CN109379011B - Ripple thrust compensation method of permanent magnet synchronous linear servo system based on MP algorithm - Google Patents

Ripple thrust compensation method of permanent magnet synchronous linear servo system based on MP algorithm Download PDF

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CN109379011B
CN109379011B CN201811108988.8A CN201811108988A CN109379011B CN 109379011 B CN109379011 B CN 109379011B CN 201811108988 A CN201811108988 A CN 201811108988A CN 109379011 B CN109379011 B CN 109379011B
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thrust
ripple
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servo system
atom
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CN109379011A (en
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卢少武
余信中
龙丁
李汐
周凤星
马娅婕
严保康
但峰
胡轶
宁博文
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Guangdong Samson Technology Co ltd
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Wuhan University of Science and Engineering WUSE
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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
    • H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
    • 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
    • H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
    • H02P21/14—Estimation or adaptation of machine parameters, e.g. flux, 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
    • H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
    • H02P21/14—Estimation or adaptation of machine parameters, e.g. flux, current or voltage
    • H02P21/18—Estimation of position or speed

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Abstract

The invention discloses a ripple thrust compensation method of a permanent magnet synchronous linear servo system based on an MP algorithm, which constructs ripple thrust feedforward compensation by adopting the MP algorithm in the permanent magnet synchronous linear servo system to realize high-precision position control of the linear servo system and comprises the following steps: constructing a ripple thrust model and an overcomplete atom library thereof; extracting a thrust current signal and actual position feedback of a permanent magnet synchronous linear servo system, performing optimal atom matching on the thrust current signal through a matching tracking algorithm, performing repeated iterative decomposition on an original signal, and selecting the optimally matched atom signal from an over-complete atom library; and reconstructing ripple thrust based on the matched atomic signals, acquiring model parameters of the ripple thrust in real time, performing feedforward compensation, and realizing high-precision position control of the permanent magnet synchronous linear servo system. The invention enables the ripple thrust to be identified and compensated in real time in the actual motor work, and has the advantages of simple control structure, strong disturbance resistance, fast speed response and the like.

Description

Ripple thrust compensation method of permanent magnet synchronous linear servo system based on MP algorithm
Technical Field
The invention relates to the technical field of high-frequency-response permanent magnet synchronous linear servo systems, in particular to a ripple thrust compensation method of a permanent magnet synchronous linear servo system based on an MP algorithm.
Background
The basic task of the position loop of the permanent magnet synchronous linear servo system is to realize accurate position tracking and positioning of the permanent magnet synchronous linear motor according to a given motion track, so that the deviation between position input and position output does not exceed an allowable range. The permanent magnet synchronous linear motor does not need an intermediate transmission device, so that the transmission rigidity of the permanent magnet synchronous linear motor is directly improved, but various disturbances (such as ripple thrust and the like) are directly acted on the permanent magnet synchronous linear motor, and no buffer or weakening link exists. In industrial application, a position loop of a permanent magnet synchronous linear servo system usually only adopts a pure P controller to inhibit system overshoot and keep certain robustness, so that various disturbances directly cause instability and performance reduction of the permanent magnet synchronous linear servo system in the operation process of a permanent magnet synchronous linear motor, and the permanent magnet synchronous linear servo system needs to have good disturbance resistance capability to inhibit various disturbances in order to realize high-precision position control.
The ripple thrust is a main disturbance factor influencing a permanent magnet synchronous linear servo system, a mathematical model of the ripple thrust is the sum of a plurality of sine functions related to the actual position, and the amplitude and the frequency of each sine function are unknown. Therefore, it is difficult to accurately model the ripple thrust during operation of the motor. The traditional ripple thrust identification method comprises the steps of firstly keeping the running state of a motor in an ideal low-speed and constant-speed state, enabling displacement and system running time to have a linear relation, calculating a characteristic frequency proportion coefficient of ripple thrust by using a frequency spectrum of thrust current, and then carrying out online estimation on the amplitude of the ripple thrust by adopting an identification algorithm. A ripple thrust amplitude identification method based on least square is proposed in the literature (S.ZHao, and K.K.Tan, Adaptive feedback compensation of force in linear motors [ J ], Control Engineering Practice,2005,13(9): 1081-; documents (S.Lu, X.Tang, B.Song, and S.Zheng, Identification and compensation of force application in PMSLM using a JITL technique [ J ], Asian Journal of Control,2015,17(5): 1559-. Meanwhile, the identification method can only identify the amplitude under the condition that the ripple thrust characteristic frequency proportionality coefficient is obtained offline in advance, and the requirements of low speed, constant speed and the like are harsh in the actual motor operation process, so the practical value of the method is limited. In view of the defects of the two compensation methods, the invention aims to adopt a permanent magnet synchronous linear servo system ripple thrust online compensation method based on a Matching Pursuit (MP) algorithm to identify ripple thrust model parameters in real time and compensate.
Disclosure of Invention
The technical problem to be solved by the invention is to provide an online compensation method for ripple thrust of a permanent magnet synchronous linear servo system based on a Matching Pursuit (MP) algorithm aiming at the defects in the prior art, and the online compensation method is used for replacing the traditional ripple thrust compensation method by ripple thrust feedforward compensation constructed by using the MP algorithm, so that high-precision position control of the permanent magnet synchronous linear servo system is realized. The compensation method can adapt to the high-frequency response characteristic of the permanent magnet synchronous linear motor, quickly track the position instruction of the system, and adapt to high-speed and high-precision application occasions with the nonlinear characteristics of load quality, load force and the like.
The technical scheme adopted by the invention for solving the technical problems is as follows:
the invention provides a ripple thrust compensation method of a permanent magnet synchronous linear servo system based on an MP algorithm, which constructs ripple thrust feedforward compensation by adopting a matching tracking algorithm in the permanent magnet synchronous linear servo system to realize high-precision position control of the permanent magnet synchronous linear servo system, and comprises the following steps:
s1, constructing a ripple thrust model and an over-complete atom library of the ripple thrust model;
s2, extracting a thrust current signal and actual position feedback of the permanent magnet synchronous linear servo system, taking the thrust current signal as an input original signal, performing optimal atom matching on the thrust current signal through a matching tracking algorithm, performing repeated iterative decomposition on the original signal, and selecting the optimal matched atom signal from an over-complete atom library;
and S3, reconstructing ripple thrust based on the matched atomic signals, acquiring model parameters of the ripple thrust in real time, and performing feedforward compensation to realize high-precision position control of the permanent magnet synchronous linear servo system.
Further, the method for constructing the ripple thrust model and the overcomplete atom library thereof in step S1 of the present invention specifically includes:
given overcomplete atom pool D1＝{gγ(ii) a 1,2, K, and D2＝{hγ(ii) a 1,2,.., K }, element g in the atom libraryγ、hγReferred to as atoms;
defining a thrust current signal as an input original signal: s ═ iq(k) (ii) a S is the original signal, iq(k) Is a thrust current signal;
setting the position signal instruction of the permanent magnet synchronous linear servo system as follows: thetar(k)＝sin(2π×f×k)；
The time domain model of ripple thrust is defined as:
Figure BDA0001808602310000031
Figure BDA0001808602310000032
Figure BDA0001808602310000033
the overcomplete atomic pool atoms of ripple thrust are therefore:
gγ(β,k)＝sin(2π×β×sin(2π×f×k))
hγ(β,k)＝cos(2π×β×sin(2π×f×k))
wherein the frequency of the ripple thrust is proportional to the position; beta is a characteristic frequency proportionality coefficient; f is the servo system position command frequency; thetafIs the actual position of the servo system, and the frequency characteristic and thetarSubstantially the same;
Figure BDA00018086023100000311
an initial phase angle of ripple thrust is obtained; a. the1、A2Beta is a model parameter to be identified; atom gγ、hγIs equal to the thrust current iqLength of (d).
Further, the present invention in step S2 is from the overcomplete atom library fripple1In the selected atom signal gγbestThe method comprises the following steps:
first, for gγ(k) And (3) carrying out energy normalization:
Figure BDA0001808602310000034
wherein the content of the first and second substances,
Figure BDA0001808602310000035
<.,.>representing the inner product operation of the two signals;
then, selecting atoms from the over-complete atom library one by one to carry out inner product with the original signal, and preliminarily decomposing the thrust current signal into:
Figure BDA0001808602310000036
wherein the remainder R after decomposition1The signal is a residual signal, namely a mixed signal of a thrust current main wave and noise;
Figure BDA0001808602310000037
and R1Is orthogonal, then we get:
Figure BDA0001808602310000038
in order to make the residual energy | | | R1||2Atom g selected for the smallest of all residual energiesγSo that
Figure BDA0001808602310000039
Maximum, i.e. the result satisfies:
Figure BDA00018086023100000310
wherein sup represents the supremum of the atomic inner product, even if the atomic inner product is the largest.
Further, in step S2 of the present invention, the residual signal is further decomposed to select and f from the overcomplete atom libraryripple2Atom h with most matched signalγbestThe specific method comprises the following steps:
first to hγ(k) And (3) carrying out energy normalization:
Figure BDA0001808602310000041
selecting atoms from an over-complete atom library one by one to carry out inner product with an original signal, and preliminarily decomposing the signal into:
Figure BDA0001808602310000042
wherein the remainder R after decomposition2Residual errors after the secondary decomposition are obtained;
Figure BDA0001808602310000043
and R2Is orthogonal, then we get:
Figure BDA0001808602310000044
to make it possible toResidual energy R2||2Atom h selected for the smallest of all residual energiesγSo that
Figure BDA0001808602310000045
Maximum; namely, the result satisfies:
Figure BDA0001808602310000046
wherein sup represents the supremum of the atomic inner product, even if the atomic inner product is the largest.
Further, in step S3, the ripple thrust is reconstructed based on the matched atomic signals, the model parameters of the ripple thrust are obtained in real time, and the method for performing the feedforward compensation specifically includes:
the original thrust current signal is expressed as follows after two times of decomposition:
Figure BDA0001808602310000047
due to the fact that
Figure BDA0001808602310000048
And
Figure BDA0001808602310000049
are respectively fripple2And fripple2The ripple thrust signal is represented by the best atomic approximation as:
Figure BDA00018086023100000410
the optimal atoms approach the original thrust current signals infinitely, and the model structure is the same as the ripple thrust model structure; at the moment, the time domain parameter of the optimal atom reconstruction is taken as the time domain parameter of the ripple thrust, and the model parameter beta of the ripple thrust is obtained by identification*：
Taking the parameter beta one by one at any time kThe same value is obtained to obtain a series of atoms g with different beta valuesγThen the original thrust current signal is made to be the normalized atom
Figure BDA00018086023100000411
Carrying out inner product one by one, and obtaining the atom with the largest inner product value with the thrust current
Figure BDA00018086023100000412
Then obtaining a parameter model most matched with the ripple thrust, wherein the beta value is the ripple thrust parameter beta to be identified*：
Figure BDA00018086023100000413
Wherein arg represents the value of the variable β taken when the inner product is maximized;
amplitude A of ripple thrust1、A2Then this can be obtained from:
Figure BDA0001808602310000051
Figure BDA0001808602310000052
thereby obtaining all model parameters to be identified of the ripple thrust and further obtaining the feedforward compensation quantity i of the ripple thrustqfComprises the following steps:
Figure BDA0001808602310000053
wherein k isfIs a thrust current constant;
the position loop control quantity of the permanent magnet synchronous linear servo system is as follows:
Figure BDA0001808602310000054
wherein iqb(k) Is the thrust current feedback component through the position loop PID controller.
The invention has the following beneficial effects:
1. under the condition that the structure of a controlled object model is known, a Matching Pursuit (MP) algorithm is adopted, specific constraint conditions of the traditional algorithm are not needed, dynamic parameters of the ripple thrust model are directly matched according to current and past thrust current data, the algorithm is strong in real-time performance, and the identification precision is high.
2. The method further expands the application range of the sparse decomposition Matching Pursuit (MP) algorithm, and the Matching Pursuit (MP) algorithm can effectively identify the model parameters of the ripple thrust under the condition that the system is globally stable.
3. The invention can meet the requirement of high-speed and high-precision position control of a permanent magnet synchronous linear servo system, and the system can also automatically complete position ring ripple thrust compensation aiming at the application occasions of nonlinear characteristics such as load quality, load force and the like.
Drawings
The invention will be further described with reference to the accompanying drawings and examples, in which:
fig. 1 is a schematic view of a vector control structure of a permanent magnet synchronous linear servo system according to an embodiment of the present invention.
FIG. 2 is a flowchart of a Matching Pursuit (MP) algorithm according to an embodiment of the present invention.
Fig. 3 is a schematic structural diagram of the ripple thrust feedforward compensation principle of the embodiment of the invention.
Fig. 4 is a flow chart of ripple thrust feed forward compensation according to an embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
FIG. 1 is a schematic view of a vector control structure of a permanent magnet synchronous linear servo system according to the present invention. In practical engineering applications, i is usually adopteddApproximate decoupling of the currents is achieved as 0. In fig. 2, the extracted thrust current signal is subjected to optimal atomic matching by a Matching Pursuit (MP) algorithm, and iterative decomposition is performed for a plurality of times to obtain an atomic signal most matched with the ripple thrust model parameter, and then the atomic signal is reconstructed to match the model parameter of the original ripple thrust signal to the maximum extent.
The basic principle of the ripple thrust feedforward compensation method based on the Matching Pursuit (MP) algorithm is shown in FIG. 3. After the position ring ripple thrust model parameters are obtained, the ripple thrust at the moment k +1 is predicted, so that online feedforward compensation is performed on the thrust current, and the best matching atoms of the ripple thrust at the next moment are corrected according to the feedback thrust current, so that the online feedforward compensation of the ripple thrust is realized, and the requirements of transient response and disturbance rejection capability of the permanent magnet synchronous linear servo system are met.
The ripple thrust feedforward compensation flow chart of the permanent magnet synchronous linear servo system based on the Matching Pursuit (MP) algorithm is shown in fig. 4, and mainly includes the following steps:
firstly, constructing an over-complete atom library, and specifically comprising the following steps:
given overcomplete atom pool D1＝{gγ(ii) a 1,2, K, and D2＝{hγ(ii) a 1,2,.., K }, element g in the atom libraryγ、hγReferred to as atoms.
Defining the original signal as the thrust current:
S＝iq(k)
setting servo system position signal commands as follows:
θr(k)＝sin(2π×f×k)
the time domain model of ripple thrust is defined as:
Figure BDA0001808602310000061
Figure BDA0001808602310000062
Figure BDA0001808602310000063
the overcomplete atomic pool atoms of ripple thrust are therefore:
gγ(β,k)＝sin(2π×β×sin(2π×f×k))
hγ(β,k)＝cos(2π×β×sin(2π×f×k))
wherein the frequency of the ripple thrust is proportional to the position; beta is a characteristic frequency proportionality coefficient; f is the servo system position command frequency; thetafIs the actual position of the servo system, and the frequency characteristic and thetarSubstantially the same;
Figure BDA0001808602310000071
an initial phase angle of ripple thrust is obtained; a. the1、A2Beta is a model parameter to be identified; atom gγ、hγIs equal to the thrust current iqLength of (d).
Second, select and from the overcomplete libraryripple1Atom g with most matched signalγbestThe method comprises the following specific steps:
first, for gγ(k) And (3) carrying out energy normalization:
Figure BDA0001808602310000072
wherein the content of the first and second substances,
Figure BDA0001808602310000073
<.,.>representing the inner product operation of the two signals.
Then, atoms are selected from the over-complete atom library one by one to be subjected to inner product with the original signals, and the thrust current signals can be preliminarily decomposed into:
Figure BDA0001808602310000074
wherein the remainder R after decomposition1The signal is a residual signal, namely a mixed signal of a thrust current main wave and noise.
It is obvious that
Figure BDA0001808602310000075
And R1Is orthogonal, then one can get:
Figure BDA0001808602310000076
in order to make the residual energy | | | R1||2Atom g selected for the smallest of all residual energiesγTo make it possible to
Figure BDA0001808602310000077
Maximum, i.e. the result satisfies:
Figure BDA0001808602310000078
wherein sup represents the supremum of the atomic inner product, even if the atomic inner product is the largest.
Thirdly, the residual signal is decomposed continuously, and the sum f is selected from the over-complete libraryripple2Atom h with most matched signalγbestThe method comprises the following specific steps:
first to hγ(k) And (3) carrying out energy normalization:
Figure BDA0001808602310000079
then, selecting atoms from the over-complete atom library one by one to carry out inner product with the original signal, and preliminarily decomposing the signal into:
Figure BDA0001808602310000081
wherein the remainder R after decomposition2As residual error after re-decomposition。
It is obvious that
Figure BDA0001808602310000082
And R2Is orthogonal, then one can get:
Figure BDA0001808602310000083
in order to make the residual energy | | | R2||2Atom h selected for the smallest of all residual energiesγTo make it possible to
Figure BDA0001808602310000084
Maximum, i.e. the result satisfies:
Figure BDA0001808602310000085
wherein sup represents the supremum of the atomic inner product, even if the atomic inner product is the largest.
And fourthly, performing signal reconstruction based on the matched atomic signals, acquiring model parameters of the ripple thrust signal in real time, and performing feedforward compensation, wherein the method specifically comprises the following steps:
finally, after the original thrust current signal is decomposed twice, the thrust current signal can be expressed as:
Figure BDA0001808602310000086
due to the fact that
Figure BDA0001808602310000087
And
Figure BDA0001808602310000088
are respectively fripple2And fripple2The ripple thrust signal can be represented by the best atomic approximation as:
Figure BDA0001808602310000089
the optimal atoms approach the original thrust current signals infinitely, and the model structure is the same as the ripple thrust model structure; at the moment, the time domain parameter of the optimal atom reconstruction can be used as the time domain parameter of the ripple thrust, and the model parameter beta of the ripple thrust can be identified and obtained*：
At any time k, different values of the parameter beta are taken one by one to obtain a series of atoms g with different beta valuesγThen the original thrust current signal is made to be the normalized atom
Figure BDA00018086023100000810
Carrying out inner product one by one, and obtaining the atom with the largest inner product value with the thrust current
Figure BDA00018086023100000811
Then obtaining a parameter model most matched with the ripple thrust, wherein the beta value is the ripple thrust parameter beta to be identified*：
Figure BDA00018086023100000812
Here, arg represents the value of the variable β taken when the inner product is maximized.
And the amplitude A of the ripple thrust1、A2Then this can be obtained from:
Figure BDA00018086023100000813
Figure BDA00018086023100000814
thereby obtaining all the model parameters to be identified of the ripple thrust. The ripple thrust feedforward compensation quantity i can be obtainedqf。
Figure BDA0001808602310000091
Wherein k isfIs the thrust current constant.
The position loop control quantity of the permanent magnet synchronous linear servo system is as follows:
Figure BDA0001808602310000092
wherein iqb(k) Is the thrust current feedback component through the position loop PID controller.
The method of the invention utilizes ripple thrust feedforward compensation constructed by a Matching Pursuit (MP) algorithm to replace the traditional ripple thrust compensation method, so that the ripple thrust can be identified and compensated in real time in the actual motor work, and the method has the advantages of simple control structure, strong disturbance resistance, fast speed response and the like.
It will be understood that modifications and variations can be made by persons skilled in the art in light of the above teachings and all such modifications and variations are intended to be included within the scope of the invention as defined in the appended claims.

Claims (5)

1. A ripple thrust compensation method of a permanent magnet synchronous linear servo system based on a matching pursuit algorithm is characterized in that a ripple thrust feedforward compensation is constructed by adopting the matching pursuit algorithm in the permanent magnet synchronous linear servo system, so that the high-precision position control of the permanent magnet synchronous linear servo system is realized, and the method comprises the following steps:
s1, constructing a ripple thrust model and an over-complete atom library of the ripple thrust model;
s2, extracting a thrust current signal and actual position feedback of the permanent magnet synchronous linear servo system, taking the thrust current signal as an input original signal, performing optimal atom matching on the thrust current signal through a matching tracking algorithm, performing repeated iterative decomposition on the original signal, and selecting the optimal matched atom signal from an over-complete atom library;
and S3, reconstructing ripple thrust based on the matched atomic signals, acquiring model parameters of the ripple thrust in real time, and performing feedforward compensation by combining with actual position feedback to realize high-precision position control of the permanent magnet synchronous linear servo system.
2. The ripple thrust compensation method of the permanent magnet synchronous linear servo system based on the matching pursuit algorithm according to claim 1, wherein the method for constructing the ripple thrust model and the overcomplete atom library thereof in the step S1 specifically comprises:
given overcomplete atom pool D1＝{gγ(ii) a 1,2, K, and D2＝{hγ(ii) a 1,2,.., K }, element g in the atom libraryγ、hγReferred to as atoms;
defining a thrust current signal as an input original signal: s ═ iq(k) (ii) a S is the original signal, iq(k) Is a thrust current signal;
setting the position signal instruction of the permanent magnet synchronous linear servo system as follows: thetar(k)＝sin(2π×f×k)；
The time domain model of ripple thrust is defined as:
Figure FDA0003265020580000011
Figure FDA0003265020580000012
Figure FDA0003265020580000013
the overcomplete atomic pool atoms of ripple thrust are therefore:
gγ(β,k)＝sin(2π×β×sin(2π×f×k))
hγ(β,k)＝cos(2π×β×sin(2π×f×k))
wherein A is the amplitude of ripple thrust modelThe frequency of the ripple thrust is proportional to the position; beta is a characteristic frequency proportionality coefficient; f is the servo system position command frequency; thetafIs the actual position of the servo system;
Figure FDA0003265020580000021
an initial phase angle of ripple thrust is obtained; a. the1、A2Beta is a model parameter to be identified; atom gγ、hγIs equal to the thrust current iqLength of (d).
3. The ripple thrust compensation method of a permanent magnet synchronous linear servo system based on a matching pursuit algorithm according to claim 2, wherein the atomic signal with the best matching is selected from the overcomplete atomic library in step S2, and the method specifically comprises:
first, for gγ(k) And (3) carrying out energy normalization:
Figure FDA0003265020580000022
wherein the content of the first and second substances,
Figure FDA0003265020580000023
<.,.>representing the inner product operation of the two signals;
then, selecting atoms from the over-complete atom library one by one to carry out inner product with the original signal, and preliminarily decomposing the thrust current signal into:
Figure FDA0003265020580000024
wherein the remainder R after decomposition1The signal is a residual signal, namely a mixed signal of a thrust current main wave and noise;
Figure FDA0003265020580000025
and R1Is orthogonal, then we get:
Figure FDA0003265020580000026
in order to make the residual energy | | | R1||2Atom g selected for the smallest of all residual energiesγSo that
Figure FDA0003265020580000027
Maximum, i.e. the result satisfies:
Figure FDA0003265020580000028
wherein sup represents the supremum of the atomic inner product, even if the atomic inner product is the largest.
4. The ripple thrust compensation method of permanent magnet synchronous linear servo system based on matching pursuit algorithm of claim 3, wherein the residual signal is decomposed continuously in step S2, and the sum f is selected from the overcomplete atomic libraryripple2Atom h with most matched signalγbestThe specific method comprises the following steps:
first to hγ(k) And (3) carrying out energy normalization:
Figure FDA0003265020580000029
selecting atoms from an over-complete atom library one by one to carry out inner product with an original signal, and preliminarily decomposing the signal into:
Figure FDA00032650205800000210
wherein the remainder R after decomposition2Residual errors after the secondary decomposition are obtained;
Figure FDA00032650205800000211
and R2Is orthogonal, then we get:
Figure FDA00032650205800000212
in order to make the residual energy | | | R2||2Atom h selected for the smallest of all residual energiesγSo that
Figure FDA0003265020580000031
Maximum; namely, the result satisfies:
Figure FDA0003265020580000032
wherein sup represents the supremum of the atomic inner product, even if the atomic inner product is the largest.
5. The ripple thrust compensation method of the permanent magnet synchronous linear servo system based on the matching pursuit algorithm according to claim 4, wherein the ripple thrust reconstruction is performed based on the matched atomic signals in step S3 to obtain model parameters of the ripple thrust in real time, and the method for performing the feedforward compensation specifically comprises:
the original thrust current signal is expressed as follows after two times of decomposition:
Figure FDA0003265020580000033
due to the fact that
Figure FDA0003265020580000034
And
Figure FDA0003265020580000035
are respectively fripple1And fripple2The ripple thrust signal is represented by the best atomic approximation as:
Figure FDA0003265020580000036
the optimal atoms approach the original thrust current signals infinitely, and the model structure is the same as the ripple thrust model structure; at the moment, the time domain parameter of the optimal atom reconstruction is taken as the time domain parameter of the ripple thrust, and the model parameter beta of the ripple thrust is obtained by identification*：
At any time k, different values of the parameter beta are taken one by one to obtain a series of atoms g with different beta valuesγThen the original thrust current signal is made to be the normalized atom
Figure FDA0003265020580000037
Carrying out inner product one by one, and obtaining the atom with the largest inner product value with the thrust current
Figure FDA0003265020580000038
Then obtaining a parameter model most matched with the ripple thrust, wherein the beta value is the ripple thrust parameter beta to be identified*：
Figure FDA0003265020580000039
Wherein arg represents the value of the variable β taken when the inner product is maximized;
amplitude A of ripple thrust1、A2Then this can be obtained from:
Figure FDA00032650205800000310
Figure FDA00032650205800000311
thereby obtaining all model parameters to be identified of the ripple thrust and further obtaining the feedforward compensation quantity i of the ripple thrustqfComprises the following steps:
Figure FDA00032650205800000312
wherein k isfIs a thrust current constant;
the position loop control quantity of the permanent magnet synchronous linear servo system is as follows:
Figure FDA0003265020580000041
wherein iqb(k) Is the thrust current feedback component through the position loop PID controller.
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