CN114759859A - Thrust fluctuation fitting method for segmented linear motor - Google Patents

Thrust fluctuation fitting method for segmented linear motor Download PDF

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CN114759859A
CN114759859A CN202210542554.9A CN202210542554A CN114759859A CN 114759859 A CN114759859 A CN 114759859A CN 202210542554 A CN202210542554 A CN 202210542554A CN 114759859 A CN114759859 A CN 114759859A
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harmonic component
thrust fluctuation
motor
thrust
pitch
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CN114759859B (en
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王明义
康凯
孙钦伟
李立毅
王鑫鑫
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Harbin Institute of Technology
Shanghai Micro Electronics Equipment Co Ltd
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Shanghai Micro Electronics Equipment Co Ltd
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    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P25/00—Arrangements or methods for the control of AC motors characterised by the kind of AC motor or by structural details
    • H02P25/02—Arrangements or methods for the control of AC motors characterised by the kind of AC motor or by structural details characterised by the kind of motor
    • H02P25/06—Linear motors
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P23/00—Arrangements or methods for the control of AC motors characterised by a control method other than vector control
    • H02P23/14—Estimation or adaptation of motor parameters, e.g. rotor time constant, flux, speed, current or voltage
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P2205/00—Indexing scheme relating to controlling arrangements characterised by the control loops
    • H02P2205/01—Current loop, i.e. comparison of the motor current with a current reference

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  • Power Engineering (AREA)
  • Control Of Linear Motors (AREA)

Abstract

A method for fitting sectional linear motor thrust fluctuation belongs to the technical field of motor thrust compensation. The invention aims at the problems that the thrust fluctuation harmonic component of a segmented linear motor is complex and the existing thrust fluctuation fitting mode is not applicable. The method comprises the following steps: acquiring a thrust fluctuation waveform of the segmented linear motor in a full stroke range; carrying out Fourier transform on the thrust fluctuation waveform, and dividing a spectrogram after Fourier transform into an intra-segment region and an inter-segment region according to harmonic features of corresponding positions of the rotor relative to the stator segments; and respectively carrying out thrust fluctuation fitting according to the intra-segment region and the inter-segment region to obtain an intra-segment region thrust fluctuation fitting result expression and an inter-segment region thrust fluctuation fitting result expression which embody the relationship between thrust fluctuation and a position function. The invention reduces the harmonic frequency to be considered and simplifies the feedforward compensation calculation of thrust fluctuation.

Description

Thrust fluctuation fitting method for segmented linear motor
Technical Field
The invention relates to a thrust fluctuation fitting method for a segmented linear motor, and belongs to the technical field of motor thrust compensation.
Background
In the field of precise position control of linear motors, thrust fluctuation has been a major concern of research and attention.
In order to further expand the application field of linear motors, segmented linear motors with long stroke gradually appear, and the linear motor is mainly different from the traditional linear motor in that the thrust fluctuation characteristic of the linear motor in the transition stage between the segments is different from that of the segmented region; the waveform of the thrust of the conventional linear motor generally presents a harmonic characteristic with a pole pitch as a period, as shown in fig. 12; however, in the inter-segment region of the segmented linear motor, the harmonic component of the thrust fluctuation is more complex, and there are both the thrust fluctuation harmonic component with the slot pitch as the period and the harmonic component with the tooth pitch as the period, as shown in fig. 2. Therefore, the traditional thrust fluctuation fitting mode is not suitable for the segmented linear motor.
Disclosure of Invention
The invention provides a thrust fluctuation fitting method for a segmented linear motor, aiming at the problems that the thrust fluctuation harmonic component of the segmented linear motor is complex and the existing thrust fluctuation fitting mode is not applicable.
The invention relates to a thrust fluctuation fitting method of a segmented linear motor, which comprises the following steps,
acquiring a thrust fluctuation waveform of the segmented linear motor in a full stroke range;
carrying out Fourier transform on the thrust fluctuation waveform, and dividing a spectrogram after Fourier transform into an intra-segment region and an inter-segment region according to harmonic features of corresponding positions of the rotor relative to the stator segments;
And respectively carrying out thrust fluctuation fitting according to the intra-segment region and the inter-segment region to obtain an intra-segment region thrust fluctuation fitting result expression and an inter-segment region thrust fluctuation fitting result expression which embody the functional relation between thrust fluctuation and position.
According to the thrust fluctuation fitting method of the segmented linear motor, the thrust embodied by the expression of the thrust fluctuation fitting result of the segmented region and the expression of the thrust fluctuation fitting result of the inter-segment region is converted into the thrust fluctuation compensation current for realizing the feedforward compensation of the linear motor.
According to the method for fitting the thrust fluctuation of the segmented linear motor, the region in the segment is analyzed, and the components of the thrust fluctuation are determined to comprise harmonic components of 0.5 time, 1 time and 2 times of the motor polar distance.
According to the thrust fluctuation fitting method of the segmented linear motor, the expression of the fitting result of the thrust fluctuation of the segmented area is as follows:
Figure BDA0003650106880000021
in the formula
Figure BDA0003650106880000022
As a value of the fitted thrust fluctuation a1Is 0.5 times of the amplitude of the sinusoidal harmonic component of the motor pole pitch, b1Is 0.5 times of the amplitude of cosine harmonic component of the motor polar distance, v is the rotor speed, tau is the motor polar distance, x is the rotor position,
Figure BDA0003650106880000023
is 0.5 times of initial phase angle, psi, of sinusoidal harmonic component of motor pole pitch1The initial phase angle is 0.5 times of the cosine harmonic component of the pole pitch of the motor; a is 2Is 1 times of amplitude of sinusoidal harmonic component of motor pole distance, b2Is 1 time of the amplitude of cosine harmonic component of the pole distance of the motor,
Figure BDA0003650106880000024
initial phase angle of 1 times of motor pole pitch sine harmonic component2The initial phase angle is 1 time of the cosine harmonic component of the pole distance of the motor; a is3Is 2 times of amplitude of sinusoidal harmonic component of motor pole distance, b3Is 2 times of the amplitude of the cosine harmonic component of the pole distance of the motor,
Figure BDA0003650106880000025
is 2 timesInitial phase angle, psi, of the sinusoidal harmonic component of the motor pole pitch3Is the initial phase angle of 2 times of the cosine harmonic component of the pole pitch of the motor.
According to the method for fitting the thrust fluctuation of the segmented linear motor, provided by the invention, the inter-segment region is analyzed, and the components of the thrust fluctuation are determined to comprise harmonic components of 0.75 time, 1 time and 2 times of the pitch of the stator.
According to the thrust fluctuation fitting method of the segmented linear motor, the expression of the thrust fluctuation fitting result of the inter-segment area is as follows:
Figure BDA0003650106880000026
in the formula a4Is the amplitude of the sinusoidal harmonic component of 0.75 times the stator pitch, b4Is 0.75 times of the amplitude, tau, of the cosine harmonic component of the pitch of the statorsIn order to obtain the pitch of the stator teeth,
Figure BDA0003650106880000027
initial phase angle, ψ, of 0.75 times stator pitch sine harmonic component4An initial phase angle of 0.75 times the cosine harmonic component of the stator pitch; a is5Is the amplitude of the sinusoidal harmonic component of 1 time of the stator pitch, b 5Is the amplitude of the cosine harmonic component of 1 time of the stator pitch,
Figure BDA0003650106880000028
initial phase angle of sinusoidal harmonic component of 1 times stator pitch, #5The initial phase angle is 1 time of the cosine harmonic component of the stator pitch; a is a6Is the amplitude of the sinusoidal harmonic component of 2 times the stator pitch, b6Is the amplitude of the cosine harmonic component of 2 times of the stator pitch,
Figure BDA0003650106880000029
initial phase angle of sinusoidal harmonic component of 2 times stator pitch, psi6Is the initial phase angle of the cosine harmonic component of 2 times the stator pitch.
The invention has the beneficial effects that: according to the method, the stroke of the motor is divided into two parts, namely an inter-section part and an intra-section part, to be compensated respectively according to the main harmonic characteristics of the harmonic waves; compared with the existing mode, the method reduces the number of harmonic waves to be considered, and simplifies the feedforward compensation calculation of thrust fluctuation.
Experiments prove that the method can well compensate the position control error caused by thrust fluctuation under the conditions of high speed and low speed, and can effectively reduce the position control error caused by the thrust fluctuation of the segmented linear motor.
Drawings
FIG. 1 is a flow chart of a thrust ripple fitting method of a segmented linear motor according to the present invention;
FIG. 2 is a thrust ripple waveform of the segmented linear motor of the present invention;
FIG. 3 is a spectral plot of FIG. 2 after Fourier transformation;
FIG. 4 is a Fourier analysis of the intra-segment region of FIG. 3;
FIG. 5 is a Fourier analysis of the inter-segment region of FIG. 3;
FIG. 6 is a plot of a split zone thrust ripple fit waveform for both intra-zone and inter-zone zones;
FIG. 7 is a block diagram of the use of the thrust ripple value obtained by the method of the present invention for feed forward compensation of a linear motor;
FIG. 8 shows a reference trajectory and a position error of the mover at a low speed v of 20mm/s without compensation for thrust fluctuations;
FIG. 9 shows a reference trajectory and a position error of the mover at a high speed v of 400mm/s without compensation for thrust fluctuations;
fig. 10 is a position error after compensating the reference trajectory of the mover when v is 20mm/s shown in fig. 8 by using the thrust fluctuation value obtained by the method of the present invention;
FIG. 11 shows a position error of the mover after compensation of the reference trajectory when v is 400mm/s as shown in FIG. 9, using the thrust fluctuation value obtained by the method of the present invention;
fig. 12 is a waveform diagram of thrust fluctuations of a conventional linear motor.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
It should be noted that the embodiments and features of the embodiments of the present invention may be combined with each other without conflict.
The invention is further described with reference to the following drawings and specific examples, which are not intended to be limiting.
First embodiment, referring to fig. 1, the present invention provides a method for fitting thrust fluctuation of a segmented linear motor, including,
acquiring a thrust fluctuation waveform of the segmented linear motor in a full stroke range;
carrying out Fourier transform on the thrust fluctuation waveform, and dividing a spectrogram after Fourier transform into an intra-segment region and an inter-segment region according to harmonic features of corresponding positions of the rotor relative to the stator segments;
and respectively carrying out thrust fluctuation fitting according to the intra-segment region and the inter-segment region to obtain an intra-segment region thrust fluctuation fitting result expression and an inter-segment region thrust fluctuation fitting result expression which embody the functional relation between thrust fluctuation and position.
Further, with reference to fig. 7, the thrust embodied by the intra-segment thrust fluctuation fitting result expression and the inter-segment thrust fluctuation fitting result expression is converted into a thrust fluctuation compensation current for realizing the feedforward compensation of the linear motor.
The thrust fluctuation suppression of the conventional linear motor shown in fig. 12 can be subjected to fourier analysis, each subharmonic component with a polar distance as a period is extracted, the component with a larger amplitude is adopted to reconstruct the thrust fluctuation, and feedforward compensation is performed according to a position command; however, this method has a great problem in the implementation of the segmented linear motor, and the fourier analysis may be performed on the segmented linear motor shown in fig. 2 to obtain a spectrogram as shown in fig. 3.
As can be seen from fig. 3, the thrust harmonic of the discontinuous segmented linear motor is very complex, and the fitting mode needs to consider many times of harmonic components, for example, thrust harmonics such as 0.5 times, 0.75 times, 1 time, 1.25 times, 1.5 times, 2 times pole pitch need to be considered, and the specific fitting expression is as follows:
Figure BDA0003650106880000041
wherein ai and bi are the sine and cosine amplitudes of 0.5 times, 0.75 times, 1 time, 1.25 times, 1.5 times and 2 times of the motor pole distance harmonic component,
Figure BDA0003650106880000042
and psi i are the sine and cosine initial phase angles of the motor pole pitch harmonic components 0.5 times, 0.75 times, 1 times, 1.25 times, 1.5 times, and 2 times, respectively, i being 1, 2, 3, 4, 5, 6; from the above formula, it can be seen that the thrust fluctuation fitting of the full stroke of the discontinuous segmented linear motor increases the complexity of the fitting formula, the number of parameters to be fitted is up to 24, and meanwhile, the calculation burden of the real-time processor is also increased when the real-time control calculation is performed.
In the embodiment, a strategy of piecewise fitting is provided for thrust fluctuation of the piecewise linear motor, and in the aspect of compensation, position instruction signals are adopted to generate feedforward compensation instead of traditional position instruction signals; firstly, a piecewise fitting strategy is adopted, thrust fluctuation of the piecewise linear motor is divided into two parts, namely an inter-segment part and an intra-segment part, according to main harmonic characteristics of harmonic waves, and harmonic components of the divided thrust fluctuation are shown in figures 4 and 5.
Still further, as shown in fig. 4, the intra-segment region is analyzed, and based on the correlation theory analysis and the FFT result, the intra-segment region can be known, and the components determining the thrust fluctuation include harmonic components of 0.5 times, 1 time, and 2 times of the motor pole pitch.
The expression of the fitting result of the thrust fluctuation of the segmented area is as follows:
Figure BDA0003650106880000051
in the formula
Figure BDA0003650106880000052
As a value of the fitted thrust fluctuation a1Is 0.5 times of the amplitude of the sinusoidal harmonic component of the motor pole pitch, b1Is 0.5 times of the amplitude of cosine harmonic component of the motor polar distance, v is the speed of the rotor, tau is the motor polar distance, x is the position of the rotor, and is measured by a grating ruler,
Figure BDA0003650106880000053
is 0.5 times of initial phase angle, psi, of sinusoidal harmonic component of motor pole pitch1The initial phase angle is 0.5 times of the cosine harmonic component of the pole pitch of the motor; a is 2Is 1 time of the amplitude of the sine harmonic component of the motor pole distance, b2Is 1 time of the amplitude of the cosine harmonic component of the pole distance of the motor,
Figure BDA0003650106880000054
initial phase angle of 1 time motor pole pitch sine harmonic component psi2The initial phase angle is 1 time of the cosine harmonic component of the pole distance of the motor; a is3Is 2 times of amplitude of sinusoidal harmonic component of motor pole distance, b3Is 2 times of the amplitude of the cosine harmonic component of the pole distance of the motor,
Figure BDA0003650106880000055
is the initial phase angle of 2 times of the sine harmonic component of the motor pole pitch, psi3Is the initial phase angle of 2 times of the cosine harmonic component of the pole pitch of the motor.
The number of parameters of the region fitting in the segment is only 12, so that the calculation process is simplified.
Still further, as shown in fig. 5, the inter-segment region is analyzed in the same principle as the analysis of the intra-segment region, and it is determined that the components of the thrust fluctuation include harmonic components of 0.75 times, 1 time, and 2 times the stator pitch.
The expression of the fitting result of the thrust fluctuation of the intersegmental region is as follows:
Figure BDA0003650106880000056
in the formula a4Amplitude of the sinusoidal harmonic component at 0.75 times the pole pitch, b4Is the amplitude, tau, of the cosine harmonic component at 0.75 times the pole pitchsIn order to obtain the pitch of the stator teeth,
Figure BDA0003650106880000057
initial phase angle, ψ, of 0.75 times pole pitch sine harmonic component4Is 0.75 times the initial phase angle of the cosine harmonic component of the pole pitch.
The expression is also fitted with 12 parameters.
Therefore, the fitting difficulty can be reduced on the one hand by the segmented fitting thrust fluctuation mode, and meanwhile, the burden of a real-time processor can be further reduced.
The main harmonic component of each segment of the region is extracted from fig. 4 and 5, and the thrust fluctuation waveform in the whole stroke range is obtained by fitting, as shown in fig. 6. The method of fitting in a subarea mode reduces the number of harmonic waves to be considered, and simplifies the feedforward compensation calculation of thrust fluctuation.
Referring to fig. 7, the thrust value determined by the method of the present invention may be used to compensate thrust of the linear motor. In FIG. 7, r is a reference position, iq1Current command, i, output for position loop controllerqffFor feed-forward compensation of the current command, iq *For the current loop, iqrCompensating the current command for thrust fluctuations, kfIs the thrust coefficient of the motor, M is the mass of the rotor of the motor, B is the viscous friction coefficient of the guide rail of the motor, FlFor load thrust, FdThe external disturbance thrust of the motor is adopted; i.e. iqfFor motor feedback current, L is motor inductance parameter, R is motor resistance parameter, s is frequency domain operation symbol, TsIs an inverter equivalent time constant, ωeIs angular velocity, #fIs a no-load permanent magnet flux linkage, tauoiIs a current feedback low pass filter time constant.
And (3) experimental verification:
building a segmented linear motor experiment platform, testing by adopting a two-degree-of-freedom control mode of PI + advanced control and acceleration feedforward by a position controller through low-speed and high-speed experiments, setting two groups of test conditions totally, and setting the S curve maximum speed of rotor motion to be v respectively1＝20mm/s，v2400mm/s, corresponding acceleration a01＝500mm/s2，a02＝5000mm/s2The moving range of the rotor is 420mm to 840mm, the position control error obtained by not performing feedforward compensation on thrust fluctuation is shown in fig. 8 and 9, and the waveform compensated by the method of the invention is shown in fig. 10 and 11, so that the position control error caused by the thrust fluctuation can be well compensated by the sub-region fitting compensation method and the thrust fluctuation feedforward compensation method based on position feedback under the conditions of high speed and low speed.
Although the invention herein has been described with reference to particular embodiments, it is to be understood that these embodiments are merely illustrative of the principles and applications of the present invention. It is therefore to be understood that numerous modifications may be made to the illustrative embodiments and that other arrangements may be devised without departing from the spirit and scope of the present invention as defined by the appended claims. It should be understood that various dependent claims and the features described herein may be combined in ways different from those described in the original claims. It is also to be understood that features described in connection with individual embodiments may be used in other described embodiments.

Claims (6)

1. A thrust fluctuation fitting method of a segmented linear motor is characterized by comprising the following steps,
acquiring a thrust fluctuation waveform of the segmented linear motor in a full stroke range;
carrying out Fourier transform on the thrust fluctuation waveform, and dividing a spectrogram after Fourier transform into an intra-segment region and an inter-segment region according to harmonic features of corresponding positions of the rotor relative to the stator segments;
and respectively carrying out thrust fluctuation fitting according to the intra-segment region and the inter-segment region to obtain an intra-segment region thrust fluctuation fitting result expression and an inter-segment region thrust fluctuation fitting result expression which embody the relationship between thrust fluctuation and a position function.
2. The piecewise linear motor thrust ripple fitting method of claim 1,
and the thrust embodied by the intra-segment region thrust fluctuation fitting result expression and the inter-segment region thrust fluctuation fitting result expression is converted into a thrust fluctuation compensation current for realizing feedforward compensation of the linear motor.
3. The piecewise linear motor thrust fluctuation fitting method of claim 1 or 2,
the area within the segment is analyzed to determine the components of the thrust ripple including harmonic components of 0.5, 1 and 2 times the motor pole pitch.
4. The piecewise linear motor thrust fluctuation fitting method of claim 3,
the expression of the fitting result of the thrust fluctuation of the intra-segment area is as follows:
Figure FDA0003650106870000011
in the formula
Figure FDA0003650106870000012
For the fitted thrust fluctuation value, a1Is 0.5 times of the amplitude of the sinusoidal harmonic component of the motor pole pitch, b1Is 0.5 times of the amplitude of cosine harmonic component of the motor polar distance, v is the rotor speed, tau is the motor polar distance, x is the rotor position,
Figure FDA0003650106870000013
is 0.5 times of the sine harmonic component of the motor pole pitchInitial phase angle of1The initial phase angle is 0.5 times of the cosine harmonic component of the pole pitch of the motor; a is2Is 1 time of the amplitude of the sine harmonic component of the motor pole distance, b2Is 1 time of the amplitude of the cosine harmonic component of the pole distance of the motor,
Figure FDA0003650106870000014
initial phase angle of 1 time motor pole pitch sine harmonic component psi2The initial phase angle is 1 time of the cosine harmonic component of the pole distance of the motor; a is3Is 2 times of amplitude of sinusoidal harmonic component of motor pole distance, b3Is 2 times of the amplitude of the cosine harmonic component of the pole distance of the motor,
Figure FDA0003650106870000015
is the initial phase angle of 2 times of the sine harmonic component of the motor pole pitch, psi3Is the initial phase angle of 2 times of the cosine harmonic component of the pole pitch of the motor.
5. The piecewise linear motor thrust fluctuation fitting method of claim 1 or 2,
the intersegment region was analyzed to determine the components of the thrust ripple including harmonic components of 0.75, 1 and 2 times the stator pitch.
6. The piecewise linear motor thrust fluctuation fitting method of claim 5,
the expression of the fitting result of thrust fluctuation of the intersegmental region is as follows:
Figure FDA0003650106870000021
in the formula a4Amplitude of the sinusoidal harmonic component of 0.75 times the stator pitch, b4Is 0.75 times of the amplitude, tau, of the cosine harmonic component of the pitch of the statorsIn order to obtain the pitch of the stator teeth,
Figure FDA0003650106870000022
is 0.75 timesInitial phase angle, ψ, of the sinusoidal harmonic component of the stator pitch4An initial phase angle of 0.75 times the cosine harmonic component of the stator pitch; a is5Is the amplitude of the sinusoidal harmonic component of 1 time of the stator pitch, b5Is 1 times the amplitude of the cosine harmonic component of the stator pitch,
Figure FDA0003650106870000023
initial phase angle of sinusoidal harmonic component of 1 times stator pitch, psi5The initial phase angle is 1 time of the cosine harmonic component of the stator pitch; a is6Is the amplitude of the sinusoidal harmonic component of 2 times the stator pitch, b6Is 2 times of the amplitude of the cosine harmonic component of the stator pitch,
Figure FDA0003650106870000024
initial phase angle of sinusoidal harmonic component of 2 times stator pitch, psi6Is the initial phase angle of the cosine harmonic component of 2 times the stator pitch.
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Citations (7)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
WO2009146821A1 (en) * 2008-06-06 2009-12-10 Robert Bosch Gmbh Reduction of force ripple in a permanent magnet linear synchronous motor
JP2011120454A (en) * 2009-10-29 2011-06-16 Yaskawa Electric Corp Linear motor control apparatus
CN103346721A (en) * 2013-06-19 2013-10-09 江苏大学 Thrust ripple suppressing method of primary permanent magnet linear motor
US20140239855A1 (en) * 2013-02-25 2014-08-28 National Taiwan University Thrust ripple mapping system in a precision stage and method thereof
CN106130432A (en) * 2016-07-07 2016-11-16 中国矿业大学 A kind of permanent magnetic linear synchronous motor force oscillation suppression technology based on complex controll
CN113219907A (en) * 2021-03-13 2021-08-06 浙江御穹电子科技有限公司 System and method for identifying disturbance force of precision motion platform
CN113746298A (en) * 2021-09-08 2021-12-03 哈尔滨工业大学 Thrust fluctuation optimization design method for moving-magnet type primary discontinuous segmented linear motor

Patent Citations (7)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
WO2009146821A1 (en) * 2008-06-06 2009-12-10 Robert Bosch Gmbh Reduction of force ripple in a permanent magnet linear synchronous motor
JP2011120454A (en) * 2009-10-29 2011-06-16 Yaskawa Electric Corp Linear motor control apparatus
US20140239855A1 (en) * 2013-02-25 2014-08-28 National Taiwan University Thrust ripple mapping system in a precision stage and method thereof
CN103346721A (en) * 2013-06-19 2013-10-09 江苏大学 Thrust ripple suppressing method of primary permanent magnet linear motor
CN106130432A (en) * 2016-07-07 2016-11-16 中国矿业大学 A kind of permanent magnetic linear synchronous motor force oscillation suppression technology based on complex controll
CN113219907A (en) * 2021-03-13 2021-08-06 浙江御穹电子科技有限公司 System and method for identifying disturbance force of precision motion platform
CN113746298A (en) * 2021-09-08 2021-12-03 哈尔滨工业大学 Thrust fluctuation optimization design method for moving-magnet type primary discontinuous segmented linear motor

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