CN108107734B - Electromechanical coupling modeling method for permanent magnet synchronous linear motor feeding system - Google Patents
Electromechanical coupling modeling method for permanent magnet synchronous linear motor feeding system Download PDFInfo
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Abstract
The invention provides an electromechanical coupling modeling method for a permanent magnet synchronous linear motor feeding system, which comprises the following steps: 1. analyzing and calculating the frequency spectrum characteristic of the servo output thrust of the permanent magnet synchronous linear motor by using an electromagnetic energy method; 2. establishing a mechanical dynamics model of a permanent magnet synchronous linear motor feeding system by utilizing a Lagrange equation; 3. analyzing the mutual coupling interaction relation between a servo drive of a permanent magnet synchronous linear motor feeding system and a mechanical system; 4. and establishing a multi-factor coupling electromechanical coupling model of the permanent magnet synchronous linear motor feeding system according to the mutual coupling interaction relationship between the servo drive and the mechanical system. The method can quickly and effectively analyze the essential rules of various coupling problems in the system. Meanwhile, the influence of various electromechanical couplings on the motion stability of the system is evaluated quickly and reliably. Further supplementing new changes caused by electromechanical coupling problems and perfecting the integrated modeling method of the complex electromechanical system.
Description
Technical Field
The invention relates to the field of dynamic performance analysis of high-speed numerical control machines, in particular to an electromechanical coupling modeling method for a permanent magnet synchronous linear motor feeding system.
Background
In recent years, with the increasing demand of high efficiency and high precision of numerical control machining, the permanent magnet linear motor feeding system has wide application prospect in high-grade numerical control machines due to the advantages of high thrust, high speed, high acceleration, high precision and the like. The unique zero transmission structure of the linear motor feeding system enables the thrust of the motor to directly act on a mechanical system, and mechanical oscillation caused by factors such as external interference and the like also directly acts on the motor. The mutual coupling relationship between the servo drive and the mechanical system is tighter, and the mutual coupling relationship becomes an important factor influencing the motion stability of the linear motor feeding system. Particularly, a linear motor feeding system actually applied to a numerical control machine tool is not an ideal single-inertia system, is influenced by characteristics of various dynamic joint parts, has a multi-order oscillation mode, and can aggravate a coupling relation between systems and deteriorate motion precision of the systems.
In the current research and analysis work, the electromechanical coupling problem in the permanent magnet synchronous linear motor feeding system is not deeply analyzed and researched due to the neglect of the dynamic characteristic of a mechanical system. Moreover, under the influence of multiple factors of audiences, a phenomenon that servo driving and a mechanical system are not in electromechanical coupling exists, and coupling loops have mutual influence, so that the difficulty of research and analysis is increased. How the electromechanical coupling problem can be modeled and analyzed systematically is of great significance for further controlling and improving the influence of the coupling.
Disclosure of Invention
Aiming at the problems in the prior art, the invention provides the electromechanical coupling modeling method for the permanent magnet synchronous linear motor feeding system, which can quickly and effectively analyze and characterize several types of typical electromechanical coupling phenomena in the system, reveal the essential law of coupling, quantitatively describe the influence of the coupling on the motion stability of the system, and has important significance for the evaluation and control improvement of the electromechanical coupling problems.
The invention is realized by the following technical scheme:
an electromechanical coupling modeling method for a permanent magnet synchronous linear motor feeding system comprises the following steps:
analyzing and calculating the frequency spectrum characteristic of the servo output thrust of the permanent magnet synchronous linear motor by using an electromagnetic energy method;
establishing a mechanical dynamics model of a permanent magnet synchronous linear motor feeding system by utilizing a Lagrange equation;
analyzing the mutual coupling interaction relationship between the servo drive of the permanent magnet synchronous linear motor feeding system and the mechanical system based on the servo output thrust frequency spectrum characteristic in the first step and the mechanical dynamics model of the feeding system in the second step from three aspects of the influence of linear motor air gap change caused by mechanical torsional oscillation, mechanical oscillation caused by thrust harmonic and mechanical torsional oscillation on grating ruler feedback signals;
step four, establishing a multi-factor coupling electromechanical coupling model of the permanent magnet synchronous linear motor feeding system according to the mutual coupling interaction relationship between the servo drive and the mechanical system obtained in the step three,
f is the thrust of the permanent magnet synchronous linear motor, k is a, b and c, and represents three phases of a, b and c of a motor coil; elkAnd EmkArmature back-emf and no-load back-emf, i, of the three-phase coil, respectivelykV is the motor motion speed; f0' nominal thrust of the machine taking into account the variation of the air gap, Fr' to account for the original thrust harmonics of the machine with air gap variation, FgTo account for the new thrust harmonic component of the air gap variation, xiIs an instruction signal, xoFor the displacement output signal, Gp(s) is the position loop control transfer function, s is the differential operator, Gv(s) is the velocity loop control transfer function, KAIs a current loop equivalent proportional gain, KFIs the motor thrust constant, FmFor the motor to output a nominal thrust, FrFor outputting harmonic forces to the machine, Gmf(s) is a model of the direction of feed of the mechanical system, Gmi(s) is a mechanical other direction dynamics model, △ delta is an encoder error generated by mechanical torsional oscillation, Ge(s) is a transfer function between encoder error and mechanical torsional oscillation; x is the number ofδ0Is a feedback signal that takes into account encoder error.
Preferably, in the first step, according to the structural composition of the driving circuit, various nonlinear factors including dead zone harmonics, modulation harmonics and back electromotive force harmonics in the driving circuit and various nonlinear factors including cogging effect, end effect and flux linkage harmonics in the motor structure are comprehensively considered, and the electromagnetic energy method is utilized to calculate the frequency spectrum characteristic of the thrust F of the permanent magnet synchronous linear motor as follows,
F＝∑(Elk+Emk)·ik/v。
preferably, in step two, the motion of the table along and about three axes, i.e., { x, y, z, θ }, is taken regardless of the flexibility of the tablex，θy，θz}TIs a generalized coordinate; neglecting the mutual coupling effect among all the vibration modes, establishing a mechanical dynamics equation of the linear motor feeding system by utilizing a Lagrange equation,
wherein X ═ X y z θxθyθz]TIn order to displace the working table, the displacement of the working table is controlled,
the first derivative and the second derivative of X are respectively, M, C and K are respectively a mass matrix, a damping matrix and a rigidity matrix, and F is an external force matrix.
Preferably, when the linear motor air gap change caused by the mechanical torsional oscillation is considered in the third step, a relative magnetic conductance function is introduced to describe the influence of the mechanical torsional oscillation on the motor air gap magnetic field, and the motor output thrust considering the air gap change is calculated by using an electromagnetic energy method,
F＝F′0+F′r+Fg。
preferably, when mechanical oscillation caused by thrust harmonic waves is considered in the third step, a PID-based three-loop control model is established, wherein a position loop adopts P control, a speed loop adopts PI control, a current loop is equivalent to proportional gain, and the motor output thrust obtained in the first step is introduced in an interference mode; the dynamic characteristics of the mechanical system in other directions except the feeding direction are respectively equivalent to relatively independent second-order oscillation systems to be introduced into the model, each parameter in the model is obtained through experimental identification, and finally an electromechanical integration model of the system under the thrust harmonic action is established,
[(xi-x0)·Gp(s)-x0·s]·Gv(s)·KA·KF＝F′0
(F′0+F′r+Fg)·Gmf(s)+∑(F′0+F′r+Fg)·Gmi(s)＝x0。
preferably, in the third step, when the influence of the mechanical torsional oscillation on the feedback signal of the grating scale is considered, based on the working principle of the grating scale, the encoder error generated by the mechanical torsional oscillation is calculated,
Δδ＝∑(F0′+Fr′+Fg)·Gmi(s)·Ge(s)，
and the obtained encoder feedback error is introduced into a feedback control loop to obtain a feedback signal considering the encoder error,
xδ0＝x0+Δδ。
compared with the prior art, the invention has the following beneficial technical effects:
the invention provides an electromechanical coupling modeling method of a permanent magnet synchronous linear motor feeding system aiming at three typical electromechanical coupling phenomena in the system, and can quickly and effectively analyze the essential rules of various coupling problems in the system. Meanwhile, the modeling method provided by the invention can be used for accurately calculating the system displacement fluctuation caused by various electromechanical coupling problems, and quickly and reliably evaluating the influence of various electromechanical couplings on the motion stability of the system. On the basis of the traditional integrated modeling method, the invention further supplements new changes caused by electromechanical coupling problems, perfects the integrated modeling method of a complex electromechanical system, and has important significance for tracing the motion error of the linear motor feeding system and analyzing, optimizing and improving the electromechanical coupling problems.
Drawings
Fig. 1 is a schematic structural diagram of a permanent magnet synchronous linear motor feeding system in an embodiment of the invention.
Fig. 2 is an electromechanical coupling model of a permanent magnet synchronous linear motor feeding system according to the present invention.
FIG. 3 shows the results of a frequency spectrum analysis of the thrust of the electric motor of the bench according to the example of the invention.
FIG. 4 shows the results of the shift fluctuation spectrum analysis of the bench according to the example of the present invention.
In the figure: 1 is a workbench; 2 is a linear guide rail and a slide block; 3 is a grating ruler scale; 4 is a grating ruler reading head; 5 is a motor rotor; 6 is a motor stator; and 7 is a lathe bed.
Detailed Description
The present invention will now be described in further detail with reference to specific examples, which are intended to be illustrative, but not limiting, of the invention.
The invention discloses an electromechanical coupling modeling method for a permanent magnet synchronous linear motor feeding system, which comprehensively considers servo driving characteristics, mechanical dynamic characteristics and the mutual coupling interaction relationship of the servo driving characteristics and the mechanical dynamic characteristics and establishes an electromechanical coupling model. The method specifically comprises the following steps:
step one, comprehensively considering various nonlinear factors (such as dead zone harmonic, modulation harmonic, back electromotive force harmonic and the like) and motor structure nonlinear factors (such as cogging effect, end effect, flux linkage harmonic and the like) in a driving circuit, and calculating the thrust frequency spectrum characteristic of the permanent magnet synchronous linear motor by using an electromagnetic energy method, namely calculating the thrust frequency spectrum characteristic of the permanent magnet synchronous linear motor
F＝∑(Elk+Emk)·ik/v
Wherein k is a, b and c, and represents three phases a, b and c of the motor coil; elkAnd EmkArmature back electromotive force and no-load back electromotive force of the three-phase coil respectively; i.e. ikServing three-phase current; v is the motor movement speed.
Step two, neglecting the flexibility of the workbench, taking the motion of the workbench along and around three axes, namely { x, y, z, thetax，θy，θz}TIs a generalized coordinate. Neglecting the mutual coupling effect among all vibration modes, establishing a mechanical dynamics equation of a linear motor feeding system by utilizing a Lagrange equation, namely
Wherein X ═ X y z θxθyθz]TIn order to displace the working table, the displacement of the working table is controlled,
the first derivative and the second derivative of X are respectively, M, C and K are respectively a mass matrix, a damping matrix and a rigidity matrix, and F is an external force matrix.
Step three, firstly considering the air gap change of the linear motor caused by the mechanical torsional oscillation, introducing a relative magnetic conductance function to describe the influence of the mechanical torsional oscillation on the air gap magnetic field of the motor, and calculating by using an electromagnetic energy method to obtain the output thrust of the motor considering the air gap change, namely
F＝F′0+F′r+Fg
Wherein, F'0Nominal thrust of the machine, F ', taking into account the variation of the air gap'rIn order to take account of the original thrust harmonics of the motor, F, of the air gap variationgTo account for new thrust harmonic components of air gap variation.
Secondly, considering mechanical oscillation caused by thrust harmonic waves, establishing a PID-based three-loop control model, wherein a position loop adopts P control, a speed loop adopts PI control, a current loop is equivalent to proportional gain, and the motor output thrust obtained in the step one is introduced in an interference mode; a mechanical system is equivalent to a relatively independent second-order oscillation system, a model is introduced, each parameter in the model is obtained through experimental identification, and finally an electromechanical integration model of the system under the thrust harmonic action, namely the electromechanical integration model is established
[(xi-x0)·Gp(s)-x0·s]·Gv(s)·KA·KF＝F′0
(F′0+F′r+Fg)·Gmf(s)+∑(F′0+F′r+Fg)·Gmi(s)＝x0
Wherein x isiIs an instruction signal, xoFor the displacement output signal, Gp(s) is the position loop control transfer function, s is the differential operator, Gv(s) is the velocity loop control transfer function, KAIs a current loop equivalent proportional gain, KFIs the motor thrust constant, FmFor the motor to output a nominal thrust, FrFor outputting harmonic forces to the machine, Gmf(s) is a model of the direction of feed of the mechanical system, GmiAnd(s) is a mechanical other direction dynamic model.
In addition, considering the influence of the mechanical torsional oscillation on the feedback signal of the grating scale, the encoder error generated by the mechanical torsional oscillation, namely the encoder error is calculated and obtained based on the working principle of the grating scale
Δδ＝∑(F′0+F′r+Fg)·Gmi(s)·Ge(s)
Wherein G ise(s) is the transfer function between encoder error and mechanical torsional oscillations.
The resulting encoder feedback error is introduced into a feedback control loop to obtain a feedback signal that takes into account the encoder error, i.e.
xδ0＝x0+Δδ
Step four, establishing a permanent magnet synchronous linear motor feeding system multi-factor coupling machine electric coupling model based on the interaction relation between the servo drive and the mechanical system obtained in the step three, namely establishing the permanent magnet synchronous linear motor feeding system multi-factor coupling machine electric coupling model
Specifically, as shown in fig. 1, the feeding system of the permanent magnet synchronous linear motor selects a single-axis linear motor feeding experiment table as a test case, displacement signals are collected by a laser interferometer, and the sampling frequency is 10 KHz. The motor thrust is collected by servo self-contained monitoring software, and the sampling frequency is 1 KHz. In the experimental tests, the feed rate was 20 m/min. The method comprises the following specific steps:
1) comprehensively considering various nonlinear factors (such as dead zone harmonic, modulation harmonic, back electromotive force harmonic and the like) and motor structure nonlinear factors (such as cogging effect, end effect, flux linkage harmonic and the like) in a driving circuit, and calculating the thrust frequency spectrum characteristic of the permanent magnet synchronous linear motor by using an electromagnetic energy method, namely calculating the thrust frequency spectrum characteristic of the permanent magnet synchronous linear motor
F＝∑(Elk+Emk)·ik/v＝F0+Fr+Fc+Fe+Fq+FL(1)
Wherein F0Is the nominal thrust of the motor, FrIs ripple thrust of the motor, FcIs the cogging force, FeIs the end force, FqIs ripple gullet coupling force, FLIs an inductive asymmetric harmonic force.
2) Ignoring the flexibility of the table, taking the movement of the table along and about three axes, i.e. { x, y, z, θ }x，θy，θz}TIs a generalized coordinate. Neglecting the mutual coupling effect among all vibration modes, establishing a mechanical dynamics equation of a linear motor feeding system by utilizing a Lagrange equation, namely
Wherein, wherein: x ═ X y z θxθyθz]TIn order to displace the working table, the displacement of the working table is controlled,
the first derivative and the second derivative of X are respectively, M, C and K are respectively a mass matrix, a damping matrix and a rigidity matrix, and F is an external force matrix.
In the test case, the mechanical structure is simple, and the coupling among the modes of the machine can be ignored. In addition, because the natural frequency of the worktable in the y direction and the z direction is high, the damping in the two directions is large, the amplitude of the oscillation response is low, and the analysis of the self-excitation response of the feeding system can not be considered. The subsequent analysis therefore mainly analyzes the vibrations of the table in the feed direction and the torsional vibrations about the respective axes.
3) Firstly, considering linear motor air gap change caused by mechanical torsional oscillation, introducing a relative magnetic conductance function to describe the influence of the mechanical torsional oscillation on a motor air gap magnetic field, and calculating by using an electromagnetic energy method to obtain motor output thrust considering the air gap change, namely
F＝F′0+F′r+Fg(3)
Wherein, F'0Nominal thrust of the machine, F ', taking into account the variation of the air gap'rIn order to take account of the original thrust harmonics of the motor, F, of the air gap variationgTo account for new thrust harmonic components of air gap variation.
In the case, the mechanical torsional oscillation amplitude is small, so that the nominal thrust of the motor and the original harmonic variation of the thrust are small, and when the influence of air gap fluctuation on the motion stability of the feeding system is analyzed, only the new harmonic of the motor thrust generated by the air gap variation is considered.
Secondly, considering mechanical oscillation caused by thrust harmonic waves, establishing a PID-based three-loop control model, wherein a position loop adopts P control, a speed loop adopts PI control, a current loop is equivalent to proportional gain, and the motor output thrust obtained in the step one is introduced in an interference mode; the feeding direction of the mechanical system is equivalent to a single-inertia system, the torsional oscillation in three directions of the mechanical system is equivalent to a relatively independent second-order oscillation system, a model is introduced, each parameter in the model is obtained through experimental identification, and finally an electromechanical integration model of the system under the thrust harmonic action is established, namely the electromechanical integration model is the system under the thrust harmonic action
[(xi-x0)·Gp(s)-x0·s]·Gv(s)·KA·KF＝F′0(4)
(F′0+F′r+Fg)·Gmf(s)+∑(F′0+F′r+Fg)·Gmi(s)＝x0(5)
Wherein x isiIs an instruction signal, xoFor the displacement output signal, Gp(s) is the position loop control transfer function, s is the differential operator, Gv(s) is the velocity loop control transfer function, KAIs a current loop equivalent proportional gain, KFIs the motor thrust constant, FmFor the motor to output a nominal thrust, FrFor outputting harmonic forces to the machine, Gmf(s) is a model of the direction of feed of the mechanical system, Gmi(s) dynamics of other directions of the machineAnd (4) modeling.
In addition, considering the influence of the mechanical torsional oscillation on the feedback signal of the grating scale, the encoder error generated by the mechanical torsional oscillation, namely the encoder error is calculated and obtained based on the working principle of the grating scale
Δδ＝∑(F′0+F′r+Fg)·Gmi(s)·Ge(s) (6)
Wherein G ise(s) is the transfer function between encoder error and mechanical torsional oscillations.
The resulting encoder feedback error is introduced into a feedback control loop to obtain a feedback signal that takes into account the encoder error, i.e.
xδ0＝x0+Δδ (7)
4) The model obtained in the previous step is synthesized, and the electric coupling model of the permanent magnet synchronous linear motor feeding system multi-factor coupling machine is established as shown in figure 2, namely
In FIG. 2, xiIs a command signal, xoTo output a response for the system, KpTo position loop gain, KvFor the gain of the speed loop, TvIntegration time of velocity loop, KFIs a thrust constant, FrThrust harmonics due to encoder error, m drive load, Jx,Jy,JzRotational inertia in three directions of the mechanical system, Cθx,Cθy,CθzDamping of three torsional oscillations of a mechanical system, Kθx,Kθy,KθzTorsional stiffness which is a mechanical three torsional oscillation; my,Mp,MrThe equivalent proportionality coefficients of the motor thrust in three torsion directions are obtained; sy,Sp,SrIs a proportional conversion coefficient between the three torsional oscillations and the feed displacement fluctuation; gp(s),Gy(s) and Gr(s) are transfer functions between the mechanical three-direction torsional oscillations and the encoder error, respectively.
5) The same section of the steady-state process of the thrust and displacement fluctuation data obtained by the experimental test is selected for frequency spectrum analysis, and the results are shown in fig. 3 and 4. In fig. 3, the numbers in parentheses in the thrust spectrum represent the deviation of the theoretical calculation and the actual measurement results; in fig. 4, numerals in parentheses indicate the frequency and amplitude of the corresponding points. According to fig. 3 and 4, the theoretically calculated displacement fluctuation results obtained by the integrated model are compared with the experimentally tested displacement fluctuation results for the main thrust harmonic components, and the results are shown in table 1.
TABLE 1 comparison of theoretical calculation and experimental test results of displacement fluctuation
As can be seen from fig. 3, fig. 4 and table 1, there are various electromechanical coupling phenomena in the linear motor feeding system, which cause the system to fluctuate in steady-state displacement, which is not negligible. The maximum deviation between the displacement fluctuation theory calculation result and the actual measurement result is 5.3%, and the accuracy and the reliability of the electromechanical coupling model calculation result are verified.
Claims (3)
1. An electromechanical coupling modeling method for a permanent magnet synchronous linear motor feeding system is characterized by comprising the following steps:
analyzing and calculating the frequency spectrum characteristic of the servo output thrust of the permanent magnet synchronous linear motor by using an electromagnetic energy method;
establishing a mechanical dynamics model of a permanent magnet synchronous linear motor feeding system by utilizing a Lagrange equation;
analyzing the mutual coupling interaction relationship between the servo drive of the permanent magnet synchronous linear motor feeding system and the mechanical system based on the servo output thrust frequency spectrum characteristic in the first step and the mechanical dynamics model of the feeding system in the second step from three aspects of the influence of linear motor air gap change caused by mechanical torsional oscillation, mechanical oscillation caused by thrust harmonic and mechanical torsional oscillation on grating ruler feedback signals;
when the linear motor air gap change caused by mechanical torsional oscillation is considered, a relative magnetic conductance function is introduced to describe the influence of the mechanical torsional oscillation on the motor air gap magnetic field, an electromagnetic energy method is utilized to calculate and obtain the motor output thrust considering the air gap change,
F＝F0′+Fr′+Fg；
when mechanical oscillation caused by thrust harmonic waves is considered, a PID-based three-loop control model is established, wherein a position loop adopts P control, a speed loop adopts PI control, a current loop is equivalent to proportional gain, and the motor output thrust obtained in the step one is introduced in an interference mode; the dynamic characteristics of the mechanical system in other directions except the feeding direction are respectively equivalent to relatively independent second-order oscillation systems to be introduced into the model, each parameter in the model is obtained through experimental identification, and finally an electromechanical integration model of the system under the thrust harmonic action is established,
[(xi-x0)·Gp(s)-x0·s]·Gv(s)·KA·KF＝F0′
(F0′+Fr′+Fg)·Gmf(s)+∑(F0′+Fr′+Fg)·Gmi(s)＝x0；
when the influence of the mechanical torsional oscillation on the feedback signal of the grating ruler is considered, the encoder error generated by the mechanical torsional oscillation is calculated and obtained based on the working principle of the grating ruler,
Δδ＝∑(F0′+Fr′+Fg)·Gmi(s)·Ge(s)，
and the obtained encoder feedback error is introduced into a feedback control loop to obtain a feedback signal considering the encoder error,
xδ0＝x0+Δδ；
step four, establishing a multi-factor coupling electromechanical coupling model of the permanent magnet synchronous linear motor feeding system according to the mutual coupling interaction relationship between the servo drive and the mechanical system obtained in the step three,
f is the thrust of the permanent magnet synchronous linear motor, k is a, b and c, and represents three phases of a, b and c of a motor coil; elkAnd EmkArmature back-emf and no-load back-emf, i, of the three-phase coil, respectivelykV is the motor motion speed; f0' nominal thrust of the machine taking into account the variation of the air gap, Fr' to account for the original thrust harmonics of the machine with air gap variation, FgTo account for the new thrust harmonic component of the air gap variation, xiIs an instruction signal, xoFor the displacement output signal, Gp(s) is the position loop control transfer function, s is the differential operator, Gv(s) is the velocity loop control transfer function, KAIs a current loop equivalent proportional gain, KFIs the motor thrust constant, FmFor the motor to output a nominal thrust, FrFor outputting harmonic forces to the machine, Gmf(s) is a model of the direction of feed of the mechanical system, Gmi(s) is a mechanical other direction dynamic model; delta delta is the encoder error, G, due to mechanical torsional oscillationse(s) is a transfer function between encoder error and mechanical torsional oscillation; x is the number ofδ0Is a feedback signal that takes into account encoder error.
2. The electromechanical coupling modeling method for the permanent magnet synchronous linear motor feeding system according to claim 1, characterized in that in the step one, according to the structural composition of the driving circuit, various nonlinear factors including dead zone harmonics, modulation harmonics and back electromotive force harmonics in the driving circuit and various nonlinear factors including cogging, end effect and flux linkage harmonics in the motor structure are comprehensively considered, and the electromagnetic energy method is utilized to calculate the frequency spectrum characteristic of the permanent magnet synchronous linear motor thrust F as follows,
F＝∑(Elk+Emk)·ik/v。
3. the electromechanical coupling modeling method for the feeding system of the permanent magnet synchronous linear motor according to claim 1, characterized in that in the second step, the motion of the worktable along and around three axes (x, y, z, theta) is obtained by neglecting the flexibility of the worktablex，θy，θz}TIs a generalized coordinate; neglecting the mutual coupling effect among all the vibration modes, establishing a mechanical dynamics equation of the linear motor feeding system by utilizing a Lagrange equation,
wherein X ═ X y z θxθyθz]TIn order to displace the working table, the displacement of the working table is controlled,
the first derivative and the second derivative of X are respectively, M, C and K are respectively a mass matrix, a damping matrix and a rigidity matrix, and F is an external force matrix.
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Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| RU2430397C2 (en) * | 2009-11-17 | 2011-09-27 | Открытое акционерное общество "Научно-исследовальский институт "Субмикрон" | Electrohydraulic servo drive adaptive control system |
| 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 |
| CN106849791A (en) * | 2017-01-05 | 2017-06-13 | 江苏大学 | It is a kind of to suppress the sliding mode speed control method based on internal model that permanent-magnetism linear motor mismatches disturbance |
| CN107203184A (en) * | 2017-06-20 | 2017-09-26 | 南京理工大学 | The dynamic control method of straight line steering wheel Electric Loading System |
| CN108021039A (en) * | 2017-12-23 | 2018-05-11 | 西安交通大学 | A kind of Linear motor feeding system electromechanics integrated modelling approach |
Family Cites Families (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN101340173A (en) * | 2008-04-30 | 2009-01-07 | 沈阳工业大学 | Method for suppressing pulse of linear motor pushing force system |
| CN202713223U (en) * | 2012-06-11 | 2013-01-30 | 桂林电子科技大学 | Non-linear interference control system for permanent magnetism synchronization linear motor |
-
2017
- 2017-12-23 CN CN201711411778.1A patent/CN108107734B/en active Active
Patent Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| RU2430397C2 (en) * | 2009-11-17 | 2011-09-27 | Открытое акционерное общество "Научно-исследовальский институт "Субмикрон" | Electrohydraulic servo drive adaptive control system |
| 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 |
| CN106849791A (en) * | 2017-01-05 | 2017-06-13 | 江苏大学 | It is a kind of to suppress the sliding mode speed control method based on internal model that permanent-magnetism linear motor mismatches disturbance |
| CN107203184A (en) * | 2017-06-20 | 2017-09-26 | 南京理工大学 | The dynamic control method of straight line steering wheel Electric Loading System |
| CN108021039A (en) * | 2017-12-23 | 2018-05-11 | 西安交通大学 | A kind of Linear motor feeding system electromechanics integrated modelling approach |
Non-Patent Citations (4)
| Title |
|---|
| 永磁同步直线电机复杂机电耦合系统分析与控制方法;曾理湛;《中国博士学位论文全文数据库》;20111015;全文 * |
| 永磁直线同步电机的建模及控制方法研究;武轲;《中国优秀硕士学位论文全文数据库》;20120115;全文 * |
| 高加速精密直线电机运动平台键合图建模与分析;孙立宁;《机器人》;20110731;全文 * |
| 高精数控机床永磁直线进给系统机电耦合法向振动研究;宁建荣;《中国博士学位论文全文数据库》;20130715;全文 * |
Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| EP4224704A1 (en) * | 2022-02-03 | 2023-08-09 | Volkswagen Aktiengesellschaft | Electronically commutated electric machine having a plurality of sub-machines and method for operating such an electric machine |
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