CN114567223A - Position tracking method based on repeated supercoiled observer and supercoiled control - Google Patents
Position tracking method based on repeated supercoiled observer and supercoiled control Download PDFInfo
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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
- 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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- 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
- H02P21/13—Observer control, e.g. using Luenberger observers or Kalman filters
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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
- H02P21/14—Estimation or adaptation of machine parameters, e.g. flux, current or voltage
- H02P21/20—Estimation of torque
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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
- H02P6/00—Arrangements for controlling synchronous motors or other dynamo-electric motors using electronic commutation dependent on the rotor position; Electronic commutators therefor
- H02P6/10—Arrangements for controlling torque ripple, e.g. providing reduced torque ripple
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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
- H02P2203/00—Indexing scheme relating to controlling arrangements characterised by the means for detecting the position of the rotor
- H02P2203/03—Determination of the rotor position, e.g. initial rotor position, during standstill or low speed operation
Abstract
The invention discloses a position tracking method based on a repeated supercoiled observer and supercoiled control, which belongs to the technical field of motor control and comprises the following steps: obtaining a state space equation of the motor based on a motion equation of the motor, analyzing the disturbance in motor control from a topological structure of the motor and a motor driving system respectively, and dividing the disturbance into aperiodic disturbance and periodic disturbance; designing a repeated supercoiled observer according to a state space equation of the motor, and compensating the observed disturbance back to the designed supercoiled controller; designing a supercoiled controller, and combining disturbance feedforward compensation to restrain periodic disturbance and non-periodic disturbance in position control. The invention enhances the inhibition capability to periodic disturbance, reduces current ripple, improves the anti-interference capability, reduces the harmonic content when the position of the motor is tracked, improves the tracking precision and reduces the torque ripple of the motor.
Description
Technical Field
The invention belongs to the technical field of motor control, and particularly relates to a position tracking method based on a repeated supercoiled observer and supercoiled control.
Background
Permanent Magnet Arc Motors (PMAMs) have become an ideal choice for large telescopes and scanners because of their advantages of high power density, non-transmission structure, and high dynamic response. However, since the direct drive method is adopted, the torque ripple generated by the motor directly affects the load. And the topological structure can generate a large amount of periodic disturbance, so that the system is required to have strong anti-interference capability in order to realize high-precision position tracking.
Since the parasitic torque ripple of the PMAM is mainly periodic and motor position dependent, the parasitic torque ripple is larger than the disturbances caused by other slow variations (e.g. cogging torque, end torque, flux linkage harmonics, etc.). A highly robust sliding mode controller requires a large gain to suppress the disturbance, but this increases the current ripple of the system and deteriorates the performance of the system. In addition, the parameters of the controller not only affect the anti-interference capability, but also affect the convergence speed, and the two need to be decoupled.
Therefore, in order to realize the high-precision position tracking of the motor, a position tracking method is needed to suppress the disturbance of the permanent magnet arc motor.
Disclosure of Invention
An object of the present invention is to solve the above problems and/or disadvantages and to provide advantages which will be described later.
To achieve these objects of the present invention, there is provided a position tracking method based on a repetitive supercoiled observer and supercoiled control, comprising the steps of:
s1, obtaining a state space equation of the motor based on the motion equation of the motor, analyzing the disturbance in the motor control from two aspects of the motor topological structure and the motor driving system respectively, and dividing the disturbance into non-periodic disturbance and periodic disturbance;
s2, aiming at aperiodic disturbance and periodic disturbance, designing a repeated supercoiled observer according to a state space equation of the motor, and compensating the observed disturbance back to the supercoiled controller designed in the next step, namely performing disturbance feedforward compensation on the supercoiled controller;
and S3, designing a supercoiled controller, and combining disturbance feedforward compensation to restrain periodic disturbance and non-periodic disturbance in position control.
Preferably, the specific implementation manner of S1 includes:
the motion equation expression of the motor is as follows:
wherein the content of the first and second substances,ω m is the rotational speed of the motor and is,Jis the moment of inertia of the motor and,pis the number of the pole pairs of the motor,φ f is a permanent magnet flux linkage of the motor,i q as an electric motorqThe current of the shaft is measured by the current sensor,T l is the load torque of the motor and is,Bis the viscosity coefficient of the motor;
the topological structure of the motor can cause cogging torque and end torque, a corresponding motor driving system can cause periodic torque ripple, and the disturbance caused by the cogging torque, the end torque and the current sampling offset error is respectively expressed as:
wherein the content of the first and second substances,T cog is the torque of the tooth socket, and,θ m is the mechanical angle of the motor and is,T n is thatnThe amplitude of the sub-slot harmonics,zis the least common multiple of the number of rotor teeth and pole pairs,T end is the end-part torque of the motor,T end n,is thatnThe magnitude of the torque at the secondary end,τis the distance between the two poles of the wire,αis a constant, Δ, related to the left and right end momentsT offset Is the disturbance caused by the current sampling offset error,A 1is a positive coefficient, Δi a And Δi b Is the current offset error of motor A, B phase;
the state space equation for the motor is expressed as:
wherein, the first and the second end of the pipe are connected with each other,T e =1.5pφ f i q in order to be an electromagnetic torque,ρandT p a non-periodic component and a periodic component in the motor load torque, respectively.
Preferably, in S2, according to the obtained state space equation of the motor, the repetitive supercoiled observer corresponding to the second-order system is established as follows:
wherein the content of the first and second substances,
an estimate of the rotational speed of the motor is indicated,
is indicative of a disturbance,
an estimate representing a periodic component of the motor load torque,
representing the error between the estimated value and the actual value of the motor speed,l、k 1、k 2andμ 1for a defined repetitive supercoiled observer coefficient,Tin order to be the period of the periodic disturbance,βthe coefficient is a positive coefficient of the number,α 11、α 12andα 22is a positive definite matrixα ij ]2×2Of (1) andl=﹣2α 22/α 12 μ 1；
in a designed repetitive supercoiled observer,ζ 1=k 1 μ 1、ζ 2=Jk 2 μ 1 2 /2 andζ 3=μ 1 β(α 11 μ 1 l+2α 12) In whichζ 1、 ζ 2Andζ 3respectively representing switching functions
The repetitive supercoiled observer records the tracking error of the motor by using a memory, and according to the given iterative learning rate:
updating to enhance the suppression capability of periodic disturbance, and simultaneously, according to the error between the estimated value of the motor rotating speed and the actual value of the motor rotating speed
To the switching function
Updating the estimated values of the motor rotation speed respectively
And the actual value of the motor speedω m Is integrated to obtain the disturbance
In which disturbance occurs
Including non-periodic disturbance and periodic disturbance, error term in formula
Error between estimated value of motor speed and actual value of motor speed
0 will also equal 0 and will not affect observer performance.
Preferably, the supercoiled controller designed in S3 for performing motor position tracking is as follows:
wherein the content of the first and second substances,
it is the torque that is given to the motor,
，
is that the angle is given by the angle,
it is the speed that is given for the speed,cis a positive coefficient of the coefficient,θ m is a mechanical angle of view of the device,ω m is the rotational speed of the motor and is,λ 1andλ 2is the coefficient of the supercoiled controller;
adding the disturbance obtained in S3 to the supercoiled controller
And obtaining a new structure of the superspiral controller as follows:
the purpose of suppressing the periodic disturbance and the non-periodic disturbance in the position control is achieved through the formula.
Preferably, in S3, the parameters of the designed supercoiled controller and the repetitive supercoiled observer are adjusted so that the position tracking methodCan sufficiently suppress disturbance
The specific method comprises the following steps:
suppose that
Then selectλ 1=1.5Δ1/2，λ 2=1.1 Δ, the supercoiled controller can track disturbances normally; furthermore, the coefficients in the repetitive supercoiled observer can be obtained by reduction:
where Δ represents an upper bound on the rate of change of motor load torque.
The invention at least comprises the following beneficial effects: the invention improves the traditional supercoil controller, combines the supercoil algorithm with the iterative learning strategy, observes periodic fluctuation and aperiodic waveforms in the sliding mode surface, and realizes the position control of the permanent magnet arc motor; compared with the traditional supercoiled controller, the invention can reduce the gain of the controller, and reduce the position and current pulsation.
Therefore, the invention can reduce current ripple, improve anti-interference capability, reduce harmonic content when the motor position is tracked, improve tracking precision and reduce torque ripple.
Additional advantages, objects, and features of the invention will be set forth in part in the description which follows and in part will become apparent to those having ordinary skill in the art upon examination of the following or may be learned from practice of the invention.
Drawings
FIG. 1 is a schematic diagram of the steps implemented by the position tracking method provided by the present invention;
FIG. 2 is a schematic structural diagram of a repetitive supercoiled observer designed by the present invention;
FIG. 3 is a schematic diagram of a configuration of a supercoiled controller designed according to the present invention;
FIG. 4 is a diagram of the variation of the tracking error of the motor position obtained by the position tracking method based on the conventional supercoiled observer;
FIG. 5 is a diagram of the variation of the tracking error of the motor position based on the position tracking method of the conventional supercoiled position controller;
FIG. 6 is a diagram of the variation of the tracking error of the motor position obtained by the position tracking method provided by the present invention;
FIG. 7 is a frequency spectrum of a motor position tracking error obtained by a position tracking method based on a conventional supercoiled observer;
FIG. 8 is a frequency spectrum of motor position tracking error obtained by a position tracking method based on a conventional supercoiled position controller;
fig. 9 is a frequency spectrum of a motor position tracking error obtained based on the position tracking method provided by the present invention.
Detailed Description
The present invention is further described in detail below with reference to the attached drawings so that those skilled in the art can implement the invention by referring to the description text.
It will be understood that terms such as "having," "including," and "comprising," as used herein, do not preclude the presence or addition of one or more elements or groups thereof.
As shown in FIG. 1, the present invention provides a position tracking method based on a repetitive supercoiled observer and supercoiled control, comprising the steps of:
s1, obtaining a state space equation of the motor based on the motion equation of the motor, analyzing the disturbance in the motor control from the two aspects of the motor topological structure and the motor driving system respectively, and dividing the disturbance into non-periodic disturbance and periodic disturbance;
s2, aiming at aperiodic disturbance and periodic disturbance, designing a repeated supercoiled observer according to a state space equation of the motor, and compensating the observed disturbance back to the supercoiled controller designed in the next step, namely performing disturbance feedforward compensation on the supercoiled controller;
and S3, designing a supercoil controller, and combining disturbance feedforward compensation to restrain periodic disturbance and non-periodic disturbance in position control.
In the above technical solution, the specific implementation manner of S1 includes:
the motion equation expression of the motor is as follows:
wherein the content of the first and second substances,ω m is the rotational speed of the motor and is,Jis the moment of inertia of the motor and,pis the number of the pole pairs of the motor,φ f is a permanent magnet flux linkage of the motor,i q as an electric motorqThe current of the shaft is measured by the current sensor,T l is the load torque of the motor and is,Bis the viscosity coefficient of the motor;
the topological structure of the motor can cause cogging torque and end torque, a corresponding motor driving system can cause periodic torque ripple, and the disturbance caused by the cogging torque, the end torque and the current sampling offset error is respectively expressed as:
wherein the content of the first and second substances,T cog is the torque of the tooth grooves,θ m is the mechanical angle of the motor and is,T n is thatnThe amplitude of the sub-slot harmonics,zis the least common multiple of the number of rotor teeth and pole pairs,T end is the end-of-line torque,T end n,is thatnThe magnitude of the torque at the secondary end,τis the distance between the two poles of the wire,αis a constant, Δ, related to the left and right end momentsT offset Is the disturbance caused by the current sampling offset error,A 1is a positive coefficient, Δi a And Δi b Is the current offset error of the motor A, B phase;
the state space equation of the motor is expressed as:
wherein the content of the first and second substances,T e =1.5pφ f i q in order to be an electromagnetic torque,ρandT p a non-periodic component and a periodic component in the motor load torque, respectively.
In the above technical solution, in S2, according to the obtained state space equation of the motor, the repeated supercoiled observer corresponding to the second-order system is established as follows:
wherein the content of the first and second substances,
an estimated value representing the rotational speed of the motor,
is indicative of a disturbance,
an estimate representing a periodic component of the motor load torque,
representing the error between the estimated value and the actual value of the motor speed,l、k 1、k 2andμ 1for a defined repetitive supercoiled observer coefficient,Tin order to be the period of the periodic disturbance,βthe coefficient is a positive coefficient of the number,α 11、α 12andα 22is a positive definite matrixα ij ]2×2Of (1) andl=﹣2α 22/α 12 μ 1；
as shown in fig. 2, in a designed repetitive supercoiled observer,ζ 1=k 1 μ 1、ζ 2=Jk 2 μ 1 2 /2 andζ 3=μ 1 β(α 11 μ 1 l+2α 12) In whichζ 1、 ζ 2Andζ 3respectively representing switching functions
The repetitive supercoiled observer records the tracking error of the motor by using a memory, and according to the given iterative learning rate:
updating to enhance the suppression capability of periodic disturbance, and simultaneously, according to the error between the estimated value of the motor rotation speed and the actual value of the motor rotation speed
To the switching function
Updating the estimated values of the motor rotation speed respectively
And the actual value of the motor speedω m Is integrated to obtain the disturbance
In which disturbance occurs
Including non-periodic disturbance and periodic disturbance, error term in formula
Error between estimated value of motor speed and actual value of motor speed
0 will also equal 0 and will not affect observer performance.
In the above technical solution, the supercoiled controller designed in S3 for performing motor position tracking is as follows:
wherein the content of the first and second substances,
it is the torque that is given to the motor,
，
it is the angle that is given for the angle,
it is the speed that is given for the speed,cis a positive coefficient of the coefficient,θ m is a mechanical angle of view of the device,ω m is the rotational speed of the motor and is,λ 1andλ 2is the coefficient of the supercoiled controller; in the designed supercoiled controller, a system command is tracked and better anti-interference performance is obtained by integrating the sign of a sliding mode surface and summing the power of 0.5;
adding the disturbance obtained in S3 to the supercoiled controller
And obtaining a new structure of the superspiral controller as follows:
the purpose of suppressing the periodic disturbance and the aperiodic disturbance in the position control is realized through the formula.
In the above technical solution, in S3, the parameters of the designed supercoiled controller and the repetitive supercoiled observer are set, so that the position tracking method can sufficiently suppressDisturbance
The specific method comprises the following steps:
suppose that
Then selectλ 1=1.5Δ1/2，λ 2=1.1 Δ, the supercoil controller can track disturbances normally; furthermore, the coefficients in the repetitive supercoiled observer can be obtained by reduction:
where Δ represents an upper bound on the rate of change of motor load torque.
Fig. 3 is a schematic structural diagram of a supercoiled controller designed by the present invention, in which system commands can be quickly tracked and better disturbance rejection performance can be obtained by integrating the sign of the sliding mode surface and summing the 0.5 th power of the sliding mode surface.
The following conclusions can be drawn: because the system contains a large amount of periodic disturbance, and the traditional supercoiling algorithm needs high gain to obtain better disturbance rejection performance, but the buffeting phenomenon inevitably exists, in order to fully utilize the characteristics of the periodic disturbance and reduce the gain of the supercoiling algorithm, the iterative learning strategy of a position domain is combined, so that the system has better performance.
The experimental effect is as follows: under the condition of a position signal with a given slope of 1, fig. 4, 5 and 6 are respectively motor position tracking error change graphs obtained by a position tracking method based on a conventional supercoiled observer, a position tracking method based on a conventional supercoiled position controller and the position tracking method provided by the present invention, wherein abscissa in fig. 4, 5 and 6 represents time, ordinate represents a tracking error (position error) of a motor, and the unit of the tracking error is rad; fig. 7, 8 and 9 are motor position tracking error frequency spectra obtained by a position tracking method based on a conventional supercoiled observer, a position tracking method based on a conventional supercoiled position controller and a position tracking method provided by the present invention, respectively, where the abscissa of fig. 7, 8 and 9 represents frequency in Hz, and the ordinate represents harmonic content (amplitude) in dB. Specifically, a position tracking error range obtained by a position tracking method based on a traditional supercoiled observer is-0.01 rad, and the corresponding first harmonic content is-51 dB; the range of position tracking error obtained by the position tracking method based on the traditional supercoiled position controller is-0.005 rad, and the corresponding first harmonic content is-55 dB; the range of position tracking error obtained by the position tracking method based on the repeated supercoiled observer and supercoiled position control is-0.002 rad, and the corresponding first harmonic content is-70 dB.
As can be seen from fig. 4 to 9, the method of the present invention can obtain the position tracking performance with a smaller fluctuation range, and meanwhile, the periodic disturbance in the motor operation process can be specifically suppressed.
The foregoing shows that the basic principles, essential features and advantages of the invention are described. It will be understood by those skilled in the art that the present invention is not limited to the embodiments described above, which are described in the specification and illustrated only to illustrate the principle of the present invention, but that various changes and modifications may be made therein without departing from the spirit and scope of the present invention, which fall within the scope of the appended claims.
The number of apparatuses and the scale of the process described herein are intended to simplify the description of the present invention. Applications, modifications and variations of the present invention will be apparent to those skilled in the art.
While embodiments of the invention have been disclosed above, it is not intended to be limited to the applications set forth in the specification and the embodiments, but rather the invention is capable of being applied to various fields adapted to the invention, and it is capable of further modifications that are readily apparent to those skilled in the art, and therefore the invention is not limited to the specific details and illustrations contained herein, without departing from the general concept defined by the claims and their equivalents.
Claims (5)
1. A position tracking method based on a repetitive supercoiled observer and supercoiled control is characterized by comprising the following steps:
s1, obtaining a state space equation of the motor based on the motion equation of the motor, analyzing the disturbance in the motor control from the two aspects of the topological structure of the motor and the motor driving system respectively, and dividing the disturbance into non-periodic disturbance and periodic disturbance;
s2, aiming at aperiodic disturbance and periodic disturbance, designing a repeated supercoiled observer according to a state space equation of a motor, and compensating observed disturbance back to a supercoiled controller designed in the next step, namely performing disturbance feedforward compensation on the supercoiled controller;
and S3, designing a supercoil controller, and combining disturbance feedforward compensation to restrain periodic disturbance and non-periodic disturbance in position control.
2. The method for position tracking based on repetitive supercoiled observer and supercoiled control of claim 1, wherein said specific implementation of S1 comprises:
the motion equation expression of the motor is as follows:
wherein the content of the first and second substances,ω m is the rotational speed of the motor and is,Jis the moment of inertia of the motor and,pis the number of the pole pairs of the motor,φ f is a permanent magnet flux linkage of the motor,i q as an electric motorqThe current of the shaft is applied to the shaft,T l is the load torque of the motor and is,Bis the viscosity coefficient of the motor;
the topological structure of the motor can cause cogging torque and end torque, a corresponding motor driving system can cause periodic torque ripple, and the disturbance caused by the cogging torque, the end torque and the current sampling offset error is respectively expressed as:
wherein the content of the first and second substances,T cog is the torque of the tooth socket, and,θ m is the mechanical angle of the motor, and the motor is a linear motor,T n is thatnThe amplitude of the sub-slot harmonics,zis the least common multiple of the number of rotor teeth and pole pairs,T end is the end-of-line torque,T end n,is thatnThe magnitude of the torque at the secondary end,τis the distance between the poles of the magnetic field,αis a constant, Δ, related to the left and right end momentsT offset Is the disturbance caused by the current sampling offset error,A 1is a positive coefficient, Δi a And Δi b Is the current offset error of motor A, B phase;
the state space equation of the motor is expressed as:
wherein the content of the first and second substances,T e =1.5pφ f i q in order to be an electromagnetic torque,ρandT p a non-periodic component and a periodic component in the motor load torque, respectively.
3. The position tracking method based on the repetitive supercoiled observer and the supercoiled control of claim 2, wherein in S2, according to the obtained state space equation of the motor, the repetitive supercoiled observer corresponding to the second-order system is established as follows:
wherein the content of the first and second substances,
estimation of motor speedThe value is evaluated in such a way that,
is indicative of a disturbance,
an estimate representing a periodic component of the motor load torque,
representing the error between the estimated value and the actual value of the motor speed,l、k 1、k 2andμ 1for a defined repetitive supercoiled observer coefficient,Tin order to be the period of the periodic disturbance,βthe coefficient is a positive coefficient of the number,α 11、α 12andα 22is a positive definite matrixα ij ]2×2Of (1) andl=﹣2α 22/α 12 μ 1；
in a designed repetitive supercoiled observer,ζ 1=k 1 μ 1、ζ 2=Jk 2 μ 1 2 /2 andζ 3=μ 1 β(α 11 μ 1 l+2α 12) Whereinζ 1、 ζ 2Andζ 3respectively representing switching functions
The repetitive supercoiled observer records the tracking error of the motor by using a memory, and according to the given iterative learning rate:
updating to enhance suppression of periodic disturbances based onError between estimated value of motor rotation speed and actual value of motor rotation speed
To the switching function
Updating the estimated values of the motor rotation speed respectively
And the actual value of the motor speedω m Is integrated to obtain the disturbance
In which disturbance occurs
Including non-periodic disturbance and periodic disturbance, error term in formula
Error between estimated value of motor speed and actual value of motor speed
0 will also equal 0 and will not affect observer performance.
4. The position tracking method based on the repetitive supercoiled observer and supercoiled control of claim 3, wherein the supercoiled controller designed in S3 to perform motor position tracking is represented by the following equation:
wherein the content of the first and second substances,
it is the torque that is given to the motor,
，
is that the angle is given by the angle,
it is the speed that is given for the speed,cis a positive coefficient of the coefficient,θ m is a mechanical angle of the light source,ω m is the rotational speed of the motor and is,λ 1andλ 2is the coefficient of the supercoiled controller; in the designed supercoiled controller, a system command is tracked and better anti-interference performance is obtained by integrating the sign of a sliding mode surface and summing the power of 0.5;
adding the disturbance obtained in S3 to the supercoiled controller
And obtaining a new structure of the superspiral controller as follows:
the purpose of suppressing the periodic disturbance and the aperiodic disturbance in the position control is realized through the formula.
5. The repetitive supercoiled observer and supercoiled control-based position tracking method of claim 4, wherein in the step S3, parameters of the designed supercoiled controller and repetitive supercoiled observer are adjusted so that the position tracking method can sufficiently suppress disturbance
The specific method comprises the following steps:
suppose that
Then selectλ 1=1.5Δ1/2，λ 2=1.1 Δ, the supercoil controller can track disturbances normally; furthermore, the coefficients in the repetitive supercoiled observer are obtained by reduction:
where Δ represents an upper bound on the rate of change of motor load torque.
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