CN103048486B - Device and method for measuring rotation speeds and positions of rotors of birotor permanent magnet wind-driven generator - Google Patents

Device and method for measuring rotation speeds and positions of rotors of birotor permanent magnet wind-driven generator Download PDF

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CN103048486B
CN103048486B CN201210584002.0A CN201210584002A CN103048486B CN 103048486 B CN103048486 B CN 103048486B CN 201210584002 A CN201210584002 A CN 201210584002A CN 103048486 B CN103048486 B CN 103048486B
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interrupt
capture
rotor
rotating speed
outer rotor
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CN103048486A (en
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张建忠
王元元
程明
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Southeast University
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Abstract

The invention discloses a device and a method for measuring the rotation speeds and positions of rotors of a birotor permanent magnet wind-driven generator. According to the device and the method, a digital signal processor is used for detecting signals generated by optical electricity encoders on the rotors of the birotor permanent magnet wind-driven generator and hall elements arranged in grooves in the surfaces of the rotors and respectively obtaining the rotation speeds and positions of the internal and external rotors. According to the device and the method, aiming at the external rotor on which a speed detector cannot be arranged, the cheap hall elements are utilized to measure rotation speed and position signals of the rotor by virtue of detecting the internal magnetic field intensity of a motor, and accurate measurement on the rotation speed of the external rotor can be ensured when in a fault state; and by virtue of hardware frequency multiplication or software frequency multiplication and the different quantities, sizes and placement positions of the hall elements, different measurement accuracy can be obtained, the combination is flexible, the measuring method is simple, the measuring device is low in cost, and the corresponding accuracy can be completely satisfied.

Description

Birotor permanent magnetic wind power generator rotor rotating speed and position-measurement device and method
Technical field
The invention belongs to generation of electricity by new energy field, particularly birotor permanent magnetic wind power generator rotor rotating speed and position-measurement device and the method measured.
Background technology
For comparatively popular in recent years double mechanical port double-rotor machine such as four-quadrant energy converter 4QT (being double-deck permanent-magnetic outer rotor formula EVT) and double mechanical port DMP (being individual layer permanent-magnetic outer rotor formula EVT) individual layer permanent-magnetic outer rotor formula, because motor itself has two mechanical output revolving shafts, it tests the speed is also eaily, can obtain by loading onto two speed measuring devices the rotating speed of two rotors, and for this list output shaft birotor permanent magnetic aerogenerator, owing to only having an output shaft to be connected with extraneous wind energy conversion system, so will obtain two rotor speeds and location comparison difficulty simultaneously, also there is no at present the apparatus and method that can measure.
Summary of the invention
Goal of the invention: exist for the rotating speed of two rotors in the birotor permanent magnetic aerogenerator of single output shaft and the problem of position measurement difficulty for prior art, the invention provides the rotating speed of two rotors of a kind of measurement and location method is simple, result apparatus and method accurately.
Technical scheme: a kind of birotor permanent magnetic wind power generator rotor rotating speed and position-measurement device, comprise stator, internal rotor and outer rotor, Hall element, wherein, photoelectric encoder is arranged in the internal rotor rotating shaft of birotor permanent magnetic aerogenerator, one group of CAP capture-port of described photoelectric encoder output signal incoming digital signal processor DSP, on stator tooth surface, be provided with groove, in described groove, be provided with Hall element, described Hall element is drawn signal and is sent into hall signal treatment circuit, another group CAP capture-port of described hall signal treatment circuit output signal access DSP, outer rotor surfaces externally and internally mounts arc-shaped permanent magnet.
Wherein, the signal that Hall element produces, through the CAP capture-port of plastic filter circuit supplied with digital signal processor DSP, can make to be input to the more convenient processing of signal waveform in digital signal processor DSP like this.
Because Hall element holds flimsy feature, so select 3 stator tooths, on its surface, groove is set respectively, Hall element is installed respectively in groove, in use can backup each other, guarantee all can accurately measure outer rotor rotating speed under the normal job failure state of Hall element.
In order to measure accurate needs, the space angle that 3 surfaces arrange between reeded stator tooth is respectively 120 °.
Wherein, internal rotor is the Wound-rotor type internal rotor that is built-in with three-phase symmetric winding.
The present invention also provides a kind of birotor permanent magnetic wind power generator rotor rotating speed and location measurement method, comprise the measurement to the rotating speed of the internal rotor of birotor permanent magnetic aerogenerator and outer rotor and position, wherein, the rotating speed of the internal rotor of described birotor permanent magnetic aerogenerator and the concrete steps of position measurement are as follows:
Step 101: in the internal rotor rotating shaft of birotor permanent magnetic aerogenerator, the output terminal of photoelectric encoder is connected with one group of CAP capture-port of digital signal processor by photoelectric coding apparatus;
Step 102: photoelectric encoder output for judging the sense of rotation of internal rotor, the A of speed of rotation, B signal and input to digital signal processor for Z signal synchronous or zeroing, wherein, digital signal processor collects A, B signal in orthogonal, the internal rotor Z signal of photoelectric encoder output that often turns around;
Step 103: when one group of CAP capture-port of signal processor captures pulse signal, enter timer and interrupt, read this moment as the count value of the timer Counter of clock reference, timer Counter is for counting for time pulse;
Step 104: the data of above-mentioned acquisition are brought into formula with in, just can obtain rotating speed and the position of the internal rotor of birotor permanent magnetic aerogenerator, in formula, ω represents internal rotor rotating speed, t represents that one group of Interruption in CAP capture-port is from once interrupt entering the time interval of interrupting next time, T (0), T (1) represent respectively the numerical value that counter records before and after the t time interval of being separated by, Δ θ represents the alternate position spike that t time interval internal rotor turns over, θ (0), θ (1) represent respectively the position angle size of t time interval front and back internal rotor, m is the raster count of photoelectric encoder, relevant with photoelectric encoder model;
Wherein, the rotating speed of the outer rotor of described birotor permanent magnetic aerogenerator and the concrete steps of position measurement are as follows:
Step 201: the surface working groove at the stator tooth of stator punching, is arranged on Hall element in groove;
Step 202: along with motor outer rotor rotates, Hall element changes and reacts generation pulse signal the power in magnetic field, the pulse signal that Hall element is produced is sent into another group CAP capture-port of digital signal processor;
Step 203: digital signal processor is caught the rising edge that carries out of the rectangular pulse signal of Hall element output, two capture interrupt are set, when rising edge arrives, read respectively the count value as the timer Counter of clock reference, acquisition enters the time pulse number of capture interrupt next time from a capture interrupt, and then obtains entering the time interval of twice capture interrupt;
Step 204: the angle turning over according to twice capture interrupt time interval inner and outer rotors, and the time interval of twice interruption obtain the rotating speed of outer rotor;
Step 205: the pulse signal that Hall element is produced carries out N frequency multiplication, and signal after frequency multiplication is sent into another CAP capture-port, when rising edge arrives each time, enters capture interrupt one time, and records the number of times of capture interrupt, obtains the position of outer rotor.
Because Hall element easily damages, preferably adopt three Hall elements to measure together, concrete grammar is as follows:
An interrupt function is first set in above-mentioned steps 203, three interrupt vectors that the hall signal of supplied with digital signal processor is differentiated are set in interrupt function, when three Hall elements normally send pulse signal, three interrupt vectors are carried out respectively 0,1 conversion, if one of them interrupt vector is not upgraded, belong to failure operation state, carry out a road hall signal and measure, if three interrupt vectors are all normally upgraded, obtain the rotating speed of outer rotor and the method for position as follows:
Step 301: three capture-ports by the digital signal processor respectively rising edge of Dui San road pulse hall signal are caught;
Step 302: capture interrupt is set, when arbitrary CAP port is caught rising edge, enters capture interrupt;
Step 303: count for the time clock in the time interval of twice adjacent capture interrupt by the timer Counter as clock reference, obtain the mistiming of adjacent twice capture interrupt;
Step 304: based on Hall element principle of work, obtain according to the locus of motor number of pole-pairs and Hall element placement the angle that outer rotor corresponding to adjacent twice capture interrupt turns over;
Step 305: the radian that the mistiming of adjacent twice capture interrupt obtaining according to above-mentioned steps and the time inner and outer rotors of adjacent twice capture interrupt turn over obtains the rotating speed of outer rotor;
Step 306: another timer is set and interrupts, enter interruption when the count value of counter of timer and the timer cycle of setting equate.Enter timer and interrupt, elapsed time between twice interruption before and after obtaining;
Step 307: obtain the elapsed time acquisition differential seat angle that outer rotor turns between twice interruption between twice interruption in the rotating speed of transferring in step 305 outer rotor obtaining and step 6.
Step 308: the position of the cumulative acquisition outer rotor by angle that the outer rotor obtaining in step 307 is turned over, and when each capture interrupt, upgrade one time rotor-position signal, obtain accurate rotor-position signal.
Beneficial effect: the present invention compared with prior art, the present invention has realized for the measurement of two rotor speeds of single output revolving shaft birotor permanent magnetic aerogenerator and position existing by software, for the outer rotor that speed measuring device cannot be installed, utilize more cheap Hall element by measuring rotor speed and position signalling for the detection of magneto internal magnetic field intensity, during malfunction, also guarantee to measure comparatively accurately outer rotor rotating speed, by hardware frequency multiplication or Double Frequency by Software, the population size of Hall element and the difference of placement location can obtain different measuring accuracy, combination flexibly, measuring method is simple, measurement mechanism is with low cost, and can meet corresponding precision completely.
Accompanying drawing explanation
Fig. 1 is the structural drawing of birotor permanent magnetic aerogenerator;
Fig. 2 is the sectional view of birotor permanent magnetic aerogenerator;
Fig. 3 is Hall element fundamental diagram in birotor permanent magnetic aerogenerator stator groove;
Fig. 4 is the actual waveform that birotor permanent magnetic aerogenerator Hall element produces that records;
Fig. 5 is birotor permanent magnetic wind-power electricity generation inboard rotor rotating speed and location measurement method FB(flow block);
Fig. 6 is for being used a road hall signal to measure the method flow block diagram of birotor permanent magnetic aerogenerator outer rotor rotating speed and position;
Fig. 7 is for being used three road hall signals to measure the method flow block diagram of birotor permanent magnetic aerogenerator outer rotor rotating speed and position.
Embodiment
Below in conjunction with the drawings and specific embodiments, further illustrate the present invention, should understand these embodiment is only not used in and limits the scope of the invention for the present invention is described, after having read the present invention, those skilled in the art all fall within the application's claims limited range to the modification of the various equivalent form of values of the present invention.
Shown in Fig. 1 and 2, birotor permanent magnetic aerogenerator comprises stator 1, internal rotor 2 and outer rotor 3, wherein, photoelectric encoder 4 is arranged in the internal rotor rotating shaft 5 of birotor permanent magnetic aerogenerator, on stator tooth surface, be provided with groove, in described groove, be provided with Hall element 6, outer rotor 3 surfaces externally and internallies mount arc-shaped permanent magnet 7, the phase-wound rotor that wherein internal rotor 2 is three-phase symmetric winding.
Shown in Fig. 3, the Hall element in device is mainly to produce pulse signal by the measurement for magnetic field power, produces principle based on switching Hall components signal simultaneously, and the pole embrace of permanent magnetism magnetic pole also has impact for the signal waveform producing; When the S utmost point or the N utmost point are when sheltering from Hall element, produce low level, all the other situations produce high level, and the hall signal of generation is positive and negative interval asymmetric.
As shown in Figure 4, what show is the actual waveform that records Hall element 5 generations that arrange respectively in the groove on three stator tooth surfaces in single output shaft birotor permanent magnetic aerogenerator, corresponding output low level when the S utmost point blocks Hall element 5, rest interval is corresponding to high level, can find out that it is interval than being approximately 2:1, now three Hall elements, the 120 ° of placements of being separated by, the electrical angle of 3 signals that as can be seen from the figure produce is separated by 120 °, and the result that the method that hence one can see that is measured is very accurate.
As shown in Figures 5 to 7, for realizing the process flow diagram of birotor permanent magnetic wind-power electricity generation inboard rotor and outer rotor rotating speed and location measurement method.There are two rotors in double-rotor machine, need to use two groups of CAP to catch mouth and catch, and internal rotor is used one group of CAP capture-port, and outer rotor is used another group capture-port; By software programming, realize the measurement of rotor speed and position, the function of the timer in measurement and the tally function of timer realize by software.
Fig. 5 is the FB(flow block) of birotor permanent magnetic wind-power electricity generation inboard rotor rotating speed and position measurement.Measurement for internal rotor rotating speed and position, on the internal rotor output revolving shaft of single output shaft birotor permanent magnetic aerogenerator, speed measuring device is housed as photoelectric encoder or rotary transformer, following embodiment be take photoelectric encoder as example, when wind energy conversion system drives birotor permanent magnetic wind driven generator rotation by rotating shaft, be installed on the exportable A of photoelectric encoder of rotating shaft, B, Z tri-road signals, carry out sending into after shaping filter one group of CAP capture-port of digital signal processor DSP, digital signal processor DSP can collect the A of quadrature, B signal and Z signal, , by timer, interrupt processing rotating speed and position signalling.
Digital signal processor DSP gathers Z signal by the CAP3 capture-port of first group, the CAP1 of first group, CAP2 capture-port gathers A, B signal, definition timer T4 interrupts processing the calculating of birotor permanent magnetic wind-power electricity generation inboard rotor rotating speed and position, in interrupting, processes T4, selecting timer T2 is clock reference, CAP1 for digital signal processor, CAP2 catches and mouthful captures pulse signal and count, while meeting the condition that enters timer interruption, enter interruption, read the now numerical value of T2 Counter, read the adjacent T2 Counter numerical value reading when T4 interrupts that enters for twice and be respectively T (0), T (1), the time pulse number that obtains twice interrupt interval is T (1)-T (0), if the grating of photoelectric encoder has 1024 lattice, motor rotates a circle, signal A and signal B are by 1024 orthogonal pulses of 90 ° of output 2 tunnel phase phasic differences, enable quadrate encode module and detect rising edge and the negative edge of each road signal, therefore motor rotates a circle, quadrate encode module will capture 4096 pulse signals, there is an impulse meter T2CNT just to count once, by timer T4, interrupt reading again the value of T2CNT, every t at regular intervals reads the count value of a T2CNT counter, can calculate angle and the current location that single output shaft birotor permanent magnetic wind-power electricity generation inboard rotor turns over is:
θ(1)=θ(0)+Δθ
The rotating speed of single output shaft birotor permanent magnetic aerogenerator is:
ω = T ( 1 ) - T ( 0 ) 4096 × t × 60
In formula, ω represents internal rotor rotating speed, t represents the time interval that adjacent twice timer interrupts, T (0), T (1) represent the counter values that counter records before and after the t time interval of being separated by, Δ θ represents the alternate position spike that t time interval internal rotor turns over, and θ (0), θ (1) represent the position angle size of t time interval front and back internal rotor.
For eliminating cumulative errors, the Z signal that can catch by CAP3 capturing unit is reorientated rotor angle simultaneously.
As shown in Figure 6, the hall signal that Hall element produces has entered digital signal processor; CAP4 capture-port in another group, hall signal is input to the CAP5 capture-port of this group of digital signal processor through the phase-locked loop circuit of N frequency multiplication simultaneously.Hall signal enters CAP4 capture interrupt, select a timer counter as clock reference, Hall element sends the radian θ that the corresponding motor of adjacent two pulses turns over, and writes down CAP4 capture interrupt from once interrupt entering to interrupt the pulse number n that hour counter is counted next time 1, according to formula
ω = θ T _ Timer × n 1
Can obtain the rotating speed of outer rotor, in formula, ω represents outer rotor rotating speed, T _ Timerthe clock reference that represents counter, i.e. time that time pulse is corresponding, n 1expression is from once interrupt entering to interrupt the pulse number that hour counter is counted next time, and θ represents that Hall element sends the radian that two pulse signals turn over corresponding to motor.
Wherein, hall signal, through the phase-locked loop circuit input CAP5 capture-port of N frequency multiplication, is often caught pulsatile once signal and is entered CAP5 capture interrupt one time, in interrupt function, variable pllnumber record is set and enters the frequency n that CAP5 interrupts 2, the pulse of catching is counted, according to formula:
θ 1 = 360 N × n 2
Can obtain the position, angle of outer rotor, θ in formula 1represent outer rotor position angle, N represents frequency multiplication numerical value, n 2represent the umber of pulse that CAP5 capture-port is caught.Wherein the phase-locked loop circuit of N frequency multiplication is that binary counting chip CD4040 by phaselocked loop integrated chip CD4060 and 12 forms.
Complete reading at every turn and calculate after in CAP4 interrupts by counter and variable pllnumber zero clearing.
As shown in Figure 7, in stator slot due to single output shaft birotor permanent magnetic aerogenerator, post 3 switching Hall components, when outer rotor rotates, can export 3 road hall signals, so can be by calculate rotating speed and the position of outer rotor for the collection of 3 road hall signals.
First three interrupt vectors that the hall signal of supplied with digital signal processor is differentiated are set in interrupt function, when three Hall elements normally send pulse signal, three interrupt vectors are carried out respectively one time 0, 1 conversion, if one of them interrupt vector is not upgraded, it is failure operation state, rotating speed and the position of according to the method for only having a road hall signal, calculating outer rotor, if three interrupt vectors are all normally upgraded by the CAP4 of digital signal processor, CAP5, CAP6 capture-port is caught for three tunnel pulse hall signal rising edges, arbitrary rising edge all can produce capture interrupt while arriving, entering interrupt function participates in calculating, obtain the radian θ that between two rising edge pulses, corresponding motor turns over outer, enter the data T3CNT[k (t-1) interrupting in hour counter T3CNT before and after reading for twice] and T3CNT[kt], the time pulse number that can calculate in time interval of adjacent two subpulses is T3CNT[kt]-T3CNT[k (t-1)], be designated as n 3, according to formula:
ω = θ outer T _ Timer 3 × n 3
Can obtain the rotating speed of outer rotor, in formula, ω represents outer rotor rotating speed, T _ Timer3represent timer clock benchmark, i.e. time that time pulse is corresponding, n 3expression is from once interrupt entering to interrupt the time pulse number that hour counter T3CNT counts, θ next time outeradjacent two radians that pulse signal turns over corresponding to motor that represent capture-port.
At T2 timer, interrupt calculating rotor-position, while entering timer interruption, process one time rotor-position at every turn, choose counter T4CNT as clock reference, enter T2 at every turn and interrupt recording the numerical value in corresponding T4CNT, the value of getting adjacent twice counter is T4CNT (0) and T4CNT (1), obtain it and interrupt interlude umber of pulse T4CNT (1)-T4CNT (0), and then must make a call to elapsed time Δ t between twice interruption, read the speed revolution value calculating in capture interrupt function, according to the speed revolution value ω in the capture interrupt reading, calculating the slip angle that motor turns over is Δ θ=ω * Δ t, because the position at edging trigger signal place is accurately, the rotor-position signal so upgrade in time when edging trigger signal arrives, while there is no edging trigger signal, by accumulate mode, obtaining rotor current location is θ=θ+Δ θ, finally calculate outer rotor position, can calculate like this rotating speed and the position signalling of outer rotor.

Claims (5)

1. a birotor permanent magnetic wind power generator rotor rotating speed and location measurement method, comprise the measurement to the rotating speed of the internal rotor of birotor permanent magnetic aerogenerator and outer rotor and position, it is characterized in that: the rotating speed of the internal rotor of described birotor permanent magnetic aerogenerator and the concrete steps of position measurement are as follows:
Step 101: in the internal rotor rotating shaft of birotor permanent magnetic aerogenerator, the output terminal of photoelectric encoder is connected with one group of CAP capture-port of digital signal processor by photoelectric coding apparatus;
Step 102: photoelectric encoder output for judging the sense of rotation of internal rotor, the A of speed of rotation, B signal and input to digital signal processor for Z signal synchronous or zeroing, wherein, digital signal processor collects A, B signal in orthogonal, the internal rotor Z signal of photoelectric encoder output that often turns around;
Step 103: when one group of CAP capture-port of digital signal processor captures pulse signal, enter timer and interrupt, read this moment as the count value of the timer Counter of clock reference, timer counter is for counting for time pulse;
Step 104: the data of above-mentioned acquisition are brought into formula with in, just can obtain rotating speed and the position of the internal rotor of birotor permanent magnetic aerogenerator, in formula, ω represents internal rotor rotating speed, t represents that one group of Interruption in CAP capture-port is from once interrupt entering the time interval of interrupting next time, T (0), T (1) represent respectively the numerical value that counter records before and after the t time interval of being separated by, Δ θ represents the alternate position spike that t time interval internal rotor turns over, θ (0), θ (1) represent respectively the position angle size of t time interval front and back internal rotor, the raster count that m is photoelectric encoder;
The rotating speed of the outer rotor of described birotor permanent magnetic aerogenerator and the concrete steps of position measurement are as follows:
Step 201: the surface working groove at the stator tooth of stator punching, is arranged on Hall element in groove;
Step 202: along with outer rotor rotates, Hall element changes and reacts generation pulse signal the power in magnetic field, the pulse signal that Hall element is produced is sent into another group CAP capture-port of digital signal processor;
Step 203: digital signal processor is caught the rising edge that carries out of the rectangular pulse signal of Hall element output, two capture interrupt are set, when rising edge arrives, read respectively the count value as the timer Counter of clock reference, acquisition enters the time pulse number of capture interrupt next time from a capture interrupt, and then obtains entering the time interval of twice capture interrupt;
Step 204: the angle turning over according to twice capture interrupt time interval inner and outer rotors, and the time interval of twice capture interrupt obtain the rotating speed of outer rotor;
Step 205: the pulse signal that Hall element is produced carries out N frequency multiplication, and signal after frequency multiplication is sent into another CAP capture-port, when rising edge arrives each time, enters capture interrupt one time, and records the number of times of capture interrupt, obtains the position of outer rotor.
2. birotor permanent magnetic wind power generator rotor rotating speed according to claim 1 and location measurement method, it is characterized in that: also comprise plastic filter circuit, the signal that the output signal of described photoelectric encoder and described Hall element produce is through two groups of CAP capture-ports of plastic filter circuit supplied with digital signal processor.
3. birotor permanent magnetic wind power generator rotor rotating speed according to claim 1 and location measurement method, is characterized in that: in described step 201, respectively at the surface working groove of 3 stator tooths, and Hall element is installed in groove.
4. birotor permanent magnetic wind power generator rotor rotating speed according to claim 3 and location measurement method, is characterized in that: the space angle that 3 surfaces arrange between reeded stator tooth is respectively 120 °.
5. according to right, want birotor permanent magnetic wind power generator rotor rotating speed and the location measurement method described in 3 or 4, it is characterized in that: in described step 203, an interrupt function is first set, three interrupt vectors that the pulse hall signal of supplied with digital signal processor is differentiated are set in interrupt function, when three Hall elements normally send pulse signal, three interrupt vectors are carried out respectively one time 0, 1 conversion, if one of them interrupt vector is not upgraded, carry out step 203-205, if three interrupt vectors are all normally upgraded, obtain the rotating speed of outer rotor and the method for position as follows:
Step 301: three capture-ports by the digital signal processor respectively rising edge of Dui San road pulse hall signal are caught;
Step 302: capture interrupt is set, when arbitrary CAP port is caught rising edge, enters capture interrupt;
Step 303: count for the time clock in the time interval of twice adjacent capture interrupt by the timer Counter as clock reference, obtain the mistiming of adjacent twice capture interrupt;
Step 304: based on Hall element principle of work, obtain according to the locus of motor number of pole-pairs and Hall element placement the angle that outer rotor corresponding to adjacent twice capture interrupt turns over;
Step 305: the angle that the mistiming of adjacent twice capture interrupt obtaining according to above-mentioned steps and the time inner and outer rotors of adjacent twice capture interrupt turn over obtains the rotating speed of outer rotor;
Step 306: another timer is set and interrupts, enter timer and interrupt when meeting timer interrupt condition, elapsed time between twice interruption before and after obtaining;
Step 307: obtain the elapsed time acquisition differential seat angle that outer rotor turns between twice interruption between twice interruption in the rotating speed of transferring in step 305 outer rotor obtaining and step 306;
Step 308: the differential seat angle turning over by the outer rotor obtaining in step 307, in conjunction with the position θ of formula θ=θ+Δ θ acquisition outer rotor, wherein, Δ θ is the differential seat angle that the outer rotor of acquisition in step 307 turns over; And when each capture interrupt, upgrade one time outer rotor position signalling, obtain accurate outer rotor position signalling.
CN201210584002.0A 2012-12-28 2012-12-28 Device and method for measuring rotation speeds and positions of rotors of birotor permanent magnet wind-driven generator Expired - Fee Related CN103048486B (en)

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采用DSP和CPLD的新型定子永磁型双功率流电机的驱动系统;姚雪峰等;《电机与控制应用》;20121210;第39卷(第12期);第20页右栏至第23页右栏,图1-2 *

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