CN104868811B - The motor operation control method that phase width based on stray currents vector is coordinated - Google Patents
The motor operation control method that phase width based on stray currents vector is coordinated Download PDFInfo
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Abstract
The motor operation control method that phase width of the present invention based on stray currents vector is coordinated, it is characterised in that the control method is three kinds of the carry out phase width coordination control in motor operation course and controls different require：The first, with output torque be to the maximum target, second, with the minimum target of torque pulsation and the third, with the minimum target of position deviation, phase angle and amplitude respectively to current phasor carries out coordination control, the control method equipment therefor, including phase width coordinating control module, current control module, power circuit, motor, position detecting module and current detection module；Phase width coordinating control module one end is connected with current control module, and the other end is connected with position detecting module；Current control module is connected with the signal control end of power circuit, the output end of power circuit is connected by wire with motor, and wire passes through current detection module, current detection module is connected with current control module again, and position detecting module is co-axially mounted with motor.
Description
Technical field
Technical scheme is related to a kind of electric machines control technology, specifically the phase width based on stray currents vector
The motor operation control method of coordination.
Background technology
Exchange step-by -step drive control is the control strategy that a kind ofization motor continuously operates to step run, to obtain motor
The methods of operation such as speed governing, micro-stepping positioning are directly driven in stepping, and it is obtained on asynchronous machine, synchronous motor and switched reluctance machines
Using.The technology of exchange stepping is that motor continuous current is pressed into discrete step number bHStaircase waveform electric current is separated into etc. step pitch, with three-phase
Motor is such as formula (1)：
Wherein k=0,1 ..., bH- 1, I are each phase current magnitude.Then spatially discrete stepping magnetomotive force (electricity is obtained
Flow vector), so as to produce the operation of stepping electromagnetic torque motor：
Wherein ε is square angle, i.e. current phasor isWith rotor flux ψrBetween angle.If Fig. 1 (a) is three phase alternating current motor bH
Stray currents waveform when=12, Fig. 1 (b) is the stair step current schematic vector diagram that three-phase current is synthesized.
At present, electric-machine directly-driven is mainly realized using constant frequency control using the method for exchange step-by -step drive controlled motor operation
Speed governing, and use crawl micro-step control, three sections of (raising frequency ramp-up stage, constant frequency constant rate period, frequency reducing deceleration and positioning stage), five
Section (raising frequency ramp-up stage, constant frequency constant rate period, frequency reducing decelerating phase, low speed jerking motion stage, positioning stage) control, realizes motor
Position control.Conventional motors progress control method is by constant current phasor amplitude and given square angle, such control
Method processed is that the angle of stator current Advancing Rotor magnetic linkage is constant, directly adjusts the frequency of given electric current, can bring speed overshoot
Greatly, torque pulsation is excessive, positioning time length and the problem of sound state angle error is big to location precision during positioning.It is necessary
A kind of new motor operation control method strategy is proposed, the advantage that exchange step-by -step drive is positioned in low speed is played, and make up
Above-mentioned weak point present in existing exchange stepper control method.
The content of the invention
The technical problems to be solved by the invention are：The motor operation control that phase width based on stray currents vector is coordinated is provided
Method processed, the motor operation control method is based on exchanging step motion control, in the stray currents vector control with locating features
On the basis of system, according to the different operation situation of motor, different control targes proposes current phasor phase with amplitude stage by stage
Coordinate control strategy, by coordinate under stray currents vector magnitude and phase, i.e. different situations calculate stray currents amplitude and
The processing of the step of phase, realizes the improvement of torque characteristics, overcomes during motor whole service, speed overshoot is big,
Torque pulsation is excessive, positioning time length and the not high defect of positioning precision.
The present invention solves the technical scheme that is used of the technical problem：The electricity that phase width based on stray currents vector is coordinated
Machine progress control method, is that the carry out phase width in motor operation course coordinates the different requirements of three kinds of controls controlled：First
Kind, with output torque be to the maximum target, second, it is minimum with position deviation with the minimum target of torque pulsation and the third
Target, the phase angle to current phasor and amplitude progress coordination control respectively, specific method is as follows：
Control method equipment therefor described in I,：
The control method equipment therefor, including phase width coordinating control module, current control module, power circuit, motor,
Position detecting module and current detection module；Phase width coordinating control module one end is connected with current control module, the other end and position
Detection module is put to be connected；Current control module is connected with the signal control end of power circuit, and the output end of power circuit is by leading
Line is connected with motor, and wire passes through current detection module, and current detection module is connected with current control module again, position detection
Module is co-axially mounted with motor；
Control method described in II, is directed to and three kinds of different control targes point that phase width coordinates control is carried out in motor operation course
Other phase angle and amplitude to current phasor carries out phase width and coordinates comprising the following steps that for control：
The first, is the phase width control method for coordinating of target to the maximum with output torque：
When motor quickly rises or slowed down, it is necessary to export maximum electromagnetic torque according to following formula (2),
Wherein ε is square angle, i.e. current phasor isWith rotor flux ψrBetween angle, obtain maximum electromagnetic torque should meet to
Determine stray currents vector magnitude | is| it is maximum Im, square angle ε is in the θ of pi/2 ± 0.5bInterior change, wherein θb=2 π/bHFor step angle,
Te is electromagnetic torque；
Phase width, which coordinates rate-determining steps, to be included：
The first step, detects the mechanical Angle Position of rotor：
Phase width coordinating control module detects the mechanical Angle Position θ of rotor by position detecting modulem, choosing number of pole-pairs is
P motor, then the number of the axis of A phase windings is p, the mechanical Angle Position θmAxial location using one of A phase windings is 0
Starting；
Second step, calculates the position of given stray currents vector：
By phase width coordinating control module by the mechanical Angle Position θ detected in the first stepmFormula (3) is brought into, according to formula
(3) the given stray currents vector i of institute is calculateds(k) sequence number：
In formula, round represents the computing that rounds up；% represents complementation；Symbol " ± " refers to when the electromagnetic torque side of exerting oneself
To it is identical with positive direction when, take "+", when electromagnetic torque go out force direction it is opposite with positive direction when, take "-", the positive direction is face
To the counter clockwise direction of motor output shaft,
According to given stray currents vector is(k) sequence number can determine the position of given stray currents vector, that is, give
The phase angle k θ of stray currents vectorb；
3rd step, the given stray currents vector of output：
By given stray currents vector is(k) amplitude | is|=ImThe given stray currents vector obtained with second step
Phase angle k θbCurrent control module is given to, using any one current control side in current hysteresis-band control or electric current PID control
Method controlled motor current following gives electric current, so as to realize the maximum control of output torque；
Second, with the phase width control method for coordinating of the minimum target of torque pulsation：
When motor travels at the uniform speed, it is desirable to which the electromagnetic torque of motor output should meet motor torque balance side with load torque
Journey, that is, meet formula (4),
In formula, TLFor load torque, J is rotary inertia, and ω is the angular rate of motor；
Now, given electromagnetic torque T is madee *Equal to load torque TL, and make Te=Te*, then give stray currents vector
Amplitude | is| according to formula (2) by given electromagnetic torque Te *Calculating is obtained, when square angle ε is in the θ of pi/2 ± 0.5bDuring interior change, make
Obtain torque pulsation minimum, wherein θb=2 π/bHFor step angle；
Phase width coordinates rate-determining steps：
The first step, detects the mechanical Angle Position of rotor：
Phase width coordinating control module detects the mechanical Angle Position θ of rotor by position detecting modulem, choosing number of pole-pairs is
P motor, then the number of the axis of A phase windings is p, the mechanical Angle Position θmAxial location using one of A phase windings is 0
Starting；
Second step, calculates the position of given stray currents vector：
By phase width coordinating control module by the mechanical Angle Position θ detected in the first stepmBring formula (3) into
In formula, round represents the computing that rounds up, and % represents complementation；Symbol " ± " refers to when the electromagnetic torque side of exerting oneself
Simultaneously, take "+" to positive direction, when electromagnetic torque go out force direction it is opposite with positive direction when, take "-", the positive direction be towards
The counter clockwise direction of motor output shaft,
The given stray currents vector i of institute is calculated according to formula (3)s(k) sequence number, further according to given stray currents vector is
(k) sequence number can determine the position of given stray currents vector, that is, give the phase angle k θ of stray currents vectorb；
3rd step, calculates given stray currents vector magnitude：
According to given electromagnetic torque and the equilibrium relation T of load torquee *=TLIt can obtain Te *, make Te=Te*, then by sin ε
=1 and Te *Bring formula (2) into, formula (5) can be obtained：
In control, T can be obtained by load-toque estimate deviceLEstimate, so as to obtain given discrete according to formula (5)
The amplitude of current phasor；
4th step, the given stray currents vector of output：
To calculate that the obtained amplitude of given stray currents vector and being calculated according to second step obtains according to the 3rd step to
Determine the phase angle k θ of stray currents vectorbCurrent control module is given to, using appointing in current hysteresis-band control or electric current PID control
A kind of current control method controlled motor current following of anticipating gives electric current, so as to realize the minimum control of torque pulsation；
The third, with the phase width control method for coordinating of the minimum target of position deviation：
When operating motor is decelerated near anchor point by braking moment, and speed it is relatively low when can make to turn there is provided one
The sub given electromagnetic torque T being parked in just at the minimum anchor point of position deviatione *, now give electromagnetic torque Te *For given value,
The phase angle and amplitude of given stray currents vector should give electromagnetic torque T according to known to this simultaneouslye *It is adjusted；
Phase width coordinates rate-determining steps：
The first step, detects the mechanical Angle Position of rotor：
The mechanical Angle Position θ of rotor is detected by position detecting modulem, choose number of pole-pairs be p motor, then A phases around
The number of the axis of group is p, the mechanical Angle Position θmUsing the axial location of one of A phase windings as 0 starting；
Second step, the phase angle of given stray currents vector is calculated with rated current：
For balanced load torque, using rated current IrThe phase of the given stray currents vector of estimation, is coordinated to control by phase width
Molding block is by the mechanical Angle Position θ detected in the first stepmBring formula (6) into,
In formula, round represents the computing that rounds up, and % represents complementation, and symbol " ± " refers to when the electromagnetic torque side of exerting oneself
To it is identical with positive direction when, take "+", when electromagnetic torque go out force direction it is opposite with positive direction when, take "-", the positive direction is face
To the counter clockwise direction of motor output shaft, wherein θb=2 π/bHFor step angle；
Given stray currents vector i is obtained according to formula (6)s(k) sequence number, further according to given stray currents vector is(k)
Sequence number can determine the position of given stray currents vector, that is, give the phase angle k θ of stray currents vectorb；
3rd step, calculates the amplitude of given stray currents vector：
Known given electromagnetic torque Te *, Te=Te* is made, by square angle ε=k θb-pθmBring formula (2) into, formula can be obtained
(7)：
So as to obtain the amplitude of given stray currents vector according to formula (7)；
4th step, the given stray currents vector of output：
To calculate that the obtained amplitude of given stray currents vector and being calculated according to second step obtains according to the 3rd step to
Determine the phase angle k θ of stray currents vectorbCurrent control module is given to, using appointing in current hysteresis-band control or electric current PID control
A kind of current control method controlled motor current following of anticipating gives electric current, so as to realize the minimum control of position deviation.
The beneficial effects of the invention are as follows：Compared with prior art, the substantive distinguishing features of protrusion of the invention and marked improvement
It is as follows：
(1) the principle on which of the present invention is：On the basis of exchange step motion control, pass through the whole service to motor
During, with the control of different control targe realizations stage by stage：In raising speed and decelerating phase, turning to export for situation one is used
Square is the phase width control method for coordinating of Target situation to the maximum；In constant rate period, use situation two with the minimum mesh of torque pulsation
Mark the phase width control method for coordinating of situation；In positioning stage, the phase with the minimum Target situation of position deviation of situation three is used
Width control method for coordinating.
(2) marked improvement of the invention is：Base of the control method of the present invention in the stray currents control with locating features
It is improved on plinth, proposes that phase angle coordinates the strategy of control with amplitude according to different situations, step motion control skill is exchanged with existing
Art is compared, and realizes the improvement of torque characteristics, is overcome during motor whole service, and speed overshoot is big, torque pulsation
Greatly, the not high defect of positioning time length and positioning precision.Shown by embodiment, among motor whole service process, point
Stage uses phase width control method for coordinating, it is possible to achieve speed up time is short, only 0.62s, and make it that torque pulsation is small, be only ±
In 1Nm, motor position fixing process, from motor position convergence and given position is reached, take only about 0.2s to complete stability, most
The position error of whole motor is less than 0.015rad, about 0.085 °, improves the positioning precision of motor, therefore this method is both played
Exchange step-by -step drive again compensate for speed overshoot present in existing exchange stepper control method in low speed, the advantage of positioning
Greatly, torque pulsation is excessive, positioning time length and the not high deficiency of positioning precision.
(3) the inventive method is applicable asynchronous machine, synchronous motor and switched reluctance machines.
Brief description of the drawings
The present invention is further described with reference to the accompanying drawings and examples.
Fig. 1 (a) is bHThe stray currents waveform of=12 three phase alternating current motors；
Fig. 1 (b) is bHThe stair step current schematic vector diagram of=12 three-phase currents synthesis；
Fig. 2 is the inventive method equipment therefor structure chart；
Fig. 3 is the given stray currents vector change schematic diagram that the phase width for being target to the maximum with output torque coordinates control；
Fig. 4 (a) is bHCoordinate the given stray currents of control when=12 with the phase width of the minimum Target situation of torque pulsation
Vector change schematic diagram；
Fig. 4 (b) is bHWith the load torque of the phase width control method for coordinating of the minimum Target situation of torque pulsation when=12
Change schematic diagram；
Fig. 5 (a) is bHWith the given discrete of the phase width control method for coordinating of the minimum Target situation of position deviation when=12
Current phasor change schematic diagram；
Fig. 5 (b) is bHWith the load torque of the phase width control method for coordinating of the minimum Target situation of position deviation when=12
With given electromagnetic torque change schematic diagram；
Fig. 6 (a) is impedance load torque 2Nm, limits maximum (top) speed 1000r/min, position gives 200rad, bH=12
When motor speed curve map；
Fig. 6 (b) is impedance load torque 2Nm, limits maximum (top) speed 1000r/min, position gives 200rad, bH=12
When motor position curve map；
Fig. 7 (a) is impedance load torque 2Nm, limits maximum (top) speed 1000r/min, position gives 200rad, bH=12
When motor output electromagnetic torque change schematic diagram；
Fig. 7 (b) is impedance load torque 2Nm, limits maximum (top) speed 1000r/min, position gives 200rad, bH=12
When current phasor amplitude change schematic diagram；
Fig. 7 (c) is impedance load torque 2Nm, limits maximum (top) speed 1000r/min, position gives 200rad, bH=12
When square angle (electrical angle) change schematic diagram.
In figure, 1. phase width coordinating control modules, 2. current control modules, 3. power circuits, 4. motors, 5. positions detection mould
Block, 6. current detection modules.
Embodiment
Fig. 1 (a) takes discrete step number b for three phase electric machine three-phase current in known technologyH=12 discrete levels obtained by formula (1)
Terraced electric current.
Wherein k=0,1,2,3 ..., 11, I be each phase current magnitude.Three-phase discrete step electric current is obtained after Vector modulation
Such as i in Fig. 1 (b)s(0)、is(1)、is(2)、is(3)、…、is(11) between Space current vector, two spaces current phasor
Angle thetab=2 π/bH=π/6 are step angle.
The structure for the motor operation control method equipment therefor that Fig. 2 coordinates for phase width of the present invention based on stray currents vector
Figure, including phase width coordinating control module 1, current control module 2, power circuit 3, motor 4, position detecting module 5 and electric current inspection
Survey module 6；Phase width coordinating control module 1 and current control module 2 by the TMS320LF2407 data signals of TI companies at
Manage device realize control, power circuit 3 using the SPM PM15RSH120 of Mitsubishi as core, position detecting module with
M205B encoders rotary encoder is core；The one end of phase width coordinating control module 1 is connected with current control module 2, the other end with
Position detecting module 5 is connected；Current control module is connected with the signal control end of power circuit 3, and the output end of power circuit 3 is led to
Wire is crossed with motor 4 to be connected, and wire passes through current detection module 6, current detection module 6 is connected with current control module 2 again,
Position detecting module 5 is co-axially mounted with motor 4.The running of said apparatus is：Position detecting module 5 and motor 4 are same
Axle is installed, and detects the mechanical Angle Position θ of motor 4m, phase width coordinating control module 1 is according to given electromagnetic torque Te *, control situation
The mechanical Angle Position θ that selection and position detecting module 5 are detectedmComplete the computing that phase width coordinates control, export it is to be controlled with
The given stray currents vector i of tracks(k), phase width coordinating control module 1 is by the given stray currents vector i of outputs(k) transmit to
Current control module 2；The actual current of the three-phase electricity of the detection input motor 4 of current detection module 6；The basis of current control module 2
Given stray currents vector is(k) actual current and by current detection module 6 detected, by output control pwm signal to work(
Switching tube in rate circuit 3, to control the output voltage of power circuit 3；Power circuit 3 is under the control of pwm signal, by direct current
Electricity is reverse into three-phase alternating current electricity output to motor 4.
Embodiment illustrated in fig. 3 shows, discrete step number bHIt is with output torque the phase width association under Target situation when=12 to the maximum
Regulate and control given stray currents vector (or current phasor) change schematic diagram of system, phase width coordinating control module 1 is examined by position
Survey module 5 and detect rotor flux ψrMechanical Angle Position be θm, the mechanical Angle Position θmUsing the axial location of A phase windings as 0
Begin.The motor that correspondence number of pole-pairs is p, its electrical angle is p θm(-π/4<pθm<- π/12), i.e. rotor flux ψrPositioned at 1. locating, and turn
Sub- direction of rotation is identical with positive direction, according to the control situation that output torque is maximum, draws and determines stray currents vector magnitude for most
High current Im, and according to formula (3)：
Now give electromagnetic torque Te *Go out that force direction is identical with positive direction, it is 3 to go out to take k during "+" in calculation formula (3),
Then it is i to give stray currents vectors(3), square angle ε now is in the θ of pi/2 ± 0.5bIt is interior.As rotor flux ψrPress positive direction in position
Go to and 2. locate, now p θm=π/12, the square angle ε=θ of pi/2-0.5b, k=4 is calculated through formula (3), given stray currents vector is cut
Shift to is(4), with this, according to the position of rotor flux, given stray currents vector i is switched length by lengths, and will be given (k)
Stray currents vector is(k) export to current control module 2, the reality of the recombination current detection module 6 of current control module 2 detection
Border current value, so as to be controlled to power circuit 3, realizes the maximum control targe of the output torque of motor 4.
Fig. 4 (a) illustrated embodiments show, discrete step number bHWith the phase width under the minimum Target situation of torque pulsation when=12
Coordinate the given stray currents vector change schematic diagram of control.Fig. 4 (b) is rotor flux ψr1. electrical angle to during 2. from bearing
The change of set torque.Phase width coordinating control module 1 detects rotor flux ψ by position detecting module 5rMechanical Angle Position be
θm, the mechanical Angle Position θmUsing the axial location of A phase windings as 0 starting.The motor that correspondence number of pole-pairs is p, its electrical angle is p θm
(-π/4<pθm<- π/12), i.e. rotor flux ψrPositioned at 1. locating, and rotor direction of rotation is identical with positive direction, according to torque pulsation
Minimum control situation, according to formula (3)：
Now give electromagnetic torque Te *Go out that force direction is identical with positive direction, the k calculated when taking "+" is 3, further according to formula
(5)
T in formula (5)e *=TL, T is made firste *=TL1, calculate the amplitude for obtaining given stray currents vector | is1|, then give
Stray currents vector is determined for is1(3), square angle ε now is in the θ of pi/2 ± 0.5bIt is interior.
Fig. 4 (b) illustrated embodiments show, from 1. to during 2., load torque is by TL1Transform to TL2, correspondingly, k's
It is still 3, T that value is calculated through formula (3)e *T will be changed intoL2, then the amplitude of given stray currents vector is obtained by formula (5) | is2|, then
Given stray currents vector is changed into is2(3).As rotor flux ψr2. position is gone to by positive direction locates, now p θm=π/12, square angle
ε=the θ of pi/2-0.5b, k=4 is calculated through (3) formula, stray currents vectors switching is given to is2(4), with this, according to rotor flux
ψrPosition and load torque TLSize, switch given stray currents vector i length by lengths(k), by given stray currents
Vector is(k) actual current value detected to current control module 2, recombination current detection module 6 is exported, so as to power electricity
Road 3 is controlled, and realizes the minimum control targe of the torque pulsation of motor 4.
Fig. 5 (a) illustrated embodiments show, discrete step number bHWith the phase width under the minimum Target situation of position deviation when=12
Coordinate the given stray currents vector change schematic diagram of control, be 3. target anchor point.Fig. 5 (b) is rotor flux ψrElectrical angle
From 1. to the change curve of load torque and given electromagnetic torque during 3., wherein load torque is potential energy type loading TL.Phase
Width coordinating control module 1 detects rotor flux ψ by position detecting module 5rMechanical Angle Position be θm, the mechanical Angle Position
θmUsing the axial location of A phase windings as 0 starting.The motor that correspondence number of pole-pairs is p, its electrical angle is p θm(-π/4<pθm<-π/
12), i.e. rotor flux ψrPositioned at 1. locating, and rotor slows down, and direction of rotation is identical with positive direction.Now, by Fig. 5 (b)
The corresponding given electromagnetic torque of middle A points, according to (6) formula, by rated current vector magnitude IrThe given stray currents vector of estimation
Sequence number：
Now give electromagnetic torque Te *Go out force direction with positive direction on the contrary, taking "-", calculating obtains k=11, further according to formula
(7) amplitude of given stray currents vector is calculated by giving electromagnetic torque：
It is i then to give stray currents vectors(11), motor continues to subtract under the collective effect of electromagnetic torque and load torque
Speed.The end points of current phasor will change along A → B, and when 2. rotor flux goes to, current phasor end points reaches B points, passes through formula
(6) k=0 arrived calculated, amplitude is Ir, the end points of current phasor will switch to C.
Fig. 5 (b) illustrated embodiments show, electric when 2. rotor flux goes to when the end points of current phasor will change along A → B
Flow vector end points reaches B points, the k=0 arrived calculated by formula (6), and amplitude is Ir, the end points of current phasor will switch to C
When, start to gradually decrease to 0 by Fig. 5 (b) absolute values for giving electromagnetic torque, according to (7) formula, the end points of current phasor is also by edge
C → D is progressively reduced to 0.When 3. motor is parked in just, for balanced load torque, given electromagnetic torque rapid will increase to
Load torque identical value, is calculated, current phasor end points will change along D → E, finally with current phasor i through formula (6) (7)s
(2) balance the load torque.Given current phasor is exported to current control module 2 in real time with this, examined with reference to current detection module 6
The actual current value of survey, so as to be controlled to power circuit 3, realizes the minimum control targe of the position deviation of motor 4.
Fig. 6 (a) embodiments show that setting load is impedance type load, and load torque 2Nm limits maximum (top) speed
1000r/min, gives position location 200rad, and take discrete number bHMotor speed curve map when=12.1. it is raising speed rank
Section, according to situation one, is to the maximum the phase width under Target situation with output torque and coordinates control, rotating speed is accelerated from 0r/min with maximum
Degree is quickly raised to 1000r/min, is 2. constant rate period, according to situation two, with the phase width under the minimum Target situation of torque pulsation
Coordinate control, rotating speed is maintained at 1000r/min, is 3. the decelerating phase, also according to situation one, is target to the maximum with output torque
Phase width under situation coordinates control, and rotating speed is slowed down since 1000r/min with peak acceleration, is 4. positioning stage, according to feelings
Shape three, coordinates to control, rotating speed gradually decreases to 0r/min, and now motor reaches with the phase width under the minimum Target situation of position deviation
To anchor point.
Fig. 6 (b) embodiments show that setting load is impedance type load, and load torque 2Nm limits maximum (top) speed
1000r/min, gives position location 200rad, and take discrete number bHMotor position curve map when=12, is 1. raising speed rank
Section, according to situation one, is to the maximum the phase width under Target situation with output torque and coordinates control, mechanical angle position curve is in parabolic
Line, slope gradually increases, i.e. motor speed increase, is 2. constant rate period, according to situation two, with the minimum target of torque pulsation
Phase width coordinates control, and linearly, slope is zero to mechanical angle position curve, i.e., speed keeps constant, is 3. the decelerating phase, equally presses
According to situation one, the phase width being to the maximum with output torque under Target situation coordinates control, and mechanical angle position curve is also parabola, but
It is that slope is gradually reduced and levels off to zero, i.e. motor and be in deceleration regime, this stage motor gradually levels off to given position, is 4. fixed
In the position stage, according to situation three, coordinate to control with the phase width of the minimum Target situation of position deviation, motor position reaches given position
200rad is put, i.e., now motor reaches anchor point, final position error is less than 0.01rad.
Fig. 7 (a) embodiments show that setting load is impedance type load, and load torque 2Nm limits maximum (top) speed
1000r/min, gives position location 200rad, and take discrete number bHElectromagnetic torque change schematic diagram when=12, is 1. liter
In the fast stage, according to situation one, the phase width being to the maximum with output torque under Target situation coordinates control, and motor is with maximum electromagnetic torque
Accelerated, maximum electromagnetic torque is 20Nm, is 2. constant rate period, according to situation two, with the minimum target feelings of torque pulsation
Phase width under shape coordinates control, in order to keep motor speed constant, and now electromagnetic torque is used for balance the load torque, electromagnetic torque
2Nm is remained, is 3. the decelerating phase, also according to situation one, the phase width being to the maximum with output torque under Target situation coordinates control
System, this stage motor is slowed down with negative maximum electromagnetic torque, and the maximum electromagnetic torque in this stage remains -20N
M, is 4. positioning stage, according to situation three, coordinates to control with the phase width under the minimum Target situation of position deviation, electromagnetic torque by
Negative maximum electromagnetic torque progressively increases to zero, and motor position reaches given position 200rad, i.e., now motor reaches positioning
Point, now electromagnetic torque is zero.
Fig. 7 (b) embodiments show that setting load is impedance type load, and load torque 2Nm limits maximum (top) speed
1000r/min, gives position location 200rad, and take discrete number bHCurrent amplitude change schematic diagram when=12, is 1. liter
In the fast stage, according to situation one, the phase width being to the maximum with output torque under Target situation is coordinated control, gives stray currents vector width
It is worth for maximum current Im, i.e. 17A, this stage motor is accelerated with maximum electromagnetic torque, is 2. constant rate period, according to situation
Two, coordinate to control with the phase width under the minimum Target situation of torque pulsation, this stage current vector magnitude is 4.2A, to produce electricity
Magnetic torque balanced load torque.3. it is the decelerating phase, according to situation one, is the phase width association under Target situation to the maximum with output torque
Regulation and control system, it is maximum current I to give stray currents vector magnitudem, i.e. 17A, this stage motor enters with maximum electromagnetic torque
Row slows down, and is 4. positioning stage, according to situation three, coordinates to control with the phase width under the minimum Target situation of position deviation, gives
Stray currents vector magnitude is gradually decrease to zero from maximum current 17A, i.e., now motor reaches anchor point.
Fig. 7 (c) embodiments show that setting load is impedance type load, and load torque 2Nm limits maximum (top) speed
1000r/min, gives position location 200rad, and take discrete number bHSquare angle change schematic diagram when=12, is 1. raising speed rank
Section, according to situation one, is to the maximum the phase width under Target situation with output torque and coordinates control, motor is carried out with maximum electromagnetic torque
Accelerate, square angle ε is maintained at the θ of pi/2 ± 0.5bInterior, i.e., 75 °~105 °, be 2. constant rate period, according to situation two, with torque pulsation most
Small is that the phase width under Target situation coordinates control, and square angle ε is maintained at the θ of pi/2 ± 0.5bIt is interior, i.e., 75 °~105 °, by adjusting electric current
Amplitude so that electromagnetic torque is balanced with load torque, is 3. the decelerating phase, according to situation one, is target to the maximum with output torque
Phase width under situation coordinates control, and this stage motor is slowed down with maximum electromagnetic torque, and square angle ε is maintained at-(pi/2 ± 0.5
θb) in, i.e., -105 °~-75 °, be 4. positioning stage, according to situation three, with the phase width under the minimum Target situation of position deviation
Coordinate control, square angle ε is from the-(θ of pi/2 ± 0.5b) start change, with the process of motor convergence anchor point, square angle by increasing twice
Plus and the adjustment process that reduces, final square angle reduces to 0, and now motor reaches anchor point.
Embodiment
The present embodiment is by taking the running of 2.2kW permagnetic synchronous motor as an example, and setting load is impedance type load,
Large inertia load torque is 2Nm, and rotary inertia is 0.089kg m2, maximum (top) speed is limited as 1000r/min, gives sprocket bit
200rad is set to, and takes discrete number bH=12, whole service process is divided into four-stage, respectively ramp-up stage 1., constant speed
Stage 2., the decelerating phase 3., positioning stage 4., whole service time 2.6s.By each rank of whole service process as shown in Figure 6, Figure 7
Section motor speed profile, position curve, electromagnetic torque curve, current phasor amplitude curve and square angular curve.In addition it is of the invention
In the phase width control method for coordinating based on stray currents vector be equally applicable to other classes such as asynchronous machine, switched reluctance machines
The motor of type.
The motor operation control method that phase width of the present embodiment based on stray currents vector is coordinated, is according to motor operation mistake
Carry out phase width in journey coordinates the different requirements of three kinds of controls of control：The first, with output torque be to the maximum target, second,
With the minimum target of torque pulsation and the third, with the minimum target of position deviation, respectively to the phase angle and amplitude of current phasor
Coordination control is carried out, specific method is as follows：
Control method equipment therefor and operation described in I,：
The control method equipment therefor, including phase width coordinating control module 1, current control module 2, power circuit 3, electricity
Machine 4, position detecting module 5 and current detection module 6；The one end of phase width coordinating control module 1 is connected with current control module 2, separately
One end is connected with position detecting module 5；Current control module 6 is connected with the signal control end of power circuit 3, power circuit 3
Output end is connected by wire with motor 4, and wire pass through current detection module 6, current detection module 6 again with current control mould
Block 2 is connected, and position detecting module 5 is co-axially mounted with motor 4；
Control method described in II, is directed to and three kinds of different control targes point that phase width coordinates control is carried out in motor operation course
Other phase angle and amplitude to current phasor carries out phase width and coordinates comprising the following steps that for control：
The first, is the phase width control method for coordinating of target to the maximum with output torque：
When motor quickly rises or slowed down, it is necessary to export torque capacity according to following formula (2),
Wherein ε is square angle, i.e. current phasor isWith rotor flux ψrBetween angle, obtain torque capacity should meet give from
Dissipate current phasor amplitude | is| it is maximum Im, square angle ε is in the θ of pi/2 ± 0.5bInterior change, wherein θb=2 π/bHFor step angle, Te is
Electromagnetic torque；
Phase width, which coordinates rate-determining steps, to be included：
The first step, detects the mechanical Angle Position of rotor：
Phase width coordinating control module 1 detects the mechanical Angle Position θ of rotor by position detecting module 5m, choose number of pole-pairs
For p motor, then the number of the axis of A phase windings is p, the mechanical Angle Position θmWith the axial location of one of A phase windings
For 0 starting；
By phase width coordinating control module by the mechanical Angle Position θ detected in the first stepmFormula (3) is brought into, according to formula
(3) the given stray currents vector i of institute is calculateds(k) sequence number：
In formula, round represents the computing that rounds up；% represents complementation；Symbol " ± " refers to when the electromagnetic torque side of exerting oneself
To it is identical with positive direction when, take "+", when electromagnetic torque go out force direction it is opposite with positive direction when, take "-", the positive direction is face
To the counter clockwise direction of motor output shaft,
According to given stray currents vector is(k) sequence number can determine the position of given stray currents vector, that is, give
The phase angle k θ of stray currents vectorb；
3rd step, the given stray currents vector of output：
By given stray currents vector is(k) amplitude | is|=ImThe given stray currents vector obtained with second step
Phase angle k θbCurrent control module 2 is given to, using any one current control in current hysteresis-band control or electric current PID control
Method controlled motor current following gives electric current, so as to realize the maximum control of output torque；
Such as Fig. 6 (a) is 1. shown, and motor speed is climbed to 1000r/min, speed up time about 0.62s from 0r/min.Such as
Fig. 6 (b) is 1. shown, and parabolically, such as Fig. 7 (a) is 1. shown for motor position curve, and motor needs to be accelerated with torque capacity,
Maximum electromagnetic torque is 17.85Nm, and such as Fig. 7 (b) is 1. shown, and it is maximum current to give stray currents vector magnitude | Im|, i.e.,
16.9A, such as Fig. 7 (c) are 1. shown, and square angle ε is maintained at the θ of pi/2 ± 0.5bIt is interior, i.e., 75 °~105 °.To ensure that motor is accelerated with maximum
Degree accelerates.
Second, with the phase width control method for coordinating of the minimum target of torque pulsation：
When motor travels at the uniform speed, it is desirable to which the electromagnetic torque of motor output should meet motor torque balance side with load torque
Journey, that is, meet formula (4),
In formula, TLFor load torque, J is rotary inertia, and ω is the angular rate of motor；
Now, given electromagnetic torque T is madee *Equal to load torque TL, and make Te=Te*, then give stray currents vector
Amplitude | is| according to formula (2) by given electromagnetic torque Te *Calculating is obtained, when square angle ε is in the θ of pi/2 ± 0.5bDuring interior change, make
Obtain torque pulsation minimum, wherein θb=2 π/bHFor step angle；
Phase width coordinates rate-determining steps：
The first step, detects the mechanical Angle Position of rotor：
Phase width coordinating control module 1 detects the mechanical Angle Position θ of rotor by position detecting module 5m, choose number of pole-pairs
For p motor, then the number of the axis of A phase windings is p, the mechanical Angle Position θmWith the axial location of one of A phase windings
For 0 starting；
Second step, calculates the position of given stray currents vector：
By phase width coordinating control module 1 by the mechanical Angle Position θ detected in the first stepmBring formula (3) into
In formula, round represents the computing that rounds up, and % represents complementation；Symbol " ± " refers to when the electromagnetic torque side of exerting oneself
Simultaneously, take "+" to positive direction, when electromagnetic torque go out force direction it is opposite with positive direction when, take "-", the positive direction be towards
The counter clockwise direction of motor output shaft,
The given stray currents vector i of institute is calculated according to formula (3)s(k) sequence number, further according to given stray currents vector is
(k) sequence number can determine the position of given stray currents vector, that is, give the phase angle k θ of stray currents vectorb；
3rd step, calculates given stray currents vector magnitude：
According to given electromagnetic torque and the equilibrium relation T of load torquee *=TLIt can obtain Te *, make Te=Te*, then by sin ε
=1 and Te *Bring formula (2) into, formula (5) can be obtained：
In control, T can be obtained by load-toque estimate deviceLEstimate, so as to obtain given discrete according to formula (5)
The amplitude of current phasor；
4th step, the given stray currents vector of output：
To calculate that the obtained amplitude of given stray currents vector and being calculated according to second step obtains according to the 3rd step to
Determine the phase angle k θ of stray currents vectorbCurrent control module is given to, using appointing in current hysteresis-band control or electric current PID control
A kind of current control method controlled motor current following of anticipating gives electric current, so as to realize the minimum control of torque pulsation；
Such as Fig. 6 (a) is 2. shown, and motor speed keeps 1000r/min, and such as Fig. 6 (b) is 2. shown, and motor position curve is in straight
Line, and slope keeps constant, such as Fig. 7 (a) is 2. shown, for the torque that balances the load, and output electromagnetic torque remains 5Nm, and
Torque pulsation is minimum, and about ± 1Nm of pulsing, such as Fig. 7 (b) is 2. shown, and this stage electromagnetic torque and load torque keep balance, institute
To there is Te=TL=2Nm, as load torque TLWhen constant, this stage determines current phasor amplitude for 4.2A, such as Fig. 7 (c) 2. institutes
Show, square angle ε is maintained at the θ of pi/2 ± 0.5bIt is interior, i.e., 75 °~105 °.To ensure that the torque pulsation of motor output is minimum.
When motor is in the decelerating phase, motor needs to be slowed down with torque capacity, according to situation one, with output torque
The phase width for being target to the maximum coordinates control, so as to realize the output of torque capacity.
Such as Fig. 6 (a) is 3. shown, and motor speed is gradually reduced since 1000r/min, is about decelerated to 100r/ by 0.43s
Below min, such as Fig. 6 (b) is 3. shown, and motor position curve parabolically, moves closer to anchor point, and such as Fig. 7 (a) is 3. shown, electricity
Machine needs to be accelerated with torque capacity, and the maximum electromagnetic torque in this stage remains -17.85Nm, and such as Fig. 7 (b) is 3. shown,
Current phasor amplitude is determined for maximum current Im, i.e. 16.9A, such as Fig. 7 (c) be 3. shown, and square angle ε is maintained at the-(θ of pi/2 ± 0.5b) in,
I.e. -105 °~-75 °.
The third, with the phase width control method for coordinating of the minimum target of position deviation：
When operating motor is decelerated near anchor point by braking moment, and speed it is relatively low when can make to turn there is provided one
The sub given electromagnetic torque T being parked in just at the minimum anchor point of position deviatione *, now give electromagnetic torque Te *For given value,
The phase angle and amplitude of given stray currents vector should give electromagnetic torque T according to known to this simultaneouslye *It is adjusted；
Phase width coordinates rate-determining steps：
The first step, detects the mechanical Angle Position of rotor：
The mechanical Angle Position θ of rotor is detected by position detecting module 5m, choose number of pole-pairs be p motor, then A phases around
The number of the axis of group is p, the mechanical Angle Position θmUsing the axial location of one of A phase windings as 0 starting；
Second step, the phase angle of given stray currents vector is calculated with rated current：
For balanced load torque, using rated current IrThe phase of the given stray currents vector of estimation, is coordinated to control by phase width
Molding block 1 is by the mechanical Angle Position θ detected in the first stepmBring formula (6) into,
In formula, round represents the computing that rounds up, and % represents complementation, and symbol " ± " refers to when the electromagnetic torque side of exerting oneself
To it is identical with positive direction when, take "+", when electromagnetic torque go out force direction it is opposite with positive direction when, take "-", the positive direction is face
To the counter clockwise direction of motor output shaft, wherein θb=2 π/bHFor step angle；
Given stray currents vector i is obtained according to formula (6)s(k) sequence number, further according to given stray currents vector is(k)
Sequence number can determine the position of given stray currents vector, that is, give the phase angle k θ of stray currents vectorb；
3rd step, calculates the amplitude of given stray currents vector：
Known given electromagnetic torque Te *, Te=Te* is made, by square angle ε=k θb-pθmBring formula (2) into, formula can be obtained
(7)：
So as to obtain the amplitude of given stray currents vector according to formula (7)；
4th step, the given stray currents vector of output：
To calculate that the obtained amplitude of given stray currents vector and being calculated according to second step obtains according to the 3rd step to
Determine the phase angle k θ of stray currents vectorbCurrent control module is given to, using appointing in current hysteresis-band control or electric current PID control
A kind of current control method controlled motor current following of anticipating gives electric current, so as to realize the minimum control of position deviation.
Such as Fig. 6 (a) is 4. shown, and motor speed is gradually decrease to zero, and such as Fig. 6 (b) is 4. shown, and motor position convergence is simultaneously reached
At given position 200rad, about 0.2s is taken to complete stability, such as Fig. 7 (a) is 4. shown, and motor is in electromagnetic torque and load torque
Slow down under collective effect, with the reduction of rotating speed, electromagnetic torque is gradually reduced, and when motor reaches anchor point, electromagnetic torque is
Zero, such as Fig. 7 (b) is 4. shown, and given current phasor amplitude is gradually decrease to zero from maximum current 17A, and such as Fig. 7 (c) is 4. shown, square
Angle ε absolute value starts to reduce, with the process of motor convergence anchor point, and the process for increasing twice and reducing is passed through at square angle, most
Whole square angle tends to 0, and now motor reaches anchor point, and position error is less than 0.015rad, about 0.085 °.
By the test data obtained in embodiment, among the whole service process of motor, by adopting stage by stage
With phase width control method for coordinating, it is possible to achieve speed up time is short, only 0.62s, and make it that torque pulsation is small, be only ± 1Nm,
In motor position fixing process, from motor position convergence and given position is reached, only about 0.2s, final motor are taken to complete stability
Position error be less than 0.015rad, about 0.085 °, improve the positioning precision of motor, therefore this method had both played exchange
Step-by -step drive compensate for that speed overshoot present in existing exchange stepper control method is big, torque again in low speed, the advantage of positioning
Excessive, positioning time length of pulsing and the not high deficiency of positioning precision.
Claims (1)
1. a kind of motor operation control method that phase width based on stray currents vector is coordinated, it is characterised in that the control method
It is the different requirements of three kinds of controls of the carry out phase width coordination control in motor operation course：The first, with output torque most
Greatly target, second, with the minimum target of torque pulsation and the third, with the minimum target of position deviation, respectively to electric current
The phase angle and amplitude of vector carry out coordination control, and specific method is as follows：
Control method equipment therefor described in I,：
The control method equipment therefor, including phase width coordinating control module, current control module, power circuit, motor, position
Detection module and current detection module；Phase width coordinating control module one end is connected with current control module, and the other end is examined with position
Module is surveyed to be connected；Current control module is connected with the signal control end of power circuit, the output end of power circuit by wire with
Motor is connected, and wire passes through current detection module, and current detection module is connected with current control module again, position detecting module
It is co-axially mounted with motor；
Three kinds of different control targes that control method described in II, is directed to progress phase width coordination control in motor operation course are right respectively
The phase angle and amplitude of current phasor carry out phase width and coordinate comprising the following steps that for control：
The first, is the phase width control method for coordinating of target to the maximum with output torque：
When motor quickly rises or slowed down, it is necessary to export maximum electromagnetic torque according to following formula (2),
Wherein ε is square angle, i.e. current phasor isWith rotor flux ψrBetween angle, obtain maximum electromagnetic torque should meet give from
Dissipate current phasor amplitude | is| it is maximum Im, square angle ε is in the θ of pi/2 ± 0.5bInterior change, wherein θb=2 π/bHFor step angle, bHFor
Discrete step number, Te is electromagnetic torque；
Phase width, which coordinates rate-determining steps, to be included：
The first step, detects the mechanical Angle Position of rotor：
Phase width coordinating control module detects the mechanical Angle Position θ of rotor by position detecting modulem, choose the electricity that number of pole-pairs is p
Machine, then the number of the axis of A phase windings is p, the mechanical Angle Position θmUsing the axial location of one of A phase windings as 0 starting；
Second step, calculates the position of given stray currents vector：
By phase width coordinating control module by the mechanical Angle Position θ detected in the first stepmFormula (3) is substituted into, is counted according to formula (3)
Calculate the given stray currents vector i of institutes(k) sequence number：
In formula, round represents the computing that rounds up；% represents complementation；Symbol " ± " refer to when electromagnetic torque go out force direction with
When positive direction is identical, take "+", when electromagnetic torque go out force direction it is opposite with positive direction when, take "-", the positive direction is towards electricity
The counter clockwise direction of machine output shaft,
According to given stray currents vector is(k) sequence number can determine the position of given stray currents vector, that is, give discrete electrical
The phase angle k θ of flow vectorb；
3rd step, the given stray currents vector of output：
By given stray currents vector is(k) amplitude | is|=ImThe phase angle k of the given stray currents vector obtained with second step
θbCurrent control module is given to, using any one current control method control in current hysteresis-band control or electric current PID control
Current of electric processed follows given electric current, so as to realize the maximum control of output torque；
Second, with the phase width control method for coordinating of the minimum target of torque pulsation：
When motor travels at the uniform speed, it is desirable to which the electromagnetic torque of motor output should meet motor torque equilibrium equation with load torque,
Formula (4) is met,
In formula, TLFor load torque, J is rotary inertia, and ω is the angular rate of motor；
Now, given electromagnetic torque T is madee *Equal to load torque TL, and make Te=Te*, then give stray currents vector magnitude |
is| according to formula (2) by given electromagnetic torque Te *Calculating is obtained, when square angle ε is in the θ of pi/2 ± 0.5bDuring interior change so that torque
Pulsation is minimum, wherein θb=2 π/bHFor step angle；
Phase width coordinates rate-determining steps：
The first step, detects the mechanical Angle Position of rotor：
Phase width coordinating control module detects the mechanical Angle Position θ of rotor by position detecting modulem, choose the electricity that number of pole-pairs is p
Machine, then the number of the axis of A phase windings is p, the mechanical Angle Position θmUsing the axial location of one of A phase windings as 0 starting；
Second step, calculates the position of given stray currents vector：
By phase width coordinating control module by the mechanical Angle Position θ detected in the first stepmSubstitute into formula (3)
In formula, round represents the computing that rounds up, and % represents complementation；Symbol " ± " refer to when electromagnetic torque go out force direction with
Positive direction simultaneously, takes "+", when electromagnetic torque go out force direction it is opposite with positive direction when, take "-", the positive direction is towards motor
The counter clockwise direction of output shaft,
The given stray currents vector i of institute is calculated according to formula (3)s(k) sequence number, further according to given stray currents vector is(k)
Sequence number can determine the position of given stray currents vector, that is, give the phase angle k θ of stray currents vectorb；
3rd step, calculates given stray currents vector magnitude：
According to given electromagnetic torque and the equilibrium relation T of load torquee *=TLIt can obtain Te *, make Te=Te*, then by sin ε=1
And Te *Formula (2) is substituted into, formula (5) can be obtained：
In control, T can be obtained by load-toque estimate deviceLEstimate, so as to obtain given stray currents according to formula (5)
The amplitude of vector；
4th step, the given stray currents vector of output：
By giving of calculating that the obtained amplitude of given stray currents vector and being calculated according to second step obtains according to the 3rd step from
Dissipate the phase angle k θ of current phasorbCurrent control module is given to, using any one in current hysteresis-band control or electric current PID control
Plant current control method controlled motor current following and give electric current, so as to realize the minimum control of torque pulsation；
The third, with the phase width control method for coordinating of the minimum target of position deviation：
When operating motor is decelerated near anchor point by braking moment, and speed it is relatively low when rotor can be made proper there is provided one
The given electromagnetic torque T at the minimum anchor point of position deviation is parked in welle *, now give electromagnetic torque Te *For given value, give
The phase angle and amplitude of stray currents vector should give electromagnetic torque T according to known to this simultaneouslye *It is adjusted；
Phase width coordinates rate-determining steps：
The first step, detects the mechanical Angle Position of rotor：
The mechanical Angle Position θ of rotor is detected by position detecting modulem, choose axle of the number of pole-pairs for p motor, then A phase windings
The number of line is p, the mechanical Angle Position θmUsing the axial location of one of A phase windings as 0 starting；
Second step, the phase angle of given stray currents vector is calculated with rated current：
For balanced load torque, using rated current IrThe phase of the given stray currents vector of estimation, by phase width coordinating control module
By the mechanical Angle Position θ detected in the first stepmFormula (6) is substituted into,
In formula, round represents the computing that rounds up, and % represents complementation, symbol " ± " refer to when electromagnetic torque go out force direction with
When positive direction is identical, take "+", when electromagnetic torque go out force direction it is opposite with positive direction when, take "-", the positive direction is towards electricity
The counter clockwise direction of machine output shaft, wherein θb=2 π/bHFor step angle；
Given stray currents vector i is obtained according to formula (6)s(k) sequence number, further according to given stray currents vector is(k) sequence
The position of given stray currents vector number can be determined, that is, gives the phase angle k θ of stray currents vectorb；
3rd step, calculates the amplitude of given stray currents vector：
Known given electromagnetic torque Te *, Te=Te* is made, by square angle ε=k θb-pθmFormula (2) is substituted into, formula (7) can be obtained：
So as to obtain the amplitude of given stray currents vector according to formula (7)；
4th step, the given stray currents vector of output：
By giving of calculating that the obtained amplitude of given stray currents vector and being calculated according to second step obtains according to the 3rd step from
Dissipate the phase angle k θ of current phasorbCurrent control module is given to, using any one in current hysteresis-band control or electric current PID control
Plant current control method controlled motor current following and give electric current, so as to realize the minimum control of position deviation.
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| Publication number | Priority date | Publication date | Assignee | Title |
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| GB2390767A (en) * | 2002-07-11 | 2004-01-14 | Visteon Global Tech Inc | Vector control system for permanent magnet synchronous motor |
| CN101741309A (en) * | 2008-11-21 | 2010-06-16 | 上海电机学院 | Directional control device and control method for magnetic field of permanent magnet synchronous motor |
| CN104506107A (en) * | 2015-01-08 | 2015-04-08 | 河北工业大学 | Operation method for stepping dispersion control on permanent magnet brushless direct current motor |
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| JP3328636B2 (en) * | 2000-03-17 | 2002-09-30 | オークマ株式会社 | Vector control method for synchronous reluctance motor |
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| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| GB2390767A (en) * | 2002-07-11 | 2004-01-14 | Visteon Global Tech Inc | Vector control system for permanent magnet synchronous motor |
| CN101741309A (en) * | 2008-11-21 | 2010-06-16 | 上海电机学院 | Directional control device and control method for magnetic field of permanent magnet synchronous motor |
| CN104506107A (en) * | 2015-01-08 | 2015-04-08 | 河北工业大学 | Operation method for stepping dispersion control on permanent magnet brushless direct current motor |
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