CN104022711A - Method for detecting initial position of surface PM synchronous motor - Google Patents

Abstract

The invention discloses a method for detecting the initial position of a surface PM synchronous motor. The method for detecting the initial position of the surface PM synchronous motor comprises the steps that on the basis that the initial position is estimated for the first time according to the pulse vibration high-frequency current injection method, an injection signal period is evenly divided into four sections, integration is conducted on the d-axis high-frequency voltage response within the section I and the section III, or integration is conducted on the d-axis high-frequency voltage response within the section II and the section IV, and the positive direction of the d axis is judged according to the symbol of an integral value. According to the method for detecting the initial position of the surface PM synchronous motor, the positive direction of the d axis is judged without the need of extra injection of a positive pulse signal and a negative pulse signal, time for estimation is shortened, and the estimation process is simplified.

Description

A kind of surface-mount type permagnetic synchronous motor initial position detection method

Technical field

The present invention relates to Motor Control Field, relate in particular to a kind of surface-mount type permagnetic synchronous motor initial position detection method.

Background technology

The method detecting for surface-mount type permanent-magnetic synchronous motor rotor initial position at present, common taking di/dt type and signal injection type as main.

Yuzawa T, Tanaka K, Moriyama R, et al.An efficient estimation method of sensorless initial rotor position for surface PM synchronous motor[C] //Electric Machines and Drives Conference, 2001.IEMDC2001.IEEE International.IEEE, 2001:44-49. utilize di/dt detection rotor position, the initial position of the rapid estimated rotor of method by binary search, but in identification process, need the rotor of fixed electrical machinery, and identification result is subject to the impact of slot effect.Liu Ying, cycle, Li Shuai, Deng. rotor magnetic steel surface-mount type permanent-magnetic synchronous motor rotor initial position detects [J]. Proceedings of the CSEE, 2011, 31 (18): the non-linear saturation characteristic of 48-54. based on SPMSM stator core, first inject high frequency sine voltage signal at the d of estimated rotor synchronous rotating frame axle, obtain the first estimated value of rotor-position by closed-loop adjustment, inject generating positive and negative voltage pulse at the d direction of principal axis of estimating again, utilize the difference of d-axis equivalent time constant under reversal effect to judge d axle positive direction, these class methods need twice Injection Signal in initial position estimation overall process.Magnetic pole positive direction deterministic process need to inject generating positive and negative voltage pulse more relatively current response decayed to for 0 time used, this process must spend the regular hour.Liu Ying, cycle, Zhao Chengliang, Deng. inject SPMSM low speed position Sensorless Control [J] based on pulsating high-frequency current. Chinese electrotechnics journal, 2012,7 (27): 139-145. adopts pulsating high frequency current injection to realize the estimation of SPMSM rotor-position first, but does not mention how d axle positive direction being judged.

Summary of the invention

Technical problem to be solved by this invention is the defect for background technology, and a kind of surface-mount type permagnetic synchronous motor initial position detection method is provided, and overall process only need be injected signal one time, and initial position testing process is obviously simplified.

The present invention is for solving the problems of the technologies described above by the following technical solutions:

A kind of surface-mount type permagnetic synchronous motor initial position detection method, comprises following steps:

Steps A), obtain the first estimated value of rotor-position;

Step B), judge d axle positive direction, obtain the offset after the judgement of d axle positive direction;

Step C), first rotor-position estimated value is added to the offset after the judgement of d axle positive direction, obtain final initial position estimation value.

As the further prioritization scheme of a kind of surface-mount type permagnetic synchronous motor initial position detection method of the present invention, the step of obtaining the first estimated value of rotor-position is as follows:

Steps A .1), the q shaft current of estimated rotor synchronous rotating frame is given as to 0, d shaft current and is given as a pulsating high frequency sinusoidal signal I _mhsin (ω _ht), wherein, I _mhfor inject the amplitude of high-frequency current, ω at d axle _hfor inject the angular frequency of high-frequency current at d axle, t represents current time;

Steps A .2), adoption rate resonant controller is controlled d shaft current and the q shaft current estimated, makes it with given consistent;

Steps A .3), the voltage of comparative example resonant controller output with carry out Park inverse transformation, obtain the voltage u under the static alpha-beta coordinate system of two-phase _αand u _β, then adopt space vector pulse width modulation strategy to obtain six path switching signals of three-phase inverter, the mounted permagnetic synchronous motor of table-drive;

Steps A .4), detect any biphase current in motor three phase winding A/B/C, first carry out Clarke conversion and obtain the current i under the static alpha-beta coordinate system of two-phase _αand i _β, then conversion obtains the d shaft current under estimated rotor synchronous rotating frame through Park with q shaft current fed back to ratio resonant controller;

Steps A .5), by the q shaft voltage response of estimated rotor synchronous rotating frame selecting frequency through band pass filter is ω _halternating current component, be the first harmonic component of q shaft voltage response again with cosine signal cos (ω _ht) multiply each other and modulate, obtaining DC component and frequency is 2 ω _halternating current component, finally by crossing low pass filter filtering alternating current component, extract DC component, obtain estimated position deviation signal f _c(Δ θ);

Steps A .6), build position deviation closed loop, by estimated position deviation signal f _c(Δ θ) is as the input of ratio resonant controller, estimated rotor angular speed for the output of ratio resonant controller, to estimated rotor angular speed integration obtains the rotor-position of estimating;

Steps A .7), repeating step 1.1) to step 1.6), until the rotor-position of estimating converges to a steady state value, be the first estimated value of initial position of rotor.

As the further prioritization scheme of a kind of surface-mount type permagnetic synchronous motor initial position detection method of the present invention, described judgement d axle positive direction to obtain the detailed step of the offset after the judgement of d axle positive direction as follows:

Step is B.1), an Injection Signal cycle (0,2 π) is evenly divided into four interval: I:(0, pi/2), II:(pi/2, π), III:(π, 3 pi/2s) and IV:(3 pi/2,2 π);

Step is B.2), in interval I and III, d axle high frequency voltage is responded carry out integration, be designated as wherein, ω _hfor inject the angular frequency of high-frequency current at d axle, t represents current time;

Step is B.3), according to k _{i, III}symbol decision d axle positive direction, if k _{i, III}be less than 0, in the same way, the offset after d axle positive direction judges is 0 to the N utmost point of d axle positive direction and magnetic pole; If k _{i, III}be greater than 0, the N of d axle positive direction and magnetic pole is extremely reverse, and the offset after d axle positive direction judges is π.

As the further prioritization scheme of a kind of surface-mount type permagnetic synchronous motor initial position detection method of the present invention, described judgement d axle positive direction the step that obtains the offset after the judgement of d axle positive direction can also be:

Step B.a), an Injection Signal cycle (0,2 π) is evenly divided into four interval: I:(0, pi/2), II:(pi/2, π), III:(π, 3 pi/2s) and IV:(3 pi/2,2 π);

Step B.b), in interval II and IV, to d axle high frequency voltage, integration is carried out in response, is designated as wherein, ω _hfor inject the angular frequency of high-frequency current at d axle, t represents current time;

Step B.c), according to k _{iI, IV}symbol decision d axle positive direction, if k _{iI, IV}be greater than 0, in the same way, the offset after d axle positive direction judges is 0 to the N utmost point of d axle positive direction and magnetic pole; If k _{iI, IV}be less than 0, the N of d axle positive direction and magnetic pole is extremely reverse, and the offset after d axle positive direction judges is π.

The present invention is adopting pulsating high frequency current injection to realize on the basis of first initial position estimation, an Injection Signal cycle is evenly divided into four intervals, in interval I and III, to d axle high frequency voltage, integration is carried out in response, or to d axle high frequency voltage, integration is carried out in response in interval II and IV, according to the symbol decision d axle positive direction of this integrated value, the method judges d axle positive direction without the extra positive negative pulse stuffing signal that injects, overall process only need be injected signal one time, shorten estimated time, initial position testing process is obviously simplified.

The present invention adopts above technical scheme compared with prior art, has following technique effect:

(1) the present invention, judging that in d axle positive direction process, the electric current of injection is always sinusoidal high-frequency signal, without injecting positive negative pulse stuffing, has simplified estimation procedure;

(2) an Injection Signal cycle is evenly divided into four intervals, in interval I and III, to d axle high frequency voltage, integration is carried out in response, or to d axle high frequency voltage, integration is carried out in response in interval II and IV, according to the symbol decision d axle positive direction of this integrated value, this process can complete within the cycle of an Injection Current signal, has shortened estimated time;

(3) avoid the small inertia machinery jitter problem that may cause in positive negative pulse stuffing injection process, can be used on the occasion that electric machine rotation inertia is little, initial position estimation process rotor positional jitter is had to strict demand.

Brief description of the drawings

Fig. 1 is the theory diagram of surface-mount type permanent-magnetic synchronous motor rotor initial position estimation process;

Fig. 2 is two-phase rest frame, actual two-phase synchronous rotating frame and the relativeness schematic diagram of estimating two-phase synchronous rotating frame;

Fig. 3 is the signal extraction of first initial position estimation and the theory diagram of modulated process;

Fig. 4 is the signal extraction of d axle positive direction judgement and the theory diagram of modulated process;

When the corresponding actual rotor of Fig. 5 (a) position is 1rad, the simulation waveform of initial position of rotor estimation procedure;

When the corresponding actual rotor of Fig. 5 (b) position is 1rad, d axle positive direction judges information k _{i, III}waveform;

When the corresponding actual rotor of Fig. 5 (c) position is 1rad, d axle positive direction judges information k _{iI, IV}waveform;

When the corresponding actual rotor of Fig. 5 (d) position is 4rad, the simulation waveform of initial position of rotor estimation procedure;

When the corresponding actual rotor of Fig. 5 (e) position is 4rad, d axle positive direction judges information k _{i, III}waveform;

When the corresponding actual rotor of Fig. 5 (f) position is 4rad, d axle positive direction judges information k _{iI, IV}waveform.

Embodiment

Below in conjunction with accompanying drawing, technical scheme of the present invention is described in further detail:

As shown in Figure 1, the invention provides a kind of surface-mount type permagnetic synchronous motor initial position detection method, specifically comprise the following steps:

Step 1), set up coordinate system graph of a relation, as shown in Figure 2, d-q is actual synchronization rotating coordinate system, for estimated rotor synchronous rotating frame, alpha-beta is actual two-phase rest frame, and definition Estimated Position Error wherein, θ is actual rotor initial position, for final initial position estimation value, initial value be 0;

Step 2), as shown in Figure 3, the q shaft current of estimated rotor synchronous rotating frame is given as to 0, d shaft current and is given as a pulsating high frequency sinusoidal signal I _mhsin (ω _ht), wherein, I _mhfor inject the amplitude of high-frequency current, ω at d axle _hfor inject the angular frequency of high-frequency current at d axle, t represents current time;

Step 3), adoption rate resonant controller (PR) is controlled d shaft current and the q shaft current estimated, makes it with given consistent;

Step 4), to the voltage of PR adjuster output with carry out Park inverse transformation, obtain the voltage u under the static alpha-beta coordinate system of two-phase _αand u _β, then adopt space vector pulse width modulation strategy to obtain six path switching signals of three-phase inverter, the mounted permagnetic synchronous motor SPMSM of table-drive;

Step 5), detect any biphase current in motor three phase winding A/B/C, first carry out Clarke conversion and obtain the current i under the static alpha-beta coordinate system of two-phase _αand i _β, then conversion obtains the d shaft current under estimated rotor synchronous rotating frame through Park with q shaft current fed back to PR adjuster;

Step 6), by the q shaft voltage response of estimated rotor synchronous rotating frame selecting frequency through band pass filter is ω _halternating current component be the first harmonic component of q shaft voltage response again with cosine signal cos (ω _ht) multiply each other and modulate, obtaining DC component and frequency is 2 ω _halternating current component, finally by crossing low pass filter filtering alternating current component, extract DC component, obtain estimated position deviation signal f _c(Δ θ);

Step 7), build position deviation closed loop, by estimated position deviation signal f _c(Δ θ) is as the input of pi regulator, estimated rotor angular speed for the output of pi regulator, to estimated rotor angular speed integration obtains the rotor-position of estimating, repeating step 2-7, until the rotor-position of estimating converges to a steady state value, is the first estimated value of initial position of rotor

Step 8), an Injection Signal cycle (0,2 π) is evenly divided into four intervals, be respectively: I:(0, pi/2), II:(pi/2, π), III:(π, 3 pi/2s) and IV:(3 pi/2,2 π).As shown in Fig. 4 (a), in interval I and III, d axle high frequency voltage is responded carry out integration, be designated as according to k _{i, III}symbol decision d axle positive direction, if k _{i, III}be less than 0, in the same way, the offset after d axle positive direction judges is 0 to the N utmost point of d axle positive direction and magnetic pole, if k _{i, III}be greater than 0, the N of d axle positive direction and magnetic pole is extremely reverse, and the offset after d axle positive direction judges is π, or as shown in Fig. 4 (b), in interval II and IV, to d axle high frequency voltage, integration is carried out in response, is designated as according to k _{iI, IV}symbol decision d axle positive direction, if k _{iI, IV}be greater than 0, in the same way, the offset after d axle positive direction judges is 0 to the N utmost point of d axle positive direction and magnetic pole, if k _{iI, IV}be less than 0, the N of d axle positive direction and magnetic pole is extremely reverse, and the offset after d axle positive direction judges is π,

As follows to judging the theory analysis of d axle positive direction:

Motor is when static, and back-emf and cross-couplings item are 0, and its d shaft voltage equation can be expressed as in formula, R _sfor stator resistance, L _d(i _d) represent d axle inductance and actual d shaft current i _drelevant, L _d(i _d> 0) expression i _dcorresponding d axle inductance when > 0, L _d(i _d< 0) expression i _dcorresponding d axle inductance when < 0.In fact work as i _dwhen > 0, because the generation of d axle magnetic field is saturated, d axle inductance reduces; Work as i _dwhen < 0 due to d axle magnetic field move back saturated, d axle inductance increase, establish i _dwithin=0 o'clock, d axle inductance is L _d0thereby, can obtain L _d(i _d> 0) < L _d0< L _d(i _d< 0).

After first initial position estimation finishes, rotor-position evaluated error Δ θ is 0 or π, estimate d shaft current under the effect of PR adjuster with given consistent, the voltage equation of estimating d axle can be expressed as further calculate ${\hat{u}}_d=R_s{I}_{\mathrm{mh}}\sin \left({\mathrm{\&omega;}}_{h}t\right)+{\mathrm{\&omega;}}_h{L}_d\left(i_d\right)I_{\mathrm{mh}}\cos \left({\mathrm{\&omega;}}_{h}t\right).$

In the time that rotor-position evaluated error Δ θ is 0, the d direction of principal axis of estimation is consistent with actual d direction of principal axis, estimates that d shaft current is also consistent with actual d shaft current.At interval I: ω _hin t ∈ (0, pi/2), meet cos (ω _ht) > 0.Therefore, ω _hl _d(i _d> 0) I _mhcos (ω _ht) < ω _hl _d0i _mhcos (ω _ht).At interval III: ω _hin t ∈ (π, 3 pi/2s), meet l _d(i _d< 0) > L _d0, cos (ω _ht) < 0.Therefore, ω _hl _d(i _d< 0) I _mhcos (ω _ht) < ω _hl _d0i _mhcos (ω _ht).Thereby obtain:

${\&Integral;}_0^{\mathrm{\&pi;}/2}{\hat{u}}_{d}d\left({\mathrm{\&omega;}}_{h}t\right)<{\&Integral;}_0^{\mathrm{\&pi;}/2}[R_s{I}_{\mathrm{mh}}\sin \left({\mathrm{\&omega;}}_{h}t\right)+{\mathrm{\&omega;}}_h{L}_{d0}{I}_{\mathrm{mh}}\cos \left({\mathrm{\&omega;}}_{h}t\right)]d\left({\mathrm{\&omega;}}_{h}t\right)=R_s{I}_{\mathrm{mh}}+{\mathrm{\&omega;}}_h{L}_{d0}{I}_{\mathrm{mh}}$ ${\&Integral;}_{\mathrm{\&pi;}}^{3\mathrm{\&pi;}/2}{\hat{u}}_{d}d\left({\mathrm{\&omega;}}_{h}t\right)<{\&Integral;}_{\mathrm{\&pi;}}^{3\mathrm{\&pi;}/2}[R_s{I}_{\mathrm{mh}}\sin \left({\mathrm{\&omega;}}_{h}t\right)+{\mathrm{\&omega;}}_h{L}_{d0}{I}_{\mathrm{mh}}\cos \left({\mathrm{\&omega;}}_{h}t\right)]d\left({\mathrm{\&omega;}}_{h}t\right)={-R}_s{I}_{\mathrm{mh}}+{\mathrm{\&omega;}}_h{L}_{d0}{I}_{\mathrm{mh}}$

Further calculate $k_{I.\mathrm{III}={\&Integral;}_0^{\mathrm{\&pi;}/2}{\hat{u}}_{d}d\left({\mathrm{\&omega;}}_{h}t\right)+{\&Integral;}_{\mathrm{\&pi;}}^{3\mathrm{\&pi;}/2}{\hat{u}}_{d}d\left({\mathrm{\&omega;}}_{h}t\right)<0.}$

Contrary, in the time that rotor-position evaluated error Δ θ is π, the d direction of principal axis of estimation is contrary with actual d direction of principal axis, estimates that d shaft current is also contrary with actual d shaft current symbol.At interval I: ω _hin t ∈ (0, pi/2), meet l _d(i _d< 0) > L _d0, cos (ω _ht) > 0.Therefore, ω _hl _d(i _d< 0) I _mhcos (ω _ht) > ω _hl _d0i _mhcos (ω _ht).At interval III: ω _hin t ∈ (π, 3 pi/2s), meet l _d(i _d> 0) < L _d0, cos (ω _ht) < 0.Therefore, ω _hl _d(i _d> 0) I _mhcos (ω _ht) > ω _hl _d0i _mhcos (ω _ht).Thereby obtain:

${\&Integral;}_0^{\mathrm{\&pi;}/2}{\hat{u}}_{d}d\left({\mathrm{\&omega;}}_{h}t\right)>{\&Integral;}_0^{\mathrm{\&pi;}/2}[R_s{I}_{\mathrm{mh}}\sin \left({\mathrm{\&omega;}}_{h}t\right)+{\mathrm{\&omega;}}_h{L}_{d0}{I}_{\mathrm{mh}}\cos \left({\mathrm{\&omega;}}_{h}t\right)]d\left({\mathrm{\&omega;}}_{h}t\right)=R_s{I}_{\mathrm{mh}}+{\mathrm{\&omega;}}_h{L}_{d0}{I}_{\mathrm{mh}}$

${\&Integral;}_{\mathrm{\&pi;}}^{3\mathrm{\&pi;}/2}{\hat{u}}_{d}d\left({\mathrm{\&omega;}}_{h}t\right)>{\&Integral;}_{\mathrm{\&pi;}}^{3\mathrm{\&pi;}/2}[R_s{I}_{\mathrm{mh}}\sin \left({\mathrm{\&omega;}}_{h}t\right)+{\mathrm{\&omega;}}_h{L}_{d0}{I}_{\mathrm{mh}}\cos \left({\mathrm{\&omega;}}_{h}t\right)]d\left({\mathrm{\&omega;}}_{h}t\right)={-R}_s{I}_{\mathrm{mh}}+{\mathrm{\&omega;}}_h{L}_{d0}{I}_{\mathrm{mh}}$

Further calculate $k_{I.\mathrm{III}={\&Integral;}_0^{\mathrm{\&pi;}/2}{\hat{u}}_{d}d\left({\mathrm{\&omega;}}_{h}t\right)+{\&Integral;}_{\mathrm{\&pi;}}^{3\mathrm{\&pi;}/2}{\hat{u}}_{d}d\left({\mathrm{\&omega;}}_{h}t\right)>0.}$

Estimate as can be seen here the voltage response of d axle at interval I: ω _ht ∈ (0, pi/2) and III: ω _hintegrated value k on t ∈ (π, 3 pi/2s) _i.IIIsymbol can be used to judge d axle positive direction, if k _i.IIIbe less than 0, the N utmost point of d axle positive direction and magnetic pole in the same way; If k _i.IIIbe greater than 0, the N of d axle positive direction and magnetic pole is extremely reverse.

In like manner known, estimate the voltage response of d axle at interval II: ω _ht ∈ (pi/2, π) and IV: ω _hintegrated value on t ∈ (3 pi/2s, 2 π) symbol also can be used to judge d axle positive direction, if k _iI.IVbe greater than 0, the N utmost point of d axle positive direction and magnetic pole in the same way; If k _iI.IVbe less than 0, the N of d axle positive direction and magnetic pole is extremely reverse.

As shown in Fig. 5 (a), Fig. 5 (b) and Fig. 5 (c), corresponding actual rotor initial position is 1rad, and d axle positive direction judges information k _{i, III}be less than 0, k _{iI, IV}be greater than 0, all represent d axle positive direction and the magnetic pole N utmost point in the same way, without to first estimated position carry out angle compensation, θ _c=0; As shown in Fig. 5 (d), Fig. 5 (e) and Fig. 5 (f), corresponding actual rotor initial position is 4rad, and d axle positive direction judges information k _{i, III}be greater than 0, k _{iI, IV}be less than 0, all represent that d axle positive direction and magnetic pole N are extremely reverse, need be to first estimated position compensation π radian, θ _c=π, final initial position estimation value is

Claims (4)

1. a surface-mount type permagnetic synchronous motor initial position detection method, is characterized in that, comprises following steps:

Steps A), obtain the first estimated value of rotor-position;

Step B), judge d axle positive direction, obtain the offset after the judgement of d axle positive direction;

Step C), first rotor-position estimated value is added to the offset after the judgement of d axle positive direction, obtain final initial position estimation value.

2. surface-mount type permagnetic synchronous motor initial position detection method according to claim 1, is characterized in that, the step of obtaining the first estimated value of rotor-position is as follows:

Steps A .1), the q shaft current of estimated rotor synchronous rotating frame is given as to 0, d shaft current and is given as a pulsating high frequency sinusoidal signal I _mhsin (ω _ht), wherein, I _mhfor inject the amplitude of high-frequency current, ω at d axle _hfor inject the angular frequency of high-frequency current at d axle, t represents current time;

Steps A .2), adoption rate resonant controller PR controls d shaft current and the q shaft current estimated, makes it with given consistent;

Steps A .3), the voltage of comparative example resonant controller output with carry out Park inverse transformation, obtain the voltage u under the static alpha-beta coordinate system of two-phase _αand u _β, then adopt space vector pulse width modulation strategy to obtain six path switching signals of three-phase inverter, the mounted permagnetic synchronous motor of table-drive;

Steps A .4), detect any biphase current in motor three phase winding A/B/C, first carry out Clarke conversion and obtain the current i under the static alpha-beta coordinate system of two-phase _αand i _β, then conversion obtains the d shaft current under estimated rotor synchronous rotating frame through Park with q shaft current fed back to ratio resonant controller;

Steps A .5), by the q shaft voltage response of estimated rotor synchronous rotating frame selecting frequency through band pass filter is ω _halternating current component, be the first harmonic component of q shaft voltage response again with cosine signal cos (ω _ht) multiply each other and modulate, obtaining DC component and frequency is 2 ω _halternating current component, finally by crossing low pass filter filtering alternating current component, extract DC component, obtain estimated position deviation signal f _c(Δ θ);

Steps A .6), build position deviation closed loop, by estimated position deviation signal f _c(Δ θ) is as the input of ratio resonant controller, estimated rotor angular speed for the output of ratio resonant controller, to estimated rotor angular speed integration obtains the rotor-position of estimating;

Steps A .7), repeating step 1.1) to step 1.6), until the rotor-position of estimating converges to a steady state value, be the first estimated value of initial position of rotor.

3. surface-mount type permagnetic synchronous motor initial position detection method according to claim 1, is characterized in that, described judgement d axle positive direction to obtain the detailed step of the offset after the judgement of d axle positive direction as follows:

Step is B.1), an Injection Signal cycle (0,2 π) is evenly divided into four interval: I:(0, pi/2), II:(pi/2, π), III:(π, 3 pi/2s) and IV:(3 pi/2,2 π);

Step is B.2), in interval I and III, d axle high frequency voltage is responded carry out integration, be designated as wherein, ω _hfor inject the angular frequency of high-frequency current at d axle, t represents current time;

Step is B.3), according to k _{i, III}symbol decision d axle positive direction, if k _{i, III}be less than 0, in the same way, the offset after d axle positive direction judges is 0 to the N utmost point of d axle positive direction and magnetic pole; If k _{i, III}be greater than 0, the N of d axle positive direction and magnetic pole is extremely reverse, and the offset after d axle positive direction judges is π.

4. surface-mount type permagnetic synchronous motor initial position detection method according to claim 1, is characterized in that, described judgement d axle positive direction the step that obtains the offset after the judgement of d axle positive direction can also be:

Step B.a), an Injection Signal cycle (0,2 π) is evenly divided into four interval: I:(0, pi/2), II:(pi/2, π), III:(π, 3 pi/2s) and IV:(3 pi/2,2 π);

Step B.b), in interval II and IV, to d axle high frequency voltage, integration is carried out in response, is designated as wherein, ω _hfor inject the angular frequency of high-frequency current at d axle, t represents current time;

Step B.c), according to k _{iI, IV}symbol decision d axle positive direction, if k _{iI, IV}be greater than 0, in the same way, the offset after d axle positive direction judges is 0 to the N utmost point of d axle positive direction and magnetic pole; If k _{iI, IV}be less than 0, the N of d axle positive direction and magnetic pole is extremely reverse, and the offset after d axle positive direction judges is π.