed omega;

Step 2, the state-space expression of setting up permagnetic synchronous motor under α β coordinate system are:

${\stackrel{.}{\mathrm{\ψ}}}_{\mathrm{\α\β}}={\mathrm{\ωJ\ψ}}_{\mathrm{\α\β}}$

In the formula (1), ψ _{α β}Be the expansion magnetic linkage, Be ψ _{α β}Differential, y for output phasor, R _sBe stator resistance, L _qFor handing over the axle inductance, p is differential operator, $J=\left[\begin{array}{cc}0& -1\\ 1& 0\end{array}\right];$

According to formula (1) set up shape suc as formula the expansion flux observer of (2) to ψ _{α β}Observe:

${\stackrel{\·}{\widehat{\mathrm{\ψ}}}}_{\mathrm{\α\β}}=\mathrm{\ωJ}{\widehat{\mathrm{\ψ}}}_{\mathrm{\α\β}}+H(u_{\mathrm{\α\β}}-R_s{i}_{\mathrm{\α\β}}-L_q{\mathrm{pi}}_{\mathrm{\α\β}}-\mathrm{\ωJ}{\widehat{\mathrm{\ψ}}}_{\mathrm{\α\β}})---\left(2\right)$

$\hat{y}=\mathrm{\ωJ}{\widehat{\mathrm{\ψ}}}_{\mathrm{\α\β}}$

In the formula (2),

Be ψ _{α β}Measured value,

For Differential,

Be the measured value of output phasor y, feedback gain matrix $H=\left[\begin{array}{cc}1& \frac{\mathrm{\ρ}}{\mathrm{\ω}}\\ -\frac{\mathrm{\ρ}}{\mathrm{\ω}}& 1\end{array}\right],$ ρ is arithmetic number;

Step 3, to second formula in the formula (1) put in order and integration get:

∫(u _αβ-R _si _αβ)＝L _qi _αβ+ψ _αβ （3）

Formula (3) the equation left side is the pure integration observation expression formula of stator magnetic linkage, gets stator magnetic linkage thus and with the pass of expanding magnetic linkage is:

ψ _s＝L _qi _αβ+ψ _αβ (4)

Get according to formula (4), when adopting the expansion flux observer to realize the expansion flux observation, the stator flux observer value

Expression formula be:

${\widehat{\mathrm{\ψ}}}_s={\hat{L}}_q{i}_{\mathrm{\α\β}}+{\widehat{\mathrm{\ψ}}}_{\mathrm{\α\β}}---\left(5\right)$

In the formula (5),

Friendship axle inductance value for the reality use.

2. a kind of permanent-magnetic synchronous motor stator flux observation method based on the expansion flux observer according to claim 1 is characterized in that the stator voltage phasor u of the permagnetic synchronous motor described in the step 1 under α β coordinate system _{α β}Acquisition mode comprise following two kinds:

(1) the permanent-magnetic synchronous motor stator line voltage u that samples and recorded in real time _AbAnd u _BcAnd obtain u through the coordinate transform of formula (6) _{α β},

$u_{\mathrm{\α\β}}=\left[\begin{array}{cc}\frac{2}{3}& \frac{1}{3}\\ 0& \frac{\sqrt{3}}{3}\end{array}\right]\left[\begin{array}{c}{u}_{\mathrm{ab}}\\ u_{\mathrm{bc}}\end{array}\right]---\left(6\right)$

(2) the inverter modulation signal that directly adopts the electric machine controller arithmetic element to calculate

Replace u _{α β}

3. a kind of permanent-magnetic synchronous motor stator flux observation method based on the expansion flux observer according to claim 1 is characterized in that the stator current phasor i of the permagnetic synchronous motor described in the step 1 under α β coordinate system _{α β}Gatherer process as follows:

(1) the permagnetic synchronous motor threephase stator current i of sampling and being recorded in real time _A, i _B, i _C,

(2) utilize the coordinate transform of formula (7) to obtain permagnetic synchronous motor stator current phasor i under α β coordinate system _{α β}:

$i_{\mathrm{\α\β}}=\frac{2}{3}\left[\begin{array}{ccc}1& -\frac{1}{2}& -\frac{1}{2}\\ 0& \frac{\sqrt{3}}{2}& -\frac{\sqrt{3}}{2}\end{array}\right]\left[\begin{array}{c}{i}_A\\ i_B\\ i_C\end{array}\right]---\left(7\right).$

4. according to claim 1 a kind of based on the permanent-magnetic synchronous motor stator flux observation method of expanding flux observer, it is characterized in that the gatherer process of the rotor electric angle speed omega of the permagnetic synchronous motor described in the step 1 under α β coordinate system is as follows:

(1) at neighbouring sample moment t ₁, t ₂Sampling is installed in the umber of pulse N that the photoelectric type rotary encoder on the motor shaft sends ₁, N ₂, described neighbouring sample difference constantly is sampling period T,

(2) according to the impulse sampling value N of rotor electric angle speed omega and photoelectric type rotary encoder ₁, N ₂And the relation between the sampling period T can calculate rotor electric angle speed omega, and its expression formula is:

$\mathrm{\ω}=\frac{N_2-N_1}{M\×T}\×N\×2\mathrm{\π}$

In the following formula, the umber of pulse that M rotates a circle and produces for the photoelectric type rotary encoder, N is the permagnetic synchronous motor number of pole-pairs.

5. according to claim 1 a kind of based on the permanent-magnetic synchronous motor stator flux observation method of expanding flux observer,

It is characterized in that the state-space expression of the described permagnetic synchronous motor of step 2 (1) obtains as follows:

At first, be that voltage equation under the dq coordinate system is write following form with permagnetic synchronous motor at the two-phase synchronous rotating frame:

$\left[\begin{array}{c}{u}_d\\ u_q\end{array}\right]=\left[\begin{array}{cc}{R}_s+{\mathrm{pL}}_d& {-\mathrm{\ωL}}_q\\ {\mathrm{\ωL}}_d& R_s+{\mathrm{pL}}_q\end{array}\right]\left[\begin{array}{c}{i}_d\\ i_q\end{array}\right]+\mathrm{\ω}\left[\begin{array}{c}0\\ {\mathrm{\ψ}}_f\end{array}\right]---\left(8\right)$

In the formula (8), d represents direct axis component, and q represents quadrature axis component, u _dAnd u _qBe stator voltage, i _dAnd i _qBe stator current, L _dBe d-axis inductance, ψ _fBe the rotor permanent magnet magnetic linkage;

Permagnetic synchronous motor voltage equation shown in the formula (8) is expressed as following form again:

$\left[\begin{array}{c}{u}_d\\ u_q\end{array}\right]=\left[\begin{array}{cc}{R}_s+{\mathrm{pL}}_q& {-\mathrm{\ωL}}_q\\ {\mathrm{\ωL}}_q& R_s+{\mathrm{pL}}_q\end{array}\right]\left[\begin{array}{c}{i}_d\\ i_q\end{array}\right]+\mathrm{\ω}\left[\begin{array}{c}0\\ {\mathrm{\ψ}}_f+(L_d-L_q)i_d\end{array}\right]+\left[\begin{array}{c}(L_d-L_q){\mathrm{pi}}_d\\ 0\end{array}\right]---\left(9\right)$

Secondly, the 3rd on equation the right is 0 in the selected formula (9), and with formula (9) transform under the α β coordinate system following form: u _{α β}=R _si _{α β}+ L _qPi _{α β}+ p ψ _{α β}(10)

pψ _αβ＝ωJψ _αβ （11）

In the formula (10), ${\mathrm{\ψ}}_{\mathrm{\α\β}}=\left[\begin{array}{c}{\mathrm{\ψ}}_f+(L_d-L_q)i_d\end{array}\right]\left[\begin{array}{c}\cos \mathrm{\θ}\\ \sin \mathrm{\θ}\end{array}\right],$ θ is the rotor flux position angle;

Under α β coordinate system, set up the state-space expression (1) of permagnetic synchronous motor according to formula (10) and formula (11):

${\stackrel{.}{\mathrm{\ψ}}}_{\mathrm{\α\β}}={\mathrm{\ωJ\ψ}}_{\mathrm{\α\β}}$

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